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Pontus Mattsson
Linnaeus University DissertationsNo 331/2018
Pontus Mattsson
Essays on Efficiency, Productivity, and Impact of Policy
Essays on E
fficiency, Productivity, and Impact of Policy
Essays on Efficiency, Productivity, and Impact of Policy
Linnaeus University Dissertations
No 331/2018
ESSAYS ON EFFICIENCY,
PRODUCTIVITY, AND IMPACT OF POLICY
PONTUS MATTSSON
LINNAEUS UNIVERSITY PRESS
Linnaeus University Dissertations
No 331/2018
ESSAYS ON EFFICIENCY,
PRODUCTIVITY, AND IMPACT OF POLICY
PONTUS MATTSSON
LINNAEUS UNIVERSITY PRESS
Abstract
Mattsson, Pontus (2018). Essays on Efficiency, Productivity, and Impact of Policy, Linnaeus University Dissertations No 331/2018, ISBN: 978-91-88898-00-5 (print), 978-91-88898-01-2 (pdf). Written in English.
This thesis consists of five self-contained empirical essays centring on total factor productivity (TFP), efficiency, and impacts of policy.
Essay I: ‘TFP Change and Its Components for Swedish Manufacturing Firms During the 2008–2009 Financial Crisis’ (co-authored with Jonas Månsson and William H. Greene). A driving force of economic development is growth in total factor productivity (TFP). Manufactured goods are, to a large extent, exports, and represent an important part of the economy for many developed countries. Additionally, a slowdown in labour productivity has been observed in many OECD countries since the financial crisis of 2008–2009. This study investigates TFP change and its components for the Swedish manufacturing industry, compared with the private service sector, during the years 1997–2013, centring on the financial crisis. Stochastic frontier analysis (SFA) is used to disentangle persistent and transient efficiency from firm heterogeneity and random noise, respectively. In addition, technical change (TC), returns to scale (RTS), and a scale change (SC) component are also identified. Along with the empirical analysis, an elaborative discussion regarding TC in SFA is provided. The persistent part for manufacturing (service) is 0.796 (0.754) and the transient part is 0.787 (0.762), indicating improvement potentials. Furthermore, TFP change is substantially lower between the years 2007–2013, compared to 1997–2007, driven by lower technological progress. Policy should, therefore, target interventions that enhance technology. However, care needs to be taken so that policies do not sustain low-productive firms that otherwise would exit the market.
Essay II: ‘A Bootstrapped Malmquist Index Applied to Swedish District Courts’ (co-authored with Jonas Månsson, Christian Andersson, and Fredrik Bonander). This study measures the total factor productivity (TFP) of the Swedish district courts by applying data envelopment analysis (DEA) to calculate the Malmquist productivity index (MPI) of 48 Swedish district courts from 2012 to 2015. In contrast to the limited international literature on court productivity, this study uses a fully decomposed MPI. A bootstrapping approach is further applied to compute confidence intervals for each decomposed factor of TFP. The findings show a 1.7% average decline of TFP, annually. However, a substantial variation between years can be observed in the number of statistically significant courts below and above unity. The averages of the components show that the negative impact is mainly driven by
Essays on Efficiency, Productivity, and Impact of Policy Doctoral Dissertation, Linnaeus University, Växjö, 2018 ISBN: 978-91-88898-00-5 (print), 978-91-88898-01-2 (pdf) Published by: Linnaeus University Press, 351 95 Växjö Printed by: DanagårdLiTHO, 2018
Abstract
Mattsson, Pontus (2018). Essays on Efficiency, Productivity, and Impact of Policy, Linnaeus University Dissertations No 331/2018, ISBN: 978-91-88898-00-5 (print), 978-91-88898-01-2 (pdf). Written in English.
This thesis consists of five self-contained empirical essays centring on total factor productivity (TFP), efficiency, and impacts of policy.
Essay I: ‘TFP Change and Its Components for Swedish Manufacturing Firms During the 2008–2009 Financial Crisis’ (co-authored with Jonas Månsson and William H. Greene). A driving force of economic development is growth in total factor productivity (TFP). Manufactured goods are, to a large extent, exports, and represent an important part of the economy for many developed countries. Additionally, a slowdown in labour productivity has been observed in many OECD countries since the financial crisis of 2008–2009. This study investigates TFP change and its components for the Swedish manufacturing industry, compared with the private service sector, during the years 1997–2013, centring on the financial crisis. Stochastic frontier analysis (SFA) is used to disentangle persistent and transient efficiency from firm heterogeneity and random noise, respectively. In addition, technical change (TC), returns to scale (RTS), and a scale change (SC) component are also identified. Along with the empirical analysis, an elaborative discussion regarding TC in SFA is provided. The persistent part for manufacturing (service) is 0.796 (0.754) and the transient part is 0.787 (0.762), indicating improvement potentials. Furthermore, TFP change is substantially lower between the years 2007–2013, compared to 1997–2007, driven by lower technological progress. Policy should, therefore, target interventions that enhance technology. However, care needs to be taken so that policies do not sustain low-productive firms that otherwise would exit the market.
Essay II: ‘A Bootstrapped Malmquist Index Applied to Swedish District Courts’ (co-authored with Jonas Månsson, Christian Andersson, and Fredrik Bonander). This study measures the total factor productivity (TFP) of the Swedish district courts by applying data envelopment analysis (DEA) to calculate the Malmquist productivity index (MPI) of 48 Swedish district courts from 2012 to 2015. In contrast to the limited international literature on court productivity, this study uses a fully decomposed MPI. A bootstrapping approach is further applied to compute confidence intervals for each decomposed factor of TFP. The findings show a 1.7% average decline of TFP, annually. However, a substantial variation between years can be observed in the number of statistically significant courts below and above unity. The averages of the components show that the negative impact is mainly driven by
Essays on Efficiency, Productivity, and Impact of Policy Doctoral Dissertation, Linnaeus University, Växjö, 2018 ISBN: 978-91-88898-00-5 (print), 978-91-88898-01-2 (pdf) Published by: Linnaeus University Press, 351 95 Växjö Printed by: DanagårdLiTHO, 2018
ambition for the mergers was to improve efficiency, no structured ex post analysis has been done. Swedish courts are shown to improve efficiency from merging. In addition to the particular application, this work may inform a more general discussion on public service efficiency measurement under structural changes, and their limits and potential.
Essay V: ‘The Impact of Labour Subsidies on Total Factor Productivity and Profit per Employee.’ Subsidizing targeted labour groups is a common intervention to prevent long-term unemployment. Lower expected productivity is the motivation for subsidizing labour, but all research, with one exception, focuses on other effects, while some investigates the total factor productivity (TFP) effects of capital subsidies. This study combines methods that, to the best of my knowledge, have not previously been used together to determine the impacts of labour subsidies on TFP. Further, the profit per employee is included as a second outcome. Coarsened exact matching (CEM) is performed on the key variables; difference-in-differences (DiD) is then applied to the matched data. It is found that firms employing workers with wage subsidies experience negative and significant effects on both TFP and profit per employee. Heterogeneity is, however, observed; the only sector to show a deficit in both TFP and profit per employee is wholesale. During the second year with a subsidy, a negative impact can be observed on the profit per employee but not on TFP. The policy conclusion from the analysis is that subsidizing individuals from particular groups is necessary to induce firms to hire workers from these groups. However, the time period for which a single firm is subsidized should be considered.
Keywords: conditional difference-in-differences (cDiD); courts; data envelopment analysis (DEA); Malmquist index; horizontal mergers; impact of policy; stochastic frontier analysis (SFA); subsidized employment; total factor productivity (TFP); Törnqvist TFP index
negative technical change (TC). Large variations are also observed over time, where the small courts have the largest volatility. Two recommendations are: (1) that district courts with negative TFP growth could learn from those with positive TFP growth, and (2) that the back-up labour force could be developed to enhance flexibility. Essay III: ‘Potential Efficiency Effects of Merging the Swedish District Courts’ (co-authored with Claes Tidanå). The Swedish district courts have undergone a substantial restructuring process in which the main reform has been to merge. As a result, the number of district courts has declined from 95 in 2000 to only 48 in 2009. All main arguments that support merging concern enhancements of efficiency. However, it has not yet been explicitly examined whether the mergers have the potential to increase efficiency ex ante. Thus, the expectation concerning higher efficiency was built on a subjective view. This paper investigates whether the mergers can be rationalized from a production economic point of view. Data envelopment analysis (DEA) is used to compute a production frontier where the conducted mergers are incorporated to identify the potential ex ante gains. Furthermore, the overall potential is decomposed into learning, scale, and harmony to investigate the source of the potential gain, e.g., an effect of adjusting to best practice or a pure merging effect such as scale. The results show diverse potentials, i.e., a number of mergers did not have the potential to gain in efficiency while others could gain substantially. A conclusion based on the analysis is that the potential production economic effects should be investigated before merger decisions are made in the future. This is also likely to be true beyond the Swedish district courts.
Essay IV: ‘Impacts on Efficiency of Merging the Swedish District Courts’ (co-authored with Per J. Agrell and Jonas Månsson). Judicial courts form a stringent example of public services using partially sticky inputs and outputs with heterogeneous quality. Notwithstanding, governments internationally are striving to improve the efficiency of and diminish the budget spent on court systems. Frontier methods such as data envelopment analysis (DEA) are sometimes used in investigations of structural changes in the form of mergers. This essay reviews the methods used to evaluate the ex post efficiency of horizontal mergers. Identification of impacts is difficult. Therefore, three analytical frameworks are applied: 1) a technical efficiency comparison over time, 2) a metafrontier approach among mergers and non-mergers, and 3) a conditional difference-in-differences (cDiD) approach where non-merged twins of the actual mergers are identified by matching. In addition, both time heterogeneity and sources of efficiency change are examined ex post. The method is applied to evaluate the impact on efficiency of merging the Swedish district courts from 95 to 48 between 2000 and 2009. Whereas the stated
ambition for the mergers was to improve efficiency, no structured ex post analysis has been done. Swedish courts are shown to improve efficiency from merging. In addition to the particular application, this work may inform a more general discussion on public service efficiency measurement under structural changes, and their limits and potential.
Essay V: ‘The Impact of Labour Subsidies on Total Factor Productivity and Profit per Employee.’ Subsidizing targeted labour groups is a common intervention to prevent long-term unemployment. Lower expected productivity is the motivation for subsidizing labour, but all research, with one exception, focuses on other effects, while some investigates the total factor productivity (TFP) effects of capital subsidies. This study combines methods that, to the best of my knowledge, have not previously been used together to determine the impacts of labour subsidies on TFP. Further, the profit per employee is included as a second outcome. Coarsened exact matching (CEM) is performed on the key variables; difference-in-differences (DiD) is then applied to the matched data. It is found that firms employing workers with wage subsidies experience negative and significant effects on both TFP and profit per employee. Heterogeneity is, however, observed; the only sector to show a deficit in both TFP and profit per employee is wholesale. During the second year with a subsidy, a negative impact can be observed on the profit per employee but not on TFP. The policy conclusion from the analysis is that subsidizing individuals from particular groups is necessary to induce firms to hire workers from these groups. However, the time period for which a single firm is subsidized should be considered.
Keywords: conditional difference-in-differences (cDiD); courts; data envelopment analysis (DEA); Malmquist index; horizontal mergers; impact of policy; stochastic frontier analysis (SFA); subsidized employment; total factor productivity (TFP); Törnqvist TFP index
negative technical change (TC). Large variations are also observed over time, where the small courts have the largest volatility. Two recommendations are: (1) that district courts with negative TFP growth could learn from those with positive TFP growth, and (2) that the back-up labour force could be developed to enhance flexibility. Essay III: ‘Potential Efficiency Effects of Merging the Swedish District Courts’ (co-authored with Claes Tidanå). The Swedish district courts have undergone a substantial restructuring process in which the main reform has been to merge. As a result, the number of district courts has declined from 95 in 2000 to only 48 in 2009. All main arguments that support merging concern enhancements of efficiency. However, it has not yet been explicitly examined whether the mergers have the potential to increase efficiency ex ante. Thus, the expectation concerning higher efficiency was built on a subjective view. This paper investigates whether the mergers can be rationalized from a production economic point of view. Data envelopment analysis (DEA) is used to compute a production frontier where the conducted mergers are incorporated to identify the potential ex ante gains. Furthermore, the overall potential is decomposed into learning, scale, and harmony to investigate the source of the potential gain, e.g., an effect of adjusting to best practice or a pure merging effect such as scale. The results show diverse potentials, i.e., a number of mergers did not have the potential to gain in efficiency while others could gain substantially. A conclusion based on the analysis is that the potential production economic effects should be investigated before merger decisions are made in the future. This is also likely to be true beyond the Swedish district courts.
Essay IV: ‘Impacts on Efficiency of Merging the Swedish District Courts’ (co-authored with Per J. Agrell and Jonas Månsson). Judicial courts form a stringent example of public services using partially sticky inputs and outputs with heterogeneous quality. Notwithstanding, governments internationally are striving to improve the efficiency of and diminish the budget spent on court systems. Frontier methods such as data envelopment analysis (DEA) are sometimes used in investigations of structural changes in the form of mergers. This essay reviews the methods used to evaluate the ex post efficiency of horizontal mergers. Identification of impacts is difficult. Therefore, three analytical frameworks are applied: 1) a technical efficiency comparison over time, 2) a metafrontier approach among mergers and non-mergers, and 3) a conditional difference-in-differences (cDiD) approach where non-merged twins of the actual mergers are identified by matching. In addition, both time heterogeneity and sources of efficiency change are examined ex post. The method is applied to evaluate the impact on efficiency of merging the Swedish district courts from 95 to 48 between 2000 and 2009. Whereas the stated
Acknowledgment
Being a Ph.D. student is challenging in many aspects meaning that both mental and methodological support are crucial. There are many people I have met during the years as a Ph.D. student whom I would like to acknowledge. Most important in these aspects are my supervisors, Dr Jonas Månsson and Dr Lars Behrenz, and I am grateful to them for their support. Jonas, as my main supervisor, is undoubtedly the most important source of support. Jonas’s relevant questions, patient suggestions, and pushes in the right direction have substantially improved the quality of this thesis.
Furthermore, I have also obtained valuable feedback from several knowledgeable people, which has been important for me, personally, by thinking of the questions from different angels and, therefore, improving the quality of this thesis. First, I would like to mention Professor Shawna Grosskopf, who was the discussant during the final seminar prior to my Ph.D. defense. Second, I am grateful for the discussion and advice received from Professor Andreas Stephan and Dr Ann Veiderpass, who were discussants during the final seminar (prior to the licentiate defence) and the licentiate defence, respectively.
During visits abroad, courses, seminars, and conferences I have received many helpful comments. In particular, my visits abroad have been important for learning, experiences, and the quality of this thesis. My first stay abroad as a visiting scholar was at Queensland University of Technology (QUT), where I was hosted by Professor Clevo Wilson. I also had the pleasure to meet several Ph.D. students who worked in similar fields as I, which was interesting. In the beginning of 2018, I had the honour to be hosted by Professor William H. Greene at Stern School of Business, New York University. Professor Greene provided many helpful advice, both generally and in terms of the co-authored paper, which appears as Essay I in this thesis. Additionally, we had many interesting discussions about academic differences between the United States and Sweden to mention only one example. During the second half of the spring semester of 2018, I visited the Center of Operations Research and Econometrics (CORE) at UC Louvain. The hosting professor was Per J. Agrell, who gave me valuable feedback in writing papers in general as well as encouraging me to develop my skills in R. In particular, these skills were practiced in our co-authored paper. At the end of my time as a Ph.D. student, I had the honour to be invited to Oregon State University (OSU) by Professor Rolf Färe and Professor Shawna Grosskopf. This was interesting and gave insights in new methodologies, valuable suggestions, and, last but not least, a lot of inspiration in deepening my knowledge in efficiency and productivity
Contents
Acknowledgement
Introduction
Essay I: TFP Change and Its Components for Swedish Manufacturing Firms During the 2008–2009 Financial Crisis
Essay II: A Bootstrapped Malmquist Index Applied to Swedish District Courts
Essay III: Potential Efficiency Effects of Merging the Swedish District Courts
Essay IV: Impacts on Efficiency of Merging the Swedish District Courts
Essay V: The Impact of Labour Subsidies on Total Factor Productivity and Profit per Employee
Acknowledgment
Being a Ph.D. student is challenging in many aspects meaning that both mental and methodological support are crucial. There are many people I have met during the years as a Ph.D. student whom I would like to acknowledge. Most important in these aspects are my supervisors, Dr Jonas Månsson and Dr Lars Behrenz, and I am grateful to them for their support. Jonas, as my main supervisor, is undoubtedly the most important source of support. Jonas’s relevant questions, patient suggestions, and pushes in the right direction have substantially improved the quality of this thesis.
Furthermore, I have also obtained valuable feedback from several knowledgeable people, which has been important for me, personally, by thinking of the questions from different angels and, therefore, improving the quality of this thesis. First, I would like to mention Professor Shawna Grosskopf, who was the discussant during the final seminar prior to my Ph.D. defense. Second, I am grateful for the discussion and advice received from Professor Andreas Stephan and Dr Ann Veiderpass, who were discussants during the final seminar (prior to the licentiate defence) and the licentiate defence, respectively.
During visits abroad, courses, seminars, and conferences I have received many helpful comments. In particular, my visits abroad have been important for learning, experiences, and the quality of this thesis. My first stay abroad as a visiting scholar was at Queensland University of Technology (QUT), where I was hosted by Professor Clevo Wilson. I also had the pleasure to meet several Ph.D. students who worked in similar fields as I, which was interesting. In the beginning of 2018, I had the honour to be hosted by Professor William H. Greene at Stern School of Business, New York University. Professor Greene provided many helpful advice, both generally and in terms of the co-authored paper, which appears as Essay I in this thesis. Additionally, we had many interesting discussions about academic differences between the United States and Sweden to mention only one example. During the second half of the spring semester of 2018, I visited the Center of Operations Research and Econometrics (CORE) at UC Louvain. The hosting professor was Per J. Agrell, who gave me valuable feedback in writing papers in general as well as encouraging me to develop my skills in R. In particular, these skills were practiced in our co-authored paper. At the end of my time as a Ph.D. student, I had the honour to be invited to Oregon State University (OSU) by Professor Rolf Färe and Professor Shawna Grosskopf. This was interesting and gave insights in new methodologies, valuable suggestions, and, last but not least, a lot of inspiration in deepening my knowledge in efficiency and productivity
Contents
Acknowledgement
Introduction
Essay I: TFP Change and Its Components for Swedish Manufacturing Firms During the 2008–2009 Financial Crisis
Essay II: A Bootstrapped Malmquist Index Applied to Swedish District Courts
Essay III: Potential Efficiency Effects of Merging the Swedish District Courts
Essay IV: Impacts on Efficiency of Merging the Swedish District Courts
Essay V: The Impact of Labour Subsidies on Total Factor Productivity and Profit per Employee
Zhizheng Wang. Regarding administrative matters, I would like to thank Hanna Sandqvist and Anna-Karin Bjuvsjö Johansson, who are always very helpful with issues related to, for example, forms and receipts.
Additionally, informally showing Stockholm to Subal C. Kumbhakar, visiting the vineyard belonging to Färe and Grosskopf, considering issues in LIMDEP with Greene or where to visit during weekends were a lot more than I expected before starting the doctoral studies. In summary, meeting so many interesting people – including famous professors such as (ordered alphabetically) Agrell, Färe, Greene, Grosskopf, Kumbhakar, and O’Donnell to only name a few – gave a lot of inspiration.
Last but not least, I want to thank my friends and family. In particular, my parents, Göran and Agneta, are the most important persons regarding talking with me as good friends, providing mental and practical support and much more. Växjö, September 2018 Pontus Mattsson
analysis. Further, I got the opportunity to join them on their vineyard and get guidance during weekend trips while visiting, which I highly appreciated. My visits at QUT, Stern, CORE, and OSU, together with the conferences and courses abroad, have without hesitation been the most inspirational time of my Ph.D.
An important part of improving the papers that this thesis consists of relates to all of the comments I have received during a number of seminars. Valuable comments have, for example, been obtained during seminars at the course on Theory and Practice of Efficiency and Productivity Measurement in Bandung 2017, the Jönköping International Business School (JIBS), Queensland University of Technology (QUT), the Swedish National Audit Office, the 15th International Conference on DEA in Prague, the 12th Asia Pacific Productivity Conference in Seoul 2018, the Swedish National Court Administration (SNCA), the SWEGPEC workshop in Linköping 2016, the SWEGPEC workshop in Stockholm 2017, and in my seminars at Linnaeus University. Furthermore, I am both honoured and grateful that my papers were selected for presentation during Early Career Research Day prior to the European Workshop on Efficiency and Productivity Analysis (EWEPA) in London, 2017, and the Young Researchers’ Workshop prior to the 10th North American Productivity Workshop (NAPW) in Miami, 2018. During these days, I am grateful for all feedback obtained from my discussants Professor Christopher J. O'Donnell and Dr Antonio Peyrache in London and Miami, respectively. Additionally, I would like to thank Dr Marijn Verschelde, whom I have met during several conferences, who has provided constructive comments on parts of this dissertation. Valuable comments to improve the quality have also been obtained from several anonymous referees, to whom I am grateful.
As previous sections show, I have had the opportunity to be a visiting scholar at several prestigious universities and attend several interesting conferences. For that, I would further like to express my appreciation to Linnaeus University, the School of Business and Economics, the Department of Economics and Statistics and the Linnaeus Academy, which made this possible by providing finance or scholarship. It has been very interesting and helpful to improve the thesis as well as general knowledge, for which I am grateful. The department consists of employees who always help and support if necessary. In particular, I am indebted for the comments I have received from Dr Peter S. Karlsson and Dr Håkan Locking. Furthermore, I am obliged for all the interesting discussions with, advice from, and friendships with the present and previous Ph.D. students (alphabetically) Dr Abdul Aziz Ali, Dr Deliang Dai, Dr Luca Fumarco, Dr Chizheng Miao, Dingquan Miao, Dr Emma Neuman, Dr Abdulaziz Abrar Reshid, Hanna Swahnberg, and
Zhizheng Wang. Regarding administrative matters, I would like to thank Hanna Sandqvist and Anna-Karin Bjuvsjö Johansson, who are always very helpful with issues related to, for example, forms and receipts.
Additionally, informally showing Stockholm to Subal C. Kumbhakar, visiting the vineyard belonging to Färe and Grosskopf, considering issues in LIMDEP with Greene or where to visit during weekends were a lot more than I expected before starting the doctoral studies. In summary, meeting so many interesting people – including famous professors such as (ordered alphabetically) Agrell, Färe, Greene, Grosskopf, Kumbhakar, and O’Donnell to only name a few – gave a lot of inspiration.
Last but not least, I want to thank my friends and family. In particular, my parents, Göran and Agneta, are the most important persons regarding talking with me as good friends, providing mental and practical support and much more. Växjö, September 2018 Pontus Mattsson
analysis. Further, I got the opportunity to join them on their vineyard and get guidance during weekend trips while visiting, which I highly appreciated. My visits at QUT, Stern, CORE, and OSU, together with the conferences and courses abroad, have without hesitation been the most inspirational time of my Ph.D.
An important part of improving the papers that this thesis consists of relates to all of the comments I have received during a number of seminars. Valuable comments have, for example, been obtained during seminars at the course on Theory and Practice of Efficiency and Productivity Measurement in Bandung 2017, the Jönköping International Business School (JIBS), Queensland University of Technology (QUT), the Swedish National Audit Office, the 15th International Conference on DEA in Prague, the 12th Asia Pacific Productivity Conference in Seoul 2018, the Swedish National Court Administration (SNCA), the SWEGPEC workshop in Linköping 2016, the SWEGPEC workshop in Stockholm 2017, and in my seminars at Linnaeus University. Furthermore, I am both honoured and grateful that my papers were selected for presentation during Early Career Research Day prior to the European Workshop on Efficiency and Productivity Analysis (EWEPA) in London, 2017, and the Young Researchers’ Workshop prior to the 10th North American Productivity Workshop (NAPW) in Miami, 2018. During these days, I am grateful for all feedback obtained from my discussants Professor Christopher J. O'Donnell and Dr Antonio Peyrache in London and Miami, respectively. Additionally, I would like to thank Dr Marijn Verschelde, whom I have met during several conferences, who has provided constructive comments on parts of this dissertation. Valuable comments to improve the quality have also been obtained from several anonymous referees, to whom I am grateful.
As previous sections show, I have had the opportunity to be a visiting scholar at several prestigious universities and attend several interesting conferences. For that, I would further like to express my appreciation to Linnaeus University, the School of Business and Economics, the Department of Economics and Statistics and the Linnaeus Academy, which made this possible by providing finance or scholarship. It has been very interesting and helpful to improve the thesis as well as general knowledge, for which I am grateful. The department consists of employees who always help and support if necessary. In particular, I am indebted for the comments I have received from Dr Peter S. Karlsson and Dr Håkan Locking. Furthermore, I am obliged for all the interesting discussions with, advice from, and friendships with the present and previous Ph.D. students (alphabetically) Dr Abdul Aziz Ali, Dr Deliang Dai, Dr Luca Fumarco, Dr Chizheng Miao, Dingquan Miao, Dr Emma Neuman, Dr Abdulaziz Abrar Reshid, Hanna Swahnberg, and
2
respectively. Each part includes non-parametric and parametric measures. Additionally, a comparison and discussion of these are provided, followed by a summary of each essay. Finally, conclusions, policy recommendations, and suggestions for future research are provided.
Measuring efficiency Non-parametric measures of efficiency Obtaining efficiency non-parametrically takes its departure in the coefficient of resource utilization by Debreu (1951) and Farrell’s (1957) measure of efficiency. The non-parametric models have their origin in activity analysis, first introduced by von Neumann (1937) and generalized by Kemeny, Morgenstern, and Thompson (1956). Nowadays, these models are frequently referred to as data envelopment analysis (DEA), introduced by Charnes, Cooper, and Rhodes (1978), which incorporates both multiple inputs and multiple outputs. The Charnes et al. (1978) model illustrates this under CRS; more flexible scale assumptions are incorporated by Banker, Charnes, and Cooper (1984). 2 DEA originates in mathematical programming and has mainly been developed by management scientists and operations researchers under the term non-parametric methods or, as activity analysis, by economists (see, e.g., Bogetoft, 2012; Färe, Grosskopf and Lovell, 2013). An exponential increase in the number of papers has been observed (Emrouznejad and Yang, 2018), and DEA can now be considered the standard procedure to examine efficiency non-parametrically.3
The distance functions by Shephard (1953, 1970) are the cornerstone of DEA. It can take an approach of input-orientation (Shephard, 1953), output-orientation (Shephard, 1970), or a mix of these in a directional distance function (Luenberger, 1992, 1995). The input-oriented approach calculates the inputs that can be saved given the same level of output, and the output-oriented how much more outputs can be produced given the input level. Furthermore, by introducing prices, the focus can be changed from production maximization to cost minimization, revenue maximization, or profit maximization (e.g., Shephard, 1953, 1970).
An issue often raised in DEA is that statistical inference cannot be drawn and a bias of the efficiency scores is present. To handle this, bootstrapping is commonly performed to provide confidence intervals and calculate bias-corrected efficiency scores (see, e.g., Efron, 1979; Simar and Wilson, 2000).
2 The introduction of VRS dates back to Kemeny et al. (1956). See also Afriat (1972), Førsund and Jansen (1974), and Førsund and Hjalmarsson (1974, 1979). 3 An alternative to DEA is free disposable hull (FDH), introduced by Deprins, Simar, and Tulkens (1984). FDH will not be further described in this study.
1
Introduction
Measuring performance is important for private companies as well as the public sector. Productivity is often referred to as the major determinant of economic growth. Krugman (1997, p. 13) states this as ‘productivity isn’t everything, but in the long run, it’s almost everything’. Furthermore, Bogetoft (2012) notes that global surveys consistently list benchmarking among the most popular management instruments. For example, between 67% and 82% of the surveyed companies performed a benchmark investigation to measure efficiency in a given year. More effective utilization of public services is also a general target for all governments to spend tax money in its best use. Focusing on Sweden, the Budget Act (SFS 2011:203) explicitly states that all public services should be provided with a high level of efficiency. Based on efficiency and productivity analysis, several policy-relevant questions can be formulated. Possible subjects for investigation could include the practice of measuring performance to obtain a benchmark of the best agencies in order for others to learn from these. Additionally, performance can be measured over time to incorporate dynamics. Performance measurements can also be utilized to evaluate the effectiveness of a reform, i.e., whether it was worthy from an efficiency point of view.
This thesis uses two separate measures of performance, i.e., productivity and efficiency. The aim of this introductory chapter is to provide a non-technical and intuitive introduction, including a comparison of different alternatives that are available to measure them.
Efficiency is, in this thesis, a relative measure, meaning that performance is measured in relation to other comparable units. There are several related definitions that are commonly used in the area. Koopmans (1951, p. 60) provides a definition of efficiency, i.e. the input-output vector is technically efficient if it is technologically impossible to increase any output without increasing inputs or, similarly, to reduce any input without reducing at least one output. Similarly, Farrell (1957) defines technical efficiency (TE) as producing on the best practice frontier, i.e., performing on the limit of the technically feasible region. Leibenstein (1966) referred to inefficiency as X-inefficiency; i.e., maximal outputs are not obtained given the level of inputs.1 Productivity is a measure that, partially or totally, relates outputs to inputs, e.g., the ratio of an aggregate of outputs over an aggregate of inputs.
The measures of efficiency and productivity can be obtained by using parametric or non-parametric methods. The remainder of this introductory chapter includes a summary of measures of efficiency and productivity,
1 Leibenstein (1966) and Farrell (1957) also consider allocative efficiency, which concerns the correct ratio of inputs in relation to their prices.
2
respectively. Each part includes non-parametric and parametric measures. Additionally, a comparison and discussion of these are provided, followed by a summary of each essay. Finally, conclusions, policy recommendations, and suggestions for future research are provided.
Measuring efficiency Non-parametric measures of efficiency Obtaining efficiency non-parametrically takes its departure in the coefficient of resource utilization by Debreu (1951) and Farrell’s (1957) measure of efficiency. The non-parametric models have their origin in activity analysis, first introduced by von Neumann (1937) and generalized by Kemeny, Morgenstern, and Thompson (1956). Nowadays, these models are frequently referred to as data envelopment analysis (DEA), introduced by Charnes, Cooper, and Rhodes (1978), which incorporates both multiple inputs and multiple outputs. The Charnes et al. (1978) model illustrates this under CRS; more flexible scale assumptions are incorporated by Banker, Charnes, and Cooper (1984). 2 DEA originates in mathematical programming and has mainly been developed by management scientists and operations researchers under the term non-parametric methods or, as activity analysis, by economists (see, e.g., Bogetoft, 2012; Färe, Grosskopf and Lovell, 2013). An exponential increase in the number of papers has been observed (Emrouznejad and Yang, 2018), and DEA can now be considered the standard procedure to examine efficiency non-parametrically.3
The distance functions by Shephard (1953, 1970) are the cornerstone of DEA. It can take an approach of input-orientation (Shephard, 1953), output-orientation (Shephard, 1970), or a mix of these in a directional distance function (Luenberger, 1992, 1995). The input-oriented approach calculates the inputs that can be saved given the same level of output, and the output-oriented how much more outputs can be produced given the input level. Furthermore, by introducing prices, the focus can be changed from production maximization to cost minimization, revenue maximization, or profit maximization (e.g., Shephard, 1953, 1970).
An issue often raised in DEA is that statistical inference cannot be drawn and a bias of the efficiency scores is present. To handle this, bootstrapping is commonly performed to provide confidence intervals and calculate bias-corrected efficiency scores (see, e.g., Efron, 1979; Simar and Wilson, 2000).
2 The introduction of VRS dates back to Kemeny et al. (1956). See also Afriat (1972), Førsund and Jansen (1974), and Førsund and Hjalmarsson (1974, 1979). 3 An alternative to DEA is free disposable hull (FDH), introduced by Deprins, Simar, and Tulkens (1984). FDH will not be further described in this study.
1
Introduction
Measuring performance is important for private companies as well as the public sector. Productivity is often referred to as the major determinant of economic growth. Krugman (1997, p. 13) states this as ‘productivity isn’t everything, but in the long run, it’s almost everything’. Furthermore, Bogetoft (2012) notes that global surveys consistently list benchmarking among the most popular management instruments. For example, between 67% and 82% of the surveyed companies performed a benchmark investigation to measure efficiency in a given year. More effective utilization of public services is also a general target for all governments to spend tax money in its best use. Focusing on Sweden, the Budget Act (SFS 2011:203) explicitly states that all public services should be provided with a high level of efficiency. Based on efficiency and productivity analysis, several policy-relevant questions can be formulated. Possible subjects for investigation could include the practice of measuring performance to obtain a benchmark of the best agencies in order for others to learn from these. Additionally, performance can be measured over time to incorporate dynamics. Performance measurements can also be utilized to evaluate the effectiveness of a reform, i.e., whether it was worthy from an efficiency point of view.
This thesis uses two separate measures of performance, i.e., productivity and efficiency. The aim of this introductory chapter is to provide a non-technical and intuitive introduction, including a comparison of different alternatives that are available to measure them.
Efficiency is, in this thesis, a relative measure, meaning that performance is measured in relation to other comparable units. There are several related definitions that are commonly used in the area. Koopmans (1951, p. 60) provides a definition of efficiency, i.e. the input-output vector is technically efficient if it is technologically impossible to increase any output without increasing inputs or, similarly, to reduce any input without reducing at least one output. Similarly, Farrell (1957) defines technical efficiency (TE) as producing on the best practice frontier, i.e., performing on the limit of the technically feasible region. Leibenstein (1966) referred to inefficiency as X-inefficiency; i.e., maximal outputs are not obtained given the level of inputs.1 Productivity is a measure that, partially or totally, relates outputs to inputs, e.g., the ratio of an aggregate of outputs over an aggregate of inputs.
The measures of efficiency and productivity can be obtained by using parametric or non-parametric methods. The remainder of this introductory chapter includes a summary of measures of efficiency and productivity,
1 Leibenstein (1966) and Farrell (1957) also consider allocative efficiency, which concerns the correct ratio of inputs in relation to their prices.
4
and Greene (2016) simplified the one-stage maximum likelihood procedure by proposing a simulated maximum likelihood approach to identify the components. On top of identifying persistent and transient efficiency, attempts to incorporate explanatory variables are also present. Kumbhakar and Lien (2017) incorporate them in a multi-stage approach. Further, incorporation of explanatory variables of efficiency, in a single stage, has also been performed by Badunenko and Kumbhakar (2017) and Lai and Kumbhakar (2018).
Measuring productivity Either all categories of inputs and outputs can be incorporated, referred to as total factor productivity (TFP), or a subset of the inputs, i.e., partial productivity. The simplest partial measure consists of output, such as sales or value added, divided by one input, such as labour; this is referred to as labour productivity. This class of productivity measures can be misleading in comparing performance, e.g., if one firm is capital intensive and the other labour intensive. Similarly, if one unit is compared over time, a partial measure ignores substitution among inputs. A preferred measure of productivity is, therefore, TFP, which this thesis uses as productivity measure. TFP can be defined as the ratio of aggregate output to aggregate inputs and is most commonly measured as a change over time, i.e., TFP change. TFP change can be obtained by frontier approaches; however, identification of a best practice is not necessary.5
TFP index numbers The TFP index numbers do not rely on identification of a best practice frontier. Instead, this approach originates from price index numbers, such as that of Fisher (1922). For TFP change, data on prices and quantities over time are used to construct an output index and an input index. A common definition of TFP change is an aggregation of output over inputs (see, e.g., Jorgenson and Griliches, 1967; Nadiri, 1970). Thus, the TFP index numbers are defined as the ratio of the output index over the input index. Common indexes are Laspeyres (1871), Paasche (1874), Fisher (1922), and Törnqvist (1936). A debate over which index measures TFP change ‘properly’ is present in the literature. For example, O’Donnell (2012b) describes several axioms that need to be fulfilled, in his opinion, for the index to be ‘proper’.6 Circularity and transitivity are axioms, which are not commonly fulfilled. Therefore, index numbers such as, for example, the geometric Young index, are proposed by
5 This thesis does not target productivity measures where entry-exit, investments, reallocation, mark-ups, frictions, or trade is particularly identified (see, e.g., Olley and Pakes, 1996; Levinsohn and Petrin, 2003; Syverson, 2011; De Loecker and Goldberg, 2014; and Ackerberg, Caves, and Frazer, 2015 regarding these issues). 6 The conditions for circularity to be satisfied can be found in Aczél (1990).
3
Parametric measures of efficiency Parametrically, efficiency can be modelled deterministically, i.e., non-stochastically; this label derives from the fact that the stochastic component contains only inefficiency. With the basis in Farrell (1957), efficiency can be obtained parametrically by using linear (or quadratic) programming, proposed by Aigner and Chu (1968) or by assuming the inefficiency to have a gamma distribution in maximum likelihood (Afriat, 1972). Another alternative is a least squares version referred to as corrected ordinary least squares (COLS) (Richmond, 1974). 4 This means that the deterministic approach makes parametric assumptions on the functional form of the technology; however, the approach still interprets all noise as inefficiency.
The residual can be seen as a measure of ignorance relating to anything outside the model (Abramovitz, 1956), e.g., errors, luck, technology, or differences in scale or operation efficiency. A potential interpretation is, therefore, that the best units, i.e., observations on the frontier, are not setting the frontier because they are operating efficiently, but doing so simply due to luck or error in the data. The third way to handle the disturbance term is as in stochastic frontier analysis (SFA), introduced by Aigner, Lovell, and Schmidt (1977) and Meeusen and van Den Broeck (1977), which also incorporate a random component. In SFA, the random component is generally assumed to have a normal distribution with mean zero, and inefficiency can, for example, be truncated, half-normal, exponential, or gamma distributed. SFA originates in econometrics and is mainly developed by economists (Bogetoft, 2012). It can, nowadays, be considered the standard method to econometrically model inefficiency.
The majority of the attention in SFA targets relaxing assumptions in modelling efficiency. Early literature, e.g., Pitt and Lee (1981) allowed efficiency to change between units but not over time. Later, Kumbhakar (1990) developed the efficiency term to allow for time-variation. Furthermore, the disturbance was decomposed into three components, i.e., persistent efficiency, time-varying efficiency, and noise (Kumbhakar and Heshmati, 1995). The issue with this is that the persistent part is, most likely, a mix of the actual persistent efficiency and firm-heterogeneity. A change in interpretation was, therefore, performed by Greene (2005a; 2005b). More recently, these models have been augmented to include four components, i.e., persistent efficiency, time-varying efficiency, firm-heterogeneity, and random noise, as proposed by Colombi, Kumbhakar, Martini, and Vittadini (2014); Tsionas and Kumbhakar (2014); and Kumbhakar, Lien, and Hardaker (2014). Colombi et al. (2014) is based on a complex maximum likelihood, Tsionas and Kumbhakar (2014) use a Bayesian solution, and the simpler multi-step procedure is suggested by Kumbhakar et al. (2014). Additionally, Filippini
4 The logic behind the COLS was first suggested by Winsten (1957).
4
and Greene (2016) simplified the one-stage maximum likelihood procedure by proposing a simulated maximum likelihood approach to identify the components. On top of identifying persistent and transient efficiency, attempts to incorporate explanatory variables are also present. Kumbhakar and Lien (2017) incorporate them in a multi-stage approach. Further, incorporation of explanatory variables of efficiency, in a single stage, has also been performed by Badunenko and Kumbhakar (2017) and Lai and Kumbhakar (2018).
Measuring productivity Either all categories of inputs and outputs can be incorporated, referred to as total factor productivity (TFP), or a subset of the inputs, i.e., partial productivity. The simplest partial measure consists of output, such as sales or value added, divided by one input, such as labour; this is referred to as labour productivity. This class of productivity measures can be misleading in comparing performance, e.g., if one firm is capital intensive and the other labour intensive. Similarly, if one unit is compared over time, a partial measure ignores substitution among inputs. A preferred measure of productivity is, therefore, TFP, which this thesis uses as productivity measure. TFP can be defined as the ratio of aggregate output to aggregate inputs and is most commonly measured as a change over time, i.e., TFP change. TFP change can be obtained by frontier approaches; however, identification of a best practice is not necessary.5
TFP index numbers The TFP index numbers do not rely on identification of a best practice frontier. Instead, this approach originates from price index numbers, such as that of Fisher (1922). For TFP change, data on prices and quantities over time are used to construct an output index and an input index. A common definition of TFP change is an aggregation of output over inputs (see, e.g., Jorgenson and Griliches, 1967; Nadiri, 1970). Thus, the TFP index numbers are defined as the ratio of the output index over the input index. Common indexes are Laspeyres (1871), Paasche (1874), Fisher (1922), and Törnqvist (1936). A debate over which index measures TFP change ‘properly’ is present in the literature. For example, O’Donnell (2012b) describes several axioms that need to be fulfilled, in his opinion, for the index to be ‘proper’.6 Circularity and transitivity are axioms, which are not commonly fulfilled. Therefore, index numbers such as, for example, the geometric Young index, are proposed by
5 This thesis does not target productivity measures where entry-exit, investments, reallocation, mark-ups, frictions, or trade is particularly identified (see, e.g., Olley and Pakes, 1996; Levinsohn and Petrin, 2003; Syverson, 2011; De Loecker and Goldberg, 2014; and Ackerberg, Caves, and Frazer, 2015 regarding these issues). 6 The conditions for circularity to be satisfied can be found in Aczél (1990).
3
Parametric measures of efficiency Parametrically, efficiency can be modelled deterministically, i.e., non-stochastically; this label derives from the fact that the stochastic component contains only inefficiency. With the basis in Farrell (1957), efficiency can be obtained parametrically by using linear (or quadratic) programming, proposed by Aigner and Chu (1968) or by assuming the inefficiency to have a gamma distribution in maximum likelihood (Afriat, 1972). Another alternative is a least squares version referred to as corrected ordinary least squares (COLS) (Richmond, 1974). 4 This means that the deterministic approach makes parametric assumptions on the functional form of the technology; however, the approach still interprets all noise as inefficiency.
The residual can be seen as a measure of ignorance relating to anything outside the model (Abramovitz, 1956), e.g., errors, luck, technology, or differences in scale or operation efficiency. A potential interpretation is, therefore, that the best units, i.e., observations on the frontier, are not setting the frontier because they are operating efficiently, but doing so simply due to luck or error in the data. The third way to handle the disturbance term is as in stochastic frontier analysis (SFA), introduced by Aigner, Lovell, and Schmidt (1977) and Meeusen and van Den Broeck (1977), which also incorporate a random component. In SFA, the random component is generally assumed to have a normal distribution with mean zero, and inefficiency can, for example, be truncated, half-normal, exponential, or gamma distributed. SFA originates in econometrics and is mainly developed by economists (Bogetoft, 2012). It can, nowadays, be considered the standard method to econometrically model inefficiency.
The majority of the attention in SFA targets relaxing assumptions in modelling efficiency. Early literature, e.g., Pitt and Lee (1981) allowed efficiency to change between units but not over time. Later, Kumbhakar (1990) developed the efficiency term to allow for time-variation. Furthermore, the disturbance was decomposed into three components, i.e., persistent efficiency, time-varying efficiency, and noise (Kumbhakar and Heshmati, 1995). The issue with this is that the persistent part is, most likely, a mix of the actual persistent efficiency and firm-heterogeneity. A change in interpretation was, therefore, performed by Greene (2005a; 2005b). More recently, these models have been augmented to include four components, i.e., persistent efficiency, time-varying efficiency, firm-heterogeneity, and random noise, as proposed by Colombi, Kumbhakar, Martini, and Vittadini (2014); Tsionas and Kumbhakar (2014); and Kumbhakar, Lien, and Hardaker (2014). Colombi et al. (2014) is based on a complex maximum likelihood, Tsionas and Kumbhakar (2014) use a Bayesian solution, and the simpler multi-step procedure is suggested by Kumbhakar et al. (2014). Additionally, Filippini
4 The logic behind the COLS was first suggested by Winsten (1957).
6
developed in a non-parametric setting by Färe, Grosskopf, Lindgren, and Roos (1992, 1994), is derived from a re-organization of the geometric mean of two Malmquist indexes. Based on this, TFP change can be decomposed into technical change (TC) and efficiency change (EC).7 TC is defined as a shift of the frontier itself, and EC is movement towards, or away, from the frontier. Moreover, Färe et al. (1994) decompose the EC into scale and pure components. Alternative decompositions are present in the literature, which is mainly due to the scale assumption requirement in DEA; i.e., components are separated by different scale assumptions. Examples are Ray and Desli (1997) and Wheelock and Wilson (1999). Grosskopf (2003) and Lovell (2003) discuss advantages and disadvantages of the decompositions of the Malmquist index. Thus, many variations of decompositions are proposed, and disagreement of which is the most appropriate is present in the literature. In addition, the Luenberger productivity indicator can be decomposed into EC and TC.
In summary of the DEA indexes, there is no ‘correct’ way to choose among the different indexes (Russell, 2018).
Parametric measures of TFP The parametric measures can, in principle, be separated into three categories depending on distribution assumptions of the disturbance. As previously mentioned, these are average, deterministic, and stochastic functions, respectively. Firms can be assumed efficient as in the average production function; i.e., all deviation from the production function is assumed to be noise. This measure centres on TFP change, because full efficiency is assumed. In such case, all variation in growth that does not correspond to changes in inputs is referred to as the Solow residual (Solow, 1957), where its change is often seen as a measure of TFP change.8
There are many reasons to believe that assuming all deviation to be noise is too restrictive. Examples are asymmetric information (Greenwald and Stiglitz, 1986) and skill differences of managers (Bloom, Lemos, Sadun, Scur, and van Reenen, 2016). Further, the presence of inefficiency can, and should, be tested statistically.
As previously pointed out, the majority of the attention in the SFA literature targets efficiency. Less attention in the SFA literature has been given to developing measurements of TFP change. However, the components of the Malmquist decomposition popularized by Färe et al. (1994) originate from the SFA literature by Nishimizu and Page (1982) and Bauer (1990). This is extended in applied research by Kumbhakar, Denny, and Fuss (2000). Similar
7 The decomposition in Färe et al. (1994) departs from Nishimizu and Page (1982) and Bauer (1990) counterparts within the SFA literature. 8 In such functions, components of TFP change are also sometimes identified. Examples are technical change and scale change.
5
O’Donnell (2012b). However, the so-called Fisher dilemma states a conflict between characteristicity and circularity, so the author has to decide which of the axioms is of more importance (Drechsler, 1973). Most of the described indexes can be decomposed by separating the price and quantity changes (see, e.g., Reinsdorf, Diewert, and Ehemann, 2002). Moreover, many of these indexes are still commonly used by national statistical offices.
Non-parametric DEA-based TFP indexes TFP change is the change of TFP over time. The most common DEA-based TFP index is the Malmquist index, which builds on the Shephard distance functions and was introduced by Caves, Christensen, and Diewert (1982) and attributed to Malmquist (1953).
To calculate the standard Malmquist index, distance functions need to be calculated for two different periods. Based on these, the Malmquist index can be defined as their ratio, using one of the periods as the base. The more common formulation is, however, the geometric average of both time periods as base. This is first proposed for a price index by Fisher (1922) and for the Malmquist index by Caves et al. (1982). Fisher (1922) referred to the geometric average as an ‘ideal’ index. Bjurek (1996) redefines what Caves et al. (1982) introduced as the Malmquist index. An argument is that Malmquist (1953) introduced a quantity index. Therefore, Bjurek (1996) defines an output (input) quantity index as the change in output (input) quantities given the input (output) quantities. Bjurek (1996) called the ratio of the output and input indexes a Malmquist index, but this is normally referred to as the Hicks-Moorsteen index, attributed to Hicks (1961) and Moorsteen (1961). Critiques regarding non-transitivity are also raised for these indexes by, for example, O'Donnell (2012b). To avoid this potential issue, it is possible to use what is often denoted the Färe and Primont (1995) index, which consists of an input and an output quantity index. Further, the Färe and Primont (1995) TFP index, i.e., the output index over the input index, is closely related to the Hicks-Moorsteen index.
To avoid choosing an input- or output-orientation, a Luenberger productivity indicator, introduced by Chambers, Chung, and Färe (1996) and Chambers and Pope (1996), can be calculated. This index is defined as an arithmetic average of differences of directional distance functions (DDF) for two periods, using one of them as reference technology (Chambers et al., 1996). Pros and cons are also present with this measurement. For example, it handles externalities, such as bad outputs, better than standard DEA. However, a direction needs to be chosen or optimized over the directional vector, i.e., determined endogenously for each unit (Färe, Grosskopf, and Whittaker, 2013).
Decomposition is more common for the DEA-based TFP indexes than the previously described TFP index numbers. The initial decomposition,
6
developed in a non-parametric setting by Färe, Grosskopf, Lindgren, and Roos (1992, 1994), is derived from a re-organization of the geometric mean of two Malmquist indexes. Based on this, TFP change can be decomposed into technical change (TC) and efficiency change (EC).7 TC is defined as a shift of the frontier itself, and EC is movement towards, or away, from the frontier. Moreover, Färe et al. (1994) decompose the EC into scale and pure components. Alternative decompositions are present in the literature, which is mainly due to the scale assumption requirement in DEA; i.e., components are separated by different scale assumptions. Examples are Ray and Desli (1997) and Wheelock and Wilson (1999). Grosskopf (2003) and Lovell (2003) discuss advantages and disadvantages of the decompositions of the Malmquist index. Thus, many variations of decompositions are proposed, and disagreement of which is the most appropriate is present in the literature. In addition, the Luenberger productivity indicator can be decomposed into EC and TC.
In summary of the DEA indexes, there is no ‘correct’ way to choose among the different indexes (Russell, 2018).
Parametric measures of TFP The parametric measures can, in principle, be separated into three categories depending on distribution assumptions of the disturbance. As previously mentioned, these are average, deterministic, and stochastic functions, respectively. Firms can be assumed efficient as in the average production function; i.e., all deviation from the production function is assumed to be noise. This measure centres on TFP change, because full efficiency is assumed. In such case, all variation in growth that does not correspond to changes in inputs is referred to as the Solow residual (Solow, 1957), where its change is often seen as a measure of TFP change.8
There are many reasons to believe that assuming all deviation to be noise is too restrictive. Examples are asymmetric information (Greenwald and Stiglitz, 1986) and skill differences of managers (Bloom, Lemos, Sadun, Scur, and van Reenen, 2016). Further, the presence of inefficiency can, and should, be tested statistically.
As previously pointed out, the majority of the attention in the SFA literature targets efficiency. Less attention in the SFA literature has been given to developing measurements of TFP change. However, the components of the Malmquist decomposition popularized by Färe et al. (1994) originate from the SFA literature by Nishimizu and Page (1982) and Bauer (1990). This is extended in applied research by Kumbhakar, Denny, and Fuss (2000). Similar
7 The decomposition in Färe et al. (1994) departs from Nishimizu and Page (1982) and Bauer (1990) counterparts within the SFA literature. 8 In such functions, components of TFP change are also sometimes identified. Examples are technical change and scale change.
5
O’Donnell (2012b). However, the so-called Fisher dilemma states a conflict between characteristicity and circularity, so the author has to decide which of the axioms is of more importance (Drechsler, 1973). Most of the described indexes can be decomposed by separating the price and quantity changes (see, e.g., Reinsdorf, Diewert, and Ehemann, 2002). Moreover, many of these indexes are still commonly used by national statistical offices.
Non-parametric DEA-based TFP indexes TFP change is the change of TFP over time. The most common DEA-based TFP index is the Malmquist index, which builds on the Shephard distance functions and was introduced by Caves, Christensen, and Diewert (1982) and attributed to Malmquist (1953).
To calculate the standard Malmquist index, distance functions need to be calculated for two different periods. Based on these, the Malmquist index can be defined as their ratio, using one of the periods as the base. The more common formulation is, however, the geometric average of both time periods as base. This is first proposed for a price index by Fisher (1922) and for the Malmquist index by Caves et al. (1982). Fisher (1922) referred to the geometric average as an ‘ideal’ index. Bjurek (1996) redefines what Caves et al. (1982) introduced as the Malmquist index. An argument is that Malmquist (1953) introduced a quantity index. Therefore, Bjurek (1996) defines an output (input) quantity index as the change in output (input) quantities given the input (output) quantities. Bjurek (1996) called the ratio of the output and input indexes a Malmquist index, but this is normally referred to as the Hicks-Moorsteen index, attributed to Hicks (1961) and Moorsteen (1961). Critiques regarding non-transitivity are also raised for these indexes by, for example, O'Donnell (2012b). To avoid this potential issue, it is possible to use what is often denoted the Färe and Primont (1995) index, which consists of an input and an output quantity index. Further, the Färe and Primont (1995) TFP index, i.e., the output index over the input index, is closely related to the Hicks-Moorsteen index.
To avoid choosing an input- or output-orientation, a Luenberger productivity indicator, introduced by Chambers, Chung, and Färe (1996) and Chambers and Pope (1996), can be calculated. This index is defined as an arithmetic average of differences of directional distance functions (DDF) for two periods, using one of them as reference technology (Chambers et al., 1996). Pros and cons are also present with this measurement. For example, it handles externalities, such as bad outputs, better than standard DEA. However, a direction needs to be chosen or optimized over the directional vector, i.e., determined endogenously for each unit (Färe, Grosskopf, and Whittaker, 2013).
Decomposition is more common for the DEA-based TFP indexes than the previously described TFP index numbers. The initial decomposition,
8
appropriate model choice is not straightforward and is likely to differ depending on the industry being studied. On the other hand, Bogetoft (2012) argues that DEA is more suitable for managers than SFA. The reason is that DEA identifies a small group of peers, which are comparable units important for managers to study in order to obtain best practice.
A distinction for when which method can be chosen regards the number of observations in the available data. Calculated TFP index numbers require only one unit over time to construct an index of TFP change for that firm; however, price information is necessary. An issue with DEA is the ‘curse of dimensionality’; i.e., the reliability drops when the dimension of the model increases (e.g., Bellman, 1957; Silverman, 1986). DEA has no strict limit; however, a rule of thumb by Cooper, Seiford, and Tone (2007) is max(m * s, 3 * (m + s)), where m is the number of outputs and s the number of inputs. However, Wilson (2017) argues that the Cooper et al. (2007) rule of thumb, among others, sets the limit too low. Further, given the sample size, there are fewer neighbours as the numbers of inputs and outputs increase in DEA. Consequently, discrimination power declines for higher dimensions.
In SFA, more observations are required because statistical inference needs to be drawn. The requirement of a large sample size can be regarded as a substantial disadvantage in cases where this is not available (Premachandra, Bhabra, and Sueyoshi, 2009), e.g., investigations of public organizations where the total number of units is few.
An advantage with the non-parametric indexes is that they do not rely on any prior assumption of the functional form or behavioural assumptions. However, this also relates to the main drawback of DEA: Any deviation from the frontier is associated with inefficiency, instead of a separation between inefficiency and random noise, as in SFA (see, e.g., Greene, 2008). DEA becomes sensitive to extreme observations by assuming that each deviation from the frontier is attributed to inefficiency, meaning that one observation can be the reason for biased results. In particular, DEA is sensitive to exceptionally well performing units since the frontier itself can be driven by these, making all peers, i.e., comparison units, more inefficient. A large amount of observations increases the probability of measurement error in at least one observation, which can be considered as an argument for a parametric approach, such as SFA. However, within the DEA literature there are several procedures available to identify outliers.11
Issues are, however, also present with the parametric approach if incorrect assumptions are made of the functional form for the frontier, distribution of the noise (generally normal with mean zero), and distribution of inefficiency (e.g., half-normal). Yatchew (1998) states that economic theory almost never exactly specifies a functional form such as these, which may lead to biased 11 Several procedures to perform this can be found in the literature, e.g., Wilson (1993), Simar (2003), and Banker and Chang (2006).
7
to the Färe et al. (1994) decomposition of the Malmquist index, TC and EC are carried out. These are identified by studying the change of the production frontier, which is assumed to be equivalent to the time derivative, and the change of the efficiency component, as the change in efficiency with respect to time, respectively. Additionally, the returns to scale (RTS) can be examined by summing the input elasticities. From that, a scale change (SC) component can be carried out. Furthermore, allocative efficiency change (AEC) can be obtained if price information is available. The sum of these components, i.e., TC + EC + SC + AEC, is proposed as the estimate of TFP change.
From an estimation point of view, one has to choose functional form for the frontier (e.g., Cobb-Douglas or Translog), which can be tested.9 Additionally, it needs to be decided whether to use a fixed or random effect, which is commonly tested by the Hausman test. The Hausman test is often rejected, which provides an argument for the fixed effect model. However, in such tests, one needs to take the economics into consideration and decide whether to rely on the statistics or the economics. For example, the RTS may be unreasonably low using fixed effects (Ackerberg et al. 2015), i.e., decreasing returns to scale, while under random effects it is approximately unity. In such case, one may believe in the random effect, since a developed economy is not likely to have decreasing RTS; i.e., one can believe more in the economics than the statistics.
Comparison and discussion There is a rich literature that applies the different efficiency and TFP measures; however, less attention has been found that considers when to choose which method. Related exceptions are, e.g., Hjalmarsson, Kumbhakar, and Heshmati (1996), which focuses on comparing results of using the different methods, and Giraleas, Emrouznejad, and Thanassoulis (2012), who quantitatively examine the accuracy of growth accounting (GA) and frontier-based productivity indexes by Monte Carlo simulations. Bartelsman and Doms (2000) and Bartelsman and Wolf (2017) review productivity measures; however, to a large extent they ignore the frontier literature. Van Biesebroeck (2007) uses simulations to compare results among five productivity measures, i.e., index numbers, DEA, stochastic frontiers, instrumental variables (GMM), and semiparametric estimation, where the last two are not considered in this thesis.10
In comparing the different frontier methods, it can first be stated that DEA is based on production axioms rather than statistical inference, such as SFA. Coelli, Rao, O’Donnell, and Battese (2005) write that guidance for the 9 If a quadratic distance function is estimated, an appropriate choice is the translog because both first- and second-order parameters are included. 10 Obviously, there are some arguments in several application studies and books.
8
appropriate model choice is not straightforward and is likely to differ depending on the industry being studied. On the other hand, Bogetoft (2012) argues that DEA is more suitable for managers than SFA. The reason is that DEA identifies a small group of peers, which are comparable units important for managers to study in order to obtain best practice.
A distinction for when which method can be chosen regards the number of observations in the available data. Calculated TFP index numbers require only one unit over time to construct an index of TFP change for that firm; however, price information is necessary. An issue with DEA is the ‘curse of dimensionality’; i.e., the reliability drops when the dimension of the model increases (e.g., Bellman, 1957; Silverman, 1986). DEA has no strict limit; however, a rule of thumb by Cooper, Seiford, and Tone (2007) is max(m * s, 3 * (m + s)), where m is the number of outputs and s the number of inputs. However, Wilson (2017) argues that the Cooper et al. (2007) rule of thumb, among others, sets the limit too low. Further, given the sample size, there are fewer neighbours as the numbers of inputs and outputs increase in DEA. Consequently, discrimination power declines for higher dimensions.
In SFA, more observations are required because statistical inference needs to be drawn. The requirement of a large sample size can be regarded as a substantial disadvantage in cases where this is not available (Premachandra, Bhabra, and Sueyoshi, 2009), e.g., investigations of public organizations where the total number of units is few.
An advantage with the non-parametric indexes is that they do not rely on any prior assumption of the functional form or behavioural assumptions. However, this also relates to the main drawback of DEA: Any deviation from the frontier is associated with inefficiency, instead of a separation between inefficiency and random noise, as in SFA (see, e.g., Greene, 2008). DEA becomes sensitive to extreme observations by assuming that each deviation from the frontier is attributed to inefficiency, meaning that one observation can be the reason for biased results. In particular, DEA is sensitive to exceptionally well performing units since the frontier itself can be driven by these, making all peers, i.e., comparison units, more inefficient. A large amount of observations increases the probability of measurement error in at least one observation, which can be considered as an argument for a parametric approach, such as SFA. However, within the DEA literature there are several procedures available to identify outliers.11
Issues are, however, also present with the parametric approach if incorrect assumptions are made of the functional form for the frontier, distribution of the noise (generally normal with mean zero), and distribution of inefficiency (e.g., half-normal). Yatchew (1998) states that economic theory almost never exactly specifies a functional form such as these, which may lead to biased 11 Several procedures to perform this can be found in the literature, e.g., Wilson (1993), Simar (2003), and Banker and Chang (2006).
7
to the Färe et al. (1994) decomposition of the Malmquist index, TC and EC are carried out. These are identified by studying the change of the production frontier, which is assumed to be equivalent to the time derivative, and the change of the efficiency component, as the change in efficiency with respect to time, respectively. Additionally, the returns to scale (RTS) can be examined by summing the input elasticities. From that, a scale change (SC) component can be carried out. Furthermore, allocative efficiency change (AEC) can be obtained if price information is available. The sum of these components, i.e., TC + EC + SC + AEC, is proposed as the estimate of TFP change.
From an estimation point of view, one has to choose functional form for the frontier (e.g., Cobb-Douglas or Translog), which can be tested.9 Additionally, it needs to be decided whether to use a fixed or random effect, which is commonly tested by the Hausman test. The Hausman test is often rejected, which provides an argument for the fixed effect model. However, in such tests, one needs to take the economics into consideration and decide whether to rely on the statistics or the economics. For example, the RTS may be unreasonably low using fixed effects (Ackerberg et al. 2015), i.e., decreasing returns to scale, while under random effects it is approximately unity. In such case, one may believe in the random effect, since a developed economy is not likely to have decreasing RTS; i.e., one can believe more in the economics than the statistics.
Comparison and discussion There is a rich literature that applies the different efficiency and TFP measures; however, less attention has been found that considers when to choose which method. Related exceptions are, e.g., Hjalmarsson, Kumbhakar, and Heshmati (1996), which focuses on comparing results of using the different methods, and Giraleas, Emrouznejad, and Thanassoulis (2012), who quantitatively examine the accuracy of growth accounting (GA) and frontier-based productivity indexes by Monte Carlo simulations. Bartelsman and Doms (2000) and Bartelsman and Wolf (2017) review productivity measures; however, to a large extent they ignore the frontier literature. Van Biesebroeck (2007) uses simulations to compare results among five productivity measures, i.e., index numbers, DEA, stochastic frontiers, instrumental variables (GMM), and semiparametric estimation, where the last two are not considered in this thesis.10
In comparing the different frontier methods, it can first be stated that DEA is based on production axioms rather than statistical inference, such as SFA. Coelli, Rao, O’Donnell, and Battese (2005) write that guidance for the 9 If a quadratic distance function is estimated, an appropriate choice is the translog because both first- and second-order parameters are included. 10 Obviously, there are some arguments in several application studies and books.
10
outputs and aggregate inputs’ (Chambers and Pope, 1996, p. 1360). Efficiency is similar, with the exception that it is obtained by a comparison with a standard, i.e., a benchmark.
Summary of the essays This thesis consists of five empirical essays on the topics of total factor productivity (TFP), efficiency, and impacts of policy. Each of them is related to TFP and/or efficiency, and three of the essays also directly concern policy interventions. The first essay centres on productivity and efficiency of the Swedish manufacturing sector, representing an important part of Swedish exports, during the financial crisis. Three of the essays target issues in public sector efficiency in general, with a focus on the Swedish district courts. Among these essays, one relates to TFP change and its decomposed factors (Essay II), and the two others consider mergers from an ex ante and ex post perspective, respectively (Essays III and IV). Finally, Essay V connects productivity analysis, impact evaluation, and labour economics by studying whether firms that hire individuals with subsidy experience any effect on productivity and profit per employee.
Essay I ‘TFP Change and Its Components for Swedish Manufacturing Firms During the 2008–2009 Financial Crisis’ (co-authored with Jonas Månsson and William H. Greene) targets the importance of sustained growth in total factor productivity (TFP) because it is a driving force of economic development (Krugman, 1997). A slowdown in labour productivity growth can be observed in a large share of the industrialized countries, where Sweden performed worse than other OECD countries after 2007 (OECD, 2015). Additionally, Cerra and Saxena (2008) showed that several countries declined in their per capita income ranking after a financial crisis, e.g., Sweden after the 1990s banking crisis. Despite the importance of investigating issues related to TFP growth after economic downturns, it has hardly been investigated since the financial crisis of 2008–2009. The manufacturing sector is of particular importance, due to its export dependence and potential spillover to other sectors (Kaldor, 1966). This is particularly the case for Sweden since manufactured goods, to a large extent, are exports and represent an important part of the Swedish economy.
The aim of this paper is to examine TFP and its decomposed factors before, during, and after the 2008–2009 financial crisis. A four-component stochastic frontier model (SFM) is applied to the Swedish manufacturing industry for the period 1997 to 2013, which permits analysis of a potential catching-up following the crisis. For a comparison purpose, the private service sector is incorporated in the analysis since it, potentially, is less affected by changes in
9
estimates. This kind of misspecification is not an issue in DEA because the best practice frontier is constructed as a linear combination of the peers observed in the data (see, e.g., Premachandra, Zhu, Watson, and Galagedera, 2016). The advantage is, therefore, that no econometric assumptions are required and no uncertainties in the TFP change, i.e., no error term. Specifically, no error term avoids statistical concerns such as endogeneity (see, e.g., O’Donnell, 2012a). DEA is particularly advantageous when the products are not sold on a market (Bogetoft and Otto, 2010), which makes it particularly suitable in the public service sector. This also relates to TFP indexes, where Førsund (2016) states that the Malmquist index is more suitable than, for example, the Törnqvist index in the public sector because output prices are generally not available. Furthermore, each of the described index numbers has the advantage of easily incorporating multiple outputs in the model. DEA is sensitive to misspecification from, for example, omitted variables, if relevant inputs or outputs are not included, however; dimensionality problems can occur if too many inputs and/or outputs are incorporated in the model.
In the frontier approaches, efficiency is a relative measure in comparison to the best practice firms, which makes it crucial that the measured units are comparable. An alternative approach that can be applied in SFA or DEA when two or more distinctive groups can be identified is the metafrontier (see, e.g., Charnes, Cooper, and Rhodes, 1981; Grosskopf and Valdmanis, 1987; Månsson, 1996), e.g., private and public banks, merged and non-merged courts, etcetera. O’Donnell, Fallah-Fini, and Triantis (2017) refer to a single technology as a book and several as a library, i.e., the standard frontier and the metafrontier, respectively.
As described, TFP can be estimated by including noise or calculated without. Using an estimated value, including a noise term, in second-stage estimations is problematic, as pointed out by Wang and Schmidt (2002). Thus, applications that incorporate a two-stage procedure should avoid estimation in the first stage; e.g., when the treatment effect is estimated in the second stage, a calculated value of TFP in the first stage is preferred. Additionally, accounting for the environment in a second stage by using DEA efficiency scores as a dependent variable is a popular and controversial method. Simar and Wilson (2007) show that commonly performed inference based on this procedure is invalid because of the estimation, which by definition creates dependency and bias. Therefore, they propose a left-truncated bias-corrected efficiency procedure to make inference valid under the separability assumption.
To summarize, no single approach of measuring TFP and efficiency has an absolute advantage over the others. Instead, the accuracy depends on the characteristics of the data (Giraleas et al., 2012). However, ‘regardless of the approach used, productivity measurement still reduces to comparing aggregate
10
outputs and aggregate inputs’ (Chambers and Pope, 1996, p. 1360). Efficiency is similar, with the exception that it is obtained by a comparison with a standard, i.e., a benchmark.
Summary of the essays This thesis consists of five empirical essays on the topics of total factor productivity (TFP), efficiency, and impacts of policy. Each of them is related to TFP and/or efficiency, and three of the essays also directly concern policy interventions. The first essay centres on productivity and efficiency of the Swedish manufacturing sector, representing an important part of Swedish exports, during the financial crisis. Three of the essays target issues in public sector efficiency in general, with a focus on the Swedish district courts. Among these essays, one relates to TFP change and its decomposed factors (Essay II), and the two others consider mergers from an ex ante and ex post perspective, respectively (Essays III and IV). Finally, Essay V connects productivity analysis, impact evaluation, and labour economics by studying whether firms that hire individuals with subsidy experience any effect on productivity and profit per employee.
Essay I ‘TFP Change and Its Components for Swedish Manufacturing Firms During the 2008–2009 Financial Crisis’ (co-authored with Jonas Månsson and William H. Greene) targets the importance of sustained growth in total factor productivity (TFP) because it is a driving force of economic development (Krugman, 1997). A slowdown in labour productivity growth can be observed in a large share of the industrialized countries, where Sweden performed worse than other OECD countries after 2007 (OECD, 2015). Additionally, Cerra and Saxena (2008) showed that several countries declined in their per capita income ranking after a financial crisis, e.g., Sweden after the 1990s banking crisis. Despite the importance of investigating issues related to TFP growth after economic downturns, it has hardly been investigated since the financial crisis of 2008–2009. The manufacturing sector is of particular importance, due to its export dependence and potential spillover to other sectors (Kaldor, 1966). This is particularly the case for Sweden since manufactured goods, to a large extent, are exports and represent an important part of the Swedish economy.
The aim of this paper is to examine TFP and its decomposed factors before, during, and after the 2008–2009 financial crisis. A four-component stochastic frontier model (SFM) is applied to the Swedish manufacturing industry for the period 1997 to 2013, which permits analysis of a potential catching-up following the crisis. For a comparison purpose, the private service sector is incorporated in the analysis since it, potentially, is less affected by changes in
9
estimates. This kind of misspecification is not an issue in DEA because the best practice frontier is constructed as a linear combination of the peers observed in the data (see, e.g., Premachandra, Zhu, Watson, and Galagedera, 2016). The advantage is, therefore, that no econometric assumptions are required and no uncertainties in the TFP change, i.e., no error term. Specifically, no error term avoids statistical concerns such as endogeneity (see, e.g., O’Donnell, 2012a). DEA is particularly advantageous when the products are not sold on a market (Bogetoft and Otto, 2010), which makes it particularly suitable in the public service sector. This also relates to TFP indexes, where Førsund (2016) states that the Malmquist index is more suitable than, for example, the Törnqvist index in the public sector because output prices are generally not available. Furthermore, each of the described index numbers has the advantage of easily incorporating multiple outputs in the model. DEA is sensitive to misspecification from, for example, omitted variables, if relevant inputs or outputs are not included, however; dimensionality problems can occur if too many inputs and/or outputs are incorporated in the model.
In the frontier approaches, efficiency is a relative measure in comparison to the best practice firms, which makes it crucial that the measured units are comparable. An alternative approach that can be applied in SFA or DEA when two or more distinctive groups can be identified is the metafrontier (see, e.g., Charnes, Cooper, and Rhodes, 1981; Grosskopf and Valdmanis, 1987; Månsson, 1996), e.g., private and public banks, merged and non-merged courts, etcetera. O’Donnell, Fallah-Fini, and Triantis (2017) refer to a single technology as a book and several as a library, i.e., the standard frontier and the metafrontier, respectively.
As described, TFP can be estimated by including noise or calculated without. Using an estimated value, including a noise term, in second-stage estimations is problematic, as pointed out by Wang and Schmidt (2002). Thus, applications that incorporate a two-stage procedure should avoid estimation in the first stage; e.g., when the treatment effect is estimated in the second stage, a calculated value of TFP in the first stage is preferred. Additionally, accounting for the environment in a second stage by using DEA efficiency scores as a dependent variable is a popular and controversial method. Simar and Wilson (2007) show that commonly performed inference based on this procedure is invalid because of the estimation, which by definition creates dependency and bias. Therefore, they propose a left-truncated bias-corrected efficiency procedure to make inference valid under the separability assumption.
To summarize, no single approach of measuring TFP and efficiency has an absolute advantage over the others. Instead, the accuracy depends on the characteristics of the data (Giraleas et al., 2012). However, ‘regardless of the approach used, productivity measurement still reduces to comparing aggregate
12
can occur in the study by SNCA, since productivity is measured by a partial measure, i.e., labour productivity, which ignores substitution between inputs.
To compute TFP, distances obtained by the data envelopment analysis (DEA) framework, proposed by Charnes et al. (1978), are used. TFP of the 48 Swedish district courts are measured by the Malmquist productivity index (MPI) for the period 2012 to 2015. Following Wheelock and Wilson (1999), the MPI is decomposed into four parts: changes in 1) pure technical efficiency, 2) scale efficiency, 3) pure technology, and 4) the scale of the technology. A known issue with all types of DEA analysis is that no statistical inference is possible (Simar & Wilson, 2000). In this study, a bootstrap approach is used to determine the confidence intervals of the different components presented above (see Efron, 1979). Another issue with DEA is the influence of outliers (see, e.g., Kapelko & Oude Lansink, 2015). The analysis of outliers is to a large extent omitted in previous studies on court performance. In this study, an outlier detection analysis is performed to investigate whether the results depend on a few extreme observations.
The findings show a 1.7% average decline of TFP annually. However, a substantial variation between years can be observed in the number of statistically significant courts below and above unity. Looking at averages of the components, it can be observed that the negative impact is mainly driven by a negative technical change. Furthermore, it can be observed that TFP change is positively correlated with the rate of change in caseload, indicating that the decline in TFP change can be a result of a shrinking demand for justice services.
Essay III ‘Potential Efficiency Effects of Merging the Swedish District Courts’, Socio-Economic Planning Sciences, forthcoming (co-authored with Claes Tidanå) focuses on whether actual merging decisions could be rationalized based on ex ante information. A number of actual mergers took place in the Swedish district courts system between 2000 and 2009. The courts merged from 96 to 48 in number; the general theoretical arguments for merging include economies of scale, economies of scope, increased central control, and risk sharing. Even though a substantial number of mergers took place, it has not been formally investigated whether the theoretical arguments are expected to be reached for the district courts in Sweden.
This paper aims to investigate how well the assumed efficiency gains had the potential to be realized by estimating the potential production economic effects of the Swedish district court mergers, ex ante. The contribution is, therefore, to evaluate whether the political decision to merge is well prepared, i.e., whether all mergers could be rationalized from an efficiency perspective. Otherwise, further enhancements of the decision basis for mergers should have been carried out. To examine the potential gain of merging, the data envelopment (DEA) model of Bogetoft and Wang (2005) is applied. An
11
world demand. Additional to the empirical analysis, a question is raised regarding interpretation of TC in stochastic frontier analysis (SFA).
To investigate and compute TFP and its components, the SFM is used that was simultaneously proposed by Colombi, Kumbhakar, Martini, and Vittadini (2014); Kumbhakar, Lien, and Hardaker (2014); and Tsionas and Kumbhakar (2014). In this model, inefficiency is decomposed into persistent and transient components separated from firm-heterogeneity and random noise, respectively. Further, technical change (TC), returns to scale (RTS) and a scale change (SC) component are identified. The TFP change is obtained as the sum of TC and SC.
The results show that there are potentials to improve efficiency. The persistent part for manufacturing (service) is 0.796 (0.754) and the transient part 0.787 (0.762). A significant decline can be observed during the financial crisis; however, a catch-up to its initial level occurred afterward. Further, the manufacturing (service) had an annual average TFP growth of 1.17% (1.24%) measured over the whole period. Targeting differences before and after 2007, it is observed that TFP change for the manufacturing sector is 1.98%, and the service sector 1.80%, during the former period, i.e., before the crisis. This can be compared with 0.44% and 0.54% in the latter. This difference between the pre and post periods is statistically significant on the 1% level. However, it has not been possible to distinguish whether this is driven by frontier firms or inefficient firms; i.e., the production function can be pushed towards the origin by inefficient firms. However, lower transient inefficiency during the crisis can also be observed when time is indicated by year fixed effects, which indicates that inefficient firms, at least to some extent, affect TC.
Essay II ‘A Bootstrapped Malmquist Index Applied to Swedish District Courts’, European Journal of Law and Economics, 1–31 (co-authored with Jonas Månsson, Christian Andersson, and Fredrik Bonander), measures total factor productivity (TFP) for the Swedish district courts. Efficiency and productivity in the public sector are a major concern for most parliaments and governments. It is explicitly stated in the Swedish Budget Act (SFS 2011:203) that all state services should be provided with a high level of efficiency. When dealing with state-provided production, this means usage of the least amount of inputs at the given output level or production of maximum amount of production at the given resource level. The motivation for studying productivity development is, therefore, from a policy perspective, straightforward. The Swedish Government has launched a number of reforms for the district courts during the last 20 years, with the major objective of increasing efficiency and productivity, while maintaining a high degree of law and order. In 1999, there were 96 districts courts in Sweden, and today only 48 exist. Despite the reforms, the Swedish National Court Administration (SNCA) reports indications that productivity has declined. However, problems
12
can occur in the study by SNCA, since productivity is measured by a partial measure, i.e., labour productivity, which ignores substitution between inputs.
To compute TFP, distances obtained by the data envelopment analysis (DEA) framework, proposed by Charnes et al. (1978), are used. TFP of the 48 Swedish district courts are measured by the Malmquist productivity index (MPI) for the period 2012 to 2015. Following Wheelock and Wilson (1999), the MPI is decomposed into four parts: changes in 1) pure technical efficiency, 2) scale efficiency, 3) pure technology, and 4) the scale of the technology. A known issue with all types of DEA analysis is that no statistical inference is possible (Simar & Wilson, 2000). In this study, a bootstrap approach is used to determine the confidence intervals of the different components presented above (see Efron, 1979). Another issue with DEA is the influence of outliers (see, e.g., Kapelko & Oude Lansink, 2015). The analysis of outliers is to a large extent omitted in previous studies on court performance. In this study, an outlier detection analysis is performed to investigate whether the results depend on a few extreme observations.
The findings show a 1.7% average decline of TFP annually. However, a substantial variation between years can be observed in the number of statistically significant courts below and above unity. Looking at averages of the components, it can be observed that the negative impact is mainly driven by a negative technical change. Furthermore, it can be observed that TFP change is positively correlated with the rate of change in caseload, indicating that the decline in TFP change can be a result of a shrinking demand for justice services.
Essay III ‘Potential Efficiency Effects of Merging the Swedish District Courts’, Socio-Economic Planning Sciences, forthcoming (co-authored with Claes Tidanå) focuses on whether actual merging decisions could be rationalized based on ex ante information. A number of actual mergers took place in the Swedish district courts system between 2000 and 2009. The courts merged from 96 to 48 in number; the general theoretical arguments for merging include economies of scale, economies of scope, increased central control, and risk sharing. Even though a substantial number of mergers took place, it has not been formally investigated whether the theoretical arguments are expected to be reached for the district courts in Sweden.
This paper aims to investigate how well the assumed efficiency gains had the potential to be realized by estimating the potential production economic effects of the Swedish district court mergers, ex ante. The contribution is, therefore, to evaluate whether the political decision to merge is well prepared, i.e., whether all mergers could be rationalized from an efficiency perspective. Otherwise, further enhancements of the decision basis for mergers should have been carried out. To examine the potential gain of merging, the data envelopment (DEA) model of Bogetoft and Wang (2005) is applied. An
11
world demand. Additional to the empirical analysis, a question is raised regarding interpretation of TC in stochastic frontier analysis (SFA).
To investigate and compute TFP and its components, the SFM is used that was simultaneously proposed by Colombi, Kumbhakar, Martini, and Vittadini (2014); Kumbhakar, Lien, and Hardaker (2014); and Tsionas and Kumbhakar (2014). In this model, inefficiency is decomposed into persistent and transient components separated from firm-heterogeneity and random noise, respectively. Further, technical change (TC), returns to scale (RTS) and a scale change (SC) component are identified. The TFP change is obtained as the sum of TC and SC.
The results show that there are potentials to improve efficiency. The persistent part for manufacturing (service) is 0.796 (0.754) and the transient part 0.787 (0.762). A significant decline can be observed during the financial crisis; however, a catch-up to its initial level occurred afterward. Further, the manufacturing (service) had an annual average TFP growth of 1.17% (1.24%) measured over the whole period. Targeting differences before and after 2007, it is observed that TFP change for the manufacturing sector is 1.98%, and the service sector 1.80%, during the former period, i.e., before the crisis. This can be compared with 0.44% and 0.54% in the latter. This difference between the pre and post periods is statistically significant on the 1% level. However, it has not been possible to distinguish whether this is driven by frontier firms or inefficient firms; i.e., the production function can be pushed towards the origin by inefficient firms. However, lower transient inefficiency during the crisis can also be observed when time is indicated by year fixed effects, which indicates that inefficient firms, at least to some extent, affect TC.
Essay II ‘A Bootstrapped Malmquist Index Applied to Swedish District Courts’, European Journal of Law and Economics, 1–31 (co-authored with Jonas Månsson, Christian Andersson, and Fredrik Bonander), measures total factor productivity (TFP) for the Swedish district courts. Efficiency and productivity in the public sector are a major concern for most parliaments and governments. It is explicitly stated in the Swedish Budget Act (SFS 2011:203) that all state services should be provided with a high level of efficiency. When dealing with state-provided production, this means usage of the least amount of inputs at the given output level or production of maximum amount of production at the given resource level. The motivation for studying productivity development is, therefore, from a policy perspective, straightforward. The Swedish Government has launched a number of reforms for the district courts during the last 20 years, with the major objective of increasing efficiency and productivity, while maintaining a high degree of law and order. In 1999, there were 96 districts courts in Sweden, and today only 48 exist. Despite the reforms, the Swedish National Court Administration (SNCA) reports indications that productivity has declined. However, problems
14
efficiency changes in courts? and 4) How do the ex post results compare with the potential effects, ex ante, obtained by the Bogetoft and Wang (2005) model? The particular research questions relate directly to national policy aiming at dimensioning the court system for potential output expansion. Moreover, the method and the empirics may also provide valuable information on horizontal mergers in public services beyond the court system.
Addressing questions related to effects of a policy intervention is, generally, problematic. Therefore, the questions are evaluated by using three different analytical frameworks. First, the technical efficiency scores calculated by DEA are compared over time by using a global frontier in order to provide a description of the development for the whole sector. Additionally, the sources of efficiency change are provided. Second, the merged and non-merged courts are compared by using a metafrontier approach. This allows decomposition into organizational – i.e., the groups compared to one another – and managerial efficiency – i.e., comparison within each group. Third, the impact of mergers on efficiency is analysed by using a conditional difference-in-differences (cDiD) approach. For this part of the analysis, merged courts are matched to non-merged courts by using the Mahalanobis distance metric. Finally, the factor-level sources are investigated based on changes in inputs and outputs. The data for the application is obtained from the Swedish National Court Administration (SNCA) and consists of all Swedish district courts from 2000 to 2017, including the identity and scope for all structural changes.
Each of the three analytical frameworks indicates that efficiency increased by merging the Swedish district courts. For example, it is shown that non-merged courts had a higher efficiency score than merged courts before the actual mergers took place. After the mergers, it is seen to be the other way around; i.e., the merged courts are on a higher efficiency level. Second, no differences can be observed within the merged and non-merged groups, i.e., no differences in managerial efficiency. However, statistically significant differences are shown between the groups, i.e., structural efficiency by the Mann-Whitney U test. Third, the cDiD analysis indicates positive impacts of merging each year after the merging took place, where three out of five were statistically significant. Furthermore, a graphical evaluation of the sources of efficiency change showed that one of the main differences between the merged and non-merged courts is that merged courts decrease their capital more, i.e., in the office area, which took several years due to rental contracts. Finally, the ex ante results calculated in Essay III are evaluated by using ex post information. Here, the overall potential gain and the learning-adjusted potential gain, i.e., only the gain obtained from HA and SC, are used. This analysis shows that the overall and the learning adjusted have a positive correlation, which is statistically significant on the 1% and 10% levels, respectively.
13
output perspective is carried out to investigate the potential gain of mergers, ex ante, based on the reason that district courts have a specific budget that they are supposed to spend optimally to maximize output. Using the output perspective, efficiency is defined as the maximum level of outputs that can be produced, given the inputs. One argument for using the applied model is that it not only estimates the potential efficiency effect of the mergers but also decomposes the potential gains into learning (LE), harmony (HA), and scale (SC) to isolate the sources. LE represents the gain from eliminating individual court inefficiency, and HA is the potential efficiency gain achieved from a more ‘powerful’ input mix, i.e., a good combination of inputs that can achieve a large amount of output, or an output mix that is easier to produce. Finally, SC is the gain or loss that occurs by operating at a larger scale.
The data are obtained from the Swedish National Court Administration (SNCA), consisting of all individual district courts, including the resigned, for the period 2000‒2009. Diverse potential in efficiency gain is found among the mergers; i.e., a few indicate substantial positive effects, while others indicate zero effect. The most positive merger shows a potential gain of 47.8%. However, 31.0% of the mergers show an overall potential efficiency gain of less than 5%. If the gain that is obtained from eliminating individual inefficiency is excluded, 44.8% of the mergers show a potential efficiency gain of less than 5%. Even though a substantial number of mergers with small potential gains are present, there are other mergers with potential to be advantageous. For example, 27.6% of the mergers have the potential to gain more than 20.1% in efficiency.
Essay IV ‘Impacts on Efficiency of Merging the Swedish District Courts’ (co-authored with Per J. Agrell and Jonas Månsson) contributes both empirically and methodologically. Evaluations of whether merging has had an impact on efficiency are of certain importance in the public service sector since more effective utilization of their services is a general target for governments. The public sector is a particularly challenging area in which to achieve efficiency since inputs are likely to be sticky; i.e., senior staff and capital are fixed or at least semi-fixed. An instrument that is frequently used is reorganizing the service through horizontal mergers, i.e., closing agencies and transferring their competencies to other existing units. The ex ante arguments presented in this regard include economies of scale, economies of scope, improved central coordination, improved operational risk sharing, and ultimately higher efficiency and lower cost (Bogetoft and Wang, 2005).
This paper applies a non-parametric evaluation model to assess the ex post effects on technical efficiency as a result of recent horizontal mergers among the Swedish district courts. Specifically, four questions are addressed: 1) What are the effects on efficiency of mergers? 2) Are the effects of mergers temporal or stationary in time? 3) What are the driving factors of observed
14
efficiency changes in courts? and 4) How do the ex post results compare with the potential effects, ex ante, obtained by the Bogetoft and Wang (2005) model? The particular research questions relate directly to national policy aiming at dimensioning the court system for potential output expansion. Moreover, the method and the empirics may also provide valuable information on horizontal mergers in public services beyond the court system.
Addressing questions related to effects of a policy intervention is, generally, problematic. Therefore, the questions are evaluated by using three different analytical frameworks. First, the technical efficiency scores calculated by DEA are compared over time by using a global frontier in order to provide a description of the development for the whole sector. Additionally, the sources of efficiency change are provided. Second, the merged and non-merged courts are compared by using a metafrontier approach. This allows decomposition into organizational – i.e., the groups compared to one another – and managerial efficiency – i.e., comparison within each group. Third, the impact of mergers on efficiency is analysed by using a conditional difference-in-differences (cDiD) approach. For this part of the analysis, merged courts are matched to non-merged courts by using the Mahalanobis distance metric. Finally, the factor-level sources are investigated based on changes in inputs and outputs. The data for the application is obtained from the Swedish National Court Administration (SNCA) and consists of all Swedish district courts from 2000 to 2017, including the identity and scope for all structural changes.
Each of the three analytical frameworks indicates that efficiency increased by merging the Swedish district courts. For example, it is shown that non-merged courts had a higher efficiency score than merged courts before the actual mergers took place. After the mergers, it is seen to be the other way around; i.e., the merged courts are on a higher efficiency level. Second, no differences can be observed within the merged and non-merged groups, i.e., no differences in managerial efficiency. However, statistically significant differences are shown between the groups, i.e., structural efficiency by the Mann-Whitney U test. Third, the cDiD analysis indicates positive impacts of merging each year after the merging took place, where three out of five were statistically significant. Furthermore, a graphical evaluation of the sources of efficiency change showed that one of the main differences between the merged and non-merged courts is that merged courts decrease their capital more, i.e., in the office area, which took several years due to rental contracts. Finally, the ex ante results calculated in Essay III are evaluated by using ex post information. Here, the overall potential gain and the learning-adjusted potential gain, i.e., only the gain obtained from HA and SC, are used. This analysis shows that the overall and the learning adjusted have a positive correlation, which is statistically significant on the 1% and 10% levels, respectively.
13
output perspective is carried out to investigate the potential gain of mergers, ex ante, based on the reason that district courts have a specific budget that they are supposed to spend optimally to maximize output. Using the output perspective, efficiency is defined as the maximum level of outputs that can be produced, given the inputs. One argument for using the applied model is that it not only estimates the potential efficiency effect of the mergers but also decomposes the potential gains into learning (LE), harmony (HA), and scale (SC) to isolate the sources. LE represents the gain from eliminating individual court inefficiency, and HA is the potential efficiency gain achieved from a more ‘powerful’ input mix, i.e., a good combination of inputs that can achieve a large amount of output, or an output mix that is easier to produce. Finally, SC is the gain or loss that occurs by operating at a larger scale.
The data are obtained from the Swedish National Court Administration (SNCA), consisting of all individual district courts, including the resigned, for the period 2000‒2009. Diverse potential in efficiency gain is found among the mergers; i.e., a few indicate substantial positive effects, while others indicate zero effect. The most positive merger shows a potential gain of 47.8%. However, 31.0% of the mergers show an overall potential efficiency gain of less than 5%. If the gain that is obtained from eliminating individual inefficiency is excluded, 44.8% of the mergers show a potential efficiency gain of less than 5%. Even though a substantial number of mergers with small potential gains are present, there are other mergers with potential to be advantageous. For example, 27.6% of the mergers have the potential to gain more than 20.1% in efficiency.
Essay IV ‘Impacts on Efficiency of Merging the Swedish District Courts’ (co-authored with Per J. Agrell and Jonas Månsson) contributes both empirically and methodologically. Evaluations of whether merging has had an impact on efficiency are of certain importance in the public service sector since more effective utilization of their services is a general target for governments. The public sector is a particularly challenging area in which to achieve efficiency since inputs are likely to be sticky; i.e., senior staff and capital are fixed or at least semi-fixed. An instrument that is frequently used is reorganizing the service through horizontal mergers, i.e., closing agencies and transferring their competencies to other existing units. The ex ante arguments presented in this regard include economies of scale, economies of scope, improved central coordination, improved operational risk sharing, and ultimately higher efficiency and lower cost (Bogetoft and Wang, 2005).
This paper applies a non-parametric evaluation model to assess the ex post effects on technical efficiency as a result of recent horizontal mergers among the Swedish district courts. Specifically, four questions are addressed: 1) What are the effects on efficiency of mergers? 2) Are the effects of mergers temporal or stationary in time? 3) What are the driving factors of observed
16
indicates a negative and significant effect on TFP and profit per employee. The negative effect on TFP is no longer statistically significant during the second year with a subsidy, which indicates a positive effect of on-the-job training. Conversely, profit per employee is negative, which can occur regardless of the zero effect on TFP if firms within the treated group do not manage to maximize their profit, i.e., equalize the input prices to the marginal revenue product.
Conclusions, policy implications, and future research The contributions of this thesis enrich the literature both methodologically and empirically. Implications to be given from the thesis are wide in the sense that the different essays are applications in different areas. Furthermore, some policy implications can be drawn based on the conclusions; however, notes are also provided on areas that are not considered but left for future research.
Essay I provides an overview of how TFP and its components change within the manufacturing and service sectors in Sweden before, during, and after the financial crisis of 2008–2009. The main conclusion is that TFP growth is substantially lower during the period 2007–2013, in comparison to the period 1997–2007, for both main sectors. This is driven by lower TC, i.e., a slower shift of the average production function. A similar pattern can be observed for all sub-sectors, with the exception of food, beverages, and tobacco. The conclusion is that TFP change is also affected by weaker demand during a longer period because inputs have not been flexible enough. A mechanism for why the same pattern cannot be observed in food, beverages, and tobacco is, potentially, that these goods are not as sensitive to business cycles. In contrast, sectors with a negative TFP change potentially believed that demand will increase again so inputs are not reduced to such a large extent based on this expectation. Regarding interpretation of the components, it is argued that it can be questioned whether TC, in fact, should be interpreted as frontier shift in SFA. If not, it also generates an issue in separating TC from EC. Future research should interpret separation of the components with care. Additionally, questions to be investigated in future research are the mechanisms behind the changes that directly link to future policies; i.e., determinants of the different components of efficiency as well as drivers of TC can be examined in further studies.
Essay II recommends that district courts with negative TFP could learn from those with positive TFP. This can hopefully result in positive TFP development in the future. Furthermore, it can be observed that the smallest courts have the largest volatility in TFP change, which is a source of
15
Essay V ‘The Impact of Labour Subsidies on Total Factor Productivity and Profit per Employee’ investigates the impact of labour subsidies on TFP since lower expected productivity is the motivation for subsidizing labour. Subsidizing labour is a common policy to prevent long-term unemployment. The targeted groups in Sweden are the already long-term unemployed, unemployed people with disabilities, and newly arrived immigrants. There is extensive research on wage subsidies from a labour supply perspective. However, only a few studies exist on the labour demand side in relation to subsidies, and the only study that considers the productivity effects on firms is Koski and Pajarinen (2015). Although only one study can be found regarding the productivity effects from labour subsidies, there is more research concerning the TFP effects as a result of subsidies on the other input factor of production, capital (see, e.g., Bergström, 2000; Bernini and Pellegrini, 2011; Harris and Trainor, 2005; Managi, 2010; Skuras et al., 2006). Thus, one motivation for this study is the lack of research on productivity effects regarding non-capital input subsidies.
This paper takes its point of departure from an employer’s perspective of subsidized employment and investigates in particular whether there is a change in productivity and profit per employee as a result of hiring employees with wage subsidies. The average treatment effect of the treated (ATT) is estimated on TFP measured by the Törnqvist TFP index and the profit per employee as outcomes. This estimation is performed on matched data obtained by coarsened exact matching (CEM), developed by Blackwell et al. (2010). There is only a limited literature in the area of TFP analysis that aims to investigate impacts of policy. Most of the previously mentioned studies regarding capital subsidies do not identify a treatment and control group to be compared over time. This makes it difficult to evaluate treatment effects. From a methodological point of view, Greene (2010), Bravo-Ureta et al. (2012) and Chen et al. (2014) are exceptions in SFA. Additionally, Bogetoft and Kromann (2018) combine propensity score matching with efficiency scores obtained by data envelopment analysis (DEA). Some empirical studies can also be found that use a proper impact design to explain variation in TFP due to political interventions by using a statistically estimated value of TFP (see, e.g., Bernini and Pellegrini, 2011). However, the impact analysis of policy is fundamental when evaluating interventions and deserves more attention in the TFP literature. The contribution of this paper is therefore twofold: 1) to be the first study to investigate the relationship between firm TFP and subsidized employees and 2) to propose a combination of a TFP index and common methods for policy evaluation, such as conditional DiD – that is, matching and DiD – in the same analysis.
The results show a negative and significant effect on both TFP and profit per employee for the whole sample. On the sector level, only wholesale
16
indicates a negative and significant effect on TFP and profit per employee. The negative effect on TFP is no longer statistically significant during the second year with a subsidy, which indicates a positive effect of on-the-job training. Conversely, profit per employee is negative, which can occur regardless of the zero effect on TFP if firms within the treated group do not manage to maximize their profit, i.e., equalize the input prices to the marginal revenue product.
Conclusions, policy implications, and future research The contributions of this thesis enrich the literature both methodologically and empirically. Implications to be given from the thesis are wide in the sense that the different essays are applications in different areas. Furthermore, some policy implications can be drawn based on the conclusions; however, notes are also provided on areas that are not considered but left for future research.
Essay I provides an overview of how TFP and its components change within the manufacturing and service sectors in Sweden before, during, and after the financial crisis of 2008–2009. The main conclusion is that TFP growth is substantially lower during the period 2007–2013, in comparison to the period 1997–2007, for both main sectors. This is driven by lower TC, i.e., a slower shift of the average production function. A similar pattern can be observed for all sub-sectors, with the exception of food, beverages, and tobacco. The conclusion is that TFP change is also affected by weaker demand during a longer period because inputs have not been flexible enough. A mechanism for why the same pattern cannot be observed in food, beverages, and tobacco is, potentially, that these goods are not as sensitive to business cycles. In contrast, sectors with a negative TFP change potentially believed that demand will increase again so inputs are not reduced to such a large extent based on this expectation. Regarding interpretation of the components, it is argued that it can be questioned whether TC, in fact, should be interpreted as frontier shift in SFA. If not, it also generates an issue in separating TC from EC. Future research should interpret separation of the components with care. Additionally, questions to be investigated in future research are the mechanisms behind the changes that directly link to future policies; i.e., determinants of the different components of efficiency as well as drivers of TC can be examined in further studies.
Essay II recommends that district courts with negative TFP could learn from those with positive TFP. This can hopefully result in positive TFP development in the future. Furthermore, it can be observed that the smallest courts have the largest volatility in TFP change, which is a source of
15
Essay V ‘The Impact of Labour Subsidies on Total Factor Productivity and Profit per Employee’ investigates the impact of labour subsidies on TFP since lower expected productivity is the motivation for subsidizing labour. Subsidizing labour is a common policy to prevent long-term unemployment. The targeted groups in Sweden are the already long-term unemployed, unemployed people with disabilities, and newly arrived immigrants. There is extensive research on wage subsidies from a labour supply perspective. However, only a few studies exist on the labour demand side in relation to subsidies, and the only study that considers the productivity effects on firms is Koski and Pajarinen (2015). Although only one study can be found regarding the productivity effects from labour subsidies, there is more research concerning the TFP effects as a result of subsidies on the other input factor of production, capital (see, e.g., Bergström, 2000; Bernini and Pellegrini, 2011; Harris and Trainor, 2005; Managi, 2010; Skuras et al., 2006). Thus, one motivation for this study is the lack of research on productivity effects regarding non-capital input subsidies.
This paper takes its point of departure from an employer’s perspective of subsidized employment and investigates in particular whether there is a change in productivity and profit per employee as a result of hiring employees with wage subsidies. The average treatment effect of the treated (ATT) is estimated on TFP measured by the Törnqvist TFP index and the profit per employee as outcomes. This estimation is performed on matched data obtained by coarsened exact matching (CEM), developed by Blackwell et al. (2010). There is only a limited literature in the area of TFP analysis that aims to investigate impacts of policy. Most of the previously mentioned studies regarding capital subsidies do not identify a treatment and control group to be compared over time. This makes it difficult to evaluate treatment effects. From a methodological point of view, Greene (2010), Bravo-Ureta et al. (2012) and Chen et al. (2014) are exceptions in SFA. Additionally, Bogetoft and Kromann (2018) combine propensity score matching with efficiency scores obtained by data envelopment analysis (DEA). Some empirical studies can also be found that use a proper impact design to explain variation in TFP due to political interventions by using a statistically estimated value of TFP (see, e.g., Bernini and Pellegrini, 2011). However, the impact analysis of policy is fundamental when evaluating interventions and deserves more attention in the TFP literature. The contribution of this paper is therefore twofold: 1) to be the first study to investigate the relationship between firm TFP and subsidized employees and 2) to propose a combination of a TFP index and common methods for policy evaluation, such as conditional DiD – that is, matching and DiD – in the same analysis.
The results show a negative and significant effect on both TFP and profit per employee for the whole sample. On the sector level, only wholesale
18
their potentials. However, it is also important to take into consideration the social cost of restructuring public service, in terms of both geographical and social proximity to the users, as well as the impact on existing staff and managers. Therefore, care needs to be taken during the ex ante process in examining whether a merger should be performed. Finally, the essay concludes that the Bogetoft and Wang (2005) model discussed in Essay III has predictive power, which gives arguments for its use prior to taking the actual merging decision. Future research should take the social cost of mergers into consideration and make a comparison to the achieved gain in order to investigate whether the merging was necessary from a cost–benefit point of view. In addition, it would be necessary to evaluate the mergers qualitatively, e.g., whether merged entities can recruit managers with higher skills. These questions are also relevant to study in other areas of the public service sector.
Essay V contributes empirically by examining the impact on firm TFP and profit per employee of hiring individuals with wage subsidies. A further contribution is the combination of the widely used methods TFP index numbers and conditional difference-in-differences (cDiD), i.e. DiD on a matched data. This is important since impacts of political interventions are crucial to evaluate for stating future policies. Empirically, the essay concludes that the subsidized employees have a negative impact on TFP, giving arguments that wage subsidies are necessary to compensate for this. Furthermore, the time-period should be considered because no TFP deficit is observed after one year with wage subsidy, which may relate to positive effects of on-the-job training. During this time-period, a negative impact on the profit per employee can, however, still be observed, which is not due to the individuals hired with subsidy and therefore nothing that should be handled by the policy makers.
A common issue with this kind of study is selection so, in spite of the difficulties, it would be interesting if subsidized individuals could be randomly assigned to firms to handle this. Additionally, a similar approach could be conducted to study whether there are changes in efficiency by incorporating the variables as determinants of efficiency in an SFA.
17
inefficiency. It is, therefore, necessary to enhance the flexibility in the Swedish district courts. One controversial solution can be to merge courts, because larger units are less affected by changes in justice demand. However, less problematic is to develop the back-up force, i.e., judges to serve more than one court, to include other personnel than judges. Peer comparisons of courts could be used in many potential aspects of the work for improving efficiency and productivity. For example, differences can be present that are not directly possible to determine in this study, such as organisational problems. This is, however, an aspect that can be taken into consideration in future research.
Essay III concludes that the potential improvements are diverse; i.e., a number of mergers appear to have large potentials to gain in efficiency as a result of the merger, and others do not seem to have any potential to gain in efficiency. This gives an indication that a large number of mergers were unnecessary from an efficiency point of view, given that only the ex ante information was available. The reason is that the negative side, i.e., the social cost, needs to be considered in a full analysis. We are confident that these results are likely to hold for other sectors, where extensive numbers of mergers have been performed without any ex ante investigation. Future research in relation to this should target other mergers, i.e., potential future mergers in different sectors where policy makers consider mergers. Additionally, this should be combined with more qualitative aspects such as the social cost aspect of merging. Another obvious extension of an ex ante examination is to evaluate the actual effects, ex post. This was performed in Essay IV.
Essay IV concludes that merging, on average, made the whole Swedish district court sector more efficient. The graphical analysis of the results indicates that the capital proxy, i.e., the office area, is the main source of difference between merged and non-merged courts. Based on this, a question as to whether a change in a sticky (fixed or semi-fixed) input in the public sector is a merger effect can be raised. For example, it is likely that a merged court would rearrange, acquire, or rent new facilities to cater to the new scale of operations. In contrast, it is less likely that an existing court would ask that their office space be reallocated for other use, even if the caseload would decrease or call for less staff. Likewise, given the staff employment conditions in the public sector, it is uncommon for an internal productivity improvement project to trigger actual reductions in the permanent staff count, especially for higher civil servants such as judges. This is an example of a ‘sticky’ input, where an increase (creation of a new unit adjusted to expected output) is easy, but a decrease (downsizing of staff or court area) is difficult or impossible.
To summarize, mergers give incentives to consider issues of modifying such fixed or semi-fixed inputs that are less likely to be changed regardless of
18
their potentials. However, it is also important to take into consideration the social cost of restructuring public service, in terms of both geographical and social proximity to the users, as well as the impact on existing staff and managers. Therefore, care needs to be taken during the ex ante process in examining whether a merger should be performed. Finally, the essay concludes that the Bogetoft and Wang (2005) model discussed in Essay III has predictive power, which gives arguments for its use prior to taking the actual merging decision. Future research should take the social cost of mergers into consideration and make a comparison to the achieved gain in order to investigate whether the merging was necessary from a cost–benefit point of view. In addition, it would be necessary to evaluate the mergers qualitatively, e.g., whether merged entities can recruit managers with higher skills. These questions are also relevant to study in other areas of the public service sector.
Essay V contributes empirically by examining the impact on firm TFP and profit per employee of hiring individuals with wage subsidies. A further contribution is the combination of the widely used methods TFP index numbers and conditional difference-in-differences (cDiD), i.e. DiD on a matched data. This is important since impacts of political interventions are crucial to evaluate for stating future policies. Empirically, the essay concludes that the subsidized employees have a negative impact on TFP, giving arguments that wage subsidies are necessary to compensate for this. Furthermore, the time-period should be considered because no TFP deficit is observed after one year with wage subsidy, which may relate to positive effects of on-the-job training. During this time-period, a negative impact on the profit per employee can, however, still be observed, which is not due to the individuals hired with subsidy and therefore nothing that should be handled by the policy makers.
A common issue with this kind of study is selection so, in spite of the difficulties, it would be interesting if subsidized individuals could be randomly assigned to firms to handle this. Additionally, a similar approach could be conducted to study whether there are changes in efficiency by incorporating the variables as determinants of efficiency in an SFA.
17
inefficiency. It is, therefore, necessary to enhance the flexibility in the Swedish district courts. One controversial solution can be to merge courts, because larger units are less affected by changes in justice demand. However, less problematic is to develop the back-up force, i.e., judges to serve more than one court, to include other personnel than judges. Peer comparisons of courts could be used in many potential aspects of the work for improving efficiency and productivity. For example, differences can be present that are not directly possible to determine in this study, such as organisational problems. This is, however, an aspect that can be taken into consideration in future research.
Essay III concludes that the potential improvements are diverse; i.e., a number of mergers appear to have large potentials to gain in efficiency as a result of the merger, and others do not seem to have any potential to gain in efficiency. This gives an indication that a large number of mergers were unnecessary from an efficiency point of view, given that only the ex ante information was available. The reason is that the negative side, i.e., the social cost, needs to be considered in a full analysis. We are confident that these results are likely to hold for other sectors, where extensive numbers of mergers have been performed without any ex ante investigation. Future research in relation to this should target other mergers, i.e., potential future mergers in different sectors where policy makers consider mergers. Additionally, this should be combined with more qualitative aspects such as the social cost aspect of merging. Another obvious extension of an ex ante examination is to evaluate the actual effects, ex post. This was performed in Essay IV.
Essay IV concludes that merging, on average, made the whole Swedish district court sector more efficient. The graphical analysis of the results indicates that the capital proxy, i.e., the office area, is the main source of difference between merged and non-merged courts. Based on this, a question as to whether a change in a sticky (fixed or semi-fixed) input in the public sector is a merger effect can be raised. For example, it is likely that a merged court would rearrange, acquire, or rent new facilities to cater to the new scale of operations. In contrast, it is less likely that an existing court would ask that their office space be reallocated for other use, even if the caseload would decrease or call for less staff. Likewise, given the staff employment conditions in the public sector, it is uncommon for an internal productivity improvement project to trigger actual reductions in the permanent staff count, especially for higher civil servants such as judges. This is an example of a ‘sticky’ input, where an increase (creation of a new unit adjusted to expected output) is easy, but a decrease (downsizing of staff or court area) is difficult or impossible.
To summarize, mergers give incentives to consider issues of modifying such fixed or semi-fixed inputs that are less likely to be changed regardless of
20
Bjurek, H. (1996). The Malmquist total factor productivity index. The Scandinavian Journal of Economics, 303-13.
Blackwell, M., Iacus, S., King, G., & Porro, G. (2010). cem: Coarsened exact matching in stata. Stata Journal, 9(4): 524-546.
Bloom, N., Lemos, R., Sadun, R., Scur, D. & van Reenen, J. (2016). International data on measuring management practices. American Economic Review, 106(5), 152-56.
Bogetoft, P. (2012). Performance benchmarking: Measuring and managing performance. New York: Springer Science & Business Media.
Bogetoft, P., & Kromann, L. (2018). Evaluating treatment effects using data envelopment analysis on matched samples: An analysis of electronic information sharing and firm performance. European Journal of Operational Research, 270(1), 302-313.
Bogetoft, P. & Otto, L. (2010). Benchmarking with Dea. Sfa. and R (Vol. 157). New York: Springer Science & Business Media.
Bogetoft, P., & Wang, D. (2005). Estimating the potential gains from mergers. Journal of Productivity Analysis, 23(2), 145–171.
Bravo-Ureta, B. E., Greene, W., & Solís, D. (2012). Technical efficiency analysis correcting for biases from observed and unobserved variables: an application to a natural resource management project. Empirical Economics, 43(1), 55-72.
Caves, D. W., Christensen, L. R. & Diewert, W. E. (1982). The economic theory of index numbers and the measurement of input, output, and productivity. Econometrica: Journal of the Econometric Society, 1393-1414.
Cerra, V. & Saxena, S. C. (2008). Growth dynamics: The myth of economic recovery. American Economic Review, 98, 439-57.
Chambers, R. G., Chung, Y. & Färe, R. (1996). Benefit and distance functions. Journal of Economic Theory, 70(2), 407-19.
Chambers, R. G. & Pope, R. D. (1996). Aggregate productivity measures. American Journal of Agricultural Economics, 78(5), 1360-65.
Charnes, A., Cooper, W. W. & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429-44.
Charnes, A., Cooper, W. W. & Rhodes, E. (1981). Evaluating program and managerial efficiency: An application of data envelopment analysis to program follow through. Management Science, 27(6), 668-97.
Chen, Y. T., Hsu, Y. C., & Wang, H. J. (2014). Treatment effect stochastic frontier models with endogenous selection (No. 14-A006). Institute of Economics, Academia Sinica, Taipei, Taiwan.
Coelli, T. J., Rao, D. S. P., O'Donnell, C. J. & Battese, G. E. (2005). An introduction to efficiency and productivity analysis. New York: Springer Science & Business Media.
19
References Abramovitz, M. (1956). Resource and output trends in the US since 1870.
American Economic Review, 46(2), 5-23. Ackerberg, D. A., Caves, K. & Frazer, G. (2015). Identification properties of
recent production function estimators. Econometrica, 83(6), 2411-51. Aczél, J. (1990). Determining merged relative scores. Journal of
Mathematical Analysis and Applications, 150(1), 20-40. Afriat, S. N. (1972). Efficiency estimation of production functions.
International Economic Review, 568-98. Aigner, D., Lovell, C. K. & Schmidt, P. (1977). Formulation and estimation of
stochastic frontier production function models. Journal of Econometrics, 6(1), 21-37.
Aigner, D. J. & Chu, S. F. (1968). On estimating the industry production function. The American Economic Review, 826-39.
Badunenko, O. & Kumbhakar, S. C. (2017). Economies of scale, technical change and persistent and time-varying cost efficiency in Indian banking: Do ownership, regulation and heterogeneity matter? European Journal of Operational Research, 260, 789-803.
Banker, R. D. & Chang, H. (2006). The super-efficiency procedure for outlier identification, not for ranking efficient units. European Journal of Operational Research, 175(2), 1311-20.
Banker, R. D., Charnes, A. & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30(9), 1078-92.
Bartelsman, E. J. & Doms, M. (2000). Understanding productivity: Lessons from longitudinal microdata. Journal of Economic Literature, 38(3), 569-94.
Bartelsman, E. J. & Wolf, Z. (2017). Measuring productivity dispersion. In Grifell-Tatjé, E., Lovell, C. K. & Sickles, R. C. (Eds.), The Oxford handbook of productivity analysis (pp. 593-624). New York: Oxford University Press.
Bauer, P. W. (1990). Decomposing TFP growth in the presence of cost inefficiency, nonconstant returns to scale, and technological progress. Journal of Productivity Analysis, 1(4), 287-99.
Bellman, R. E. (1957). Dynamic programming. Princeton, NJ: Princeton University Press.
Bergström, F. (2000). Capital subsidies and the performance of firms. Small business economics, 14(3), 183-193.
Bernini, C., & Pellegrini, G. (2011). How are growth and productivity in private firms affected by public subsidy? Evidence from a regional policy. Regional Science and Urban Economics, 41(3), 253-265.
20
Bjurek, H. (1996). The Malmquist total factor productivity index. The Scandinavian Journal of Economics, 303-13.
Blackwell, M., Iacus, S., King, G., & Porro, G. (2010). cem: Coarsened exact matching in stata. Stata Journal, 9(4): 524-546.
Bloom, N., Lemos, R., Sadun, R., Scur, D. & van Reenen, J. (2016). International data on measuring management practices. American Economic Review, 106(5), 152-56.
Bogetoft, P. (2012). Performance benchmarking: Measuring and managing performance. New York: Springer Science & Business Media.
Bogetoft, P., & Kromann, L. (2018). Evaluating treatment effects using data envelopment analysis on matched samples: An analysis of electronic information sharing and firm performance. European Journal of Operational Research, 270(1), 302-313.
Bogetoft, P. & Otto, L. (2010). Benchmarking with Dea. Sfa. and R (Vol. 157). New York: Springer Science & Business Media.
Bogetoft, P., & Wang, D. (2005). Estimating the potential gains from mergers. Journal of Productivity Analysis, 23(2), 145–171.
Bravo-Ureta, B. E., Greene, W., & Solís, D. (2012). Technical efficiency analysis correcting for biases from observed and unobserved variables: an application to a natural resource management project. Empirical Economics, 43(1), 55-72.
Caves, D. W., Christensen, L. R. & Diewert, W. E. (1982). The economic theory of index numbers and the measurement of input, output, and productivity. Econometrica: Journal of the Econometric Society, 1393-1414.
Cerra, V. & Saxena, S. C. (2008). Growth dynamics: The myth of economic recovery. American Economic Review, 98, 439-57.
Chambers, R. G., Chung, Y. & Färe, R. (1996). Benefit and distance functions. Journal of Economic Theory, 70(2), 407-19.
Chambers, R. G. & Pope, R. D. (1996). Aggregate productivity measures. American Journal of Agricultural Economics, 78(5), 1360-65.
Charnes, A., Cooper, W. W. & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429-44.
Charnes, A., Cooper, W. W. & Rhodes, E. (1981). Evaluating program and managerial efficiency: An application of data envelopment analysis to program follow through. Management Science, 27(6), 668-97.
Chen, Y. T., Hsu, Y. C., & Wang, H. J. (2014). Treatment effect stochastic frontier models with endogenous selection (No. 14-A006). Institute of Economics, Academia Sinica, Taipei, Taiwan.
Coelli, T. J., Rao, D. S. P., O'Donnell, C. J. & Battese, G. E. (2005). An introduction to efficiency and productivity analysis. New York: Springer Science & Business Media.
19
References Abramovitz, M. (1956). Resource and output trends in the US since 1870.
American Economic Review, 46(2), 5-23. Ackerberg, D. A., Caves, K. & Frazer, G. (2015). Identification properties of
recent production function estimators. Econometrica, 83(6), 2411-51. Aczél, J. (1990). Determining merged relative scores. Journal of
Mathematical Analysis and Applications, 150(1), 20-40. Afriat, S. N. (1972). Efficiency estimation of production functions.
International Economic Review, 568-98. Aigner, D., Lovell, C. K. & Schmidt, P. (1977). Formulation and estimation of
stochastic frontier production function models. Journal of Econometrics, 6(1), 21-37.
Aigner, D. J. & Chu, S. F. (1968). On estimating the industry production function. The American Economic Review, 826-39.
Badunenko, O. & Kumbhakar, S. C. (2017). Economies of scale, technical change and persistent and time-varying cost efficiency in Indian banking: Do ownership, regulation and heterogeneity matter? European Journal of Operational Research, 260, 789-803.
Banker, R. D. & Chang, H. (2006). The super-efficiency procedure for outlier identification, not for ranking efficient units. European Journal of Operational Research, 175(2), 1311-20.
Banker, R. D., Charnes, A. & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30(9), 1078-92.
Bartelsman, E. J. & Doms, M. (2000). Understanding productivity: Lessons from longitudinal microdata. Journal of Economic Literature, 38(3), 569-94.
Bartelsman, E. J. & Wolf, Z. (2017). Measuring productivity dispersion. In Grifell-Tatjé, E., Lovell, C. K. & Sickles, R. C. (Eds.), The Oxford handbook of productivity analysis (pp. 593-624). New York: Oxford University Press.
Bauer, P. W. (1990). Decomposing TFP growth in the presence of cost inefficiency, nonconstant returns to scale, and technological progress. Journal of Productivity Analysis, 1(4), 287-99.
Bellman, R. E. (1957). Dynamic programming. Princeton, NJ: Princeton University Press.
Bergström, F. (2000). Capital subsidies and the performance of firms. Small business economics, 14(3), 183-193.
Bernini, C., & Pellegrini, G. (2011). How are growth and productivity in private firms affected by public subsidy? Evidence from a regional policy. Regional Science and Urban Economics, 41(3), 253-265.
22
Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 222 , 309-68.
Førsund F. R. (2016) Productivity Interpretations of the Farrell Efficiency Measures and the Malmquist Index and Its Decomposition. In: Aparicio J., Lovell C., Pastor J. (eds) Advances in Efficiency and Productivity (pp. 121-47). International Series in Operations Research & Management Science, vol 249. Springer, Cham.
Førsund, F. R. & Hjalmarsson, L. (1974). On the measurement of productive efficiency. The Swedish Journal of Economics, 141-54.
Førsund, F. R. & Hjalmarsson, L. (1979). Generalised Farrell measures of efficiency: An application to milk processing in Swedish dairy plants. The Economic Journal, 89(354), 294-315.
Førsund, F. R. & Jansen, E. S. (1974). Average practice and best practice production function with variable scale elasticity: An empirical analysis of the structure of the Norwegian mechanical pulp industry. University of Oslo, Inst. of Economics., Oslo.
Giraleas, D., Emrouznejad, A. & Thanassoulis, E. (2012). Productivity change using growth accounting and frontier-based approaches: Evidence from a Monte Carlo analysis. European Journal of Operational Research, 222(3), 673-83.
Greene, W. (2005a). Fixed and random effects in stochastic frontier models. Journal of Productivity Analysis, 23, 7-32.
Greene, W. (2005b). Reconsidering heterogeneity in panel data estimators of the stochastic frontier model. Journal of Econometrics, 126, 269-303.
Greene, W. (2008). The econometric approach to efficiency analysis. The Measurement of Productive Efficiency and Productivity Growth, 1, 92-250.
Greene, W. (2010). A stochastic frontier model with correction for sample selection. Journal of productivity analysis, 34(1), 15-24.
Greenwald, B. C. & Stiglitz, J. E. (1986). Externalities in economies with imperfect information and incomplete markets. The Quarterly Journal of Economics, 101(2), 229-64.
Grosskopf, S. (2003). Some remarks on productivity and its decompositions. Journal of Productivity Analysis, 20(3), 459-474.
Grosskopf, S. & Valdmanis, V. (1987). Measuring hospital performance: A non-parametric approach. Journal of Health Economics, 6(2), 89-107.
Harris, R., & Trainor, M. (2005). Capital subsidies and their impact on Total Factor Productivity: Firm‐level evidence from Northern Ireland. Journal of Regional Science, 45(1), 49-74.
Hicks, J. R. (1961). The measurement of capital in relation to the measurement of other economic aggregates. In The theory of capital (pp. 18-31). Palgrave Macmillan, London.
21
Colombi, R., Kumbhakar, S. C., Martini, G. & Vittadini, G. (2014). Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency. Journal of Productivity Analysis, 42, 123-36.
Cooper, W. W., Seiford, L. M. & Tone, K. (2007). Data envelopment analysis: A comprehensive text with models, applications, references and DEA-solver software. Springer US.
De Loecker, J. & Goldberg, P. K. (2014). Firm performance in a global market. Annual Review of Economics, 6(1), 201-27.
Debreu, G. (1951). The coefficient of resource utilization. Econometrica: Journal of the Econometric Society, 273-92.
Deprins, D., Simar, L. & Tulkens, H. (1984). Measuring labor-efficiency in post offices. In: Chander P., Drèze J., Lovell C.K., Mintz J. (eds) Public goods, environmental externalities and fiscal competition (pp. 285-309). Springer, Boston, MA.
Drechsler, L. (1973). Weighting of index numbers in multilateral international comparisons. Review of Income and Wealth, 19(1), 17-34.
Efron, B. (1979). Bootstrap methods: Another look at the jackknife. The Annals of Statistics, 7(1), 1–26.
Emrouznejad, A., & Yang, G. L. (2018). A survey and analysis of the first 40 years of scholarly literature in DEA: 1978–2016. Socio-Economic Planning Sciences, 61, 4-8.
Färe, R., Grosskopf, S., Lindgren, B., & Roos, P. (1992). Productivity changes in Swedish pharmacies 1980–1989: A non-parametric Malmquist approach. Journal of productivity Analysis, 3(1-2), 85-101.
Färe, R., Grosskopf, S., Lindgren, B. & Roos, P. (1994). Productivity developments in Swedish hospitals: A Malmquist output index approach. In A. Charnes, W. W. Cooper, A. Y. Lewin & L. M. Seiford (Eds.), Data envelopment analysis: Theory, methodology, and applications (pp. 253-72). Boston: Kluwer Academic Publishers.
Färe, R., Grosskopf, S. & Lovell, C. K. (2013). The measurement of efficiency of production (Vol. 6). Springer Science & Business Media.
Färe, R., Grosskopf, S. & Whittaker, G. (2013). Directional output distance functions: Endogenous directions based on exogenous normalization constraints. Journal of Productivity Analysis, 40(3), 267-69.
Färe, R. & Primont, D. (1995). Multi-output production and duality: Theory and applications. Springer Science & Business Media.
Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal Statistical Society. Series A (General), 120(3), 253-90.
Filippini, M. & Greene, W. (2016). Persistent and transient productive inefficiency: A maximum simulated likelihood approach. Journal of Productivity Analysis, 45, 187-96.
22
Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 222 , 309-68.
Førsund F. R. (2016) Productivity Interpretations of the Farrell Efficiency Measures and the Malmquist Index and Its Decomposition. In: Aparicio J., Lovell C., Pastor J. (eds) Advances in Efficiency and Productivity (pp. 121-47). International Series in Operations Research & Management Science, vol 249. Springer, Cham.
Førsund, F. R. & Hjalmarsson, L. (1974). On the measurement of productive efficiency. The Swedish Journal of Economics, 141-54.
Førsund, F. R. & Hjalmarsson, L. (1979). Generalised Farrell measures of efficiency: An application to milk processing in Swedish dairy plants. The Economic Journal, 89(354), 294-315.
Førsund, F. R. & Jansen, E. S. (1974). Average practice and best practice production function with variable scale elasticity: An empirical analysis of the structure of the Norwegian mechanical pulp industry. University of Oslo, Inst. of Economics., Oslo.
Giraleas, D., Emrouznejad, A. & Thanassoulis, E. (2012). Productivity change using growth accounting and frontier-based approaches: Evidence from a Monte Carlo analysis. European Journal of Operational Research, 222(3), 673-83.
Greene, W. (2005a). Fixed and random effects in stochastic frontier models. Journal of Productivity Analysis, 23, 7-32.
Greene, W. (2005b). Reconsidering heterogeneity in panel data estimators of the stochastic frontier model. Journal of Econometrics, 126, 269-303.
Greene, W. (2008). The econometric approach to efficiency analysis. The Measurement of Productive Efficiency and Productivity Growth, 1, 92-250.
Greene, W. (2010). A stochastic frontier model with correction for sample selection. Journal of productivity analysis, 34(1), 15-24.
Greenwald, B. C. & Stiglitz, J. E. (1986). Externalities in economies with imperfect information and incomplete markets. The Quarterly Journal of Economics, 101(2), 229-64.
Grosskopf, S. (2003). Some remarks on productivity and its decompositions. Journal of Productivity Analysis, 20(3), 459-474.
Grosskopf, S. & Valdmanis, V. (1987). Measuring hospital performance: A non-parametric approach. Journal of Health Economics, 6(2), 89-107.
Harris, R., & Trainor, M. (2005). Capital subsidies and their impact on Total Factor Productivity: Firm‐level evidence from Northern Ireland. Journal of Regional Science, 45(1), 49-74.
Hicks, J. R. (1961). The measurement of capital in relation to the measurement of other economic aggregates. In The theory of capital (pp. 18-31). Palgrave Macmillan, London.
21
Colombi, R., Kumbhakar, S. C., Martini, G. & Vittadini, G. (2014). Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency. Journal of Productivity Analysis, 42, 123-36.
Cooper, W. W., Seiford, L. M. & Tone, K. (2007). Data envelopment analysis: A comprehensive text with models, applications, references and DEA-solver software. Springer US.
De Loecker, J. & Goldberg, P. K. (2014). Firm performance in a global market. Annual Review of Economics, 6(1), 201-27.
Debreu, G. (1951). The coefficient of resource utilization. Econometrica: Journal of the Econometric Society, 273-92.
Deprins, D., Simar, L. & Tulkens, H. (1984). Measuring labor-efficiency in post offices. In: Chander P., Drèze J., Lovell C.K., Mintz J. (eds) Public goods, environmental externalities and fiscal competition (pp. 285-309). Springer, Boston, MA.
Drechsler, L. (1973). Weighting of index numbers in multilateral international comparisons. Review of Income and Wealth, 19(1), 17-34.
Efron, B. (1979). Bootstrap methods: Another look at the jackknife. The Annals of Statistics, 7(1), 1–26.
Emrouznejad, A., & Yang, G. L. (2018). A survey and analysis of the first 40 years of scholarly literature in DEA: 1978–2016. Socio-Economic Planning Sciences, 61, 4-8.
Färe, R., Grosskopf, S., Lindgren, B., & Roos, P. (1992). Productivity changes in Swedish pharmacies 1980–1989: A non-parametric Malmquist approach. Journal of productivity Analysis, 3(1-2), 85-101.
Färe, R., Grosskopf, S., Lindgren, B. & Roos, P. (1994). Productivity developments in Swedish hospitals: A Malmquist output index approach. In A. Charnes, W. W. Cooper, A. Y. Lewin & L. M. Seiford (Eds.), Data envelopment analysis: Theory, methodology, and applications (pp. 253-72). Boston: Kluwer Academic Publishers.
Färe, R., Grosskopf, S. & Lovell, C. K. (2013). The measurement of efficiency of production (Vol. 6). Springer Science & Business Media.
Färe, R., Grosskopf, S. & Whittaker, G. (2013). Directional output distance functions: Endogenous directions based on exogenous normalization constraints. Journal of Productivity Analysis, 40(3), 267-69.
Färe, R. & Primont, D. (1995). Multi-output production and duality: Theory and applications. Springer Science & Business Media.
Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal Statistical Society. Series A (General), 120(3), 253-90.
Filippini, M. & Greene, W. (2016). Persistent and transient productive inefficiency: A maximum simulated likelihood approach. Journal of Productivity Analysis, 45, 187-96.
24
Lovell, C. K. (2003). The decomposition of Malmquist productivity indexes. Journal of Productivity Analysis, 20(3), 437-58.
Luenberger, D. G. (1992). New optimality principles for economic efficiency and equilibrium. Journal of Optimization Theory and Applications, 75(2), 221-64.
Luenberger, D. G. (1995). Microeconomic theory. New York: McGraw-Hill College.
Malmquist, S. (1953). Index numbers and indifference surfaces. Trabajos deestadística, 4(2), 209-42.
Managi, S. (2010). Productivity measures and effects from subsidies and trade: an empirical analysis for Japan's forestry. Applied Economics, 42(30), 3871-3883.
Månsson, J. (1996). Technical efficiency and ownership: The case of booking centres in the Swedish taxi market. Journal of Transport Economics and Policy, 83-93.
Meeusen, W. & van Den Broeck, J. (1977). Efficiency estimation from Cobb-Douglas production functions with composed error. International Economic Review, 435-44.
Moorsteen, R. H. (1961). On measuring productive potential and relative efficiency. The Quarterly Journal of Economics, 75(3), 451-67.
Nadiri, M. I. (1970). Some approaches to the theory and measurement of total factor productivity: A survey. Journal of Economic Literature, 8(4), 1137-77.
Nishimizu, M. & Page, J. M. (1982). Total factor productivity growth, technological progress and technical efficiency change: Dimensions of productivity change in Yugoslavia, 1965-78. The Economic Journal, 92(368), 920-36.
O’Donnell, C. J. (2012a). An aggregate quantity framework for measuring and decomposing productivity change. Journal of Productivity Analysis, 38(3), 255-72.
O’Donnell, C. J. (2012b). Alternative indexes for multiple comparisons of quantities and prices (No. WP052012). School of Economics, University of Queensland, Brisbane, Australia.
O’Donnell, C. J., Fallah-Fini, S. & Triantis, K. (2017) Measuring and analysing productivity change in a metafrontier framework. Journal of Productivity Analysis, 47, 117-28.
OECD (2015), OECD Compendium of Productivity Indicators 2015, OECD Publishing, Paris. http://dx.doi.org/10.1787/pdtvy-2015-en.
Olley, G. S. & Pakes, A. (1996). The dynamics of productivity in the telecommunications equipment industry. Econometrica, 64(6), 1263.
Paasche, H. (1874). Uber die Preisentwicklung der letzten Jahre. Jahrbiicher fur Nationalokonomie und Statistik, 23, 168.
23
Hjalmarsson, L., Kumbhakar, S. C. & Heshmati, A. (1996). DEA, DFA, and SFA: A comparison. Journal of Productivity Analysis, 7(2-3), 303-27.
Jorgenson, D. W. & Griliches, Z. (1967). The explanation of productivity change. The Review of Economic Studies, 34(3), 249-83.
Kaldor, N. (1966). Causes of the slow rate of economic growth of the United Kingdom: An inaugural lecture. Cambridge University Press.
Kapelko, M. & Oude Lansink, A. (2015). Technical efficiency and its determinants in the Spanish construction sector pre- and post-financial crisis. International Journal of Strategic Property Management, 19, 96-109.
Kemeny, J. G., Morgenstern, O. & Thompson, G. L. (1956). A generalization of the von Neumann model of an expanding economy. Econometrica, Journal of the Econometric Society, 115-35.
Koopmans T. (1951). Activity analysis of production and allocation. New York: John Wiley & Sons.
Koski, H., & Pajarinen, M. (2015). Subsidies, the shadow of death and labor productivity. Journal of Industry, Competition and Trade, 15(2), 189-204.
Krugman, P. R. (1997). The age of diminished expectations: US economic policy in the 1990s. MIT Press.
Kumbhakar, S. C. (1990). Production frontiers, panel data, and time-varying technical inefficiency. Journal of Econometrics, 46, 201-11.
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, 312-20.
Kumbhakar, S. C. & Heshmati, A. (1995). Efficiency measurement in Swedish dairy farms: An application of rotating panel data, 1976–88. American Journal of Agricultural Economics, 77, 660-74.
Kumbhakar, S. C. & Lien, G. (2017). Yardstick regulation of electricity distribution: Disentangling short-run and long-run inefficiencies. Energy Journal, 38, 17-37.
Kumbhakar, S. C., Lien, G. & Hardaker, J. B. (2014). Technical efficiency in competing panel data models: A study of Norwegian grain farming. Journal of Productivity Analysis, 41, 321-37.
Lai, H. P. & Kumbhakar, S. C. (2018). Endogeneity in panel data stochastic frontier model with determinants of persistent and transient inefficiency. Economics Letters, 162, 5-9.
Laspeyres, K. (1871). IX. Die Berechnung einer mittleren Waarenpreissteigerung. Jahrbücher für Nationalökonomie und Statistik, 16(1), 296-318.
Leibenstein, H. (1966). Allocative efficiency vs. "X-efficiency." The American Economic Review, 56(3), 392-415.
Levinsohn, J. & Petrin, A. (2003). Estimating production functions using inputs to control for unobservables. The Review of Economic Studies, 70(2), 317-41.
24
Lovell, C. K. (2003). The decomposition of Malmquist productivity indexes. Journal of Productivity Analysis, 20(3), 437-58.
Luenberger, D. G. (1992). New optimality principles for economic efficiency and equilibrium. Journal of Optimization Theory and Applications, 75(2), 221-64.
Luenberger, D. G. (1995). Microeconomic theory. New York: McGraw-Hill College.
Malmquist, S. (1953). Index numbers and indifference surfaces. Trabajos deestadística, 4(2), 209-42.
Managi, S. (2010). Productivity measures and effects from subsidies and trade: an empirical analysis for Japan's forestry. Applied Economics, 42(30), 3871-3883.
Månsson, J. (1996). Technical efficiency and ownership: The case of booking centres in the Swedish taxi market. Journal of Transport Economics and Policy, 83-93.
Meeusen, W. & van Den Broeck, J. (1977). Efficiency estimation from Cobb-Douglas production functions with composed error. International Economic Review, 435-44.
Moorsteen, R. H. (1961). On measuring productive potential and relative efficiency. The Quarterly Journal of Economics, 75(3), 451-67.
Nadiri, M. I. (1970). Some approaches to the theory and measurement of total factor productivity: A survey. Journal of Economic Literature, 8(4), 1137-77.
Nishimizu, M. & Page, J. M. (1982). Total factor productivity growth, technological progress and technical efficiency change: Dimensions of productivity change in Yugoslavia, 1965-78. The Economic Journal, 92(368), 920-36.
O’Donnell, C. J. (2012a). An aggregate quantity framework for measuring and decomposing productivity change. Journal of Productivity Analysis, 38(3), 255-72.
O’Donnell, C. J. (2012b). Alternative indexes for multiple comparisons of quantities and prices (No. WP052012). School of Economics, University of Queensland, Brisbane, Australia.
O’Donnell, C. J., Fallah-Fini, S. & Triantis, K. (2017) Measuring and analysing productivity change in a metafrontier framework. Journal of Productivity Analysis, 47, 117-28.
OECD (2015), OECD Compendium of Productivity Indicators 2015, OECD Publishing, Paris. http://dx.doi.org/10.1787/pdtvy-2015-en.
Olley, G. S. & Pakes, A. (1996). The dynamics of productivity in the telecommunications equipment industry. Econometrica, 64(6), 1263.
Paasche, H. (1874). Uber die Preisentwicklung der letzten Jahre. Jahrbiicher fur Nationalokonomie und Statistik, 23, 168.
23
Hjalmarsson, L., Kumbhakar, S. C. & Heshmati, A. (1996). DEA, DFA, and SFA: A comparison. Journal of Productivity Analysis, 7(2-3), 303-27.
Jorgenson, D. W. & Griliches, Z. (1967). The explanation of productivity change. The Review of Economic Studies, 34(3), 249-83.
Kaldor, N. (1966). Causes of the slow rate of economic growth of the United Kingdom: An inaugural lecture. Cambridge University Press.
Kapelko, M. & Oude Lansink, A. (2015). Technical efficiency and its determinants in the Spanish construction sector pre- and post-financial crisis. International Journal of Strategic Property Management, 19, 96-109.
Kemeny, J. G., Morgenstern, O. & Thompson, G. L. (1956). A generalization of the von Neumann model of an expanding economy. Econometrica, Journal of the Econometric Society, 115-35.
Koopmans T. (1951). Activity analysis of production and allocation. New York: John Wiley & Sons.
Koski, H., & Pajarinen, M. (2015). Subsidies, the shadow of death and labor productivity. Journal of Industry, Competition and Trade, 15(2), 189-204.
Krugman, P. R. (1997). The age of diminished expectations: US economic policy in the 1990s. MIT Press.
Kumbhakar, S. C. (1990). Production frontiers, panel data, and time-varying technical inefficiency. Journal of Econometrics, 46, 201-11.
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, 312-20.
Kumbhakar, S. C. & Heshmati, A. (1995). Efficiency measurement in Swedish dairy farms: An application of rotating panel data, 1976–88. American Journal of Agricultural Economics, 77, 660-74.
Kumbhakar, S. C. & Lien, G. (2017). Yardstick regulation of electricity distribution: Disentangling short-run and long-run inefficiencies. Energy Journal, 38, 17-37.
Kumbhakar, S. C., Lien, G. & Hardaker, J. B. (2014). Technical efficiency in competing panel data models: A study of Norwegian grain farming. Journal of Productivity Analysis, 41, 321-37.
Lai, H. P. & Kumbhakar, S. C. (2018). Endogeneity in panel data stochastic frontier model with determinants of persistent and transient inefficiency. Economics Letters, 162, 5-9.
Laspeyres, K. (1871). IX. Die Berechnung einer mittleren Waarenpreissteigerung. Jahrbücher für Nationalökonomie und Statistik, 16(1), 296-318.
Leibenstein, H. (1966). Allocative efficiency vs. "X-efficiency." The American Economic Review, 56(3), 392-415.
Levinsohn, J. & Petrin, A. (2003). Estimating production functions using inputs to control for unobservables. The Review of Economic Studies, 70(2), 317-41.
26
Solow, R. M. (1957). Technical change and the aggregate production function. The Review of Economics and Statistics, 312-20.
Syverson, C. (2011). What determines productivity? Journal of Economic Literature, 49(2), 326-65.
Törnqvist, L. (1936). The Bank of Finland's consumption price index. Bank of Finland Monthly Bulletin, 10.
Tsionas, E. G. & Kumbhakar, S. C. (2014). Firm heterogeneity, persistent and transient technical inefficiency: A generalized true random effects model. Journal of Applied Econometrics, 29, 110-32.
van Biesebroeck, J. (2007). Robustness of productivity estimates. The Journal of Industrial Economics, 55(3), 529-69.
von Neumann, J. (1937). Uber ein ökonomsiches Gleichungssystem und eine Verallgemeinering des Browerschen Fixpunktsatzes. In Ergebnisse Mathmatischen Kolloquiums. (Vol. 8, pp. 73-83), translated as, "A Model of General Economic Equilibrium," Review of Economic Studies, Vol. 13, No. 22, (1945-1946), pp. 1-9.
Wang, H.-J. & Schmidt, P. (2002). One-step and two-step estimation of the effects of exogenous variables on technical efficiency levels. Journal of Productivity Analysis, 18(2), 129-44.
Wheelock, D. C. & Wilson, P. W. (1999). Technical progress, inefficiency, and productivity change in US banking, 1984-1993. Journal of Money, Credit and Banking, 31(2), 212-34.
Wilson, P. W. (1993). Detecting outliers in deterministic nonparametric frontier models with multiple outputs. Journal of Business and Economic Statistics, 11(3), 319-23.
Wilson, P. W. (2017). Dimension reduction in nonparametric models of production. European Journal of Operational Research, 267(1), 349-67.
Winsten, C. B. (1957). Discussion on Mr. Farrell’s paper. Journal of the Royal Statistical Society, 120(3), 282-84.
Yatchew, A. (1998). Nonparametric regression techniques in economics. Journal of Economic Literature, 36(2), 669-721.
25
Pitt, M. M. & Lee, L. F. (1981). The measurement and sources of technical inefficiency in the Indonesian weaving industry. Journal of Development Economics, 9, 43-64.
Premachandra, I., Bhabra, G. S. & Sueyoshi, T. (2009). DEA as a tool for bankruptcy assessment: A comparative study with logistic regression technique. European Journal of Operational Research, 193(2), 412-24.
Premachandra I.M., Zhu J., Watson J., Galagedera D.U.A. (2016) Mutual Fund Industry Performance: A Network Data Envelopment Analysis Approach. In: Zhu J. (eds) Data Envelopment Analysis (pp. 165-228). International Series in Operations Research & Management Science, vol 238. Springer, Boston, MA.
Ray, S. C. & Desli, E. (1997). Productivity growth, technical progress, and efficiency change in industrialized countries: Comment. The American Economic Review, 87(5), 1033-39.
Reinsdorf, M. B., Diewert, W. E. & Ehemann, C. (2002). Additive decompositions for Fisher, Törnqvist, and geometric mean indexes. Journal of Economic and Social Measurement, 28(1, 2), 51-61.
Richmond, J. (1974). Estimating the efficiency of production. International Economic Review, 515-21.
Russell, R. R. (2018). Theoretical productivity indices . In Grifell-Tatjé, E., Lovell, C. K. & Sickles, R. C. (Eds.), The Oxford handbook of productivity analysis (pp. 153-82). New York: Oxford University Press.
SFS 2011:203. Den svenska budgetlagen, kapitel 1, 3§ [The Swedish Budget Act, Chapter 1, 3§]. Stockholm: Ministry of Justice.
Shephard, R. W. (1953). Cost and production functions. Princeton, NJ: Princeton University Press.
Shephard, R. W. (1970). The theory of cost and production functions. Princeton, NJ: Princeton University Press.
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Simar, L. (2003). Detecting outliers in frontier models: A simple approach. Journal of Productivity Analysis, 20(3), 391-424.
Simar, L. & Wilson, P. W. (2000). Statistical inference in nonparametric frontier models: The state of the art. Journal of Productivity Analysis, 13(1), 49-78.
Simar, L. & Wilson, P. W. (2007). Estimation and inference in two-stage, semi-parametric models of production processes. Journal of Econometrics, 136(1), 31-64.
Skuras, D., Tsekouras, K., Dimara, E., & Tzelepis, D. (2006). The effects of regional capital subsidies on productivity growth: A case study of the Greek food and beverage manufacturing industry. Journal of Regional Science, 46(2), 355-381.
26
Solow, R. M. (1957). Technical change and the aggregate production function. The Review of Economics and Statistics, 312-20.
Syverson, C. (2011). What determines productivity? Journal of Economic Literature, 49(2), 326-65.
Törnqvist, L. (1936). The Bank of Finland's consumption price index. Bank of Finland Monthly Bulletin, 10.
Tsionas, E. G. & Kumbhakar, S. C. (2014). Firm heterogeneity, persistent and transient technical inefficiency: A generalized true random effects model. Journal of Applied Econometrics, 29, 110-32.
van Biesebroeck, J. (2007). Robustness of productivity estimates. The Journal of Industrial Economics, 55(3), 529-69.
von Neumann, J. (1937). Uber ein ökonomsiches Gleichungssystem und eine Verallgemeinering des Browerschen Fixpunktsatzes. In Ergebnisse Mathmatischen Kolloquiums. (Vol. 8, pp. 73-83), translated as, "A Model of General Economic Equilibrium," Review of Economic Studies, Vol. 13, No. 22, (1945-1946), pp. 1-9.
Wang, H.-J. & Schmidt, P. (2002). One-step and two-step estimation of the effects of exogenous variables on technical efficiency levels. Journal of Productivity Analysis, 18(2), 129-44.
Wheelock, D. C. & Wilson, P. W. (1999). Technical progress, inefficiency, and productivity change in US banking, 1984-1993. Journal of Money, Credit and Banking, 31(2), 212-34.
Wilson, P. W. (1993). Detecting outliers in deterministic nonparametric frontier models with multiple outputs. Journal of Business and Economic Statistics, 11(3), 319-23.
Wilson, P. W. (2017). Dimension reduction in nonparametric models of production. European Journal of Operational Research, 267(1), 349-67.
Winsten, C. B. (1957). Discussion on Mr. Farrell’s paper. Journal of the Royal Statistical Society, 120(3), 282-84.
Yatchew, A. (1998). Nonparametric regression techniques in economics. Journal of Economic Literature, 36(2), 669-721.
25
Pitt, M. M. & Lee, L. F. (1981). The measurement and sources of technical inefficiency in the Indonesian weaving industry. Journal of Development Economics, 9, 43-64.
Premachandra, I., Bhabra, G. S. & Sueyoshi, T. (2009). DEA as a tool for bankruptcy assessment: A comparative study with logistic regression technique. European Journal of Operational Research, 193(2), 412-24.
Premachandra I.M., Zhu J., Watson J., Galagedera D.U.A. (2016) Mutual Fund Industry Performance: A Network Data Envelopment Analysis Approach. In: Zhu J. (eds) Data Envelopment Analysis (pp. 165-228). International Series in Operations Research & Management Science, vol 238. Springer, Boston, MA.
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