A new method for measuring total factor productivity growth based on the full industry equilibrium approach: The case of the Greek economy

Tsounis, Nicholas; Steedman, Ian Article A new method for measuring total factor productivity growth based on the full industry equilibrium approach: The case of the Greek economy Economies Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Tsounis, Nicholas; Steedman, Ian (2021) : A new method for measuring total factor productivity growth based on the full industry equilibrium approach: The case of the Greek economy, Economies, ISSN 2227-7099, MDPI, Basel, Vol. 9, Iss. 3, pp. 1-21, https://doi.org/10.3390/economies9030114 This Version is available at: https://hdl.handle.net/10419/257272 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ economies Article A New Method for Measuring Total Factor Productivity Growth Based on the Full Industry Equilibrium Approach: The Case of the Greek Economy Nicholas Tsounis 1,2,* and Ian Steedman 3   Citation: Tsounis, Nicholas, and Ian Steedman. 2021. A New Method for Measuring Total Factor Productivity Growth Based on the Full Industry Equilibrium Approach: The Case of the Greek Economy. Economies 9: 114. https://doi.org/10.3390/economies 9030114 Academic Editor: Michele Meoli Received: 24 June 2021 Accepted: 5 August 2021 Published: 16 August 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1Laboratory of Applied Economics, Department of Economics, University of Western Macedonia, 52100 Kastoria, Greece 2 Economic Analysis and Policy Lab, School of Social Sciences, Hellenic Open University, 26335 Patras, Greece 3Department of Economics, Manchester Metropolitan University, Manchester M15 6BH, UK; [email protected] *Correspondence: [email protected] Abstract: A new method of identifying the sources of output growth and measuring total factor productivity (TFP) is proposed, with an application to data from the Greek economy. The price accounting approach, based on the full industry equilibrium (FIE) framework introduced by Opocher and Steedman, where technical progress not only increases outputs relative to inputs but also reduces output prices relative to input rewards, is used. The contributions of this paper are that, first, it amends the FIE TFP measurement approach to account for heterogeneous labor inputs, imported inputs, and indirect taxes, and applies the method to real-world data from the Greek economy; second, it provides a comparison of the results with those found by the use of the neoclassical approach to TFP measurement arguing that the FIE approach measures better sectoral TFP change, and third, it provides an estimate of the effects of sectoral research and development (R&D) expenditures and R&D diffusion from other sectors on TFP change for the Greek economy. Keywords: total factor productivity growth; R&D diffusion; full industry equilibrium JEL Classification: O33; O47; D24 1. Introduction Total factor productivity (TFP) change is an inherent and important part of both Solow’s (1956) and Lucas (1988) and Romer’s (1986,1994) growth theories. It is recognized to be an important factor in both long-term economic growth and short-term growth fluctuations and is an important long-term factor in raising the living standards of a country. Since total factor productivity (TFP) is the portion of output not explained by the amount of inputs used in production, its level is determined by how efficiently and intensely the inputs are utilized in production. There are thousands of studies on TFP growth in many countries; the following paragraphs review the most recent ones. Tsamadias et al. (2019) examined TFP growth among the OEDC countries, dividing the sample countries into two groups, the European Union (EU) members and the non-EU, to account for country heterogeneity for the period 1995–2015. Research and development (R&D) expenditure and human capital (HC) were found to have a positive effect on TFP, while foreign direct investment (FDI) had a positive and significant effect only in the case of non-European countries. However, they found that the contribution of R&D was considerably higher than that of HC and FDI in all cases. Pegkas et al. (2020) empirically analyzed the influence of domestic and foreign R&D capital on TFP in Eurozone countries for the period 1995–2016. They discovered that variations in local and international R&D capital accounted for TFP changes. Their findings demonstrate that R&D capital has a beneficial impact on TFP. The contribution of foreign R&D capital to Economies 2021,9, 114. https://doi.org/10.3390/economies9030114 https://www.mdpi.com/journal/economies Economies 2021,9, 114 2 of 21 TFP is higher than that of local R&D capital. Sharif et al. (2021) focused on the Asia-Pacific region to analyze the impact of R&D spending on TFP growth. The role of public and private R&D and their capacity to generate economic spillovers were examined. Their results show that the impact of both public and private R&D varies across countries. Huang et al. (2019) investigated how indigenous R&D spending, as well as technological spillovers from foreign direct investments, export, and import, affected China’s TFP. Their findings, which were based on Chinese provincial panel data encompassing 30 provinces from 2000 to 2014, demonstrate that indigenous R&D investments play a key role in fostering TFP growth. There are also TFP growth benefits from technology spillovers caused by openness. However, the varied behaviors of these technology spillovers are determined by factors impacting technological absorptive capacity, such as human capital and domestic R&D investments. Yue et al. (2019) added two environmental indicators into the TFP framework: ecological footprint, which reflects human ecological consumption, and human development index, which assesses human well-being levels. The indicator of sustainable total factor productivity takes into consideration ecological inputs such as energy consumption, built-up land use, and biological resource occupation, as well as the comprehensive outputs of economic growth, life expectancy, and educational attainment. From 1994 through 2014, data were collected for 55 countries. The findings demonstrate that, first, TFP change has a decreasing tendency, indicating that most states have placed less emphasis on long-term growth. The slow pace of sustainable technical advancement was the primary cause of the declining trend. Second, 19 of the 55 countries had a positive, long-term TFP increase and were able to maintain it. In a more recent article on this line of analysis, Shen et al. (2020) used a sustainable TFP growth index derived from translog production functions to assess the process of sustainable development. From 2006 to 2016, the sustainable TFP growth of 30 Chinese provinces was estimated. The findings reveal that China’s TFP growth was modest, indicating poor long-term development. Second, variables including labor productivity and environmental legislation were shown to increase sustainable technological efficiency in a favorable way, but capital deepening, economic openness, and industrial structure harmed it. Third, TFP growth in China’s regions showed a range of increasing tendencies, from high to low, in the order of western, central, and eastern regions. Four, the high incidence of economic imbalance was shown by the dispersion of TFP growth among provinces. Amri et al. (2019) investigated the linkage between carbon dioxide (CO 2 ) emissions, TFP, and information and communication technology (ICT) in Tunisia from 1975 to 2014. The results demonstrate the rejection of the Environmental Kuznets Curve (EKC) hypothesis by obtaining a higher value of the long-term TFP coefficient compared to the short-term one. Furthermore, for the period 1990 to 2006, Haider et al. (2021) looked at how R&D, trade, and ICT affected TFP growth in 25 European countries, Japan, and the United States. They broke down TFP growth into two components: catching up and innovation (frontier shifts). Frontier shifts tend to be lower with increasing distance from the frontier, and major disparities occur and remain between sectors and countries, although catching-up effects are statistically significant. Shabbir and Yaqoob (2019) calculated TFP for the India and Pakistan cotton production sector. Their findings demonstrate that in Pakistan, overall improvements in farm inputs have a more stable impact on cotton productivity, whereas in India, mechanization and area are the reasons for the sector’s TFP rise. Saleem et al. (2019) investigated the factors that influence TFP and economic growth in Pakistan. For the period 1972–2016, TFP was calculated from an aggregate Cobb–Douglas production function. The findings show that innovation has a substantial impact on Pakistan’s economic growth and output levels. TFP and its determinants were investigated in 420 agricultural firms in Vietnam by Giang et al. (2019). Agriculture is a crucial sector for the country’s economic growth and poverty alleviation. Fixed and random effects models were used to calculate TFP. According to the study’s results, reform efforts should concentrate on increasing the productivity of small agricultural businesses. Furthermore, they found that foreign investment, effective utilization of bank loans, and internet accessibility should all be improved to Economies 2021,9, 114 3 of 21 contribute to the country’s long-term progress. Ngo et al. (2020) employed the generalized method of moments (GMM) to identify factors that affect TFP across 21 manufacturing sectors in Vietnam for the period 2010–2015. In several fragmentations of companies in terms of both labor and total capital, as well as in particular manufacturing sectors, the results reveal that large firms have much higher TFP levels than small enterprises. Doumi (2017) explored the evolution of TFP in the agricultural sector of ten Mediterranean countries for the period 1980–2012. The results show that Morocco experienced positive TFP change during the past two decades, ahead of Portugal and behind the rest of the countries in the sample. Kéïta and Hannu (2021) investigated the link between corruption and taxation hampering TFP. The empirical study used panel data from 90 countries from 1996 to 2014. The results show that both corruption and tax burden deteriorate TFP. All the above studies and the literature until now suggest TFP growth rate is residually determined (the famous Solow residual) after subtracting the growth rates of normally employed factor inputs, weighted by their income shares, from the output growth rate. A completely different and novel approach to measuring TFP change is proposed here where TFP change measurement is based on decomposing the effects of technological progress on prices. This new method is based on the full industry equilibrium (FIE) framework introduced recently by Opocher and Steedman (2015) and on the pioneering work of Opocher (2010). FIE has its foundations in the modern classical economic theory and attempts to combine two competing approaches to microeconomics; namely, the neoclassical long-run theory of the firm and the Sraffa-inspired classical version of economics. Both approaches share some common ground, and their amalgamation may be profitably utilized to develop firmer theoretical conclusions of practical significance. The FIE approach (or price accounting approach) achieves a synthesis between the two theories via the method of comparative statics analysis, according to which one starts with a state of equilibrium and then hypothesizes an exogenous change to a variable, such as, for example, the real wage (or profit rate), taxation, terms of trade, price of a strategic input (e.g., the price of oil), factor productivity, etc. Then the object of study becomes the movement of all relative prices which, following the aforementioned exogenous event, must change to be consistent with arriving at a situation of zero maximum profits earned by all industries. This is called, using a Wicksellian term, “full industry equilibrium” (FIE). The question at issue concerns predicting the sign of such price changes by taking into account the inter-industry structure of the economy and the attainment of the final equilibrium state, where there are no net (excess economic) profits. It is noteworthy that FIE differs from neoclassical general equilibrium since it is independent of consumer preferences or demand decisions associated with them. In a FIE context, the firm in the industry competes with other similarly motivated firms for produced and non-produced inputs under the scheme of maximum net profits equal to zero. This is another methodological concession made to the standard neoclassical theory, according to which the mere presence of profits is sufficient to attract an inflow of firms until profits become equal to zero. In FIE the use of twice differentiable cost functions is often adopted and possible complementarities between inputs are often ruled out. In other words, the cost functions used in the analysis are assumed to be “well behaved”. Competition leads to changes in the structure of relative commodity prices and, as far as the prices of primary inputs are concerned, it is possible to derive qualitative restrictions within the framework of comparative statics analysis1. Taking into account the above, this paper examines the effects of total factor productivity (TFP) change on prices, under the FIE framework. These effects could be quite similar to those of taxation, but there is an important difference in that, while taxation is directly a policy variable, productivity is not. The TFP growth rate in neoclassical economics is residually determined after subtracting the growth rates of normally employed factor inputs, weighted by their income shares, from the output growth rate. The advantage of the FIE approach is that it breaks down the technical change measured by TFP into the changes in both average primary input prices and distribution. Moreover, FIE price Economies 2021,9, 114 4 of 21 accounting enables the identification of trend components of productivity in each industry. Lastly, the change in the primary input prices may be broken down to industry productivity change per se and to changes due to other industries. The contributions of this paper are: (a) it introduces a completely new method for TFP measurement, based on the FIE, but extending FIE to account for heterogeneous labor inputs, imported inputs, and indirect taxes, and applies the method to real-world data from the Greek economy; (b) using econometric analysis it accounts for the effects of sectoral monopoly power on TFP changes, providing a comparison of the results with those found by the use of the neoclassical approach to TFP measurement; and (c) provides an estimate of the effects of technical change measured by sectoral research and development (R&D) and diffused R&D expenditures on sectoral TFP change for the Greek economy. Measuring productivity in each industry of the Greek economy by applying the FIE methodology has economic policy significance because it might show that the effects of technical progress on the disembodied productivity of the factors of production are different when the methodology used deviates from that of the orthodox neoclassical economic theory, and state intervention with targeted sectoral R&D policy might be misleading if the latter has been used as a measurement of TFP. This could lead to quite different policy emphases concerning R&D tax breaks and direct R&D investments. The paper proceeds as follows: Section 2develops the methodology for the measurement of TFP change under the FIE approach and derives a comparable formula for the neoclassical TFP change. Data used for the empirical part of the paper are also described in this section. Section 3describes and discusses the results and Section 4concludes. 2. Methodology and Data Description 2.1. The FIE Approach to Measuring TFP Change The full industry equilibrium (FIE) approach (Opocher and Steedman 2015) is an alternative for measuring sectoral TFP change. When there is one primary factor input (labor), of the same quality across sectors, the TFP price accounting approach can be used as follows (ibid. pp. 158–63): Let p , u , l , A ,w,c be the vector of commodity input prices, the unit vector, the vector of factor inputs per unit of output, the matrix of commodity inputs per unit of gross output, the factor price, and the indirect cost function, respectively (small bold letters indicate vectors and capital bold letters indicate matrices). Then p=c(w,p;T); where Tindicates time. By totally differentiating: bp= ( b wwl−γ)(I−A)−1; where γ≡ − ∂c ∂T1 c is the rate if productivity growth. Since wl=u(I−A)then bp=b wu− γ(I−A)−1 . TFP change for each sector can be calculated from vector γ ; ˆ indicates the rate of change. We amend the indirect cost function above to account for many primary inputs and imported inputs: pj=cj(mj,p,fj,tj;T) (1) where m, p ,f,t,care monetary wage, the vector of commodity input prices, the value of imported inputs, net indirect taxes (assuming that prices are expressed at a consumer level and include net indirect taxes), and the indirect cost function, respectively. Tindicates time. By totally differentiating (1) it is derived that: . pj=lj . mj+ n ∑ i=1 αij . pi+bj . fj+zj . tj+∂cj ∂T; (2) Economies 2021,9, 114 5 of 21 Dotted variables denote change (d(.)); lis the primary input coefficient, band zare input coefficients for imported inputs and net indirect taxes, and nis the number of sectors; (2), in a rate of change terms denoted by a hat become: b pj= mjlj pj!c mj+∑i aij pi pj!b pi+ bjfj pj!bfj+ zjtj pj!b tj−γj(3) where γj= =∂cj ∂T1 ∂cj ,jdenotes sector jand ˆ indicates the rate of change. γj is TFP change in sector j. In (3), by replacing the share of wages of sector jin gross output with σ∗ j , the share of imports of jsector in gross output with β∗ j , the share of net indirect taxes of jin gross output with ζ∗ j , and aij pi pj , the value of input iin the value of one unit of output jwith α∗ j , we get: b pj=σ∗ jc mj+∑ i α∗ ij b pi+β∗ jbfj+ζ∗ jb tj−γj or b pj=σ∗ jc mj+bpA∗ j+β∗ jbfj+ζ∗ jb tj−γj(4) where A∗ j is the jth column of the A* matrix of commodity inputs per unit of gross output expressed in unit values. Equation (4) decomposes percentage change in product price of sector jto its components: the first RHS term is the effect of change in factor rewards, the second the relative change in the prices of produced inputs effect, the third is the effect in the terms of trade change, and the fourth the effect from a change in net indirect taxes. γj is the TFP change in the sector. Solving (4) for γjwe get: γj=σ∗ jc mj+bpA∗ j+β∗ jbfj+ζ∗ jb tj−b pj(5) Apart from the factors in (1) that affect prices, economic theory, since Lerner (1934), has proven that monopoly power has a rising effect on prices. Although FIE assumptions considered that all sectors are in a long-run equilibrium with zero profit rates, in the real world this assumption might be quite unrealistic. Therefore, since the TFP change calculation in (5) is based on price change rates, the effects of sectoral monopoly power on prices must be accounted for. Monopoly power is usually measured, in empirical studies, by an industry’s concentration using the Herfindahl–Hirschman index (Hirschman 1964). However, the calculation of the latter requires information on the market shares of each individual firm in each sector and such disaggregated data are not available for the Greek economy. As an alternative, for measuring sectoral concentration, the Schmalensee (1977) firms concentration index is used from the following formula: SIj=ASj1−ASj22n2 j1−1 3nj1 +nj1AS2 j1+nj−nj1AS2 j2 where ASj1 , ASj2 , nj are the average market shares of the five first in terms of sales firms, the average market shares of the remaining firms in sector j, and the total number of firms in sector j, respectively. nj1 is the number of the largest firms in sector jand in our case is set equal to five. An increase in sectoral concentration is an indication of an increase in monopoly power; therefore, a positive relationship is expected between changes in prices and the change in market concentration. From Equation (5) it can be observed that the TFP change rate of a sector j( γj ) is affected negatively by the change rate of prices in that sector. To account for the effect of the change rate in monopoly power of a sector on the TFP change rate, γjs are regressed on c SIj: γj=a1+b1c SIj+uj; (6) Economies 2021,9, 114 6 of 21 uj is the disturbance term. The residuals of this regression are the sectoral TFP change rates ( γj ’s) without the effect the change in monopoly power on price change rates. The expected sign of the estimated coefficient of c SIj is negative. The results are reported in Section 3, below. Several studies have theoretically and empirically identified factors that determine TFP (see Silveira et al. 2021 for a review of literature of TFP determinants). Theory suggests that human capital (ibid; Arazmuradov et al. 2014;Danska-Borsiak 2018;Akinlo and Adejumo 2016), trade (Bhattacharya et al. 2021;Kim 2016), FDI/imports (Bhattacharya et al. 2021;Kim 2016;Akinlo and Adejumo 2016;Harris and Moffat 2020), and R&D expenses (Danska-Borsiak 2018; Otsuka 2017;Kim 2016) are the main determinants of TFP growth. However, it is recognized that the latter is the main driver of TFP growth (among others, Saleem et al. 2019;Huang et al. 2019;Shabbir and Yaqoob 2019;Sharif et al. 2021;Pegkas et al. 2020;Tsamadias et al. 2019;Haider et al. 2019;Griliches 1979,1994;Griffith et al. 2004;Edquist and Henrekson 2006;Hall et al. 2009;Eberhardt et al. 2013;Donghyun et al. 2014;Gehringeer et al. 2015;Venturini 2015) because it facilitates the adoption and implementation of new technologies exogenously facilitating the domestic production of technological innovations. Productivity gains are linked to R&D diffusion because innovative producers are more receptive to new technologies and thus can maximize gains and reduce costs. Therefore, R&D is recognized to be the main driver of TFP growth as it is the most commonly used measure of technical change. Direct R&D expenditure affects the innovative capacity of a sector both directly and indirectly by increasing its absorptive capacity for knowledge created in other sectors. The relationship between TFP change rates calculated by FIE ( γj ’s) and R&D expenditure was examined by the regression of γj ’s on total sectoral R&D expenditure over the period for which the γj ’s are calculated, i.e., 2010–2015. A variable ( RD_DIFj ) measuring R&D diffusion from the total R&D expenditure of other sectors of the economy into sector j(indirect R&D expenditure or embodied R&D) was also included in the model2. γj 0=c1+d1logRDj+d2logRD_DIFj. (7) Equation (7) is in semi-log form because it is convenient that the coefficient of total sectoral R&D be interpreted as elasticity ( γj ’s are already expressed in percentage change rates). The estimated R&D coefficients d 1 and d 2 are expected to be positive and statistically significant. 2.2. The Neoclassical Framework for Measuring TFP Change TFP growth rate in neoclassical economics is residually determined after subtracting the growth rates of normally employed factor inputs, weighted by their income shares, from the output growth rate. An attempt is made here to review this method and amend it to be comparable to Equation (5). The literature on the issue is quite extensive. Both theoretical and empirical studies measure TFP as an indication of disembodied technical progress caused by R&D and R&D spillovers. Several literature reviews cover the subject (among others, Gollop and Jorgenson (1980); Mohnen (1989); Kydland and Prescott (1982); Griliches (1992); Coe and Helpman (1993); Bernstein and Mohnen (1994) ;Nadiri (1993); Katsoulacos and Tsounis (2000); Athanasoglou et al. (2008); Sakurai et al. (1996); Vamvakidis (2002); Aulin-Ahmavaara (2004); Vournakis (2007); Jones and Romer (2010); Sheng and Song (2013); Voutsinas and Tsamadias (2014) ;Gogos et al. (2013); Comin (2010); Haider et al. (2021); Próchniak (2016); Manasse (2016)). Usually, TFP is expressed as production per unit of a composite index of inputs, appropriately aggregated. Two methods can be distinguished in the literature to calculate TFP: the growth accounting approach and the production function approach. Both methods produce the same results under the assumption of constant returns to scale and perfect competition in product and factor markets. TFP growth then corresponds to the concept of Economies 2021,9, 114 7 of 21 technical change which causes shifts in the production function, distinct from movements along the production function caused by factor substitution due to changes in relative factor prices (Jorgenson and Griliches 1967). The growth accounting approach with input–output data will be used here. The use of input–output accounts allows the identification of a detailed cost structure in a given industry, covering the production structure of both primary and intermediate inputs. A word of caution is required regarding TFP indicators; they do not exactly correspond to technical change if competition does not prevail in both products and factor markets, or there are regulations distorting competition and/or externalities that cause scale economies. In particular, the effect of economies of scale is likely to be a major part of productivity growth in capital-intensive industries. In practice the distinction between economies of scale and pure technical change is difficult, but in theory, the contribution of economies of scale is distinguished from that of technical change in productivity growth. TFP, for a sector or the economy as a whole, is generally defined as the ratio of the volume of production Y relative to the total volume of input X, i.e., TFP =Y X . Therefore, the growth rate of TFP is computed as: . TFP TFP = . Y Y− . X X(8) where the dot indicates change (it can be seen also as the first derivative against time, i.e., for Y, . Y=dY dt etc). From Equation (8) it is seen that TFP growth is a residual between the rate of change in production and the rate of change in production inputs. TFP change then is calculated as the change in output growth between two distinct points in time when all the remaining sources of output growth are subtracted. Therefore, we can identify apart from TFP, the contribution of primary factor productivity change in output growth, the contribution of capital, and the contribution of intermediate inputs of domestic and of imported origin. When examining Equation (8) for several successive points in time, substitution effects among inputs (intermediate of domestic and imported origin and labor and capital) can also be identified. It is known that using value-added instead of gross output is a better indication of resource allocation 3 . Consequently, the value-added approach will be used here for measuring the TFP change according to the neoclassical approach. Let YVA j=pjYj−∑ipiXi−∑itiXi−∑ipm iXm i(9) be the value-added output of sector jat factor cost. Ydenotes final product in physical units, Xintermediate inputs in physical units, subscripts denote sectors, superscript m denotes imports, pdenotes price, and tnet indirect taxes per unit of product. Further, . TFPj TFPj = [ TFPj=∂YVA j ∂T 1 YVA j = ∂Yj ∂T 1 Yj!pjYj YVA j (10) By totally differentiating Equation (9), substituting from Equation (8), and solving for [ TFPjwe get: [ TFPj=d YVA j−∑ i wiLi YVA jb Lj!−Yjpjb pj YVA j +∑ i Xipi YVA jb pi!+∑ i Xm ipm i YVA jc pm i!+∑ i Xiti YVA jb ti!(11) By substituting in Equation (11) l∗ i , y∗ j , x∗ i , m∗ iand t∗ i —the share of the value of the ith labor input in value-added j, the ratio of the value of output jover value-added j, the share of the value of domestic inputs in value-added j, the share of the value of imported inputs in value-added jand the share of net indirect taxes in value-added j, respectively—we get: [ TFPj=d YVA j−∑ i l∗ ib Lj−y∗ jb pj+∑ i x∗ ib pi+∑ i m∗ ic pm i+∑ i t∗ ib ti(12) Economies 2021,9, 114 8 of 21 As can be seen, in Equation (12) [ TFPj depends on b pj and therefore, the effects of monopoly power on sectoral TFP change rate have to be accounted for. So, an estimation similar to Equation (6) has been performed: [ TFPj=α2+β2c SIj+vj(13) The residuals of this regression are the sectoral TFP change rates without the effect of change of monopoly power on price change rates ( \ TFPj0) . 4 The expected sign of the coefficient again is negative. This can be derived easily from Equation (12); empirical studies examining the relationship between TFP change and change in sectoral concentration establish also a negative relationship (Bournakis 2012;Tsekouras and Daskalopoulou 2006). The results are reported in Appendix B. Equation (7) is estimated again with \ TFPj0 as the dependent variable. A comparison of the estimation results of the two regressions will indicate which TFP methodology measures better technical progress caused by R&D expenditure, the neoclassical or FIE. 2.3. Data Description Both FIE and neoclassical methods of TFP measurement have been applied to realworld data from the Greek economy to provide a comparison of the results between the two methods. As a background, we quickly remind the reader about the macroeconomic indicators in Greece during the studied period of 2010 to 2015. During this period Greece was struck by a deep recession as a result of the adjustment program imposed by the Troika to deal with the huge budget deficit and sovereign debt crisis following the 2008 financial crisis. The average annual real GDP growth for the period was − 3.93%, the average price changes over the period were − 2.3%, the average annual unemployment rate was 24.2% of the labor force, and the average annual current account balance was USD − 9.9 billion (IMF 2021). Furthermore, there was an emigration of the most skilled and qualified individuals together with a fall in employment coupled with wage cuts of 22.5% to 23.2% dictated by the Troika (Agiomirgianakis et al. 2019). The choice of the Greek economy was made for two reasons: (a) data availability, and (b) suitable macroeconomic indicators for making a comparison between the FIE and the neoclassical methods. Regarding the first reason, the use of Equation (5) for empirical work requires that input–output (i–o) table data report also labor inputs in physical terms; i.e., total hours worked per sector. These kinds of data are not available in the i–o tables reported for the EU countries by Eurostat and the OECD and were available for the Greek economy for the two years of the study only. Secondly, macroeconomic indicators for Greece during the examined period made the country ideal to compare the results of TFP growth calculated according to the new method introduced here (FIE) and the neoclassical one because according to theory 5 , when prices decrease, the neoclassical approach would underestimate TFP changes. Sixty-four sector input–output tables of the Greek economy using the NACE rev.2 classification scheme for 2010 and 2015 (Hellenic Statistical Authority 2010,2015) were used for the calculation of both the neoclassical and FIE approaches to sectoral TFP change. Output and import price data for the 64 sectors of the input–output tables were also extracted from Hellenic Statistical Authority (2016a,2016b). Total sales data of the largest firms in each sector and total sectoral sales for the calculation of the Schmalensee index were obtained from the Hellenic Statistical Authority after special request (these data are not publicly available). Sectoral R&D expenditure data in constant prices for the period 2011–2015 were extracted from the OECD database (OECD 2011–2015). 3. Results and Discussion Equations (5) and (12) were applied to the dataset and then Equation (6) was estimated to isolate the effect of change in monopoly power on sectoral TFP changes. Estimation results were checked for robustness by estimating Equation (6) using γj values calculated by Economies 2021,9, 114 15 of 21 Table A3. Cont. No Sector Description γ0 j Laspeyres Rank γ0 j Paasche Rank Terms of Trade Effect Laspeyres Terms of Trade Effect Paasche 20 Motor vehicles, trailers, and semi-trailers 0.127 10 0.116 10 −0.009 −0.009 21 Other transport equipment 0.145 6 0.133 6 0.000 0.000 22 Furniture; other manufactured goods 0.102 12 0.104 12 0.007 0.007 23 Repair and installation services of machinery and equipment 0.029 24 0.014 25 0.000 0.000 24 Electricity, gas, steam, and air-conditioning −0.240 62 −0.338 63 −0.009 −0.010 25 Natural water; water treatment and supply services −0.053 47 −0.012 35 0.000 0.000 26 Sewerage; waste collection, treatment, and disposal activities; materials recovery; remediation activities and other waste management services −0.013 39 0.010 30 0.003 0.002 27 Constructions and construction works −0.059 49 −0.062 46 0.000 0.000 28 Wholesale and retail trade and repair services of motor vehicles and motorcycles −0.018 41 −0.034 41 0.000 0.000 29 Wholesale trade services, except of motor vehicles and motorcycles 0.011 31 0.002 32 0.000 0.000 30 Retail trade services, except of motor vehicles and motorcycles 0.049 20 0.026 23 0.000 0.000 31 Land transport services and transport services via pipelines −0.164 61 −0.218 61 0.001 0.001 32 Water transport services −0.010 36 −0.027 39 0.000 0.000 33 Air transport services 0.193 4 0.261 3 0.041 0.079 34 Warehousing and support services for transportation −0.010 37 −0.046 45 0.003 0.002 35 Postal and courier services 0.065 17 0.069 16 0.003 0.003 36 Accommodation and food services −0.041 44 −0.042 43 0.000 0.000 37 Publishing services −0.098 54 −0.139 59 −0.002 −0.003 38 Motion picture, video and television program production services, sound recording and music publishing; programming and broadcasting services −0.051 46 −0.063 47 −0.011 −0.018 39 Telecommunications services −0.010 38 −0.021 37 −0.002 −0.002 40 Computer programming, consultancy and related services; information services −0.007 35 −0.020 36 −0.006 −0.004 41 Financial services, except insurance and pension funding −0.027 42 −0.039 42 −0.001 −0.001 42 Insurance, reinsurance and pension funding services, except compulsory social security 0.066 16 0.065 17 −0.034 −0.023 Economies 2021,9, 114 16 of 21 Table A3. Cont. No Sector Description γ0 j Laspeyres Rank γ0 j Paasche Rank Terms of Trade Effect Laspeyres Terms of Trade Effect Paasche 43 Services auxiliary to financial services and insurance services −0.074 52 −0.063 48 0.000 0.000 44 Real estate activities without imputed rents 0.245 2 0.706 1 0.000 0.000 45 Imputed rents 0.203 3 0.183 5 0.000 0.000 46 Legal and accounting services; services of head offices; management consulting services −0.123 60 −0.110 55 −0.001 −0.001 47 Architectural and engineering services; technical testing and analysis services −0.071 51 −0.081 50 0.000 0.000 48 Scientific research and development services −0.115 57 −0.117 56 0.000 0.000 49 Advertising and market research services −0.087 53 −0.101 53 0.000 0.000 50 Other professional, scientific and technical services; veterinary services 0.022 28 0.043 20 −0.002 −0.002 51 Rental and leasing services 0.100 13 0.092 13 −0.023 −0.008 52 Employment services −0.368 63 −0.301 62 0.000 0.000 53 Travel agency, tour operator and other reservation services and related services 0.029 25 0.013 26 0.000 0.000 54 Security and investigation services; services to buildings and landscape; office administrative, office support and other business support services −0.113 55 −0.101 54 −0.001 −0.001 55 Public administration and defense services; compulsory social security services 0.026 27 0.013 27 0.000 0.000 56 Education services −0.017 40 −0.029 40 0.000 0.000 57 Human health services −0.053 48 −0.081 51 0.000 0.000 58 Social work services −0.113 56 −0.208 60 0.000 0.000 59 Creative, arts, and entertainment services; library, archive, museum and other cultural services; gambling and betting services 0.056 18 −0.003 34 −0.005 −0.001 60 Sporting services and amusement and recreation services 0.182 5 0.200 4 0.000 0.000 61 Services furnished by membership organizations 0.272 1 0.315 2 0.000 0.000 62 Repair services of computers and personal and household goods 0.077 14 0.119 9 0.000 0.000 63 Other personal services 0.056 19 0.034 22 0.000 0.000 64 Services of households as employers; undifferentiated goods and services produced by households for own use −0.119 58 −0.132 58 0.000 0.000 Negative change rates in red. Source: Authors’ calculations. Economies 2021,9, 114 17 of 21 Table A4. TFP change measured according to the neoclassical approach. Sector Description [ TFPj 0Rank 1 Products of agriculture, hunting, and related services 0.006 11 2 Products of forestry, logging, and related services 0.019 3 3 Fish and other fishing products; aquaculture products; support services to fishing −0.030 34 4 Mining and quarrying −0.400 63 5 Food products, beverages, and tobacco products −0.037 38 6 Textiles, wearing apparel, and leather products −0.019 26 7 Wood and products of wood and cork, except furniture; articles of straw and plaiting materials −0.148 62 8 Paper and paper products −0.051 44 9 Printing and recording services −0.040 41 10 Coke and refined petroleum products −1.359 64 11 Chemicals and chemical products 0.014 5 12 Basic pharmaceutical products and pharmaceutical preparations −0.124 59 13 Rubber and plastics products −0.010 22 14 Other non-metallic mineral products −0.055 47 15 Basic metals 0.002 17 16 Fabricated metal products, except machinery and equipment −0.018 25 17 Computer, electronic, and optical products 0.003 13 18 Electrical equipment 0.009 8 19 Machinery and equipment n.e.c. 0.002 15 20 Motor vehicles, trailers, and semi-trailers 0.002 14 21 Other transport equipment 0.011 6 22 Furniture; other manufactured goods −0.005 21 23 Repair and installation services of machinery and equipment 0.001 18 24 Electricity, gas, steam, and air-conditioning −0.083 53 25 Natural water; water treatment and supply services −0.028 32 26 Sewerage; waste collection, treatment, and disposal activities; materials recovery; remediation activities and other waste management services −0.036 37 27 Constructions and construction works −0.119 58 28 Wholesale and retail trade and repair services of motor vehicles and motorcycles −0.069 50 29 Wholesale trade services, except for motor vehicles and motorcycles −0.013 24 30 Retail trade services, except for motor vehicles and motorcycles −0.023 28 31 Land transport services and transport services via pipelines −0.067 49 32 Water transport services −0.010 23 33 Air transport services 0.008 9 34 Warehousing and support services for transportation −0.020 27 35 Postal and courier services −0.092 55 36 Accommodation and food services −0.046 43 37 Publishing services −0.097 57 38 Motion picture, video, and television program production services, sound recording and music publishing; programming and broadcasting services −0.095 56 39 Telecommunications services −0.040 42 Economies 2021,9, 114 18 of 21 Table A4. Cont. Sector Description [ TFPj 0Rank 40 Computer programming, consultancy, and related services; information services −0.037 39 41 Financial services, except insurance and pension funding −0.053 46 42 Insurance, reinsurance, and pension funding services, except compulsory social security −0.089 54 43 Services auxiliary to financial services and insurance services −0.030 33 44 Real estate activities without imputed rents 0.018 4 45 Imputed rents 0.010 7 46 Legal and accounting services; services of head offices; management consulting services −0.052 45 47 Architectural and engineering services; technical testing and analysis services −0.057 48 48 Scientific research and development services −0.078 52 49 Advertising and market research services −0.026 30 50 Other professional, scientific, and technical services; veterinary services −0.028 31 51 Rental and leasing services 0.006 10 52 Employment services −0.147 61 53 Travel agency, tour operator, and other reservation services and related services 0.002 16 54 Security and investigation services; services to buildings and landscape; office administrative, office support, and other business support services −0.030 35 55 Public administration and defense services; compulsory social security services −0.002 19 56 Education services −0.025 29 57 Human health services −0.039 40 58 Social work services −0.076 51 59 Creative, arts and entertainment services; library, archive, museum, and other cultural services; gambling and betting services 0.005 12 60 Sporting services and amusement and recreation services 0.021 2 61 Services furnished by membership organizations 0.023 1 62 Repair services of computers and personal and household goods −0.003 20 63 Other personal services −0.034 36 64 Services of households as employers; undifferentiated goods and services produced by households for own use −0.138 60 Negative change rates in red. Source: Authors’ calculations. Appendix C. Test of the Equality of Means and Medians of TFP Change Measured According to the Neoclassical and FIE Approaches d TFP vs. γ0Laspeyres d TFP vs. γ0Paasche Test for Equality of Means Anova F-test, significance level in parentheses 5.006844 (0.0272) 4.237668 (0.0416) Test for Equality of Medians Kruskal–Wallis, significance level in parentheses 9.565793 (0.0020) 6.093841 (0.0136) Test for Equality of Medians Kruskal–Wallis (tie-adj.), significance level in parentheses 9.565793 (0.0020) 6.093841 (0.0136) Test for Equality of Medians van der Waerden, significance level in parentheses 9.938526 (0.0016) 6.613421 (0.0101) Source: Authors’ calculations. Economies 2021,9, 114 19 of 21 Notes 1 In the empirical work that follows it is considered that this assumption cannot be applied to real-world data. The existence of monopoly power is acknowledged and its effects on prices is isolated using regression analysis. 2Following Leontief’s methodology (Leontief 1986)RD_DIF =RD0(I−A∗)−1−RD.RD_DIFjis the jth element of RD_DIF. 3See Opocher and Steedman (2015, pp. 161–63) and Sakurai et al. (1996, pp. 36–38) for the relevant discussion. 4\ TFPj0 throughout the paper is used to denote the per centage change in sectoral TFP calculated according to the neoclassical methodology. 5See Section 3Results and Discussion for a further explanation on this. 6See Opocher and Steedman (2015, pp. 162–63) for its theoretical proof. 7TFP’ change according to the neoclassical approach was estimated from (13) and the results are reported in Appendix B. 8 These sectors are: 6 Textiles, wearing apparel and leather products, 8 Paper and paper products, 9 Printing and recording services, 13 Rubber and plastics products, 14 Other non-metallic mineral products, 16 Fabricated metal products, 22 Furniture, 29 Wholesale trade services, 30 Retail trade services, 35 Postal and courier services, 42 Insurance, 50 Other professional, scientific and technical services, 55 Public administration and defence services, 62 Repair services of computers, 63 Other personal services. 9If a model is more than 2 AIC units lower than another, it is considered significantly better than that model. 10 By ‘conservatives estimates’ we mean the coefficients eatimated when TFP growth was calculated according to the Paasche method of base year since these are systematically lower that those calculated accoring to the Laspeyres method of base year. 11 Since, the estimation results were obtained by total R&D expedtiture over the period 2010–2015 an 1% increase in R& expenditure does not refer to the annual figures but to the total five-year period. 12 It was not possible to include in the present paper the effects of R&D diffusion from abroad because import matrices were not available. 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