Public and private inputs in aggregate production and growth: a cross-country efficiency approach

Abstract

In a cross section of OECD countries, we replace the macroeconomic production function by a production possibility frontier, total factor productivity being the composite effect of efficiency scores and possibility frontier changes. We consider, for the periods 1970, 1980, 1990 and 2000 one output – GDP per worker – and three inputs – human capital, public physical capital per worker and private physical capital per worker. We use a semi-parametric analysis, computing Malmquist productivity indexes, and we also resort to stochastic frontier analysis. Results show that private capital is important for growth, although public and human capital also contribute positively. A governance indicator, a nondiscretionary input, explains inefficiency. Better governance helps countries to achieve a better performance. Nonparametric and parametric results coincide rather closely on the movements of the countries vis-à-vis the possibility frontier and on their relative distances to the frontier.

Keywords:

• economic growth
• public spending
• efficiency
• data envelopment analysis
• Malmquist index

JEL Classification:

• C14
• D24

Acknowledgements

We are grateful to Jürgen von Hagen, Geraint Johnes, Martin Larch, Ad van Riet and Emmanuel Thanassoulis, participants at DG ECFIN Workshop ‘The Quality of Public Finances and Economic Growth’ (Brussels), 3rd Meeting of the Portuguese Economic Journal (Funchal), 3rd Workshop on Efficiency and Productivity Analysis (Porto) and 37th Eastern Economic Association Annual Meetings (New York), and to two anonymous referees for helpful comments and suggestions on previous versions. The opinions expressed herein are those of the authors and do not necessarily reflect those of the ECB or the Eurosystem. UECE is financed by FCT (Fundação para a Ciência e a Tecnologia) under Strategic Project PEst-E/EGE/UI0436/2011.

Appendix A: Data

Appendix B: Additional Estimates

Table 9. Table A2. Descriptive statistics

Table 10. Table B1. Output-oriented DEA VRS technical efficiency scores (output: GDP per employee; inputs: private and public capital)

Table 11. Table B2. Malmquist efficiency, technology and total factor productivity change indices (output-oriented: 1970–2000; output; GDP; inputs: private and public capital)

Table 12. Table B3. Output-oriented DEA VRS technical efficiency scores (output: GDP per employee; inputs: total capital and human capital)

Table 13. Table B4. Malmquist efficiency, technology and total factor productivity change indices (output-oriented: 1970–2000; output; GDP; inputs: total capital and human capital)

Table 14. Table B5. Stochastic frontier estimation results (without time trend)

Table 15. Table B6. SFA efficiency scores (without time trend)

Table 16. Data codes and sources

Notes

1. Aschauer (1989), Barro and Sala i Martin (1995).

2. Recall that the widely used Cobb–Douglas production function imposes simultaneously a log-linear functional form and a unit elasticity of factor substitution and constant returns to scale.

3. For instance, Baldacci et al. (2004) argue that governance-related factor productivity responses increase growth, while Afonso and Jalles (2011) report a positive effect on growth stemming from institutional quality.

4. Coelli et al. (2002) and Thanassoulis (2001) offer introductions to DEA.

5. We present here the most important features. See Coelli et al. (2002) for a more detailed explanation.

6. Australia, Austria, Belgium, Canada, Germany, Denmark, Spain, Finland, France, UK, Greece, Ireland, Italy, Japan, Netherlands, Norway, Portugal, Sweden and USA.

7. Using output, private and public capital per employee implicitly assumes constant returns to scale in physical capital and labour and has been a common strategy in the related literature (e.g. Kumar and Russell, 2002; Krüger, 2003; Henderson and Russell, 2005; Delgado-Rodríguez and Álvarez-Ayuso, 2008, use physical capital per worker). From a technical point, with this hypothesis, one less input is used so that the occurence of efficiency by default in DEA is less likely and degrees of freedom in econometric estimations are increased.

8. DEA scores and Malmquist index computations were done with the software Win4DEAP, written by Tim Coelli. http://www.umoncton.ca/desliem/dea/

9. Our results cannot easily be compared to the ones reported, for instance, by Kumar and Russell (2002) since such study covered a different time span (1965–1990) and most importantly mixed both developed and developing contries. Indeed, in that study, several developing countries show up in the efficiency frontier, raising the issue of country nonheterogeneity. On the other hand, the study of Krüger (2003), for the period 1960 to 1990, while not providing country-specific results, reports that technological progress occurred for the OECD countries.

10. Delgado-Rodríguez and Álvarez-Ayuso (2008) followed a similar procedure but did not impose the unit sum restriction.

11. The model is estimated by maximum likelihood using the software Frontier, version 4.1c, written by Tim Coelli, available at http://www.uq.edu.au/economics/cepa/frontier.htm

12. In the Appendix, we report additional SFA estimations without considering a time trend, which confirm these results.

13. Using only SFA-related analysis for the period 1908 to 1990 and not splitting the capital input into private and public components, Koop et al. (2000) report that the most efficient countries are the Netherlands, Canada, Belgium, Australia, Luxembourg and USA.

14. The shorter timespan availability for the government effectiveness variable prevents us from using it directely in the estimation of Equation 9.