Whither Greece? Productivity before and after the Subprime Crisis

Mike G. Tsionas¹, Mara E. Vidali², George N. Leledakis^3*, Anastasios E. Tasiopoulos⁴

¹Department of Economics, Lancaster University Management School, Lancaster, UK.
²Department of Economics, Athens University of Economics and Business, Athens, Greece.
³Department of Accounting and Finance, School of Business, Athens University of Economics and Business, Athens, Greece.
⁴Hellenic Parliamentary Budget Office (HPBO), Athens, Greece.

DOI: 10.4236/tel.[phone]                

Abstract

This paper employs a stochastic production frontier model with time-varying inefficiency to assess the performance and productivity growth of 9054 Greek firms from 1996 to 2017. Various forms of capital are incorporated, extending beyond physical capital and labor, to estimate productivity growth and disentangle its components. Our results indicate that, despite a significant decrease in productivity growth after 2007, it remains positive on average, albeit with notable variations among firms. These findings offer valuable insights to inform future policy decisions in Greece, which may have implications for other nations as well.

Keywords

Productivity Growth, Production Functions, Stochastic Frontiers

1. Introduction

The global financial crisis that began in 2007 triggered by the collapse of the U.S. subprime mortgage market, resulted in one of the worst post-war economic recessions worldwide. Although public finances were severely impacted, several countries managed to ensure their sustainability and recovery. However, Greece experienced a decade-long recession of unprecedented magnitude and duration among modern developed economies, losing approximately 20% of real per capita Gross Domestic Product (GDP) between 2007 and 2017 (see Avramidis et al., 2021 ; Chodorow-Reich et al., 2019 ; Giannoulakis & Sakellaris, 2021 ; Gourinchas et al., 2017 ).

Greece faced three quasi-simultaneous and interlinked shocks: a sovereign debt crisis, a banking crisis, and a sudden stop (see the seminal paper of Gourinchas et al., 2017 , which provides the first systematic analysis of the Greek economic crisis). Consequently, the Greek economy became even less competitive than other European Union (EU) and Organization for Economic Cooperation and Development (OECD) countries, which led to low productivity (see Alogoskoufis & Featherstone, 2021 ; Chodorow-Reich et al., 2019 ; Genakos, 2018 ; Katsoulakos et al., 2017 ; Pelagidis & Mitsopoulos, 2014 ). Therefore, the Greek economic crisis presents a unique opportunity to examine the factors that influence productivity and economic growth in a small open economy operating within a currency union during a crisis of unparalleled magnitude and duration.

This paper addresses the following question: How severely was productivity impacted in the aftermath of the crisis? This inquiry holds particular significance for investors, business professionals, and policymakers since enhancing productivity is essential for a country’s economic growth, which, in turn, leads to economic recovery. While there is a growing body of literature that measures productivity at the firm level and elucidates its importance for economic growth (see, for example, Bournakis & Mallick, 2018 ; Li & Liu, 2011 ; Rath, 2018 ), to the best of our knowledge, there is limited empirical evidence available for Greece (see Belegri-Roboli & Michaelides, 2006 ; Bournakis, 2011 ; Halkos & Tzeremes, 2007 ; Voutsinas & Tsamadias, 2013 ). However, none of these studies offer evidence regarding productivity growth in the aftermath of the crisis.

The aim of this paper is threefold: First, to measure productivity at the firm level and identify its primary drivers. Second, to assess productivity growth and its underlying sources, revealing valuable policy-related insights that could contribute to sustained growth in Greece. Finally, to investigate the role of firm size. In particular, we utilize detailed firm-level data and differentiate between various forms of capital, including financial capital services, which represents a novel approach in applied modeling. We adopt a stochastic production frontier model with time-varying inefficiency, enabling us to disentangle the components and gain a comprehensive understanding of the factors influencing productivity changes among 9054 Greek firms from 1996 to 2017¹.

Related to our work is the study of Genakos (2018) , which investigates the role of managerial practices in understanding productivity differences across firms and across countries and notes that “it is almost as if there are two types of firms inside Greece (i.e. “two Greeces”): one that is outdated, inefficient, and ignorant of its own quality of management and one that is up-to-date, efficient and is trying to improve itself and achieving world standards” (p. 888). His paper does not directly measure the productivity in Greece, though. In our paper, management is more related to efficiency or efficiency change.

The term “Total Factor Productivity (TFP) growth”, first introduced by Solow (1957) , also called “the Solow residual”, is defined as the growth rate of output that cannot be explained by the changes of traditional inputs (labor and capital). However, this index does not allow for efficiency change which if there exists, it contributes to productivity change. The study of Kumbhakar et al. (2000) was the first to address the estimation and decomposition of TFP change within a stochastic frontier framework that permits efficiency change which is a fundamental assumption in this paper (see Cornwell et al., 1990 ; Kumbhakar, 1990 ). Assuming that technical inefficiency remains constant over time implies that firms or economies never learn. This assumption may be unrealistic in a competitive market or in a long panel framework. To account for time-varying technical inefficiency, one must make assumptions about the functional form of this term (see Kumbhakar, 1990 ; Battese & Coelli, 1992 ; Lee & Schmidt, 1993 ; Kumbhakar & Wang, 2005 ).

We use two popular approaches, as introduced by Kumbhakar (1990) and Battese and Coelli (1992) . Our findings indicate that, on average, productivity growth remains positive, although it has decreased significantly since the subprime crisis. This outcome is primarily attributed to technical change. The role of efficiency change also appears to be significant, but its magnitude depends on the specific model used for efficiency estimation. Furthermore, we observe substantial variations in productivity among different firm size categories, indicating that larger firms generally exhibit higher average productivity. However, in the aftermath of the crisis, these differences are nearly eradicated.

In conclusion, despite a significant decline in productivity resulting from the shock of the financial crisis, it has managed to remain in positive territory. This suggests that certain policies have been effective in maintaining positive productivity growth. However, it is worth noting that these results have led to the narrowing of the productivity gap among firms that previously contributed to productivity growth and, consequently, economic growth in the past. In our view, these findings indicate that if policymakers were to tailor their reforms to the specific needs of different firm size categories, productivity growth could potentially act as a catalyst for economic growth and expedite the path to economic recovery.

The remainder of this paper is organized as follows. Section 2 presents the model specification and the method we use to estimate productivity growth and its component. In Section 3, we describe the data and Section 4 presents the results. Our concluding remarks are presented in Section 5.

2. Model

We consider the following production frontier model $y_{it}=f\left(x_{it},t;\beta \right)\exp \left({\epsilon }_{it}\right)$ , where the error term ${\epsilon }_{it}=v_{it}-u_{it}$ is the difference of $v_{it}$ the two-sided error component, and $u_{it}$ , the nonnegative time-varying technical inefficiency component. The output of firm i at time t, $y_{it}$ is produced using a vector of inputs $x_{it}\in {ℝ}_{+}^{{\rm K}}$ through a production function where t is the time trend used here as a proxy for technical change. A time-varying stochastic production frontier is assumed, originally proposed by Aigner et al. (1977) and Meeusen and van den Broeck (1977) in a cross-sectional framework:

$\begin{array}{c}\ln y_{it}={\beta }_0+{\beta }_{01}t+\frac{1}{2}{\beta }_{02}{t}^2+{\displaystyle \underset{k=1}{\overset{K}{\sum }}{\beta }_k\ln x_{kit}}+\frac{1}{2}{\displaystyle \underset{k=1}{\overset{K}{\sum }}{\displaystyle \underset{j=1}{\overset{K}{\sum }}{\beta }_{kj}\ln x_{kit}\ln x_{jit}}}\\ +{\displaystyle \underset{k=1}{\overset{K}{\sum }}{\beta }_{1k}t\ln x_{kit}}+v_{it}-u_{it}\end{array}$ (1)

for $i=1,\cdots ,N$ , $t=1,\cdots ,T$ .

We also assume that:

$v_{it}\sim iidN\left(0,{\sigma }_v^2\right)$ (2)

$u_{it}=G\left(t\right)u_i$ (3)

$u_i\sim iid{N}^{+}\left(\mu ,{\sigma }_u^2\right)$ (4)

where $G\left(t\right)\ge 0$ is function of time t. For $G\left(t\right)$ , we use two functional forms, one proposed by Kumbhakar (1990) :

$G\left(t\right)={\left(1+\exp \left(\gamma t+\delta t^2\right)\right)}^{-1}$ (5)

and the other by Battese and Coelli (1992) :

$G\left(t\right)=\exp \left(\gamma \left(t-T\right)\right)$ (6)

We estimate the parameters using maximum likelihood and obtain estimates for productivity change and its sources (detailed derivations are presented in the Appendix A and parameter estimates are available on request):

$T\stackrel{\dot{}}{F}{P}_{it}=T{C}_{it}+\left(e_{it}-1\right){\displaystyle {\sum }_{k=1}^K\left(\frac{e_{itk}}{e_{it}}\right){\stackrel{\dot{}}{x}}_{kit}}+TE{C}_{it}$ (7)

where

${\widehat{TC}}_{it}={\hat{\beta }}_{01}+{\hat{\beta }}_{02}t+{\displaystyle {\sum }_{k=1}^K{\hat{\beta }}_{1k}\ln x_{kit}}$ (8)

${\hat{e}}_{itk}={\hat{\beta }}_k+{\hat{\beta }}_{1k}t+{\displaystyle {\sum }_{j=1}^K{\hat{\beta }}_{kj}\ln x_{jit}}$ (9)

${\hat{e}}_{it}={\displaystyle {\sum }_{k=1}^K{\hat{e}}_{itk}}$ (10)

The estimation of efficiency change (TEC) depends on the choice of $G\left(t\right)$ so, following Kumbhakar (1990) (Equation (5)), we obtain:

${\widehat{TEC}}_{it}=-{\hat{u}}_i\left(\hat{\gamma }+2\hat{\delta }t\right)\exp \left(\hat{\gamma }t+\hat{\delta }{t}^2\right){\left(1+\exp \left(\hat{\gamma }t+\hat{\delta }{t}^2\right)\right)}^{-2}$ (11)

If we adopt Battese and Coelli’s (1992) approach (Equation (6)), we have:

${\widehat{TEC}}_{it}=-{\hat{u}}_i\hat{\gamma }\exp \left(\hat{\gamma }\left(t-T\right)\right)$ (12)

where ${\hat{u}}_i=E\left(u_i|{\epsilon }_i\right)$ of the distribution of $u_i|{\epsilon }_i$ , where ${\epsilon }_i={\left({\epsilon }_{i1},\cdots ,{\epsilon }_{iT}\right)}^{\prime }$ .

3. Data

The data is an unbalanced panel of 9054 firms for the period 1996-2017. We include companies from several sectors except for banks and financial institutions that are active in Greece during the period under investigation. The data was obtained from the database of ICAP, a Greek private research company that collects detailed business information, which includes accounts and ratios from the firms’ annual financial statements². We measure output $y_{it}$ as the sum of final and semifinal products. The inputs include labor $l_{it}$ , measured as the number of employees and different types of capital: Services from use of buildings, $x_{1it}$ , the services of mechanical equipment $x_{2it}$ , the services of intangible assets $x_{3it}$ , materials $x_{4it}$ , services of financial capital $x_{5it}$ and other inputs $x_{6it}$ . To the best of our knowledge, use of such detailed data at the firm level is quite novel. Summary statistics are presented in Table 1 and industry classification (SIC) in Table 2, respectively.

Table 1. Descriptive statistics.

Note: All variables, except for l, are measured in euros. Labor is defined as the number of employees. We use a sample of 42,391 observations and 9054 firms.

Table 2. Industry classification.

Note: The total number of firms is 9054.

4. Empirical Results

In this section, we present the results of our analysis. Using the method of maximum likelihood, we estimate the parameters of production frontier and derive the sources of productivity change and its components. As we described in Section 2, we use two different functional forms for $G\left(t\right)$ and hence, we have two models; Model 1 stands for the approach proposed by Kumbhakar (1990) and Model 2 stands for the approach proposed by Battese and Coelli (1992) .

4.1. Full Sample

Table 3 presents the descriptive statistics of elasticities. We observe that elasticities are almost identical for both models. Figure 1 shows the distribution of elasticities. The estimation of input elasticities suggests that labor, financial capital, and intermediate inputs (materials) are the most important, on average.

Figure 2 shows the distribution of scale elasticity, an initial measure for returns to scale. The distribution of both models that lies between .4 and 1.4. Scale elasticity, on the average, is less than zero and equal to .84. Since we are interested in testing whether the production function is characterized by constant returns to scale or decreasing returns to scale on average, we perform a Wald test and reject the null hypothesis of constant returns to scale in favor of the alternative hypothesis (p-value = .003). However, we observe that scale elasticity is above unity for 5.8% of firms of our sample suggesting increasing returns to scale (N = 521, RTS > 1).

The distribution productivity growth and its sources are depicted in Figure 3 for the whole period for both models and Table 4 reports the descriptive statistics.

Figure 1. Elasticities. Note: This figure shows the distribution of input elasticity for each input. We use a sample of 42,391 observations.

Figure 2. Returns to scale. Note: This figure shows the distribution of Returns to scale for each model. We use a sample of 42,391 observations.

Table 3. Summary elasticities.

Note: The elasticities of output with respect to each of the inputs are estimated according to Equation (9) and then we take sample means for all years and firms. We use a sample of 42,391 observations and 9054 firms.

Table 4. Decomposition analysis.

Note: The TFP growth rate and its components are based on Equations (7) to (12). Analytical calculations are provided in the appendix. The estimates are averaged across firms and years. We use a sample of 33,231 observations.

Figure 3. Productivity change and its sources. Note: This figure shows the distribution of productivity change and its sources for each model. We use a sample of 33,231 observations.

The upper left panel of Figure 3 illustrates the scale component, representing scale economies. On average, it falls slightly below zero, but its impact is minimal.

The term ${\displaystyle {\sum }_{k=1}^K\left(\frac{e_k}{e}\right){\stackrel{\dot{}}{x}}_k}$ which presents the use of inputs is positive indicating

an expansion in input use over the period. However, since the average scale elasticity is below unity, its effect on productivity change is negative but very modest. Additionally, we note that the scale component is positive for a group of firms, suggesting a positive contribution to productivity change. Throughout the period, the primary driver of TFP growth is the distribution of Technical Change (TC), as shown in the upper right panel. The TC distribution exhibits multiple modes, and its values range from slightly below zero to nearly 10%, indicating the presence of firm clusters with varying growth rates. The distribution of efficiency change (TEC) is concentrated around the mean in Model 1, while in Model 2, the distribution is truncated below zero. On average, productivity growth stands at approximately 3%, with values ranging from just below zero to almost 10%, as depicted in the lower right panel of Figure 3.

4.2. Role of Financial Crisis

Our next objective is to assess the extent to which productivity change was impacted by the financial crisis. Given that the recession in Greece endured longer than in other European or OECD countries, primarily due to the sovereign debt crisis, we divide the period from 1996 to 2017 into two subperiods. The first subperiod spans from 1996 to 2007, characterized by a period of economic growth in Greece, and the second subperiod covers the crisis from 2008 to 2017. We will examine productivity change and its underlying sources during these two distinct timeframes³.

The distribution of productivity growth and its sources can be found in Figure 4, while Table 5 provides descriptive statistics. Since 2008, both models consistently demonstrate a leftward shift in the distribution of productivity growth. For Model 1, the range spans from −5% to 7%, while for Model 2, it extends from −5% to 5%. Table 5 reveals a decrease in productivity growth between the pre- and post-crisis periods. In Model 1, the estimated decline in productivity is approximately 77%, and in Model 2, it is estimated at around 85%. Surprisingly, despite the challenges faced since 2008, productivity growth has managed to remain positive on average.

In terms of efficiency change, Model 1 indicates a leftward shift in the distribution of TEC, transitioning from positive to negative values, suggesting a decline in efficiency change. On the other hand, for Model 2, the distribution post-crisis remains largely consistent with the pre-crisis distribution.

Consequently, both models concur that TC is the primary driver of positive productivity growth, although it is notably lower in the post-crisis period, averaging around 2% as opposed to 6% during the pre-crisis period. The pre-crisis

Figure 4. Productivity change and its sources before and after the sub-prime crisis. Note: This figure shows the distribution of productivity change and its sources for each model before and after the subprime crisis. We use a sample of 33,231 observations.

Table 5. Decomposition analysis before and after crisis.

Note: The TFP growth rate and its components are based on Equations (7) to (12). Analytical calculations are provided in the appendix. The estimates are averaged across firms and years. From 1996 to 2007, the sample size is 10,542 while, from 2008 to 2017, it is 22,689, respectively.

distribution of TC exhibits a distinctive minor mode at approximately 8% to 10%, depending on the model, indicating the presence of a group of firms with exceptionally high growth rates. While this group continues to grow in the aftermath of the crisis, the growth rate has slowed considerably, approaching 4%. Nevertheless, the bimodality of the TC distribution remains apparent.

4.3. Role of Firm Size

Finally, this paper addresses the question if there are differences in productivity and its sources across various firm size categories. We categorize firms based on the number of employees. Small firms are those with fewer than 50 employees, medium-sized firms fall within the range of 50 to 249 employees, and large firms consist of those with at least 250 employees. Both models (Table 6, Figure 5) are consistent with the result that the larger a firm is the greater its TFP growth on the average.

Table 6. Decomposition analysis across firm size.

Note: The TFP growth rate and its components are based on Equations (7) to (12). Analytical calculations are provided in the appendix. Our sample consists of 22,402 observations in the case of small firms, 8825 in the case of medium firms and 2004 in the case of large firms.

Table 6 provides the descriptive statistics. TFP growth (on average) ranges from almost 3% for small firms, increases to 4% for medium-sized firms, and reaches 5% for large firms. In Model 2, the corresponding values are 1%, 2%, and 3%, respectively. Thus, both models concur that, on average, there is a positive correlation between firm size and productivity growth. Figure 5 illustrates the distributions of productivity and its sources across firm sizes, following the structure of the previous figures. While the positive relationship between firm

Figure 5. Productivity and its sources across firm size. Note: This figure shows the distribution of productivity change and its sources for each model across firm size. We use a sample of 33,231 observations.

size and productivity is evident, Figure 5 also reveals that there is a group of small and medium-sized firms outperforming some large firms in terms of productivity growth. This may be occurred because small and medium enterprises can be in growing industries or at a catching up stage (see Tsionas & Mallick, 2019 ).

Regardless of the size of the firm, TC is the main source of growth. We observe that there are substantial differences in TC among firm size categories and both models support that the larger the firm the larger the TC, on the average. Conversely, the Scale component, while exhibiting a small negative effect for small and medium-sized firms, approaches zero and even becomes slightly positive for large firms (.1%). This minor positive shift is a direct result of the larger firms having a total elasticity greater than unity and their tendency to expand the use of inputs over the examined period. The variance in the scale component’s impact between large firms and those of smaller sizes can be attributed to the fact that medium and small-sized firms, despite expanding input usage over time, exhibit diminishing returns to scale in their performance. In terms of TEC, we observe that the larger the firm, the lower its inefficiency. The extent of these differences among firm size categories depends on the model employed. According to Model 1, inefficiency decreases from .3% for small firms to .2% for medium-sized firms and approaches almost zero for large firms. In contrast, the corresponding figures for Model 2 are 2%, 1.8%, and 1.7%.

Another aspect we examine is how firm size influenced TFP growth during both the pre- and post-crisis periods. Figure 6 displays the distributions of productivity and its sources for different firm sizes before and after the subprime crisis, while Table 7 provides the corresponding descriptive statistics. The evidence from Figure 6 suggests that the distribution of productivity growth for all firm sizes has shifted to the left since the subprime crisis. This indicates that, on average, productivity growth worsened after the crisis, although it still remains positive for all firm sizes. Additionally, the bottom right panel of Figure 6 vividly illustrates that before 2008, significant differences existed in the distribution of productivity growth among firm size categories, implying that the distinct growth experiences have been partially equalized in the aftermath of the crisis. However, the positive correlation between firm size and productivity growth persists in each subperiod, especially in the case of Model 2. Here, the smaller the firm, the greater the negative impact of the crisis on productivity growth. Specifically, small firms experienced an average loss of 89.3% in their growth rate, medium-sized firms lost 77.5%, and large firms lost 75%. In Model 1, the pattern is less clear, with corresponding rates of 78.5%, 76.3%, and 77.3%. Both models indicate that regardless of firm size, there was a reduction of at least 3/4 of the post-crisis productivity growth rate compared to the pre-crisis period.

As we described above, in both periods, the primary factor contributing to productivity growth is TC. The decline in TC since the crisis is distributed fairly evenly among firms of various sizes, accounting for approximately 65% according to Model 1 and 52% according to Model 2. In the top right panel of Figure 6, significant differences in the distribution of TC among firm size categories before 2008 are prominently visible. Following the subprime crisis, the distributions are nearly identical, indicating that although firms continue to grow at varying rates, these rates have significantly decreased, erasing the disparities among firm size categories. This finding suggests that TC is one of the factors contributing to the absence of substantial differences in terms of productivity growth in the aftermath of the crisis. Furthermore, the two models yield different results regarding the impact of TEC on productivity during the pre-crisis period. Model 1 estimates that the average TEC is around .7% for all firm sizes, while Model 2 suggests it’s approximately −.17%. Model 1 indicates that TEC is not influenced by firm size, even before 2008, whereas Model 2 suggests that firm size has a small positive effect on TEC. Nevertheless, it is evident from both models that TEC deteriorates after the crisis for all firm sizes. As for the scale component, the results in each period are qualitatively similar to those presented in Table 6 and Figure 5.

Figure 6. Productivity change and its sources before and after the subprime crisis across firm size. Note: This figure shows the distribution of productivity change and its sources for each model across firm sizes before and after the subprime crisis. We use a sample of 33,231 observations.

Table 7. Decomposition analysis across firm size before and after crisis.

Note: The TFP growth rate and its components are based on Equations (7) to (12). Analytical calculations are provided in the appendix.

5. Concluding Remarks

We estimate a stochastic production frontier model with time-variant inefficiency that allows us to estimate productivity change and disentangle its sources. Utilizing detailed firm-level data for Greece, our findings reveal that, on average, productivity growth remains positive, albeit significantly reduced since the subprime crisis. This is primarily driven by technical change, though the role of efficiency change is also substantial, depending on the specific efficiency estimation model used. These results challenge the conventional belief that the crisis severely damaged the productive foundations of the Greek economy, demonstrating that there is still potential for both efficiency enhancements and technical advancements. Even in the aftermath of the crisis, there exists a group of firms that exhibit growth. Additionally, our research demonstrates the significant influence of firm size on productivity growth, although this impact appears to weaken in the post-crisis period. We observe a partial elimination of differences in growth experiences among firm size categories.

Compared to Genakos (2018) , our results indicate although it may be true that there is “evidence demonstrating the low ranking of firms in the Greek economy compared with other EU and OECD countries” (Genakos, 2018: p. 896) , it does not necessarily be true that productivity is low, especially as Genakos (2018) does not present direct productivity-related evidence. Our work contributes to this discussion by showing that, apart from the role of management, which in our paper is more related to efficiency and efficiency change, other factors are responsible for both: 1) the dramatic decline in productivity growth, and 2) the fact that this productivity growth is still positive (although unevenly distributed across firms) despite institutional rigidities and other exogenous factors (Bloom & Van Reenen, 2007, 2010) . An interesting extension of this paper is the evaluation of productivity growth among different sectors. However, we leave an investigation of this important question to future research.

Acknowledgements

We would like to thank the participants at the 2019 Conference of the Association of Southern European Economic Theorists (ASSET) for their valuable comments and suggestions. Authors acknowledge financial support from the project co-financed by Greece and the European Union (European Social Fund), through the Operational Program “Human Resources Development, Education and Lifelong Learning 2014-2020” (MIS-5006583). All remaining errors and omissions are our own.

Appendix A: Productivity Change Decomposition

Assume the following production frontier $y_{it}=f\left(x_{it},t;\beta \right)\exp \left({\epsilon }_{it}\right)$ . By taking logs and differentiating with respect to time t we obtain:

${\stackrel{\dot{}}{y}}_{it}=\frac{\partial \ln f\left(x_{it},t;\beta \right)}{\partial t}+\underset{k=1}{\overset{K}{{\displaystyle \sum }}}\frac{\partial \ln f\left(x_{it},t;\beta \right)}{\partial x_{kit}}\frac{\partial x_{kit}}{\partial t}-\frac{\partial u_{it}}{\partial t}$

${\stackrel{\dot{}}{y}}_{it}=TC+\underset{k=1}{\overset{K}{{\displaystyle \sum }}}\frac{\partial f\left(x_{it},t;\beta \right)}{\partial x_{kit}}\frac{1}{f\left(x_{it},t;\beta \right)}\frac{\partial x_{kit}}{\partial t}+TEC$

${\stackrel{\dot{}}{y}}_{it}=TC+{\displaystyle \underset{k=1}{\overset{K}{\sum }}{e}_k{\stackrel{\dot{}}{x}}_{kit}}+TEC$

where $e_k=\frac{\partial f\left(x,t;\beta \right)}{\partial x_k}\frac{x_k}{f\left(x,t;\beta \right)}$ are the elasticities of output with respect to each of the inputs⁴, ${\stackrel{\dot{}}{x}}_{kit}=\frac{\partial \ln x_{kit}}{\partial t}$ . TC stands for technological change and TEC for Efficiency change. Following Kumbhakar and Lovell (2000: p. 283) ,

$T\stackrel{\dot{}}{F}P=\stackrel{\dot{}}{y}-{\displaystyle \underset{k=1}{\overset{K}{\sum }}{s}_k{\stackrel{\dot{}}{x}}_k}=TC+{\displaystyle \underset{k=1}{\overset{K}{\sum }}\left(e_k-s_k\right){\stackrel{\dot{}}{x}}_k}+TEC$

By adding and subtracting the term ${\displaystyle {\sum }_{k=1}^K\left(\frac{e_k}{e}\right){\stackrel{\dot{}}{x}}_k}$ , we obtain

$T\stackrel{\dot{}}{F}P=TC+\left(e-1\right)\underset{k=1}{\overset{K}{{\displaystyle \sum }}}\left(\frac{e_k}{e}\right){\stackrel{\dot{}}{x}}_k+\underset{k=1}{\overset{K}{{\displaystyle \sum }}}\left(\left(\frac{e_k}{e}\right)-s_k\right){\stackrel{\dot{}}{x}}_k+TEC$

where $e={\displaystyle {\sum }_{k=1}^K{e}_k}$ is the scale elasticity and provides a measure of returns to scale characterizing the production frontier, $s_k=w_k{x}_i/E$ , the observed expenditure share, $E={\displaystyle {\sum }_{k=1}^K{w}_k{x}_i}$ the total expenditure and $w_k>0$ for $k=1,\cdots ,K$ are the input prices. So, according to Kumbhakar and Lovell (2000: p. 284) , we assume that $s_k=e_k/e$ and finally we obtain a measure that involves only quantity information (Equation (7)):

$T\stackrel{\dot{}}{F}P=TC+\left(e-1\right)\underset{k=1}{\overset{K}{{\displaystyle \sum }}}\left(\frac{e_k}{e}\right){\stackrel{\dot{}}{x}}_{kit}+TEC$

Appendix B: Robustness Tests of Productivity Change Decomposition

Table B1. Decomposition analysis before and after crisis. Cutoff 2008.

Note: The TFP growth rate and its components are based on Equations (7) to (12). Analytical calculations are provided in the appendix. The estimates are averaged across firms and years. From 1996 to 2008, the sample size is 13,061 while, from 2009 to 2017, it is 20,170, respectively.

Table B2. Decomposition analysis before and after crisis. Cutoff 2009.

Note: The TFP growth rate and its components are based on Equations (7) to (12). Analytical calculations are provided in the appendix. The estimates are averaged across firms and years. From 1996 to 2009, the sample size is 15,579 while, from 2010 to 2017, it is 17,652, respectively.

NOTES

¹See Bournakis and Mallick (2018) for a comprehensive discussion of the most up to date approaches in measuring firm level total factor productivity. They conclude that “each method deals with a different challenge in estimating the production function. The approach of each methodology relies on different assumptions whose empirical verification is always subject to data scrutiny” (p. 582).

²Other recent studies used the same database (see Avramidis et al., 2021 ; Giannoulakis & Sakellaris, 2021 ).

³For robustness, we also split the sample into two different subperiods, 1996-2008, 2009-2017 and also, 1996-2009, 2010-2017. The results are qualitatively similar. See Appendix B, Table B1 and Table B2.

⁴We suppress the indices i and t, for the elasticities and expenditure share, to keep the notation simple.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

References

[1]	Aigner, D., Lovell, C. A. K., & Schmidt, P. (1977). Formulation and Estimation of Stochastic Frontier Production Function Models. Journal of Econometrics, 6, 21-37. https://doi.org/10.1016/0304-4076(77)90052-5
[2]	Alogoskoufis, G., & Featherstone, K. (Eds.) (2021). Greece and the Euro: From Crisis to Recovery. https://www.lse.ac.uk/Hellenic-Observatory/Assets/Documents/ Publications/Staff-Publications/Greece-and-the-Euro.pdf
[3]	Avramidis, P., Asimakopoulos, I., Malliaropulos, D., & Travlos, N. G. (2021). Do Banks Appraise Internal Capital Markets during Credit Shocks? Evidence from the Greek Crisis. Journal of Financial Intermediation, 45, Article ID: 100855. https://doi.org/10.1016/j.jfi.2020.100855
[4]	Battese, G. E., & Coelli, T. J. (1992). Frontier Production Functions, Technical Efficiency, and Panel Data: With Application to Paddy Farmers in India. Journal of Productivity Analysis, 3, 153-169. https://doi.org/10.1007/BF00158774
[5]	Belegri-Roboli, A., & Michaelides, P. G. (2006). Measuring Technological Change in Greece. The Journal of Technology Transfer, 31, 663-671. https://doi.org/10.1007/s10961-006-0021-9
[6]	Bloom, N., & Van Reenen, J. (2007). Measuring and Explaining Management Practices across Firms and Countries. Quarterly Journal of Economics, 122, 1351-1408. https://doi.org/10.1162/qjec.2007.122.4.1351
[7]	Bloom, N., & Van Reenen, J. (2010). Why Do Management Practices Differ across Firms and Countries? Journal of Economic Perspectives, 24, 203-224. https://doi.org/10.1257/jep.24.1.203
[8]	Bournakis, I. (2011). Economics: Productivity Performance, Determinants and Future Prospects. In R. Prouska., & M. Kapsali (Eds.), Business and Management Practices in Greece: A Comparative Context (pp. 26-48). Palgrave Macmillan. https://doi.org/10.1057/9780230306530_2
[9]	Bournakis, I., & Mallick, S., (2018). TFP Estimation at Firm Level: The Fiscal Aspect of Productivity Convergence in the UK. Economic Modelling, 70, 579-590. https://doi.org/10.1016/j.econmod.2017.11.021
[10]	Chodorow-Reich, G., Karabarbounis, L., & Kekre, R. (2019). The Macroeconomics of the Greek Depression. NBER Working Paper Series No. 25900. https://doi.org/10.3386/w25900
[11]	Cornwell, C., Schmidt, P., & Sickles, R. C. (1990). Production Frontiers with Cross-Sectional and Time-Series Variation in Efficiency Levels. Journal of Econometrics, 46, 185-200. https://doi.org/10.1016/0304-4076(90)90054-W
[12]	Genakos, C. (2018). The Tale of Two Greeces: Some Management Practice Lessons. Managerial and Decision Economics, 39, 888-896. https://doi.org/10.1002/mde.2971
[13]	Giannoulakis, S., & Sakellaris, P. (2021). Financial Crisis, Firm-Level Shocks and Large Downturns: Evidence from Greece. International Journal of Finance and Economics, 1-24. https://doi.org/10.2139/ssrn.3630244
[14]	Gourinchas, P. O., Philippon, T., & Vayanos, D. (2017). The Analytics of the Greek Crisis. NBER Macroeconomics Annual, 31, 1-81. https://doi.org/10.1086/690239
[15]	Halkos, G. E., & Tzeremes, N. G. (2007). Productivity Efficiency and Firm Size: An Empirical Analysis of Foreign Owned Companies. International Business Review, 16, 713-731. https://doi.org/10.1016/j.ibusrev.2007.06.002
[16]	Katsoulakos, Y., Genakos, C., & Houpis, G. (2017). Product Market Regulation and Competitiveness: Towards a National Competition and Competitiveness Policy in Greece. In C. Meghir, C. Pissarides, D. Vayanos, & N. Vettas (Eds.), Beyond Austerity: Reforming the Greek Economy (pp. 139-178). MIT Press.
[17]	Kumbhakar, S. C. (1990). Production Frontiers, Panel Data, and Time-Varying Technical Inefficiency. Journal of Econometrics, 46, 201-211. https://doi.org/10.1016/0304-4076(90)90055-X
[18]	Kumbhakar, S. C., & Lovell, C. A. K. (2000). Stochastic Frontier Analysis. Cambridge University Press. https://doi.org/10.1017/CBO9781139174411
[19]	Kumbhakar, S. C., & Wang, H. J. (2005). Estimation of Growth Convergence Using a Stochastic Production Frontier Approach. Economics Letters, 88, 300-305. https://doi.org/10.1016/j.econlet.2005.01.023
[20]	Kumbhakar, S. C., Denny, M., & Fuss, M. (2000). Estimation and Decomposition of Productivity Change When Production Is Not Efficient: A Panel Data Approach. Econometric Reviews, 19, 312-320. https://doi.org/10.1080/07474930008800481
[21]	Lee, Y., & Schmidt, P. (1993). A Production Frontier Model with Flexible Temporal Variation in Technical Efficiency. In H. Fried, K. Lovell, & S. Schmidt (Eds.), The Measurement of Productive Efficiency (pp. 237-255). Oxford University Press. https://doi.org/10.1093/oso/9780195072181.003.0008
[22]	Li, K. W., & Liu, T. (2011). Economic and Productivity Growth Decomposition: An Application to Post-Reform China. Economic Modelling, 28, 366-373. https://doi.org/10.1016/j.econmod.2010.08.013
[23]	Meeusen, W., & van den Broeck, J. (1977). Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error. International Economic Review, 18, 435-444. https://doi.org/10.2307/2525757
[24]	Pelagidis, T., & Mitsopoulos, M. (2014). Greece: From Exit to Recovery? Brookings Institution Press.
[25]	Rath, B. N. (2018). Productivity Growth and Efficiency Change: Comparing Manufacturing- and Service-Based Firms in India. Economic Modelling, 70, 447-457. https://doi.org/10.1016/j.econmod.2017.08.024
[26]	Solow, R. M. (1957). Technical Change and the Aggregate Production Function. Review of Economics and Statistics, 39, 312-320. https://doi.org/10.2307/1926047
[27]	Tsionas, M., & Mallick, S. K. (2019). A Bayesian Semiparametric Approach to Stochastic Frontiers and Productivity. European Journal of Operation Research, 274, 391-402. https://doi.org/10.1016/j.ejor.2018.10.026
[28]	Voutsinas, I., & Tsamadias, K. (2013). Does Research and Development Capital Affect Total Factor Productivity? Evidence from Greece. Economics of Innovation and New Technology, 23, 631-651. https://doi.org/10.1080/10438599.2013.871169