Demand for food products in Finland: A demand system approach Ilkka P. Laurila The Research Council for Agriculture and Forestry, the Academy of Finland, and the Department ofEconomics and Management, the University of Helsinki ACADEMIC DISSERTATION To be presented, with the permission of the Faculty ofAgriculture and Forestry of the University ofHelsinki, for public criticism in Auditorium XU, the University, Aleksanterinkatu 5, Helsinki, on October 14, 1994, at 12 noon. https://www.c-info.fi/en/info/?token=fRjlZpiM5Brd5phl.OWT7HwJj_fEoOqOnOk7Dnw.kabtdlYgcqtJkWjLRggxETEbUeXhDoXhNPcRdvvYiAdGQW3GbE77TVuSmcN0Sfm4Jxh9h2iAVDn9zSK_992zFC_KaZLoIjmerJBoTGQgejpOVUQfpWqE-Og6g422ixC0OkNUT1OsFdeRKbEnLQb-o-oURmb97RY23nODAtcXSmfP1Vsu7C4p5vn-RpoUNAWw8-y2b6GIFCdXM3XS2raz1IzYzzaHhYzwRkRC5bEphtPfULyoZBq2i-KCy_7eHnYpd8n_kOCcAw ACKNOWLEDGEMENTS As this study goes to press, I wish to express my sincere gratitude to all those who helped me with this work. I am indebted to Dr. Paavo Mäkinen for first suggesting the topic of the study to me. During the initial phase of this study I had the opportunity to receive valuable guidance from my teacher, Rector, Professor Risto Ihamuotila, and Acting Professor Petri Ollila. Professor Viljo Ryynänen showed endless interest in my work and provided the necessary facilities at the Department of Economics and Management, University of Helsin- ki. To Professor Karl Johan Weckman I owe a particular debt of gratitude for encouraging me in my work during the whole research process. I wish to express my thanks to my colleagues at the Department for providing the pleasant atmosphere during these years. The study was supervised by Acting Professor Jukka Kola, Dr. Juhani Rouhiainen, and Professor Karl Johan Weckman, and reviewed by Professor Lauri Kettunen and Professor Arie J. Oskam. I am greatly indebted to all of them for valuable guidance and suggestions. The study was carried out parallel to the research project “Models and Projections of Demand for Food in the Nordic Countries,” guarded by the Scandinavian Association of Agricultural Scientists. I want to express my sincere gratitude for the fruitful co-operation and stimulating discussions to my co-researchers Associate Professor Bengt Assarsson, As- sociate Professor David Edgerton, Anders Hummelmose, Associate Professor Kyrre Rickert- sen, and Associate Professor Per Halvor Vale. Special thanks are due to David Edgerton for providing me with the software routines used in the computations, and Anders Hummelmose for collecting the data concerning retail prices in Denmark. This work was completed during my stay as a visiting research fellow at the Department of Agricultural Economics and Policy of Wageningen Agricultural University, the Nether- lands. I am grateful to Professor Piet C. van den Noort and Professor Arie J. Oskam for providing the congenial surroundings of the Department. I wish to thank Dr. Alison Burrell, Alfons Oude Lansink, Dr. Jack Peerlings, and Dr. Geert Thijssen for their constructive criticism during the final preparation of the thesis. The research was financed by the Research Council for Agriculture and Forestry, the Academy of Finland, and, in part, by grants from Kyösti Haataja Foundation of Okobank Group, the Scandinavian Association of Agricultural Scientists, and August Johannes and Aino Tiura Foundation of Agricultural Research. I acknowledge my debt of gratitude to the institutions for the resources they have awarded me for this study. I thank the Central Statistical Office of Finland and the Research Institute of the Finnish Economy (ETLA) for providing me with the data for the study. I thank Jaana Kola for checking the English text and Sari Torkko for editorial assistance. I would also like to thank the editorial board of Agricultural Science in Finland for accepting this study to be published in their Journal. I am grateful to my dear wife Suvi for her support throughout this work. Little Pellervo was a major contributor of bringing joy to every-day life. I wish to thank my mother-in-law for taking care of our household during the last stage of this research. In addition, I would like to thank my parents and godmother for being inspiring examples of minds that are open for new innovations in life. Wageningen, August 1994 Ilkka P. Laurila CONTENTS Abstract 321 1 Introduction 322 1.1 Background of food demand analysis in Finland 323 1.2 Objectives of the study 324 2 Food consumption in Finland in 1950-1991 325 2.1 Definition of commodity bundles and variables 326 2.2 Data sets 329 2.3 Budget shares 329 2.4 Volumes and prices 330 3 Demand theory and empirical analysis 337 3.1 Determinants of consumer demand for food 337 3.2 System ofchoice: preferences and utility maximisation 339 3.3 Duality in deriving a demand system 340 3.4 Slutsky conditions for symmetry and negativity 342 4 Demand system specification and estimation 343 4.1 Complete demand systems approach: literature review 343 4.2 Derivation of the Almost Ideal Demand System 346 4.3 Slutsky conditions on the AIDS 348 4.4 Extensions of the AIDS 350 4.4.1 Dynamic AIDS 350 4.4.2 Switching static and dynamic AIDS 352 4.5 Aggregation over consumers 353 4.6 Aggregation over goods: separability and multi-stage budgeting 356 4.7 Specification of the hierarchic demand system 358 4.8 Elasticities of the AIDS 360 4.9 Estimation methods 363 5 System of demand for food products: model selection and evaluation 364 5.1 Selection ofpreferred specifications: testing parameter restrictions 364 5.2 Evaluation of the preferred model specifications 367 5.2,1 Negativity condition 367 5.2.2 Parameter estimates 367 5.2.3 Goodness of fit 368 5.2.4 Diagnostic checking 369 6 Elasticity estimates 376 6.1 Within-group elasticities 376 6.2 Total elasticities 381 6.3 Elasticities compared with elasticities obtained in other studies 384 7 Projections to year 2000 390 7.1 Introductory remarks 390 7.2 Forecasting accuracy 391 7.3 Projections of exogenous variables 393 7.4 Projected volumes for 2000 396 7.5 Projected budget shares for 2000 397 8 Discussion and conclusions 399 8.1 Food consumption in Finland 399 8.2 Food demand system for Finland 400 8.3 Elasticity estimates 402 8.4 Projections to year 2000 404 8.5 Conclusions and policy implications 406 Summary 409 References 413 Selostus 419 Appendix I Definition ofcommodity bundles Appendix 2 Food demand system for Finland: parameter estimates Appendix 3 Glossary Demand for food products in Finland: A demand system approach Ilkka P. Laurila Laurila, LP. 1994. Demand for food products in Finland: A demand system approach. Agricultural Science in Finland 3: 315-420. (Department of Economics and Management, P.O. Box 27, FIN-00014 University of Helsinki, Finland.) The study was concerned with the estimation of food-demand parameters in a system context. The patterns of food consumption in Finland were presented over the period 1950-1991, and a complete demand system of food expenditures was estimated. Price and expenditure elasticities of demand were derived, and the results were used to obtain projections on future consumption. While the real expenditure on food has increased, the budget share of food has decreased. In the early 19505, combined Food-at-Home and Food-away-from-Home corresponded to about 40% of consumers’ total expenditure. In 1991 the share was 28%. There was a shift to meals eaten outside the home. While the budget share of Food-away-from-Home increased from 3% to 7% over the observation period, Food-at-Home fell from 37% to 21%, and Food-at-Home exclud- ing Alcoholic Drinks fell from 34% to 16%. Within Food-at-Home, the budget shares of the broad aggregate groups, Animalia (food from animal sources), Beverages, and Vegetablia (food from vegetable sources), remained about the same over the four decades, while structural change took place within the aggregates. Within Animalia, consumption shifted from Dairy Products (other than Fresh Milk) to Meat and Fish. Within Beverages, consumption shifted from Fresh Milk and Hot Drinks to Alcoholic Drinks and Soft Drinks. Within Vegetablia, consumption shifted from Flour to Fruits, while the shares of Bread and Cake and Vegetables remained about the same. As the complete demand system, the Almost Ideal Demand System (AIDS) was employed. The conventional AIDS was extended by developing a dynamic generalisation of the model and allowing for systematic shifts in structural relationships over time. A four-stage budgeting system was specified, consisting of seven sub-systems (groups), and covering 18 food categories. Tests on parameter restrictions and misspecification tests were used to choose the most preferred model specification for each group. Generally, the estimated models did not satisfy the Slutsky conditions. The goodness-of-fit measures were good, and, compared to static specifications, dynamics usually provided a better fit. The misspecification tests indicated that the dynamic specification was correct, but some form of misspecification was found. The structural change in parameters indicated that the modelling failed to track a stable preference structure - if there is one. The estimated demand system was employed in projecting the future consumption of food products in Finland to the year 2000. The approach was to choose a certain change in the real total consumption expenditure and alternative sets of relative prices for the forecast period. Four different options of price variables were defined. Three of the options relied on the historical price trends recorded in Finland, whereas one option measured the expected consequences of Finland's possible membership in the European Union. A predicted consequence of the membership in the European Union is that the share of food in consumers’ budget would decrease. The expected decrease is somewhat faster than the decrease that would take place if future price developments were based on the historical trends. If Finland joins the Union, the budget share of Food-at-Home would decrease from 21% in 1991 to 18% in 2000, whereas the budget share of Food-at-Home excluding Alcoholic Drinks would decrease from 16% in 1991 to 14% in 2000. Key words: Almost Ideal Demand System, consumption, expenditure elasticity, food consump- tion, habit persistence, price elasticity, projections 321 Agricultural Science in Finland 3 (1994) 1 Introduction Substantial changes have occurred in consump- tion patterns in Finland over the past four dec- ades. There has been a marked increase in the proportion of food expenditures spent away from home: the real expenditure on food consumed in restaurants and cafes more than quadrupled, while the real expenditure on food consumed at home doubled. Real incomes have also risen - in the early 1950 s the average consumer spent 40% of his or her total budget on food and drink, while by the early 1990 s the proportion had declined to 28%. Within food budget, processed meat products, cheese, fruits, soft drinks, and alcoholic drinks have become increasingly important, while flour, milk, butter, eggs, and coffee have lost impor- tance. Flistory shows large shifts in the consump- tion structure. For example, expenditures on car- case meat and soft drinks increased rapidly in the late 1960 s and early 19705. In both cases, the increase coincided with a decrease in respective real prices. Some of the trends that were visible in the past were cut off in the early 19905. For example, the downturn in consumption of alco- holic drinks coincided with the downturn in the economy. The objective of the present study is to explain the changes in food consumption patterns in Fin- land. In order to do that, the determinants of food demand will be identified and quantified. By knowing the past, future developments can be projected. After predicting exogenous variables, such as total expenditure, population, and prices, projections of food consumption patterns will be derived. The study focuses on consumer demand, which refers to the demand given rise by individuals and households. Roughly speaking, it refers to all non-public demand in the economy. The con- cept demand structure or demand system or sim- ply demand is a function that refers to the re- sponses of a consumer to various economic and related factors, such as levels and changes in prices and income, that produce the observable consump- tion behaviour or consumption. The aggregate de- mand structure or market demand refers to the combined consumption responses of all consum- ers in the economy to the factors that determine the levels and changes in per capita consumption (Haidacher 1992, Johnson et al. 1986). When the distinction between the micro- and macro- level phenomena is not essential, the behaviour 322 Agricultural Science in Finland 3 (1994) of both an individual and all consumers will be called demand. 1.1 Background of food demand analysis in Finland Economic analysis of food demand in Finland is well-founded. Three traditions can be named ac- cording to the data employed: studies using house- hold budget data, studies using National Accounts data, and studies using disappearance data at the national level, often referred to as the Food Bal- ance Sheets. Kaarlehto (1961) pioneered in us- ing the household budget data in order to esti- mate income elasticities for food commodities. A special interest was on how food expenditures depend on income levels. Marjomaa (1969) start- ed a series of studies employing the aggregate level National Accounts data, which became avail- able from the year 1948 (later on, Laurila (1985, 1987) derived the series backwards). In some stud- ies the annual time-series were accompanied by household budget data, which have been collect- ed at intervals of about five years since 1949 (e.g. Marjomaa 1969, Hämäläinen 1973). In ad- dition to food items, the studies covered all pat- terns of households’ expenditures. Hämäläinen (1973) was the first to introduce forecasts for a wide range of food commodities. Haggrén and Kettunen (1976) and Kettunen (1976) pub- lished the first forecasts for food commodities using the Food Balance Sheets, the annual series of which became available from the year 1950. Rouhiainen (1979) estimated demand elasticities and derived forecasts by using the Food Balance Sheets. In addition to the mentioned studies, which covered a wide range of food commodities, there were several studies that covered one commodi- ty or a small number of commodities (Kaar- lehto 1959, Sandelin 1959, Koivisto and Ko- ponen 1961a, b, Koivisto and Naapuri 1961, Koponen 1961, 1964, Nyberg 1967, Kettunen 1968). Household budget data are cross-sectional data, whereas the National Accounts and the Food Bal- ance Sheets are time-series data. Household budg- et data are micro-data, where observations con- sist of records of individual households, whereas the other two data sets record consumption at the aggregate level. Household budget data usually offer substantial variation in expenditure levels and limited variation in relative prices (unless there are several cross-sections). Thus, the data set has an advantage in estimating expenditure responses. Studies which use household budget data benefit from a large number of observations, but have several disadvantages, such as the prob- lem of zero-purchases (i.e. all households do not consume all the analysed categories). Empirical demand analysis based on household budget data has traditionally focused on demographic effects and expenditure effects, and has ignored price effects (Pollak and Wales 1992, p. 66-67). Time-series data usually offer substantially more variation in relative prices and less variation in expenditure. Thus, they have an advantage in es- timating cross-price effects. By using micro-data, it is difficult to derive direct implications at the macro level. If interest is on macro-level market demand and, for in- stance, on (pre-)evaluation of policy instruments, micro-level responses do not offer the necessary information. In the present study, the interest is on macro-level market demand. Studies that em- ploy macro-level disappearance data (the Food Balance Sheets) have the advantage that only by means of that data set one can study consump- tion in terms of physical quantities. However, the approach suffers from the fact that the price and volume series come from different sources. The price series can be derived by using representa- tive goods. However, the derivation of consump- tion expenditures essential to a system-wide anal- ysis with allocation models, which dominate the modern methodology, would be rather artificial. Moreover, by measuring the consumption in terms of kilograms rather than in monetary terms, for instance, the increase in the consumption of proc- essed products is easily ignored. The present study joins the tradition that em- ploys the National Accounts data. Since the pio- neering study by Marjomaa (1969), a number of studies have been published. Hämäläinen (1973) 323 Agricultural Science in Finland 3 (1994) showed that Engel’s law - that the budget share of food decreases as incomes increase - was evi- dent in Finland. 1 Väisänen (1980) updated the description and forecasts. Virén (1983) was the first to use a system-wide approach. He estimat- ed the price and income elasticities by using an extended Linear Expenditure System. The series of studies was continued by Rahiala (1984) and Mankinen (1988). In addition to the cited stud- ies, a contribution was made concerning histori- cal consumption: Laurila (1985, 1987) present- ed a pioneer work on private consumption over the period 1880-1980. Mellin(l9B3, 1985) com- pared static and dynamic properties of the con- sumption expenditures in Finland. The referred contributions have increased the understanding of the factors and relationships af- fecting food demand. However, recent develop- ments in demand models provide new possibili- ties for empirical analysis. For example, models that are more consistent with the consumer theo- ry have been developed (flexible functional forms). In addition to this, a great number of diagnostic tests and evaluation criteria are avail- able for testing the model performance. A gener- al feature with very few exceptions is that the former studies employed only the single equation methodology. There are several reasons why one should adopt a system-wide approach, which is nowadays a standard in demand analysis. An em- pirical demand system, in which interproduct de- pendencies are estimated in a simultaneous frame- work, gives information about the complete in- terdependent nature of food choice, which is not explored by single equation analysis. 1 Ernst Engel observed in the mid-19th century that the poorer a family was, the greater proportion of total expen- ditures was allocated to food, which may be restated that, as consumer incomes increase, the proportion of income spent on food decreases, ceteris paribus. Engel’s observa- tion is one of the few patterns that has been observed with sufficient persistence to be called a law of economics (Senauer et al. 1991, p. 134-136). In terms of elastici- ties, Engel’s law states that food is income inelastic. The effect of income on the expenditure patterns, or the Engel function, has been one of the most extensively studied empirical relationships in economics. 1.2 Objectives of the study Because of the budget constraint, increased con- sumption of one food item can occur only at the expense of another. As a result, food items com- pete with each other, and it is important to study intergroup and interproduct relations, substitutes and complements. Although the interest is in food demand, the interdependence in demand between food items and other commodities makes it rea- sonable to estimate a complete demand structure or system. The complete system approach allows the estimation of cross-commodity substitutions, which are essential in the demand theory. Food demand is an interesting subject from various points of view. Applying a demand sys- tem on food is interesting as a methodological matter. The food system altogether - linking farm- ers and consumers by producing, transporting, storing, and processing agricultural commodities into food products and services - is dependent on consumption and, thus, information on demand structure and factors affecting it is essential. Man- ufacturers, retailers, and nutritionists are inter- ested in consumption trends. Farmers are inter- ested in consumer-oriented production and mar- keting. The estimated models and elasticities will be used for structural analysis, which examines the causes for the changes in consumption patterns. Elasticities are important in the design and oper- ation of policy and regulatory schemes. Together with some other elements (such as supply, for- eign trade, environmental measures, and taxes), the demand for food is a central issue in making agricultural and food policy. For example, to some degree, farmers’ income depends on the market demand for food products. Nutritional policy af- fects consumption by recommending to diminish or increase the consumption of certain products. Many policies that are not intended to affect the market may have indirect influence on food con- sumption patterns. To be able to evaluate the ef- fects of various policy instruments, responses to income and price changes are of central impor- tance. Government policy-makers and regulators are interested in changes in consumption in order 324 Agricultural Science in Finland 3 (1994) to adjust production control. Demand analysis pro- duces information which is needed when govern- ments aim at intervening in the markets to achieve certain goals, for example, to increase or decrease the consumption of a certain item. The anticipat- ed efficiency of the programme can be pre-evalu- ated. In addition to the knowledge of the current structure of food consumption, strategic food sec- tor planning often requires forecasts on future food demand. The estimated models will be used to forecast food expenditures to the year 2000. The sensitivity of these forecasts to alternative options of price developments will be examined. The objectives of the present study are: I. To present the food consumption patterns in Finland over the period 1950-1991. 2. To estimate a demand system for a 18-catego- ry breakdown of food expenditures. 3. To verify how well the Finnish consumer be- haviour corresponds to the consumer theory. 4. To estimate price and expenditure elasticities of food commodities. 5. To obtain projections on future food demand in Finland. 6. To examine the sensitivity of the projections to alternative price developments. 7. To derive policy implications. The description of food consumption is proba- bly interesting to anyone who likes to know about Finland’s social and economic history. Demand- system estimation as a methodological matter in- terests researchers, teachers, and students in eco- nomics. The derived elasticities and projections are useful for policy-makers as well as players in the food system. The study is organised as follows. Chapter 2 defines the data sources, variables, and commod- ity bundles. It also explores the long-term devel- opments of food consumption and food prices in Finland. Chapter 3 concerns the basic theoretical elements of the demand analysis. The discussion should facilitate the understanding of the nature and conditions the theory states for empirical anal- ysis. Chapter 4 describes the methodology of the empirical analysis, and complete demand systems approach is presented. The formulation of the functional form starts from a static specification, then, dynamic behaviour is incorporated and, fi- nally, variables allowing for structural change in consumer demand are introduced. The hierarchic demand system is specified. Chapter 5 describes the selection and evaluation of preferred model specifications. Chapter 6 provides the estimated price and expenditure elasticities. The elasticities are compared with elasticities obtained in other studies. Chapter 7 concerns consumption projec- tions. The estimated models are used for simula- tions, both for evaluating the model performance over the sample period, and for projecting food expenditures to the year 2000. In Chapter 8, the results of the present study are discussed, and they are compared with the results obtained in other studies. The implications for future research and the suggestions for data revision are provid- ed. Finally, concluding remarks are presented. 2 Food consumption in Finland in 1950-1991 Over the last four decades, the final consumption expenditure has corresponded to about three-quar- ters of the gross domestic product in Finland. Most of that has been the total private consump- tion. In the 19505, the total private consumption expenditure was an average of 63% of the gross domestic product. The public sector and also pri- vate non-profit bodies have increased their ex- penditure over the years, so that in the 1980 s the proportion of the total private consumption was 51%. In 1990 the proportion was 49%. Because in 1991 private consumption still increased, while 325 Agricultural Science in Finland 3 (1994) Table I. Consumption in Finnish economy in 1950-1991.“ Category % (gross domestic product in current prices, FIM million) 1950-59 1960-69 1970-79 1980-89 1990 1991 average average average average Gross domestic product 10,139 26,373 98,108 326,740 525,900 503,645 ofwhich, % Gross fixed capital forma- tion and net imports 24 25 27 27 27 21 Final consumption 76 75 73 73 73 79 ofwhich, % Public consumption 15 19 23 27 29 30 Private consumption 6 85 81 77 73 71 70 ofwhich, % Non-profit bodies' 2 4 4 4 6 6 Total Private Consumption0 98 96 96 96 94 94 ofwhich, % Durables 6 8 10 12 11 9 Semi-Durables 19 15 14 13 13 13 Private Consumption 75 77 76 75 76 78 ofwhich, % Services 29 36 38 40 44 45 Non-Durables 19 19 20 20 19 19 Food 52 46 43 40 37 36 ofwhich, % Food-away-from-Home 8 10 17 21 26 26 Food-at-Home 92 90 83 79 74 74 Sources: Hjerppe (1989), Bulletin of Statistics (1986:1, 1989:1, 1993:1), National Accounts. “A guide to compute, for example, the expenditure on Food-at-Home in the 19505: FIM 10,139 mi11i0n*.76*.85*.98*.75*.52*.92. lion*.76*.85*.98*.75*.52*.92. The outcome corresponds with the FIM 2,312 million which is the actual value of the consumption. The figures have been rounded to the nearest final digit. Thus, there may de an apparent slight discrepancy between the actual values and the values derived as guided. b Consumption of private and non-profit bodies. Non-profit bodies are housing corporations, etc. c Consumption of non-profit bodies, and net value of direct purchases abroad. d Final consumption expenditure of households in the domestic market. the gross domestic product and investments dropped, total private consumption covered 52% of the gross domestic product. About one-quarter of the total private expendi- ture has been classified as the consumption of durables and semi-durables, the rest is the bundle that is under consideration in the present study. This bundle, private consumption excluding du- rables and semi-durables, accounted for 47% of the gross domestic product in the 19505. The share gradually declined to an average of 38% in the 1980s, and was 37% in 1990. In 1991 the share under consideration rose to 41 %, due to increased private consumption and decreased gross domes- tic product, investments, and purchases of dura- bles (Table 1). 2.1 Definition of commodity bundles and variables The demand system approach adopted in the present study allocates the total expenditure into smaller segments. In a few cases the “total” re- 326 Agricultural Science in Finland 3 (1994) fers to the total private consumption (including durables and semi-durables) which covers the fi- nal consumption expenditure of households in the domestic market. However, in most cases the “to- tal” refers to private consumption which covers the final consumption expenditure of households in the domestic market excluding durables and semi-durables. The approach follows Alessie and Kapteyn’s (1991) application of the AIDS. They removed durable components from the expendi- ture categories to avoid complications due to the investment nature of durables. By removing du- rables, it is implicitly assumed that the house- holds’ utility function is weakly separable in du- rables and non-durables (Alessie and Kapteyn 1991, p. 412). The consumption structure in Finland is studied by means of time-series on expenditure and prices. Altogether 28 groups of commodities are defined (Table 2, a detailed description of the categories is in Appendix 1). Hereafter, capital initials are used when referring to the defined categories. The following variables are considered: Quantity, or consumption volume, or real ex- penditure of good i at period t (q.) is measured as the per capita consumption in Finnish Markkaa (FIM) in prices of the year 1985. Since the data operate at the aggregate level, the implied con- sumption has to be interpreted with caution. The figures refer to the national averages, and there probably exists considerable variation in the be- haviour between individuals. In order to obtain per capita figures, mean population of each re- spective year is used as the measure of the popu- lation size. To make the description consistent, mean population is used as the measure also in Alcoholic Drinks, despite the fact that alcohol is mainly consumed by adults. Budget share, or expenditure share of good i at period t (w ) is defined as the value of pur- chases of a commodity group compared with the aggregate: = pi' q‘> = Mi' " v (1) i = 1 where p is the price of good i, x is the total expenditure, and n is the number of goods in the system. Various definitions of x are used. In this chapter, either Total Private Consumption or, al- ternatively, the expenditure on Food-at-Home is used as the aggregate. In later chapters, also sub- groups ofFood-at-Home are employed. Relative price , or price ratio of good i at peri- od t (pJ) is computed as follows. The data set contains two vectors for each good, qjt and c. ( , which is the per capita consumption of good i in current values (FIM) at period t. The transforma- tion from current to real values has been carried out by the Central Statistical Office by using a consumer price index [of Laspeyres type] for good i. A derived price index [of Paasche type],2 or the implicit price index of good i (p.) is measured by dividing the value of purchases in current terms by the value of purchases in fixed 1985 terms (ic.Jq , ( ). To obtain pj, the implicit price index is deflated by the implicit price index of the aggre- gate, or r = Pi< = Cit /(lit = c,/g,7 p n n n ' I ‘,/1 *„ vS *„ I=l i=i i=i In the present chapter, n refers to all the cate- gories that are included in Private Consumption. Thus, P roughly indicates the general price lev- el. In the econometric analysis, n refers to the categories that are included in the group under examination. Consequently, Pt indicates the price level of that particular group. 2 The Laspeyres price index is a ratio of incomes need- ed in different years to purchase year I bundle. More exactly, it shows the ratio between the income needed to buy the year 1 bundle at year 2 prices and the actual year 1 income. By comparing the Laspeyres index (or, alterna- tively, the Paasche index) to the ratio of his or her actual income in the two years, a consumer can measure the change in his or her welfare over the two years. The Paasche price index is a ratio of incomes needed in differ- ent years to purchase year 2 bundle. More exactly, it shows the ratio between the income needed to buy the year 2 bundle at year 2 prices and the income needed to have purchased the same year 2 bundle at year 1 prices (e.g. Call and Holahan 1983, p. 102-109). 327 Agricultural Science in Finland 3 (1994) Table 2. Definition of the commodity bundles. Category Composition (budget shares, %, in 1991 in parentheses) Category number and mutual dependency Total Private Consumption (including Durables and Semi-Durables) Private Consumption Food-at-Home - Animalia (food from animal sources) - Meat and Fish - Meat Products - Carcase Meat - Fish - Dairy Products (other than Fresh Milk) - Cheese - Sour Milk and Cream - Butter - Margarine - Eggs - Beverages - Alcoholic Drinks - Fresh Milk - Soft Drinks - Hot Drinks - Groceries - Vegetablia (food from vegetable sources) - Bread and Cake - Fruits - Vegetables - Flour Food-away-from-Home Non-Durables Services Private Consumption (78%), Semi- Durables (13%), Durables (9%) Food-at-Home (27%), Food-away-from- Home (9%), Non-Durables (19%), Services (45%) Animalia (34%), Beverages (32%), Vegetablia (26%), Groceries (9%). Meat and Fish (64%), Dairy Products (33%), Eggs (4%). Meat Products (53%), Carcase Meat (36%), Fish (10%) Sausages (56%), etc. Beef and veal (59%), pork (22%), poultry (12%), etc. Unprocessed fish (69%), etc. Cheese (40%), Sour Milk and Cream (31 %), Butter (17%), Margarine (12%) Emmentaler and edam (51%), etc. Sour milk products (64%), cream (36%) Dairy butter, etc. Margarine (90%), oils (10%) Eggs Alcoholic Drinks (68%), Fresh Milk (16%), Soft Drinks (9%), Hot Drinks (8%) Beverages which contain alcohol Standard milk, low fat milk, etc. Soft drinks and mineral waters Coffee (89%), tea (5%), cocoa (4%), etc. Candies and chocolate (36%), ice-cream (17%), sugar (15%), etc. Bread and Cake (41%), Fruits (28%), Vegetables (19%), Flour (13%) Coffee cake (52%), bread (48%) Cultivated fruits and berries (58%), etc. Vegetables and potatoes Flour and hulled grain (68%), etc. Food and drink in restaurants and cafes, food catered at places ofwork Non-durables excluding Food-at-Home Services excluding Food-away-from-Home 0 =l+2+3+4 1 = 1.1 + 1.2+ 1.3+ 1.4 1.1 = 1.1.1 + 1.1.2+ 1.1.3 1.1.1 = 1.1.1.1 + 1.1.1.2+ 1.1.1.3 1.1.1.1 1.1.1.2 1.1,1.3 1.1.2 = 1.1.2.1 + 1.1.2.2 + 1.1.2.3 + 1.1.2.4 1.1.2.1 1.1.2.2 1.1.2.3 1.1.2.4 1.1.3 1.2 = 1.2.1 + 1.2.2+ 1.2.3+ 1.2.4 1.2.1 1.2.2 1.2.3 1.2.4 1.3 1.4 = 1.4.1 + 1.4.2 + 1.4.3 + 1.4.4 1.4.1 1.4.2 1.4.3 1.4.4 2 3 4 In line with the interpretation of the relative price, if it is stated that a certain commodity has become cheaper, this must not imply that the nominal pric- es have gone down, but it is rather an outcome of the phenomenon where the price of the commodity increased less than the general price level. Thus, if a price changes by the rate of the general inflation, the relative price has not changed. 328 Agricultural Science in Finland 3 (1994) 2.2 Data sets The annual data consist of expenditure series of goods and services for household consumption supplied in both current and constant monetary forms. The National Accounts time series for 1970-1991 were obtained from the Central Sta- tistical Office. Because the volume series based on the year 1985 are available only from 1975, to make the older values agree with the values after the year 1974, a level adjustment for the years 1970-1974 was made. The data that cover the years 1960-1969 were partly obtained from the Research Institute of the Finnish Economy, part- ly they were built up by the author by means of the data presented in Laurila (1985). Data cov- ering years 1950-1959 were built up by the au- thor utilising the series presented in Laurila (1985), To make these values agree with the post- -1960 values, a level adjustment was made. As a result, the base year for all the series was 1985. The data covering 1950-1991 were used to de- scribe the development of consumption patterns, whereas the econometric analysis employed the data covering 1960-1991. The reasons for not using the data from the 1950 s in the econometric analysis are as follows: (a) a number series are available only from 1960; (b) most of the post- -1960 values are derived from a uniform data source which is different from the data source utilised when deriving the pre- 1960 values; and (c) consumer preferences tend to change over time, and, consequently, the observation period must not cover too long time period, because most of the econometric methods implicitly assume con- stant consumer preferences. The National Accounts values refer to market values. The data are prepared according to the United Nations conventions. The data of the present study follow the ‘new’ Systems of Na- tional Accounts (United Nations 1968). For fur- ther discussion on the consumption in the Na- tional Accounts, see Hämäläinen (1973), Söder (1984), Laurila (1985, Ch. A). Implicit price series were derived by dividing current monetary expenditures by constant ones. The expenditure series were transformed to per capita expenditures. For diagnostic checking, data on disposable incomes were needed. The series of population and disposable income were taken from official statistics (Statistical Office 1992, Bulletin of Statistics). It is noteworthy that the consumption in terms of expenditure is different from the consumption in terms of physical units. For example, the Food Balance Sheets by OECD and FAO measure the consumption as a raw-material disappearance, and in some commodities, as physical quantities of processed products. The Food Balance Sheets mostly ignore the changes in quality and the de- gree of preparation. In the case of food, changes in quality, rather than changes in quantity meas- ured as raw materials, explain much of the changes in expenditures allocated to individual bundles. For example, per capita real expenditure on Food- at-Home excluding Alcoholic Drinks increased by 78% from 1950 to 1991, while the average intake of energy, excluding Alcoholic Drinks, de- creased from 2990 kcal per day in 1950 to 2770 kcal per day in 1991, or 7% (Rouhiainen 1979, MTTL 1992). The apparent contradictions be- tween the volume trends in terms of monetary and physical units (Laurila 1990) can be ex- plained by the fact that food has become more prepared before it reaches the consumer. More has been spent per energy unit. Therefore, the consumption in terms of value may be increasing parallel to a decrease in the consumption in terms ofweight. The added value originates mainly from services: the purchased good is further prepared than it used to be. Often there are several goods in one bundle. If those goods that are more proc- essed increase their share in a bundle, the real expenditure of the bundle increases, although no quality changes have taken place in individual goods. 2.3 Budget shares Although food expenditures have increased over decades, the share of food in the total expendi- ture has declined gradually. In the early 19505, combined Food-at-Home and Food-away-from- 329 Agricultural Science in Finland 3 (1994) Home corresponded to some 40% of consumers’ expenditure. In 1991 the share was 28% (for a historical perspective over 100 years, see Lauri- la 1987). There has been a shift to meals eaten outside the home. While the budget share ofFood- away-from-Home increased from 3% to 7% over the observation period, Food-at-Home fell from 37% to 21%. Also Food-at-Home excluding Al- coholic Drinks was studied. That is because alco- hol is specially treated in the Finnish tax-system, making it an artificially expensive commodity. Probably because good substitutes are lacking, alcohol is a big factor in households’ budget. In 1991 the budget share of Food-at-Home exclud- ing Alcoholic Drinks was 16% (Figure 1). The data show that the budget shares of Cheese, Meat Products, Alcoholic Drinks, Soft Drinks, and Fruits have increased strongly over the observation period. The budget shares of Butter, Eggs, Fresh Milk, Hot Drinks, and Flour have decreased the most. A continuing shift from Carcase Meat to Meat Products has been record- ed. The budget shares of the broad aggregate groups, Animalia, Beverages, and Vegetablia have remained quite steady over the observation peri- od. Until the 19705, the consumption of Vege- tablia decreased in proportion to the consump- lion of Animalia. After that the trend disappeared (Table 3). When studying the budget shares, it should be noted that a change in a share is a result of two components: change in the relative price and change in the relative volume. For example, the dramatic decrease in the budget share of Hot Drinks is, from one dimension, a consequence of a 300% increase in the consumption volume and, from another dimension, a consequence of an al- most 90% decrease in the relative price. 2.4 Volumes and prices Although the share of food in the total expendi- ture has decreased, food expenditures have in- creased over the observation period. On the per capita basis, Total Private Consumption (includ- ing Durables and Semi-Durables) became 3.4- fold in four decades, while Food-at-Home dou- bled, and Food-at-Home excluding Alcoholic Drinks grew just 78%. Over the observation peri- od, Total Private Consumption increased, on an average, by 3.1% annually, while expenditure on Food-at-Home and Food-away-from-Home in- creased by 1.7% and 3.8%, respectively. Food- Fig. I. Food expenditures related to Total Private Consumption (including Durables and Semi-Dura bles) in 1950-1991. Note: Combined food consists of Food-at-Home and Food-away-from-Home. 330 Agricultural Science in Finland 3 (1994) 331 Table 3. Budget shares of food items from 1950 to 1991. Share of Food-at-Home, % 1950-59 1960-69 1970-79 1980-89 1990 1991 average average average average Food-at-Home 100 100 100 100 100 100 -Animalia 33.7 36.9 36.6 35.2 34.1 33.5 -Meat and Fish 18.1 20.4 22.6 21.6 21.7 21.3 - Meat Products 5.6 9.5 11.0 11.1 11.5 11.4 -Carcase Meat 9.8 8.5 9.0 8.1 8.1 7.8 -Fish 2.7 2.4 2.6 2.4 2.1 2.2 - Dairy Products 13.2 14.4 12.2 12.0 11.0 11.0 -Cheese 1.5 1.9 2.4 3.4 4.1 4.4 - Sour Milk and Cream n.a.“ 3.0 3.7 3.4 3.4 3.4 -Butter 11.8b 7.5 4.2 3.7 2.1 1.9 -Margarine n.a. b 2.1 1,9 1.5 1.4 1.3 -Eggs 2.3 2.1 1.7 1.6 1.3 1.2 -Beverages 32.0 30.6 32.6 29.9 31.4 31.9 - Alcoholic Drinks 8.2 10.6 16.0 17.2 20.9 21.6 -Fresh Milk 14.3“ 11.5 8.4 6.1 5.2 5.1 -Soft Drinks 1.0 1.3 2.0 2.3 2.7 2.7 -Hot Drinks 8.5 7.1 6.2 4.2 2.7 2.5 -Groceries 9.5 8.7 9.0 9.2 9.2 9.1 - Vegetablia 24.8 23.8 21.9 25.7 25.4 25.5 - Bread and Cake 8.1 10.2 9.3 10.1 10.4 10.4 -Fruits 4.7 4.8 5.9 7.1 7.0 7.1 -Vegetables 4.5 3.7 4.0 5.3 4.8 4.8 -Flour 7.5 5.1 2.7 3.1 3.2 3.2 Source: National Accounts; n.a.: not available “Fresh Milk and Sour Milk and Cream cannot be separated. The combination is reported, h Fats cannot be separated. The combination is reported. at-Home excluding Alcoholic Drinks has been even slower to grow: 1.5% annually over the ob- servation period (Table 4). The growth rates fluctuated a great deal over the observation period. In 1991 the consumption of Food-away-from-Home fell strongly for the third time over the observation period. The falls have been associated with falls in Total Private Con- sumption. A fall in Total Private Consumption has been realised as a stronger fall in Food-away- from-Home, indicating an expenditure-elastic de- mand. The demand has also been elastic during the economic booms of 1951, 1955, the late 19605, and the 1980s. Expenditure on Food-at-Home has followed the changes in Total Private Consump- tion much more closely (Figure 2). The consumption ofFood-at-Home doubled in four decades. The highest volume was recorded in 1989. In both years 1990 and 1991, the con- sumption declined by 3%. Related to the general price level, Food-at-Home became 24% cheaper over the observation period (Figure 3). In 1991, an average Finn consumed at home worth FIM 10,800 of food (in current values). This corre- sponded to FIM 900 per month, The volume of Food-away-from-Home in- creased most of the time until 1990, with short drawbacks in the 1950 s and late 19705. The vol- ume rose by 370% from 1950 to 1989, and by 250% from 1960 to 1989. The consumption stag- nated in 1990, and fell by 8% in 1991. The con- sumption ofFood-away-from-Home became more Table 4. Growth in the consumption volume from 1950 to 1991. Per capita real expenditure, change from previous year, % Change 1951-59 1960-69 1970-79 1980-89 1951-91 l° average average average average average Total Private Consumption (including Durables and Semi-Durables) 3.0 4.3 3.2 2.9 3.1 237 Private Consumption (excluding Durables and Semi-Durables) 2.8 3.7 3.0 2.4 2.8 209 Combined Food-at-Home and Food-away-from-Home 1.7 3.4 2.4 1.7 2.1 127 Food-at-Home 1.5 3.1 2.1 1.1 1.7 100 Food-at-Home excluding Alcoholic Drinks 1.6 2,4 1,9 0.8 1.5 78 Food-away-from-Home 2.9 5.6 4.3 3.8 3.8 333 Source: National Accounts expensive over the decades. The price in 1991 was 85% higher than the all-time-low in 1952 (Figure 3). In 1991, an average Finn consumed away from home worth FIM 3,800 of food (in current val- ues). This corresponded to FIM 320 per month. Meat and Fish Meat and Fish together corresponded to 18.1% ofFood-at-Home in the 19505. The share rose to 22.6% in the 19705, then decreased to 21.6% in Fig. 2. Growth rates of Food-at-Home, Food-away-from-Home, and Total Private Consumption (in- cluding Durables and Semi-Durables) in 1951-1991: change in per capita real expenditure from previous year. 332 Agricultural Science in Finland 3 (1994) the 1980s. Of the sub-categories, Carcase Meat and Fish lost some of their importance in the consumer budget, while the budget share of Meat Products doubled over the observation period. The changing shares were due to the increased vol- umes of Meat Products, relatively slow increase in the volume of Carcase Meat, and the decreased price ofFish (Figure 4). The consumption of Meat Products increased at an annual rate of 8% over the period 1950 to 1974. After 1974, the volume decreased for some years, then it started to increase again, and the 1974 consumption level was attained in 1987. The relative price of Meat Products has shown a decreasing trend: from 1950 to 1991, the price decreased by 35%. The consumption of Carcase Meat decreased rapidly in the early 19505. A clear turn upwards started in 1969, and the consump- tion increased by 50% in 11 years. After the all- time-high in 1979, the volume gradually declined by an average annual rate of 1.3%. The price of Carcase Meat was at its highest in 1969. The price in 1991 was 16% below that level. The consumption of Fish rose gradually over the ob- servation period, reached a peak in 1990, and declined in 1991. The Fish prices dropped by 57% between 1956 (all-time-high) and 1991 (Fig- ure 4). Dairy Products Dairy Products consisting of Cheese, Sour Milk and Cream, Butter, and Margarine took a share of 13.2% of Food-at-Home in 19505, 14.4% in the 19605, and about 12% in the 1970 s and 1980s. Over time, fats, especially Butter, have had a decreasing budget share, the share of Sour Milk and Cream has remained about the same, while the budget share of Cheese has increased (Ta- ble 3). Cheese consumption became eight-fold be- tween 1950 and 1991, and five-fold between 1960 and 1991. The price series showed major shifts downwards in 1951, 1977, and 1985. As a result, Cheese was 40% cheaper in 1991 than it was in 1950. The consumption of Sour Milk and Cream doubled from 1960 to 1972. The prices of Sour Milk and Cream rose gradually until 1972, and since then declined so that in 1991 the price level was 19% below the level of the year 1972. Butter consumption reached a peak in 1962, and since then has declined at an average annual rate of 3.2%. It is noteworthy that the consumption increased by 6% in 1991, while the price de- creased by 22%. Butter was most expensive in 1968, i.e. 58% more expensive than in 1991. Mar- garine consumption was at its lowest in 1962, the very same year as the consumption of Butter was at its highest. During the following 12 years, the consumption of Margarine grew by 90%. Over the years 1974-1984, the consumption fell at an annual rate of 3.6%. Since then, the consumption has increased at the rate of 2.8% per year. The relative price declined gradually over the years 1960-1975, rose rapidly during the following two years, remained about the same until 1984, and since then has declined at an annual rate of 5% (Figure 4). Fig. 3. Consumption and price of Food-at-Home and Food-away-from-Home in 1950-1991 333 Agricultural Science in Finland 3 (1994) There have been two major quality changes in Margarine. Soft margarine has been available since 1969, thus widening margarine’s use as a spread. Low-fat spreads were launched in 1987. In addi- tion to quality shifts, an abnormality in fats mar- ket was recorded during the years 1961-1965: the market was affected by antagonistic publicity concerning production processes of margarine (Rouhiainen 1979). Fig. 4. Consumption and price of Animalia in 1950-1991. 334 Agricultural Science in Finland 3 (1994) Eggs The consumption of Eggs doubled from the early 1950 s to the late 19705. During the 1980s, the consumption of Eggs decreased, with a noticea- ble exception in 1986, when a 10% price drop was reported. 3 The fall in volumes speeded up in 1991. As a result, in 1991 Eggs were consumed in volumes which correspond to the volumes in the late 1960 s (Figure 4). The consumption was probably affected by a growing concern on die- tary cholesterol. The budget share of Eggs fell from 2.3% in the 1950 s to 1.2% in 1991 (Table 3). The fall was not created only by the fall in volume, but the decrease was speeded up by a falling relative price. Beverages Over the observation period. Beverages corre- sponded to 30-33% of Food-at-Home. Behind the 3 At the beginning of 1986, a dual price system for eggs came into effect, causing a decrease in retail prices. At the same time, strong marketing efforts were carried out. budget share there were mixed volume and price combinations. Over the observation period, the consumption of Alcoholic Drinks, Soft Drinks, and Hot Drinks increased by 360%, 320%, and 290%, respectively. From 1960 to 1991, the con- sumption of Fresh Milk decreased by 36% (Fig- ure 5). Over the observation period. Alcoholic Drinks took an increasing share of the food budget of households. The rise was due to the consumption volume, which increased faster than the total con- sumption. The reasons for the increasing trend were supposed to be increasing incomes, better availability, and more positive attitudes towards Alcoholic Drinks (Simpura and Österberg 1989). Over the observation period, the relative price of Alcoholic Drinks was at its highest in 1951 and in 1956. In the mid-19705, the price shifted down- wards, and tended upwards after that. Fresh Milk consumption was at its highest in 1964. Over the years 1965-71, the consumption decreased annually by about 2%. Then, the vol- umes increased until 1975. After that, the slope has been steadily downwards. From 1975 to 1991, Fresh Milk drinking diminished by 35%, or at Fig. 5. Consumption and price of Beverages in 1950-1991 335 Agricultural Science in Finland 3 (1994) the annual rate of 2.7%. The long-term price trend tended downwards, but there were several fluctu- ations that broke the trend. The price in 1991 was 13% below the level in 1960. The consumption of Soft Drinks was at its high- est in 1973. Parallel to a strong increase in the consumption during the period 1963-1973, there was a strong price fall. Interestingly enough, si- multaneously with the decrease in Soft Drinks consumption over the period 1974-1977, the pric- es of Soft Drinks increased rapidly. In the 1980s, both the prices and volumes increased. A considerable change took place in the budg- et share of Hot Drinks. The average of 8.5% in the 1950 s decreased to 2.5% in 1991, while the consumption quadrupled. The phenomenon is ex- plained by falling prices: the relative price of Hot Drinks in 1991 was one-eighth of that in the early 19505. Groceries The budget share of Groceries remained about the same over the observation period: around 9% of Food-at-Home (Table 3). While the consump- tion volume more than doubled, the increase was partially offset by the relative price that dropped by one-third (Figure 6). Fig. 6. Consumption and price of Groceries and Vegetablia in 1950-1991 336 Agricultural Science in Finland 3 (1994) Vegetablia The budget share of Vegetablia remained at 24- 26% over the observation period, with an excep- tion in the 19705, when the share was 22%. The consumption of Bread and Cake, Fruits, and Veg- etables increased over time, while the consump- tion of Flour decreased. The price of Bread and Cake increased, that of Fruits decreased, while that of Vegetables and Flour fluctuated heavily (Figure 6). Bread and Cake consumption reached the peak in 1974. In the 1980 s the consumption was quite steady, but in 1990 and 1991 the volume decreased by 5% each year. In 1991, 20% less was con- sumed than in 1974. The price of Bread and Cake was at its lowest in 1956. After that, the price changes have been mostly upwards, and in 1991 Bread and Cake were 71% more expensive than in 1956. Over the observation period, the con- sumption of Fruits became 12-fold, or increased at an average annual rate of 6.2%, which was double compared with the growth of Private Con- sumption. From 1960 to 1991, the growth was 270%. The growth in the budget share of Fruits was more moderate, rising from an average of 4.7% in the 1950 s to 7.1% in the 1980s. From 1950 to 1991, the prices of Fruits decreased by 72%, or at an annual rate of 3.1%. The consump- tion of Vegetables was at its highest in 1988- 1990, when the volume was nearly twice as much as the volume in the 1950 s and 19605. The price trend of Vegetables exhibited a great deal of in- consistency over time. Flour consumption de- creased by 60% from the early 1950 s to the be- ginning of the 19705. Between 1974 and 1991, the consumption ofFlour increased by 60% (Fig- ure 6). 3 Demand theory and empirical analysis 3.1 Determinants of consumer demand for food The neoclassical theory of consumer behaviour names incomes and prices as the factors that de- termine demand. Extensions of the neoclassical model take into account socio-economic, demo- graphic, socio-psychological, and nutritional fac- tors, choices under risk and uncertainty, plus new commodities, multi-period consumption decisions, and time (Capps and Havlicek 1987, p. 17-23). In the present study, the static theoretical frame- work of consumer demand is extended to a dy- namic theoretical framework in order to take into account multi-period consumption decisions. Haidacher (1992) reviewed demand studies in order to evaluate the relative importance of price, income, and demographic factors in ex- plaining year-to-year changes in consumption of dairy and related products in the United States. He stressed not to ignore cross-commodity inter- dependencies that have shown to be economical- ly significant. He concluded that the changes were predominantly the result of changes in relative prices (own-price and other prices) and changes in income. Demographic variables were more im- portant in explaining variations in expenditures between households than in explaining yearly fluc- tuations in market demand patterns. That was be- cause demographic factors changed slowly over time (Haidacher 1992, p. 205-209). Heien and Wessells (1988) also studied the relative impor- tance of demographic and economic variables in explaining the decrease in demand for milk and butter in the United States. They argued that the main cause was the own-price impact. An economic analysis lays emphasis on possi- bilities and preferences. In this framework, given prices and income, the consumer is able to buy various combinations of quantities (possibilities), and consumers rank all relevant bundles of goods (preferences). Consumers are assumed to seek to 337 Agricultural Science in Finland 3 (1994) maximise their own utility or satisfaction through a series of choices that are constrained by their limited income. The outcome is that a consumer picks a certain bundle of goods which ranks high- est within the constrains. The observed outcomes, the demand relationships, reflect the optimum amount of each good to purchase, depending on the consumer’s income, the set of prices (that is outside his control), and the consumer’s prefer- ences. This theoretical model suggests that eco- nomic factors, such as income4 and prices, should have a major impact on the choices which gener- ate certain observable consumption patterns ( c.f, Tangermann 1986, Senauer et al. 1991, Ch. 5). However, in economic analysis, some aspects in human food selection remain unexplained. The models are able to track the reality only as far as history repeats itself. The error term in econo- metric models has to absorb a number of factors which are difficult to identify. Many non-income demographic variables can- not be separated from simple time trends. Lew- bel (1989, p. 353) concluded that there is insuf- ficient variation in time-series data to identify a reasonable range of demographic effects on tastes. Although non-economic factors are not explicit in the statistical analysis, they may be absorbed by economic factors. A perfect capturer is the expenditure variable, 5 which shows an almost monotonically increasing trend over the observa- tion period. There is some evidence that price effects have also been attributed to demographic variables that are correlated with prices (Buse 4 In the present study, the consumption decisions are assumed to be based on current income. This current in- come hypothesis could be replaced by e.g. the permanent income hypothesis or by the relative income hypothesis. In the case of cross-sectional data, the relative income hypothesis could be interpreted as “keeping up with the Joneses” effect, in the case of time-series data consumers are assumed to keep up with their own established stand- ard of living, and thus consumers’ income is related to the prior level. Since the present study focuses on analysing merely non-durable goods which are consumed within the same period they are purchased, the current income hy- pothesis is a relevant approach. ’Because of the requirements of the econometric meth- odology applied, in the present study households’ total expenditure is used as an indicator of income. 1986). Potential variables-to-be-absorbed are the demographic variables that show linear popula- tion dynamics, such as age structure and changes in the size of household, diminishing rural popu- lation, ethnic food consumption, shift from food producers to food consumers, and increase of ca- tered food (see Roos and Ahola 1989 on demo- graphic and life-style factors in Finland). Contrary to certain demographic variables, many socio-cultural variables are probably much less linear. For example, Prättälä (1989, p. 53- 54) found a duality in cultural attitudes towards food that divides food into “real” foods and “junk” foods, or foods filling nutritional needs and foods for fun, such as energy-rich, high-fat desserts and snacks. Consumers have an interest in healthier eating and drinking. Growing interest in nutrition means that less fat, especially animal fat, less cholesterol, and more fibre are used. Some of the shift from butter to margarine must be attributed to health concerns related to butter. Consumers worry about chemicals, additives, and hard tech- nology. The concern ranges from the way the raw-materials are grown to the nutritional value of the product, from well-being of domestic ani- mals to environmental friendliness of packaging. Consumption patterns have become more frag- mented. Some favour convenience in food pur- chasing and consumption, others favour less processing. Some life styles increase the interest in gourmet food. Travelling and internationalisa- tion ofall sorts probably brings more variation in eating. Advertising, accompanied with conven- ience-oriented supply of value-added items, fan- cy packaging, and myriad brandname aim to in- fluence consumers’ preferences and increase the overall consumption. Some foods are for break- fast, some for Christmas dinner, some for snacks, some for “real” meals. A whole new research scheme would be required to study the changes in the rule of etiquette, the nature of the occa- sions on which food items are consumed, and the symbolic meaning of food {e.g. Gofton 1986). It is obvious that the changes in the consump- tion of food items depend on a great number of determinants. However, to make the analysis fea- sible, the number of factors under consideration 338 Agricultural Science in Finland 3 (1994) must be limited. While the importance of demo- graphic and socio-cultural variables must not be forgotten, they probably play a minor role at the aggregation level adopted in this study. For ex- ample, the demand for fresh milk will be studied as a combined bundle, rather than the demand for various types of fresh milk. The adopted method- ology allows the demand system to take into ac- count certain amount of socio-cultural effects via the structural change parameters. For example, possible changes that have taken place in con- sumer attitudes towards milk products, butter, margarine, and alcoholic drinks can be taken into account to some degree. The paradigm of the present study follows the main-stream of economics, which implies that the demand theory is employed in order to focus on essential factors. Consequently, the models will be a group of abstractions that represent simplifi- cations of a very complex reality. 3.2 System of choice: preferences and utility maximisation In the present study a complete demand system approach is adopted. The approach gives sub- stantial importance to the properties of consumer behaviour implied by the demand theory. Thus, it is reasonable to discuss the theory which gives a framework to derive demand functions from a model of utility-maximising consumer and a rep- resentation of the consumer’s budget constraint. In the theory, preference ordering gives rise to a utility function that, in turn, gives rise to demand functions. Let q= (q ~..,qn ) be a commodity vector, where n is the number of goods and q. is the quantity of the ith commodity (for i = 1 ~..,n). Let the sym- bols >, >, ~ denote “strictly preferred to,” “weak- ly preferred to,” and “indifferent to,” respective- ly. The following axioms of choice describe the consumer’s preferences (Deaton and Muellbau- er 1980b, Ch. 2.1, Varian 1992, Ch. 7.1): (a) Completeness, or comparability. For any two bundles qt and qr q t >q 2 or q 2 >q, or q 2 and q 2 >q } then qt > q( , which is to say, for example, that if the consumer prefers an apple to an orange and an orange to a banana, he is expected to pre- fer an apple to a banana. (c) Continuity means that all the vectors of goods in the choice set are closed, i.e. the sets con- tain their own boundaries. (d) Non-satiation, or strong monotonicity, states that for any two bundles qt and q„ if q,> q2 then q > q 2, or, the consumer prefers more to less. This axiom restricts the preferences so that the best choice lies on the budget con- straint, not inside it. (e) Strict convexity states that, if q : ~ q 2 and q : A q 2, then Xq t +(1 -X)q2 > q2 <=> D(0,) > x>(q2 ). The term u stands for a certain level of utility. The direct utility function (3) is an ordinal measure showing in which order the bundles are situated, ranging from the least pre- ferred bundle to the most preferred bundle. Giv- en also the axiom (e), the utility function is strictly quasi concave (Chiang 1984, p. 403). The axioms on the consumer’s preference or- dering define a rational consumer who chooses the most preferred bundle from the set of bundles that the consumer can afford. Given the conven- 339 Agricultural Science in Finland 3 (1994) tional linear budget constraint, utility maximisa- tion states that the consumer allocates his total expenditure, x , so that expenditure necessary to reach a certain level of utility u: n " Minimise x= V p jqi subject to t) ( q) = u (7) Maximise u= \) (q) subject to pj q j = x (4) _ j = 1 where p. is the price of good i. To attain from utility to demand functions, one solves the first order conditions of (4), or the primal (or origi- nal) problem. The result is the system of Mar- shallian [income-uncompensated] demand func- tions, for i = 1,...,n, ) (5) Substituting (5) into (3) yields the indirect util- ity function U = M [g,- (x, p) ] =Mf(x,p) (6) The weakness of the primal problem is that the first order conditions are rarely solvable. Du- ality provides an alternative way to construct a demand function which is solvable in terms of the preferences and utility maximisation princi- ple presented above. 3.3 Duality in deriving a demand system Duality provides four equivalent ways of repre- senting consumer preferences: (a) direct utility function, (b) indirect utility function, (c) expend- iture function, and (d) transformation or distance function. By using duality relationships, theoreti- cally plausible demand systems can be obtained by relatively simple differentiationrather than by direct optimisation techniques (Blanciforti et al. 1986). The primal problem, or utility maximisation, states that a consumer maximises utility for a given expenditure. The solution is a set of Mar- shallian demand functions, defined on prices and expenditure. Now the problem is reformulated. The dual problem, or cost minimisation, states that the consumer selects goods to minimise the Solution of this cost-minimising problem is the system of Hicksian [income-compensated] de- mand functions, 6 defined on prices and utility, for i = 1,...,n, q i = h t (u,p) (8) Substitution of (8) into the budget constraint yields the cost or expenditure function n x = X PihM>p) =c(nf p) i = 1 (9) The expenditure function shows the minimum expenditure of attaining a given level of utility with alternative prices. The Marshallian demand functions indicate how q is affected by prices with x held constant, while Hicksian demand functions tell how q is affected by prices with u held constant. In both problems, optimal bundles are sought. The solutions of the primal and dual problems are identical, or q = =h [v(g {x.p })/>]. Thus, the vector ofgoods chosen is the same in both cases, and the expend- iture in the primal problem is the cost minimum in the dual problem. The choice of functions de- pends on the accessibility of the required varia- bles. Utility cannot be measured directly. The em- pirical work concentrates on the resulting demand functions, and uses the underlying utility theory as a benchmark to understand the dependencies. Thus, the demand equations which are applied for empirical analysis should be the Marshallian type. 6 For example, the income-compensated effect of a change in the price of commodity i requires that the in- come effect is eliminated by compensating the fall in real expenditure, and what remains is the substitution effect. Thus, compensated demand function assumes constant ex- penditure in real prices, while uncompensated demand function assumes constant expenditure in nominal prices. 340 Agricultural Science in Finland 3 (1994) A stepwise procedure is used to derive Mar- shallian demand functions from the expenditure function that is available. First, Shephard’s Lem- ma is employed to move from the known ex- penditure function to the cost-minimising demand functions that underlie it. In the procedure, the expenditure function is partially differentiated to obtain Hicksian demand functions, which conse- quently are the partial derivatives of the expendi- ture function with respect to prices (Step 1 in Figure 7). Then, since the expenditure and indi- rect utility functions are inverses, the expendi- ture function is inverted to obtain the correspond- ing indirect utility function (Step 2). The indirect utility function indicates the highest level of util- ity that can be obtained for the given prices and income. Finally, the indirect utility function is substituted into the Hicksian demand functions. The result is the desired system of Marshallian demand functions (Step 3). The functions attached to the Almost Ideal Demand System (AIDS), the demand system used in the present study, are spec- ified in more detail in Chapter 4. The duality approach to the consumer theory is presented com- pletely in Deaton and Muellbauer (1980b, Sec- tion 2.3). There are five properties that the expenditure function must satisfy before it can be used in the procedure: (a) Homogeneity. The expenditure function is ho- mogeneous of degree one in prices, or for 0 > 0, c(u,6pr ...,0pn ) = 6c(u,p t ,...,pn). The prop- erty follows from the linear budget constraint. For example, if prices double, twice as much total expenditure is required to stay on the same indifference curve. Note the difference between overall price level and relative pric- es. If all prices go up by 5%, there will be no relative price effect, but only an impact on the real purchasing power of incomes, which would decline by 5% in real terms. (b) “No-free-lunch.” The expenditure function is increasing in u, non-decreasing in p, and in- creasing in at least one price. Thus, for ex- ample, at given prices the consumer has to spend more to be better off, or if u > u ’ then c(M,p 1,...,pn ) > c(m’ ,p x And, if the pric- es increase, at least as much expenditure is needed to stay on the same utility level, or if P, P ’ then c(u,pv ...,pn ) > c(u,p{„ The properties follow from the non-satiation axi- om. (c) Concavity. The expenditure function is con- cave in prices, or for 0 < 0 < 1, c[u,Qp + (1- 6)p t ',....9pn + (1 ~0)P„1 > dc(u,pr ...,pj + (1- The concavity implies, for ex- ample, that, when prices increase, expendi- ture will increase no more than linearly be- cause the consumer minimises expenditures by rearranging purchases in order to take ad- vantage of the changes in the price structure. A necessary condition for concavity is that all the diagonal elements of the matrix of the compensated price elasticities are non-posi- tive. Thus, violation of concavity may be the reason if one obtains positive compensated own-price elasticities. (d) Continuity. Following from the concavity, the Fig. 7. Duality in deriving the Marshallian demand func- tions. 341 Agricultural Science in Finland 3 (1994) expenditure function is continuous in prices p , for p. > 0 for all i. (e) Applicability. Following from the continuity, where they exist, the partial derivatives of the expenditure function with respect to pric- es p. are the Hicksian demand functions. Shep- hard’s Lemma - employed in deriving the demand system (Figure 7) - is derived from this property. It is relatively easy to specify an expenditure function which satisfies the five properties stated above. Duality provides a procedure to derive the required Marshallian demand functions. The strength of the method is that the attained func- tions automatically satisfy certain restrictions, namely adding-up, homogeneity, symmetry, and negativity. On the contrary to the described meth- od, Marshallian demand functions could also be specified directly. Whatever was the method - derivation or direct specification - the fulfillment of the four requirements may be checked ex post, and the results show whether the demand func- tions correspond to the consistent preference or- dering. 3.4 Slutsky conditions for symmetry and negativity To be able to test symmetry and negativity of a set of demand functions, one has to calculate the substitution or Slutsky matrix, S, of compensated price responses, which is symmetric and nega- tive semidefinite by the symmetry and negativity properties. 7 To make it empirically attainable, S must be defined in terms of the Marshallian de- mand functions. This is done through the Slutsky equation dh; _ dgt dg,. S ‘j dpj + dpj (10) 7 The adding-up, homogeneity, symmetry, and negativ- ity properties, and the decomposition of a price change into a substitution effect and income effect were first stat- ed explicitly in Slutsky (1915). where s.. is the unobservable substitution effectu of a price change, or compensated price response, where i denotes the commodity affected, and j the commodity the price of which has changed. g. is the Marshallian demand function (5), h i is dg, the Hicksian demand function (8), is the observable income effect of price change, and dg, is the observable uncompensated price re- sponse. Thus, the Slutsky equation links the price derivatives of compensated and uncompensated demand functions. By rearranging, the Slutsky equation dgi dg, Sfj = s‘rTx qJ (ID dB, divides the total effect of price change, into a substitution effect, s , and an income ef- ‘J dx, feet, Qj . If s > O, goods i and j are substi- tutes, or Hicksian substitutes, and if .? < 0, the fJ goods are complements, or Hicksian complements (the definitions originate from Hicks 1936). If dg, dg, > 0 or < 0, goods i and j are classified into gross substitutes or gross complements, re- spectively. The conditions also state a negative own-price and symmetric cross-price effects. However, the “law of demand” (Section 4.3) does not neces- sarily apply to the Marshallian demand functions. It becomes clear when rearranging (11) such as dg/ "s"- a 7 q‘ (12) As the price changes, the quantity demanded depends on the combination of income and sub- 342 Agricultural Science in Finland 3 (1994) stitution effects. Although the compensated own- positive price response is possible if the good is price response, s, is negative, it is possible that highly inferior and it is purchased in large quan- it is outweighed by a positive income effect. A tities. This kind of good is called a Giffen good. 4 Demand system specification and estimation 4.1 Complete demand systems approach: literature review In the previous chapter, the framework for the further work was provided. The presented de- mand theory is not informative about appropriate choices for functional form and other aspects of the model specification. Various specifications have been suggested. The short history of empirical demand analy- sis presented here starts with a single equation methodology known as Stone’s analysis (Stone 1954a). Stone’s methodology models commodity demands individually, equation by equation. The elasticities can be measured directly as the pa- rameters of a regression equation linear in the logarithms of total expenditure and prices. The advantage of the methodology is flexibility, i.e. if necessary, the functional form can be varied and extra explanatory variables can be attached from commodity to commodity. However, the methodology is not consistent with the demand theory, which implies that, for example, most of the restrictions derived from the theory have no consequence for the analysis. Since Stone’s analysis is not very well consist- ent with the theory, researchers started to work with the applications to complete systems of equa- tions where theory becomes more relevant. Com- plete demand systems approach gives substantial importance to the preference ordering, which gives rise to the utility function, which, in turn, gener- ates the demand functions. The common feature for the systems is that they allow - at least after the estimation- for checking if the model is con- sistent with the Slutsky conditions (adding-up, homogeneity, symmetry, and negativity). The sys- tems describe the allocation of expenditures among commodities in a way that the expendi- tures on sub-groups sum up to the total expendi- ture. Also, the systems account for interdepend- ency among commodities, and they try to specify a sound correspondence between the theory on an individual consumer and the market data. In specifying a complete Marshallian demand sys- tem, two approaches have commonly been used: (1) an approach based on a specific functional form for (a) direct utility function (e.g. the Line- ar Expenditure System), (b) indirect utility func- tion (the Translog model), or (c) expenditure func- tion (e.g. the Almost Ideal Demand System); and (2) an approach approximating the demand sys- tem directly (the Rotterdam model) (Huang and Haidacher 1983). Stone (1954b) started the era of complete sys- tems approach in demand analysis with his Line- ar Expenditure System (LES). The revolutionary point in the new approach was the attempt to incorporate the elements of microeconomic theo- ry of consumer demand in the analysis. The aim was to formulate a model which allows an empir- ical application of the theory at a very general level. The big advantage of the LES, in addition to the consistency with the theory, is that only (2n-l) parameters have to be estimated, and thus the method can be applied to a relatively large number of commodity groups (n is the number of commodities in the system). On the other hand, the LES suffers from inflexibility: the system has too few parameters to allow to test the consumer theory. There was a need for more general ap- proaches. Various types of empirical demand systems have been proposed since the LES. The Rotter- dam model was introduced as more testable (Theil 1965, 1975, 1976, Barten 1969). The Rotter- 343 Agricultural Science in Finland 3 (1994) dam model is still widely used. Model devel- opment was directed towards flexible function- al forms.8 The most commonly cited flexible functional forms are the Indirect Translog System by Christensen et al. (1975) and the Almost Ideal Demand System (AIDS) by Deaton and Muellbauer (1980a, b), but there are many other forms (for a review, Edgerton 1990). Flexibility in the context of demand systems analysis means that the model has so many esti- mated parameters that the direct or indirect utili- ty or expenditure function - which presumably generates the demand - can be estimated. The demand system allows explicit testing of the re- strictions implied by the demand theory. Flexi- bility implies that the demand equations are de- rived by approximating a generating function ( i.e. the expenditure function in case of the AIDS) in such a way that the Slutsky conditions and local flexibility are satisfied. A function is locally flex- ible if it can provide arbitrary (i.e. inconsistent) values of the elasticities at a particular set of prices and expenditure (Edgerton 1990). On the other hand, an inflexible function has elasticities that are constant, while prices and expenditure vary. Regarding to scientific journals, the AIDS (or its linear approximation, the LAIDS) now ap- pears to be the most popular of all demand sys- tems. However, all the introduced functional forms are widely used. Large is also the literature in which various functional forms are compared with each others. Manser (1976) presented a compar- ison between various specifications of the Trans- log model. She concluded that elasticity estimates for four food aggregates in the United States were very sensitive to the choice of the functional form. Klevmarken (1979) compared various specifi- cations of the LES, the Rotterdam model, and the Translog model by using Swedish expenditure data. In terms of goodness of fit, prediction error, and negativity of own-price elasticities, e.., the 8 Recently the Rotterdam model has been found to be as flexible as any other locally flexible functional form (Alston and Chalfant 1993). LES with habit formation was named as the pre- ferred specification. Goddard (1983) compared the LES and the AIDS using Canadian time-se- ries on food aggregates. The results suggested that, because of the greater sensitivity of the AIDS to the data (the LES is too restrictive a form), its use in research designed to estimate demand elas- ticities is preferable. Blanciforti et al. (1986) compared static and dynamic versions of the AIDS, the LAIDS, and the LES by employing expenditure data on four food aggregates in the United States. They con- cluded that (a) dynamic models were preferred over their static counterparts, (b) the AIDS was superior on a within-sample error criterion, where- as the LES was superior for the particular years outside the sample, and (c) in general, the AIDS and LAIDS gave higher price elasticities, e , and lower expenditure elasticities, E., than the LES. Hansen and Sienknecht (1989) compared dif- ferent flexible functional forms, for example, a generalisation of the LES, various versions of the Translog model, and the AIDS. They con- cluded that the compared flexible demand sys- tems gave similar results with respect to good- ness-of-fit measures and income elasticities, while there was rather great variation with respect to own-price elasticities. Mergos and Donatos (1989) compared elasticities obtained from the Rotterdam model, the AIDS, and the LES using time-series on food expenditures in Greece. The elasticities obtained using the AIDS were rather similar to those of the Rotterdam model, but quite different from those of the LES. The LES gave smaller expenditure elasticities than the AIDS and the Rotterdam model, whereas the LES gave con- sistently the lowest and the Rotterdam model the highest price elasticities among the three models. The authors concluded that the elasticities ob- tained using the AIDS were superior when judged on the basis of a priori expectations. Alston and Chalfant (1993) developed a test of the LAIDS against the Rotterdam model, and vice versa. In an application to the meat demand in the United States, the LAIDS was rejected, while the Rotterdam model was not. However, the authors stressed that the result should not be 344 Agricultural Science in Finland 3 (1994) interpreted as evidence that the Rotterdam model is superior in any general way. The AIDS has several advantages over the other forms. First, the AIDS is derived from a utility function which assumes weak separability (Sec- tion 4.6). Thus, the AIDS is indirectly non-addi- tive, allowing the consumption of one good to affect the marginal utility on another good. Weak separability is a less restrictive assumption than the assumption behind the LES, i.e. strong sepa- rability (additivity of preferences). Derived from additive utility functions, the LES assumes that the preference ordering is additive. This means that the marginal utility provided by the consump- tion of a good is independent of the consumption of other goods. An implication is that the LES shows an approximate proportional relationship between estimated expenditure and own-price elasticities (so-called Pigou’s law or relationship). This non-flexibility is not true with the AIDS (Deaton and Muellbauer 1980b, p. 137-142, Craven and Haidacher 1987). There are more non-flexibilities in elasticities of the LES. In the LES, marginal budget shares are restricted to be positive. An implication is that the expenditure elasticity becomes more elastic for a non-inferior necessity (0 < E.< 1) as its budget share, w, decreases. This is quite a restrictive assumption. In the AIDS, marginal budget shares are not re- stricted to be positive and, thus, expenditure elas- ticity can become less elastic as its budget share decreases. In the LES, as the ith budget share decreases, the own-price elasticity becomes more inelastic (assuming the marginal budget share to be between 0 and 1). Actually, this is the phe- nomenon that one would expect, but still it is a restrictive assumption. The AIDS does not pre- judge the sign to the change in e with respect to a change in w. (Blanciforti and Green 1983b, Blanciforti et al. 1986). Second, the AIDS expenditure function has the property of a flexible functional form: it contains sufficient parameters to be regarded as a close approximation to any expenditure function and hence any underlying preference ordering. Con- sequently, the AIDS demand functions contain sufficient parameters to be regarded as a first- order approximation to any observed demand sys- tem - i.e. the unknown relation between w , In x, ir r and In p : - derived from utility maximisation. This generality holds whether the system is con- sistent with the demand theory or not. Despite the flexibility, the AIDS is easier to estimate than e.g. the Translog models. Moreover, the Translog models require more sample information since the number of parameters to be estimated is larg- er (Thomas 1985, p. 153, Teklu et al. 1992, p. 53-54). Third, systems whose derivation starts from preferences represented by a price-independent, generalised logarithmic (PIGLOG) (or price-in- dependent, generalised linear, PIGL) expenditure function will in general have better aggregation properties than other systems (Edgerton 1990, p. 32). Contrary to, for example, the LES, the Rotterdam model, and the Translog model, the AIDS is based on PIGLOG. The AIDS is as flex- ible as other locally flexible functional forms (such as the Translog), but has the additional advan- tage of being compatible with aggregation over consumers (Alston and Chalfant 1993). Al- though the AIDS is principally valid only at the micro level, it can be generalised to the aggre- gate level by redefining w as the aggregate budg- et share, and x as the mean expenditure. The ag- gregate expenditure should be divided by an ap- propriate measure of the population size, which should take into account demographic changes. In time-series data the rate of demographic change is, however, probably so slow that a reasonable approximation can be obtained by dividing the aggregate expenditure by the mean population (Edgerton 1992b). Fourth, both the LES and the AIDS are de- rived from the microeconomic theory. When the AIDS suits well for testing the Slutsky condi- tions of homogeneity and symmetry, in the LES the restrictions are imposed a priori, and thus it is impossible to test them. The AIDS suffers from the same disadvantag- es as most of the methods employed to analyse demand. First, the AIDS suffers from lack of de- grees of freedom, and if this is overcome by im- posing restrictions, there may exist a contradic- 345 Agricultural Science in Finland 3 (1994) tion between these restrictions and the data (Dea- ton and Muellbauer 1980b, p. 79). Second, there is a separability problem that arises from the fact that econometric analysis deals, not with individ- ual commodities, but with bundles. Third, there is an aggregation problem that arises from the fact that the demand theory describes the behav- iour of one consumer, while the data set which is used in the present analysis refers to markets in which all the consumers operate. Aggregation the- ory is intended to provide the necessary condi- tions under which it is possible to treat aggregate consumer behaviour as if it were the outcome of the decisions of a single maximising consumer. Deaton and Muellbauer (1980b, p. 79) men- tion two other disadvantages, i.e. the existence of dynamic misspecification and important explana- tory variables other than prices and total expend- iture. These problems are alleviated in the present study by introducing dynamics and allowing struc- tural change in parameters. 4.2 Derivation of the Almost Ideal Demand System Engel curves show the relationships between various income (expenditure) levels and pur- chased volumes, per unit of time, given constant prices and constant consumer preferences or in- difference map. A number of functional forms for Engel curves has been experimented (Deaton and Muellbauer 1980b, p. 19-20). A form which is consistent with adding up originates from Working (1943) and Leser (1963). The AIDS is an extension of their Engel curve formu- lation - extended by Deaton and Muellbauer (1980a, b) - where value shares at time t , w.t, are related to the logarithm of the total expendi- ture, x’ t w i, = «, + A lnx , (13) However, the parameters have to be made func- tions of prices to extend the model to include price effects. The ground for that is laid using duality (Section 3.3). Instead of choosing quanti- ties to maximise utility subject to budget con- straint, the quantities are chosen to minimise ex- penditure needed to obtain a given utility. The AIDS Marshallian demand function is derived by minimising the expenditure function (rather than maximising the utility function). Thus, the ex- penditure function has to be specified first. The AIDS is derived from the consumer expenditure function. In c(u tp), for the price-independent, gen- eralised logarithmic (PIGLOG) class of consum- er preferences In*, = Inc ( m,, p t ) = a (/>,) + ufi (p,) (14) that is linear in utility and nonlinear in prices, and where x is the minimum level of expenditure that is necessary to achieve a given utility level U' (0 < m ( < 1) (or, minimum cost of reaching indifference curve u) at given vector of prices p {=p 1t,...,pn), and a(p) and bip ) are functions of prices alone that are to be chosen. Two selection criteria have been used. For In a(p), a sufficient number of parameters was desired in order to obtain a locally flexible functional form; for In b(p ), a convenient choice led to the Engel curves (13) (Chalfant 1987). The price aggregator func- tion a(p) shows the fixed cost, or the cost of subsistence consumption (« = 0), of the follow- ing form n a W = «o + Z ak lnPk, * = 1 (15) n n + '/>Z Z ylj lnPk,' n Pp k = l7=l and b(pt ) shows the cost of joyconsumption (u=l) such as n h(p,) =PoUPP k, (16) k = I where pk and p are prices. The equations (14) to (16) generate the AIDS expenditure function of 1346 Agricultural Science in Finland 3 (1994) the following form (Deaton and Muellbauer 1980a) n Inx, = Inc («,./>,) = a o + £ ak \np kl k = 1 (17) n n n +'h Z Z yljXnPk, lnPj, + uA O p p kt k=l7= I k = 1 where a f), at, /J n , j3k , and y are parameters. For c(urp) to be homogeneous of degree one in pric- es p r the parameters should satisfy Z«* = Z y*kj = Z Skj =Zh = 0 (18) * = I * = I 7=l * = I By using the duality, (17) will be minimised to yield the AIDS Marshallian demand functions. Referring to Figure 7, a three-step procedure to derive the AIDS is as follows. Step 1: From expenditure function to the Hick- sian demandfunctions Shephard’s Lemma is applied to achieve the Hick- sian or compensated demand functions. The Lem- ma means that (17) is differentiated with respect to prices. Simultaneously, the equation is switched to budget shares w . The result is a Hicksian de- mand function for commodity i, dine(ur pt ) _ 9lnxf _ pjtqit _ ainp. “ 01np ~ x ~ “ " " ' (19) n n = «, + Z yik XnPk, + Pi uAU.Pki k= 1 k = 1 where q is quantity, x total expenditure, and y = V 2 (Y*it+fj (Deaton and Muellbauer 1980a). Step 2: From expenditurefunction to the indirect utilityfunction Since u is unobservable, the expenditure function (17) and the resulting share equations (19) can- not be estimated. That is why (14) is inverted to gather an expression for utility, or the correspond- ing indirect utility function In x -a(p ) - 1 = Vl*rP,>- bf ) ‘ (20) n n n lnv,-«o- Z ak [n Pk,~'/i Z Z ylj lnPk, ]nPj, k_=_\ k = 1 / = 1 h fl pH k = I which is the real value of expenditure in excess of that required for subsistence (Deaton and Mu- ellbauer 1980b, p. 144). Step 3: From indirect utilityfunction to the Mar- shallian demandfunctions Finally, (20) is substituted into each share equa- tion (19), which gives a Marshallian demand func- tion, or the AIDS, for commodity j=1,...,n, "(x ' wu = «/+ Z Vn p„+A |n y (2i) 7=l x wherep. t is the price of theyth commodity within the group, x is the representative total expendi- ture of the group, which is approximated by the per capita total expenditure of the group (Sec- tion 4.5). The term (x/F) is the nominal expendi- ture deflated by the group price index P defined by n Xnp , = «0+ Z ak XnPkl k = 1 (22) n n +'A Z Z VnVn/,y, k =ly=l It is noteworthy that (21) is nonlinear in the parameters because of the definition of (22); it is only the term /JinPt in (21) that causes non-line- arity in the parameters. A linear form of the AIDS, the LAIDS, is obtained by replacing the price index (22) by Stone’s (1954a) geometric share- weighted price index, such as n \nP* = ao + £ wkl \npkt k = 1 (23) 347 Agricultural Science in Finland 3 (1994) The LAIDS has shown to be a good approxi- mation to the AIDS (e.g. Blanciforti and Green 1983b), and it has been used more often than the AIDS. The interpretation of the parameters in (21) and (22) is as follows. The intercept a represents the ith budget share when expenditure is at the subsistence level, or all logarithmic prices and logarithmic real expenditure In(x/P) equal zero (then w.= a). The parameters y.{= dw/dlnp) meas- ure the change in the /th budget share following a unit proportional (one percent) change in p with (x/P) held constant. The parameter 6 [= dwJ d\n(x/P)] measures the change in the Ith budget share with respect to a one percent change in the real expenditure with prices held constant. With B. > 0, w. increases with x so that good i is a luxury; with 6 < 0, the good is a necessity. The intercept a () can be interpreted as the expenditure required for a minimum standard of living when prices equal one, as in the base year [then a(p ) = «o >n (15)]. 4.3 Slutsky conditions on the AIDS To be consistent with the consumer preferences (utility maximisation), a set of Marshallian de- mand functions, like the AIDS functions (21) and (22), ought to add up, be homogeneous of degree zero in prices and the total expenditure, and their compensated price responses ought to be sym- metric and form a negative semidefinite matrix. The properties, called the Slutsky conditions (Bar- ten 1967), are presented in terms of the AIDS parameters and elasticities, and budget shares. Negativity can be imposed on the AIDS only lo- cally at a point, whereas adding-up, homogenei- ty, and symmetry can be globally imposed by means of parametric restrictions. Adding-up The adding-up restriction is an implication of the linearbudget constraint and the non-satiation prop- erty of consumer preferences. The property means that demand functions satisfy the budget con- straint, or the sum of the purchases equals the total expenditure, or n n x = X P.Bi (x’ P ] '■ Xwi = 1 (24) I=l / = 1 where g is the Marshallian demand function [ zr =Z— <=> •J J‘ dpj 3/7,. Pj (30) = «J( eji +w iE? Pi where an element in the Slutsky matrix (s ) is expressed in terms of quantities, budget shares, and elasticities (Edgerton 1990). An implication of the condition is that, for i,y=1,...,n, i A j k.. = k o vv. (e. +vv E ) = w (e . + w E .) ij ji / v ij j i> j y ji i j' (31) <=> we - = w e • • u J Ji where k is an element in a substitution matrix K •J(k.. = ppsjx), and e.. is the compensated price elasticity (Edgerton 1990). For (21) the Slutsky symmetry condition implies that, for i,j = !,...,« (Deaton and Muellbauer 1980b, p. 76) dw. dw ■ y.. = y .. <=> ——— = J 'J‘ 3lnpj 3lnp( (32) Negativity of compensated own-price elasticities Negativity or concavity is another consequence of the existence of consistent preferences and the Slutsky equation. Negativity implies e.g. that the compensated price responses of demand functions form a negative semi-definite Slutsky matrix S. The diagonal elements of the Slutsky matrix must be non-positive for all commodities. Thus, an increase in p. with utility held constant cannot increase the compensated demand for /, or, for all i. 5,.<° (33) which is the “law of demand” that compensated demand functions can never slope upwards (Dea- ton and Muellbauer 1980b, p. 44). This means that an increase in the price with utility held con- stant must cause the demand for that good to fall or remain unchanged. Within the AIDS, it is easi- er to use, not matrix S, but matrix K, the ele- ments of which are, for all i and j k.. =y. + 88.ln[ -w5 .+ww .i; lij nt'j V PJ 1 ‘J 1 J (34) where 5 is the Kronecker’s delta (5 = 1 when i ij v ij = j and 5, = 0 when i *j) (Deaton and Muell- bauer 1980a). Since the diagonal elements of matrix K have the same signs as those of matrix S (k.. - ppsjx), negativity is obtained when the matrices K are negative semidefinite. Accompa- nied with the implication for elasticities, the prop- erty is written as eu + wjE j k u < 0 (35) 349 Agricultural Science in Finland 3 (1994) where e is uncompensated own-price elasticity, and e is compensated own-price elasticity (Edg- erton 1990). Non-negativity of quantities Non-negativity ofquantities or monotonicity sim- ply means that Marshallian demand functions must imply non-negative quantities consumed. Conse- quently, for the restriction, budget shares must all be between 0 and 1. The restriction is trivial if the data set is properly defined. Estimation of the AIDS automatically satisfies adding-up (provided the data do). In restricted estimation homogeneity and symmetry are en- forced by imposing (29) and (32) on (21) and (22). In unrestricted estimation, (29) and (32) are not imposed. The conditions can be used to test the consistency of the demand system with the theory. The negativity condition can be checked after the model is estimated. 9 Providing the con- dition is satisfied, é ,.s are non-positive. Imposition of the restrictions is reasonable be- cause it decreases the number of parameters to be estimated. In absence of restrictions, given the demand functions (5), there will be n2 + n param- eters to be estimated (n 2 price and n expenditure parameters), where n is the number of equations in the system and also the number of commodi- ties. Imposing adding-up, which implies one re- striction, the number of estimated parameters is reduced to n 2 + n- 1. Imposing also symmetry, which implies xh (n 2 -n) restrictions, the number of independent parameters is reduced to V 2 n2 + n + y2 «—1. Adding-up and symmetry together im- ply homogeneity, which implies n restrictions and, thus, the number of estimated parameters is re- duced to V2(n2 + n)- 1. Negativity has to be ig- nored because it is difficult to impose. Given in- tercepts are incorporated, the number of independ- ent parameters increases to V 2(n2 + n)- 1 + (n-1). 9 The negativity can only be checked for a particular range of prices and expenditure. It is obvious that the AIDS can merely be locally regular (Edgerton 1990, p. 13, 20). To be globally regular, the AIDS should satisfy the Slutsky conditions for all prices and expenditures. In the present study, there are 18 food bundles to be estimated. The system estimation is required, since the imposition of adding-up and symmetry requires simultaneous estimation of all demand equations in the system. Thus, at least 170 pa- rameters should be estimated simultaneously (giv- en only price and expenditure parameters are es- timated). If the homogeneity and symmetry re- strictions were not imposed, the number of inde- pendent parameters would increase. The increase in the number of parameters caused by the non- imposition of homogeneity and symmetry is some- what compensated by the fact that the adding-up restriction will replace n of the symmetry restric- tions. However, related to the available data and computing power, the number of parameters to be estimated is too high. Thus, further restric- tions on demand equations has to be imposed. This is done by making assumptions about the consumer’s preferences. Separability of prefer- ences is of great importance in demand systems analysis (Section 4.6). 4,4 Extensions of the AIDS In order to achieve a better fit of the data, several variations of the standard static AIDS have been suggested. In the empirical application of the present study, a dynamic AIDS and a dynamic AIDS incorporating systematic demand shifters are employed. 4.4.1 Dynamic AIDS The consumer choice problem in a neoclassical model depends on decisions for a single period of time. However, due to factors such as consum- er adjustments to changes in prices and income the choice problem may not be complete during the single period of time, thus making past con- sumption patterns an important determinant of present consumption patterns (Pollak 1970,God- dard 1983, Johnson et al. 1986, Blanciforti et al. 1986. Capps and Havlicek 1987). Hence, the static theoretical framework is extended to a dy- namic theoretical framework. There are alterna- 350 Agricultural Science in Finland 3 (1994) live approaches to consumer dynamics in the con- text of the AIDS. One alternative, referred to as translating, is to allow some of the parameters of the demand equations to depend upon previous consumption levels (Pollak and Wales 1981, Blanciforti and Green 1983a, Blanciforti et al. 1986, Chen and Veeman 1991). In translat- ing, the dynamic feature in the adjustment of de- mand is incorporated by introducing w-period lagged consumption levels, q ,to the PIGLOG consumer expenditure function. Another alterna- tive, adopted in the presented study, is to speci- fy a dynamic expenditure function through the introduction of m-period lagged budget shares, w. ,to the PIGLOG consumer expenditure func- tion. Consequently, the demand equations will include lagged dependent variables. From the econometric point of view, the dy- namics is introduced because static models often suffer from serious serial correlation in the esti- mated residuals, thus indicating that the underly- ing models are misspecified. The Slutsky condi- tions may be rejected in empirical studies, be- cause too little attention is paid to the dynamic aspects of consumer behaviour. The existence of cost adjustment and the costs involved in obtain- ing the information necessary for an immediate equilibrium decision imply that dynamic specifi- cations should be considered when modelling de- mand functions (Deaton and Muellbauer 1980a, Anderson and Blundell 1982). It is unlikely that consumers adjust to equilib- rium within a time period (Anderson and Blun- dell 1983). Habit persistence, adjustment costs, incorrect expectations, and misinterpreted real price changes are examples of the many possible reasons for such short-term behaviour. Due to habit formation and adjustment costs, a consum- er faces a utility loss because it takes a certain time before he fully adjusts his consumption in response to changes in prices and income. Re- stated, consumers are supposed to carry stocks of habits which cause adjustments costs when con- sumers change habits. For example, if a consum- er is used to eating meat, it takes time before he will take full advantage of a sharply decreased price of fish. The consumer is allowed to adjust his budget gradually to the change in relative prices. A dynamic AIDS with a vector of lagged budget shares was proposed by Alessie and Kapteyn (1991) 10 and Assarsson (1991) (see also Edger- ton 1992a, Rickertsen 1992). The model was modified from the interrelated partial-adjustment model suggested by Anderson and Blundell (1982, 1983, 1984). Habits are introduced as ad- justment costs in the AIDS expenditure function (17) such as (Rickertsen 1992): n In*, = Inc(u p pr w t_ m) = a,, + £ «*lnpt, * = 1 n M n + 1 X 'L dkjm Wj(l -m)'n Pk, k= 1 m = 1 y=l (36)n n +V: Z S Vn/>*, ln P„ £ = 1 y=l +uA nPu k = 1 where m is the length of a lag. In order to save degrees of freedom, only a one-period lag is used n M n (M-\). The term XXX 0 vv In», describes an adjustment cost resulting from habit persistence. Derived from (36), the Marshallian demand functions, or the dynamic AIDS with a one period lag is defined by n wu = «,-+ X V)(i-D y= i (37) " f* 'I+Z V + A ln J j~ i '' “According to Alessie and Kapteyn (1991), the mi- cro-model should include at least three taste shifters, viz. demographic effects, habit formation, and preference in- terdependence. They built these effects into the AIDS. 351 Agricultural Science in Finland 3 (1994) where w.t is the ith budget share, w is the jth budget share in the previous period, and d.. pa- rameters measure a phenomenon which may be interpreted as habit persistence. Since the con- sumer’s adjustment is assumed to be consistent with a stable long-run equilibrium, it is expected that 0 < 0.. < 1. The term P ; is a price index defined by n 'nP,= ao + Z ak ]n Pk, k = l n n + X EViN) lnpK k = l7=l (38) n n + '/= X IVnP*,lnp y7 it = 1 y=l In addition to the restrictions (27), (29), (32), and (35), to avoid a violation of budget constraint an extra adding-up restriction requires, for n y e. = ou i = 1 (39) and to enable identification of (37) and (38), the condition i v° 7=l (40) is imposed. In restricted estimation, homogeneity and symmetry are enforced by imposing (29) and (32) on (37) and (38). In unrestricted estimation, (29) and (32) are not imposed. 4.4.2 Switching static and dynamic AIDS There are many hypotheses on what might cause changes in tastes concerning food choice. Health and nutrition concerns probably explain part of the change from butter to margarine and from high-fat to reduced-fat fluid dairy products, and the increasing consumption of fruits and vegeta- bles. Changes in life-style (for example, increased opportunity cost of leisure) have increased the demand for convenience food and food-away- from-home. In addition, changes in the demo- graphic composition of the population, develop- ment of household equipment (e.g. deep-freeze, micro-wave oven), advertising and product pro- motion are probably sources of changes in de- mand. The adopted model features a habit-form- ing mechanism as well as allows structural change in parameters. Parametric analyses of structural change in de- mand systems can be carried out by (a) splitting the data set into sub-groups and testing for struc- tural stability of the parameters, (b) allowing for systematic and stochastic variation in the param- eter values over time, using techniques such as the Kalman filter, or (c) explicitly allowing for systematic structural change in parameters by in- corporating time trends (Burton and Young 1992). The method (c) is adopted in the present study. A switching regression technique is used to allow for a period of structural stability fol- lowed by an interval of change, followed by fur- ther stability. The change from one regime to the other is assumed to be gradual, rather than abrupt. A gradually-switching dynamic form of the AIDS was modified by Edgerton (1992a, b) from the model suggested by Moschini and Meilke (1989). The model is like the dynamic AIDS, but it incorporates a group-wise demand shifter h: n W; = a + y 0..W.,, ~ it i Z-i lj j(t- 1) 7=l (41) " t (x > + Z Vn/V + (ft + /***») ln f j= i v " where h, =O. far t= 1 t, t~ T, h t = r T'f°r,= Xl + 1 T2l 2 M (42) h, = 1, fort= x 2 + 1 352 Agricultural Science in Finland 3 (1994) and 3,* is a shifting expenditure parameter, and InP is as given in (38). The definition (42) im- plies that (41) becomes a gradually-switching re- gression model, where r, and r 2 are points in time associated with the beginning and ending of the transition period between regimes. Jointpoint T, represents the end point of the first regime, whereas joint point t 2 is the starting point of the second regime, where the transition path between the two regimes is linear. To save degrees of free- dom, no other parameters than the expenditure parameter 6 are allowed to vary. The dynamic model becomes a static one by imposing d.s to be zero in (41). An alternative to B,* would have been to use shifting intercept a as the demand shifter (as done, for example, by Burton and Young 1992). Although a is interpreted as the ith budget share when expenditure is at the sub- sistence level, in empirical work its interpreta- tion is hindered by the fact that values vary con- siderably from one model specification to the other and, for example, negative values are frequent. That is why an interpretation in which a structur- al change of demand influences the demand func- tion through an expenditure effect was preferred. In addition to the restrictions (27), (29), (32), (35), (39), and (40), adding-up implies that (Edg- erton 1992a) irf-o i = 1 (43) In restricted estimation, homogeneity and sym- metry are enforced by imposing (29) and (32) on (41) and (38), whereas in unrestricted estimation, (29) and (32) are not imposed. 4.5 Aggregation over consumers Aggregation problem arises when making an em- pirical estimation of demand systems using ag- gregate time-series data. There are two separate aggregation problems. The first problem refers to the transition from the demand theory to the anal- ysis of market demand. In this case the aggrega- tion is made over consumers, and this will be discussed in this section. The following section deals with the second aggregation problem that refers to the structuring of food items into bun- dles and sub-bundles and the desirable level of commodity disaggregation. In this case the ag- gregation is made over goods. The discussion fol- lows Deaton and Muellbauer (1980b, Ch. 5 and 6) and Edgerton (1990, Ch. 3). The problem of aggregation over consumers arises from the fact that the microeconomics of consumer behaviour describes the behaviour of one consumer (household), while the data set used in the analysis describes the markets in which all the consumers (households) operate (for a review of discussion, Teklu et al. 1992). The restric- tions on demand functions, or the Slutsky condi- tions (Section 4.3), refer to the micro (house- hold) level. A successful macro demand function must be able to aggregate over households to the macro level in such a way that the Slutsky condi- tions still hold at the macro level. Deaton and Muellbauer (1980a, b) pioneered in deriving the macro demand functions from the consumer the- ory. The most critical condition is the generalised linearity of the aggregate expenditure function, which has given the PIGLOG type of expendi- ture function that was the starting point in deriv- ing the AIDS (Section 4.2). The concept of exact aggregation provided by the aggregation theory defines the necessary con- ditions under which aggregate consumer behav- iour can be treated as if it were an outcome of decisions of a single consumer. Given these as- sumptions hold, the aggregate per capita values used in the present study relate to a representa- tive consumer, or, the average behaviour of the population. Exact aggregation can be divided into exact linear aggregation and exact nonlinear ag- gregation. Quasi-homotheticpreferences Quasi-homotheticity of preferences is a neces- sary and sufficient condition for the linearity of Engel curves. Preferences are homothetic if utili- ty can be produced under constant returns to scale. This implies that, for some normalisation of the 353 Agricultural Science in Finland 3 (1994) utility function, doubling quantities doubles util- ity. Consequently, budget shares are independent of utility or of the total expenditure. Homothetic preferences imply that Engel curves are straight lines through the origin and, consequently, all expenditure elasticities are unity, and the expend- iture patterns are independent of the total expend- iture or of utility. Homotheticity is too restrictive an assumption. Quasi-homothetic behaviour (preferences) is assumed in the present study. Quasi-homothetic preferences imply that Engel curves of each indi- vidual are parallel straight lines, but not neces- sarily through the origin (i.e. the curves have the same slope but intercepts are allowed to vary). Consequently, expenditure elasticities only tend to unity as the total expenditure increases. Quasi- homothetic preferences allow (a) subsistence ex- penditure and (b) expenditure in excess of that required for subsistence (i.e. the expenditure of joy consumption). The aggregate expenditure pat- terns are a weighted average of the budget shares appropriate to very rich and very poor consum- ers. Exact linear aggregation The micro level Marshallian demand function for a household h is %i = ShMh’P) (44) where qh . is the household’s demand for good i, p is a price vector, and xh is the household’s total expenditure. Exact aggregation is possible if av- erage market response is a function of the aver- age total expenditure and prices, or, for all i, q, = gi(x.p) (45) where q. (= Y.q.JH, for h = 1,...,//) is the aver- age demand and x (= ZxJH, for h=\,...,H) is the average total expenditure (H is the number of households in the population). Average demand functions will automatically satisfy the Slutsky conditions if households maximise utility and households’ preferences satisfy the aggregation condition. The aggregation problem would be solved if one could find a function g,(x,/7) in (45) that is consistent with the utility function, which requires that the Slutsky conditions are satisfied (Deaton and Muellbauer 1980b, p. 150). If expenditure distribution varies over time, average expenditure can be used as a varia- ble in (45) only if Engel curves are linear, and all households have income high enough to cre- ate non-negative demand of i. The aggregation condition of quasi-homothetic preferences may be unrealistic, especially if one wants to cover disaggregated commodity groups which are not necessarily consumed by all households. Under these circumstances, part of the measured macro level expenditure response is due to an entry of new consumers into the market, not just be- cause “old” consumers increase their purchases. To allow for this, probably nonlinear, market re- sponse, a less restrictive assumption would be reasonable. Exact nonlinear aggregation Exact nonlinear aggregation requires that the mar- ket response should hold for some representative level of expenditure, which is not necessarily the same as the average level of expenditure. The exact aggregation is defined so that one aggre- gates over the different expenditure patterns of different consumers. Exact aggregation is possi- ble if the aggregate budget share, w , is a func- tion of prices and representative expenditure, xO, or, for all i, W i = f, (*o> /») (46) Note that x() can be a function of, for example, the distribution of expenditures and prices. A spe- cial case would be to allow x 0 to be the average expenditure. This would lead to the conditions for the exact linear aggregation (45). The condi- tion for (46) to exist is that, for household h, the expenditure function takes the form ch (u h’P) = e/, + h(p) are linearly homogeneous func- tions ofp, o(iis0 (i is linearly homogeneous in a(p) and b(p), and, over all consumers, ZQJp) = 0 (Dea- ton and Muellbauer 1980b, p. 154-155). The aggregate expenditure function is given by, for the same functions a(p) and b(p). c(uo,p) = 6[u0, a (p) , h (p) ] (48) where u () is the representative utility level given the prices and the representative level of the total expenditure, or u o = ip(xo,p). If the representative expenditure level is independent of prices and depends only on the distribution of expenditures, then the household expenditure functions are ch («/,. P) = [u(p) “(1 ~uh ) +h{p) a u h ] (49) where kh stands for household tastes or prefer- ences which, however, is a scalar at this stage indicating identical preferences over time. The scalar k h depends on household characteristics, for example, demographic factors, and it is de- fined in such a way that representative preferenc- es, kO , equal one. The representative, or the ag- gregate, expenditure function is given by, for the functions of the price vector p, a(p) and b(p). c(uo.p) = [a(p) a (l - U 0) +h(p) a u 0 ] (50) The functions (49) and (50) are known as the price independent generalised linear (PIGL) form. When the parameter a equals one, one has a spe- cial case of linear aggregation (the expenditure function is linear) and linear Engel curves and, consequently, the representative and average ex- penditures are the same. When a approaches zero, (50) can be written in a logarithmic form, known as PIGLOG, logc(M 0 , p) = (1 -M0 )loga(p) +Uologb{p) (51) where a(p) and b(p) are linear homogeneous con- cave functions. The form (51) is an approxima- tion to the logarithm of the expenditure function that is linear in utility and nonlinear in prices. The PIGLOG expenditure function is a converter between micro and macro models. Given the PI- GLOG expenditure function is appropriate, the parameters of both models are identical. For par- ticular forms for a(p) and b(p), the AIDS can be derived from (51) (Section 4.2). Consequently, the aggregate AIDS budget share equations are written as (Edgerton 1990) n wi, = «, + X Vnp7' + A ( lnX/ “ ,nZr - ln/> ,) (52) j = 1 where X(- Ijc h, for h = I,denotes the aggre- gate expenditure, the price index P is defined by (22) and InZ, Theil’s entropy measure of disper- sion, is defined as H H |nZ = £ (xh /X)\nkh - £ (xh/X) In (xh/X) (53) h=l h = 1 Contrary to linear aggregation, nonlinear ag- gregation allows nonlinear Engel curves. For the nonlinear aggregation, representative rather than average expenditure must be available. Given the expenditure distribution and, given differences in k hs, the demographic composition vary over time, the representative expenditure is not proportional to the average expenditure ( c.f Deaton and Mu- ellbauer 1980b, p. 157-158). Thus, to estimate the model, one needs to know the variable Z and, thus, the taste variables k h, the distribution of the total expenditure, and the correlation between taste and expenditure (Edgerton 1990). However, be- cause this information is not available, one sets Z = N , where N is the number of individuals in the population. 11 Thus, the representative level of the total expenditure, xO, is set equal x(= X/N), or the average per capita expenditure. Consequently, the usual approximation of the set of aggregate AIDS 11 One could also use H instead of N. An alternative approach would be to measure k h by specifying household or adult equivalence scales, a special case of which is that kh is set equal the number of household members (for adult equivalence scales in the context of demand for food, see Price 1986, Gould et al. 1990). 355 Agricultural Science in Finland 3 (1994) budget share equations (21) is obtained. Almost all empirical applications of the AIDS model de- flate the total expenditures by population. House- hold budget data would probably supply a suffi- cient basis to estimate k h s and the distribution of the total expenditure. However, for example in Finland, household budget survey is carried out only in every five years. Only after annual infor- mation is available, x could be replaced by x 0 in (21). Since the aggregate budget share is a function of prices and the average - instead of representa- tive - expenditure, one is back in the conditions for linear aggregation. This, however, probably does not jeopardize the analysis. For example, Ray’s (1985) results indicate that the idea of lin- ear Engel curves or quasi-homotheticity of pref- erences may not be unacceptable for time-series data on broad groups of commodities. Deaton and Muellbauer (1980b, p. 151-153) concluded that, if linear aggregation is to work at all, it can only do so for broad aggregate goods which are probably consumed by all households. In the present analysis, one covers relatively aggregat- ed commodity groups. Under these circumstanc- es, a major part of the measured macro level ex- penditure response is due to the fact that “old” consumers increase (decrease) their purchases, not so much due to the entry of new consumers into the market (the exit of “old” consumers from the market), causing nonlinearity to the market re- sponse. 4.6 Aggregation over goods: separability and multi-stage budgeting Aggregation over goods is the second type of aggregation problem. Multi-stage budgeting, or the structuring of bundles and defining the desir- able aggregation level, extensively applies the terms (a) aggregation, which implies that frag- mented categories are considered a single unit, and (b) separation of decision-making, which states that the allocation problem is handled in more manageable units (Deaton and Muellbau- er 1980b, p. 119-120). For example, one is ag- gregating when the expenditure on Food-at-Home rather than its components, such as Beverages and Groceries, is made a function of the total expenditure and broad group price indices (for example, Food-at-Home and Services). Separa- ble decision-making implies that research prob- lems are constructed into sub-problems. For ex- ample, after determining the budget of Food-at- Home, the allocation within Food-at-Home is made separately from allocation between Food- at-Home and Services. The problem of aggrega- tion over goods is faced by using separability concepts. The implications of assuming separa- bility are that (a) one can analyse aggregate groups and thus reduce the number of unknown parame- ters, and (b) one can specify a multi-stage budg- eting process. Separability ofpreferences Certain restrictions on the preferences or behav- iour are needed if one wants to include more than four or five commodities in a demand system. Separability states the conditions for aggregating the commodities into additive utility functions. Additivity means that the direct utility function can be written in an additive form if and only if the cross-price derivatives are proportional to the income derivatives. The restriction means, for ex- ample, that a change in the demand for Food-at- Home caused by a change in the price of Servic- es is proportional to the change in the demand for Food-at-Home caused by a change in the to- tal expenditure. Under additivity, a change in the price of any other good will affect the demand for the good in consideration. It is well-known that many flexible functional forms may have bad separability properties (e.g. Baccouche and Laisney 1991). The question is how to approximate the structure of consumers’ preferences, and whether the separability can be modelled. Various separability concepts have been sug- gested, such as (a) direct separability (separabili- ty of the utility function; quantities in the direct utility function are broken up into separable groups); (b) indirect separability (separability of 356 Agricultural Science in Finland 3 (1994) the indirect utility function); (c) quasi or implicit separability (separability of the expenditure or distance function; prices in the expenditure func- tion are broken up into separable groups); (d) direct pseudo separability (separability of an im- plicit representation of the direct utility function); and (e) indirect pseudo separability (separability of an implicit representation of the indirect utili- ty function). Pudney (1981), who provided for- mal definitions of the separability concepts, showed that the various definitions make little difference to the empirical results. In addition, there is the concept of (f) strong separability (ad- ditivity of preferences), which implies, for exam- ple, that there is an approximate linear relation- ship between expenditure and price elasticities (Pigou’s law). In the present study, a priori structure of weak separability in consumers’ preferences is assumed. The separability is presented in terms of direct separability, but the more general term of weak separability is used. Under the assumption of weak separability of the utility function, independence between sub-sets is not required. When aggregat- ing commodities for the additive utility functions, the aim is to sort the consumption set into sub- sets which include commodities that are closer substitutes or complements to each other than to members of other sub-sets. A utility function is weakly separable if [and only if] the marginal rate of substitution between any two goods be- longing to the same group is independent of the level of consumption of a third good in any other group (Phlips 1983, p. 66-69; the theorem origi- nates from Leontief 1947). Under weak separa- bility, the utility function is written as, for com- modity groups (sub-systems) r - 1,...,nand goods i = 1,...,m within each r, (54)l where v is a sub-utility function and q is con- sumed quantity (Phlips 1983, p. 68, Baccouche and Laisney 1991). Separability means that goods can be allocated into groups, and within each group the preferences can be described independ- ently from goods in other groups. Under weak separability, goods can be divided into a number of separate groups where a change of a price in one group affects the demand for all goods in other groups in the same manner. The main effort is required by the within-group allocation prob- lem. The assumption of separability permits spec- ifying a separate maximisation problem in which, for example, expenditure on Food-at-Home per- forms as a constraint. The advantage gained by imposing the weak separability can be shown by the following notation. If the utility in (54) is maximised subject to a budget constraint, the Mar- shallian demand functions are obtained, for groups r=1,...,n and goods <*=!,.„,m within each r. � * Qri = Bri(X’P8r i(X ’P 11> ■■'P\m'P2V "•>Plm’ •"> (55) P Pnm where p is price and x(= YLq ri prj, for r = !,...,« and i = 1 is the total expenditure. Weak separability allows to limit the number of param- eters to be estimated so that the demand function for good i within group r is «ri = Sri (Xr,prV ...,Prm ) (56) where xr {= "Lq rp ri, for i= 1 is the group expenditure. Thus, in Marshallian terms, weak separability implies that the quantities demanded are a function of within-group prices and group expenditure, while in Hicksian terms, weak sepa- rability implies that the quantities are a function of within-group prices and group utility. In the context of the AIDS, the Marshallian demand function for the rth group is approximated by (57)qr = 8r( X' P V ’ P n) where qr is the rth group’s real expenditure, P is the true cost of living index (for specification, Edgerton 1992a, p. 4), x{= 2xr , for r = 1,...,n) is the real total expenditure (where xr = qPr and qr - Y.q r., for i= 1 ~..,m, where qr . is the ith good’s real expenditure). 357 Agricultural Science in Finland 3 (1994) The assumption of weak separability enabled solving the allocation problem within separate groups, which allowed to increase the number of commodities under consideration. Since the pur- pose of the present study is to analyse disaggre- gated food categories, a multi-stage budgeting process is adopted. Multi-stage budgeting Weak separability of preferences permits budget- ing in stages. The separability is a necessary con- dition for the consistency of the multi-stage max- imisation procedure which appears as a utility tree. In the multi-stage budgeting, consumers al- locate the budget into successively disaggregated commodity groups. There is a sub-utility func- tion for each group. The sub-utilities sum up to the utility of the group, and the values of all sub- utilities sum up to the total utility. The first step is to allocate the total expendi- ture into broad aggregate commodity groups like Food-at-Home and Services. The subsequent steps allocate group expenditures into sub-sets. At each stage, only the group expenditure and the set of group prices are needed. It is important that com- modities related to each other, either as substi- tutes or complements, are in the same group. If the separability of preferences is maintained, the results of multi-stage budgeting are identical to the results which are attained if the allocation is made in one stage. 4.7 Specification of the hierarchic demand system There is no objective method for judging the rel- evance of a certain separability structure. How- ever, afterwards it is possible to evaluate whether the separability assumptions hold. The aggrega- tion problem is solved in terms of the research problem and data availability. First, since interest in the present study is in the demand for various food items, as detailed commodity partitioning as possible is desired. Consistent series starting from 1960 cover at most 18 sub-groups of food. If one wanted to make a more detailed analysis, the data would be available only from 1970, which allows too short series regarding the employed estimation methods. Second, public dietary recommendations han- dle food consumption as aggregate categories that should be in balance with each other. Within those bundles, food items can be chosen more freely. Agricultural policy measures may affect the price and supply conditions of only one item, e.g. But- ter, but often the effect covers an aggregate bun- dle as a whole, e.g. Dairy Products. Since the results of the present study will be used for poli- cy analysis, the functional interdependence be- tween food items was maintained. For dietary reasons, analysing cross-effects within Animalia, Beverages, and Vegetablia, and also cross-effects between those aggregates was of interest. A pri- ori theoretical expectations and conventional wis- dom suggested that various types of beverages, Butter and Margarine, Meat Products and Car- case Meat, and Bread and Cake and Flour are closer substitutes to each others than to the com- modities in other aggregates. Third, therequirement for computational pow- er increases rapidly with the size of the system. The criteria suggests the estimation of four si- multaneous equations at the most. Also the length of available data series (32 observations) discour- ages the estimation of large systems (the number of degrees of freedom in the unrestricted switch- ing dynamic AIDS, which is the most general model specification in the present analysis, is 23 in a 3-equation system, 21 in a 4-equation sys- tem, and 19 in a 5-equation system). Given the predetermined conditions mentioned above, the estimated demand system forms a hi- erarchic process that is presented in Figure 8. The demand system is composed of stages and groups. Stage refers to an allocation round. Sub- system, or group, refers to one set of equations which are estimated simultaneously. At Stages 1 and 2, there is only one allocation process, and thus stage and group can be used interchangea- bly. All stages together form a system. A consumer starts by determining the amount to spend on four commodity groups, one of which 358 Agricultural Science in Finland 3 (1994) is Food-at-Home. Food-at-Home is allocated into Animalia, Beverages, Groceries, and Vegetablia. Then, the broad groups are divided into 11 sub- groups. Finally, two sub-groups are disaggregat- ed further. The demand for Butter, for example, is assumed to be a result of a four-stage budget- ing process, expressed as a function of the prices within Dairy Products and the total expenditure allocated on Dairy Products. The fact that just the within-group variables are used does not mean, however, that goods in different groups are inde- pendent of each others. Weak separability allows, for example, a change in the price of Butter to affect the demand for Services. The effect is chan- Fig. 8. The four-stage budgeting system employed in the present study. 359 Agricultural Science in Finland 3 (1994) neled through stages so that, first, the change affects the demand for Dairy Products, then Ani- malia, then Food-at-Home, and finally the cross- dependency between Food-at-Home and Servic- es, which belong to the same group, determines the effect. Thus, the response of the price of But- ter on the demand for Services depends on the mutual relationship between Food-at-Home and Services. However, the response does not tell an- ything about the substitution effects between But- ter and Services, since a change in any price within Food-at-Home affects the demand for Services in the same way as a change in the price of Butter. The multi-stage budgeting process has to be taken into account when deriving elasticities. A change in a relative price causes (a) direct effects on the allocation of expenditures within the group and, by affecting the group price index, (b) indi- rect effects on the allocation of expenditures be- tween the groups at the preceding stages. This indirect effect influences all goods in the system, also the goods within the group where the initial price change took place. There the indirect effect is a “second wave.” 4.8 Elasticities of the AIDS Elasticities are used to interpret the estimation results. The derivation of the AIDS elasticities follows Edgerton (1992a,b). The elasticities are point rather than arc elasticities. The expenditure elasticity, 12 reflecting the responsiveness of con- sumption to expenditure changes, is derived for commodity i, and for t = B + B* h, E- = 1 +- " (58) 12 Although it is common to talk about ‘income’ elas- ticity, in the present study, the term ‘expenditure’ elastici- ty is used because expenditure, rather than income, is used as an independent variable in models. Sometimes the two concepts are used as synonyms (as Intriligator 1978, p. 222), sometimes a clear distinction between them is made (as Manser 1976). When referring to the total ex- penditure elasticities, to be presented later in this section, it would be almost appropriate to talk about income elas- ticities. where w is the ith bundle’s budget share. The expenditure elasticity of demand measures the percentage change in purchases of i due to a per- centage increase in the total expenditure [of the group], ceteris paribus. The price elasticities, re- flecting the responsiveness of consumption to price changes, are for all i and j, and for t = 1 T, eiji = thi + U + o**/) ['( + V/) ln^--'Pin>n--"p wSw is the yth good’s budget share within the rth group, w (s) [= (P qjlx\ is the vth group’s budget share, and tvy[= (p( q( )!x] is theyth good’s budget share. Edgerton (1991) has shown the cross-elastic- ities between goods and groups. Given the tth commodity belongs to the rth group, then (66)C (s)i - W(r)i e(s)(r) e iU) r)i g (r)(s) (67) The total expenditure elasticities are used to classify goods into three types. A good is said to be expenditure elastic or luxury if E > 1, or the budget share of a good tends to increase with expenditure. This implies that luxuries are the goods that take up a larger share of the budget of better-off households. A good is said to be ex- penditure inelastic or necessity if E < 1, or the budget share of a good tends to decrease with the total expenditure. Necessities are the goods that take up a larger share of the budget of lower- income households. Usually the expenditure elas- ticity is positive, E > 0. Given this, the Engel curve is positively sloped, and the good is said to be superior. Otherwise it is an inferior good with E< o, or the purchases decline absolutely, not just proportionately, as expenditure increases. For in- ferior goods, the Engel curve is negatively sloped. It is noteworthy that inferiority can only apply to a part of the expenditure range, because other- wise the good would never have started to be consumed. Considering total own-price elasticities, the good i is said to be price elastic if led > 1 and price inelastic if \e.\ < 1. A price increase of a price-elastic good i decreases the expenditure on i, whereas a price increase of a price-inelastic good i increases the expenditure on i. A price change of the good i that shows unit-elastic de- mand, le i = 1, implies an unchanged expenditure on i. Usually the own-price elasticity is negative; given this, the good is said to be normal. Other- wise, it is a Giffen good with a positive own- price elasticity. If the demand for good / goes up as a result of price increase of good j, or e > 0, then good i is a substitute for good j. In the con- text of food, substitutes are items that play ap- proximately the same role in the diet, and, thus, one can easily replace one by another (e.g. beef and pork). On the other hand, good i is a comple- ment to good j if e < 0. Complements are eaten 362 Agricultural Science in Finland 3 (1994) together and, thus, a decline in the consumption of one also decreases the consumption of another (bread and spread). If e.. > 0, then good i is a Hicksian substitute (a change in the price with utility held constant) for good j and if e < 0, good i is a Hicksian complement to good j. If 8 = 0, the goods are independent. 4.9 Estimation methods A stochastic specification for each model is ob- tained by adding a vector of disturbance terms to the systems of equations (21), (37), and (41). For example, the stochastic specification of the switch- ing dynamic AIDS is written as, for i=1,...,n and t= 1 T, n n w., = a + V 6 w. ., + V 7 Inn.,n i A-i ij J (.1 -I) i-j ' v r jt ]= i i = i (68) f x ) + (P, + p]h')ln - +£,, V tJ where £ is the vector of disturbances correspond- ing to each observation, and P is given by (38). Assuming separability, the whole system is es- timated stage by stage and group by group. First, the allocation is made between four major groups, then a further allocation is made between goods within each group. In most cases, the process is repeated so that goods which were already allo- cated turn into sub-groups which are further allo- cated into smaller bundles. The n equations are estimated together. Thus, one can utilise the esti- mated correlation structure between the error terms within the group. By doing that one is perform- ing a sub-system estimation which utilises more information than a single equation estimation (where no information on the error correlation structure is utilised) and less information than a full system estimation (where all the information on the error correlation structure in the system is utilised) (Edgerton 1992b). In order to estimate (68) and (38), certain as- sumptions have to be made concerning £ ( , which is a (n * 1) vector of disturbance or error terms in the equations. The errors (a) have zero mean (av- erage or expected value will be zero), E(et ) =O, (b) have zero covariance (serial non-correlation), E(ei é ) = 0 for (t s), (c) have scalar diagonal variance-covariance matrix of errors (homoske- dasticity), E{e t e) = (fl , where the scalar cf is unknown, and (d) are normally distributed, £ ~ N(o, (70) where is the number of tested restrictions per equation (m ] = n/2 for symmetry hypothesis, oth- erwise = 1), m 2 is the number of estimated equations in the group ( m2 = n-1, nis the number of equations in the group). The other definitions are (Edgerton 1992b) + I |(m,w,) 2 -4 h = T-k- ;s=2 .22,Mm j + m 2 - 5 (71) m \ m 2 , „ -A/Tr = 1; U = e A* is approximately distributed as F under the null hypothesis. Given identical restrictions in the equations, an exact Wald statistic, W\ is also available (Edgerton 1992b): (72) The statistic is distributed as f ._ . under then-I.T-k-n null hypothesis. The exact LR test (70) is applied for homoge- neity, symmetry, and dynamics. The exact Wald test (72) is applied for the homogeneity and switching hypotheses, whereas the corrected Wald test (69) checks symmetry and dynamics. The test statistics are calculated by the ANALYZ pro- 365 Agricultural Science in Finland 3 (1994) Table 6. Tests of parameter restrictions for the switching dynamic AIDS and the preferred model specifications: P-values of corrected Wald test ( CW), exact Wald test (W), and exact likelihood ratio test (A*). Group3 Model b Homogeneity Symmetry Symmetry No dynamics No (conditional on switch homogeneity) W A• CW A’ CW A' CW A" W 1 SwDUnr 0.0091 0.0259 0.0000 0.0005 0.0000 0.0100 0.0000 2 SwDUnr 0.0000 0.0017 0.0000 0.0009 0.0000 0.0058 0.0000 31 SwDUnr 0.0000 0.0001 0.0000 0.0001 0.9151 0.9052 0.0020 31 TUnr 0.0001 0.0003 0.0000 0.0003 32 SwDUnr 0.0000 0.0003 0.0000 0.0000 0.0000 0.0125 0.0000 32 DUnr 0.0001 0.0010 0.0000 0.0066 0.0000 0.1024 33 SwDUnr 0.0010 0.0019 0.0000 0.0057 0.0000 0.0000 0.0003 41 SwDUnr 0,6029 0.5654 0,5595 0.4217 0.2555 0.1929 0.0179 0.0807 0.0000 41 SwDHS 0.6029 0.5654 0.5595 0.4217 0.2555 0.1929 0.0187c 0.0807 0.0000c 42 SwDUnr 0.0001 0.0001 0.0000 0.0007 0.0000 0.0000 0.0000 11 The groups are as follows. Group I: Private Consumption; Group 2: Food-at-Home; Group 31: Animalia; Group 32; Beverages; Group 33: Vegetablia; Group 41: Meat and Fish; and Group 42: Dairy Products. b The abbreviated notations are SwDUnr (switching dynamic AIDS, unrestricted), TUnr (static AIDS, unrestricted), DUnr (dynamic AIDS, unrestricted), and SwDHS (switching dynamic AIDS, homogeneity and symmetry restricted). c Conditional on homogeneity and symmetry. cedure of TSP. In the Wald test. White’s robust standard errors are used to avoid the trouble caused by the presence of unknown heteroske- dasticity. The LR test assumes homoskedasticity. The indicator of each test is the P-value of the test statistic. If the P-value is less than 0.05, the given hypothesis is rejected at the 5% signifi- cance level. Given this, the tested restriction should not be imposed on the system. The results are presented for the unrestricted switching dy- namic AIDS, which is the most general model specification and, in addition, for the model which was chosen as the preferred specification for each particular group (Table 6). Keeping unrestricted switching dynamic AIDS as the starting point, switching was accepted eve- rywhere. In Animalia (Group 31), the switching static AIDS produced some peculiarities in own- price elasticities and, moreover, the Cusumsq test16 indicated parameter instability. By rejecting the switching parameter, the problem was alleviated. Dynamics was rejected in Animalia (Group 31) 16 Misspecification tests will be presented in Section 5.2.4. by the Wald and LR tests, and in Meat and Fish (Group 41) by the LR test. The RESET, Haus- man-Wu, and Cusumsq tests indicated a serious misspecification in Beverages (Group 32). The misspecification was alleviated by rejecting the switching parameter. After this, the LR test sug- gested to reject dynamics, while the Wald test did not. When the dynamic AIDS was replaced by the static AIDS and the results of diagnostic tests were compared, the Hausman-Wu tests in- dicated a serious misspecification in the static AIDS, while other tests remained about the same. Consequently, the dynamic specification was cho- sen for Beverages. In all cases except Meat and Fish (Group 41), both homogeneity and symmetry were rejected. In Meat and Fish, the homogeneity and symme- try restricted specification of the switching static AIDS suffered from functional misspecification (the RESET test), group expenditure endogeneity (the Hausman-Wu tests), and parameter instabili- ty (the Cusumsq test). The problems were allevi- ated by accepting dynamics which was, in fact, suggested by the Wald test but rejected by the LR test. 366 Agricultural Science in Finland 3 (1994) Table 7. Preferred specifications of the AIDS with estimated joint points (ij and r 2). a Group Preferred specification Joint points T! T 2 Private Consumption (Group 1) Switching dynamic AIDS, unrestricted 1975 1984 Food-at-Home (Group 2) Switching dynamic AIDS, unrestricted 1961 1984 Animalia (Group 31) Static AIDS, unrestricted Beverages (Group 32) Dynamic AIDS, unrestricted Vegetablia (Group 33) Switching dynamic AIDS, unrestricted 1961 1989 Meat and Fish (Group 41) Switching dynamic AIDS, homogeneity 1967 1975 and symmetry restricted Dairy Products (Group 42) Switching dynamic AIDS, unrestricted 1965 1974 a Joint point t represents the end point of the first regime, whereas joint point T, is the starting point of the second regime. The unrestricted switching dynamic AIDS was chosen as the preferred model specification for four groups. Static specification was chosen for one group (Table 7). The joint points, to present the beginning and end of the gradually switching period, were estimated by the maximum-likeli- hood procedure. The joint points vary from group to group. In Food-at-Home and Vegetablia (Groups 2 and 33), the first joint point is 1961, whereas in Meat and Fish and Dairy Products (Groups 41 and 42) it is 1967 and 1965, respec- tively. In Private Consumption and Food-at-Home (Groups I and 2), the second joint point is 1984, whereas in Meat and Fish and Dairy Products (Groups 41 and 42) it is 1975 and 1974, respec- tively (Table 7). The models for Animalia and Beverages (Groups 31 and 32) did not include a switching parameter. 5.2 Evaluation of the preferred model specifications 5.2.1 Negativity condition The negativity condition was tested by checking if all compensated (Hicksian) own-price elastici- ties were negative. The restriction cannot be ac- cepted because the non-positivity did not hold for the whole range of prices and expenditures in all commodities. In the preferred specifications of the AIDS, 16 of the 26 categories satisfied the negativity condition. Food-at-Home, Bever- ages, Vegetablia, and Dairy Products (Groups 2, 32, 33, and 42) showed only a few violations, whereas Private Consumption, Animalia, and Meat and Fish (Groups 1,31,and 41) included catego- ries where all the estimated compensated own- price elasticities were positive (Table 8). It re- mains unexplained why all the estimated models did not satisfy the negativity condition. The dis- cussion on potential causes for the outcome is postponed to Chapter 8. 5.2.2 Parameter estimates Altogether 133 of the 258 estimated parameters, or 52%, were at least twice the size of the corre- sponding standard error, which is roughly the con- dition for the significance at 5% level. Using the share of significant parameters from all estimat- ed parameters as the criteria, the expenditure pa- rameters for the switch (JT) had the best per- formance. Noteworthy is that the shifting varia- ble was included only in those models where its relevance was accepted by a diagnostic test. The performance of the expenditure variable was not good in Beverages (Group 32), where all the co- efficients (/}.) were insignificant. The perform- ance of the price parameters (coefficients y) was not good in Meat and Fish and Dairy Products (Groups 41 and 42). The habit persistence pa- 367 Agricultural Science in Finland 3 (1994) Table 8. Number ofviolations of the negativity condition. Group (group number Model* Number of positive compensated in brackets) own-price elasticities Category6 12 3 4 Private Consumption (1) SwDUnr 31° 0 15 31 Food-at-Home (2) SwDUnr 0 0 0 0 Animalia(3l) TUnr 31 18 4 Beverages (32) DUnr 0 0 0 4 Vegetablia (33) SwDUnr 0 7 0 0 Meat and Fish (41) SwDHS 31 0 0 Dairy Products (42) SwDUnr 11 0 0 0 a The abbreviated notations are SwDUnr (switching dynamic AIDS, unrestricted), TUnr (static AIDS, unrestricted), DUnr (dynamic AIDS, unrestricted), and SwDHS (switching dynamic AIDS, homoge- neity and symmetry restricted). b The categories refer to the commodity bundles presented in Table 2. c The maximum number of violations of negativity is 31, or the total number of estimated elasticities. rameters (0) were estimated for all groups except Animalia (Group 31). Especially Food- at-Home and Meat and Fish (Groups 2 and 41) suffered from insignificant 0 y estimates (Ta- ble 9). Parameter estimates are presented in Ap- pendix 2. 5.2.3 Goodness of fit Goodness of fit was measured by the usual coef- ficient of determination R 2, which is the ratio of explained variation to the total variation, written for each equation in an allocation model as Table 9. Significance of the estimated parameters in the preferred model specifications,* Groupb a. 6.. y fi. /J‘. Sum t> 2 Total t> 2 Total t> 2 Total t> 2 Total t> 2 Total t> 2 Total t>2, % 1 1 4 10 16 10 16 3 4 3 4 27 44 61 2 3 4 3 16 10 16 3 4 3 4 22 44 50 31 3 3 - - 8 9 2 3 - - 13 15 87 32 2 4 7 16 9 16 0 4 - - 18 40 45 33 2 4 8 16 7 16 3 4 4 4 24 44 55 41 3 3 2 9 0 9 3 3 3 3 11 27 41 42 3 4 9 16 2 16 2 4 2 4 18 44 41 Sum 17 26 39 89 46 98 16 26 15 19 133 258 52 Sum, % 65 100 44 100 47 100 62 100 79 100 52 100 * Groups I, 2, 33, and 42; switching dynamic AIDS, unrestricted; Group 41: switching dynamic AIDS, homogeneity and symmetry restricted: Group 32: dynamic AIDS, unrestricted; Group 31: static AIDS, unrestricted: The r-values were obtained by dividing the value of the estimated parameter by the corresponding standard error. A f-value greater than two roughly indicates the condition for significance at 5% level. b The groups are as follows. Group 1: Private Consumption; Group 2: Food-at-Home; Group 31: Animalia; Group 32: Beverages; Group 33: Vegetablia; Group 41: Meat and Fish; and Group 42: Dairy Products. 368 Agricultural Science in Finland 3 (1994) T R 1 = 1-LjtJ (73) X i = i where T is the number of observations and w is the average of the dependent variable. R 2 can be adjusted for the loss in degrees of freedom due to the addition of more explanatory variables. The statistics, adj/?2 , was derived as adjR 2 = R 2 - k^-k (\-R 2 ) (74) As a system-wise counterpart, the following measure was used (Edgerton 1992b): , 2 I detl. R=l (75) where m = n- 1, or the number of estimated equa- tions in the group, 1,. is the covariance matrix of the estimated residual, co\{efe), and is the estimated covariance matrix of the dependent var- iables, cov(vv,,vv ). R 2 is a form of the weighted geometric mean of the equation-wise R2s, and it was adjusted for degrees of freedom (Edgerton 1992b, p. 30). To measure the relative improvement of a dy- namic model over a nested static model (static model was nested within the dynamic model), one can write „2 4-*S "O:S “ 2‘-«s (76) where R2 D is the goodness of fit from a dynamic model, and R2 S is the goodness of fit from a static model. R2 d s , was adjusted for degrees of freedom to obtain adj/?2 0 i , as a^jRD: S “ J (77) Restated, adj/?2 0 is the coefficient of determi- nation for the dynamic model adjusted for the static model and degrees of freedom. R2 DS and adj/?2 DS can be applied for single equations and systems (Edgerton 1992b). The goodness of fit was low in Beverages, Groceries, Carcase Meat, Fish, and Margarine; in other cases it was rather high. A comparison be- tween dynamic and static models showed that dynamics generated an improvement in the good- ness of fit in most cases. Measured by adj/?2 o s, in 5 of the 23 dynamic equations more than 50% of the variation remaining in the static model was explained. More than 20% was explained in 16 cases. In addition to Animalia (Group 31), which was estimated as a static specification (because of the poor performance of dynamics), only Gro- ceries and Fish did not benefit from dynamics (Table 10). 5.2.4 Diagnostic checking The diagnostic tests are used in applied work to check whether something is wrong with the mod- el under consideration, and thus to reduce the risk of accepting misspecified models. The tests are described in the context of a single-equation linear regression model, for t = y, = x!p +£, (78) where y is an observation of the dependent vari- able, x is a £xl vector of independent variables, p is a kx I vector of estimated parameters, and e is an error term. Where possible, system-wise diagnostic tests were calculated by generalising the equation-wise tests for the whole system. The methodology employs Godfrey’s (1988) theory of local equivalent alternatives. The description follows Edgerton (1992b), Rickertsen (1992), Pagan and Wickens (1989), Stewart (1991), and Maddala (1992). There are alternative principles which can be used for generating test statistics. The statistics are often asymptotically equivalent, but their small sample distributions are generally different (En- gle 1984). In the present study, an exact small 369 Agricultural Science in Finland 3 (1994) Table 10. Goodness-of-fit measures of the preferred model specifications. 3 * 2 adj R* VD:S adj/? ; /) V Private Consumption (Group 1) 0.9780.969 0.2980.198 - Food-at-Home 0.9960.995 0.3130.214 - Food-away-from-Home 0.9960.994 0.244 0,136 - Non-Durables 0.9370.909 0.153 0,032 - Services 0.9930.990 0.5470.482 Food-at-Home (Group 2) 0.8910.844 0,315 0.218 - Animalia 0.9270.895 0.1450.023 -Beverages 0.8870.839 0.5170.448 - Vegetablia 0.9520.932 0.6080.552 - Groceries 0.8600.800 0.087 -0.043 Animalia (Group 31) 0.8730.854 (0.023) b (-0.062) b - Meat and Fish 0.9350.926 (0.044) b (-0.040) b - Dairy Products 0.9080.894 (0.044) b (-0.039) b -Eggs 0.9180.905 (0.001) (-0.086) b Beverages (Group 32) 0.9260.899 0.2030.094 -Alcoholic Drinks 0.9910.988 0.3680.282 -Fresh Milk 0.988 0.984 0.306 0.211 - Soft Drinks 0.976 0.967 0.453 0.379 -Hot Drinks 0.986 0.981 0.339 0.249 Vegetablia (Group 33) 0.940 0.915 0.501 0.430 - Bread and Cake 0.939 0.913 0.156 0.035 - Fruits 0,944 0.920 0.766 0.732 -Vegetables 0.940 0.914 0.528 0.461 -Flour 0.978 0.969 0.676 0.630 Meat and Fish (Group 41) 0.767 0.715 0.173 0.105 - Meat Products 0.940 0.927 0.321 0.266 -Carcase Meat 0.867 0.837 0.138 0.067 -Fish 0.591 0,499 0.037 -0.041 Dairy Products (Group 42) 0.935 0.908 0.509 0.439 -Cheese 0.976 0.966 0.615 0.560 - Sour Milk and Cream 0.956 0.937 0.516 0.446 - Butter 0.976 0.965 0.606 0.550 -Margarine 0.848 0.782 0.362 0.270 a Groups 1,2, 33, and 42: switching dynamic AIDS, unrestricted; Group 41: switching dynamic AIDS, homogeneity and symmetry restricted: Group 32: dynamic AIDS, unrestricted; Group 31: static AIDS, unrestricted. b The measures are from the switching dynamic AIDS, unrestricted. sample adjustment to the LR test statistic was employed. The adjusted LR test is a special case of the exact LR statistic (70). The F- (rather than X 2-) distributions were used, as suggested by Kivi- et (1986). 17 This LR principle was followed in -17 Kiviet (1986) compared the effectiveness of vari- ous small sample correction factors in the model with lagged dependent variables in the context of serial corre- lation. He showed that the Lagrange-multiplier type F- test has a type I error probability that is relatively invari- ant to sample size, order of serial correlation, true coeffi- cient values, and redundant regressors (type I error is a the tests for autocorrelation (BG), heteroskedas- ticity (BP and ARCH), and functional misspeci- fication (RESET and HWu). The P-values of the test statistics are presented in Table 11. The P- values less than 0.05 indicate that a given hy- probability of rejecting H() even when it is true). The BG test used in the present study, although employing the adjusted LR test, is asymptotically equivalent to the Lagrange multiplier test (Edgerton 1992b, p. 21). Con- sequently, the use of F-distributions should yield better small sample approximations than the use of tions. 370 Agricultural Science in Finland 3 (1994) Table 11. Misspecification tests: small sample /'-values.8 BG BP ARCH RESET HWu(x) HWu(di) JB Cusumsq 1’ Private Consumption (Group 1) 0.694 0.599 0.197 0.197 0.497 - Food-at-Home 0.3600.555 0.3320.359 0.1860.339 0.010 - Food-away-from-Home 0.3650.595 0.1820.736 0.3730.911 0.011 -Non-Durables 0.738 0.943 0.867 0.014 0.603 0.861 0.005 -Services 0.813 0.360 0.464 0.782 0.386 0.982 0.010 Food-at-Home (Group 2) 0.180 0.494 0.919 0.158 0.688 0.356 - Animalia 0.878 0.593 0.592 0.434 0.724 0.703 0.960 0.108 -Beverages 0.462 0.052 0.344 0.238 0.341 0.128 0.633 0.050 -Vegetablia 0.885 0.318 0.853 0.643 0.302 0.118 0.950 0.578 -Groceries 0.829 0.096 0.860 0.887 0,339 0.208 0.778 0.005 Animalia (Group 31) 0.799 0.681 0.646 0.799 0,519 0.312 -Meat and Fish 0,288 0.266 0.916 0,927 0.319 0.125 0.378 0.904 - Dairy Products 0.337 0.333 0.988 0.856 0,400 0.144 0.322 0.997 -Eggs 0.602 0.789 0.806 0.233 0.521 0.804 0.945 0.324 Beverages (Group 32) 0.030 0.489 0.001 0.000 0.220 0.043 - Alcoholic Drinks 0.878 0.539 0.979 0.022 0.950 0.835 0.000 0.001 -Fresh Milk 0.199 0.532 0.773 0.079 0.574 0.303 0.000 0.000 -Soft Drinks 0.518 0.679 0.240 0.350 0.218 0.166 0.575 0.011 -Hot Drinks 0.330 0.788 0,572 0.719 0.127 0.066 0.633 0.209 Vegetablia(Group 33) 0.583 0.242 0.997 0.857 0.150 0.280 - Bread and Cake 0.618 0.131 0.945 0.632 0.065 0.047 0.787 0.000 -Fruits 0.131 0.256 0.596 0.599 0.791 0.985 0.888 0.003 -Vegetables 0.057 0.821 0.707 0.938 0.699 0.958 0.506 0.027 -Flour 0.720 0.740 0.453 0.231 0.027 0.083 0.621 0.001 Meat and Fish (Group 41) 0.728 0.073 0.285 0.001 0.477 0.520 - Meat Products 0.248 0.560 0.512 0.877 0.934 0.967 0.838 0.075 -Carcase Meat 0.287 0.995 0.289 0,011 0,638 0.619 0,888 0.202 -Fish 0.811 0.002 0.079 0.000 0.168 0.192 0.770 0.000 Dairy Products (Group 42) 0.218 0.257 0.354 0.046 0.078 0.107 -Cheese 0.337 0.178 0.256 0.030 0.068 0.143 0.430 0.288 - Sour Milk and Cream 0.636 0.013 0.109 0.084 0.208 0.192 0.817 0.102 -Butter 0.825 0.181 0.550 0.811 0.055 0.129 0.134 0.553 -Margarine 0.222 0.138 0.466 0.033 0.111 0.103 0.582 0.007 * The preferred model specification for each group was applied. The abbreviated notations are BG (Breusch-Godfrey statistics), BP (first order Breusch-Pagan test), ARCH (first order autoregressive conditional heteroskedasticity model), RESET (Ramsey’s regression equation specification error test), HWu(x) (Hausman-Wu test which uses the total expenditure as the instrument), HWu(di) (Hausman-Wu test which uses disposable income as the instrument), JB (Jarque-Bera Lagrange multiplier test), and Cusumsq (cumulative sum of squares test). b The computations of the P-values of the Cusumsq statistics were performed by David Edgerton by using the method described in Edgerton and Wells (1993, 1995). pothesis of the correctness of the model was re- jected at 5% significance level. Autocorrelation Autocorrelation, or serial correlation, especially combined with lagged endogenous variables, yields inconsistent estimates. The Breusch-God- frey statistics (BG) indicates the amount of auto- correlation (Breusch 1978, Godfrey 1978, Eng- le 1984, p. 807). Contrary to the familiar Durbin- Watson test, the BG is valid in the presence of lagged endogenous variables.The BG test against autoregressive errors of the first order is defined as a test where H 0 is = 0 in, for t= 1 371 Agricultural Science in Finland 3 (1994) y, = x/p+al £[ _ l +v t (79) where the error term v is assumed to be a white noise process NID{O.o2), i.e. the values of v ( are assumed to be drawn independently from a nor- mal distribution with a zero mean and + yo ln F (83) \ r t ) \ r t J where P is the AIDS estimate of P. Predicted i i values y were obtained. At the second step, budget shares were regressed on x , the set of explanato- ry variables, and yt : ( X ' wi, =«, + IVn/VA ln j +V, + v,, (84) \ r t J The significance of the prediction term was tested. H() was y= o, or the group expenditure was exogenous. Two instruments z were used. The HWu(x) used the total per capita expenditure (which equals x t at Stage I) as the instrument, and the HWu(di) used disposable per capita in- come in the complete system as the instrument. If a is assumed exogenous, its use in the instru- merit set can be justified elsewhere but at the first stage. If xt is assumed endogenous, instead of that, disposable income should be used in the instrument set. Disposable income can be applied for all stages. The Hausman-Wu test was significant in two equations in Group 33, namely Bread and Cake and Flour, and in one group, namely Beverages (Group 32). In Bread and Cake and Flour, the misspecification was probably a problem with group expenditure endogeneity since the RESET was not significant in those bundles (c.f Edger- ton 1993, p. 17-19). In Beverages, both the RE- SET and HWu(di) were significant, which could, for example, indicate that the separability struc- ture was incorrectly specified. In all three cases, however, the result is less clear since only one of the two tests was significant. Thus, it can be con- cluded that the recursive manner in which the group expenditures appeared in the system did not lead to any significant misspecification. If the exogeneity hypotheses were rejected more clearly, some form of instrumental variables meth- od should have been applied. Separability structure No explicit test was carried out to check whether the separable groups that were compounded from individual food items were consistent with con- sumer preferences. 18 However, implicitly it can be concluded that omitted variables and endog- eneity of explanatory variables may suggest non- separability (Edgerton 1992b). The RESET test searched for some form of misspecification, for example, omitted variables and endogeneity in 18 The problem with most separability tests is that they use either the Wald or LR criteria and, thus, parameter estimates from the unrestricted (non-separable) model are needed. In the present study the estimates were not avail- able. Bales and Unnevehr (1988) derived a parametric restriction which they used to test for weak separability in an AIDS model. The test showed that consumers chose among meat products rather than meat aggregates, such as beef or chicken. Hayes et al. (1990) tested for separabili- ty hypothesis by using parametric restrictions in the AIDS model of the Japanese meat demand system. Separability between meats and fish was accepted. 373 Agricultural Science in Finland 3 (1994) the explanatory variables. Thus, it can be em- ployed to test for separability. The second test suitable for this purpose is the Hausmann-Wu test (Alston and Chalfant 1987, Edgerton 1992b). The total per capita expenditure and dis- posable per capita income were included as ex- tra variables in the model (the HWu(x) and HWu(di) tests, respectively). If the separability assumption is correct, the extra variable should have no effect. By using the RESET test as the criteria, the separability assumption may have been wrong in Beverages, Meat and Fish, and Dairy Products (Groups 32, 41, and 42). By using the HWu(x) endogeneity criteria, the specification of the sep- arability structure was correct. According to the HWu(di) endogeneity criteria, separability struc- ture was questioned in Beverages (Group 32). Normality The asymptotic Jarque-Bera Lagrange multiplier test (JB) was performed to approximate the nor- mality of observations (Jarque and Bera 1987). The test checks the departure from normality due to either skewness or kurtosis. The small sample approximation, which approaches the asymptotic results more rapidly, is written as 2 r- 2 j, _ LlulL h _i r-2 6 (85) (r-1) (T+l)ft r-n 2 + 2 " r+lj_ where r = (T-k) is the degrees of freedom, b = pjp 2 m is the measure of the skewness of distri- bution (the degree of symmetry), and b 2 = p/p 2 is the measure of the kurtosis of distribution (the peakness of the distribution and the thick- ness of its tails) (p. are sample moments). The statistic A is asymptotically distributed as x2 2 (Edgerton 1992b. Judge et al. 1988, p. 890- 892). Normality cannot be tested in Godfrey’s local equivalent alternatives form. Thus, only equation-wise rather than multivariate normality was tested. The hypothesis of the normality of observations was rejected for the equations of Alcoholic Drinks and Fresh Milk within Bever- ages (Group 32). Parameter instability The cumulative sum of squares test (Cusumsq) tests for the stability (over time) of regression relationships, or structural changes in parame- ters. The application follows the ordinary-least- squares-residuals form of the test (McCabe and Harrison 1980, Moschini and Meilke 1984). 19 The Cusumsq statistic, C, based on the iterated- seemingly-unrelated-regression residuals, is cal- culated as, for (k + 1 ) < s V+l ”yj +l) ~ (87) where T is 1990. For comparison, the AIDS mod- els were estimated with data covering 1960-1990, and the year 1991 was predicted. The perform- ance criteria are based on the out-of-sample pre- diction errors. The procedure is similar to the model selection procedure known as cross-vali- dation (Maddala 1992, p. 504-506). Since only one period ahead is predicted, the MAPE meas- ures the difference between the predicted and ac- tual budget share in 1991, expressed in percent- ages. In the case of the random walk model, the MAPE measures the deviation of the 1990 actual budget share from the actual 1991 budget share, whereas in the case of the AIDS, the MAPE meas- ures the deviation of the AIDS projection for 1991 from the actual 1991 budget share. For example, the AIDS model predicted that the budget share of Food-at-Home is 0.2675 in 1991. However, the actual value was 0.2650. Thus, the absolute error was 0.0025, which is 0.9% (the MAPE in Table 25) of the actual value. The ratio of the 391 Agricultural Science in Finland 3 (1994) 392 Table 25. Model performance in ex post predictions over the sample period (1961-1991) and in ex ante predictions for 1991 (estimation period 1961-1990).“ Within sample Predictions for 1991 (estimation period predictions 1961-1990) MAPE R 2RMSE MAPE R 2RMSE AIDS AIDS Random AIDS Random AIDS walk walk Private Consumption (Group 1) - Food-at-Home 0.6 0.996 4.0 0.9 0.936 0.997 - Food-away-from-Home 1.5 0.996 5.4 6.3 0.918 0.888 -Non-Durables 1.1 0.932 0.1 1.8 1.000 0.900 -Services 0.5 0.993 3.4 1.1 0.556 0.955 - average 0,9 3,2 2.5 Food-at-Home (Group 2) -Animalia 0,8 0.920 1.7 1.2 0.794 0.894 -Beverages 1.2 0.873 1.7 0.3 0.839 0.994 -Groceries 2.0 0.835 1.5 2.0 0.953 0.910 -Vegetablia 1.3 0.950 0.6 1.3 0.992 0.968 -average 1.3 1.4 1.2 Animalia (Group 31) -Meat and Fish 1.1 0.931 0.3 0.5 0.997 0.992 - Dairy Products 1.9 0.899 1.7 0.2 0.966 1.000 -Eggs 3.3 0.910 10.4 10.7 0.692 0.669 -average 2.1 4.1 3.8 Beverages (Group 32) -Alcoholic Drinks 1.6 0.991 1.7 1.6 0.987 0.989 -Fresh Milk 2.4 0.988 2.4 8.9 0.998 0.964 -Soft Drinks 2.9 0.975 0.9 3.5 0.997 0.957 -Hot Drinks 2.4 0.986 11.1 8.7 0.961 0.976 - average 2.3 4.0 5.7 Vegetablia (Group 33) - Bread and Cake 1.4 0.937 0.3 3.4 0.999 0.782 -Fruits 3.3 0.941 1.0 7.6 0.995 0.716 - Vegetables 2.6 0.936 0.7 2.3 0.997 0.967 -Flour 3.6 0.978 0.3 2.1 1.000 0.997 - average 2.7 0.6 3.8 Meat and Fish (Group 41) - Meat Products 1.5 0.937 0.5 1.3 0.994 0.965 -Carcase Meat 2.2 0.852 1.8 1.4 0.949 0.969 -Fish 4.6 0.259 3.8 1.6 0.881 0.978 -average 2.8 2.0 1.4 Dairy Products (Group 42) -Cheese 4.3 0.975 6.1 0.9 0.884 0.997 - Sour Milk and Cream 2.8 0.954 0.4 13.4 0.999 0.151 -Butter 3.3 0.975 13.5 16.9 0.946 0.915 -Margarine 3.9 0.820 1.9 7.5 0.979 0.684 - average 3.6 5.5 9,7 * The AIDS refers to the preferred model specifications which were named in Table 7. The abbreviated notations are MAPE (mean absolute percentage error) and /?2RMSE (coefficient of determination derived from the root-mean- square prediction error). explained variation to the total variation is 0.997 (the tf’RMSE). Within the sample, mean absolute errors of 3% and above were recorded in Eggs, Fruits, Flour, Fish, Cheese, Butter, and Margarine. In groups Vegetablia, Meat and Fish, and Dairy Products (Groups 33, 41, and 42) the errors were relative- ly large (Table 25). In ex ante predictions, the random walk model performed better than the AIDS in Beverages, Vegetablia, and Dairy Prod- ucts (Groups 32, 33, and 42). In Vegetablia and Dairy Products, several low coefficients of deter- mination were recorded. The results indicate that the preferred AIDS specifications were good forecasting models in a number of groups. Within Vegetablia and Dairy Products (Groups 33 and 42), the prediction er- rors were large both in ex post and ex ante pre- diction. This suggests that the models specified should not be used for these two groups for fore- casting. Forecasts on the demand for Eggs and Fish must be interpreted with caution since large prediction errors were recorded. Otherwise the models specified for Groups 31 and 41, includ- ing Eggs and Fish, respectively, showed such a good performance that the groups were included in simulations. The model specified for Beverag- es (Group 32) showed large prediction errors in ex ante predictions, but relatively small predic- tion errors in ex post predictions. The group was included in the simulations. As a result of checking the forecasting accura- cy, future consumption will be projected for all groups, except Vegetablia and Dairy Products (Groups 33 and 42). For projecting, the preferred AIDS specifications will be used (Table 7). Be- cause the forecasting accuracy was evaluated con- cerning only one year (1991), the evidence would not have been sufficient, for example, to replace the AIDS with the random walk model, even if the random walk model showed better forecast- ing accuracy in some groups. This is because long-term (9 years) projections will be made, and the budget shares in most commodities have changed considerably in 10-year periods (Table 3). Thus, the assumption that budget shares will remain at the 1991 level during the whole 1990s is quite unjustified. The comparison between the models was made in order to evaluate how good short-term forecasts can be attained by using the AIDS, compared with the forecasts attained by using the random walk model. The prediction er- ror tests stressed a need to interpret the results with caution. The measured errors implied prob- lems to long-term projections since prediction er- rors are cumulative over time and, thus, the error is likely to be the greater the longer is the projection. 7.3 Projections of exogenous variables Predictions for future patterns of relative prices, total expenditure, and mean population are re- quired. Four alternative predictions are made con- cerning prices. All the price hypotheses employ the same budget constraint and size of popula- tion. The growth path of Private Consumption is mainly based on the predictions made by the Min- istry of Finance, whereas the growth path of the size of population is based on the projections made by the Central Statistical Office (Table 26). Table 26. Predictions for private consumption expendi- tures and mean population in 1992-2000. Year Private Consumption," Mean Population, change from previous millions year, % 1992 -2.5 5.037 1993 -4.5 5.054 1994 1.5 5.066 1995 3.5 5.075 1996 3.5 5.081 1997 3.0 5.087 1998 2.0 5.091 1999 2.0 5.093 2000 2.0 5.095 "The 1992 figure excludes Durables and Semi-Durables. Other figures refer to Total Private Consumption (in- cluding Durables and Semi-Durables). The figures refer to changes in aggregate demand; the per capita figures would be on an average 0,1%-points lower. Sources of Private Consumption: The 1992 figure. Sta- tistical Office (1993); 1993-1997 figures, Ministry of Finance (1993, p. 31); 1998-2000 figures, Vartia and Ylä-Anttila (1992, p. 297). Source of mean popula- tion: Statistical Office (1992). 393 Agricultural Science in Finland 3 (1994) 394 Table 27. Projections of relative prices in 2000: change from 1991 to 2000, %. Category Price change related to group Price change related to general price index price index (price of Private Consumption) Price option Price option 1960-91 1980-91 Structural 1960-91 1980-91 Structural trend trend change trend trend change Food-at-Home -4 -5 -11 -4 -5 -II -Animalia -1 -2 1 -5 -7 -10 - Meat and Fish -12 0 -6 -5 -10 - Meat Products -0 2 -1 -6 -3 -11 - Carcase Meat 4 8 2 -2 2 -8 -Fish -14 -37 0 -18 -41 -10 - Dairy Products 2 -4 -2 -3 -11 -11 -Eggs -8 -8 10 -13 -14 -I -Beverages -4 5-8 -8 -1 -18 - Alcoholic Drinks -1 2-11 -8 2 -27 -Fresh Milk -0 -12 20 -8 -12 -1 - Soft Drinks 6 6 -1 -2 5 -19 - Hot Drinks -2 -2 55 -9 -3 27 -Groceries 0 -6 1 -4-11 -10 -Vegetablia 5 -1 7 1 -7 -5 Food-away-from-Home 11 18 4 II 18 4 Non-Durables 1 -12 4 I -12 4 Services 15 4 15 4 An analysis which starts from the total consump- tion has the advantage that it is not necessary to assume food expenditures to be exogenously de- termined. Thus, the total expenditure is needed only for Stage I, since for the following stages it is supplied by the preceding stage. The variables h t in (68) are imposed to be one over the prediction period. This is justified by the fact that shifting parameters are not useful for the projections, because one cannot explain the cause of structural change and forecast the direction and magnitude of the change (c.f Myers 1986, p. 180). One of the four alternative price options as- sumes that prices remain at the 1991 level, two options assume historical trends to continue, whereas one option assumes a structural change in price patterns; 1. The 1991-price option. The prices are assumed to remain at the 1991 level, which is the last year of observation in the data set. The option implies that there will be no changes in rela- live prices between the years 1991 and 2000. 2. The 1960-91-trend option. The relative prices over 1992-2000 are assumed to follow the 1960-1991 trend in Finland, which, for ex- ample, for Food-at-Home, implies a decrease of 4% in relative price extended over 1992- 2000 (Table 27). 3. The 1980-91-trend option. The relative prices over 1992-2000 are assumed to follow the 1980-1991 trend in Finland which, for exam- pie, for Food-at-Home, implies a decrease of 5% in relative price extended over 1992-2000 (Table 27). 4. The structural-change option. The relative pric- es over 1992-2000 are assumed to face a struc- tural change. The set of relative prices in Den- mark in 1992 was taken as a characterisation what the relative prices would be in Finland in 2000. The prices are assumed to change gradually and, thus, the prices concerning the years between 1991 and 2000 are derived from a linear trend starting from the year 1991 prices and ending to the year 2000 prices. Thus, full adjustment is assumed to be reached by 2000. The option can be seen as a potential price path if Finland joins the European Union. As a benchmark for the structural-change op- tion, a comparison of price patterns in Denmark and Finland was used. For the comparison, aver- age retail prices of forty food items were col- lected in Denmark and Finland. The aim was to choose representative goods for the commodity bundles presented in Table 2. The Danish krona was converted to the Finnish markka by the ex- change rate of DKK 1 = FIM 0.7809.22 The ex- penditure patterns studied in the 1990 Finnish Household Expenditure Survey were used to weight both the Danish and Finnish prices. For example, the retail price for Fresh Milk is a com- bination of 1992 prices of standard milk and skim milk, weighted by the mutual budget shares of the commodities in Finland in 1990. No refer- ence prices concerning Food-away-from-Home, Non-Durables, and Services were available. The structural-change option implies that the price of Food-at-Home would decrease by 11% related to the price of Private Consumption (Table 27). No prediction concerning the development of gener- al price index was made. Thus, to offset the de- crease of the relative price of Food-at-Home, Food-away-from-Home, Non-Durables, and Serv- ices were assumed to become 4% more expen- sive related to the price of Private Consumption by the year 2000. No reference price concerning Fish was available, either. The relative price of Fish was assumed to remain at the 1991 level in the structural-change option. In the simulations the relative prices within groups are used (rather than prices related to the price of Private Consumption). For example, if one price in a group increases, at least one price has to decrease. All the relative prices cannot be projected independently of each other, but an ad- 22 Average of the Bank of Finland middle rates in De- cember 31, 1991, June 30, 1992, December 31, 1992, and June 30, 1993. justment must be carried out. The changes in rel- ative prices - weighted by budget shares - must add up to zero. In the first price option no price changes were predicted, and the size of the in- consistency is zero, i.e. the condition is automat- ically satisfied. For other options, the condition has to be imposed. The equation is, for goods i within group r. X- P i, 1991 L a w (r)i,il.Ol Meat Products Alcoholic Drinks Food-away-from-Home Flot Drinks Fruits Vegetables Groceries Table 34. Schematic presentation of the demand elasticities at the 1991 values. Range of total Range of total uncompensated own-price elasticity expenditure elasticity 0..-0.30 -0.31,.-1.00 <-1,01 -0.20..0.30 Sour Milk and Cream Butter Margarine Flour 0.31..1.00 Carcase Meat Fish Soft Drinks Cheese Bread and Cake Fresh Milk Hot Drinks* >l.Ol Meat Products Alcoholic Drinks Food-away-from-Home Eggs Fruits Vegetables Groceries a Own-price elasticity of 0.56 was estimated. sequences. The consumption of categories like Meat Products, Alcoholic Drinks, and Groceries tends to increase no matter what price policy is chosen - the question is how much. Instead, the consumption of Carcase Meat, Dairy Products, and Vegetablia tends to be stagnated no matter what price policy is chosen. If the policy is to maintain the relative prices as they were in 1991, the consumption of Meat Products, Alcoholic Drinks, Soft Drinks, Grocer- ies, and Food-away-from-Home would increase substantially by the year 2000, while the con- sumption ofFresh Milk and Dairy Products would remain unchanged. As a consequence of a policy that allows the historical price trends in Finland to continue, the consumption of Meat Products and Fish would increase substantially, while the consumption of Carcase Meat, Dairy Products, and Soft Drinks - possibly also Eggs, Fresh Milk, and Hot Drinks - would decrease. The price de- velopment that was presumed to follow from en- tering the European Union would imply that the 408 Agricultural Science in Finland 3 (1994) consumption of Groceries and Food-away-from- Home would increase substantially, while the con- sumption of Soft Drinks and Vegetablia would remain unchanged. A predicted consequence of the membership in the European Union is that the share of food in consumers’ budget would decrease. The expect- ed decrease is faster than the decrease that would take place if future price developments were based on the historical trends. If Finland joins the Un- ion, the budget share of Food-at-Home would decrease from 21% in 1991 to 18% in 2000, whereas the budget share of Food-at-Home ex- cluding Alcoholic Drinks would decrease from 16% in 1991 to 14% in 2000. Under other price options, the budget shares of Food-at-Home and Food-at-Home excluding Alcoholic Drinks would be up to 22% and 17% in 2000, respectively. In Finland many agricultural commodities are produced in excess of domestic consumption. Di- verse measures of control policy have targeted to achieve more balanced supply and demand (Kola 1991). According to the present analysis, aggre- gate demand is expected to contribute to more balanced markets of milk, meat, and eggs. The aggregate demand for Fresh Milk is expected to increase 1 % annually until 2000 under the price option that describes Finland entering the Euro- pean Union, while the demand for Dairy Prod- ucts (other than Fresh Milk) is expected to in- crease 0.5% annually. Under the other price op- tions, the increases would be the same or smaller. However, the slightly increasing aggregate de- mand would not solve the problem of overpro- duction, since the domestic production of milk was about one-fourth above the domestic con- sumption in 1992 (National Board of Agriculture 1993). Moreover, the increase in the demand for raw milk can even be adverse if consumers shift to consuming higher-valued dairy products, in- stead of increased physical quantities. The price option describing Finland entering the European Union is expected to increase the aggregate demand for Meat Products and Car- case Meat 0.8% annually until 2000, while the demand for Eggs is expected to increase 0.5% annually. Under the other price options, the in- creases would be about twice that much (with an exception of Eggs under the 1980-91-trend op- tion: the demand would remain unchanged). How- ever, especially in meats the impact in the aggre- gate demand for raw materials will be smaller, since part of the increase will probably affect the quality of consumption (in terms of value), rath- er than physical quantities. Foreign trade can change rapidly the balance between domestic demand and supply. For exam- ple, increased amount of imported food easily offsets the slow increase in aggregate demand and, consequently, the need for production con- trol would not be lessened. Summary The objectives of the study were: (a) to present the food consumption patterns in Finland over the period 1950-1991, (b) to estimate a demand system for a 18-category breakdown of food ex- penditures, (c) to verify how well the Finnish consumer behaviour corresponds to the consum- er theory, (d) to estimate price and expenditure elasticities of food products, (e) to obtain projec- tions on future food demand in Finland, (f) to examine the sensitivity of the projections to al- ternative price developments, and (g) to derive policy implications. The National Accounts provided annual vol- ume and price series on household consumption. While the real expenditure on food has increased, the share of food of the total expenditure has decreased. In the early 19505, combined Food-at- Home and Food-away-from-Home corresponded to about 40% of consumers’ expenditure. In 1991 the share was 28%. There was a shift to meals 409 Agricultural Science in Finland 3 (1994) eaten outside the home. While the budget share of Food-away-from-Home increased from 3% to 7% over the observation period, Food-at-Home fell from 37% to 21%, and Food-at-Home ex- cluding Alcoholic Drinks fell from 34% to 16%. Within Food-at-Home, the budget shares of the broad aggregate groups, Animalia (food from an- imal sources), Beverages, and Vegetablia (food from vegetable sources), remained about the same over the four decades, while structural change took place within the aggregates. Within Anima- lia, consumption shifted from Dairy Products (oth- er than Fresh Milk) to Meat and Fish. Within Beverages, consumption shifted from Fresh Milk and Hot Drinks to Alcoholic Drinks and Soft Drinks. Within Vegetablia, consumption shifted from Flour to Fruits, while the shares of Bread and Cake and Vegetables remained about the same. The empirical application examined the exist- ing market demand structure and estimated mar- ket level parameters for food demand in Finland. With a strong consideration on methodological aspects, the analysis was carried out within the framework of a standard demand analysis, which lays emphasis on estimating the responses of pric- es and total expenditure. A complete demand sys- tems approach was adopted. The advantage of the methodology is - compared with a single equa- tion approach - that the systems account for in- terdependency among commodities, and they try to specify a sound correspondence between the microeconomic theory of an individual consumer and the market data. Moreover, the systems de- scribe the allocation of expenditures among com- modities in a way that the expenditures on sub- groups sum up to the total expenditure. As a complete demand system, the Almost Ideal Demand System (AIDS) was employed. The AIDS is a system of demand equations in a budget share form. The AIDS form is based on a specific func- tional form for the consumer expenditure func- tion. The expenditure function was specified, and the AIDS Marshallian demand functions were de- rived by minimising the expenditure necessary to reach a certain utility level. The necessary condi- tions for the procedure were called the Slutsky conditions. Ideally, the resulting demand func- tion to be applied to aggregate data will be con- sistent with the conditions and, consequently, with the microeconomic theory ofconsumer behaviour. A four-stage budgeting system was specified, consisting of seven sub-systems. First, consum- ers were presumed to decide the amount to spend on four aggregate groups, one of which was Food- at-Home, one was Food-away-from-Home. Sec- ond, Food-at-Home was allocated into Animalia, Beverages, Groceries, and Vegetablia. Third, the broad categories were divided into 11 sub-cate- gories. Finally, two sub-categories were disag- gregated further. The conventional AIDS was extended by de- veloping a dynamic generalisation of the model and allowing for systematic shifts in structural relationships over time. Four modifications of the AIDS were specified: static AIDS, dynamic AIDS, switching static AIDS, and switching dynamic AIDS. Each variant was estimated either as an unconstrained form, a homogeneity-constrained form, and a homogeneity-and-symmetry-con- strained form. The equations were estimated us- ing the iterated feasible generalised least squares method. Tests on parameter restrictions (static, non-switching, homogeneity, and symmetry) and misspecification tests (testing the assumptions concerning the error terms) were used to choose the most preferred model specification for each group. The following specifications were chosen: (a) the switching dynamic AIDS, unrestricted, for four groups (Private Consumption, Food-at-Home, Vegetablia, and Dairy Products), (b) the switch- ing dynamic AIDS, homogeneity and symmetry restricted, for one group (Meat and Fish), (c) the dynamic AIDS, unrestricted, for one group (Bev- erages), and (d) the static AIDS, unrestricted, for one group (Animalia). The preferred models were evaluated by test- ing the Slutsky conditions, measuring the good- ness of fit, and testing the assumptions that lay behind the estimation. The estimated models did not usually satisfy the Slutsky conditions, which implies that the correspondence between the consumer behaviour and the theory was not good. There are several potential causes for the outcome, besides the con- 410 Agricultural Science in Finland 3 (1994) elusion that the theory is inappropriate. For ex- ample, preferences may have been unstable, the data may have been improper, the Slutsky condi- tions may have been valid, but maybe the func- tional form was misspecified, some variables may have been missing, or maybe the conditions held for an individual consumer and for a complete range of goods, but the chosen groupings of con- sumers and goods were inappropriate. The goodness-of-fit measures were good, and, compared to static specifications, dynamics usu- ally provided a better fit. The misspecification tests indicated that (a) the dynamic specification was correct, (b) some form of misspecification was found, for instance, there were one or more omitted variables or the func- tional form was incorrect, and (c) there was struc- tural change in parameters. Interpretation of the models was made by de- riving own-price, cross-price, and expenditure elasticities. A distinction was made between with- in-group and total elasticities. Within-group elas- ticities showed the effects within a particular group, whereas total elasticities also accounted for the effects channeled through group expendi- tures. The total expenditure elasticity is widely employed in the literature, but it is common that only within-group price elasticities are derived. The study showed that this approach is mislead- ing. A price change has simultaneous effects on the quantities demanded of a wide range of prod- ucts. Associated with the adopted complete de- mand system framework, the advantage of using total elasticities was that the effects ofprice chang- es could be pursued across all demand catego- ries. The implications of the estimated elasticities are as follows: I. In all categories, an increase in the own price decreases the consumption. Given the own prices of Soft Drinks and Food-away-from- Home increase, the expenditure on the cate- gories decreases. In other categories, a price increase increases the expenditure on the re- spective category. 2. An increase in the prices of Services and Food- away-from-Home shifts consumer expenditure on Food-at-Home downwards, and a decrease in the prices of Services and Food-away-from- Home shifts expenditure on Food-at-Home upwards. 3. Given a change in the prices of Food-away- from-Home and Food-at-Home, the demand for Food-away-from-Home is affected more strongly than the demand for Food-at-Home. 4. If the price ratios within Food-at-Home alter, the effect on the demand for Carcase Meat, Dairy Products, Eggs, Alcoholic Drinks, Fresh Milk, Hot Drinks, Groceries, and Vegetablia would be small, whereas the effect on the de- mand for Meat Products, Fish, and Soft Drinks would be great. 5. A change in the price ratio between Carcase Meat and Fish easily causes a shift to Fish (if Carcase Meat becomes more expensive) or a shift away from Fish (if Carcase Meat be- comes cheaper). The change in the price ratio causes a shift to or away from Carcase Meat less easily (if the price of Fish changes). 6. As a result of a change in the price ratio be- tween Butter and Margarine, consumers shift to the fat the relative price of which decreas- es. 7. A change in the price ratio between Flour and Bread and Cake easily causes a shift to or away from Flour (if Bread and Cake become more expensive or cheaper, respectively). The change in the price ratio causes a change in the demand for Bread and Cake less easily (if the price ofFlour changes). 8. An increase in the price of Alcoholic Drinks makes consumers shift to Soft Drinks, and a decrease in the price of Alcoholic Drinks makes consumers shift away from Soft Drinks. Change in the prices of Soft Drinks do not make consumers change the consumption of Alcoholic Drinks. 9. If private consumption increases by 1%, the consumption of Meat Products, Alcoholic Drinks, Hot Drinks, Fruits, Vegetables, Gro- ceries, and Food-away-from-Home increases more than 1%, the consumption of Marga- rine and Bread and Cake decreases, whereas 411 Agricultural Science in Finland 3 (1994) the consumption of other categories increas- es by 0-1%. 10. An increase in private consumption enlarges the demand for Food-away-from-Home com- pared to the demand for Food-at-Home, whereas a decrease in private consumption reduces the demand for Food-away-from- Home compared to the demand for Food-at- Home. The estimated demand system was applied for projecting the future consumption of food prod- ucts in Finland to the year 2000. The approach was to choose a certain change in the real total consumption expenditure and alternative sets of relative prices for the forecast period. Four dif- ferent options of price variables were defined. These were (a) assuming the price structure re- corded in the year 1991 to remain until the year 2000 (the 1991-price option), (b) assuming the price trends recorded over the period 1960-91 to continue until 2000 (the 1960-91-trend option), (c) assuming the price trends of the period 1980- 91 to continue until 2000 (the 1980-91-trend op- tion), and (d) assuming the Finnish price struc- ture to converge to the price structure recorded in Denmark in 1992 (the structural-change option). Unlike the other price options, the structural- change option implied that, over the forecast pe- riod, relative prices would no longer rely on the historical trends recorded in Finland. Before simulating, forecast accuracy was checked by means of prediction errors tests. With- in two groups, Vegetablia and Dairy Products, the prediction errors were large and, therefore, the projections were made only for the groups, rather than for the within-group categories. The projections were sensitive to alternative price developments. The greatest variation in the projected volumes for the year 2000 were ob- tained in Meat Products, Fish, Soft Drinks, and Food-away-from Home, where the gaps between the lowest and highest forecasts were 16-44%. In Food-at-Home, Animalia, Dairy Products, Gro- ceries, and Vegetablia the gaps between the low- est and highest forecasts were 6% or less. The 1980-91-trend option generated the lowest fore- cast in 10 of the 16 cases, whereas the 1991- price option generated the highest forecast in 13 of the 16cases. The following implications were derived: I. The 1991-price option implied that the per capita consumption of Meat Products, Alco- holic Drinks, Soft Drinks, Groceries, and Food- away-from-Home would increase substantial- ly by the year 2000, while the consumption of Fresh Milk and Dairy Products would remain unchanged. 2. The 1960-91-trendoption implied that the per capita consumption of Meat Products and Fish would increase substantially, while the con- sumption of Carcase Meat, Dairy Products, and Soft Drinks would decrease. 3. The 1980-91-trendoption implied that the per capita consumption of Meat Products and Fish would increase substantially, while the con- sumption of Carcase Meat, Dairy Products, Eggs, Fresh Milk, Soft Drinks, and Hot Drinks would decrease. 4. The structural-change option implied that the per capita consumption of Groceriesand Food- away-from-Home would increase substantial- ly, while the consumption of Soft Drinks and Vegetablia would remain unchanged. The structural-change option measured the ex- pected consequences ofFinland’s possible mem- bership in the European Union. A consequence of the membership is that the share of food in consumers’ budget would decrease. 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Laurila Suomen Akatemia ja Helsingin yliopisto Tutkimuksen tarkoituksena oli (a) tarkastella elintarvik- keiden kysynnän rakennetta Suomessa, (b) estimoida elin- tarvikkeiden kysyntäjärjestelmä, jossa elintarvikkeet on jaettu I 8 ryhmään, (c) testata, miten hyvin suomalainen kulutuskäyttäytyminen vastaa kuluttajan teorian kuvaamaa käyttäytymistä, (d) estimoida elintarvikkeiden hinta- ja menojoustot, (e) laatia ennusteet elintarvikkeiden kulu- tuksen kehitykselle vuoteen 2000, (f) tarkastella ennustei- den riippuvuutta vaihtoehtoisista hintaskenaarioista ja (g) tarkastella, miten tutkimuksen tuloksia voidaan ottaa huo- mioon, kun valmistellaan elintarvikkeiden hintoihin vai- kuttavia toimenpiteitä. Havaintoaineistona käytettiin kansantalouden tilinpidon yksityisiä kulutusmenoja kuvaavia aikasarjoja vuosilta 1950-1991. Aineisto osoitti, että vaikka elintarvikkeisiin käytetty rahamäärä kasvoi reaalisesti, elintarvikkeiden osuus kaikista kulutusmenoista supistui. 1950-luvun alus- sa kuluttajat käyttivät kotona ja kodin ulkopuolella nautit- tuihin elintarvikkeisiin 40% kaikista menoistaan; vuonna 1991 osuus oli 28%. Ruokailu kodin ulkopuolella lisään- tyi kotona tapahtuvan ruokailun kustannuksella. Kodin ul- kopuolella nautittujen elintarvikkeiden osuus kokonais- menoista kasvoi havaintojakson aikana 3%:sta 7%:iin sa- malla kun kotiin hankittujen elintarvikkeiden osuus koko- naismenoista laski 37%:sta 2l%:iin, Jos alkoholijuomat jätetään ottamatta huomioon, kotiin hankittujen elintar- vikkeiden osuus kokonaismenoista laski 34%:sta 16%:iin. Kotiin hankittujen elintarvikkeiden keskinäiset budjet- tiosuudet säilyivät 40 vuoden ajan varsin muuttumattomi- na, kun asiaa tarkastellaan suurryhmien tasolla. Näitä suur- ryhmiä ovat eläinkunnan tuotteet, kasvikunnan tuotteet ja juomat. Sen sijaan suurryhmien sisällä tapahtui siirtymiä. Eläinkunnan tuotteissa kulutusmenot siirtyivät meijerituot- teista lihaan ja kalaan. Kasvikunnan tuotteissa kulutusme- not siirtyivät jauhoista hedelmiin samalla kun leipomo- tuotteiden ja vihannesten osuudet säilyivät entisellään. Juo- missa kulutusmenot siirtyivät maidosta ja kahvista alko- holijuomiin ja virvoitusjuomiin. Kotitalouksien kuluttamat elintarvikkeet jaettiin 18 tuo- teryhmään, ja näiden tuoteryhmien kulutuksen riippuvuus hinnoista, kokonaismenoista ja aiemmasta kulutusraken- teesta haluttiin selvittää. Tutkimusongelmaa lähestyttiin nk. täydellisen kysyntäjärjestelmän avulla. Menetelmän etu yhden yhtälön menetelmiin verrattuna on ensinnäkin se, että hyödykkeiden väliset riippuvuudet on mahdollista ottaa analyysissä huomioon ja toiseksi se, että täydellinen kysyntäjärjestelmä on suora linkki kuluttajan teorian ku- vaarnan yksittäisen kuluttajan jakansantalouden tason ha- vaintoaineiston välillä. Täydellisenä kysyntäjärjestelmänä käytettiin AIDS-mallia (Almost Ideal Demand System, ”lä- hes täydellinen kysyntäjärjestelmä”). Tavanomaisen staat- tisen AIDS-mallin ohella estimoinnissa käytettiin dynaa- mista AIDS-mallia sekä mallia, jossa joidenkin parametri- en arvojen annettiin muuttua ajan funktiona (nk. raken- teellisen muutoksen AIDS). Nelitasoinen hierarkkinen ky- syntäjärjestelmä muodostui seitsemästä osaongelmasta. Kullekin osaongelmalle valittiin sopivimman tyyppinen AIDS-malli. Valintakriteereinä käytettiin tuloksia testeis- tä, joissa testattiin kysyntäteoriasta johdettuja parametri- en rajoituksia sekä mallin hyvyyttä tilastollisessa mieles- sä. Valtaosa estimoiduista malleista ei täyttänyt kysyntä- teoriasta johdettuja Slutskyn ehtoja, mikä on tavallinen tulos vastaavissa tutkimuksissa. Mallien selitysasteet oli- vat korkeita, ja useimmiten dynamiikan lisääminen korot- ti selitysastetta huomattavasti. Testien mukaan mallien dy- namiikka oli määritelty oikein, mutta jäljelle jäi ongel- mia, muun muassa parametrien arvojen epävakautta. Estimoidut mallit tulkittiin hinta- ja menojoustojen avul- la. Havaintojakson aikana kysynnässä tapahtui rakenteel- lisia muutoksia niin että 1960-luvun joustot poikkesivat 1990-luvun joustoista. Seuraavassa esitettävät joustot ku- vaavat kysyntää keskimäärin vuosina 1961-1991. Lihaja- losteet, alkoholijuomat, kahvi, kuivatuotteet (makeiset, mausteet, keittoainekset, jäätelö, sokeri ja hillot), hedel- mät sekä vihannekset olivat luksustuotteita (menojousto yli yhden). Sama koski kodin ulkopuolella tapahtuvaa ruo- kailua. Muut tuoteryhmät olivat välttämättömyyshyödyk- keitä (menojousto alle yhden). Voin, margariinin, hapan- maitotuotteiden ja kerman sekä leipomotuotteiden meno- joustot olivat lähellä nollaa, mikä tarkoittaa sitä, että ko- konaismenojen kehityksellä oli vain vähäinen vaikutus ky- seisten elintarvikkeiden kulutukseen. Virvoitusjuomat ja kodin ulkopuolella tapahtuva ruokailu olivat hintajousta- via, eli niiden kulutus muuttui herkästi oman hinnan muu- tosten seurauksena. Kaikkien muiden tuoteryhmien kulu- tus oli oman hinnan suhteen jäykkää (taulukko). Estimoitua kysyntäjärjestelmää käytettiin tulevan kulu- tuksen ennustamiseen. Vuoteen 2000 ulottuvien ennustei- den laadintaa varten arvioitiin kokonaiskulutusmenojen tuleva kehitys sekä laadittiin neljä vaihtoehtoista skenaa- riota hyödykkeiden hintasuhteiden kehityksestä. Kaksi ske- naariota perustui Suomessa havaittuun aikaisempaan ke- hitykseen (1960-91 ja 1980-91 trendit), yksi skenaario 419 Agricultural Science in Finland 3 (1994) Taulukko. Kysynnän hinta-ja tulojoustot Suomessa keskimäärin vuosina 1961-1991. Menojouston Hintajousto oman hinnan suhteen (kompensoimaton) vaihteluväli 0..-0.30 -0.31.-1.00 <-1.01 -0.20..0.30 Jalostamaton liha Kala Hapanmaitotuotteet ja kerma Voi Margariini Leipomotuotteet 0,31..1.00 Kananmunat Jauhot Virvoitusjuomat Maito Juusto > 1.01 Lihajalosteet Alkoholijuomat Kodin Kahvi Hedelmät ulkopuolinen Vihannekset ruokailu Kuivatuotteet jähmetti hintasuhteet sellaisiksi kuin ne olivat vuonna 1991, ja yksi skenaario kuvasi hintasuhteiden kehitystä siinä ti- lanteessa, että Suomesta tulisi Euroopan unionin jäsen. Lukuunottamatta skenaariota, jossa hintasuhteet säilyisi- vät sellaisina kuin ne olivat vuonna 1991, kotiin hankittu- jen elintarvikkeiden oletettiin halpenevan keskimäärin 4- 11% vuodesta 1991 vuoteen 2000. Ennusteet olivat herkkiä hintasuhteiden muutoksille. Suurin merkitys sillä, mikä skenaario toteutuu, on lihaja- losteiden, kalan ja virvoitusjuomien kulutukseen sekä ko- din ulkopuolella tapahtuvaan ruokailuun. Sen sijaan laa- jojen tuoteryhmien, kuten kasvikunnan tuotteiden sekä mei- jerituotteiden - ja yleisemminkin eläinkunnan tuotteiden - kulutus kehittyy ennusteen mukaan 1990-luvulla suu- remmin riippumatta hintasuhteiden muutoksista. Jos kulutushyödykkeiden hintasuhteet säilyisivät 1990- luvun sellaisina kuin ne olivat vuonna 1991, lihajalostei- den, alkoholijuomien, virvoitusjuomien ja kuivatuotteiden kulutus sekä kodin ulkopuolinenruokailu kasvaisivat huo- mattavasti, kun taas maidon ja muiden meijerituotteiden kulutus säilyisi ennallaan. Jos kulutushyödykkeiden hin- tasuhteet noudattaisivat historiallisia trendejä, lihajalos- teiden ja kalan kulutus kasvaisi huomattavasti, kun taas jalostamattoman lihan, meijerituotteiden (muiden kuin maidon) ja virvoitusjuomien - mahdollisesti myös kanan- munien, maidon ja kahvin - kulutus alenisi. Euroopan unionin jäsenyyden mahdollisesti mukanaan tuoma hinta- rakenne kasvattaisi kuivatuotteiden kulutusta sekä kodin ulkopuolista ruokailua, kun taas virvoitusjuomien ja kas- vikunnan tuotteiden kulutus säilyisi ennallaan. Suomen jäsenyyden Euroopan unionissa arvioitiin vai- kuttavan siten, että elintarvikkeiden osuus kuluttajien bud- jetissa laskee. Lasku olisi nopeampi kuin lasku, joka syn- tyisi siitä, että hyödykkeiden hintasuhteet jähmettyisivät vuoden 1991 tilanteen mukaisiksi tai muuttuisivat histori- allisten trendien viitoittamana. Euroopan unioni -vaihto- ehdossa kotiin hankittujen elintarvikkeiden jakodin ulko- puolella tapahtuvan ruokailun yhteinen budjettiosuus las- kisi vuoden 1991 28%:sta 27%:iin vuonna 2000. Kotiin hankittujen elintarvikkeiden budjettiosuus laskisi 21%:sta 18%:iin, kun taas kotiin hankitut elintarvikkeet vähennet- tynä alkoholijuomilla vastaisivat keskivertokuluttajan bud- jetista 14% vuonna 2000, kun budjettiosuus vuonna 1991 oli 16%. 420 Agricultural Science In Finland 3 (1994) Definition of commodity bundles The following categories were used in the present study. Budget shares describe the composition of the categories. Total Private Consumption (including Durables and Semi-Durables) refers to the final consumption expenditure of households in the domestic market. The category is composed of Private Consumption (78% of the expenditure in 1991), Semi-Durables (13%), and Durables (9%). Private Consumption refers to the final consumption expenditure of households in the domestic market excluding Durables and Semi-Durables. The category consists of Food-at-Home (27% of the expenditure in 1991), Food-away- from-Home (9%), Non-Durables (19%), and Services (45%). Food-at-Home is that part of consumers’ expenditure which is allocated to food and drink consumed at home. The bundle is composed of Animalia (34% of the expenditure in 1991), Beverages (32%), Vegetablia (26%), and Groceries (9%). Food-away-from-Home consists of expenditure on food and drink in restaurants and cafes. Consumers’ expendi- ture on food catered at places of work is included. Noteworthy is that the share of services of the expenditure is remarkable. Non-Durables consist of non-durable goods excluding Food-at-Home. Fuels, medicines, home cleaning chemicals, and literature are the largest groups. Services consist of services excluding expenditure on Food-away-from-Home. The biggest expenditure groups are rents and insurance, house service, medical and sanitational treatment, travel tickets, telecommunications, education, culture, hotel fees, TV licenses, and lottery. Animalia (food from animal sources) is composed of Meat and Fish (64% of the expenditure in 1991), Dairy Products (33%), and Eggs (4%). Beverages refer to Alcoholic Drinks (68% of the expenditure in 1991), Fresh Milk (16%), Soft Drinks (9%), and Hot Drinks (8%). Vegetablia (food from vegetable sources) are Bread and Cake (41% of the expenditure in 1991), Fruits (28%), Vegetables (19%), and Flour (13%). Groceries cover candies and chocolate (36% of the expenditure in 1991), spices and soups (24%), ice-cream (17%), sugar (15%) jam (7%), and honey (1 %). Meal and Fish is composed of Meat Products (53% of the expenditure in 1991), Carcase Meat (36%), and Fish (10%). Dairy Products include Cheese (40% of the expenditure in 1991), Sour Milk and Cream (31%), Butter (17%), and Margarine (12%). Meat Products are combined of sausages (56% of the expenditure in 1991), canned and prepared meat (34%), and other meat products (10%). Carcase Meat consists of beef and veal (59% of the expenditure in 1991), pork (22%), poultry (12%), game (5%), mutton, lamb, and reindeer (2%). Unlike in some other definitions, the bundle includes poultry. Fish covers unprocessed fish (69 % of the expenditure in 1991) and canned and processed fish (31%) Alcoholic Drinks refer to beverages which contain alcohol. Fresh Milk is composed of standard milk, i.e. pasteurised and homogenised milk with fat content close to the raw- material, low fat milk (since 1970), skimmed milk (altogether 94% in 1991), and whole milk, i.e. the milk delivered directly from the farm and the milk consumed by the producer’s household (6%). Soft Drinks consist of soft drinks and mineral waters. Hot Drinks are coffee (89% of the expenditure in 1991), tea (5%), cocoa (4%), and coffee and tea extracts (2%). Bread and Cake is composed of coffee cake (52% of the expenditure in 1991) and bread (48%). Fruits consist of cultivated fruits and berries (58% of the expenditure in 1991), juices (19%), canned fruits (11%), wild berries (10%), and dried fruits and nuts (2%). Vegetables are a combination ofpotatoes from farms (36% of the expenditure in 1991), vegetables and roots from industry (31%), vegetables and roots from farms (28%), mushrooms (3%), and potatoes from industry (2%). Flour covers flour and hulled grain (68% of the expenditure in 1991), potato flour (5%), rice (4%), malt (1%), and other cereal products (21%). Cheese consists of emmentaler (swiss) and edam (51% of the expenditure in 1991) and others (49%). Sour Milk and Cream cover sour milk products (64% of the expenditure in 1991) and cream (36%). Butter covers dairy butter, butter-vegetable-oil mixtures, and cottage butter, which, however, was only 0.2% of the total in 1991. Margarine covers margarine (90% of the expenditure in 1991) and oils (10%). Appendix 1. Food demand system for Finland: parameter estimates In the following tables, parameter coefficients of the preferred specifications of the AIDS models are presented. Group by group, the presentation follows the same mode. First come the sample period, the two joint points in the switching regressions (for the beginning and the end of switch period), and the [natural] logarithm of the subsistence expenditure (a 0 ). There are three tables for each group: (a) parameter values, (b) their robust standard errors (White’s heteroskedas- ticity consistent standard errors), and (c) the r-values, which were obtained by dividing the coefficient by the respective standard error, a. is the constant in equation i, y is the price parameter for commodity j in equation i, /}. is the expenditure parameter in equation i, fT. is the shifting expenditure parameter in equation i, 0.. is the dynamic parameter for share j in equation i. GROUP 1: PRIVATE CONSUMPTION MODEL: SWITCHING DYNAMIC AIDS (UNRESTRICTED) Sample period: 1961-1991 loint points: 1975 and 1984 ctO: 8.4634 PARAMETER ESTIMATES i ou yil yi2 ]t3 yi4 Pi P»i 0U oi2 oi3 6i4 1 0.0319 0.2565 -0.1061 -0.0535 -0.1082 0.0693 -0.0114 0.2777 -0.8025 0.2433 0,2816 2 -0.0493 0.0118 -0.0151 0.0037 -0.0156 0.0951 0.0021 -0.0786 0.2075 -0.1146 -0.0143 3 0.0719 -0.0364 0,0290 0.1530 -0.1265 0.0334 -0.0205 0.2092 -0.4283 0.0828 0.1363 4 0.9455 -0.2320 0.0923 -0.1032 0.2503 -0.1978 0.0298 -0.4083 1.0233 -0.2115 -0.4035 STANDARD ERRORS OF PARAMETERS (ROBUST) i ca yil yi2 yi3 yi4 Pi p*i 0U 6i2 6i3 Bt4 1 0.0731 0.0242 0.0140 0.0255 0.0464 0.0217 0.0029 0.0807 0.1615 0.0913 0.1239 2 0.0582 0.0147 0.0130 0.0102 0.0180 0.0171 0,0012 0.0487 0.1296 0.0416 0.0711 3 0.1061 0.0284 0,0166 0.0247 0.0510 0.0283 0.0029 0.0858 0.2576 0.0937 0.1559 4 0.0649 0.0201 0.0143 0.0201 0.0277 0.0205 0.0028 0.0752 0.1464 0.0768 0.0979 T-STATISTIC i ai yil yi2 yi3 yi4 Pi P»i 0U oi2 6i3 6i4 1 0.44 10.60 -7.59 -2.10 -2.33 3.20 -3.93 3.44 -4.97 2.66 2.27 2 -0.85 0.80 -1.17 0,36 -0.87 5.55 1.68 -1.61 1.60 -2.76 -0.20 3 0.68 -1.28 1.74 6.19 -2.48 1.18 -7.05 2.44 -1.66 0.88 0.87 4 14.58 -11.52 6.43 -5.13 9.03 -9.64 10.48 -5.43 6.99 -2.76 -4.12 Appendix 2. GROUP 2: FOOD-AT-HOME MODEL: SWITCHING DYNAMIC AIDS (UNRESTRICTED) Sample period: 1961-1991 Joint points: 1961 and 1984 Ot0: 7.5380 PARAMETER ESTIMATES i at yil yi2 yi3 yi4 pi p*t 9il 9i2 oi3 9i4 1 0.3332 0.0850 -0.0904 -0.0461 -0,0194 -0.1465 0.1217 0.0750 0,1511 0.0519 -0.2780 2 0.2598 0.0920 0.0850 -0.1000 -0.0258 0.1155 -0.0819 -0.0029 0.2115 -0.3688 0.1603 3 0.3897 -0.1523 0,0307 0.1258 -0.0081 -0.0642 0.0199 -0.1263 -0.3333 0.2495 0.2101 4 0.0173 -0.0248 -0.0253 0.0204 0.0532 0.0952 -0.0597 0.0542 -0.0293 0.0675 -0.0924 STANDARD ERRORS OF PARAMETERS (ROBUST) i ai yil yi2 yi3 yi4 Pi Pn oil oi2 9i3 9i4 1 0.0465 0.0263 0.0234 0.0220 0.0115 0.0323 0.0244 0.1059 0.0874 0.0834 0.1721 2 0.0520 0.0377 0.0245 0.0291 0.0119 0.0399 0.0309 0.0990 0.1004 0.0916 0.1374 3 0.0563 0.0319 0.0278 0.0361 0.0133 0.0442 0.0366 0.1160 0.1403 0.1264 0.2482 4 0.0233 0.0193 0.0133 0.0198 0.0093 0.0209 0.0158 0.0559 0.0633 0.0469 0.0773 T-STATISTIC i cu yil yi2 yi3 yi4 j3i j3n 9il 9C oi3 6i4 1 7.16 3.23 -3.86 -2.09 -1.69 -4.54 4.98 0.71 1.73 0.62 -1.62 2 5.00 2.44 3.47 -3.44 -2.17 2.89 -2,65 -0.03 2.11 -4.03 1.17 3 6.92 -4.78 1.11 3.48 -0.61 -1.45 0.54 -1.09 -2.37 1.97 0.85 4 0.74 -1.28 -1.91 1.03 5.74 4.55 -3.78 0.97 -0.46 1.44 -1.20 GROUP 31: ANIMALIA MODEL: STATIC AIDS (UNRESTRICTED) Sample period: 1961-1991 Joint points: none aO: 6.5058 PARAMETER ESTIMATES t a_i yU yi2 yii p_i p*_i 0U 6_i2 9 i 3 1 0.1830 0.2278 -0.1369 -0.1018 0.2730 2 0.7688 -0.1618 0.1171 0.0619 -0.2733 3 0.0481 -0.0661 0.0197 0.0398 0.0003 STANDARD ERRORS OF PARAMETERS (ROBUST) i at yi2 P_i pM 9_il oj2 9 i 3 1 0.0462 0.0494 0.0408 0.0179 0.0304 2 0.0476 0.0490 0.0414 0.0151 0.0312 3 0.0095 0.0131 0.0113 0.0089 0.0066 T-STATISTIC i a_t yU y_i2 y_i3 P_t js»_i 9_il 9_t2 9 i 3 1 3.96 4.61 -3.35 -5.70 8.98 2 16.16 -3.30 2.83 4.10 -8.76 3 5.04 -5.03 1.75 4.47 0.05 Appendix 2. GROUP 32: BEVERAGES MODEL; DYNAMIC AIDS (UNRESTRICTED) Sample period: 1961-1991 Joint points: none otO: 6.2005 PARAMETER ESTIMATES i g i Y_U y_i3 yi4 p_i p* i 9U 6 i 2 9 t 3 9 i 4 1 0.6616 0.1667 -0.0890 0.0019 -0.0613 0.1623 -0.4968 -0.7176 1.5869 -0.3725 2 0.1813 -0.1704 0.1148 0.0558 -0.0437 -0.1088 0.2394 0.5546 -0.9503 0.1563 3 0.1422 0.0270 0.0065 -0.0205 -0.0039 -0.0224 -0.0176 -0.1514 0.1815 -0.0125 4 0.0149 -0.0234 -0.0323 -0.0373 0.1089 -0.0311 0.2750 0.3144 -0.8181 0.2287 STANDARD ERRORS OF PARAMETERS (ROBUST) a i yU yj2 y_t3 y t 4 p_i p» t 9U 9 t 2 9 t 3 9 t4I 0.15750.0455 0.04740.0216 0.02060.0888 0.13270.0348 0.03170.0203 0.01510.0759 0.05300.0150 0.01200.0070 0.00390.0113 0.11910.0305 0.03800.0140 0.01040.0397 0.38610.1747 0.67310.2387 0.35280.1326 0.61570.2183 0.08860.0550 0.19810.0683 0.14200.1298 0.32930.1084 1 2 3 4 T-STATISTIC at yil yi2 yt3 yi4 pi (5n 6U 9t2 9t3 9t4I 4.203.67 -1.88 0.09 -2.98 1.83 1.37 -4.89 3.62 2.75 -2.89 -1.43 2.681.80 0.55 -2.91 -1.01 -1.98 0.13 -0.77 -0.85 -2.67 10.50 -0.78 -1.29 -4.11 2.36 -1.56 0.68 4.18 -1.54 0.72 -0.20 -2.75 0.92 -0.18 1.94 2.42 -2.48 2.11 2 3 4 GROUP 33: VEGETABLIA MODEL: SWITCHING DYNAMIC AIDS (UNRESTRICTED) Sample period: 1961-1991 Joint points: 1961 and 1989 a0: 6.3008 PARAMETER ESTIMATES oi yU yi2 yi3 yi4 [il p*i 0U oi 2 6i3 Bi4I 0.7764 -0.1835 -0.0246 0.0182 0.0630 -0.0350 0.1490 0.0792 -0.0637 -0.0712 -0.0959 -0.0213 -0.0229 0.0620 -0.0445 0.35460.0559 -0.0317 -0.0165 0.0527 -0.5450 0,2907 0.0942 0,0776 -0.1120 -0.0597 0.3555 -0.2169 0.0914 0.27240.1598 -0.5236 0.13940.0764 0.09720.0092 -0.2142 0.1079 0.0501 -0.1502 -0.2828 -0.3591 0.1665 0.4754 1 2 3 4 STANDARD ERRORS OF PARAMETERS (ROBUST) i ai yil yi2 yi3 yi4 pi j3n 9il 9i2 9i3 9i4 1 0.0671 0.0370 0.0493 0.0291 0.0435 0.0574 0.0439 0.0752 0.0717 0.0741 0.0779 2 0.1080 0.0433 0.0420 0.0176 0.0313 0.0947 0.0603 0.0883 0.0844 0.1089 0.0807 3 0.0663 0.0326 0.0263 0.0234 0.0213 0.0612 0.0336 0.0508 0.0458 0.0448 0.0326 4 0.0984 0.0301 0.0285 0.0187 0.0228 0.0794 0.0365 0.0801 0.0653 0.0724 0.0376 T-STATISTIC i ai yil yi2 yi3 yi4 p> (i*! ÖU oi 2 oi 3 6i4 1 11.56 -4.97 -0.500.62 1.45 -9.496.63 1.251.08 -1.51 -0.77 2 -0.323.44 1.89 -3.62 -2.273.75 -3.601.04 3.231.47 -6.49 3 -1.45 -0.65 -0.872.65 -2.092.28 2.271.91 0.20 -4.783.30 4 3.601.85 -1.11 -0.882.31 0.63 -4.11 -3.53 -5.502.30 12.66 Appendix 2. GROUP 41: MEAT AND FISH MODEL: SWITCHING DYNAMIC AIDS (HOMOGENEITY AND SYMMETRY RESTRICTED) Sample period: 1961-1991 Jointpoints: 1967 and 1975 CtO: 5.8289 PARAMETER ESTIMATES t a_i yil yi2 y_i3 P_i j)*_i 0U oi2 9 t 3 1 -0.1839 0.0852 -0.0662 -0.0191 0.4343 -0.0891 0.2054 0.1192 -0.3246 2 0.8977 -0.0662 0.0573 0.0088 -0.3369 0.0659 -0.1268 -0.0445 0.1713 3 0.2862 -0.0191 0.0088 0.0102 -0.0974 0.0232 -0.0786 -0.0747 0.1532 STANDARD ERRORS OF PARAMETERS (ROBUST) t a_i y_il yj2 y_i3 p_i j3*_i o_il oi2 6 i3 1 0.0685 0.0665 0.0621 0.0187 0.0465 0.0113 0,0690 0.1178 0.1353 2 0.0688 0.0621 0.0631 0,0184 0.0519 0.0121 0.0980 0.1388 0.1843 3 0.0431 0.0187 0.0184 0.0108 0.0264 0.0067 0.0573 0.0862 0.1333 T-STATISTIC t o_i yU y_i2 yi3 p_i p*_i 6U o_v2 6 i 3 1 -2.68 1.28 -1.07 -1.02 9.34 -7.88 2.98 1.01 -2.40 2 13.05 -1.07 0.91 0.48 -6.49 5.45 -1.29 -0.32 0.93 3 6.64 -1.02 0.48 0.94 -3.69 3.46 -1.37 -0.87 1.15 GROUP 42: DAIRY PRODUCTS MODEL: SWITCHING DYNAMIC AIDS (UNRESTRICTED) Sample period: 1961-1991 Joint points: 1965 and 1974 ot0: 5.6733 PARAMETER ESTIMATES i ai yil yi2 yi3 yi4 p> fin oxl 6i2 oi 3 6i4 1 0.04070.0462 0.05380.0117 -0.0233 0.3730 -0.1307 0.1634 -0.0198 -0.4573 0.3137 2 0.2158 -0.0306 0.0911 -0.0764 -0.0413 -0.1094 0.1032 0.25700.1959 0.0274 -0.4803 3 0.2790 -0.0826 -0.0357 0.0017 0.10470.0150 0.0004 -0.3773 -0.2902 0.5641 0.1034 4 0.46450.0670 -0.1092 0.0629 -0.0401 -0.2786 0.0270 -0.0431 0.1141 -0.1343 0.0632 STANDARD ERRORS OF PARAMETERS (ROBUST) at ytl yt2 yt3 yi4 Pi pn 0U ot2 ot3 ot4I 0.08420.0567 0.07130.0602 0.0473 0.10520.0344 0,0684 0.03270.0378 0.11640.0609 0.09580.0517 0.0625 0.05260.0304 0.05490.0329 0.0425 0.07290.0308 0.11480.1194 0.08380.1112 0.07440.0224 0.07490.0782 0.05540.0875 0.09940.0399 0.13830.1383 0.10500.1470 0.03820.0140 0.05170.0665 0.04030.0684 1 2 3 4 T-STATISTIC i ai ]ol yi2 yi3 ]fi4 (3i p»i Gil oi 2 oi 3 9i4 1 0.480.81 0.750.20 -0.495.12 -4.251.42 -0.17 -5.462.82 2 2.05 -0.891.33 -2.33 -1.09 -1.474.61 3.432.51 0.50 -5.49 3 2.40 -1.36 -0.370.03 1.680.15 0.01 -2.73 -2.105.37 0.70 4 8.822.21 -1.991.91 -0.94 -7.301.93 -0.831.72 -3.330.92 Appendix 2. Glossary Symbols a, 0 a 0 P. c , = qPi £,v y» h= 1 H H h , ij,k = l or k K ‘h m m 2 = n- 1 n N p = c jqt P = iPr-’P,) P