Skip to main content

TFP growth and its determinants: a model averaging approach


Total Factor Productivity (TFP) accounts for a sizable proportion of the income differences across countries. Two challenges remain to researchers aiming to explain these differences: on the one hand, TFP growth is hard to measure empirically; on the other hand, model uncertainty hampers consensus on its key determinants. This paper combines a non-parametric measure of TFP growth with Bayesian model averaging techniques in order to address both issues. Our empirical findings suggest that the most robust TFP growth determinants are time-invariant unobserved heterogeneity and trade openness. We also investigate the main determinants of two TFP components: efficiency change (i.e., catching up) and technological progress.

This is a preview of subscription content, access via your institution.


  1. 1.

    In order to apply the method to our panel of countries, we consider the panel data version of the approach discussed in Moral-Benito (2012).

  2. 2.

    Only the country-specific effects are robust determinants of both TFP components, giving support to the importance of unobserved heterogeneity at the country level in TFP growth rates.

  3. 3.

    Details on the estimation of production frontiers by means of DEA can be found in Chapter 6 of Coelli et al. (1998).

  4. 4.

    For the sake of brevity we do not present here the results but are available from the authors upon request.

  5. 5.

    Following Färe et al. (1994), each of the distance function terms in equation (1) can be calculated with a linear programming-based DEA approach and combined to form the overall Malmquist TFP index.

  6. 6.

    The list of countries, which includes 20 OECD and 47 non-OECD countries, is provided in Table 1.

    Table 1 List of countries
  7. 7.

    For instance, in this respect we only include one indicator of trade openness. These concerns are also echoed by Kraay and Tawara (2010) in a different context.

  8. 8.

    For example, the TFP growth indices for Algeria and Argentina are, respectively, 0.9991 and 1.008. Although these numbers are very similar, translated into growth terms, they indicate that while Algeria’s TFP performance is characterized by a yearly decline of 0.09 % on average, Argentina shows an average TFP growth of 0.18 % each year.

  9. 9.

    Kumar and Russell (2002) and Suhariyanto and Thirtle (2001) also found Mexico to be technically efficient.

  10. 10.

    This situation resembles the literature on growth regressions since it is not clear which empirical specification must be preferred a priori.

  11. 11.

    Note also that the number of models to be estimated in the BMA setting is enormous and might be intractable in practice. In this paper, we consider the MC\(^3\) algorithm in order to overcome this computational issue (see Koop 2003).

  12. 12.

    This prior is a multivariate normal with mean the MLE of the parameters and variance the inverse of the expected Fisher information matrix for one observation.

  13. 13.

    For ease of interpretation we include \(\eta _i\) as a component of the error term but it can also be interpreted as a country-specific constant within the traditional fixed effects approach.

  14. 14.

    Since specification tests within the BMA setting are not available in the literature, we consider the estimates from the full model with all the candidate regressors included to conduct the specification tests in this section.

  15. 15.

    We also check this conclusion in Sect. 4.1 based on a Hausman test, and looking at the posterior inclusion probability of the country dummies as a whole.

  16. 16.

    Note that including some of these time invariant variables in our setting would require an additional identifying assumption, namely, independence between such regressors and the effects.

  17. 17.

    Note that the results in Table 5 for the case of uniform priors on the model space remain qualitatively unaltered when using the dilution priors (e.g., George 1999; Durlauf et al. 2008). In contrast to the uniform prior, the dilution prior assigns uniform probability to neighborhoods rather than models taking into account the correlations among regressors.

  18. 18.

    Note that this result also emerges in the subsamples of OECD and non-OECD countries; however, to save space these results are not reported but are available upon request.

  19. 19.

    Sala-i-Martin et al. (2004) note that in most cases, having a ratio of posterior mean to posterior standard deviation around two in absolute value indicates an approximate 95 % Bayesian coverage region that excludes zero.

  20. 20.

    The significant and negative coefficient on initial GDP gives evidence in favor of a convergence effect in the evolution of TFP across countries. Growth rates of TFP in poorer countries tend to be higher than in richer countries.


  1. Abramovitz M (1956) Resources and output trends in the United States since 1870. Am Econ Rev 46:5–23

    Google Scholar 

  2. Acemoglu D (2010) When does labor scarcity encourage innovation? J Polit Econ 118:1037–1078

    Article  Google Scholar 

  3. Acemoglu D, Johnson S, Robinson J (2001) The colonial origins of comparative development: an empirical investigation. Am Econ Rev 91:1369–1401

    Article  Google Scholar 

  4. Badunenko O, Henderson D, Zelenyuk V (2008) Technological change and transition: relative contributions to worldwide growth during the 1990s. Oxf Bull Econ Stat 70:461–492

    Article  Google Scholar 

  5. Barro R (1991) Economic growth in a cross section of countries. Q J Econ 106:407–443

    Article  Google Scholar 

  6. Beaudry P, Green D (2002) Population growth, technological adoption, and economic outcomes in the information era. Rev Econ Dyn 5:749–774

    Article  Google Scholar 

  7. Benhabib J, Spiegel M (1994) The role of human capital in economic development: evidence from aggregate cross-country data. J Monet Econ 34:143–174

    Article  Google Scholar 

  8. Benhabib J, Spiegel M (2005) Human capital and technology diffusion. In: Aghion P, Durlauf S (eds) Handbook of economic growth, vol 4. North Holland, Elsevier, Amsterdam

    Google Scholar 

  9. Brock W, Durlauf S (2001) Growth empirics and reality. World Bank Econ Rev 15:229–272

    Article  Google Scholar 

  10. Caselli F (2005) Accounting for cross-country income differences. In: Aghion P, Durlauf S (eds) Handbook of economic growth, vol 1. North Holland, Elsevier, Amsterdam

    Google Scholar 

  11. Caves D, Christensen L, Diewert W (1982a) The economic theory of index numbers and measurement of input, output and productivity. Econometrica 50:1393–1414

    Article  Google Scholar 

  12. Caves D, Christensen L, Diewert W (1982b) Multilateral comparison of output, input and productivity using superlative index numbers. Econ J 92:73–86

    Article  Google Scholar 

  13. Ciccone A, Jarocinski M (2010) Determinants of economic growth: will data tell? Am Econ J: Macroecon 4:222–246

    Google Scholar 

  14. Coelli T, Rao D, Battese G (1998) An introduction to efficiency and productivity analysis. Kluwer, Boston

    Book  Google Scholar 

  15. Collins S, Bosworth B (1996) Economic growth in East Asia: accumulation versus assimilation. Brookings Pap Econ Act 2:135–203

    Article  Google Scholar 

  16. Daraio C, Simar L (2007) Advanced robust and nonparametric methods in efficiency analysis: methodology and applications. Springer, New York

    Google Scholar 

  17. De Long B, Summers L (1991) Equipment investment and economic growth. Q J Econ 106:445–502

    Article  Google Scholar 

  18. Durlauf S, Kourtellos A, Tan C (2008) Are any growth theories robust? Econ J 118:329–346

    Article  Google Scholar 

  19. Easterly W (1993) How much do distortions affect growth? J Monet Econ 32:187–212

    Article  Google Scholar 

  20. Easterly W, Levine R (2001) It’s not factor accumulation: stylized facts and growth models. World Bank Econ Rev 15:177–219

    Article  Google Scholar 

  21. Eaton J, Kortum S (2001) Technology, trade, and growth: a unified framework. Eur Econ Rev 45:742–755

    Article  Google Scholar 

  22. Eicher T, Papageorgiou C, Raftery A (2011) Default priors and predictive performance in Bayesian Model Averaging, with application to growth determinants. J Appl Econom 26:30–55

    Article  Google Scholar 

  23. Färe R, Grosskopf S, Norris S, Zhang Z (1994) Productivity growth, technical progress, and efficiency change in industrialized countries. Am Econ Rev 84:66–83

    Google Scholar 

  24. Fernandez C, Ley E, Steel M (2001) Model uncertainty in cross-country growth regressions. J Appl Econom 16:563–576

    Article  Google Scholar 

  25. Gallup J, Mellinger A, Sachs J (1999) Geography datasets. Center for International Development at Harvard University (CID)

  26. George E (1999) Discussion of Bayesian model averaging and model search strategies. In: Bernardo J, Berger A, Dawid P (eds) Bayesian statistics. Oxford University Press, Oxford

    Google Scholar 

  27. Grossman G, Helpman E (1991) Innovation and growth in the global economy. MIT Press, Cambridge

    Google Scholar 

  28. Hall R, Jones C (1999) Why do some countries produce so much more output per worker than others? Q J Econ 114:83–116

    Article  Google Scholar 

  29. Helpman E, Rangel A (1999) Adjusting to a new technology: experience and training. J Econ Growth 4:359–383

    Article  Google Scholar 

  30. Isaksson A (2007) Determinants of total factor productivity: a literature review. Research and Statistics Staff Working Paper 2/2007, United Nations Industrial Development Organization, Vienna

  31. Klenow P, Rodriguez-Clare A (1997) The neoclassical revival in growth economics: has it gone too far? NBER Macroeconomics Annual 12:73–102

    Google Scholar 

  32. Kneller R, Stevens P (2006) Frontier technology and absorptive capacity: evidence from OECD manufacturing industries? Oxf Bull Econ Stat 68:1–21

    Article  Google Scholar 

  33. Koop G (2003) Bayesian econometrics. Wiley, New York

    Google Scholar 

  34. Koop G, Osiewalski J, Steel M (1999) The components of output growth: a stochastic frontier analysis. Oxf Bull Econ Stat 61:455–487

    Article  Google Scholar 

  35. Kraay A, Tawara N (2010) Can disaggregated indicators identify governance reform priorities? World Bank Policy Research Working Paper 5254

  36. Krüger J (2003) The global trends of total factor productivity: evidence from the nonparametric Malmquist index approach. Oxf Econ Pap 55:265–286

    Article  Google Scholar 

  37. Krugman P (1994) The age of diminishing expectations: US Economic Policy in the 1990s. MIT Press, Cambridge

    Google Scholar 

  38. Kumar S, Russell R (2002) Technological change, technological catch-up, and capital deepening: relative contributions to growth and convergence. Am Econ Rev 92:527–548

    Article  Google Scholar 

  39. Makiela K (2009) Economic growth decompositon. An empirical analysis using Bayesian frontier approach. Cent Eur J Econ Model Econom 1:333–369

    Google Scholar 

  40. Malmquist S (1953) Index numbers and indifference surfaces. Trabajos de Estadistica y de Investigacion Operativa 4:209–242

    Article  Google Scholar 

  41. Miller S, Upadhyay M (2000) The effects of openness, trade orientation, and human capital on total factor productivity. J Dev Econ 63:399–423

    Article  Google Scholar 

  42. Moral-Benito E (2011) Model averaging in economics. Working Paper Bank of Spain 1123

  43. Moral-Benito E (2012) Determinants of economic growth: a Bayesian panel data approach. Rev Econ Stat 94:566–579

    Article  Google Scholar 

  44. Nehru V, Dhareshwar A (1993) A new database on physical capital stock: sources, methodology and results. Revista de Analisis Economico 8:37–59

    Google Scholar 

  45. Pesaran H (2004) General diagnostic tests for cross section dependence in panels. Cambridge Working Papers in Economics 0435, University of Cambridge

  46. Porter M, Stern S (2000) Measuring the ‘ideas’ production function: evidence from international patent output. NBER Working Paper, 7891

  47. Raftery A (1995) Bayesian model selection in social research. Sociol Methodol 25:111–163

    Article  Google Scholar 

  48. Romer P (1990) Endogenous technological change. J Polit Econ 98:71–102

    Article  Google Scholar 

  49. Sala-i-Martin X, Doppelhofer G, Miller R (2004) Determinants of long-term growth: a Bayesian averaging of classical estimates (BACE) approach. Am Econ Rev 94:813–835

    Article  Google Scholar 

  50. Simar L (2003) Detecting outliers in frontier models: a simple approach. J Prod Anal 20:391–424

    Article  Google Scholar 

  51. Solow R (1957) Technical change and the aggregate production function. Rev Econ Stat 39:312–320

    Article  Google Scholar 

  52. Suhariyanto K, Thirtle C (2001) Asian agricultural productivity and convergence. J Agric Econ 52:96–110

    Article  Google Scholar 

  53. Valdes B (1999) Economic growth: theory, empirics and policy. Edward Elgar, Gloucester and Northampton

    Google Scholar 

  54. Vandenbussche J, Aghion P, Meghir C (2006) Growth, distance to frontier and composition of human capital. J Econ Growth 11:97–127

    Article  Google Scholar 

  55. Wallich H (1969) Money and growth: a country cross-section analysis. J Money Credit Bank 1:281–302

    Article  Google Scholar 

  56. Wooldridge J (2002) Econometric analysis of cross section and panel data. MIT Press, Cambridge

    Google Scholar 

Download references


We would like to thank Atsu Amegashie, Cristian Bartolucci, Joan Llull, and Jonathan Temple for helpful comments and suggestions. We also thank an Associate Editor and two anonymous referees for insightful suggestions that led to a substantial improvement of the paper.

Author information



Corresponding author

Correspondence to Enrique Moral-Benito.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Danquah, M., Moral-Benito, E. & Ouattara, B. TFP growth and its determinants: a model averaging approach. Empir Econ 47, 227–251 (2014).

Download citation


  • Bayesian model averaging
  • Productivity
  • Nonparametric methods

JEL Codes

  • O47
  • C11
  • C14
  • C23