Skip to main content

Advertisement

SpringerLink
Log in

Endogenous productivity: a new Bayesian perspective

  • Original Research
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

This study develops a methodology to address the endogeneity of productivity in the cost minimization framework where input demands and productivity itself depend on input prices and desirable and undesirable outputs. Specifically, we model toxic chemical releases (emissions) as an undesirable output in the production process. We apply our theoretical cost system approach to a panel data set of 2462 US manufacturing facilities over the period 1958–2007, which we estimate via Bayesian Markov Chain Monte Carlo semi-parametric methods subject to theoretical regularity conditions. The empirical findings reveal a non-linear inverted-U-shaped productivity curve concerning toxic emissions. This has important policy implications as the reduction in toxic emissions can be achieved without a decrease in productivity growth. The empirical findings are also consistent with productivity “divergence” across the U.S. manufacturing sectors and the formation of individual productivity clusters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Notes

  1. “The double-dividend hypothesis suggests that increased taxes on polluting activities can provide two kinds of benefits. The first is an improvement in the environment, and the second is an improvement in economic efficiency from the use of environmental tax revenues to reduce other taxes such as income taxes that distort labor supply and saving decisions” (Fullerton and Metcalf, 1997).

  2. We must stress though that our data do not contain information on abatement cost. One could use an alternative measure (proxy) for the estimation of the abatement rate. We can aggregate the total pounds of toxic chemicals that each facility treated, recycled, or recovered and divide this measure of abated pollution by facility-level pollution (see Simon and Prince, 2016). However, due to severe data limitations the calculation of this proxy was not possible.

  3. RTS(x) is a standard ray- based measure of returns to scale, and \(RTS(x) \equiv \sum\nolimits_{k = 1}^{K} {\frac{\partial f(x)}{{\partial x_{k} }}} \frac{{x_{k} }}{f(x)}.\) It should be noted that we do not require an independent estimate of RTS.

  4. Non-production worker hours (NPHW) are obtained by subtracting the production worker hours, from the total number of worker hours employed in each industry.

  5. We do not allow for an error term in this equation because, in this case, the system would be highly complicated by the fact that we would have random effects appearing in nonlinear form. These, in turn, must be integrated out of the likelihood function using simulation—based techniques. Moreover, from (19) we drop \(\hat{r}_{it}\).

  6. We have used fortran 77 subroutine conmax from netlib library.

  7. This definition applies to multiple outputs, say y1,…,yM.

  8. The relevant assumption though of a common translog cost function comprising of individual effects to address the heterogeneity across different industries may be valid only for firms belonging to the same sector. However, since the sample contains non-financial manufacturing facilities (plants), it is reasonable to assume that the input relative prices across the different manufacturing sectors, remain non-heterogeneous (Tsionas and Mallick, 2019).

  9. We define productivity growth as: \(\Delta \Omega_{it} = \frac{{\Omega_{it} - \Omega_{i,t - 1} }}{{\Omega_{i,t - 1} }}.\qquad \qquad \qquad (28)\)

  10. We must mention though that the inclusion of allocative inefficiency in our theoretical setup is beyond the scope of this study, since the model would be overly complicated (see for example Kumbhakar, 1997; Kumbhakar and Tsionas, 2005a,b).

  11. In a recent study, Li and Quyang, (2020), examine the nonlinear impact of technical change on green productivity in China by applying a panel smooth transition regression approach. They find a non-linear relationship between technical change and green productivity.

  12. However, since we have disaggregated data, this argument needs some refinement, as it is certain that much more technologies are used.

  13. The underlying identification test based on GMM marginal posterior densities is fully described in Tsionas and Polemis (2019).

  14. We must mention that a Bayes factor between 3 and 10 is interpreted as substantial evidence in favor of the non-parametric model (see Assaf and Tsionas, 2018).

  15. We are thankful to an anonymous referee for pointing this out.

References

  • Abad, A. (2015). An environmental generalised Luenberger-Hicks-Moorsteen productivity indicator and an environmental Generalised Hicks-Moorsteen productivity index. Journal of Environmental Management, 161, 325–334.

    Article  Google Scholar 

  • Ackerberg, D. A., Caves, K., & Frazer, G. (2015). Identification properties of recent production function estimators. Econometrica, 83(6), 2411–2451.

    Article  Google Scholar 

  • Andersen, D. C. (2020). Default risk, productivity, and the environment: theory and evidence from U.S. manufacturing. Environmental and Resource Economics, 75, 677–710.

    Article  Google Scholar 

  • Aparicio, J., Barbero, J., Kapelko, M., Pastor, J., & Zofío, J. L. (2017). Testing the consistency and feasibility of the standard Malmquist-Luenberger index: Environmental productivity in world air emissions. Journal of Environmental Management, 196, 148–160.

    Article  Google Scholar 

  • Assaf, A. G., & Tsionas, E. G. (2018). Bayes factors vs. P-values. Tourism Management, 67, 17–31.

    Article  Google Scholar 

  • Atkinson, S. E., & Cornwell, C. (1998). Estimating radial measures of productivity growth: Frontier vs non-frontier approaches. Journal of Productivity Analysis, 10(1), 35–46.

    Article  Google Scholar 

  • Baumann, U., and Vasardani, M. (2016). The slowdown in US productivity growth- What explains it and will it persist? Bank of Greece. Working paper series No 215.

  • Blanco, M., Dalton, P. S., & Vargas, J. F. (2016). Does the unemployment benefit institution affect the productivity of workers? Evidence from the Field. Management Science, 63(11), 3691–3707.

    Article  Google Scholar 

  • Bournakis, I., & Mallick, S. (2018). TFP estimation at firm level: The fiscal aspect of productivity convergence in the UK. Economic Modelling, 70, 579–590.

    Article  Google Scholar 

  • Cardarelli, R., & Lusinyan, L. (2015). U.S. Total Factor Productivity Slowdown: Evidence from the U.S. States. IMF working paper, WP/15/116.

  • Chen, C., Polemis, M., & Stengos, T. (2018). On the examination of non-linear relationship between market structure and performance in the US manufacturing industry. Economics Letters, 164(C), 1–4.

    Article  Google Scholar 

  • Chen, L., Wang, Y. M., & Lai, F. (2017). Semi-disposability of undesirable outputs in data envelopment analysis for environmental assessments. European Journal of Operational Research, 260(2), 655–664.

    Article  Google Scholar 

  • Chen, X., Huang, B., & Lin, C.-T. (2019). Environmental awareness and environmental Kuznets curve. Economic Modelling, 77, 2–11.

    Article  Google Scholar 

  • Chen, Y., & Ali, A. I. (2004). DEA Malmquist productivity measure: New insights with an application to computer industry. European Journal of Operational Research, 159(1), 239–249.

    Article  Google Scholar 

  • Cherchye, L., De Rock, B., & Walheer, N. (2015). Multi-output efficiency with good and bad outputs. European Journal of Operational Research, 240(3), 872–881.

    Article  Google Scholar 

  • Cornwell, C., Schmidt, P., & Sickles, R. C. (1990). Production Frontiers with cross-sectional and time-series variation in efficiency levels. Journal of Econometrics, 46, 185–200.

    Article  Google Scholar 

  • Dearden, L., Reed, H., & Van Reenen, J. (2006). The Impact of training on productivity and wages: Evidence from British panel data. Oxford Bulletin of Economics and Statistics, 68, 397–421.

    Article  Google Scholar 

  • Desbordes, R., & Verardi, V. (2012). Refitting the Kuznets curve. Economics Letters, 116, 258–261.

    Article  Google Scholar 

  • Diewert, W. E., & Wales, T. J. (1987). Flexible functional forms and global curvature conditions. Econometrica, 55, 43–68.

    Article  Google Scholar 

  • Doraszelski, U., & Jaumandreu, J. (2013). R&D and productivity: Estimating endogenous productivity. Review of Economic Studies, 80, 1338–1383.

    Article  Google Scholar 

  • Du, J., Duan, Y., & Xu, J. (2019). The infeasible problem of the Malmquist-Luenberger index and its application on China’s environmental total factor productivity. Annals of Operations Research, 278, 235–253.

    Article  Google Scholar 

  • Färe, R., Grosskopf, S., & Pasurka, C. (2016). Technical change and pollution abatement costs. European Journal of Operational Research, 248(2), 715–724.

    Article  Google Scholar 

  • Fernald, J. (2014). Productivity and potential output before, during, and after the great recession. In: NBER 29th annual conference on macroeconomics, retrieved from http://conference.nber.org/confer/2014/Macro14/macro14prg.html

  • Ferrara, G. & Vidoli, F. (2017). Semiparametric stochastic frontier models: A generalized additive model approach. European Journal of Operational Research, 258(2), 761–777.

    Article  Google Scholar 

  • Fullerton, D., & Metcalf, G.E. (1997). Environmental taxes and the double-dividend hypothesis: Did you really expect something for nothing?, NBER Working Papers 6199, National Bureau of Economic Research.

  • Fuss, M., McFadden, D., & Yair, M. (1978). A survey of functional forms in the economic analysis of production. In M. Fuss & D. McFadden (Eds.), Production economics: A dual approach to theory and applications, 1(4). North Holland.

    Google Scholar 

  • Genius, M., Stefanou, S., & Tzouvelekas, V. (2012). Measuring productivity growth under factor non-substitution: An application to US steam-electric power generation utilities. European Journal of Operational Research, 220(3), 844–852.

    Article  Google Scholar 

  • Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In J. M. Bernardo, J. Berger, A. P. Dawid, & A. F. M. Smith (Eds.), Bayesian statistics 4 (pp. 169–193). Oxford University Press.

    Google Scholar 

  • Girolami, M., & Calderhead, B. (2011). Riemann manifold Langevin and Hamiltonian Monte Carlo methods. Journal of the Royal Statistical Society: Series B, 73(2), 123–214.

    Article  Google Scholar 

  • Gordon, R., (2012). Is U.S. Economic growth over? Faltering innovations confronts the six headwinds, NBER working paper 18315.

  • Gordon, R. (2013). U.S. Productivity growth: the slowdown has returned after a temporary revival. International Productivity Monitor, 25, 13–19.

    Google Scholar 

  • Gray, W., & Shadbegian, R. (1995). Pollution abatement costs, regulation, and plant-level productivity, NBER working papers 4994.

  • Grifell-Tatjé, E., & Lovell, C. A. (1997). DEA-based analysis of productivity change and intertemporal managerial performance. Annals of Operations Research, 73, 177–189.

    Article  Google Scholar 

  • Halkos, G., & Polemis, M. (2018). The impact of economic growth on environmental efficiency of the electricity sector: A hybrid window DEA methodology for the USA. Journal of Environmental Management, 211, 334–346.

    Article  Google Scholar 

  • Halkos, G., & Tzeremes, N. (2013). A conditional directional distance function approach for measuring regional environmental efficiency: Evidence from UK regions. European Journal of Operational Research, 227(1), 182–189.

    Article  Google Scholar 

  • Horta, I. M., & Camanho, A. S. (2015). A nonparametric methodology for evaluating convergence in a multi-input multi-output setting. European Journal of Operational Research, 246(2), 554–561.

    Article  Google Scholar 

  • Jerzmanowski, M. (2007). Total factor productivity differences: appropriate technology vs efficiency. European Economic Review, 51, 2080–2110.

    Article  Google Scholar 

  • Jorgenson, D., Ho, M., & Stiroh, K. (2005). Growth of US industries and investments in information technology and higher education. In C. Corrado, J. Haltiwanger, & D. Sichel (Eds.), Measuring capital in the new economy (pp. 403–478). Chicago: University of Chicago Press.

    Chapter  Google Scholar 

  • Jorgenson, D. (2001). Information technology and the US economy. American Economic Review, 91(1), 1–32.

    Article  Google Scholar 

  • Jorgenson, D. W., Mun, S. H., & Stiroh, K. J. (2008). A Retrospective look at the U.S. productivity growth resurgence. Journal of Economic Perspectives, 22(1), 3–24.

    Article  Google Scholar 

  • Kapelko, M. (2019). Measuring productivity change accounting for adjustment costs: Evidence from the food industry in the European Union. Annals of Operations Research, 278, 215–234.

    Article  Google Scholar 

  • Karagiannis, G., & Lovell, C. A. K. (2016). Productivity measurement in radial DEA models with a single constant input. European Journal of Operational Research, 251(1), 323–328.

    Article  Google Scholar 

  • Kounetas, K., & Zervopoulos, P. (2019). A cross-country evaluation of environmental performance: Is there a convergence-divergence pattern in technology gaps? European Journal of Operational Research, 273(3), 1136–1148.

    Article  Google Scholar 

  • Krol, M., Brouwer, W., & Rutten, F. (2013). Productivity costs in economic evaluations: Past, present, future. PharmacoEconomics, 31(7), 537–549.

    Article  Google Scholar 

  • Krugman, P. (1994). The age of diminished expectations (3rd ed.). Cambridge: The MIT Press.

    Google Scholar 

  • Kumbhakar, S. (1997). Modeling allocative inefficiency in a translog cost function and cost-share equations: An exact relationship. Journal of Econometrics, 76(1–2), 351–356.

    Article  Google Scholar 

  • Kumbhakar, S., & Tsionas, E. (2005a). The joint measurement of technical and allocative inefficiencies: an application of Bayesian inference in nonlinear random-effects models. Journal of the American Statistical Association, 100, 736–747.

    Article  Google Scholar 

  • Kumbhakar, S., & Tsionas, E. (2005b). Measuring technical and allocative inefficiency in the translog cost system: A Bayesian approach. Journal of Econometrics, 126(2), 355–384.

    Article  Google Scholar 

  • Lee, Y., & Mukoyama, T. (2015). Productivity and employment dynamics of US manufacturing plants. Economics Letters, 136, 190–193.

    Article  Google Scholar 

  • Levinsohn, J., & Petrin, A. (2003). Estimating production functions using inputs to control for unobservables. The Review of Economic Studies, 70(2), 317–341.

    Article  Google Scholar 

  • Li, P., & Ouyang, Y. (2020). Technical change and green productivity. Environmental and Resource Economics, 76, 271–298.

    Article  Google Scholar 

  • Malikov, E., Kumbhakar, S. C., & Tsionas, M. G. (2016). A cost system approach to the stochastic directional technology distance function with undesirable outputs: the case of us banks in 2001–2010. Journal of Applied Econometrics, 31, 1407–1429.

    Article  Google Scholar 

  • Mallick, S. K., & Sousa, R. M. (2017). The skill premium effect of technological change: New evidence from the United States manufacturing. International Labour Review, 156, 113–131.

    Article  Google Scholar 

  • Mavi, N. K., & Mavi, R. K. (2019). Energy and environmental efficiency of OECD countries in the context of the circular economy: Common weight analysis for Malmquist productivity index. Journal of Environmental Management, 247, 651–661.

    Article  Google Scholar 

  • Millimet, D., List, J., & Stengos, T. (2003). The environmental Kuznets curve: Real progress or misspecified models? Review of Economics and Statistics, 85(4), 1038–1047.

    Article  Google Scholar 

  • Oliner, S. & Sichel, D. (2002). Information technology and productivity: Where are we now and where are we going? Federal reserve board finance and economic discussion series.

  • Oliner, S., Sichel, D., & Stiroh, K. (2007). Explaining a productive decade, Brookings papers on economic activity (1).

  • Olley, S., & Pakes, A. (1996). The dynamics of productivity in the telecommunications equipment industry. Econometrica, 64, 1263–1297.

    Article  Google Scholar 

  • Podinovski, V. (2019). Direct estimation of marginal characteristics of nonparametric production frontiers in the presence of undesirable outputs. European Journal of Operational Research, 279(1), 258–276.

    Article  Google Scholar 

  • Quah, D. (1993). Galton’s fallacy and tests of the convergence hypothesis. Scandinavian Journal of Economics, 95(4), 427–443.

    Article  Google Scholar 

  • Quah, D. (1996). Twin peaks: Growth and convergence in models of distribution dynamics. Economic Journal, 106(437), 1045–1055.

    Article  Google Scholar 

  • Sharma, S. C., Sylweste, K., & Margono, H. (2007). Decomposition of total factor productivity growth in U.S. states. The Quarterly Review of Economics and Finance, 47, 215–241.

    Article  Google Scholar 

  • Simon, D., & Prince, J. (2016). The effect of competition on toxic pollution releases. Journal of Environmental Economics and Management, 79, 40–54.

    Article  Google Scholar 

  • Sun, K., Kumbhakar, S. C., & Tveteras, R. (2015). Productivity and efficiency estimation: A semiparametric stochastic cost frontier approach. European Journal of Operational Research, 245(1), 194–202.

    Article  Google Scholar 

  • Sun, Y., Du, J., & Wang, S. (2020). Environmental regulations, enterprise productivity, and green technological progress: Large-scale data analysis in China. Annals of Operations Research, 290, 369–384.

    Article  Google Scholar 

  • Thanassoulis, E., Shiraz, R. K., & Maniadakis, N. (2015). A cost Malmquist productivity index capturing group performance. European Journal of Operational Research, 241(3), 796–805.

    Article  Google Scholar 

  • Tran, K. C., & Tsionas, M. (2013). GMM estimation of stochastic frontier models with endogenous regressors. Economics Letters, 118, 233–236.

    Article  Google Scholar 

  • Tsionas, M., & Andrikopoulos, A. (2020). On a high-dimensional model representation method based on Copulas. European Journal of Operational Research. https://doi.org/10.1016/j.ejor.2020.01.026

    Article  Google Scholar 

  • Tsionas, M., & Mallick, S. (2019). A Bayesian semiparametric approach to stochastic frontiers and productivity. European Journal of Operational Research, 274(1), 391–402.

    Article  Google Scholar 

  • Tsionas, M., & Polemis, M. (2019). On the estimation of total factor productivity: A novel Bayesian nonparametric approach. European Journal of Operational Research, 277(3), 886–902.

    Article  Google Scholar 

  • Walheer, B. (2016). Growth and convergence of the OECD countries: A multi-sector production-frontier approach. European Journal of Operational Research, 252(2), 665–675.

    Article  Google Scholar 

  • Wu, Y., & P., Sun, J., Chu, J., & Liang, L. (2016). Evaluating the environmental efficiency of a two-stage system with undesired outputs by a DEA approach: An interest preference perspective. European Journal of Operational Research, 254(3), 1047–1062.

    Article  Google Scholar 

  • Yang, H., & Pollitt, M. (2009). Incorporating both undesirable outputs and uncontrollable variables into DEA: The performance of Chinese coal-fired power plants. European Journal of Operational Research, 197(3), 1095–1105.

    Article  Google Scholar 

Download references

Acknowledgements

We would like to thank Endre Boros (Editor-in-Chief) for allowing us to revise and improve our work both in substance and presentation. We also thank two anonymous referees of this journal for constructive comments and suggestions that enhanced the merit of the paper. The authors are responsible for any possible errors. The usual disclaimer applies.

Author information

Authors and Affiliations

  1. Department of Economics, University of Piraeus, 185 34, Piraeus, Greece

    Michael L. Polemis

  2. Hellenic Competition Commission, Athens, Greece

    Michael L. Polemis

  3. Hellenic Open University, Patras, Greece

    Michael L. Polemis

  4. Montpellier Business School, Montpellier, France

    Mike G. Tsionas

  5. Lancaster University Management School, Lancaster, United Kingdom

    Mike G. Tsionas

Authors
  1. Michael L. Polemis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mike G. Tsionas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael L. Polemis.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Polemis, M.L., Tsionas, M.G. Endogenous productivity: a new Bayesian perspective. Ann Oper Res 318, 425–451 (2022). https://doi.org/10.1007/s10479-021-04514-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-021-04514-1

Keywords

JEL Classification

Search

Navigation