(2 rânduri libere, 11p) Studies and Scientific Researches. Economics Edition, No 21, 2015 http://sceco.ub.ro 38 TOTAL FACTOR PRODUCTIVITY - INFLUENCE FACTOR OF THE ECONOMIC GROWTH POTENTIAL. PRACTICAL APPLICATION∗ Florina Popa Institute of National Economy - Romanian Academy florinapopa2007@gmail.com Abstract Adequate to the new requirements of economy, the economic research has achieved progresses in addressing the issues regarding the growth and development, the economists drawing a number of theories and models, in order to find resorts that lead to sustainable growth. The paper refers to the means of assessment and forecast of the potential growth of an economy, by using a mathematical model, whose production function takes into consideration the role of three factors, being highlighted the role of the Total Factor Productivity, as an element of influence on growth with the other two factors. The study includes an application of the model use, for the analysis of the growth potential of the economy, at national level. Keywords Total Factor Productivity; mathematical model; growth potential JEL Classification C53; D24 1. Introduction The economic literature has given a particular interest to the analysis of growth problems and its determinants, trying to explain the forms of economic phenomena occurrence and provide alternatives concerning the ways to achieve growth. The emphasis was on measures which lead to performance achievement regarding the welfare and sustainable growth: capital investments, stimulate research and development activities and, respectively, technical progress, well-trained workforce etc. The economic research has achieved progresses in addressing problems regarding the development, economic growth, world trade, the economists initially, formulating theories and models based on perfect competition and, subsequently, moving to models of imperfect competition, according to the new requirements of economy, the aim being to find the springs which lead to sustainable growth. 2. Total Factor Productivity The estimation and forecast of the growth of an economy potential, basically, takes into account: the available amount of labour, the amount of capital that can be used and the Total Factor Productivity, the latter being considered a "residual", respectively, that part of the output unexplained by the amount of inputs used in production. ∗This article is part of the scientific research paper for 2014, entitled ”Dezvoltarea economică endogenă la nivel regional – aspecte teoretice și practice”, achieved by a team of researchers of the Institute of National Economy - Romanian Academy (coordinator PhD. Daniela Antonescu). Popa 39 Assimilated to technical progress, the Total Factor Productivity, more broadly, includes the other sources of growth, different from the factors, labour and capital, its level being determined by the extent of efficiency and intensity of the inputs used in production. The Total Factor Productivity (TFP) is based on the determination of estimated GDP, using the homothetic Cobb-Douglas production function. Y = AKαL1-α, where: Y – the output – GDP; α - the elasticity coefficient; A – the productivity; K – the capital stock; L – the workforce "Toupictionnaire"1 defines the concept of "Total Factor Productivity or multifunctional productivity, as a ratio of the production value to the total value of the inputs used (labour and capital)", allowing to measure the effectiveness of productive combination of labour and capital. The TFP is determined, in general, at a scale of a country or economic zone, its evolution, over time, allowing the evaluation of the relative growth, other than the one in relation to the use of production factors, labour and capital. The parties of capital and labour are dissociated by the elasticity coefficient, α. The capital and labour remain the major contributors of production, but the growth vector is considered the Total Factor Productivity (TFP), which can influence the economic growth, its corner stone being the technical progress. The technical progress determine the increase in the factors productivity, leading to their qualitative and not only quantitative growth, what gives growth an intensive nature. The production growth is superior to the growth of each factor, as such, the effectiveness of factors, respectively, the productivity increases due to the process of innovation or improvement of work setup. The difficulty in applying the model results from the assumptions taken into account and the interpretation of results: - a number of elements may influence the quality of factors productivity (the technical progress), respectively, change of the production structure (the production of more goods and services, with saving of capital and labour) or of its setup, the education, research and development (R&D), the growth of skilled workforce, what makes it difficult to correctly determine the technical progress; - the information required by the calculation of capital stock and labour development, also, of prices development; - considering the elasticity rates taken in the series of that two factors. 3. Application for Romania In the following, it is presented an application regarding the analysis of the potential of economy growth, at national level, using as model, the Cobb-Douglas production function with TFP. 1Toupictionnaire – Le dictionnaire de politique – „Productivité globale des facteurs (PGF)”, La Toupie, http://www.toupie.org; TOTAL FACTOR PRODUCTIVITY - INFLUENCE FACTOR OF THE ECONOMIC GROWTH POTENTIAL. PRACTICAL APPLICATION 40 The used model (Ghizdeanu, I.; Tudorescu, V.; Neagu, M.)2: the Cobb-Douglas production function 1-Y = N K TFPα α⋅ ⋅ , where: Y = GDP N = the employed population K = the stock of capital TFP = the Total Factor Productivity For the expression of factors, in a single unit, it is using the linearly-homogeneous function, obtained by logarithm: lnY = lnN + (1- ) lnK+lnTFP y = n + (1- ) k+tfpα α α α⋅ ⋅ → ⋅ ⋅ where: y = lnY; n = lnN; tfp = lnTFP; α – coefficient of elasticity of the labour factor - N 1- α – coefficient of elasticity of the capital factor – K, 0< α<1 3.1. The work steps of the application I. The determination of the Total Factor Productivity, as a residual variable in the considered production function, at a given value of the parameter α; the tfp value is determined on each year, based on the values Y, N, K of ASR - INS, for the period 2000-2012; this is the time series of the observed tfp. tfp= y-[ n+(1- ) k]α α⋅ ⋅ II. For the time series of tfp (from the step 1) it is applied the TREND function and, thus, it is obtained the adjusted series of tfp, for the period taken into account (2000- 2012), as well as the ptf forecast for the years 2013-2015 (noted by tfp*). III. For the time series corresponding to n labour factor (the employed population) observed, based on the data from ASR (time series 2000-2012) it is applied the TREND function, achieving thus, the adjusted series of the factor - n - for the period taken into account (2000 -2012), as well as the forecast for the period 2013-2015 (noted by n*). IV. The determination of the capital stock for each year of the period (2013-2015), considering the forecast of the indicator gross fixed capital formation determined according to the relation: t-1 tKt = (1- ) K +Iδ ⋅ where: Kt - the capital stock for the year t; δ - the rate of capital depreciation; I t – the investment for the year t. •The estimation of the size of current investment is accomplished by applying a constant rate - β - to the GDP value of the previous year. t-1It = GDPβ ⋅ •The values determined above shall be entered in the logarithmic production function to obtain the y values for the years for which the forecast it shall be accomplished. •It shall be determined the Y value, respectively GDP, for the forecast years (by antilogarithm). 2Ghizdeanu, I.; Tudorescu, V.; Neagu M, Model de determinare a potenţialului de creştere a economiei româneşti în perioada 2005-2025 – sinteză preliminară, Comisia Naţională de Prognoză, www.presidency.ro/ include/nssd. Popa 41 The calculations associated with the national level take place alternatively, every year in part, because the current I investment, is determined based on the previous year GDP. 3.2. Calculations and analysis associated with work steps Following the previously announced work steps, the analysis highlights the following issues: I.The tfp calculation α = 0.30: tfp = y-[ n+(1- ) k]α α⋅ ⋅ tfp = y-(0.30 n+ 0.70 k)⋅ ⋅ . The evolution of GDP and the main determinant factors (the employed population, capital, tfp) taken into account for the analysis (time series 2000-2012), is mentioned in the Annexes 1 and 2 and shown in the graphics below (Figures 1-3): GDP 80984,6 117945,8 152017 197427 247368 288954 344650 416006 514700501139,4 523693,3 557348 586750 0 100000 200000 300000 400000 500000 600000 700000 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Y=GDP (RON millions) Years Figure 1 The evolution of the observed GDP in the period 2000-2012 Source: data processing based on the data from ASR 2012, ASR 2013, INS, Bucureşti, 2013, 2014, www.insse.ro The data in Figure 1 reflects an upward evolution throughout the period, interrupted in the year 2009 (peak of the crisis), but resumed in 2010. Employed population (N) 10508 10440 9234 9223 9158 9147 9313 9353 9369 9243 9240 9138 9263 8000 8500 9000 9500 10000 10500 11000 20 00 20 01 20 02 20 03 20 04 20 05 20 06 20 07 20 08 20 09 20 10 20 11 20 12 N= Employed Population (thoudsands people) Years Figure 2 The evolution of the employed population in the period 2000-2012 Source: data processing based on the data from ASR 2012, ASR 2013, INS, Bucureşti, 2013, 2014, www.insse.ro http://www.insse.ro/ http://www.insse.ro/ TOTAL FACTOR PRODUCTIVITY - INFLUENCE FACTOR OF THE ECONOMIC GROWTH POTENTIAL. PRACTICAL APPLICATION 42 The employed population had a sharp decrease in the year 2002 beside the year 2000 (1274 thousands people), respectively, 12%, unrecovered until the year 2012, the increases and decreases in the period, being sensitively contiguous. Capital (K) 15245 24171 32366 42496 53850 68526 88272 125645 164279 122442 129422 145193 154280 0 20000 40000 60000 80000 100000 120000 140000 160000 180000 20 00 20 01 20 02 20 03 20 04 20 05 20 06 20 07 20 08 20 09 20 10 20 11 20 12 K=Capital (RON millions) Years Figure 3 The evolution of the capital in the period 2000-2012 Source: data processing based on the data from ASR 2012, ASR 2013, INS, Bucureşti, 2013, 2014, www.insse.ro The capital had an evolution, similarly to GDP, but the decrease in 2009 had not integrally been recovered, by 2012. II.The determination of the adjusted tfp (time series 2000-2012) and the forecast tfp* (2013-2015) should be found in the Annex 3, represented according to the graphic in the Figure 4. tfp YYears Figure 4 The evolution of the observed, adjusted and forecast tfp Source: data processing based on the data from ASR 2012, ASR 2013, INS, Bucureşti, 2013, 2014, www.insse.ro 1.782 1.276 2.801 1.994 2.056 2.043 2.037 1.977 2.001 2.184 2.190 2.175 2.180 1.894 1.921 1.947 1.974 2.000 2.027 2.054 2.080 2.107 2.133 2.160 2.186 2.213 2.239 2.266 2.292 0.0 0.5 1.0 1 .5 2.0 2.5 3.0 2000 2003 2006 2009 2012 2015 Observed tfp Adjusted tfp 2000-2012 Forecast tfp - 2013-2015 http://www.insse.ro/ http://www.insse.ro/ Popa 43 The evolution of the observed tfp shows a higher level of its, at the end of the period - 2012 – beside the start 2000, respectively, 2.18 unto 1.78, the oscillations, increasing or decreasing , in the interval series, being correlated with the changes in other factors and expressing the contribution of tfp to GDP achievement, such as: •The tfp level increase in the years 2002, 2004, 2005, beside the previous years, given the conditions of a sensitive decrease of the employed population, expressing the contribution of tfp to GDP growth (the capital is also increasing). •The tfp level decrease, in the year 2007, compared to the year 2006, the GDP being sustained by the growth both of the capital and of the employed population, compared to the previous year. •The tfp increase in the year 2009 compared to 2008 (from 2.0 to 2.18) sustaining the GDP achievement that decreased, given the fact that both the employed population and the capital had a substantial decrease, as an effect of the crisis. • The adjusted tfp data, determined based on the trend, follow the same evolution, being sensitively contiguous to the observed tfp. III.The determination of the adjusted n factor (the time series 2000-2012) and of the forecast n* , for the years 2013-2015, should be found in the Annex 4, represented according to the graphic in the Figure 5. Adjusted n and forecast n* 9,195261 9,187866 9,180472 9,173078 9,165684 9,15829 9,150895 9,143501 9,136107 9,128713 9,121319 9,113924 9,10653 9,099136 9,091742 9,084348 9,02 9,04 9,06 9,08 9,1 9,12 9,14 9,16 9,18 9,2 9,22 2000 2002 2004 2006 2008 2010 2012 2014 Adjusted n 2000-2012 Forecast n*2013-2015 Years Figure 5 The evolution of the adjusted and forecast n factor Source: data processing based on the data from ASR 2012, ASR 2013, INS, Bucureşti, 2013, 2014, www.insse.ro The evolution of the employed population, highlights, also, in the data determined based on the trend, the continuous decrease of the indicator, both in the period 2000- 2012 and in forecast, 2013-2015. IV.The determination of the capital factor – K and, respectively, GDP, alternatively, in forecast each year. There are considered constant rates, throughout the forecast period, respectively: • the rate of capital depreciation - 0.15 δ = 0.15 • the investment rate - 0.048 β = 0.048 • It – the investment in the current year gdp t = α*n t+(1-α)*k t + tfp t K t = (1-δ)*K t-1 + It I t= β*GDPt-1 http://www.insse.ro/ TOTAL FACTOR PRODUCTIVITY - INFLUENCE FACTOR OF THE ECONOMIC GROWTH POTENTIAL. PRACTICAL APPLICATION 44 According to the calculations above, for the period 2013-2015, the forecast values of the model factors, are presented in the Table. 1. YEAR 2013 gdp2013= 2013 2013 2013n +(1- ) k + tfpα α⋅ ⋅ The factors tfp and n should be found in the data from the Step 2 and, respectively, 3. K 2013 = 0.85·K 2012 + I 2013; K2012 = 154288 (Data base – ASR 2013) I2013 = 0.048· GDP2012; GDP2012 = 586750 (Data base – ASR 2013) I2013 = 0.048·586750 I2013 = 28164 K2013 = 0.85·154288 + 28164 = 131144.8 + 28164= 159308.8 K2013 = 159308.8 k2013 = lnK = ln159308.8 = 11.97859 k2013 = 11.97859 gdp2013 = 0.30·9.099 + 0.70·11.97859+2.24 gdp 2013 = 2.7297 + 8.385013+ 2.24=13.354713 pib2013 = 13.354713 GDP2013 = EXP13.354713 = 630780.4 (the natural antilogarithm of the number 13.354713) GDP2013 = 630780.4 YEAR 2014 gdp2014 = α·n 2014 + (1- α) · k2014 + tfp2014 K2014 = 0.85· K 2013 + I 2014 I2014 = 0.048· GDP2013 I2014 = 0.048 ·630780.4 I2014 = 30277.46 K 2014 = 0.85·159308.8 + 30277.46= 135412.5 + 30277.46= 165689.9 K2014 = 165689.9 k2014 = ln K 2014 = ln165689.9 = 12.01787 k2014 = 12.01787 gdp2014 = 0.30·9.092 + 0.70·12.01787 + 2.26 gdp2014 = 2.7276 + 8.412509 + 2.26 = 13.400109 gdp2014 = 13.400109 GDP2014 = EXP13.4001= 660009 GDP2014 = 660009 YEAR 2015 gdp2015 = α·n 2015 + (1-α) ·k 2015 + tfp2015 K2015 = 0.85·K2014 + I2015 I2015 = 0.048·GDP2014 I2015 = 0.048·660009 I2015 = 31680.4 K2015 = 0.85·165689.9 + 31680.4 = 140836.4 + 31680.4 = 172516.8 K2015 = 172516.8 k2015 = ln K = ln172516.8= 12.05825 k2015 = 12.05825 gdp2015 = 0.30·9.084 + 0.70·12.05825 + 2.29 gdp2015 = 2.7252+8.44077+2.29 gdp2015 = 13.45597 GDP2015 = EXP13.45597 =697996.9; GDP2015= 697997 GDP2015 = 697997 Popa 45 Table 1 The forecast of GDP and of its determinant factors in the period 2013-2015 Year Y=GDP (RON millions) N (thousands people) K capital (RON millions) tfp 2013 630780 8946 159309 2,24 2014 660009 8884 165690 2,26 2015 697997 8813 172517 2,29 Source: data processing based on the data from ASR 2012, ASR 2013, INS, Bucureşti, 2013, 2014, www.insse.ro The forecast data show that, for national level, there is the possibility of a GDP growth due to the growth of capital and total factor productivity, the employed labor being in decrease. Taking into consideration the average annual growth rhythm during the 3 years period, the contribution of factors to potential GDP growth, is presented according to data in Table 2. Table 2 The factors contribution to potential GDP growth Contributions (%) Year GDP Employed population Capital tfp 2013-2015 5,2 -0,9 4 2,4 Source: data processing based on the data from ASR 2012, ASR 2013, INS, Bucureşti, 2013, 2014, www.insse.ro The growth rhythm of GDP of 5.2%, is sustained by the capital, 4% and by the total factor productivity, 2.4%. The negative increase of the labour factor, 0.9%, is the consequence of the significant decrease of population in the series taken into account, respectively, from 10508 thousands people, in the year 2000, to 9263 thousand people, in the year 2012. The calculations based on testing the parameters, respectively, the coefficients of elasticity, for labour and capital, the rate of investment and the rate of capital depreciation, followed to obtain values for the forecast GDP in the period 2013- 2015, as close as to the values announced, in perspective, by Comisia Națională de Prognoză (CNP). Thus, the data forecast by calculation, for the years 2013, 2014 and 2015 are close to those forecast by Comisia Națională de Prognoză (CNP)3 (March 5, 2014) (Table 3) Table 3 The Gross Domestic Product (RON billions) Year Forecast in the paper Forecast by CNP (March 5 2014) 2013 630,8 631,1 2014 660,0 664,4 2015 698,0 698,8 Source: own processing. The results reveal the verity of applying the model 3 Comisia Naţională de Prognoză, Proiecţia principalilor indicatori macroeconomici pentru perioada 2014-2017, 5 martie 2014, www.cnp.ro/prognoză http://www.insse.ro/ http://www.insse.ro/ TOTAL FACTOR PRODUCTIVITY - INFLUENCE FACTOR OF THE ECONOMIC GROWTH POTENTIAL. PRACTICAL APPLICATION 46 4. Conclusions To estimate the forecast GDP and the contribution of factors to its achievement, there were taken into account, in the production function for national level, the following parameters: the coefficients of elasticity for labour and capital factors, α = 0.30, and, respectively, (1-α) = 0.70, the rate of capital depreciation, δ = 15%, the investment rate, β = 4.8%. The analysis showed the contribution of the labour and capital factors to the national GDP achievement, but also, the total factor productivity contribution, in the case of this indicator, the participation degree being different, by years, depending on the level of the other two factors, the labour and capital. The data obtained reflect an increase in production, in the forecast period, higher to the growth of each of the labour and capital factors, the level of total factor productivity expressing the efficaciousness of factors use. The results lead to the conclusion that, the use of the model, although it exposes some difficulties in implementation, as mentioned in the introductive part, may be relevant to such analysis, if should be taken into account a careful testing of the value of the used parameters and a statistical data base, large enough, to be considered methodologically satisfactory. References Cabannes, Pierre-Yves.; Montaut, A.; Pionnier, Pierre-Alain (2013), Évaluer la productivité globale des facteurs: l'apport d'une mesure de la qualité du capital et du travail, Institute National de la Statistique et des Études Économiques, L'économie française - Insee Références - Édition 2013, http://www.insee.fr/fr/themes. Comin, D. (2006), Total Factor Productivity, New York University and NBER, http://www.people. hbs.edu/ dcomin/def.pdf. Ghizdeanu, I.; Tudorescu, V.; Neagu, M., Model de determinare a potenţialului de creştere a economiei româneşti în perioada 2005-2025 – sinteză preliminară, Comisia Naţională de Prognoză, www.presidency. ro/include/nssd. Lipsey, Richard G.; Carlaw Kenneth I. (2004), Total factor productivity and the measurement of technological change, Canadian Journal of Economics/Revue canadienne d'économique, Volume 37, Issue 4, pag. 1118-1150, Wiley Online Library, onlinelibrary.wiley.com. Quijada, A., (2004), Productivitè Globale des Facteurs et Croissance dans un contexte de Changement Institutionnel: Le cas du Venezuela (1942-2002), https://www.gate.cnrs.fr/. Romer, Paul, M. (1994), The Origins of Endogenous Growth, Journal of Economic Perspectives, Volume 8, No.1, pag.3-22, www.jstor.org/stable, www.development.wne.uw.edu.pl. Comisia Naţională de Prognoză, Proiecţia principalilor indicatori macroeconomici pentru perioada 2014-2017, 5 martie 2014, www.cnp.ro/prognoză. Institutul Naţional de Statistică, Anuarul Statistic al României-ASR 2012, 2013, INS Bucureşti, 2013, 2014, www.insse.ro. Toupictionnaire – Le dictionnaire de politique –Productivité globale des facteurs (PGF), La Toupie, http://www.toupie.org. Productivité globale des facteurs, www.fr.wikipedia.org/wiki/Productivité_globale_des_facteurs; Teorii şi modele referitoare la cresterea economică, http://www.rasfoiesc.com/business/economie/. Evoluţia teoriei creşterii economice, https://teoriieconomice.wikispaces.com/. http://www.insee.fr/fr/themes https://www.gate.cnrs.fr/ http://www.jstor.org/stable http://www.development.wne.uw.edu.pl/ http://www.fr.wikipedia.org/wiki/Productivit%C3%A9_globale_des_facteurs http://www.rasfoiesc.com/business/economie/ https://teoriieconomice.wikispaces.com/ Popa 47 Quelles sont les Sources de la Croissance Économique?, http://www.cours- seko.fr/resources/Economie/croissance/cours-croissance-1.pdf. Théorie de la croissance endogène, http://fr.wikipedia.org/wiki/. Croissance économique et croissance exogène. Modèle du Solow, http://fr.wikipedia.org. Annex 1 Database for the calculation of logarithm values to: GDP, employed population, capital t YEAR Y=GDP RON millions y=Ln GDP N= Employed Population thoudsands persons n=LnN K=Capital RON millions k= Ln K 1 2000 80984,6 11,30201 10508 9,259892151 15245 9,632007 2 2001 117945,8 11,67798 10440 9,253399861 24171 10,89396 3 2002 152017 11,93175 9234 9,130647603 32366 11,13497 4 2003 197427 12,19312 9223 9,129455643 42496 10,65717 5 2004 247368 12,41863 9158 9,122383093 53850 10,89396 6 2005 288954 12,57402 9147 9,121181236 68526 11,13497 7 2006 344650 12,75028 9313 9,1391665 88272 11,38818 8 2007 416006 12,93845 9353 9,143452426 125645 11,74122 9 2008 514700 13,15134 9369 9,145161646 164279 12,00932 10 2009 501139,4 13,12464 9243 9,131621787 122442 11,71539 11 2010 523693,3 13,16866 9240 9,131297165 129422 11,77083 12 2011 557348 13,23095 9138 9,120196822 145193 11,88582 13 2012 586750 13,28235 9263 9,133783249 154280 11,94652 Source: data processing based on the data from ASR 2012, ASR 2013, INS, Bucureşti, 2013, 2014, www.insse.ro Annex 2 Database for the calculation of observed tpf t YEAR 0.30*n 0.70*k 0.30*n+ 0.70*k Observed tfp 2000-2012 1 2000 2,777968 6,742405 9,52037 1,7816 2 2001 2,77602 7,62577 10,4018 1,2761 3 2002 2,739194 6,391453 9,13065 2,8011 4 2003 2,738837 7,460016 10,1989 1,9942 5 2004 2,736715 7,62577 10,3625 2,0561 6 2005 2,736354 7,794478 10,5308 2,0431 7 2006 2,74175 7,971725 10,7135 2,0368 8 2007 2,743036 8,218851 10,9619 1,9765 9 2008 2,743548 8,406525 11,1501 2,0012 10 2009 2,739487 8,200775 10,9403 2,1843 11 2010 2,739389 8,239584 10,979 2,1896 12 2011 2,736059 8,320073 11,0561 2,1748 13 2012 2,740135 8,362567 11,1027 2,1796 Source: data processing based on the data from ASR 2012, ASR 2013, INS, Bucureşti, 2013, 2014, www.insse.ro Annex 3 The calculation of adjusted tfp and of forecast tfp* http://www.cours-seko.fr/resources/ECONOMIE/CROISSANCE/COURS-croissance-1.pdf http://www.cours-seko.fr/resources/ECONOMIE/CROISSANCE/COURS-croissance-1.pdf http://fr.wikipedia.org/wiki/Th http://www.insse.ro/ http://www.insse.ro/ TOTAL FACTOR PRODUCTIVITY - INFLUENCE FACTOR OF THE ECONOMIC GROWTH POTENTIAL. PRACTICAL APPLICATION 48 t YEAR Observed tfp Adjusted tfp 2000-2012 and forecast tfp* 2013-2015 1 2000 1,781642 1,894303 2 2001 1,27619 1,920838 3 2002 2,8011 1,947374 4 2003 1,994272 1,97391 5 2004 2,056147 2,000446 6 2005 2,04319 2,026982 7 2006 2,03681 2,053517 8 2007 1,976568 2,080053 9 2008 2,001266 2,106589 10 2009 2,184378 2,133125 11 2010 2,189689 2,15966 12 2011 2,174813 2,186196 13 2012 2,179652 2,212732 14 2013 2,239268 15 2014 2,265803 16 2015 2,292339 Source: data processing based on the data from ASR 2012, ASR 2013, INS, Bucureşti, 2013, 2014, www.insse.ro Annex 4 The calculation of adjusted n and forecast n* t YEAR Observed n Adjusted n 2000-2012 Forecast n*2013-2015 1 2000 9,259892 9,195261 2 2001 9,2534 9,187866 3 2002 9,130648 9,180472 4 2003 9,129456 9,173078 5 2004 9,122383 9,165684 6 2005 9,121181 9,15829 7 2006 9,139167 9,150895 8 2007 9,143452 9,143501 9 2008 9,145162 9,136107 10 2009 9,131622 9,128713 11 2010 9,131297 9,121319 12 2011 9,120197 9,113924 13 2012 9,133783 9,10653 14 2013 9,099136 15 2014 9,091742 16 2015 9,084348 Source: data processing based on the data from ASR 2012, ASR 2013, INS, Bucureşti, 2013, 2014, www.insse.ro http://www.insse.ro/ Cabannes, Pierre-Yves.; Montaut, A.; Pionnier, Pierre-Alain (2013), Évaluer la productivité globale des facteurs: l'apport d'une mesure de la qualité du capital et du travail, Institute National de la Statistique et des Études Économiques, L'économie ...