Journal of Agricultural Science in Finland Maataloustieteellinen Aikakauskirja Voi. 59: 251—354 THE RETURNS TO INVESTMENT IN AGRICULTURAL RESEARCH IN FINLAND 1950—1984 Selostus: Maataloustutkimuksen tuotto Suomessa 1950—1984 JOHN SUMELIUS Agricultural Economics Research Institute, Luutnantintie 13 SF-00410 HELSINKI, Finland Academic Dissertation TO BE PRESENTED, WITH THE PERMISSION OF THE Faculty of Agriculture and Forestry of the University of Helsinki, for public criticism in Auditorium Porthania 111, on December 18, 1987, AT 12 O’CLOCK NOON. SUOMEN MAATALOUSTIETEELLINEN SEURA HELSINKI https://www.c-info.fi/en/info/?token=Kbyk4AP6nE5hVVQ8.2YcFahd6BfYmO4rn4jfxHA.ivjqNtakXwB8FkXleNwmvOS1p5hRr0K57kS9x8CUBaFmvU8fCyMA8gMk_iNSog3hRZ1jRblZnyI0nAOx2-HAUo5iu9Vf0SiPdiRWOfRecXR3B4OOTyrDCmVCNxOR0W5DySRtBSk-rZS_eHcWWvGNF4SCmSS16k0AE_yH Preface The returns to agricultural research have been analysed to a rather limited extent in the Nordic countries. The interest in the research on this subject is, however, increasing. On the initiative of The Scandinavian Association of Agricultural Scien- tists (NJF) a research symposium was held in the spring 1985 in Sweden where the topic was discussed. The participants from Finland and Sweden decided to start working on this field immediately. Some preliminary results were presented on the XVIII Congress of NJF in the summer 1987. The present study is an outcome of this concrete cooperation between the Nordic countries. The study was carried out at the Agricultural Economics Research Institute. With- out the encouragement, guidance and generous help of Professor Lauri Kettunen, Head of the Marketing Research Department of the Institute, the study would not have reached its present extent. His daily readiness to listen, discuss and suggest methodological solutions to specific problems has been an invaluable help for me. I also owe a debt of gratitude to my teacher in agricultural economics, Professor Karl Johan Weckman, for his continuous interest and enthusiasm. His support has been important. Without the facilities, assistance and equipment offered by the AERI, I would not have been able to carry out the investigation. I sincerely wish to thank Professor Matias Torvela, Head of the Institute, for this possibility. Professor Ulf Renborg, Swedish University of Agricultural Sciences, has been a special source of inspiration. He has made many valuable suggestions on the manuscript. Professor Viljo Ryynänen has also provided me with useful comments. Among all the persons offering me moments of fruitful discussion and construc- tive criticism Paavo Mäkinen, Bureau Chief, National Board of Agriculture, Mik- ko Ryökäs, M. Sc., and Jukka Kola, M.Sc., need to be mentioned. I also want to thank the personnel at the AERI, including Seppo Holmström, B.Sc., Jaana Ahl- stedt and Arja Jauhiainen for their assistance. Special thanks also to Riitta Kunnas, M. Sc., and Marjatta Lahtinen, Bureau Chief, National Board of Vocational Education, for help with collecting data. Sevastiana Kuusamo, M.A., has revised the English text for which I am most grateful. The study was supported by grants from the Finnish Cultural Foundation and the Svenska Vetenskapliga Centralrädet. In addition to these, I want to thank the Scientific Agricultural Society of Finland for including this study in their journal. Finally, I want to express my thanks to Heidi for her patience during my work. Helsinki, October 1987 John Sumelius 255 Contents Page Abstract 257 1. Introduction 259 2. Methods of Estimating the Economic Returns to Research 263 2.1. Early Attempts to Measure the Returns to Research 263 2.1.1. The Value of Inputs Saved Calculated by Schultz and the Follow-up Study of Peterson 263 2.1.2. The Estimate of Tweeten and Hines; Contributions of Agricultural Pro- ductivity to National Economic Growth 265 2.2. External and Internal Rates of Return, Average and Marginal Rates of Return 265 2.3. Production Function Analysis 267 2.3.1. General Features 267 2.3.2. The Aggregated Production Function Study of Griliches 267 2.3.3. The Poultry Study of Peterson 268 2.3.4. Production Function Studies of Evenson 268 2.3.5. The Studies of Evenson and Kislev 270 2.3.6. Some Other Production Function Studies 271 2.4. The Welfare Economics Approach 272 2.4.1. General Features 272 2.4.2. The Study on Hybrid Maize by Griliches 273 2.4.3. The Welfare Economics Approach According to Hertford and Schmitz 274 2.4.4. Comments on the Welfare Economics Approach 275 2.4.5. Returns from Rice Breeding in Japan Estimated by Akino and Hayami 277 2.4.6 The Study on Returns to Pasture Improvement Research by Duncan .. 277 2.4.7. Canadian and Spanish Studies of Crop Development Research 277 2.4.8. The Distribution of Economic Benefits from Agricultural Research .... 278 2.5. Criticism of the Examined Studies 279 2.5.1. General Criticism 279 2.5.2. Criticism of the Production Function Approach 280 2.5.3. Criticism of the Welfare Economics Approach 281 3. The Returns to Investment in Agricultural Research 1950—1984 An Aggregated Production Function Study 283 3.1. Productivity Increase, Technological Change and Economies of Scale the Con- nections 283 3.1.1. The Concept of Productivity 283 3.1.2. Technological Change ; 283 3.1.3. Economies of Scale and Changes in the Prices of Production Factors .. 285 3.2. Starting Point for the Specification 286 3.3. Specification of the Model 288 3.3.1. The Form of the Production Function and the Variables 288 3.3.2. Research Stock 290 3.3.3. A Productivity Index Specification 291 3.3.4. Distributed Lags 291 3.4. How the Model Works 294 4. Data 296 4.1. Time Series 296 256 4.2. Gross Production in Agriculture 296 4.3. Capital Stock 296 4.4. Labour and Education 298 4.5. External Inputs Used in Production 299 4.6. Extension 300 4.7. The Research Input in the Public Sector in 1950—1984 301 4.7.1. Research at Institutions under the Ministry of Agriculture and Forestry 301 4.7.2. The University of Helsinki and the College of Veterinary Medicine .... 302 4.7.3. The Academy of Finland 303 4.7.4. Finnish National Fund for Research and Development and Public Founda- tions 303 4.7.5. Work Efficiency Association 304 4.7.6. Agricultural Research Outside the Research Definition 304 4.7.7. The Development of Public Research Input in 1950—1984 305 4.8. The Research Input in the Private Sector in 1950—1984 305 5. Presentation of the Results 308 5.1. The Research Input Measured as a Flow 308 5.1.1. Linear Models without Lags 309 5.1.2. Cobb-Douglas Models without Lags 313 5.1.3. Multicollinearity and Ridge Analysis 315 5.1.4. Ridge Traces 319 5.1.5. Autocorrelated Errors and Autoregressive Models 319 5.1.6. Cobb-Douglas Models for Shorter Periods 322 5.2. Cobb-Douglas Flow Models with Lags 323 5.2.1. Regressions with Simple Lags 323 5.2.2. Regressions with Almon Lags 324 5.3. The Research Input Measured as a Stock 326 5.3.1. Undepreciated Research Stock 326 5.3.2. Depreciated Research Stock 327 5.3.3. Productivity Index Model 329 6. The Returns to Agricultural Research and University Education 330 6.1. The Selection of an Elasticity 330 6.2. Research Flow Elasticities 330 6.3. Research Capital Elasticities 331 6.4. Value Marginal Product 332 6.5. Marginal Internal Rate of Return 334 7. Summary and Conclusions 336 REFERENCES 339 APPENDICES 342 JOURNAL OF AGRICULTURAL SCIENCE IN FINLAND Maataloustieteellinen Aikakauskirja Vol. 59: 257—354, 1987 The Returns to Investment in Agricultural Research in Finland 1950—1984 Abstract. This study attempts to estimate the value marginal product and the marginal internal rate of return for agricultural research in Finland. Based on production function analysis, different Cobb-Douglas and linear models are specified and estimated. A variable for the research input is measured through the flow of public expenditures for research and university-level education in 1950—1984. In addition, a stock of research capital consisting of funds accumulated since 1920 is constructed and included in the models. The estimates of elasticity with respect to public research are used to compute rates of return. State expendi- tures for extension agencies are also taken into account on the cost side. It is concluded that the stock of research capital estimates are more believable than the flow estimates, because of difficulties in identifying an appropriate lag. Based on the stock estimates, the value marginal product for public research during the period studied seems to have been 1.83—1.91. The conclusion implies that additional public investment in agricultural research would have annually returned by 183—191 % over the inflation rate. The marginal internal rate of return for public research is calculated to have been 20—62 % depending on the length of the lag (4—10 years). Index words: Returns to research, value marginal product, agricultural research 257 258 1. Introduction The most important variable explaining dif- ferences from one country to another as to ag- ricultural productivity is the ability to create a technology adapted to the particular coun- try’s physical, environmental and cultural en- dowments. Despite the importance of this ability, however, the processes by which this capacity creates and diffuses technical inno- vations have received relatively little attention until recently. The role of agricultural research was pointed out explicitly only in the 1950s and 19605. Since then, considerable effort has focused on measuring the impact of research on growth in productivity (Arndt and Rut- tan, 1977). Estimation of the valueof research is a dif- ficult task complicated by great uncertainties. In spite of these difficulties the task seems to be important. Many studies carried out in the USA, Canada, Japan, India, Mexico, Aus- tralia, and Brazil have found that the returns to investment in agricultural research and ex- tension in many cases have been very high. The estimated annual rate of return in these countries has varied from approximately 20 to 80 %. Both consumers and producers bene- fit from this social rate of return through lower costs of food and reduced production costs (Pinstrup-Andersen, 1982). In the 1950 s T.W. Shultz (1956, 1958) pointed out how important it wouldbe to cal- culate the costs and benefits of technical im- provements. He contended that technical im- provements in agriculture are not manna from heaven, but represent inputs that should be taken into account when explaining an in- crease in agricultural production or in agri- cultural productivity. The majority of studies carried out thereafter have had a similar con- elusion; society as a whole, both producers and consumers, benefit from agricultural re- search. It is not known whether agricultural re- search has created a positive economic surplus in the Nordic countries, particularly in Fin- land. The table in Appendix 1, presenting the estimated annual rate of return from 50 dif- ferent research programmes, shows a high rate of return in other countries. On average, the annual rate of return was somewhat below 50 °7o and only four programmes showed an annual rate of return below 20 % (Pinstrup- Andersen, 1982). A similar compilation of data from 32 studies on research profitabil- ity, put together by Evenson et al. (1979) in the magazine Science, illustrates approximate- ly the same rates of return. The agricultural research input in Finland needs to be investi- gated in order to determine whether the high rates of return are also true for a northern en- vironment. More specifically, empirical estimations of the economic returns to agricultural research (or of its benefits) can be justified as follows: 1. Research is an economic activity, com- peting for the scarce resources of society, which creates something of value by produc- ing knowledge that can be further refined into an input in the production process. To be able to allocate funds between research and other activities of society decision-makers need some measure for determining optimal allocation (Schultz 1971). If the future value of re- search to society could be estimated, the ex- tent of public spending on agricultural re- search could be determined on the basis of its relative benefits (Pinstrup-Andersen 1982). 2. Research leads to a more effective use 259 of resources by providing knowledge to be used instead of more expensive and scarcer re- sources, e.g. land, water and labour. The constraints on production imposed by the most expensive or least available resource are alleviated through research; the same produc- tion volume is achieved with less inputs than previously (Hayami and Ruttan 1971). Quantification of this marginal product of research enables valuationof the gain in effi- ciency. 3. It is possible to demonstrate that, in the long run increases in productivity are trans- ferred to consumers through lower food prices. Welfare economics also makes it pos- sible to estimate the consumers’ surplus and the producers’ surplus thereby making it pos- sible to determine which group benefits more. The total economic surplus is principally often sufficient to compensate probable losers, i.e. late adopters of new methods and means of production (Hertford and Schmitz 1977). 4. According to one assertion, landowners obtain a large part of the utility from in- creased productivity, the input industry an- other part. Thus Rosine and Helmberger (1975) claim that land rents dramatically in- creased in USA in 1948—1972 as a result of improved productivity. Technological change led to a drop in the prices of agricultural prod- ucts, whereas the prices of inputs rose and labour did not benefit from increases in pro- ductivity. An important question thus is whether landowners and the input industry share in the benefits from investment in agri- cultural research and extension, and how big is their share ? This study makes no attempt to answer this question since circumstances differ in Finland from those in the USA. 5. It is difficult to set an exchange value on real or expected research results, yet it must be possible, as such values are set all the time, in the form of decisions concerning the allo- cation of resources to research. Current price setting is insufficient because it is based on im- perfect information. The authorities granting funds for agricultural research need objective evaluation of research (Paulsen 1971). 6. There appears to be a lag between the point in time when research funding takes place and actual results in the form of higher productivity. This lag can be expressed as a function of time, as is illustrated in Figure 1. Investment in research in theperiod t starts producing a stream of benefits at t + 3; this stream increases to m at t + 10, and thereafter decreases. Attempts have been made to esti- mate such a lag, with various success. Can a lag be found for aggregate agricultural re- search in Finland? Whether or not the growth of knowledge is cumulative, a topic that has been discussed in the philosophy of science, becomes relevant in this connection. Those who, like Karl Popper, are apt to look upon science as a steady process of approaching truth in infinity probably contend that research results have an eternal component of value. From this point of view, research results accumulate rather than replace each other. Those who, like Thomas Kuhn, advocate a view that science should be seen as a sequence of paradigms replacing each other probably consider all knowledge to be perishable even with respect to its practical utilization. Even though Kuhn thought of rather long periods, later philo- sophers of science e.g. Lakatos have used his concept in the context of shorter intervals. In principle this distinction is important, since the decision whether the benefits of research are cumulative (lasting forever) or concern only a few decades might affect the estimated rate of return. Varying opinions about how the benefits of research should be depreciated Fig I. The timing of research benefits (Evenson 1977). 260 are associated with a more general philosophi- cal discussion. 7. In recent years administrators have be- come engaged in the evaluation of research. The returns of agricultural research can be understod as one of many criteria by which the quality of research is assessed. Research certainly can be justified on grounds other than purely economic ones (environmental, sociopolitical, or quality aspects). This does not, however, decrease the importance of the social rate of return. These are some resons for evaluating the re- turns to investment in agricultural research. It is, however, important to keep some cen- tral circumstances in mind. First: The end results are essentially affected by what is included in the research costs, and what is not. According to Zentner and Pe- terson (1984), this question is difficult to answer. Most studies have included costs for extension too; thus investment in research is also covering the public expenditure for ex- tension. In this study, all funds for university- level agricultural education have also been in- cluded. The estimation is thus a calculation of the profitability of research, where the costs of extension and university education are credited on the cost side, a procedure which may overestimate the cost component. Second: An important part of all research takes place in the private sector. Farmers, however, pay for this research as its costs are included in the prices of agricultural inputs. For this reason it may be unnecessary to in- clude research done in the private sector; in- clusion or exclusion of such research depends on the study methods used for a particular investigation. Third: It should be kept in mind that re- search spreads across national borders; the benefits of research are not confined to the country of origin. This is often characterized as a “spillover effect”. Changing technology is seldom completely specific to the country where the research has been carried out. A central part of research findings is also im- ported from other countries. It is, however, very difficult to distinguish between the effects of imported research findings and the effects of domestic research on agricultural produc- tion. One can only assume that borrowed knowledge plays a greater role in small coun- tries than in large countries. An interesting topic for investigation would be to distinguish imported research from domestic research. Fourth: How should improved productivity be accounted for when it leads to a national surplus of agricultural products, with little prospects for sales? Is it realistic to assume that all resources find alternative employment at zero cost? Fifth; Schultz (1956) and Peterson (1971) point out that research contains a stochastic element and can be compared to drilling oil, when most holes turn out to be dry. Perhaps one out of ten holes strikes oil. The value of this tenth hole, however, makes up for the nine earlier trials that were fruitless. There is a major gap in knowledge about the yield of Finnish agricultural research in relation to its costs. The purpose of this study is to fill that gap by seeking an answer to the following question; What has been the value marginal product (marginal rate of return) as well as the marginal internal rate of return for public expenditure on agricultural research and for total public and private expenditures on agricultural research 1950—1984? The study concentrates mainly on public research, which includes university education, but also takes into account the private re- search even though farmers pay for the re- search done in the private sector. The empirical study is based on production functions where a specific research variable forms the core of analysis. The estimates of regression coefficients are derived through regression analysis. Two different measures are used to approximate the research input. The first is the conventional measure of re- search flow, comprising the flow of annual funds to research. The second is a stock mea- sure of the accumulated research capital. The stock of research capital has not been widely 261 used in earlier empirical analyses of returns to agricultural research. Theoretical discussion of the methods that can be used to estimate economic benefits, earlier studies and the criticism of these are reviewed in chapter 2. Furthermore, produc- tivity can increase because of factors other than research. These issues as well as the speci- fication of a model for estimating thereturns to research are presented in chapter 3. The data is explained in chapter 4, and the results of the estimations are reported in chapter 5. In chapter 6 a value marginal product and a marginal internal rate of return for the period studied are calculated, whereas conclusions are summarized in chapter 7. 262 2. Methods of Estimating the Economic Returns to Research The methods used for evaluating the returns to research can be divided roughly into two groups. The first approach consists of esti- mating a production function, in which a vari- able for research and extension is included. In the next stage the contribution of the research variable to production or to growth in pro- ductivity is determined on the basis of the coefficients. Normally the marginal rate of return serves as a measure of profitability. This group of methods is classified here as production function analysis. Sometimes these methods are referred to as the regression analysis approach or sources of growth meth- ods. The second basic approach makes use of either welfare analysis or cost and benefit analysis. An average rate of return is usually calculated and generally refered to as the in- ternal or social rate of return. These methods are said here to use the welfare economics ap- proach. Sometimes this group is referred to as an index number or consumers’ surplus method. Many scholars in the field have used both approaches. Griliches (1958, 1964) is mostly cited for his pioneering cost-benefit work on hybrid maize research, but has also made a profound contribution to the produc- tion function analysis. Both major approaches are reviewed in sections 2.3. and 2.4. Before we proceed to scrutinize these meth- ods, a couple of early attempts belonging to neither major approach will be examined. We shall also define some of the central measures used in these types of studies. 2.1. Early Attempts to Measure the Returns to Research 2.1.1. The Value ofInputs Saved Calculated by Schultz and the Follow-up Study of Peterson Schultz (1953) uses the value of inputs saved method in the first study to measure quantitatively the returns to investment in ag- ricultural research. Schultz includes all public expenditures for research and extension in his analysis. He examinesresearch at the level of total agricultural production. Schultz estimates the growth in productivity in American agriculture in the period 1910— 1950. Thereafter he proceeds to calculate the value of inputs saved by the increase in pro- ductivity. Growth in productivity is attributed to improved production technology and agri- cultural research. This value is related to total expenditures for research and extension ac- tivities. Schultz makes a rough calculation of the re- sources needed to produce the agricultural output of 1950 with the technology of 1910. The difference in resource inputs is equal to the value of inputs saved. An upper and a lower limit for this value is set. The upper limit is established by deter- mining a 14 % growth in resources needed using the prices of 1946—1948 as weights. In 1950 total agricultural production was 75 % higher than in 1910. The output-input ratio had thus grown by 54 %. In other words, 54 % more resources would be needed to pro- 263 duce the output of 1950 with the technology of 1910, this 54 % being worth USD 16.2 bil- lion. Correspondingly, a lower limit is set using the prices of 1910—1914 as weights for the resources needed. With these weights, in- puts had grown by 33 % whereas the value of the resources saved to produce the output of 1950 were USD 9.6 billion (the output-input ratio was thus improved by 32 %). This fig- ure, USD 9.6 billion is consequently the lower limit for resources saved during one single year, 1950. After these calculations Schultz assumes that the expenditures for research and exten- sion per year during 1910—1950 were as great as in 1950, which in fact is a gross over- estimation of the actual research costs. Using Shultz’s assumption, total expenditures in 1910—1950 would have been USD 7 billion. The total expenditures for a period of 40 years thus were less than the value of inputs saved during one single year, i.e. USD 9.6billion in 1950. This figure indicates tremendous returns from research. Schultz however presents a double warning in his argument. First he points out that ex- tension costs may be overestimated since not all of these resources are used to advance ag- ricultural techniques. Second, he points out that the research of the private sector have not been taken into account, and that productivity may rise because of reasons not associated with research (economies of scale, education etc.). On the other hand, the research costs are heavily overestimated and some of the re- search is necessary to maintain the same level of production as before. Peterson (1971) used the method of Schultz to follow up the development 1950 1967. The valueof inputs saved in 1950 alone, measured in the price level of 1957—1959,was USD 10.11 billion (USD 9.6 billion in the price level of 1950). Using the same price level the value of inputs saved was USD 26 billion in 1967. Even if one assumes that the research expenditures of the private sector are equal those of the public sector, the sum of total research costs for the period 1910—1967 (USD 18.914 billion dollar) is less than the value of inputs saved only in 1967. The values calculated by Peterson are shown in Table 1. In the table the expendi- tures of the public sector have been doubled to take into account the expenditures of the private sector. The figure of O/I shows the output-input ratio; the table thus reveals growth of the productivity ratio. An interesting feature is that the value of inputs saved has risen faster than the expendi- tures for research and extension. (In 1930, changes in the O/l ratio and the value of inputs saved were negative, and thereforewere omitted by Peterson). Peterson also calculated a rate of return for the investments in agri- cultural research; it is described in section 2.2. Table 1. Value of inputs employed in agriculture, proportionate change in productivity (O/l) since 1900, values of inputs saved, and expenditure for agricultural research and extension, in millions of 1957—1959 dollars for selected years (Peterson 1971). Year Value of Proportionate Value of Research and Inputs Increase in Inputs Saved Extension O/I from 1900 1930 USD 22,380 —' —' USD 193 1940 22,349 0.091 USD 2,034 335 1950 35,103 0.288 10,110 390 1960 34,895 0.591 20,623 727 1967 40,729 0.636 25,904 882 1 Changes in the O/I ratio and value of inputs saved were negative for 1930 and, thus omitted. 264 2.1.2. The Estimate of Tweeten and Hines: Contributions of Agricultural Productivity to National Economic Growth In the mid 19605, Tweeten and Hines (1965) launched a method for roughly esti- mating the effects of investment in agricultural research and education. Their method of esti- mation is based on following reasoning. The national income in the USA in 1963 was USD 476 billion. Of this 3.7 % originated in the agricultural sector. In 1963, the natio- nal income per capita was USD 1,310 in the agricultural sector and USD 2,617 in the rest of the economy. Due to research, extension and vocational training, the need for labour in agricultural production had decreased, and human labour had thus been released from American farms in 1910—1963. This released labour now works in the nonagricultural sec- tor. According to this reasoning the contribu- tion to national income can be calculated on the basis of per capita income differences in the agricultural and the nonagricultural sec- tors. In 1910 35 % of the American popula- tion lived on farms, after which the figure declined. Tweeten and Hines concluded that had the distribution of agricultural people/ nonagricultural people of 1910 prevailed in 1963, the national income would have been USD 68 billion, or 14 % lower than the actual national income of USD 476 billion. The earnings from growth in productivity were USD 1—1.5 billion a year in the be- ginning of the 19605. Discounted with a 5 % discount rate, this makes for about USD 20 billion. Public investments in agricultural re- search, education and vocational training, farm programme expenses and various mis- cellaneous items accounts for a total expendi- ture of USD 10 billions. This sum thus in- cludes much more than research expenditures. On thebasis of these sums, one can easily see that a benefit/cost quota of 2 is obtained. Peterson (1971) points out that since costs are estimated only for a current year (1963), it is not possible to compute an internal rate of return. A 10 % external rate of return is obtained with a 5 % discount rate. Peterson (1971) also points out a bias in this technique. The estimated contributionto national income depends on the extent of dis- equilibrium between per capita income in the agricultural and nonagricultural sectors. The larger this difference is, the greater the con- tribution to national income will be. But through extension the per capita income will increase in the agricultural sector, thereby de- creasing the gap in per capita income, making the contribution lower. There is obviously a paradox in the argument. In addition, the in- creases in productivity of American agricul- ture during 1910-1930 were not worth men- tioning whereas big increases occured in the late 1950 s and early 19605. The method of using per capita income as a determinant, however, gives the same contribution to na- tional income for both periods. The method is evidently incomplete. The method of Tweeten and Hines has not been applied to a large extent, and is men- tioned here as a curiosity. 2.2. External and Internal Rates of Return, Average and Marginal Rates of Return By comparing the costs of research with the value of inputs saved, like Shultz did, one can form a rough idea of the relation between in- puts and returns. More exact measures are needed to create a more detailed picture of the returns fromresearch. Two such general mea- sures are the external and the internal rate of return, commonly refered to as the social rate of return. The external rate of return according to Griliches (1958) is measured as follows: One assumes the development to end at a point in time, cumulating all past expenditures at a rea- sonable interest, which reflects for instance the opportunity cost in the economy. The cumu- lated research costs are expressed as a capital sum. The past returns are cumulated to the same point in time, and are also expressed a capital sum. At the same discount rate as 265 earlier used, therate of return on these cumu- lated returns is projected into the future. The estimated flows of future returns are added to past returns, to arrive at a perpetual flow of returns. This flow, divided by the cumu- lated research expenditures gives us the ex- ternal rate of return. Akino and Hayami (1975) define the ex- ternal rate of return by the formula (2.1.) (2.1) , - rc = external rate of return P = the value of past returns F = the value of future returns C = research expenditures i = discount rate The external rate of return is a subjective measure because it depends on the discount rate chosen. The formula (2.1) can be applied to Petersons figures in Table 1; the result is Table 2. The returns extend from 1937 to per- petuity, the calculating point in time being 1967. All research and extension costs for 1910—1967 are accumulated to 1967. Table 2. Calculation by Peterson (1971) of the ex- ternal rate of return, USD billions. 1. Cumulated past returns 1,238 2. Past returns as an annual flow 124 3. Annual future returns 25 4. Total annual return (2 +3) 149 5. Cumulated past research expenditures 200 6. External rate of return (100 x 4/5) 75 «to An external rate of return of 75 % is ob- tained. This should be interpreted to mean that the invested research expenditures have returned to society at an annual rate of 10 % until 1967. From now on, each dollar invested in 1910—1967 will yield 75 % annually by saved inputs (Peterson 1971). Hayami and Ruttan (1971, p. 41) present a formula for converting the external rate of return to a benefit/cost ratio. Annual rate of returnBenefit/cost ratio = 100 interest rate The external rate of return can thus be interpreted closely to a benefit/cost ratio (Griliches 1958). The external rate of return above of 75 % and a discount rate of 10 % equal a benefit/cost ratio of 0.75. Critical questions are whether the value of inputs saved are due only to research, and if they can be thought of as extending to perpetuity? According to Peterson (1971), the internal rate of return can be defined as the rate of in- terest that makes the accumulated present value of the flow of costs equal to the dis- counted present value of the flow of returns, at a given point in time. Another formulation of the internal rate of return is the rate of return for which the B/C ratio =l. The in- ternal rate of return can be calculated from the formula (Akino and Hayami 1975): (2.2) I = 0 •= o (i + rj )‘ R, = the social benefit (return) in year t C, = the research cost in year t T = the year the research ceases to produce returns r, = the internal rate of return If we know R, and C„ then we are also able to calculate t|. For a given interest rate, the discounted flow of returns is equal to the discounted flow of costs. This interest rate r, is to be interpreted to mean that every unit of investment has, on average, returned by q per cent annually above the rate of inflation from the moment the investment was made (Zentner and Peterson 1984). It is important to note that the internal rate of return is sensitive to the length of the studied period. Peterson observed that if the figures in Ta- ble 1 are applied to the formula of the inter- nal rate of return, the returns were negative for 1910—1937 and positive for 1937—1967. The average internal rate of return for this period was 19 %, clearly less than the 75 % external rate of return. This discrepancy is due to the sensitivity of the rate of return to the length of the period. During 1910—37 costs were also included but no returns were ob- 266 2 tained, obviously because of a long lag between investment and visible results in pro- ductivity ratios. Evenson (1977, p.239, 245) calls it a seri- ous matter that some of the estimates of the returns from research have been derived through the use of systematic econometric for- mulations. He argues that rates of returns must be seen in a systematic context and that overvalued estimates of the returns have often been reported. He claims it is necessary to supplement the calculations of rates of return with other information. Yet the average rate of return, which preceding formulas (2.1) and (2.2) both measure, is meaningful only in a historical sense. The relevant measure to re- search policy is, in his opinon, not the aver- age but the more conventional marginal prod- uct of research. The marginal product tells us the additional productivity or production gain for one more unit invested in agricultural re- search. The marginal product is easily con- verted into a marginal rate of return in pro- duction function analysis. The partial regres- sion coefficients give us information about the elasticity of research. According to Evenson (1977), production function analysis should be less subject to error than the welfare eco- nomics approach. In order to assess the returns from research, a lag structure should be involved in the con- text of a production function analysis. Re- search does not yield returns immediately but only after a number of years, when the results are applied to the production process. The length of this lag varies, depending on the type of research. The lag structure has been the object of many estimation procedures (cf. Evenson 1967, and Ravenscraft and Scherer 1982). Though it would be interesting to know the average rate of return, Evenson seems to look upon the marginal rate of return as the more appropriate measure for decision-makers. Pe- terson and Hayami (1977) found in a com- parison of studies that the marginal rate of return was higher than the average rate of re- turn. Peterson (1971) found the marginal returns to be 42 °7o in the previously men- tioned study whereas the internal rate of re- turn was 19 %. 2.3. Production Function Analysis 2.3.1. General Features One of the major approaches in assessing the profitability of research starts from the estimation of a production function. The es- timation may focus upon a special product, a group of products or the whole of agricul- ture. The production function includes vari- ables for research and/or education. The co- efficients of the production function can be estimated by regression analysis, normally with ordinary least squares method (OLS). The coefficients for research can be converted to a marginal product and a marginal rate of return for the research input. A marginal in- ternal rate of return can be derived for the coefficients. 2.3.2. The Aggregated Production Function Study of Griliches Zwi Griliches (1964) was one of the first to include a research variable in the produc- tion function. In his estimation of an aggre- gate Cobb-Douglas function for American agriculture, he used one variable for educa- tion per worker and one variable for research and extension. In addition to these variables five “traditional” variables were included. The data consisted of three different cross- sections of data (1949, 1954, 1959) from 39 different states in the USA. In order to allow for some lags in effects, the research variable was defined as an aver- age of the flow of expenditures in the previ- ous year and the level six years before. Thus the average of 1953 and 1958 was used in the cross-section for 1959. The estimated research elasticity 0.059 may seem small. Keeping in mind, however, that the expenditures for research and extension for the whole period 1949—54—59 were only 267 USD 32 per farm and per year (the variable was defined as research expenditure per farm) while gross output per farm and year was USD 7,205, the absolute effect becomes consider- able. The estimated marginal product for re- search and extension is then 0.059 X 7,205/32 or, approximately USD 13 of output for every additional dollar invested in research and ex- tension (equal to a rate of return of about 1300 % per cent per year). Even accounting for a large share of re- search in the private sector and for the fact that the marginal product stated above is an overestimation, the result from Griliches’ study indicates a very high return from invest- ment in agricultural research. Griliches him- self adjusted the calculations so that both re- search in the private sector and the support to agriculture were considered. The adjusted marginal product then was found to be USD 3 (a rate of return equal to 300 %). Peterson (1971) converted Griliches’ mar- ginal product of USD 6.50 (assuming that re- search in the private sector was roughly equal to that in the public sector) to an internal rate of return of 53 °7o. This 53 % was based on the assumption that the returns continue to perpetuity. If all benefits are assumed to return once and for ail, the internal rate of return becomes 36 °7o. Griliches (1963 a) also made a study in which he tried to break down the technical change into different sources of growth in productivity during 1940-1960. Education ac- counts for some of the growth in agricultural productivity. Griliches first computed a sta- tistically significant variable for education, concluding that education affects productiv- ity. However, it was found to be easier to adjust the series for labour by an index of education rather than to include a separate variable for education. Later in the same study he constructed such an index of education per man-year in agriculture. This index was com- puted by weighting years of school, high school and college completed by the rural population by the average income of all American males in respective schoolyear class. He thereby obtained a rising index, which was multiplied with the labour input series. In this way Griliches was able to reduce the number of variables by one while still taking notice of the effects of education. 2.3.3. The Poultry Study of Peterson In his attempt to estimate the benefits of poultry research carried on by state agricul- tural experiment stations, the U.S. Depart- ment of Agriculture, and suppliers of poul- try inputs, Peterson (1967) applied both a production function approach and a welfare economics approach (“index number ap- proach”). With a method similar to the one used by Griliches, Peterson calculated the ad- justed marginal product of poultry research to be USD 6 which is equivalent to a 33 % internal rate of return if the time lag is ten years. This internal rate of return was actual- ly a marginal return. Calculated with the wel- fare economics approach, the average inter- nal rate of return was found to be 18 %. In a later comment Peterson (1971) states that a ten year lag is probably too long. If a lag of six years is assumed, the marginal in- ternal rate of return is about 50 %, not 33 %. 2.3.4. Production Function Studies ofEvenson Evenson (1967, 1971, 1977) has carried out a number of studies using the production function approach. An investigation done to- gether with Kislev summarizes several studies (see section 2.3.5.). Evenson (1967) estimated the marginal rate of return to aggregate investment in research on the experiment stations and in the United States Department of Agriculture. The analy- sis applied cross-sectional data on research ex- penditures for the different states and time- series data for total research. The average lag between research expenditures and effect on production was also estimated. In the most simple econometric models technological change is treated exogenously as 268 a shift in the production function. Evenson presumes that the contributions of agricultural research cannot be explained by a small num- ber of important research findings. Instead he thinks of the contributions as small changes in the quality of inputs. In the production function (2.3.) Y = f(X„, X 12)... X2l , X22,... Xn2 ,...Xnm ) the subscript n indicates the type of input and the subscripts m denote various qualities. The variables are usually aggregated using relative price weights. The quality differences are not reflected in this typical aggregation. Evenson therefore found that conventional input mea- sures fail to reflect changes in the quality of inputs. Thus it became important to put for- ward the hypothesis that a specific “research production function” exists in the form: (2.4.) Q = f(Z ik> u) where Z ik denotes the research input in the form of scientific skill, supporting staff, and buildings and supplements, whereas u is an error term. The research input can be mea- sured by public expenditures for research. The quality improvements in year t are de- fined as R,, in the year t—l as R t_~ etc. If a lag operator is included, the research pro- duction function becomes: (2.5.) R, = W(L)Z, + C(L)u, where W(L) indicates a distributed lag func- tion with weights W|(W|Z, + w,Zt _,, etc.) of research expenditures. C(L)U, is a distributed lag function of error terms. With the research production function R,, a stock of knowledge K is defined. The stock of knowledge is filled in with the help of R, at the same time as some of the knowledge depreciates (becomes obsolete). Evenson attempted, in particular to esti- mate the mean time lag. In doing so he ex- plores both an exponentially declining and a symmetric or inverted V distribution. The length of lag is estimated by ordinary least squares and the alternative with the highest coefficient of determination R 2 is chosen. The data used is from American agriculture. Two different functions are used. The first is an aggregate Cobb- Douglas function in- cluding a research variable, and the second is a “residual” function with the ratio of output to input as the dependent variable (Y/J = ARd). His conclusions are: 1. The highest R 2 is found at six to seven and a half years. The average lag between in- vestment in research and results in production thus seems to be six to seven and a half years. With a 95 % confidence interval, the mean time lag would be three and a half to eleven years. 2. Griliches calculated the marginal prod- uct of research and extension to be USD 13 of output produced for each dollar invested in research and extension. Using the same cross- sectional data, Evenson reports to have calculated a similar marginal product of USD 10. Using time-series data, he reports estimates of a marginal product of about USD 40. 3. Cross-sectional data tend to underesti- mate the research results, as the “spillover” effect (cf. chapter 1) between states is not in- cluded in the cross-section. The state of re- search origin cannot capture all the benefits of research, since some of it passes over to other states. The research carried out in one state thus affects the production function of other states. A study carried out later (Evenson 1971) concerning the organization of agricultural re- search uses the same theoretical framework. The conclusions of this study support the as- sumption that economies of scale also applies to research at the experiment stations. It is also commented that a stochastic term could well be included in the research production func- tion R,. Evenson (1977) later points out that at- tempts should be made to distinguish between different types of skills inventive, techni- cal and engineering, technical-scientific, con- ceptual-scientific etc. because their rele- vance applies to the production function in 269 different ways. Correspondingly an attempt could be made to distinguish between differ- ent types of research so that several categories could be utilized. 2.3.5. The Studies Carried out by Evenson and Kislev Evenson and Kislev (1975) summarized their studies on the economics of agricultural research in the book Agricultural Research and Productivity. The perspective is interna- tional, and focuses on the diffusion of agri- cultural innovations to developing countries. Only a few parts of the book will be touched upon here. A special “knowledge production func- tion” is defined on the basis of scientific publications in agricultural sciences, scientific man-years in agricultural research, expendi- tures on agricultural research, GNP per cap- ita and the number of newspapers per 10,000 people. Cross-sectional data is used to esti- mate a Cobb-Douglas knowledge production function. The data is collected from 44 dif- ferent countries. Determinants of research investment are es- timated in a similar way. The explaining vari- ables used are the value of the product in ques- tion out of total output, its share of exports, the proportion of farm labour out of the total labour force, etc. One chapter deals with research program- mes for wheat and maize. The period analyzed is 1948—1968, and the data was collected from 68 differentcountries. The yields are de- fined as a function of soil, climate and tech- nology. Technology is determined by the stock of knowledge, which is partly indigenous, partly imported from other countries. Func- tions for estimating both the regional and the borrowed stocks of knowledge are specified. Figure 2 illustrates the internal relation be- tween the stocks of knowledge. Two different sets of estimates are calcu- lated, one on the basis of cross-sections and one on the basis of cross-sections and time- series. The growth of yields in maize and wheat production are expressed as a function of a knowledge function. The knowledge function is expressed through the sum of counts of ar- ticles in “Plant Breeding Abstracs” from 1948 to 1968. Regressions were used to calculate the marginal rate of return for one publication. Other explaining factors of the yield increa- Fig. 2. Stocks of knowledge in regions and countries. Region 2’s stock of knowledge is the total stock of country 3 plus parts of the stocks of countries 1 and 4. Country I’s borrowable knowledge is the total knowledge of country 3 and parts of 2 and 4 (Evenson and Kislev 1975). 270 271 ses in 1948—1968 are the rate of change of yield in 1920—1939 and a time factor. The marginal rate of return ten years later is USD 30,822 for maize and USD 20,287 for wheat. In the first year the marginal rate of return is USD 2,330 for maize respectively USD 1,581 for wheat. Besides this direct contribution to produc- tivity by indigenous research, the publication has another indirect value. It consists of ac- celerating effects of the country’s own work on knowledge borrowed from abroad. Still another value is the spillover effect, spreading over the borders of the original country of research. One chapter examines the aggregate pro- duction function for 36 different countries. The production function is specified in order to consider the differences in productivity, partly between countries (“level” coefficient) and partly over time (time trend coefficient) as illustrated by Figure 3. Four different regressions are calculated, one with both level and time trend differences, two with one difference considered each, and one without either difference. In each case the research variable is positive. On the basis of these estimations a marginal benefit/cost quota of 2 is obtained. This quota, however, does not take into account that the knowledge becomes obsolete. Accord- ing to this study, the marginal productivity of research would be considerable. 2.3.6. Some Other Production Function Studies Kahlon et al. (1977) used two different methods in a study of Indian agricultural re- search. The first method was similar to the one described in section 2.3.1. The second method consisted of estimating the output for two dif- ferent periods with fixed levels of inputs. The difference in production between these periods was attributed to additional investment in ag- ricultural research. The returns from research were estimated partly on the state-level, partly on the all-India level. In the analysis the relative share of each factor in the growth of output for the two Fig. 3. Country-specific “level” differences and country-specific trend differences (Evenson and Kislev 1975) Table 3. Returns to investment in agricultural research in India. Output and Investment First Period Second Period Difference 0) (2) (2)-(l) Estimated output (million rupees) 6,592.00 6,945.00 353.00 Average investment in agricultural research (thousand rupees) 3,372.05 6,412.28 3040.23 n , . ~ 353.00 million rupees , , ~Return to 1 rupee invested = - = 11.61 rupees. 3,040.23 thousand rupees periods, 1960/61 1964/65 and 1967/68 1972/73, are calculated. Using dummies, the shares of net sown area, human labour, fer- tilizers and irrigation in the output growth rate are presented. The production function is of the Cobb-Douglas type. The returns from research estimated through the different periods are presented in Table 3. From the table it is possible to see that 1 rupee invested in agricultural research yields 11.61 rupees, with a lag of five years. This is equal to an annual internal rate of return of 63.3 %. This estimate is comparable to the estimated internal rate of return to Indian re- search of 50 % calculated by Evenson and Jha when the lag was assumed to be eight years. Bredahl and Peterson (1976) estimated the marginal product and the internal rates of return for the four most important commodity groups in American agriculture. These four groups were cash grains, poultry, dairy, and livestock. The purpose was to determine the internal importance of the marginal return by commodity group. By reallocating research in- puts in favour of products with a high mar- ginal rate of return, the efficiency of research could be improved. Production functions were used in the estimation of the rate of return. The marginal internal rate of return for the USA as a whole varied between 36 and 46 °7o. The returns fluctuated more at state level. The commodity with the highest payoff to research was generally found to be the commodity with the largest absolute value of output. Thus on state-level the highest returns were in the most important commodity group. The spillover effect between states, however, was not con- sidered. A final comment is made that the fig- ures should not be read literally. They are in- teded to complement rather than to serve as a substitute for common sense and good jud- gement. The purpose of a study by Knutson and Tweeten (1979) was to determine an optimal rate of future investment in agricultural re- search. In doing this, marginal rates of return for earlier decades were calculated first. These were then projected from 1976 to 2015 under various scenarios defining the rate of increase in research expenditures, demand for farm output, and inflation. The results showed that the optimal rate of future investment in agri- cultural research depends on the growth of demand. For instance, slow growth of de- mand coupled with rapid increases in research could pose economic hardships for farmers. If on the other hand demand grows fast, in- cremental research outlays are required to keep the rate of return as low as 10 %. 2.4. The Welfare Economics Approach 2.4.1. General Features The second major approach used in esti- mating the returns to research is based on wel- fare economics. The intersections of the de- mand and supply curve and the shift of the supply curve are used to determine the bene- fits from research. Changes in prices and quantities serve as the base for estimating a consumers’ surplus and a producers’ surplus or, taken together, an economic surplus for the whole society. Sometimes separate bene- fits and costs have been estimated instead of 272 the economic surplus. Normally not the mar- ginal but the average returns to research are estimated. The pioneering study in this field was the study on the returns from hybrid maize research carried out by Zvi Griliches. 2.4.2. The Study on Hybrid Maize by Griliches Griliches (1958) estimates the realized so- cial rate of return of private and public funds invested in hybrid corn research. He calculates the loss in surplus to society that would take place if hybrid corn were to disappear. Griliches computes an external rate of return exceeding 700 °/o. The internal rate of return, however, was 35—40 %. Griliches starts from the assumption that the annual gross social returns of research approximately equal the value of an increase in maize production as a result of this re- search. The additional costs for producing this maize are subtracted from these gross returns, giving an annual flow of net social returns. These are then compared to the costs of re- search, expressed as a capital sum. The value of hybrid maize research is illus- trated by Figure 4. In case a) in the figure the supply of maize is assumed to be infinitely elastic, in case b) as completely inelastic. Both cases represent extremes. Griliches now calculates the loss of benefits, had no hybrid maize been developed, i.e. the shift of both curves from S to S'. In case a) the benefits of research are equal to the value of lower production costs for the production volume Q 2 and the growth of consumers’ surplus as a consequence of lower prices. This value is equal to the area of the rectangle P|P 2P 2'P,' and the triangle Pi'P 2 'Pi". In this case the total loss to so- ciety would be equal to the area P,P 2P 2 ' P,". This area can be approximated by the for- mula: (2.6) LOSS 1 = kP,Q, (1 1/2 kn) k = Percentage change in yield n = Absolute value of the price-elasticity of demand P, = Price Q, = Quantity In case b) the loss to society consists of the loss of the production (P,' Pj" Q,Q 2 ) to the old price P, and the additional loss in con- sumers’ surplus (P,'P2 'P|") or: (2.7) LOSS 2 = kP,Q, (1 + 1/2 kn) On the basis of (2.6) which gives a lower estimate, Griliches calculates the returns to hybrid maize research using the following figures. Yields have increased by 15 °/o, the price elasticity is 0.5, 90 % of all future maize cropping areas are planted with hybrid seed and the value of the average production vol- ume for 1937—1948 was USD 3 billion (in the prices of 1955). According to (2.7) the loss to society had no hybrid seed research taken place would be: 0.9 X 15/115 X USD 3 billion (1 1/2 X 0.9 x 15/115 x 0.5) = USD 341 million. Fig. 4. The effects of a shift in supply caused by increasing productivity (Griliches 1958) 273 Subtracting the annual cost of hybrid seed, production and research, USD 93 million, the net social return becomes USD 248 million. The study gives an external rate of return of 743 % and an internal rate of return of 35—40 % for hybrid maize research. This is the average (historical) rate of return, not the marginal rate of return. This study of Griliches has since been criti- cized on some points. It only takes into ac- count research applying directly to hybrid maize, neglecting all resources devoted to basic research on hybridization. There can be no doubt, however, that genetic research has strongly affected the development of hybrid maize (Peterson and Hayami 1977). As such, research expenditures seem to have been underestimated. Evenson (1977) critcizes Griliches among others, for having estimated extraordinarily high rates of return on the basis of erroneous econometric formulations. He finds this a serious matter. According to Evenson and Kislev (1975) Griliches is guilty of a systema- tic mistake in neglecting quality improvements in labour. 2.4.3. The Welfare Economics Approach According to Hertford and Schmitz Many different variations of the welfare economics approach have been used since the study of Griliches. A general theoretical fra- mework has been outlined by Hertford and Schmitz (1977). The central Marshallian con- cept of economic surplus is important in this analysis. The economic surplus consists of consum- ers’ surplus and producers’ surplus as earlier pointed out. These concepts are illustrated by Figure 5. According to Hertford and Schmitz (1977), the consumers’ surplus has the fol- lowing meaning: The demand curve D in the figure shows the maximum price a consumer would be prepared to pay for successive, ad- ditional units of a commodity. Thus to buy one more unit, the consumer is only willing to pay a lower price. If we assume the falling demand curve to intersect the supply curve at Q,, the consumer is only ready to pay P, per unit purchased. Had he bought the units suc- cessively, the total costs would be equal to the area left of the demand curve. When buying all units directly on the market instead, he only has to pay P, for each of the units. His savings are thus equal to a + b + c. This area is the consumers’ surplus. It can be regarded as a collective surplus for all consumers on the market. The producers’ surplus analogically refers to the difference of what a producer receives for the sale of a good and the smallest price at which he would be prepared to sell the good. In Figure 5 the supply curve S 0 reflects the lowest price the producer is willing to sell for, thus being 0 in origo and P Q at market balance. On the market he can sell all units for a higher price than successive sales of addi- tional units would bring in. The producers’ surplus for the supply curve S 0 is thus the area equal to b + d, i.e. the collective surplus of return resulting from selling on the market. The supply curve of the industry represents the sum of the marginal costs curves of the producers, while the area under the supply curve of the industry is equal to the variable costs of production. If productivity increases Fig. 5. Combined consumers’ and producers’ surplus (Hertford and Schmitz 1977). 274 the supply curve shifts from S Q to S,, and costs will decrease. If the price stays at the preceeding level P„, the producer will receive an increase in his surplus equal to e + c -E f, the total producers’ surplus now being b + d-t- --e + c + f. When productivity in agriculture increases due to new research results, the supply curve shifts in Figure 5 from the initial position of S Q to the new position of S,, and the price falls from P D to P,. The increase in consum- ers’ surplus that results from the price fall is then equal to the area b + c in the figure. The increase in producers’ surplus due to the sale of a larger quantity is c + f, and the decrease in producers’ surplus due to the price fall is equal to b + c, or the net change in producers’ surplus will bec +f—b—c = f b. When both surpluses are combined the total economic surplus is b +c + f-b =c + f. The latter area can be calculated from the formula (2.8). (2.8) kP,Q, (1———) n + e where k = percentage increase in production due to research n = price elasticity of demand e = price elasticity of supply The percentage increase k can be calculated by dividing the distance between the supply curves with the value of final production Q,. In practice the critical determinant of the eco- nomic returns from research is the factor k. Hertford and Schmitz point out that when research leads to the development of new pro- duction methods for a certain product, the finding can affect the use of other resources. For instance, producers who lack the possi- bility to utilize the new production methods may be forced out of business, and other pro- duction resources may not find any alterna- tive use. The benefits may be overestimated if this is not taken into account. An advantage of the welfare economics approach is that it enables classification of who benefits from research, producers or con- sumers, and how the returns are divided between these groups. Comments on the welfare economics ap- proach have led to the consideration of more complex issues. Some of these are reviewed in the next section. 2.4.4. Comments on the Welfare Economics Approach Normally the demand and supply curves are not linear as in Figure 5. A more realistic illus- tration is shown in Figure 6. The increase in the combined consumers’ and producers’ surpluses in the figure above is indicated by the area OBA. This area cor- responds to the area c fin Figure 6. Lindner and Jarrett (1978) note the es- sential difference between the assumption of a parallel, a divergent and a convergent shift in the supply curve. This is shown in Figure 7, where the demand curve is conveniently as- sumed to be completely inelastic. According to Lindner and Jarrett, earlier studies did not distinguish between the types of supply shift. Important comments on the shift of the supply curve have also been made by Jarrett and Lindner (1977), Rose (1980), Wise and Fell (1980) and Lindner and Jar- rett (1980). Wise (1981, 1984 a) outlined a welfare eco- nomics analysis of the benefits from research which is not based on the consumers’ and producers’ surplus concepts, but on costs and Fig. 6. Effect of a new technology in shifting supply curves (Dai.rympl.e 1977). 275 benefits. Wise argues that the essential curve to consider in benefit analysis is the cost curve and not the supply curve. In elementary models the two coincide, but Wise draws upon Capstick for many cases when factors other than costs affect the supply. Wises analysis is shown in Figure 8. Figure 8 a) corresponds to Figure 6, and is based on the assumption of identical cost and supply curves. In Figure b) AM is the original cost curve showing the national output X. According to Wise, it is not necessary to estimate the new curve resulting from tech- nological change. It is enough to note that the original level of production X changes to a new level X*. The economic benefits in case b) consist of three components 8,, B 2 and 83.B3 . B, is equal to the value of increased production. B 2 cor- responds to the value of fewer producers being able to produce the previous output, enabling some of theproducers to move into other sec- tors. Essential for this part of the benefits is that alternative possibilities for employment are found. All costs of creating places for work for displaced people must otherwise be Fig. 7. Divergent (a) and convergent (b) shifts of the supply curves Fig. 8. Conventional construction in terms of surpluses (a) and alternative approach in terms of benefits (b) (Wisi 1981). 276 277 subtracted from 82.B 2 . B, is, finally, the value of specific input savings needed to produce X. The input savings are a consequence of better production methods. Freebairn et al. (1982) analyzed the impor- tance of research at different levels of produc- tion; research on nonfarm input, farming and marketing. In a model based on pure competi- tion the benefits of research will, however, be equally divided between the various levels. Discussion of the welfare economics ap- proach has shown that the conclusions and the size of the rate of return are largely dependent on the assumptions made about the form and shift of the supply curve. Practical application of the welfare economics approach thus must be done with care. 2.4.5. Returns from Rice Breeding in Japan Estimated by Akino and Hayami With the help of a model of demand and supply curves like the one in Figure 6, Akino and Hayami (1975) estimated an internal rate of return for rice breeding in Japan for two different periods, 1915—1953 and 1932 1961.Two different cases, an autarky case and an open economy case, and two alternative as- sumptions as to the streams of returns were used. One assumption was that net returns in 1935 and in 1951 would have continued for- ever, the other assumption was that net re- turns would become zero after 1953 and after 1961. The difference between the autarky ca- se and the open economy case was minimal. For the first period the internal rate of return was 26—27 % in the autarky case and 25 % in the open economy case. These figures con- cern both assumptions on the stream of re- turns. The internal rate of return was 73—75 % for both cases and both asumptions in the second period. 2.4.6. The Study on Returns to Pasture Improvement Research by Duncan Duncan (1972) attempted a) to identify im- portant pasture research findings and b) to estimate the internal rate of return to research on pasture improvement. The study focused on an input resource, pasture. What was the effect of this research on demand for pas- tures? The benefits were assumed to corre- spond to the area between the new and the old demand curve for pastures above the price. Three different regions were separated in the study. Figure 9 shows that supply is assumed to be perfectly elastic. A regression model was formulated to estimate the own price elasticity of demand. The demand for pastures was as- sumed to be a function of the real price and the state of pasture technology. Polynomial distributed lags of degree three and four (Almon lags) were fitted to each of these independent variables. Briefly, the results were as follows: 1) The most important research contribution has been in the field of plant nutrition 2) The internal rate of return was very high, 20—80 °7o depending on region and elas- ticity. 3) Both adoption lags and lags in adjustment of the stock of improved pastures to changes in prices were very short No firm conclusion could be made con- cerning the effects of research on the demand for pastures. 2.4.7. Canadian and Spanish Studies of Crop Development Research Nagy and Furtan (1978) studied the re- turns from public and private investment in Fig. 9. The gains from an increase in the productivity of an input (Duncan 1972). rapeseed breeding in Canada. Consumers’ and producers’ surpluses were estimated. A com- puted internal rate of return of 101 % indi- cated that the investment level in rapeseed breeding has been too low. Consumers ob- tained 53 % of the total net benefits, pro- ducers 47 °7o. The method used was similar on the whole, to that of Akino and Hayami (1975) in their study of rice breeding in Japan. The relevant figure is the same as illustrated by Figure 6. The recent Canadian studies include the one carried out by Zentner and Peterson (1984). The internal rates of return for research on new varieties and for all research dealing with wheat production ranged between 30 and 39 %. Only direct resource expenditures and extension activities were considered as costs. Herruzo (1985) has estimated the returns to rice breeding in Spain. Following the work of Schmitz and Seckler (1970), the study as- sessed two types of social benefits from rice breeding: gross social benefits and net social benefits their difference being wage losses resulting from the adoption of new technol- ogy. The internal rate of return as computed from gross social benefits was 18 %. If labour displacement is considered, with 50 % of the displaced population receiving compensation, the value of the internal rate of return drops to 17 °7o. The study further showed the con- sumers to be the sole beneficiaries of research, whereas producers suffered losses due to the low price elasticity of demand. 2.4.8. The Distribution ofEconomic Benefits from Agricultural Research The introduction of new production meth- ods created by research affects the prices of the products. An increase of the supply de- creases the price. Conventionally measured, some of the benefits will accrue to consumers and some to producers through the drop in prices. The distribution of these mutual bene- fits has been explained in Figure 5. Are there any losers in agricultural research? Producers unable to apply the new meth- ods, whether because of the small size of their firm or for other reasons are the losers. The total social benefits from modern technology have generally been sufficient to compensate the losers, though compensation has not usually been made even in cases were it would have been possible (Pinstrup-Andersen 1982). In a well-known, controversial study of the tomato harvester in California, Schmitz and Seckler (1970) concluded that the gross so- cial rate of return from aggregate research and development expenditures on the tomato har- vester was nearly 1,000 %. If displaced toma- to workers are compensated the net social ra- te of return ranges —8 to 929 %, depending on the amount of compensation (from 0 to 100 %). If 50 % of the displaced workers do not find alternative working opportunities and receive compensation, the net social return is 460 %, thus still an extremely high rate. Hertford and Schmitz (1977) emphasize that aggregative models tend not to consider distributional effects. For a given commodity there are many types of producers: small-scale farmers, large-scale farmers, landowners, sha- recroppers, and farmers with unmechanized and mechanized farms. The estimated returns often tend to neglect this subdivision between producers and the respective distribution of benefits. Schultz (1977) argues that, in the long run, the major share of benefits from research is transferred to consumers. The distribution between various consumer groups can also be different, since the price elasticity of demand may vary between different consumer groups. On the whole, however, lower food prices tend to decrease income disparities (Pinstrup- Andersen 1979). Many studies have focused on the distribu- tion of benefits between producers and con- sumers. It was pointed out in section 2.4.7. that Nagy and Furtan (1978) estimated con- sumers’ gains from rapeseed breeding in Canada to be 53 % and producers’ gains to be 278 47 %. Akino and Hayami (1975) examined two cases in their study of the returns from rice breeding in Japan. In the first case made under the autarky assumption all benefits went to consumers, while in the second case, based upon an open economy assumption, both producers and consumers became better off. Scobie and Posada (1978) found that the major share of the benefits of technological change in rice production in Colombia went to consumers, wheras small producers suf- fered losses. The benefits exceeded total costs in spite of this. Herruzo (1985) concluded that consumers were the main beneficiaries of rice breeding in Spain while producers, or at least some of them, became worse off because of the low price elasticity of demand. Scobie (1976) argues that analysis of the distribution of the economic surplus should include two additional simple questions: 1) Under what conditions will consumers gain more than producers as a result of technolo- gical change?, and 2) Under what conditions will the producers’ surplus be positive? Scobie presents a clear example in order to show the difficulties in calculating how bene- fits are distributed. A Minister for Allocation of Agricultural Research Funds is confronted with a proposal to grant USD 10 million for research on the “bongoyam”. His office in- forms him that the demand and supply elas- ticities for bongoyams respectively are —0.7 and 0.4. After receiving this information he poses both the above mentioned questions to his economists. The answers they give him depend on the formula used, and are illus- trated in Table 4. Table 4. Relative magnitudes of consumer and producer benefits for bongoyams (Scobie 1976). Formula used Will con- Will produc- sumers gain ers’ benefits more than be positive? producers? Akino and Hayami Hertford and Schmitz Ramalho de Castro and Schuh YES YES NO YES NO YES The conclusion is that the Minister must be confused by these contradictory answers. This fable also illustrates some of the difficulties connected with the welfare economics ap- proach. 2.5. Criticism of the Examined Studies 2.5.1. General Criticism The research field of estimating the eco- nomic returns to research has been a contro- versial subject since the first study made by Schultz in 1953. The credibility of estimated returns has been questioned, in particular the reliability of the earlier studies. Both of the reviewed methods for estimating the returns to research have been criticized on many points. The criticism has resulted in more detailed models where a more accurate ap- proximation of research costs and a bigger cautiousness in estimations have been con- sidered. According to Ruttan (1982), this tendency has led to more recent credible studies which tend rather to underestimate the returns to research. Anyhow it is clear that many of the earlier studies, particularly those with a welfare economics approach, have been subject to methodical errors and insufficient data on research costs. The next sections re- view these aspects. Rosenberg (1982, p. 25, 141—159) main- tains that the rate of growth of an industry’s output depends on factors of demand at least as much as it does depend on factors of sup- ply. This can even be expressed in another way, i.e. technological change should not be seen as a predetermined exogenous factor automatically evolving according to a given pattern. Rather, it should be regarded as an endogenous force. Economists have tended to be interested more in the consequences of technological change than in the determining factors. Omission of these decisive, exogenous factors and the assumption that technologi- cal change develops according to a past pat- tern mean that science and technology are treated as though independent from economic and social circumstances. 279 Rosenberg further stresses the importance of inter-industry relationships when consid- ering the contribution of technical progress to productivity growth. The growth of produc- tivity, for instance in American agriculture during the 19th century, was dependent on a stronger regional product specialization. This, in turn, was connected with the development of transport facilities (roads, railways, the steam engine and refrigeration) which made regional specialization possible. Technologi- cal improvements in one sector clearly depend on developments in other sectors. This fact has not been considered clearly enough in the early studies of returns to research. Rosenberg also notes that the estimation of returns to industrial research overlooks the improvement in the quality of final products bought by the consumers, which may prove to be as important as growth in productivity. Agricultural research is easier to evaluate in this respect, since the final products are more homogeneous because the food industry is not included in most of the studies. In connection with Rosenberg’s inter-indus- try relationships it is worth mentioning the considerable importance of the spillover effect particularly in small countries. A large pro- portion of the research results are imported from other countries, modified only to a cer- tain degree. It could thus be argued that the wisest thing for small countries to do would be to let bigger nations carry out all research and only to import ready results. There are, however, two functions of a domestic research capacity that cannot be compensated, as pointed out by Edwards and Freebairn (1981). One function is to facilitate the utili- sation of imported research results, both basic and applied. The other function is to investi- gate those promising areas and specific prob- lems which are not covered by foreign re- search. Feeding methods based on silage as the main source of protein is perhaps one such from Finland. Nevertheless the problem of how to measure the spillover contribution from abroad still seems to be an unsolved problem in the field. Vuori (1984) argues that estimates may be too high if one or more variables indirectly affecting productivity not have been taken into account. One such variable could be the growth of human capital. Usually this factor is attributed to increased education and in- creased experience through learning by doing. Human behaviour, however, consists of many factors that are difficult to estimate. Pasour and Johnson (1982) also question whether the calculated rates of return are ap- propriate measures for comparing agricultural research and other public activities. Wise (1984 b) emphasizes that an economic crite- rion of welfare is only one of several possible criteria for political decision-making. Thus our values will decide whether or not this eco- nomic criterion is a sufficient criterion. A modest analysis of the economic benefits will be better suited to detect not only the many logical pitfalls but also the influence of value assumptions, and it should take care not to extend the economic quantification beyond normative and technical limits. 2.5.2. Criticism of the Production Function Approach One of the most difficult methodical prob- lems in the production function analysis is the collinearity between the research variable and other variables. According to Lund et al. (1980), this fact in connection with the in- capacity to analyze separate production branches has led to the conclusion that the production function approach has only lim- ited applicability. Wise (1984 b) reports that re-interpretation of several earlier studies reveals the estimated rates of return to have been considerably lower in reality. According to him, both pro- duction function analysis and the welfare eco- nomics approach have used relatively simple models which are insufficient. They are in- adequate in explaining how research affects the system it is part of. Wise points out that the marginal product was calculated as b Q/R in Peterson’s (1967) 280 production function study of poultry research in the USA. Here b represents the index for the research variable in the production func- tion and R/Q the value of the research input in relation to the output. A ten-year lag was incorporated. According to Wise, the model is faulty. He argues that the marginal product should be calculated as b Q/RN, where N is the number of years over which the original research continues to affect output. If N is infinite, the marginal product approaches zero. Should Wise’s criticism be justifiable at this point, the estimated value of the marginal product is highly overestimated. But it seems hard to understand the criticism, since b repre- sents the elasticity of production in the Cobb- Douglas function. According to the definiti- on of elasticity, it shows the percentage change in production when research input is changed by 1 %. It is difficult to understand why this change should be divided by the number of years the research affects output. Peterson (1985) calls attention to the con- ventional inputs in the production function. If they have not been corrected for a change in quality, the research variable will pick up these quality improvements. As the quality of fertilizer, buildings and other external inputs has risen faster than their prices, these chan- ges will influence output. If the research vari- able only measures public research, the effects of private research will be included incorrect- ly . These changes in the quality of inputs are hard to measure if only the publicly funded research is taken into account. This argument is a call to pay explicit attention, in one way or another, to private research in the models. On the other hand, expenditures for private research are included in the prices of products. Farmers thus actually pay for private research. Thus the problem of taking private research expenditures into account is not self-evident if a variable for external inputs is included in the production function. Depending on which view is accepted, private research is either in- cluded or omitted. Vuori (1984) calls attention to the treat- ment and content of the research variable which, she thinks, considerably influences esti- mated returns. It is especially difficult to value how the effects of research are distributed among individual years. In her own study on the rates of return from industrial research in Finland and Sweden in 1964—1980 Vuori used geometrically distributed lags and an Almon lag of second degree. Still one more difficulty, Vuori states, is the aggregation of research ex- penditures. Different types of research have different lengths of lags; in other words the time lags are assymetric. The difficulties in estimating the profitability of industrial re- search are further aggravated by the disparity between different industries, a cicumstance which does not concern agricultural research to the same degree. 2.5.3. Criticism of the Welfare Economics Approach Pinstrup-Andersen (1979) states that a considerable portion of the studies on how the returns from research have been distributed between consumers and producers are based on incomplete analysis. Various supply curves of production costs should be considered in order to observe the division of producers’ surplus between separate groups of farmers. However, he contends that distributional issues are more easily dealt with through political measures than through research. There is a significant difference between an open and a closed economy. In countries where technological change has contributed to production growth but where export possibili- ties are limited because of unprofitable price relations, the situation is near that of a closed economy. Wise (1981, 1984 a, 1984 b) has stated that methods based on consumers’ and pro- ducers’ surpluses have been too simple. He considers the internal rate of return to be an inappropriate measure for the economic utility of research. It is a suitable indicator of pro- fitability only when the returns can be re- invested, while its analogous use in the con- 281 text of a national economy has not a compar- able content. Pasour and Johnson (1982) and later, Peterson (1985) have also suggested that a “social internal rate of return” not is comparable to the internal rates of return in the private sector. Wise (1984 b) further points out that the treatment of costs of implementing new in- novations has been ambiguous in the earlier studies. Implementation costs can be treated as negative benefits and subtracted from the sum of benefits whereafter the differencebe- comes a benefit/cost quota. But implementa- tion costs can also be treated directly as costs. The alternative chosen will considerably in- fluence the result, as can be seen from the ex- pressions B/(P +Q) and (B —P)/Q. In the former case the implementation costs repre- sent pure costs, whereas they represent nega- tive benefits in the latter. As Wise puts it: “No great mathematical skill is required to see that the negative benefit approach can lead to very high benefit-cost ratios if, say, P is large but Q is smalland P is treated as a nega- tive benefit” (Wise 1984 b). In Griliches’ (1958) hybrid maize study and in Peterson’s (1967) poultry study, im- plementation costs were treated as negative benefits; this may have lead to overestimated rates of return. Wise (1981, 1984 a) has presented his alter- native to the economic surplus method on the basis of cost and benefit analysis (see section 2.4.4.). He still stresses that the magnitude of error probably has not been great in the earlier formulation. Wise establishes four criteria that should be met in order to calculate reli- able estimates of the benefits: (i) The appropriate market mechanism must be identified. (ii) The original cost curve must be adequate- ly defined. (iii) The technical parameters relating to willingness to adopt new technology, to the implementation costs of so doing and to the yield increases obtained must be satisfactorily established; any variations among producers in these respects must also be duly incorporated in the calcula- tions. (iv) There must be no covert, and possibly un- justifiable, assumptions such as that dis- placed resources, at zero cost, immedi- ately find equivalent employment else- where in the economy, that demand curves adequately evaluate agricultural surpluses, or that there is a large pool of efficient producers waiting on the side- lines, etc. (Wise 1984 a). Wise (1984 b) further questions whether the studies carried out have considered pos- sible defects or adverse effects appropriately. Mechanical use of formulas without criticism can lead to distorted views of the long-term benefits of research. Thus he calls attention to the fact that the internal rate of return in the welfare economics approach avoids the problem of dealing with certain drawbacks. If, for instace, some built-in defect in the hybrid maize in the study of Griliches (1958) had led to all maize production being wiped out forever after 1955, the internal rate of return would have sunk only from 35 % to 34 %. Helander (1985) states that the funda- mental goals of society for agricultural policy should be the starting point for evaluating the relevance of research. If the economic bene- fits represent one aspect of this overall rele- vance to society, the social benefits of research represent the other aspect. This study makes no attempt to evaluate social benefits. Certain examples of what such social benefits could consist of need to be mentioned, however. Improved working and social conditions for the agricultural population, a decreased use of energy, environmental aspects and new complementary sources of livelihood for the rural population could represent social bene- fits which should be evaluated on basis other than the strict econometric analysis used in this study. 282 3 3. The Returns to Investment in Agricultural Research An Aggregated Production Function Study 1950—1984 3.1. Productivity Increase, Technological Change and Economies of Scale the Connections 3.1.1. The Concept of Productivity In two previous chapters we reviewed the reasons for estimating the returns to agricul- tural research as well as methods that have been applied to do so. Research raises the quality of inputs in such a way that it is pos- sible to produce a greater output with a given quantity of resources. This is analogous to growth in productivity. Because other factors can influence increases in productivity as well, a distinction between these sources needs to be made. The internal relations between technologi- cal change, productivity and economies of size are illustrated by Uhlin (1985) in Figure 10: Productivity is defined as the empirical rela- tion between production and unit of input: p = Q A P = productivity Q = production A = input Growth in productivity implies that less resources are used for the production of one unit of a good, alternatively a higher produc- tion for a given quantity of resources. Growth in productivity accounts for that portion of a production increase that cannot be explained by an increase in the amounts of inputs. Economies of scale is defined by Peterson and Hayami (1977) as a more efficient or- ganization of traditional inputs stemming from an increase in the size of the firm. Tech- nological change refers to an increase in pro- ductivity stemming from new inputs or quali- ty improvements of traditional inputs. Economies of scale refers to the effect of increased output on average costs when all inputs are increased in the same proportions. The similar concept economies of size, how- ever, refers to the effect of an increased out- put on average cost when inputs are increased not in proportional but in least cost combina- tions (Doll and Orazem 1978). Difficulties in distinguishing between the concepts arise from the fact that technologi- cal innovations are often developed with cer- tain requirements for the minimal size of the firm. By definition technological change is conceptually different from scale economies. 3.1.2. Technological Change Adaption of a technology not previously used in the production process implies tech- nological change. There are numerous defini- tions of technological or technical change. Ac- cording to Hayami and Ruttan (1971), it is the substitution of cheaper and more abun- dant factors of production for more expen- Fig. 10. The connections between sources of growth in productivity. 283 sive and scarcer ones at a certain volume of production. The constraints on production caused by inelastic supplies of resources can be released through technological change. The quality of inputs will be improved or totally new inputs will be developed. The quality im- provements of inputs, both physical and labour, are due to research, education and learning by experience. Pinstrup-Andersen (1982) refers to the technological state of any given production process as the composition and combination of inputs and technologies that exist at a given time. Thus, technological change describes a movement from one technological state to another. According to Vuori (1984), al- though difficulties are encountered in the es- timation of technological change, it is usual- ly measured with growth in productivity. In the context of production function analy- sis, technological change manifests itself in several ways. We examine the Cobb-Douglas function (3.1) Q, = aK t“ L t f» where Q, represents production, K capital, L labour, a is a constant and a and P corre- sponding elasticities of production. According to Heertje (1977, p. 126, 147), technological change can be mirrored, firstly, as an increase in coefficient a, which means that the maxi- mum of Q is higher though the combination of production factors remains the same. At the same time, it can be viewed as a shift in the production function. In the case of a mic- roeconomic production function, technologi- cal change, secondly, can alter the elasticity of scale (a + P), but a difficulty here is that such alteration can also be caused by growth of the firm. Thirdly, technological change can alter the elasticity of production so that growth in either a or P occurs separately, resulting in more capital-intensive or labour- intensive production methods. Heertje (1977) reviews two forms of tech- nological change: the case when technologi- cal change is embodied in capital goods used by the firm and the case of disembodied tech- nological change not related to capital goods. The division is made in order to create an operationally suitable distinction between quality improvements in capital goods and ot- her quality improvements (cf. also Hemilä 1982). The embodied form of technological change implies that the farm is supplied with inno- vations in the form of capital assets and equip- ment of a certain vintage (machines, build- ings, seed etc.). One central force behind this type of technological change is agricultural research, which increases productivity in many ways. It lowers production costs, increases production, improves the quality of the prod- uct, creates totally new products or lessens the vulnerability to uncontrolled factors. The disembodied form of technological change is not dependent on capital. It consists mainly of factors that increase farmers pro- fessional skills, e.g. education and learning by doing. Increased opportunities for education raise the farmer’s own productivity and in- crease the marginal product for a given vol- ume of inputs. Better education also increases the ability to acquire information, to interpret statements about costs and prices, and the adaption of new production methods. There are, however, also a number of fac- tors affecting changes in productivity which are more difficult to grasp. According to Rosenberg (1982), the role of inter-industry relations, improved roadnetworks and trans- port facilities are important in considering the contribution of technical progress to growth in productivity. Changing patterns in values and attitudes probably have a substantial in- fluence in the very long run. They may be of crucial importance when technical change is viewed with a historical perspective. The im- portance ofknowledge borrowed from abroad has also been discussed rather little. All these factors are examples of disembodied tech- nological change. It is important to distinguish between the two types when attempts are made to quan- tify the technological change. Heertje (1977, p. 174—178) shows that the production func- 284 tion can be expressed in the following way. When technological change is embodied in capital goods produced in the year v (vintage) production in the year t will depend on the state of technology in the year v. The produc- tion function becomes: (3.2.) Q(v,t) = A(v)F(K(v,t), L(v.t)) If technical change is not embodied in capi- tal goods the level of production (as far as technological change is concerned) depends only on the general trend factor in period t: (3.3.) Q(v,t) = A(t)F(K(v,t), L(v,t» In the former case one should construct a model which shows that the productivity of capital goods depends on the year v in which they were made. With a Cobb-Douglas func- tion, the technological change embodied in ca- pital goods can be expressed as: (3.4.) Q(v,t) = Be" L(v,t)° K(v,t)'-° where e TV is the embodied technological change. The disembodiedtechnological change is easy to introduce through the trend factor erv+rl where r is a measure of the rate of dis- embodied technological change. Another important divider between differ- ent forms of technological change is that be- tween exogenous and endogenous technologi cal change. When technological change is treated as an externally predetermined factor without explaining the sources behind it, it is exogenous. Technological change is then at- tributed the passing of time. The previous ex- pressions (3.2), (3.3) and (3.4) can all be con- sidered exogenous treatments. Technological change embodied in capital goods is always exogenous, while the increase in the produc- tivity of capital goods is attributed time (the vintage) (Heertje 1977). According to Sato (1981) endogenous technical progress is regarded as the result of the rational behaviour of human beings. Mod- els that treat technological change endoge- nously can explain it with one or more fac- tors, e.g. (Heertje 1977): a) changes in the long run in price relations between factors of production, b) a process of learning by experience, c) an investment in education and research. Technological change is not then treated as a predetermined quantitative factor in the pro- duction function, but as a result of how scarce resources with alternative use are allocated. Technological change has an endogenous character. Heertje (1977) therefore advo- cates an endogenous treatment when using production function analysis. It is, however, important at the same time to observe that an exogenous treatment does not necessarily im- ply that technological change is independent of economic factors, such as education, ex- tension and research. This study attempts to explain technologi- cal change endogenously. The endogenous explaining factors consist of investment in agricultural research and extension. 3.1.3. Economies of Scale and Changes in the Prices of Production Factors In the context of a production function, technological change can be seen as a shift in the function,, whereas economies of scale can be thought of as moving along the function in the direction of increased production. Natu- rally, it is possible that the firm is situated on a point below the production function, being efficient neither technically nor in the sense of scale (Uhlin 1985). In a Cobb-Douglas function economies or disceconomies of scale are reflected in the sum of elasticities (the sum a+ 3in (3.1)) (Hemilä 1982). Price reductions shift the supply curve to the right. They are connected with technologi- cal change and research, but can also stem from reductions of monopoly power or easing of import restrictions. An important example of price reductions at a given quality of input is the reduction in the real price of fertilizer (Peterson & Hayami 1977). Agricultural research can result in new knowledge and new materials. These may be 285 used directly for technology, or can serve as new inputs in the research process. Research which serves only as a base for further re- search is sometimes called basic research, whereas research with a direct application is called applied research. Yet this division is largely arbitrary and sometimes misleading. Through improving technical efficiency and lowering production risks, agricultural re- search exerts an influence on farm and con- sumer real income, on exchange earnings and on human nutrition. These effects have con- sequences for the three major goals of socie- ty, shown in Figure 11: growth, equity and se- curity against crises (Pinstrup-Andersen 1982). 3.2. Starting Point for (he Specification Let us repeat that the purpose of this study is to estimate the value marginal product of agricultural research in Finland. The second chapter reviewed studies carried out in the field, and issues related to technological change were accounted for in section 3.1. In the study an aggregated production func- tion for agriculture is estimated. A separate research variable is included in the production function. On the basis of the regression co- efficient with respect to research a value mar- ginal product, i.e. a marginal rate of return and a marginal internal rate of return for in- vestment in agricultural research and univer- sity education will be calculated. The method used is therefore reminiscent of the studies presented under the heading “2.3. Production Function Analysis”. The study focuses on the whole agricultural sector and the aggregated research input. The welfare economics approach would offer another method for estimating the rate of return. This method has been criticized on the basis of the arguments reviewed in section 2.5. The main reasons for not using this approach in the current study are, however, twofold. Firstly, the supply curve in a heavily regu- lated market like the Finnish one is affected by a multitude of market interventions. Since the economic surplus is calculated as the area between the old and the new supply curve, the supply management linked with several mea- sures dictated by agricultural policy make it even more difficult to decide upon the nature of the supply shift depending on research. In addition, the assumption of an open or a closed economy is crucial. Secondly, the object of study is aggregate agricultural research. Application of the wel- fare economics approach requires an estima- tion of the real supply and demand curve. Since elasticities are estimated by product and aggregated supply and demand curves seem impossible to estimate, supply curves for the different products need to be estimated. The question of how to split up the research input Fig. 11. Illustration of the potential outcome and impli- cations of agricultural research (Pinstrup-An- dersen 1982). 286 for different products then arises; how should, for instance, research on agricultural machines be divided among plant, dairy, and meat pro- duction? This argument is the major reason for abandoning the welfare economics ap- proach. In addition, the elasticities of the vari- ous products change over time, a fact further complicating the estimation. The method chosen is the production func- tion approach. Technological change is treated as an investment in research, extension and university education. This method makes it possible to attribute relative shares of the various independent variables in production growth. Unfortunately it is not possible to cal- culate the distribution of the returns between consumers and producers with this method. At the same time, the returns to agricultural research are seen from the viewpoint of the whole national economy. The inclusion of university education as well as agricultural research needs to be explained. In data collection, it was impossible to sepa- rate university education from university re- search. In fact, it seemed like such a division would have been rather arbitrary. If there was no university education, there would probably be a drastic decrease in the number of agri- cultural researchers. Thus the university edu- cation was included in the research costs. Uni- versity research and education during 1950—1984 has been 24—52 °/o of total re- search input. Most persons educated at the university have, however, not been working with research after graduating. The research costs would thus be overvalued for that com- ponent of education which actually does not belong to the research input. In the study the imported research results, based on studies originally carried out in other countries, were not taken into account. The spillover effect, in other words, is assumed to be zero, i.e. the benefits exported from in- digeneous research are assumed to be as great as the imported benefits. This assumption is not correct, since the major share of agricul- tural machines and plant protectants are im- ported, while exports are small. The spillover effect is clearly a problematic issue, and needs to be treated more exhaustively than has been possible within this study. The same simpli- fying assumption of no spillover effects from abroad, however, has been made e.g. in the work by Wyatt (1983) on the rates of return from industrial research in Finland and Swe- den in 1960 to 1980. The possibility to include the effects of edu- cation in the form of a variable measured with a knowledge and skill index, as in the study by Ihamuotila (1972), was considered. In that study the knowledge and skill index was constructed on the basis of the number of farmers with professional training as listed in the agricultural censuses of 1950, 1959 and 1969. The proportion of farmers with profes- sional training was further adjusted by the farmer’s share of total labour input. Because of high intercorrelation problems with the explanatory variables, which make the tests on individual regressors weak, edu- cation was not included in the specification. The possibilities to adjust labour for quality improvements according to the number of years in vocational schools were also investi- gated. The data on school years proved to be quite rough, thus being dubious; in addition, the effects of adjusting the labour series would not have been great. The idea of adjusting the labour series for training was therefore dropped. The relationship specified between the in- puts in the Cobb-Douglas function is comple- mentary. According to the Wicksell-Johnson theorem the sum of the two elasticities a and p in the Cobb-Douglas function is equal to the elasticity of scale (Heertje 1977). This is true if one is prepared to assume no relevant fac- tors have been excluded. Increasing, constant or decreasing returns to scale prevail depend- ing on whether a small proportional increase in all inputs leads to a more than propor- tionate, proportionate or less than propor- tionate increase in output (Heady and Dillon 1961) (cf. also Hemilä 1982). The enlarge- ment of average farm size and exploited eco- nomies of scale are therefore reflected by a 287 change in the elasticity of scale (a + P) in ex- pression (3.1). The sum of these elasticities should be about 1.0or slightly more since eco- nomies of scale have not been exploited to a very big extent in Finland. Substitution of capital for labour is reflected in the changes in both a and P (cf. also Griliches 1963 a). Changes in the relative prices due to re- search are reflected in the research variable. The development of productivity during the 1960 s and 1970 s was most likely affected by production and import restrictions on farm products and production inputs. The effects of these measures were contradictory at least to certain degree; On the one hand, the whole production capacity has not been in use, a situation which has resulted in a smaller out- put than the potential; on the other hand, the protection of agriculture from imports has guaranteed a higher price for outputs. Here the assumption is made that the combined effect of these interventions on the market equals zero. Owing to the relatively homogeneous con- ditions in Finnish agriculture, a time series study appears to be the most natural. The study should not be seen as a prognosis of re- search contribution in the future, but as a his- torical study of past returns to agricultural re- search. In other words, the study is of the ex post and not of the ex ante type. 3.3. Specification of the Model 3.3.1. The Form of theProduction Function and the Variables The basic model in the study is an aggre- gated production function that explains the gross production of agriculture. A production function can be expressed as: (3.5) Y = f(X„ X 2,..., where Y denotes gross production and the different inputs and the form of the function. The simplest form of the production function is the linear function: (3.6) Y = b,X, + b,X 2 + ... + b„Xn + e 288 The linear production function expresses a constant marginal ratio between output and the various inputs. The random disturbance term e is an expression for the unsystematic component of the variation which cannot be explained by the systematic component X, + X 2 + ... +Xn (Heady and Dillon 1961). At declining marginal products the Cobb- Douglas function (3.7) Y = aX, b| X X 2 b> X ... X Xn b" has been used frequently because of its sta- tistical simplicity and convenience. In expres- sion (3.7), a is a constant and bj are expo- nents equal to the elasticity of the various inputs i.e. ~ dy dx x dy xE = : = - x = -xb| y x y dx y When bj < 1, the marginal products will decline as X increases because Xb < X. Graphically illustrated the curve of the pro- duction function flattens out. The Cobb-Douglas function is easily changed into logarithmic form: (3.8) Log(Y) = Log(a) + b,Log(X,) + b 2Log(X 2) + + b nLog(X n ) + e In Finnish studies of aggregate agriculture or aggregate crop and livestock production functions the Cobb-Douglas function has been used by Rouhiainen (1972), Kettunen and Rouhiainen (1972) and Ihamuotila (1972). Ihamuotila also used linear production func- tions. The Cobb-Douglas function has been com- monly used to estimate the returns from agri- cultural research. Two pioneering examples are the studies by Griliches (1964) and Even- son (1967) (see sections 2.3.2. and 2.3.4). Other possible forms of the production function could be offered by the transcen- dental function, the quadratic function, the Spillman function (cf. Heady and Dillon 1961) and the CES function (cf. Hemilä 1982). This study is, however, based on the conventional Cobb-Douglas function. A lin- ear production function is also estimated, though mainly in order to compare results with the Cobb-Douglas form. In the formulation of the production func- tion the specifications of Griliches (1964), Evenson (1967) and Norton and Davis (1981) have been followed. The choice of vari- ables has, to a large extent, been done ana- logically with the production function study of Ihamuotila (1972). The agricultural gross production is pro- duced by labour, external purchased inputs and by capital (including cultivated area, soil and water constructions, machinery, buildings and animals). The vocational skills acquired through education, experience and extension also influence the production results. The dependent and independent variables can be seen from the model formulated below: (3.9) Q = A L b| K bk I b' R" N° Q = the volume of production A = a constant L = labour input K = capital input 1 = external purchased inputs R = research input N = extension factor bj = elasticities of the different inputs a = elasticity of research o = elasticity of extension This production function differs from the one formulated by Ihamuotila in including a research variable and an extension variable. Ihamuotila, on the other hand, included a special variable for human knowledge and skill, measured by an index of farmers’ share of total labour input adjusted in proportion to an index of trained farmers. Furthermore, Ihamuotila also had a certain technological factor constructed on the basis of an index where the real capital stock was divided by the corresponding labour input (assuming that technological change is reflected by the amount of human labour saved). In this re- spect, the present study differs by measuring technological change as a result of investment in research. Labour input is not quality ad- justed (for discussion, see section 4.4.). No weather variable is included. In comparison with the model by Ter- leckyj (1980), there are two additional vari- ables in this specification; purchased inputs and extension. The effect of an increase in average farm size and its contribution to growth in produc- tivity is reflected by the change in relation between the elasticities of different inputs fy. Increasing returns to scale are indicated by growth in the sum of elasticities, which be- comes larger than 1 (Heady and Dillon 1961, p. 589). The variables of capital, labour and external inputs in (3.9) may be specified on two dif- ferent levels, the aggregate level and the farm level. Farm level variables can be derived by dividing the aggregate variables by the num- ber of farms. Research and extension are mea- sured only at aggregate level. This is due to the way research affects agriculture. On a single farm, it is difficult to single out a spe- cial research input in the way it is possible to point at purchased inputs, fields, machines or labour. In most studies the expenditures for re- search and extension have been added up and expressed as one single variable. The reason for this is that research results spread to farm- ers primarily through information activities. According to earlier studies this is, strictly taken, the correct procedure. The practice has probably been used, since in many cases the data for research and extension are not sepa- rated but presented together. There are, how- ever, two immediate reasons why this course of action not has been applied here. Firstly, the data available for extension activities is based on State support for extension which actually was bigger than research expenditures in the first half of the 19505. Since the pur- pose of this study is to estimate the returns primarily to research, not extension, the use of a single variable cannot be considered ap- propriate here. Secondly, the data on exten- sion is deficient, since linear extrapolation was used to derive the figures between 1951—55, 1955—60, 1960—1965 and 1965—1970. The figures on research expenditures, however, can be characterized as fairly reliable. 289 290 Since State support for extension will be taken into account as costs in the final calcu- lation of the value marginal product (section 6.4.), the returns will not be biased in a posi- tive direction. In fact, one could argue that the omission of extension expenditures when calculating the elasticity of research probably leads to a more realistic elasticity. Extension merely represents a complementary input for spreading research results, not a measure of research input. It should certainly be credited on the cost side in the final calculation. But the effect of extension on increasing the stock of knowledge or improving the quality of inputs is minor. One can ask whether studies not distinguishing between research and exten- sion in elasticity calculation really are as valid as if a distinctionhad been made? A separate parameter for extension to use for sensitivity analysis is still incorporated in the models. After consideration, a trend factor was not included in the model. The trend is assumed to pick up some of thepotentially omitted va- riables. The trend could be assumed to include a number of factors rather difficult to mea- sure. These could comprise changes in the pat- tern of valuesand attitudes which, in the long run, may considerably affect agriculture; the effects of agricultural policy; development in other sectors; infrastructural improvements; and other factors with effects on a higher hierarchical level. The problem is that it un- certain what a trendfactor (a linearly growing series) actually measures. Preliminary results showed that a trend component did not im- prove the model in any way. There is good reason to believe that the trend factor does not add any significant explanatory power to the model. In the alternative formulation in sec- tion 3.3.3. a factor representing the disem- bodied technological change, i.e. a trend, is incorporated. The form of the theoretically somewhat illogical linear production function is (3.10.) Q= A + b,L + bk K + b,I + brR + b n N where bj = the marginal product of the input In the estimation of the Cobb-Douglas function, the ordinary least squares criterion is used. In addition, ridge regressions and autoregressive models are applied. The esti- mates of the different parameters are derived from index series of the different variables. When we take the logarithms of (3.9), we obtain: (3.11) ln(Q) = ln(A) + b,ln(L) + bkln(K) + b i ln(I) + brln(R) + b„ln(N) Here the elasticities br and b n indicate the share of growth in production due to research and extension respectively. 3.3.2. Research Stock There are two different possibilities for measuring the research input; as either a flow or a stock. The flow concept has been used in the absolute majority of studies on the eco- nomic returns to research. A different possi- bility is, however, offered by formulating a stock of research capital. In the following, a research capital R k is formulated, on the basis of a specification of Peterson (1985) for three different cases: a) The research capital is assumed to be equal to the sum of of all previous funds for agricultural research since 1920, i.e. is accu- mulating to 100 % (d, = 0). Funds allocated to research before 1920 are assumed not to have had any effect on production. (3.12) R k = L (K, d,K,), where d, = O R k = research capital K, = accumulated funds d, = rate of depreciation b) Half of the research capital is assumed to become obsolescent 20 years after the funding took place, and is thus depreciated by 50 %. The other half is added to the research stock. Research carried out before 1920 does not have any effect. (3.13) R k = L(Kt -dtK,_M), where d, = 0.5 c) As in b), except that all of the research capital is assumed to become obsolescent 20 years after funding, and is depreciated by 100 %. (3.14) R K = T (K, dtK t_20), where d, = 1.0 The initial figure for the research capital is derived by simple trend analysis back to 1920, omitting the years 1940—1944, since normal research activities were seriously disturbed during the war years. In (3.12) —(3.14) K = 54.3 + 16.6 t for public research, 23.0 + 22.5 t for total research. Accumulating the flows up to 1950 gives an initial stock. On the basis of the index series of real flows of funds for research, this initial value is further ac- cumulated up to 1984. A series of accumu- lating research capital is thereby obtained. The research capital has the convenient advantage of not demanding any lag operator. In this respect the research stock measure seems rasier to handle than the research flow measure. In the estimations both the flow and the stock concept of the research input will be used to estimate (3.9). 3.3.3. A Productivity Index Specification The research stock will also be needed in the specification of an alternative model. In the empirical part of the study, the internal col- linearity of the variables was found to be a serious problem. One purpose of this alterna- tive specification is, therefore, to reduce the number of independent variables and thus to reduce the multicollinearity. The following presentation of an alterna- tive model is largely based upon the works of Terleckyj (1980), Griliches (1980) and Vuo- Ri (1984). The difference in relation to the presentation in section 3.3.1. lies mainly in the use of a productivity index instead of gross production as the dependent variable. Nor- ton and Davis (1981) state that an alternative specification similar to (3.15) has been popu- lar because of intercorrelation problems with time series in models like (3.9). The advantage with this specification is that the traditional variables can be omitted, and thus the prob- lem of internal collinearity disappears, or at least becomes smaller. A general lack of data for conventional variables has also contributed to the use of this model. The purpose of specifying a produc- tivity index model is to obtain another esti- mate of the returns to research in order to see whether the estimates lie in the same range. The productivity at a point in time t can on the basis of (3.9) be explained as the relation between gross production Q and the “conven- tional” inputs labour, capital and external inputs, i.e. L, K and I: (3.15.) P, = = eATI R ON° L, b| K tbk I t b‘ t = time factor x = coefficient of time factor This relation consists of three parts: one component representing the cumulative effects of autonomous technological change (e raised to the power of it), i.e. a trend factor (this autonomous technological change factor has been added to (3.9)); one component repre- senting the stock of research capital R raised to the power of an exponent representing the elasticity of research with respect to this re- search capital; and one extension component. In order to simplify the presentation the ex- tension component N, raised to the power of o is omitted. Thus we obtain (3.16.) P t = Ae T'R“ The function can then be written as (3.17) In P, = In (AeTt R“) By estimating a research capital R as speci- fied in section 3.3.2., it is possible to avoid a long and difficult deduction such as those in the specifications of Griliches (1980), Ter- leckyj (1980) and Vuori (1984). x denotes the autonomous technological change (trend). The dependent variable is thus an produc- tion/input index. 3.3.4 Distributed lags The contribution of research to growth in productivity is not immediately observable in 291 the same year that research was funded. There is one lag in the “availability” of technology, i.e. between research funding and ready pro- duction inputs, and another lag in the “ac- ceptance” of technology. The incorporation of lags is thus an important and critical issue in estimating the returns to research (see, for instance, Pasour and Johnson 1982). Never- theless, satisfactory treatments of the lag structure are rare in the field. The formulationof a lag function seems to be a difficult part of evaluating the returns to research. Vuori (1984) points at the difficul- ties in specifying a general lag for aggregated research. The length of the lag may vary for differentcategories of research, and the prob- lem consequently consists of finding an aver- age lag. Griliches (1964) basic way of treating the lags was to define research costs as the aver- age of the research costs of the previous year and six years prior to the observed output year. This arbitrary treatment cannot be con- sidered sufficient. Since simple lags do not provide a satisfactory explanation; a specific lag function needs to be specified. One possibility is to estimate different lags directly by applying the ordinary least squa- res criterion. According to Pindyck and Ru- binfeld (1981) this leads to problems through losses of degrees of freedom and because of the heavy multicollinearity resulting from the large number of variables. Moreover, the pic- ture of the form of the lag may remain unclear. Ravenscraft and Scherer (1982) note that it takes three years, on average, to complete industrial research and development projects. They also state that in measuring the returns from research and development, the time-lag factor in most econometric studies has been assumed to have a constant rate of decline, because of the convenience of the Koyck transformation. They argue that, for instance a bell-shaped curve describing the lag struc- ture may be more correct. Such a curve could be provided by Almon lags. Preliminary ex- periments with Almon lags, however, uncov- ered serious drawbacks, according to them. Whether this is the case for agricultural re- search is not known. Pindyck and Rubinfeld (1981) present the general form for a distributed lag model as: (3.18) Y, a + P OX, + P|X,_! + P2x._2 + = a + [^o PzX._z + e, Vuori (1984) used a geometric (Koyck) time lag and an Almon lag. Duncan (1972) also used Almon lags of degrees three and four in estimating the returns from Australian pasture research (see section 2.4.6.). The geo- metric lag depends on only two parameters. The parameters p are assumed to decrease ex- ponentially with time (Wonnacott and Won- nacott 1970). If the general form of the model is: (3.19) Y, = 30X t + P,X,_ I + p 2X,-2 + • • • + 3nX,_„ + e, the geometric lag will be expressed by: (3.20) Pj = p 0 Tj where 0 < x < 1 Since the weights of the lagged explanatory variables decline with time, the geometric lag cannot be considered the best possible. Instead a polynomially distributed lag, or Almon lag, theoretically could fit the research variable. The Almon lag is based on the assumption that the lag structure is a polynomial of some degree n, with n + 1 parameters. The original lag specification with S number of lags is: (3.21) Y, = 3, + 32x, + P,X.-, + .. + 3s + 2 X._s + e, Instead of estimating the coefficients P, di- rectly (as could be done in the geometric lag), we think of the lag as a polynomial. The poly- nomial of degree three is: (3.22) =Y0 + Y.j + Y2j 2 + Y3j 3 In a more general formulation P ; is a func- tion f(j). The polynomial (3.22) can be approximated by more simple functions. Through the Almon procedure these simpler 292 transformations are estimated in order to receive estimates Pj. The procedure reduces the number of parameters to be estimated, and probably also problems with losses of degrees of freedom and multicollinearity. Figure 12 shows possible shapes of the Almon lag for polynomials of various degrees. The Almon lags of degrees higher than one seem to provide a suitable possibility to take the adjustment process into account. The main effect of the explanatory variables can be assumed to lie many periods of time in the past. In order to estimate the transformed variables, certain assumptions on the distri- bution and length of the lag structure need to be made. The polynomial of degrees two and three seem to be logical in estimating the lags for research. The Almon procedure was used by Neva- la (1976) in a model estimating the lagged responses of firms to changes in the variations in prices of fertilizer. The model below is, to a great extent, based on the formulation of Nevala. The dependent variable here is, how- ever, gross production, and the explanatory variable is the lagged research input. A basic model including distributed lags, where the effects of research are distributed over m num- ber of years, can be presented as: m (3.23) Y, = j So P JX,_ j Y, = gross output in year t X,_j = research input in year t—j If the coefficients of regression p ; (j = 2,... m —2) can be assumed to be on the numerator of a polynomial of degree three, which is equal to zero when i =m the vector Pj can be compensated by 3 (m i) f (3.24) P; = I b r -v f=o f Sf m (3.25) where Sf = E (m j)f , j =o (f = O, 1,2, 3) When this transformation is substituted for bj in (3.23) we have: m (m j)°(3.26) Y, =b0 I i Xt_j + j = ° s 0 s Ib' R'* OO is introduced as follows (5.4) b(0) = (X'X + 01)-' X'y In applications the interesting numbers of 0 are usually found in the range of 0.1, though values up to 1.0 are used. When 0 = 0 the re- sulting ridge estimator is the same as the OLS estimator. For different values of 0 we can 316 plot different values of the estimates, i.e. we can plot a ridge trace to enable a direct com- parision to be made between the relative ef- fect of the various coefficients. As 0 is in- creased the estimates become smaller in ab- solute value, tending to zero in infinity. At a certain value of 0 the system will stabilize and have the general characteristics of an orthogonal system. Cofficients with incorrect signs will change to become correct (Draper and Smith 1981). According to Draper and Smith, blind use of ridge regression can be dangerous and mis- leading. They suggest two cases for which it is absolutely correct to use ridge regressions in spite of the subjective element involved (the choice of 0). The first is when prior knowledge (or belief) exist that smaller values of the es- timates are more likely than larger ones. If a small value is used for 0 it means that we believe the OLS is not producing unreasonably big values. The second case we need not deal with here. We note two dangers involved in ridge regressions: 1. Are we really sure about the prior knowl- edge of too high coefficients? 2. The nonsignificant estimated regression coefficients change to a greater extent than the significant estimated coefficients. On the basis of the OLS estimates presented in subsections 5.1.1 and 5.1.2., prior questions on the size of the capital estimate could have been raised. In the linear production function, the estimate of capital (the marginal product) was slightly above or below 1.00. In the Cobb- Douglas functions the estimate (the elasticity) was approximately 0.7—0.9. This is rather much, as the sum of elasticities not should ex- ceed 1.00 in the case of constant returns to scale over time. The external inputs had a negative sign in many cases. This prior knowl- edge makes it reasonable to believe that the capital coefficient is likely to be too high. The aim of our use of the ridge regressions is still a different. We can hypothetisize that the estimated research elasticities are too high as a consequence of the intercorrelation be- tween explaining variables. If this is the case their value should drop in ridge regressions. Our actual purpose in doing this is, however, the opposite. If the values of the research coef- ficients do not fall, it means that the estimates of research are not overvalued because of multicollinearity . If this holds true, we do not speculate whether the estimates are too low, but simply accept the estimates as not being overestimated. This means that ridge regres- sions are not used in order to produce new biased estimates but are used to investigate in which direction the serial correlation affects the elasticity of research. In order to avoid the second danger out- lined above, parameters which are insignifi- cant to a large degree should not be tested. The significance determined by the t-test is a partial guide as to which of the regressions should be analysed. In the OLS regressions chosen for investigation by ridge regressions, the significance of the research coefficient (public or total) was according to Table 17: Table 17. Research coefficient and significance level for different regressions. Regression Traditional Research Significance variables coefficient (1) linear aggregate 0.018 0.154 (4) linear per farm 0.040 0.101 (5) linear aggregate 0.025 0.057 (9) Cobb-Douglas aggregate 0.059 0.120 (10) Cobb-Douglas aggregate 0.034 0.374 (12) Cobb-Douglas per farm 0.059 0.121 (14) Cobb-Douglas aggregate 0.078 0.079 317 318 Fig. 19. Ridge traces. Horizontal axis value for ridge parameter theta, vertical axis corresponding values for the coefficients. The ridge regressions correspond to the following OLS regressions: a) = (1), b)= (4), c) = (5), d) = (9), e) = (10), 0 = (12). g) =(14). Table 18. The research coefficient by OLS and by ridge regressions. l Regression (1) (4) (5) (9) (10) (12) (14) OLS 0.018 0.040 0.025 0.059 0.034 0.059 0.078 Ridge parameter 9 = 0.000 0.132 0.080 0.249 0.189 0.108 0.082 0.289 9 = 0.025 0.164 0.192 0.229 0.280 0.178 0.217 0.341 9 = 0.050 0.185 0.217 0.226 0.293 0.191 0.253 0.333 9 = 0.100 0.204 0.230 0.225 0.294 0.199 0.277 0.317 “Statgraphics”, the data program used here, standardizes and centers all variables at the same time so that the resulting estimates differ from the OLS for 6 = 0 (the values for 9 = 0 should be equal to the OLS). This will not affect its use here, since only the development of 6 is relevant, not the absolute values of 0. Next these seven different ridge traces for the unlagged production functions earlier es- timated are examined. It should be noted that the elasticities are not directly comparable, since the interpretation differ for the various regressions. 5.1.4. Ridge Traces The seven regressions chosen for ridge analysis are presented in Figure 19. As 0 in- creases, the effects of multicollinearity de- creases at the same time as the bias of the es- timates increases. The estimates decrease, tending to zero in infinity. For values on 0<0.05 the coefficients change rapidly, sta- bilizing at 0 = 0.05 or slightly less. After this the increased effects of the bias can be seen in sinking curves. Obviously the critical values for 0 should lay between 0 and 0.05. As was mentioned earlier, values of 0> 1.00 are sel- dom used because of the stronger bias. A general feature of all the figures is the fall in the regression coefficients of capital and labour. The prior belief that the capital coef- ficient is too big is supported by the ridge traces. It is difficult to understand that the coefficient of labour in some regressions be- comes negative for 9>0.05 or even less. Ob- viously, values of 9>0.05 should be con- sidered critically and with caution. The ex- ternal inputs seem to increase and turn from negative (in some of the OLS regressions) to positive. The estimate of the research parameter does not change much. In all regressions except (5) (where it stays almost constant) it increases slightly. Taking into account the purpose of the ridge analysis stated in the preceding sec- tion, it is now possible to draw a conclusion: rather small values for the ridge parameter 0 show that the internal correlation between explanatory variables does not lead to overes- timated coefficients of the research parameter. Table 18 gives the ridge estimates a nu- merical description. The trend in the development of the re- search coefficient is that it grows as the bias increases. The coefficient starts to decrease when the bias becomes sufficiently large. The use of ridge analysis may be subject to criticism. Taking into account what has been stated above, it is put to careful use here; it is not, e.g. used to produce separate elasticities. Still we cannot be completely sure whether or not the multicollinearity is a problem. But at least the incidence given by ridge analysis shows that the multicollinearity need not be problematic. 5.1.5. Autocorrelated Errors and Autoregressive Models The models (3.9) and (3.10) are based on the assumptions stated in section 3.4. One of these assumptions was that errors were not serially correlated. In case such autocorrela- tion occurs, the coefficient may be overes- 319 timated or underestimated. The results of the estimation show that this basic assumption was erroneous. A misspecification of the model results in autocorrelation, which may depend on the omission of variables or an in- correct form of the production function. Be- cause of the wrong specification, some of the information appears as serial correlation in the errors. The Durbin-Watson test value in the flow models with no lags varied from 0.96 to 1.16, thus showing substantial autocorrela- tion. The autocorrelation is further examined through the use of autoregressive models. In these models the correlation in the errors is used to explain the variation in the dependent variable. If the basic form of the Cobb-Douglas func- tion is (5.5) Q = A Lb| K bk I 6* R“ N° + e t where the number of observations is t, the simplest assumption on the form of correla- tion between errors is (5.6) e, = 0et_| +v, o 0.01 autoregressions of second order it ranges from 1.91 to 1.98, thereby indicating that practically all of the serial correlation is explained. From the tables it is evident that the estimate of elasticity with respect to research decreases to 0.011 —0.013 in the first order models and to 0.014—0.016 in the second order models. The significance also decreases. This should be compared with regressions (9) and (10), where the estimate was 0.034—0.059. The coefficient of determinationslightly increases. The regression coefficients of the residuals are big, about 0.05—0.07 and significant, thus explaining a large part of the variations. It is evident, therefore that the explaining power of the error term is considerable, indicating a certain degree of misspecification in the basic model (3.9). It is still possible that some of the information in the errors is connected with the research coefficient. On the whole, the second order autoregressive models seem to have a better explanatory power, though none of the research coefficients in either model is significant. In addition to the elasticity estimate with respect to research, the elasticity estimate with respect to extension decreases. The sign of ex- ternal inputs shifts to negative in the first or- der models, which is hardly understandable, but changes to positive again in the second or- der models. The effects of intercorrelated var- iables should be the same as explained earlier. Using autoregressive models on the research measure, total funds give much the same re- sults as for public research (Appendices 10 and 11). The elasticity estimates with respect to total research decrease to 0.022—0.025 in the autoregressions of first order and to 0.028—0.031 in the autoregressions of second order, again with insignificant values. The influence of autocorrelation decreases in the first order autoregressions and virtually disappears in those of second order. Cor- respondingly, the coefficients of the residuals 6, and 02 are big, especially for the first one. The coefficient of determination reaches a level of 0.990 in (25). The inclusion of ex- tension in the regressions changes the coef- 321 ficients of neither public nor total research more than slightly. To summarize the section, it is concluded that the elasticity estimate with respect to re- search decreases in the autoregressive models. The OLS estimates may therefore be over- valued because of serial correlation in the er- rors. In the autoregressive models theregres- sion coefficients of research are between one- half and one-fourth of the values in the OLS regressions. But because of the high regression coefficients of the residuals, which may in- clude some information connected with the research variable, the estimates in this sec- tion are not necessarily more correct. The estimates in the autoregressive models are not necessarily closer to the real parameter values, but give an explanation where the influnce of serial correlation is not allowed to exert influence on the coefficients of the other parameters. What we have gained in this sec- tion is a picture of the possible effects of the autocorrelation. 5.1.6. Cobb-Douglas Regressions for Shorter Periods In the preceding section unlagged elasticities with respect to research were estimated for the period 1950—1984. During the same period the funds for agricultural research have grown manifold. From this point of view the fol- lowing question arise: How have the elasticity and value marginal product developed over time? Have the returns increased or decreased since the 19505? Has the elasticity changed or has it stayed on the same level as previously even though more resources were allocated to research? Cobb-Douglas functions were estimated for shorter periods of 20 years, i.e. 1950—1969 and 1965—1984. The estimates of the elastic- ity with respect to public research in Table 21 correspond to the regressions (9) and (10) in Table 13. The estimates of the elasticity with respect to total research in Appendix 12 cor- respond, in turn to regressions (14) and (15) in Appendix 8. Table 21. Cobb-Douglas production functions with public research for shorter periods. All variables measured at aggregate level. Regression (26) (27) (28) (29) 1950—69 1965—84 S.I. s.l. s.l. s.l. Constant —2.497 0.162 —2.721 0.044 4.311 0.113 4.351 0.174 (1.697) (1.230) (2.559) (3.035) Capital 1.231 0.015 1.216 0.002 0.089 0.874 0.079 0.912 (0.450) (0.325) (0.555) (0.699) Labour 0.242 0.034 0.194 0.023 —0.087 0.229 —O.OBB 0.309 (0.103) (0.076) (0.070) (0.084) External 0.029 0.828 0.004 0.965 0.015 0.905 0.016 0.906 inputs (0.131) (0.095) (0.120) (0.129) Public research 0.034 0.523 —0.059 0.215 0.092 0.050 0.092 0.059 (0.052) (0.045) (0.043) (0.045) Extension 0.235 0.002 0.003 0.979 (0.061) (0.096) R : 0.977 0.989 0.920 0.920 Stand.error of estimate 0.025 0.018 0.019 0.020 F-ratio 160.65*** 248.28*** 43.22*** 32.27*** D-W test value 0.905 1.425 1.708 1.711 322 It is interesting to note that the estimate of the elasticity with respect to research seems to have increased in the period studied. The estimate for the earlier period of 1950—1969 is insignificant and even becomes negative when extension is added. This negative sign is illogical and must be attributed to the in- clusion of the extension variable. The estimate for theperiod 1965—1984 is significant, with a confidence of approximately 95 %. The latter period has a low coefficient of deter- mination (0.92) and the error terms are not very serially correlated, as is the case for the whole period. The F-value for the whole model has dropped in the latter period, but is still significant at a level of 0.001 %. We can compare the elasticities for the pe- riod 1965—1984, 0.092 with the ones for the whole period 1950—1984, which were 0.059 and respectively 0.034 in Table 13. Taking into account the sixfold rise in research input, it should not be surprising to find that the elasticity has increased over time. The low t- values of regressions (26) and (27), however, limit our conclusions, so that it is not possible to compute a reliable value marginal product for the period 1950—1969. Contrary to the research coefficient, the table shows significant parameter estimates for capital, labour and extension in the period 1950—1969 and insignificant estimates for the period 1965—1984. The sign of labour be- comes negative for the latter period. If any conclusion could be drawn on the basis of Table 28, it is that research has taken over part of the importance as a production factor earlier possessed by capital and labour. Interpretation of the total research regres- sions (see Appendix 12) are much similar to Table 21. Many of the coefficients are again insignificant, and some of them have illogical signs. The elasticity estimate with respect to total research seems to increase, as did the public research estimate. A negative sign appears again in the earlier period. The elas- ticities with respect to capital and labour once more seem to decrease, as does extension. It is difficult to say anything about the external inputs estimate. The same explanation is likely for the regressions including a total research variable; part of the role earlier played by traditional production factors has been taken over by research. Since the total research input has increased eightfold this has not necessarily led to a higher value marginal product, how- ever. 5.2. Cobb-Douglas Flow Models with Lags There will be a lag between the point in time when money is being funded for research pur- poses and the final effects in the form of higher production per input unit (or less in- puts per produced unit). The previous estima- tions are based on the obviously unrealistic implicit assumption of research funds im- mediately affecting production results. One step forward towards a closer resemblance to the real world, therefore, is to take a lag into account in the model. The lag structure of ag- ricultural research seems to be a problematic issue in studies of returns from research and thus far most production function studies make assumptions concerning the length and form of a distributed lag function. Naturally this does not apply to the welfare economics approach. Estimations which include lags are exam- ined in this sections. Simple lags were used to start with, after which Almon lags of degree two and three according to (3.37) were in- cluded in the model. 5.2.1 Regressions with Simple Lags The simple lags estimated are based on the lag operator x,_j = (3 k x t . The research input is thus allowed to affect the gross production only a certain numberof years after the funds have been allocated. The effects of research thus take place at once instead of being dis- tributed over a period of years, as in the case of a distributed lag. The estimated lags are allowed to vary between two and 15 years. The results of the estimations are not very encouraging. When simple lags of less than ten 323 years were included in the previous regressions (1) —(17), almost all of them showed the same tendency. The coefficient of determination falls, the drop being greater the longer the lag is. The research coefficient decreases in the be- ginning and partly becomes negative when lags of four to eight years are added and so does the significance, which makes it hard to be- lieve the coefficients. For lags less than ten years the same autocorrelation problem as earlier appears. The highest coefficient of determination (0.991 —0.997), the best sig- nificance and the least serially correlated er- rors are achieved in regressions where the traditional variables are defined on farm level. Estimations using lags of 12—13 years are somewhat more encouraging, since they are both positive and significant. The serial cor- relation of errors is also less here (Durbin- Watson test value = 1.45—1.75 for the re- gressions in next table). Closer inspection of Figure 17, however, shows this should not be surprising, as the autocorrelated errors seem to appear mostly in the early part of the time series. Lags of ten years or more only make it possible to estimate the period of 1960— 1984, which automatically eliminates the problematic period of serially correlated er- rors. It can therefore be doubted whether the longer simple lags of 12—13 years are any better. In order to illustrate the simple lags, the estimates for public research for two dif- ferent sets of regressions are presented in Table 22. When no lags are included the re- gressions are similar to regressions (9) and (12) in Tables 13 and 14. From the table it is clear that only estimates which include lags of 13 years are both posi- tive and significant. These elasticity estimates were also higher than the estimates in regres- sions (9) and (12). It was, however, already pointed out that there is reason to believe this is because of theproblems inherent in the time series. In addition, the above table does not show the negative parameter estimates of the other elasticities, which appeared regularly in the regressions (the intercorrelation problem is the same as earlier). Table 22. The coefficient of research for different values on the simple lags. The table corresponds to (9) and (12). Length of Coefficient of research 8 ' (9) s.l. (12) s.l. in years 2 0.016 0.694 0.035 0.296 3 0.013 0.741 0.028 0.401 4 —0.041 0.318 0.002 0.941 5 —O.OBB 0.027 —0.034 0.312 6 —0.046 0.194 —0.014 0.629 7 —0.048 0.163 —0.009 0.763 8 —0.021 0.555 0.016 0.629 9 0.000 0.991 0.014 0.630 10 0.013 0.663 0.008 0.762 11 0.003 0.931 0.010 0.752 12 0.033 0.359 0.046 0.194 13 0.092 0.005 0.089 0.006 14 0.089 0.019 0.084 0.033 15 —0.021 0.642 —0.038 0.432 A conlusion of the simple lag regressions is that the lag structure should be subject to more advanced methods of analysis. In spite of the problems encountered, some estima- tions including Almon lags are presented in the next section. 5.2.2. Regressions with Almon Lags The a priori assumption of a polynomially distributed (Almon) lag revealed significant drawbacks. Not only were the estimates of elasticity with respect to research including a polynomial lag mostly insignificant; they were also negative, indicating a negative coefficient for research, which is most improbable. In addition, the size of the estimated coefficients varied to a large degree. This may be caused by intercorrelation between the various re- search variables in the lag structure, but it is more likely that theAlmon lags do not fit the dataand thus cannot give any sensible results. The polynomial lag behaved similarly when applied to a linear function. The coefficient of determination was clearly lower than for the unlagged functions except when tradi- tional variables were measured at farm level where this difference not was as noticeable. The results for Almon lags of degree two and 324 three for three different lengths of the lag are illustrated in Appendix 13. A cumulated elasticity can be summed up on the basis of (3.36). The sum of estimated lag coefficients according to this are as fol- lows (see Table 23): Table 23. Sum of Almon lag coefficients, a = aggre- gated conventional variables, p = conven- tional variables per farm. Sum of coefficients Regres- Length Degree sion of lagof lag 3 2 a 2 P 3 a 3 P 2 a 2 p 3 a 3 p 2 a 2 P 3 a 3 P 0.047(34) (35) (36) (37) (38) (39) (40) (41) (42) (43) (44) (45) 0.0443 0.0463 0.0423 —0.2667 —0,0477 7 —0.266 —0.0497 13 —0.041 13 —0.064 0.01913 13 —0.026 From Table 23 it is evident that the nega- tive sum of estimated lag coefficients is very illogical. In addition, the positive estimates are often found in the beginning or at the end of each lag, thus indicating an upside down bell- shaped structure (a positive parable) of the lag. The choice of estimated polynomial sum of elasticities cannot be made upon any ra- tional criteria. Thus the Almon lag does not provide any help in estimating a research elas- ticity. Why doesn’t the Almon lag fit the data? Why are estimates of the elasticity with respect to research for the simple lags negative? The reason may be the aggregated data, which do not consider that different types of research have different lengths of the lag. Research on machine technology may have a more im- mediate effect on production than, for in- stance, crop breeding, which depends on the vegetation period. Since the aggregated data include research institutions which have been founded during the period 1950—1984, the proportions of different types of research have changed, and the average aggregate lag has probably changed accordingly. One way of dealing with this problem could have been to split up the data into different branches, each of which would be estimated separately for different lengths of the lags. A more plausible hypothesis is, however, connected with the distinction between re- search stocks and research flows. By far the most common way of measuring the research input in production function analysis has been in the form of an annual flow of re- search funds (Peterson 1985). It is obvious that the research input for one year does not represent the total stock of research capital accumulated over the years. If the relevant measure is the research stock and not the annual research flow, an initial basis value should be found for 1950. This initial value should grow with the annual research funds and depreciate according to the formulas (3.12)—(3.14) presented in section 3.3.2. Con- ceptually, computation of the research stock is similar to the calculation of a stock of tractors. An annual flow of tractors bought does not measure the same thing as the total stock of tractors. Because the earlier tractors are omitted, the production effects measured neglect the effects of all previously purchased tractors. The annual flows of tractors fluctu- ate considerably more than the total stock of tractors. As a consequence, the fluctuations of the research flow vary more than the fluc- tuations of the research stock. The research stock is a kind of proxy for all the physical, scientific, and intellectual resources that exist at a point in time. If one thinks of the research stock concept in this sense, it will possess a computational ad- vantage, since lags seem not to be needed. The gathered effect of an accumulated stock is im- mediate. It is more troublesome to decide on the right rate of depreciation. On the one hand, there is a view that all research ac- cumulates and contributes to an ever-growing stock of knowledge (which according to Pop- per approaches truth in infinity). According- ly, research would have a value that does not 325 depreciate at all. On the other hand, there is the view that research results replace each other totally, either through obsolescence or as a result of changes in the environment. A third view, somewhere between these two standpoints, states that some research results lose their relevance while other provide use- ful knowledge for later scientists to build upon. The three different standpoints can be thought of as a 0 %, a 50 % and a 100 % depreciation 20 years after funding, as for- mulated in (3.12)—(3.14). All three cases are examined next. 5.3. The Research Input Measured as a Stock The estimations of elasticities with respect to research analyzed up to this point have been based on the research flow concept. This sec- tion presents estimations specifying the re- search input as a research capital. The Cobb- Douglas function (3.9) serves as the basic model of regression. Contrary to the research flow models, no lag structure seems to be needed with a research stock. This is because of the different nature of the research capital. A stock which mainly includes investments in research made several years earlier does not seem to need an additional lag. The initial figure for the research capital was derived by simple trend analysis from 1950—1984 back to 1920. The period 1940 1944 was, however, excluded because of the Second World War, when normal research activities were seriously disrupted. This initial figure is used to formulate a research capital for the three different rates of research de- preciation formulated in expressions (3.12), (3.13) and (3.14) in section 3.3.2. The research carried out is accumulated on the basis of three different assumptions: a) no depreciation b) a 50 % depreciation 20 years after the re- search funding and finally c) a 100 % depreciation (total obsolescence) 20 years after funding. At first a research capital is constructed only for public research, whereafter a total re- search capital is derived. The derivation and the index series obtained by this procedure are found in Appendices 14 and 15. 5.3.1. Undepreciated Research Stock. When the public research stock is R k = E(Rt —d,R,) and d,=0, the estimations of the Cobb-Douglas model (3.9) will be according to Table 24. All the variables are measured at aggregate level. The table should be com- pared with Table 13, since all variables ex- cept the research input are estimated with the same series. The results from the regressions specifying research as an undepreciated re- search stock for total research are presented in Appendix 16. Compared to the estimations with research measured as a flow, the coefficient of deter- mination is slightly higher and, respectively, the standard error of total estimation slightly lower. The F-ratio is high, and the model is again acepted at a level of significance of less than 0.001 %. The autocorrelation decreases as the Durbin-Watson test value shows (it rises from 0.96—1.02 to 1.09—1.11), but is still high. The estimate of the research capital parameter seems to fit the model slightly better than does the research flow estimate. Inspection of the elasticity estimates with respect to the different variables immediately draws attention to the considerably lower estimates for capital, which, however, has also lost confidence. The significance of the elasticity with respect to labour is modest, while the external inputs estimate is clearly in- significant and in the former regression has a negative sign. Inclusion of an extension variable does not affect the model very much. The elasticity estimate with respect to the research capital changes in an interesting way. First of all, compared to the flow elasticities the estimate increases to 0.338 in regression (46) and 0.247 in regression (47). This is nat- ural, since the estimate represents an elasticity relating a percentage change in production to a percentage change in the research input. 326 Table 24. Cobb-Douglas production functions with public research measured as an undepreciated stock. Regression (46) (47) s.l. s.l. Constant 1.326 0.286 1.224 0.313 (1.219) (1.193) Capital 0.171 0.714 0.242 0.598 (0.462) (0.454) Labour 0.207 0.007 0.135 0.117 (0.071) (0.834) External inputs —0.005 0.953 0.015 0.868 (0.090) (0.089) Research stock 0.338 0.016 0.247 0.093 (0.133) (0.142) Extension 0.096 0.131 (0.062) R : 0.985 0.987 Stand.error of estimate 0.023 0.022 F-ratio 507.71*»* 425.876*** D-W test value 1.094 1.115 Since a percentage change in the whole re- search capital is considerably higher than a percentage change in the annual funds, the elasticity is naturally higher. The second in- teresting feature is the rise in the confidence of the research coefficient. In regression (9) the significance was 0.120, and in (46) it is 0.016. The significance in (10), was, analo- gously, about 0.374, and in (47) it is 0.093. Obviously, the elasticity estimate with respect to the undepreciated research capital seems to be more reliable than the research flow esti- mate as the significance is higher. The results from the total research stock in Appendix 16 mainly show the same results as for the public research. The most obvious feature is the slightly smaller estimate of elasticity with respect to the total research stock than the elasticity estimate of the pub- lic research stock. The difference is, however, not large. 5.3.2. Depreciated Research Stock In the following the estimations including a depreciated research stock are reported. Research results were assumed to become obsolescent or superfluous because of changes in the environment 20 years after research grants were made. The two alternative as- sumptions of depreciation for Rk = I (R, d,R,_2O) were d,= 0.5 and d,= 1.0, i.e. a5O % and a 100 % rate of depreciation. The results when the research stock includes only public research are presented in Tables 25 and 26. Only minor changes take place in the pa- rameter estimates. The coefficient of deter- mination, the F-ratio and the Durbin-Watson test value in Table 24 are slightly better than in Table 25. The significance of capital in Table 25 is, however, better and no nega- tive signs for external inputs appeared. The elasticity of the research capital in Table 25 is almost the same in size, or 0.212—0.297, and the confidence is a little lower. The dif- ferences are so small, however, that it is dif- ficult to judge which table gives more reliable results. Table 26 shows that a total depreciation of the research capital does not improve the regressions. The same tendencies continue as when research capital was depreciated by 50 %. The estimate of the research coefficient decreases to 0.174-0.252, the former value 327 Table 25. Cobb-Douglas production functions with public research measured as a stock with 50 % depreciation after 20 years. Regression (50) (51) 8.1. S.l. Constant 0.757 0.482 0.774 0.463 (1.063) (1.040) Capital 0.349 0.402 0.387 0.344 (0.411) (0.403) Labour 0.185 0.007 0.116 0.144 (0.064) (0.077) External inputs 0.002 0.979 0.021 0.813 (0.090) (0.089) Research stock 0.297 0.018 0.212 0.113 (0.119) (0.129) Extension 0.096 0.137 (0.063) R; 0.985 0.986 Stand.error of estimate 0.023 0.022 F-ratio 503.63*** 421.38*** D-W test value 1.082 1.105 Table 26. Cobb-Douglas production functions with public research measured as a stock with 100 % depreciation after 20 years. Regression (52) (53) 1.1. 1.1. Constant 0.215 0.820 0.368 0.692 (0.936) (0.020) Capital 0.535 0.151 0.530 0.146 (0.363) (0.355) Labour 0.158 0.009 0.093 0.186 (0.057) (0.069) External inputs 0.006 0.951 0.025 0.785 (0.091) (0.090) Research stock 0.252 0.023 0.174 0.142 (0.106) (0.115) Extension 0.098 0.133 (0.063) R ; 0.985 0.986 Stand.error of estimate 0.023 0.022 F-ratio 496.44*** 416.05*** D-W test value 1.045 1.084 being insignificant, however. The capital coef- ficient continues to increase. The depreciated research stock for the total research capital at both depreciation rates is presented in Appendices 17 and 18. The esti- mate of elasticity with respect to the total research stock for some reason seems to be slightly smaller than the elasticity estimate with respect to the public research stock. In order to investigate the autocorrela- tion for the three different cases of research capital, autoregressive models of first order 328 were also investigated. The autoregressions corresponded to the regressions (46)—(57) reported above. Autocorrelation declined substantially in these regressions. This could be noticed from the Durbin-Watson test value which showed values of 1.68—1.71. The re- search coefficient in these autoregressive es- timations varied from 0.10 to 0.15 for public research and from 0.08 to 0.12 for the total research. In the autoregressions the estimate of the elasticity with respect to the research stock was clearly insignificant, and the regres- sion coefficient of the residual was high (ap- proximately 0.50) and significant. The auto- correlation procedure has been explained in section 5.1.5. As a summary of the estimates of elasticity with respect to the research capital, it is now possible to state that resasonably reliable elasticity estimates of the research capital seem to be found in the range of 0.15—0.30 depending on depreciation rate. The autocor- relation, however, is still a problem since the model assumes that the residuals are not cor- related. The total research coefficient is slight- ly lower than the public research coefficient despite good t-value for both, a result which is hard to explain. Autocorrelation disappears in the autoregressive models, and the elasticity falls to 0.10—0.15 for public research and to 0.08—0.12 for total research, but is insignifi- cant. 5.3.3. Productivity Index Model In order to avoid the problem caused by multicollinearity an alternative model using a productivity index as dependent variable was specified in subsection 3.3.3. Through the specification of (3.17), the number of regres- sors was reduced to two variables, the research capital and a time factor. The dependent variable was a production/input index which included labour, capital costs (4 % of the stock of gross capital) and external inputs in the inputs. The results for this regression are presented in Table 27. Tabic 27. Cobb-Douglas functions with productivity index as dependent variable. Research stock undepreciated. Regression (58) s.l Constant 3.036 0.000 (0.563) Public research stock 0.346 0.008 (0.122) Time factor —0.002 0.787 (0.008) R- 0.973 Stand.error of estimate 0.036 F-ratio 575.18*** D-W test value 0.807 The estimate of elasticity with respect to public research shows a good significance at a level of 0.008 (i.e., a confidence level over 99 %). The time factor is insignificant and has an illogical sign. The coefficient of deter- mination is slightly lower than in the regres- sions with gross production as dependent variable. The autocorrelation is, however, substantial. The elasticity estimate with re- spect to research should be interpreted in a dif- ferent way from previous estimates. The simplest way is to say that for a 1 % increase in research funds, the relation of production to input rises by 0.346 %. 329 6. The Returns to Agricultural Research and University Education 6.1. The Selection of an Elasticity The primary question to be answered was stated in the introduction as: What has been the value marginal product (marginal rate of return) and the marginal internal rate of return for public expendi- ture in agricultural research and for total public and private expenditures on agricul- tural research in 1950—1984? To be able to draw a conclusion, a set of parameter estimates with respect to public and to total research was estimated in the previous chapter, and is used to calculate the value marginal product, which is easily changed to a marginal rate of return. Various options for the estimations were presented in Figure 15. It was possible to use either a flow elasticity or a stock elasticity. For the research flow it is possible to distinguish between an unlagged elasticity and an elasticity that includes a lag. For research stock it is possible to use either an undepreciated or a depreciated parameter estimate. Which estimate, then, should be used? 6.2. Research Flow Elasticities On the basis of the coefficients of the linear production function, an unlagged marginal product for public research of 0.016 was esti- mated which, however, was insignificant. This parameter estimate of the marginal product is equal to an elasticity 0.04 with respect to public research. When the capital, labour and purchased input variables were specified on farm level, marginal products of 0.046 and 0.040 were estimated (the latter when the extension variable was added). Both these unlagged marginal products could be accepted by the t-test at reasonable significance levels. Converting them into elasticities (according to expression 5.1) gives elasticities of 0.099 and 0.114 with respect to public research. The Cobb-Douglas function elasticities with respect to public research were 0.034 and 0.059 in the regressions where capital, labour and external inputs variables were specified on the aggregate level. If these conventional vari- ables were specified on farm level, the param- eter estimate of the elasticity with respect to research was 0.059 without the extension factor and 0.018 if extension was added. It is note- worthy that the lower elasticities, 0.018 (con- ventional variables on the farm level) and 0.034 (conventional variables on the aggregate level), which appear when extension is added have very low t-values and therefore are not reliable. Multicollinearity between the explaining variables was strong. Ridge regressions, how- ever, showed that the internal correlation did not lead to overestimated research coeffi- cients. The problem with all the unlagged parame- ter estimates of elasticities was heavy autocor- relation. In the autoregressive models of first degree, the autocorrelation declined and prac- tically disappeared when models of degree two were used to explain the output. The parame- ter estimates of elasticities with respect to pub- lic research in these unlagged models were 0.010—0.016. The regression coefficients of the lagged residuals were high, however, and their content is unclear. In addition, the elas- ticity estimates with respect to research were clearly insignificant. The parameter estimates of the unlagged elasticities with respect to public research thus vary between 0.010 and 0.114. Taking the pos- 330 6 sibility of errors into account, an estimate of elasticity of 0.040, previously used in section 5.1.1. may be too high. A modest approxima- tion of the unlagged elasticity estimate may thereforelie in the range of 0.015 —0.025. This approximation, however, suffers from lack of reliability because of the omission of a lag. The estimation of total research parameters by linear functions with conventional variables specified at the aggregate level gave an es- timate of the marginal product of 0.022 0.025, which was converted to an elasticity of 0.066—0.075. When traditional variables are specified at the farm level, the research marginal product estimate varies from 0.047 to 0.054 and the estimate of elasticity is con- sequently higher (0.141 —0.162). The signifi- cance was good. The Cobb-Douglas functions produced estimates of elasticities with respect to total research of 0.050—0.078 when the conventional variables were specified on the aggregate level, and of 0.021 —0.061 on the farm level. Both the higher parameter esti- mates of 0.078 and 0.061 were accepted by the t-test at a 10 % confidence level. In the auto- regressive models, autocorrelation declined and insignificant estimates of elasticity with respect to total research of 0.022—0.031 were obtained. The estimate of the unlagged elas- ticity of total research thus ranges from 0.021 to 0.162. Taking into account the deficient data an approximation of 0.030 for the esti- mate of the unlagged elasticity for total re- search seems appropriate. The estimation of elasticities with respect to public research including simple lags (Table 22) proved to be troublesome as many nega- tive signs appeared, and they were also statis- tically insignificant in most cases. The only estimates of elasticities which could be ac- cepted by the t-test were an estimate for a simple five-year lag with a negative sign ( —0.088) anc four rather high estimates of elasticities (0.084—0.092) for lags of 13 to 14 years. The results for estimations including Almon lags of degrees two and three were discourag- ing. The total inconsistency of signs for dif- ferent lengths of the lag proved to be no better than for the simple lags. As to the estimates of lagged elasticities with respect to the re- search flow, no acceptable estimate could thus be found. Thus the estimations carried out in this respect have clearly failed. 6.3. Research Capital Elasticities On the basis of three different assumptions of depreciation of the stock of research capital (0 %, 50 % and 100 % depreciated 20 years after research grants were made), elasticities with respect to a research capital of 0.252— 0.338 were estimated at a significance of 0.016—0.023. The inclusion of an extension variable in the regression decreased this esti- mate of elasticity to 0.174—0.247 and de- creased the significance to 0.093—0.142. Autocorrelation problems appeared in all cases. In the autoregressive models of first order, research elasticities of 0.10—0.15 were esti- mated and autocorrelation decreased substan- tially. These estimates suffered from being clearly insignificant. Taking these facts into consideration, approximation of the estimate of elasticity with respect to an undepreciated research capital at a value of 0.20 seems ac- ceptable. In case a depreciation rate of 50 % and 100 % after 20 years is practised, the es- timate of elasticity should be in the range of 0.17 and, respectively, 0.15. The estimates of elasticities with respect to total research stock were smaller than with respect to public research, a result which is hard to explain since the flow estimates in- dicated the opposite. The coefficients varied from 0.219—0.278, with a significance of 0.017—0.022. When extension was added the estimates declined to 0.169—0.222, with a sig- nificance of 0.052—0.074. The autoregressive models of first order gave insignificant esti- mates (0.08 and 0.12) of the elasticities with respect to total research stock. The estimate of the elasticity of an un- depreciated total research capital could, on this basis be approximated to 0.15, or slightly 331 lower than public research. Depending on the rate of depreciation, the elasticity estimate is approximated by 0.12—0.13. The reason for the lower value of total research probably depends on deficiencies in data, and a clear warning concerning this point is in order. 6.4. Value Marginal Product On thebasis of the elasticities discussed in the previous sections of this chapter, it is now possible to calculate a value marginal product VMP (a marginal rate of return) for agricul- tural research. This is done by relating the in- crease in output to the costs of the marginal increase in research costs. As agricultural and veterinary university-level education has been included in research costs, the calculated value marginal product concerns both research and university education. Extension activities car- ried out to speed up the adaption of innova- tions by farmers also need to be considered in some way. To do so, the public expendi- tures for extension services are included in the costs. The formula for calculation of the marginal product is, according to Davis (1981): (6.1) MP = d - ' R where MP = marginal product of research Q = gross production R = research expenditures d = elasticity of research If research has been measured as a flow, research expenditures are the average annual expenditures. Research capital must be re- garded as research expenditures when a stock elasticity is used. If the original production level is Q, the value marginal product is the MP priced by product price P,: (6.2) VMP = d R When extension costs are added the value marginal product is: (6.3) VMP = d Q|Pj - R + N 332 Davis (1981) points out two assumptions underlying the VMP calculations (6.1), (6.2) and (6.3). The first is that the level of use of all other inputs remains the same. This assumption can, on the one hand, be questioned, since it implies that technological change is neutral (neither capital nor labour intensive) to a change in research intensity. It means that the marginal products of the other inputs do not change as a consequence of research activities. But in reality new research results affect the volume of capital, labour and external inputs. On the other hand, as we are only dealing with a marginal increase in the research input, this assumption may be acceptable. This assumption of fixed input levels also implies a divergent shift in the supply curve, caused by research. If the supply curve in reality shifts in a parallel! direction, the VMP may be underestimated by up to half. The second implicit assumption is that the product price is not affected by the change in output and that demand is perfectly elastic. In reality demand is unlikely to be perfectly elastic and so the VMP overestimates the benefits. The overestimation caused by this latter assumption is, according to Davis, rela- tively small in comparison to the first pos- sibility of underestimation. The volume of gross production for the pe- riod 1950—1984 is derived by the same index series as were used to measure independent variables in the regressions. The volume of this production was reported by Kettunen (1985) to have been FIM 21,022.3 million in 1984. Because State subsidies, State com- pensations and outdoor garden production are included in this figure, they are subtracted. The gross production figure derived is then FIM 19,403.9 million at the domestic price level of 1984. Public expenditures for research and uni- versity education in 1984 were FIM 157.028 million, the value of total research FIM 230.132 million. Public expenditures for ex- tension were FIM 60.557 million. Use of the explaining index series for research and ex- tension gives the cumulated total value of these inputs in 1950—1984 at the price level of 1984. This results in following figures (see Table 28): Table 28. Cumulated and average volume in 1950— 1984 ofgross production, research flow and State expenditures for extension, (FIM mil- lion). Cum.vol. Average 1. Volume of gross production in 1950—1984 558,252 15,950 2. Public research flow in 1950—1984 3,138 89.7 3. Total research flow in 1950—1984 4,336 123.9 4. State expenditures for exten- sion in 1950—1984 1,791 51.2 If the unlagged estimate of elasticity with respect to the public research flow, approxi- mated at 0.020, is used, the VMP according to (6.3) will be ww„ 0.020 % x FIM 15,950 millionVMP„ = p 1% x FIM (89.7 + 51.2) million = 2.26 The value marginal product of 2.26 would imply that every additional Finnish mark invested in agricultural research and uni- versity education would have returned by 2.26 mark annually since that moment. This value marginal product is equal to a marginal rate of return of 226 %, which seems to be ex- ceedingly high. Since no lag was applied this is obviously an overvalued estimate. Applying the same formula to the total research flow with an unlagged elasticity of 0.030 gives „„„ 0.030% x FIM 15,950 million VMP' " 1 % X FIM (123.9 + 51.2) million _ 2 77- The value marginal product of total public and private research thus seems somewhat higher than for only public research. So far, the research flow concept has been considered. If the focus is changed to the research capital, do these high estimates gain validity from the estimations of the stock of research capital? In order to calculate the rate of return to research capital, we need to sum up the research capital existing each year in 1950— 1984. The accumulated sums as well as the figures for the derivation of research capital are found in Appendices 14 and 15. Table 29 presents the summed up research capitals and averages for different assumptions of the depreciation: Table 29. The sum and average of accumulated research capitals 1950—84 mill. FIM. TotalPublicRate of depreciation _ „ ... Sum Average Sum Averageafter 20 years s 56,685 1,619.6 70,272 2,007.8 50,122 1,432.1 63,284 1,808.1 43,559 1,244.5 56,295 1,608.4 0 °7o 50 % 100 % The sum of accumulated undepreciated research capitals during the whole period 1950—1984 was FIM 56,685 million (public) and, respectively, FIM 70,272 million (total). On average the undepreciated public research capital was FIM 1,619.6 million, the unde- preciated total research capital FIM 2,007.8 million. The value of the undepreciated re- search capital only in 1984 was estimated to FIM 3,480.0 million (public) and, respective- ly, FIM 4,688.3 million (total). The estimates of elasticities with respect to the undepreciated public research capital and the undepreciated total research capital were approximated at 0.2 and 0.15. If these approximations are used in formula (6.3), the following value marginal products are ob- tained: Research stock dePreciation rate = 0 % 0.2% X FIM 15,950 millionVMP = p 1% X FIM (1,619.6 + 51.2) million = 1.91 0.15 % X FIM 15,950millionVMP. - 1 % x FIM (2,007.8 + 51.2) million = 1.16 333 In the case of a 50 % and a 100 % depreci- ated research capital, the estimates of elas- ticities with respect to the public research were approximated at 0.17 and, respectively 0.15. The elasticity estimates with respect to the total research capital for both depreciation rates are 0.13 and 0.12. Since the estimations carried out would not give reason to more than minor change in these coefficients, there is reason to say the elasticities chosen well represent the depreciated research capital. The value marginal product then becomes: Research stock depreciation rate = 50 % „w„ 0.17 % X FIM 15,950 million VMP„ = p 1 «Vo X FIM (1,432.1 + 51.2) million = 1.83 .... _ 0.13% X FIM 15,950 millionVMP. = 1 % X FIM (1,808.1 + 51.2) million = 1.12 Research stock depreciation rate = 100 % ~.„,. 0.15 % X FIM 15,950millionVMP„ = p 1% x FIM (1,244.5 + 51.2) million = 1.85 0.12% x FIM 15,950million ' ~ 1 % x FIM (1,608.4 + 51.2) million = 1.15 The VMP for public research thus varies between 1.83 and 1.91 for public research depending on the assumed depreciaton rate. Correspondingly, the VMP for total research varies between 1.12 and 1.16. In fact, the undepreciated and depreciated research stocks give almost identical value marginal products. This is an interesting feature. The value mar- ginal product of the public research stock is 80 % of the research flow VMP. The value marginal product for the total research capital is only about 40 % of the flow VMP. Since the research stock conceptually does not need any lag, the estimates in this respect are more reliable than the flow estimates. The research stock estimates are also more reliable with respect to significance and autocorrelation. The critical issue is: Are we sure the stock of research capital needs no lag? Further assessment of the returns to research estimated on the basis of a research capital would seem interesting. There is one more way to determine a mar- ginal rate of return. Through the produc- tion/input elasticity with respect to public research, 0.346 as reported in subsection 5.3.3., it is possible to calculate the value of the improved production/input ratio. This ratio would have risen with 0.346 % for an additional 1 % of research capital. In other words, with the same set of inputs production would have risen with 0.346 % for a 1 % in- crease in research capital. The production/in- put index was measured in the prices of 1970; the average annual production in 1950—1984 was FIM 3,503.3 million in this price level, with an average annual undepreciated research capital of FIM 381.5 million in the prices of 1970 (FIM 1,619.6 million in the prices of 1980, deflated by the market price index), and extension, respectively, FIM 12.1 million. The value marginal product becomes: 0.346 «7o x FIM 3,503.3 million 1 <% x FIM (381.5 + 12.1) million " In other words, if the whole stock of re- search capital had increased by FIM 1, then FIM 3.08 more of production would have been gained. The difference from the former VMPs is partly caused by the fact that rela- tively minor differences in the elasticities are reflected as large differences in VMPs. It is also necessary to take into account that the errors were heavily autocorrelated in the re- gression, which casts some doubt on the reliability of the elasticity estimate. 6.5. Marginal Internal Rate of Return The internal rate of return (IRR) is a meth- od of investment analysis which explicitly con- siders the time value of money. The method is best understood with the net present value (NPV) method as a starting point. With the NPV method the cash flows of an investment project are discounted at a minimum ac- 334 ceptable compound annual rate. If the present value of net cash returns exceeds the initial in- vestment outlays, i.e the net present value is greater or equal to zero the investment is ac- cepted. The IRR method in turn, computes the discount rate for which the net present value equals zero. The discount rate is thus the maximum interest rate a project can pay out and still cover total outlays (Lee et al., 1980). According to (2.2) the IRR was formulated as z <*=£) = 0 (=o(l + fj)' R t = the social benefit (return) in year t C, = the research cost in year t T = the year the research ceases to produce returns t; = the internal rate of return Besides the value marginal product this measure is the most widely used rate of return for the returns to agricultural research. In general an average IRR is computed, but Pe- terson (1967, 1971) and Russell (1987) have computed a marginal internal rate of return (MIRR). For shorter periods, the MIRR is very sensitive to the length of the period dis- counted (i.e. the value of T). If T grows, however, the MIRR stabilizes around a cer- tain value. MIRRs for the estimates, with respect to the unlagged research flow elasticities of 0.02 (public research) and 0.03 (for total re- search), are computed according to (2.2). A lag is incorporated afterwards, assuming that the unlagged elasticity affects production alternatively, four, six or ten years later. In other words, a four-year lag assumes that the research input in 1950—1980 has affected pro- duction in 1954—1984. Extension is thought to have an immediate effect, i.e. the costs are credited for the same year as the production increase. The returns are assumed to stop at 1984. The results of the MIRR calculation on the various assumptions of the lag are presented in Table 30. Table 30. The marginal internal rate of return (MIRR), °7o. Public research Assumed Total researchlength of lag 76.862.24 years 6 years 10 years 37.7 46.0 25.920.9 The MIRR for public research according to this would be in the range of 20—62 °/o (above inflation) for various assumptions of the length of the lag. The corresponding MIRR for total research is approximately 25—76 %. It is noteworthy that this is a marginal figure, not an average. If the assumption that benefits stop at 1984 is eased, the change in MIRR is minor (less than 1 %). The MIRR for total research may be overestimated because too few costs have been included. On the other hand, extension expenditures are included for both public and total MIRR, which sub- stantially decreases the estimates. This MIRR falls in the same range as the average IRRs (cf. Appendix 1) computed in other studies. The difference from the VMP and corre- sponding marginal rates of return (226 % for public research and 273 ®/o for total research) seems to depend on the fact that the flow measure took no account of lags and the esti- mates were biased upwards. The VMP and the corresponding marginal rates of return esti- mated by research capital, 183—191 % for public research and 112—116 % for total re- search, rest on the assumption of a research stock which can be estimated. The different rates of return give different expressions of the same phenomenon. 335 7. Summary and Conclusions This study undertook to estimate the returns to investment in agricultural research in Fin- land in 1950—1984. The primary reason moti- vating this investigation is the fact that public research funds are limited. A measure for as- sessing the allocation of resources to research could be created, in part based on these study results, if the monetary value of agricultural research could be estimated. A second reason is the current interest of administrators in re- search evaluation. More specifically the purpose of the study was to estimate the following two measures of returns to agricultural research: 1. The value marginal product (VMP, a mar- ginal rate of return) 2. The marginal internal rate of return (MIRR). These rates of return were estimated for two different definitions of resource expenditures: a) Public expenditures on agricultural re- search and university education and b) Total public and private expenditures on agricultural research and university educa- tion. Two major approaches production func- tion analysis and welfare economics have been used in most studies estimating the re- turns to investment in agricultural research. These approaches and studies, carried out in North America, Asia and Australia, were re- viewed in chapter 2. In the production function analysis, a sepa- rate variable for research is included in the production function. A value marginal prod- uct can be computed on the basis of the esti- mate of elasticity with respect to research. The welfare economics approach is based on the changes in consumers’ and producers’ surpluses. Welfare economics makes it possi- ble to determine an average rate of return and the distribution of benefits from research between producers and consumers. This study used the production function ap- proach. Two models, a linear and a Cobb- Douglas model, were specified. Gross produc- tion was the dependent variable, and the ex- planatory variables were capital, labour, pur- chased inputs, extension and research. Capi- tal included buildings, machinery, water constructions, land and livestock. The re- search input was measured in two alternative ways: firstly, as a flow of annual funds granted for research and university education; secondly, as a stock of research capital, which consisted of funds accumulated since 1920 with three different assumed rates of depre- ciation. Almon lags of second and third de- gree were specified for the former way of mea- suring the research input. Finally, a third model with a productivity index as the de- pendent variable was specified. The time series data for public research ex- penditures included the agricultural research institutes and other institutions under the Ministry of Agriculture and Forestry, the Faculty of Agriculture and Forestry of the University of Helsinki for the part of agri- culture, the College of Veterinary Medicine, the Academy of Finland, the Finnish Na- tional Fund for Research and Development (SITRA), public foundations, the Work Efficiency Association and joint research projects financed by the Ministry. In the final calculation of the VMP and the MIRR, pu- blic expenditures for extension agencies were accounted on the cost side. Because of deficiencies in the data on the research input of the private sector, the total 336 public and private research VMPs and MIRRs should be interpreted with care. The expen- ditures accounted for on the side of the private sector did not cover the total expenditures. This biased the estimate positively. The results of the estimations are presented in chapter 5. Models measuring the research input as a flow of expenditures were analysed first, whereafter the models measuring re- search input as a stock of accumulated ex- penditures were examined. Finally, four dif- ferent return measures were calculated. The results were as follows: The results for estimations with the research input specified as a flow including no lags were discussed first. A preliminary VMP was derived on the basis of the linear models, though because lags were omitted it was an overestimation. The results for the linear and the Cobb-Douglas models were somewhat am- biguous. Multicollinearity between explana- tory variables as well as serial correlation in the residuals posed problems. The multicol- linearity was investigated by ridge regressions, which strongly indicated that the internal cor- relation between explanatory variables does not lead to overestimated estimates of the re- search elasticity. The autocorrelated errors were analysed by autoregressive models of first and second order. In the autoregressive models of the first order, the autocorrelation decreased considerably, and it virtually disap- peared in the second order models. The esti- mate of elasticity withrespect to research also decreased considerably, and the regression coefficients for the error terms increased. The results for models including either simple lags or Almon lags were somewhat paradoxical: Negative signs appeared for the estimate of elasticity with respect to research. The estimate was also insignificant. The biggest problem encountered in the study, therefore, was the failure to determine a satisfactory lag structure. The study proceeded to report results for Cobb-Douglas models measuring the research input as a stock of research capital based on a 0 %, a 50 % and a 100 % depreciation of the research capital 20 years after grants were made. Reliable elasticity estimates of the research capital were located in the range of 0.15—0.30, depending on the depreciation ra- te. The estimates of total research elasticity were somewhat lower. The research capital concept was thought to have an advantage, since it needs no lags. The estimates of returns presented in this study were based on the assumption that no research results were imported, which biased the returns positively. The total university education and the public expenditures for ex- tension, however, constituted a substantial share of the cost side, which may have under- estimated the rate of return. At the risk of oversimplifying the entire interpretation, the following conclusions on the returns to re- search, discussed at length in chapter 6, can be made: 1. Estimations using the flow measure of research input give a VMP for public research of 2.26 and of 2.73 for total public and private research. The marginal rates of return accord- ing to these estimates have been 226 % for public research and 273 % for total research (both over the inflation rate) from the moment the investment was made. The lack of any lag, however, biases the estimate positively, making additional measures necessary. 2. The estimates of elasticity with respect to a research capital give a VMP of 1.83— 1.91 for public research and a VMP of 1.12 1.16 for total research. These figures are in- terpreted as follows: Every additional public investment in agricultural research in 1950—1984 would have returned by 183 ®/o to 191 % annually over the inflation rate from the moment the investment was made. An ad- ditional investment in the total public and private research input would corresponding- ly have returned by 112 %to 116 % annual- ly. These research capital estimates are likely to be closer to the real VMPs than the flow estimates, since the lack of a lag should not be problematic conceptually. 3. A model using a production/input index as the dependent variable, and in which the 337 number of explaining variables are reduced to only two (a research capital and a time fac- tor) gives a marginal rate of return of 308 %. The errors, however, were heavily autocor- related in this model. 4. A fourth measure of returns is the mar- ginal internal rate of return (MIRR). This method is used to calculate the discount rate for which the net present value equals zero. On the basis of the research flow elasticity estimates, MIRRs are calculated, with lags of alternatively 4, 6 and 10 years included in these computations. 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Estimated rates of return from investment in agricultural research. (Pinstrup-Andersen 1982). Commodity Country Period Annual rate Source of return (%) Aggregate India 1953—71 40 Evenson and Jha (1973) Aggregate India 63 Kahlon et al. (1977) Aggregate Japan 1880—1938 35 Tang (1953) Aggregate USA 1949—59 35—40 Griliches (1964) Aggregate USA 1949—59 47 Evenson (1969) Aggregate USA 1937—42 50 Peterson and Fitzharris (1977) Aggregate USA 1947—52 51 Peterson and Fitzharris (1977) Aggregate USA 1957—62 49 Peterson and Fitzharris (1977) Aggregate USA 1967—72 34 Peterson and Fitzharris (1977) Aggregate USA 1938—48 30 Lu, Cline and Quance (1979) Aggregate USA 1949—59 28 Lu, Cline and Quance (1979) Aggregate USA 1959—69 26 Lu, Cline and Quance (1979) Aggregate USA 1969—72 24 Lu, Cline and Quance (1979) Hybrid maize USA 1940—55 35—40 Griliches (1958) Maize Chile 1940—77 32—34 Yrarrazaval, Navarrete and Valdivia (1979) Maize Peru 1954—67 35—40 Hines, (1972) Maize and sorghum Mexico 1943—64 26—59 Ardito-Barletta (1970) Hybrid sorghum USA 1940—57 20 Griliches (1958) Wheat Mexico 1943—64 69—104 Ardito-Barletta (1970) Wheat Colombia 1953—73 11 —l2 Hertford et al. (1977) Wheat Bolivia 1966—75 —4B Wennergren and Whitaker (1977) Wheat Chile 1949—77 Yrarrazaval, Navarrete and Valdivia (1979) Rice Colombia 1957—72 60—82 Hertford et al. (1977) Rice Colombia 1957—74 94 Scobie and Posada (1978) Rice Japan 1915—50 25—27 Akino and Hayami (1975) Rice Japan 1930—61 73—75 Akino and Hayami (1975) Rice Asia 1950—65 32—39 Evenson and Flores (1978) Rice Asia 1966—75 73—78 Evenson and Flores (1978) Rice Tropics 1966—75 46—71 Flores-Moya et al. (1978) Rice Philippines 1966—75 27 Flores-Moya et al. (1978) Cash grains USA 1969 36 Bredahl and Peterson (1976) Soybeans Colombia 1960—71 79—96 Hertford et al. (1977) Potatoes Mexico 1943—64 69 Ardito-Barletta (1970) Sugar cane South Africa 1945—62 40 Evenson (1969) Sugar cane Australia 1945—58 50 Evenson (1969) Sugar cane India 1945—58 60 Evenson (1969) Cocoa Brazil 1923—74 16 Monteiro (1975) Cocoa Brazil 1958—74 60 Monteiro (1975) Cotton Brazil 1924—67 77+ Ayer (1970) Cotton Colombia 1953—72 Negative Hertford et al. (1977) Rubber Malaysia 1932—73 25 Pee (1977) Rapeseed Canada 1964—75 95—105 Nagy and Furtan (1978) Pastures Australia 1948—69 65—80 Duncan (1972) Poultry USA 1915—60 21—25 Peterson (1967) Poultry USA 1969 37 Bredahl and Peterson (1976) Sheep Bolivia 1966—75 44 Wennergren and Whitaker (1977) Dairy India 1963—75 29 Kumar, Maji and Patel (1977) Dairy USA 1969 43 Bredahl and Peterson (1976) Livestock USA 1969 47 Bredahl and Peterson (1976) Tomato harvest USA 1958—69 37—46 Schmitz and Seckler (1970) Appendix 2. Index series used in the regressions. Year Agricultural Deflated Deflated Deflated Capital Labour External gross public total extension 1 inputs production research research input input and univ. and univ. education education 1950 100 100 100 100 100 100 100 1951 102 137 133 100 103 92 99 1952 105 127 128 99 106 93 108 1953 108 119 123 102 109 91 109 1954 110 118 125 95 111 88 120 1955 108 142 145 91 114 88 135 1956 112 162 167 99 116 85 151 1957 116 154 164 107 118 86 153 1958 117 230 235 116 120 87 145 1959 124 226 233 117 123 86 155 1960 130 213 225 114 126 86 174 1961 136 222 236 128 128 84 182 1962 140 295 311 141 131 88 199 1963 142 303 329 151 134 85 228 1964 148 296 323 157 137 83 222 1965 149 356 399 164 139 74 230 1966 148 366 419 166 141 74 234 1967 146 365 443 163 143 68 242 1968 149 398 479 152 143 68 254 1969 152 373 470 153 146 65 269 1970 152 346 454 155 145 57* 283 1971 157 345 467 149 147 50 296 1972 160 394 579 138 147 49 298 1973 153 399 561 136 148 45 303 1974 155 370 491 134 150 43 313 1975 159 457 562 147 151 41 326 1976 169 479 634 150 153 40 327 1977 169 622 754 145 154 39 310 1978 164 526 665 148 155 37 343 1979 167 623 758 143 156 34 365 1980 171 633 758 148 158 32 391 1981 172 650 750 152 160 33 391 1982 170 610 754 160 162 31 419 1983 172 614 811 161 163 27 406 1984 174 620 795 161 164 26 394 1 Before 1970 interpolated with five years intervals. The value 1950 assumed to be equal to 1951. 2 The labour input of 1970 calculated as an average of 1969 and 1971. 343 344 Appendix 3. The absolute figures for the index series. Year Nominal GDP Deflated Nominal Deflated External Gross Number public price public mterpol. interpol. inputs in capital of farms' research index to research public public prices of stock in input and market input and extension extension 1970 prices of university price university support support (FIM 1000) 1980 education education (FIM 1000) in prices (FIM (FIM 1000) in prices of 1980 of 1980 (FIM 1000) (FIM 1000) million) 1950 2,087 11.85 17,610 3,396 1951 3,133 12.96 24,180 3,396 1952 3,008 13.40 22,437 3,484 1953 2,810 13.42 20,936 3,572 1954 3,034 14.64 20,727 3,660 1955 3,925 15.74 24,934 3,749 1956 4,566 16.05 28,442 4,150 1957 4,425 16.30 27,151 4,551 1958 6,597 16.28 40,513 4,953 1959 6,936 17.47 39,713 5,354 1960 7,201 19.20 37,507 5,756 1961 7,904 20.20 39,130 6,749 1962 10,919 21.00 51,995 7,743 1963 11,784 22.10 53,319 8,736 1964 12,333 23.70 52,039 9,730 1965 15,622 24.90 62,740 10,723 1966 16,837 26.10 64,508 11,324 1967 17,982 28.00 64,221 11,925 1968 22,005 31.40 70,080 12,527 1969 21,469 32.70 65,653 13,128 1970 20,639 33.90 60,882 13,729 1971 22,191 36.50 60,798 14,205 1972 27,453 39.60 69,325 14,332 1973 31,711 45.10 70,312 16,132 1974 36,068 55.30 65,222 19,376 1975 50,959 63.30 80,503 24,304 1976 60,194 71.30 84,423 28,110 1977 86,145 78.60 109,600 29,824 1978 78,435 84.60 92,712 32,731 1979 100,534 91.60 109,753 34,432 1980 111,538 100.00 111,539 38,775 1981 127,430 111.40 114,390 44,328 1982 130,617 121.50 107,503 51,079 1983 142,914 132.10 108,186 55,849 1984 157,028 143.90 109,123 60,556 28.658.2 650,465 56,448 465,655 26,203.7 643,413 58,012 450,723* 26,000.0 700,746 60,097 435,790* 26,617.0 710,871 61,307 420,858* 25,000.0 778,143 62,861 405,925* 23.818.3 876,732 64,303 390,993* 25.856.7 984,696 65,401 376,060* 27,920.2 995,795 66,615 361,128* 30.423.8 941,957 67,845 346,195* 30.646.8 1,007,398 69,169 331,263 29.979.2 1,133,112 70,868 327,826* 33.410.9 1,184,491 72,480 324,462* 36.871.4 1,294,008 74,124 321,061* 39.529.4 1,482,652 75,734 317,661* 41,054.9 1,442,212 77,075 314,260* 43.064.3 1,494,078 78,197 310,859* 43,387.0 1,520,249 79,626 307,459* 42.589.3 1,575,007 80,528 304,058* 39,894.9 1,653,091 80,948 300,658* 40,146.8 1,746,600 82,234 297,257 40.498.5 1,840,000 81,701 289,640* 38.917.8 1,927,600 82,749 282,023* 36.191.9 1,937,900 83,026 274,406 35.769.4 1,972,900 83,763 265,938 35,038.0 2,036,100 84,408 258,200 38,394.9 2,121,839 85,071 248,736 39,425.0 2,129,517 86,134 242,682 37.944.0 2,019,477 86,876 237,679 38.689.1 2,229,699 87,354 232,820 37.589.5 2,375,850 88,278 229,349 38,775.0 2,546,052 89,428 224,721 39.791.7 2,541,191 90,525 218,904 42,040.3 2,726,488 91,293 212,630 42.277.8 2,642,618 92,276 208,229 42,082.0 2,562,952 92,777 203,933 1 * = interpolated 345 Appendix 4. Total expenditures and State support for the agricultural extension agencies (Asso- ciation of Agricultural Centres, the Agri- cultural Centres, Association for Agri- cultural Societies of Swedish Speaking Farmers, the Agricultural Societies and the small farmer organizations) (FIM 1000). Year Total Total State support expendi- State in % of total tures support expenditures 1950 1951 6,581 3,396 51.61 1955 8,249 3,748 45.44 1960 11,281 5,756 51.03 1965 19,143 10,723 56.01 1970 20,613 13,729 66.60 1971 22,229 14,205 63,90 1972 23,563 14,332 60.82 1973 28,421 16,132 56.76 1974 32,292 19,376 60.00 1975 41,762 24,304 58.20 1976 53,563 28,110 52.48 1977 54,940 29,824 54.28 1978 64,380 32,730 50.84 1979 72,671 34,432 47.38 1980 81,668 38,775 47.47 1981 95,489 44,328 46.42 1982 107,333 51,079 47.60 1983 120,374 55,849 46.40 1984 133,013 60,557 45.40 Appendix 5. Gross capital stock in basic agriculture according to the national accounts in prices of 1980 (FIM million). 1968 49,899.6 1969 50,931.7 1970 51,719.2 1971 52,608.2 1972 53,240.7 1973 54,038.8 1974 54,683.3 1975 55,582.1 1976 56,485.6 1977 57,138.4 1978 57,803.5 1979 58,724.7 1980 60,004.5 1981 60,958.0 1982 62,237.4 1983 63,359.2 1984 64,100.3 1950 28,381.2 1951 29,625.0 1952 31,232.4 1953 32,492.3 1954 33,708.5 1955 34,975.7 1956 36,066.1 1957 37,087.3 1958 38,098.9 1959 39,279.2 1960 40,551.9 1961 41,967.7 1962 43,223.8 1963 44,621.6 1964 45,778.8 1965 47,009.2 1966 48,346.4 1967 49,269.7 Appendix 6. Linear production functions with total research. All variables measured at aggregate level. Regression coefficients and their standard errors in parenthesis below coefficients, significance levels, coefficient of determination, F-ratio and Durbin-Watson test values. 1 Regression (5) (6) s.l. 2 1.1. Constant —46.232 0.004 —27.315 0.251 (14.949) (23.312) Capital 1.227 0.000 1.074 0.000 (0.150) (0.208) Labour 0.195 0.070 0.095 0.511 (0.107) (0.143) External inputs —O.OlO 0.809 —0.012 0.767 (0.041) (0.041) Total public & 0.025 0.057 0.022 0.102 private research (0.013) (0.013) Extension 0.077 0.300 (0.073) R-- 0.983 0.984 Stand.error of estimate 3.263 3.257 F-ratio' 444.85*** 357.47*** D-W test value 0.963 0.990 1 These coeffients, the F-ratio and D-W test-value will be presented in all the regression tables. 2 Significance levels with t-test. The abbreviation applies to all regression tables. 3 **� = Significance level for F-ratio < 0.001 Vo. The abbreviation applies to all regression tables. 346 Appendix 7. Linear production functions with total research. Output, capital, labour, external inputs measured at farm level, research and extension at aggregate level. Regression (7) (8) s.l. 1.1. Constant —20.175 0.059 —20.087 0.063 (10.303) (10.401) Capital 0.982 0.000 0.983 0.000 (0.134) (0.136) Labour 0.130 0.197 0.084 0.493 (0.098) (0.121) External inputs 0.0001 0.997 —0.0007 0.985 (0.037) (0.037) Total research 0.054 0.020 0.047 0.067 (0.022) (0.025) Extension 0.053 0.512 (0.080) R 2 0.997 0.997 Stand.error of estimate 5.158 5.201 F-ratio 2479.2*** 1946.48*** D-W test value 1.132 1.121 Appendix 8. Cobb-Douglas production functions with total research. All variables measured at aggregate level. Regression (14) (15) 1.1. 1.1. Constant 0.009 0.993 0.283 0.773 (1.000) (0.969) Capital 0.808 0.019 0.696 0.036 (0.324) (0.317) Labour 0.048 0.060 0.012 0.685 (0.024) (0.030) External inputs 0.058 0.534 0.062 0.494 (0.093) (0.089) Total public & 0.078 0.079 0.050 0.261 private research (0.043) (0.044) Extension 0.116 0.067 (0.061) R- 0.984 0.986 Stand.error of estimate 0.024 0.023 F-ratio 462.60*" 403.05*** D-W test value 1.048 1.115 7 Appendix 9. Cobb-Douglas production functions with total research. Output, capital, labour, external inputs measured at farm level, research and extension at aggregate level. Regression (16) (17) s.l. s.l. Constant —0.307 0.362 —0.574 0.116 (0.332) (0.355) Capital 0.898 0.000 0.958 0.000 (0.138) (0.138) Labour 0.048 0.078 0.012 0.707 (0.026) (0.033) External inputs 0.053 0.510 0.025 0.755 (0.080) (0.079) Total research 0.061 0.089 0.021 0.602 (0.035) (0.041) Extension 0.103 0.089 (0.059) R- 0.997 0.997 Stand.error of estimate 0.024 0.023 F-ratio 2423.0*** 2074.5*** D-W test value 0.966 0.976 Appendix 10. First order autoregressive Cobb-Douglas production functions with total research. All variables measured at aggregate level. Regression (22) (23) 1.1. |.l. Constant —1.798 0.144 —1.338 0.325 (1.199) (1.335) Capital 1.329 0.001 1.184 0.006 (0.343) (0.394) Labour 0.046 0.184 0.029 0.489 (0.034) (0.041) External inputs —0.022 0.806 —O.Oll 0.905 (0.088) (0.091) Total aggregate research 0.025 0.497 0.022 0.561 (0.036) (0.037) Extension 0.057 0.481 (0.080) 9, 0.516 0.001 0.495 0.002 (0.147) (0.149) R- 0.986 0.988 Stand.error of estimate 0.020 0.020 F-ratio 579.29*** 455.38*** D-W test value 1.741 1.755 347 348 Appendix 11. Second order autoregressive Cobb-Douglas production functions with total research. All variables measured at aggregate level. 1 Regression (24) (25) s.l. s.l. Constant —0.632 n.s. —0.429 n.s. (0.945) (0.932) Capital 1.017 < 0.002 0.930 <0.005 (0.2%) (0.297) Labour 0.037 n.s. 0.014 n.s. (0.030) (0.033) External inputs 0.047 n.s. 0.031 n.s. (0.086) (0.087) Total aggregate research 0.031 n.s. 0.028 n.s. (0.035) (0.036) Extension 0.088 n.s. (0.061) 6, 0.679 < 0.001 0.600 <0.001 (0.162) (0.163) 9 2 —0.287 < 0.100 —0.259 n.s. (0.162) (0.163) R 2 0.989 0.990 Stand.error of estimate 0.020 0.019 D-W test value 1.931 1.989 n.s. = not significant, s.l. > 0.01 Appendix 12. Cobb-Douglas production functions with total research for shorter periods. All variables measured at aggregate level. Regression (30) (31) (32) (33) 1950—69 1965—84 1.1. s.l. s.l. s.l. Constant —2.383 0.164 —2.600 0.048 3.162 0.184 4.361 0.145 (1.626) (1.198) (2.268) (2.823) Capital 1.168 0.019 1.217 0.002 0.219 0.664 —0.120 0.863 (0.445) (0.327) (0.495) (0.683) Labour 0.266 0.022 0.159 0.071 —0.035 0.627 —0.061 0.453 (0.104) (0.082) (0.070) (0.080) External 0.026 0.842 —O.OlO 0.913 0.012 0.920 0.042 0.741 inputs (0.129) (0.095) (0.116) (0.125) Total 0.052 0.368 —0.066 0.225 0.138 0.028 0.150 0.025 research (0.056b) (0.052) (0.057) (0.060) Extension 0.243 0.002 0.070 0.475 (0.066) (0.095) R 2 0.978 0.989 0.925 0.928 Stand.error of estimate 0.025 0.018 0.018 0.019 F-ratio 165.26*** 247.07*** 46.46*** 36.13*** D-W test value 1.052 1.373 1.617 1.784 Appendix 13. Coefficients of regression for different Almon lags with different lengths of lag and different degrees of the polynomial, a = aggregateted conventional variables p = per farm conventional variables Reg. Length Degree No. of lag X, X,_| X,_, X,_, X,_4 X,_ 5 X,_ 6 X,_ 7 X t_8 X,_, X,_ 10 X,_ n X t _, 2 X,_, 3 (34) 3 2 a 0.024 0.004 0.002 0.017 (0.041) (0.029) (0.029) (0.039) (35) 3 2p —0.003 0.011 0.018 0.018 (0.047) (0.028) (0.025) (0.036) (36) 3 3 a 0.030 —0.009 0.013 0.012 (0.045) (0.049) (0.046) (0.043) (37) 3 3 p 0.001 0.001 0.026 0.014 (0.051) (0.049) (0.043) (0.040) (38) 7 2 a —0.024 —0.026 —0.028 —0.030 —0.034 —0.037 —0.041 —0.046 (0.035) (0.021) (0.018) (0.019) (0.018) (0.016) (0.016) (0.029) (39) 7 2 p —O.OlO —0.009 —0.007 —0.006 —0.005 —0.004 —0.003 —0.003 (0.036) (0.019) (0.014) (0.016) (0.017) (0.013) (0.013) (0.026) (40) 7 3 a 0.001 —0.039 —0.048 —0.039 —0.025 —0.017 —0.028 —0.071 (0.045) (0.026) (0.029) (0.021) (0.021) (0.028) (0.022) (0.040) (41) 7 3 p —0.003 —0.012 —0.012 —O.OOB —0.003 —O.OOl 0.000 —O.OlO (0.051) (0.023) (0.027) (0.020) (0.020) (0.028) (0.020) (0.040) (42) 13 2 a 0.010 0.001 —0.006 —0.012 —0.016 —O.OlB —O.OlB —0.017 —0.013 —O.OOB —O.OOl 0.008 0.018 0.031 (0.029) (0.025) (0.021) (0.018) (0.016) (0.014) (0.013) (0.011) (0.009) (0.008) (0.007) (0.008) (0.010) (0.014) (43) 13 2 p 0.003 —0.004 —O.OlO —0.015 —O.OlB —0.019 —O.OlB —0.016 —0.013 —O.OOB —O.OOl 0.008 0.018 0.029 (0.022) (0.016) (0.012) (0.009) (0.008) (0.009) (0.009) (0.009) (0.009) (0.008) (0.007) (0.008) (0.010) (0.014) (44) 13 3 a —0.027 —0.004 0.007 0.010 0.006 —0.002 —O.Oll —0.019 —0.024 —0.024 —0.015 0.004 0.036 0.082 (0.036) (0.024) (0.022) (0.022) (0.020) (0.017) (0.013) (0.011) (0.011) (0.012) (0.011) (0.008) (0.015) (0.035) (45) 13 3 p —0.047 —0.017 —O.OOO 0.006 0.005 —O.OOl —O.OlO —0.019 —0.024 —0.024 —0.015 0.004 0.037 0.087 (0.034) (0.016) (0.012) (0.014) (0.014) (0.012) (0.010) (0.009) (0.010) (0.012) (0.010) (0.007) (0.014) (0.034) 349 Appendix 14. Derivation of the public research capital in prices of 1984. Grants Derived 1950—84 grants Undepreciated research capital Depreciated research capital dep.rate = 50 % dep.rate = 100 %1920—50 FIM 1000 Index FIM 1000 Index FIM 1000 Index 1920 2,930 2,930 1921 3,826 6,757 1922 4,722 11,479 1923 5,618 17,097 1924 6,514 23,611 1925 7,410 31,021 1926 8,306 39,326 1927 9,201 48,528 1928 10,097 58,625 1929 10,993 69,618 1930 11,889 81,507 1931 12,785 94,292 1932 13,681 107,973 1933 14,577 122,550 1934 15,473 138,022 1935 16,368 154,391 1936 17,264 171,655 1937 18,160 189,815 1938 19,056 208,871 1939 19,952 228,823 1945 20,848 249,670 248,205 246,740 1946 21,744 271,414 268,036 264,657 1947 22,639 294,053 288,314 282,574 1948 23,535 317,589 309,040 300,492 1949 24,431 342,020 330,214 318,409 1950 25,327 25,327 367,347 100 351,836 100 336,326 100 1951 34,698 402,045 109 382,382 109 362,719 108 1952 32,165 434,210 118 409,946 117 385,682 115 1953 30,139 464,349 126 435,036 124 405,724 121 1954 29,886 494,235 135 459,426 131 424,617 126 1955 35,964 530,199 144 489,445 139 448,691 133 1956 41,030 571,229 156 524,083 149 476,937 142 1957 39,004 610,233 166 556,246 158 502,260 149 1958 58,252 668,485 182 607,210 173 545,935 162 1959 57,239 725,724 198 656,713 187 587,702 175 1960 53,947 779,671 212 702,475 200 625,280 186 1961 56,226 835,897 228 750,069 213 664,242 197 1962 74,715 910,612 248 815,704 232 720,797 214 1963 76,741 987,353 269 882,917 251 778,482 231 1964 74,968 1,062,321 289 947,909 269 833,498 248 1965 90,164 1,152,485 314 1,027,650 292 902,814 268 1966 92,697 1,245,182 339 1,109,475 315 973,768 290 1967 92,444 1,337,626 364 1,190,599 338 1,043,572 310 1968 100,801 1,438,427 392 1,279,632 364 1,120,838 333 1969 94,470 1,532,897 417 1,361,887 387 1,190,877 354 1970 87,632 1,620,529 441 1,436,855 408 1,253,182 373 1971 87,378 1,707,907 465 1,506,884 428 1,305,862 388 1972 99,789 1,807,696 492 1,590,591 452 1,373,486 408 1973 101,055 1,908,751 520 1,676,576 477 1,444,402 429 1974 93,710 2,002,461 545 1,755,343 499 1,508,226 448 1975 115,745 2,118,206 577 1,853,106 527 1,588,007 472 1976 121,317 2,239,523 610 1,953,908 555 1,668,294 496 1977 157,535 2,397,058 653 2,091,941 595 1,786,825 531 1978 133,220 2,530,278 689 2,196,035 624 1,861,793 554 1979 157,787 2,688,065 732 2,325,203 661 1,962,341 583 1980 160,321 2,848,386 775 2,458,550 699 2,068,715 615 1981 164,626 3,013,012 820 2,595,063 738 2,177,115 647 1982 154,495 3,167,507 862 2,712,201 771 2,256,895 671 1983 155,508 3,323,015 905 2,829,338 804 2,335,662 694 1984 157,028 3,480,043 947 2,948,882 838 2,417,722 719 SUM 1920—84 56,684,590 50,121,819 43,559,049 SUM 1950—84 53,402,955 46,871,121 40,339,287 Appendix 15. Derivation of the total research capital in prices of 1984. Grants Derived Undepreciated Depreciated research capital .950-84 research capital dep, rate = 50 % dep.rate = 100 %' F'M'OOO index p[M mtUX» Index 1920 1,097 1,097 1921 2,168 3,265 1922 3,240 6,505 1923 4,311 10,816 1924 5,382 16,197 1925 6,453 22,650 1926 7,524 30,174 1927 8,595 38,770 1928 9,666 48,436 1929 10,738 59,174 1930 11,809 70,982 1931 12,880 83,862 1932 13,951 97,813 1933 15,022 112,835 1934 16,093 128,928 1935 17,164 146,093 1936 18,236 164,328 1937 19,307 183,635 1938 20,378 204,013 1939 21,449 225,462 1945 22,520 247,982 247,434 246,885 1946 23,591 271,573 269,941 268,308 1947 25,734 297,307 294,054 290,802 1948 26,805 324,112 318,704 313,296 1949 27,876 351,987 343,889 335,790 1950 28,947 28,947 380,934 100 369,609 100 358,284 100 1951 38,500 419,434 110 404,347 109 389,260 109 1952 37,053 456,487 120 437,103 118 417,718 117 1953 35,605 492,092 129 467,874 127 443,656 124 1954 36,184 528,276 139 498,690 135 469,103 131 1955 41,974 570,250 150 534,759 145 499,268 139 1956 48,342 618,592 162 576,661 156 534,730 149 1957 47,474 666,066 175 617,160 167 568,253 159 1958 68,026 734,092 193 677,675 183 621,257 173 1959 67,447 801,539 210 737,075 199 672,611 188 1960 65,132 866,671 228 793,625 215 720,579 201 1961 68,316 934,987 245 852,823 231 770,659 215 1962 90,026 1,025,013 269 933,196 252 841,378 235 1963 95,237 1,120,250 294 1,018,244 275 916,238 256 1964 93,500 1,213,750 319 1,101,019 298 988,289 276 1965 115,500 1,329,250 349 1,205,259 326 1,081,268 302 1966 121,290 1,450,540 381 1,314,754 356 1,178,967 329 1967 128,237 1,578,777 414 1,430,124 387 1,281,471 358 1968 138,658 1,717,435 451 1,555,380 421 1,393,324 389 1969 136,053 1,853,488 487 1,677,495 454 1,501,501 419 1970 131,421 1,984,909 521 1,794,442 485 1,603,975 448 1971 135,184 2,120,093 557 1,910,376 517 1,700,659 475 1972 167,606 2,287,699 601 2,059,456 557 1,831,212 511 1973 162,395 2,450,094 643 2,204,048 596 1,958,002 546 1974 142,132 2,592,226 680 2,328,088 630 2,063,950 576 1975 162,685 2,754,911 723 2,469,786 668 2,184,661 610 1976 183,527 2,938,438 771 2,629,142 711 2,319,846 647 1977 218,264 3,156,702 829 2,823,669 764 2,490,636 695 1978 192,500 3,349,202 879 2,982,156 807 2,615,110 730 1979 219,421 3,568,623 937 3,167,854 857 2,767,084 772 1980 219,421 3,788,044 994 3,354,709 908 2,921,373 815 1981 217,106 4,005,150 1051 3,537,657 957 3,070,163 857 1982 218,264 4,223,414 1109 3,710,908 1004 3,198,401 893 1983 234,764 4,458,178 1170 3,898,053 1055 3,337,928 932 1984 230,132 4,688,310 1231 4,081,435 1104 3,474,560 970 SUM 1920—84 70,271,929 63,283,710 56,295,492 SUM 1950—84 67,123,932 60,154,653 53,185,374 352 Appendix 16. Cobb-Douglas production functions with total research measured as an undepreciated stock. Regression (48) (49) 1.1. 1.1. Constant 1.023 0.375 1.237 0.268 (1.136) (1.095) Capital 0.299 0.486 0.247 0.550 (0.424) (0.408) Labour 0.207 0.007 0.143 0.072 (0.072) (0.077) External inputs —O.OOB 0.930 0.010 0.052 (0.091) (0.087) Research stock 0.278 0.017 0.222 0.052 (0.110) (0.110) Extension 0.109 0.066 (0.057) R 2 0.985 0.987 Stand.error of estimate 0.023 0.022 F-ratio 505.25*** 440.57*** D-W test value 1.095 1.164 Appendix 17. Cobb-Douglas production functions with total research measured as a stock with 50 % depreciation after 20 years. Regression (54) (55) 1.1. s.!. Constant 0.586 0.570 0.868 0.388 (1.021) (0.991) Capital 0.433 0.273 0.362 0.341 (0.387) (0.374) Labour 0.191 0.008 0.129 0.085 (0.067) (0.072) External inputs —0.005 0.958 0.013 0.879 (0.091) (0.088) Research stock 0.252 0.020 0.199 0.061 (0.102) (0.102) Extension 0.109 0.069 (0.058) R 2 0.985 0.987 Stand.error of estimate 0.023 0.022 F-ratio 501.59*** 436.47*** D-W test value 1.066 1.141 353 Appendix 18. Cobb-Douglasproduction functions with total research measured as a stock with 100 % depreciation after 20 years. Regression (56) (57) s.l. s.l. Constant 0.119 0.896 0.474 0.600 (0.908) (0.894) Capital 0.585 0.102 0.493 0.154 (0.347) (0.337) Labour 0.170 0.009 0.110 0.108 (0.060) (0.066) External inputs —O.OOl 0.990 0.017 0.848 (0.091) (0.088) Research stock 0.219 0.022 0.169 0.074 (0.091) (0.091) Extension 0.108 0.073 (0.058) R 2 0.985 0.987 Stand.error of estimate 0.023 0.022 F-ratio 497.80*** 431.49*** D-W test value 1.037 1.117 SELOSTUS Maataloustutkimuksen tuotto Suomessa 1950—1984 John Sumelius Maatalouden taloudellinen tutkimuslaitos Tämän tutkimuksen tarkoituksena on estimoida yh- teiskunnan tuotto maataloustutkimuksesta vuosina 1950—1984. Arvioimalla maataloustutkimuksen yhteis- kuntataloudellista korkoa voidaan luoda eräs mittapuu tutkimusvarojen allokoinnille. Tarkemmin määriteltynä estimoidaan maataloustutkimuksen rajakorko sekä sisäi- nen rajakorko ajanjaksolle 1950—1984. Maataloustutki- muksen tuottoa arvioitaessa on käytetty pääasiassa kah- ta päämenetelmää; tuotantofunktioanalyysia ja hyvin- vointiteoriaa. Menetelmien pääperiaatteet sekä aikaisem- mat tutkimukset on selostettu toisessa luvussa. Tuotan- tofunktioanalyysiin perustuen tässä tutkimuksessa spe- sifioidaan Cobb-Douglas ja lineaarisia malleja, joihin si- sällytetään tutkimusmuuttuja kolmen perinteisen ja yh- den neuvontamuuttujan lisäksi. Tutkimusmuuttuja on määritelty kahdella eri tavalla; toisaalta julkisten tutki- mus- ja korkeakoulumäärärahojenrahavirran perusteella, toisaalta karttuvan tutkimuspääomanperusteella. Tutki- muspanos on samoin määritelty toisaalta pelkän julkisen tutkimuspanoksen jakorkeakouluopetuksen perusteella, toisaalta julkisen ja yksityisen sektorin tutkimuspanok- sen perusteella. Tutkimusjoustoestimaattien avulla laske- taan rajakorko. Valtiontuki neuvontajärjestöille huo- mioidaan lopullisessa laskelmassa. Tutkimuspääomaestimaatteihin nojautuen julkisen maataloustutkimuksen rajakoroksi on saatu 183—191 %. Tämä on tulkittava niin, että maataloustutkimuksen yh- den markan lisäys kyseessä olevina vuosina olisi palau- tunut lähes kaksinkertaisena vuotuisena reaalikorkona tuottajille ja kuluttajille. Tutkimusmäärärahojen raha- virran perusteella estimoitu sisäinen rajakorko on ollut 20—62 % riippuen viiveen pituudesta (4—10 vuotta). 354