Interfaces with Other DisciplinesOn the consistency of aggregate production frontiers
Introduction
There is an extensive amount of literature devoted to the application of efficiency frontiers at the aggregate level. Indeed, following the numerous applications at the firm level, in particular in banking and public utilities, the methodology of efficiency frontiers is currently adopted to measure the macroeconomic performance of countries in the aim to analyze the impact of various macroeconomic or institutional variables on macroeconomic performance (e.g. Adkins et al. (2002) for the economic and political freedom, Nourzad (2002a) for real money balances, Méon and Weill (forthcoming) for corruption), or to assess the macroeconomic performance of countries (e.g. Moroney and Lovell, 1997, Koop et al., 2000, to compare the performance of market and planned economies).
The advantages of such a methodology are obvious, as it provides sophisticated performance measures, the efficiency scores, that are synthetic and relative measures of performance. Unlike basic productivity measures, these techniques present the advantage of the inclusion of several input and output dimensions in the evaluation of performances. Furthermore, they allow the assumption of variable returns-to-scale, allowing to disentangle the scale effects from the pure efficiency effects.
A quite surprising aspect of this literature is that no application of aggregate production frontiers has taken into consideration the possible lack of consistency of the frontier methods at the aggregate level. However, the results obtained in the applications of aggregate production frontiers might be sensitive to the adopted methodological choices. Indeed, robustness of the efficiency frontiers can be suspicious in three aspects.
Firstly, there exists several techniques to measure the frontier efficiency, notably data envelopment analysis (DEA) and the stochastic frontier analysis (SFA), which have three main differences.1 The first—and major difference—between these both techniques deals with the adopted tools to measure the efficiency scores. DEA uses linear programming techniques, whereas SFA applies econometric tools. The second difference concerns the decomposition of the distance to the frontier for each observation: while DEA considers the entire distance to the frontier as inefficiency, resulting in the inclusion of exogenous events in the inefficiency term, SFA disentangles this distance between a random error, taking into account exogenous events, and an inefficiency term. The third difference is based on the fact that SFA requires to assume a functional form for the frontier, unlike DEA that allows the frontier to envelop tightly the data.
Because of these differences, the frontier efficiency methods might provide various results. Literature in banking provides ambiguous evidence on the robustness of these techniques when applied to measure efficiency of banks: while Ferrier and Lovell, 1990, Resti, 1997 conclude to a very high rank correlation of scores between SFA and DEA, Bauer et al., 1998, Weill, 2004 observe no correlation between the rankings of efficiency scores provided by SFA and DEA. The analysis of the consistency of the frontier techniques at the aggregate level is therefore a relevant issue, as most studies use SFA without taking care of the robustness of the efficiency scores estimated with this approach.
Secondly, there may also exist large differences in the efficiency scores, depending on the choice of the inputs and outputs. At the aggregate level, there is a consensus on the use of national income as the only output. However the choice of the inputs is more ambiguous, with in particular the question of the inclusion of the human capital. Some studies use human capital as an input of the production frontier next to capital and labor (e.g. Adkins et al., 2002), some do not (Moroney and Lovell, 1997). It might then happen that this inclusion affects the ranking of countries’ efficiency scores and therefore the conclusions extracted from the applications of aggregate production frontiers.
Finally, another difference in the applications comes from the nature of returns-to-scale. Some consider that “at the aggregate (economy-wide) level, constant returns-to-scale is virtually compelling” (Moroney and Lovell, 1997, p. 1086). Many others including Adkins et al., 2002, Nourzad, 2002a use variable returns-to-scale.
In this paper, we compute efficiency scores on a large set of countries. We estimate eight aggregate production frontiers, depending on three methodological choices for the specification of the frontier: the choice of the estimation technique (SFA or DEA), the specification of human capital as an input, and the nature of returns-to-scale. We then compare the properties of the distributions of the efficiency scores, and proceed to the analysis of the correlations of the rankings of the efficiency scores. The structure of the paper is as follows. Section 2 presents the methodology. Section 3 develops the empirical results. Finally, we provide some concluding remarks in Section 4.
Section snippets
Methodology
Data are extracted from the Growth Development Network database of the World Bank. We use data for 93 countries, both developed and developing, for 1990.2 Output (Y) is measured as GDP in
Results
This section presents the results of the estimations of efficiency scores. We first display the maximum likelihood estimates obtained with SFA in Table 2. All parameter estimates are significant at the 1% level. As the estimate of γ indicates the proportion of the variance of the inefficiency term in the total variance of the composed error term ε, a higher estimate of γ means greater inefficiencies. Therefore, the large value of γ suggests that most of the deviation from the production
Conclusion
The increasing amount of literature devoted to the application of frontier techniques at the aggregate level raises the problem of the consistency of these techniques. This study has then proceeded to the methodological cross-checking of frontier methods at the aggregate level. We have investigated the influence of the frontier method, using parametric SFA and non-parametric DEA, the introduction of human capital as an input, estimating production frontiers with and without this input, the
List of countries
Algeria, Argentina, Australia, Austria, Burundi, Belgium, Benin, Bangladesh, Bulgaria, Bolivia, Brazil, Cameroon, Canada, Central African Republic, Chile, China, Congo (Republic of), Colombia, Costa Rica, Cyprus, Denmark, Dominican Republic, Ecuador, Egypt, El Salvador, Finland, Fiji, France, Gambia, Germany, Ghana, Greece, Guatemala, Guinea-Bissau, Guyana, Hong Kong, Honduras, Hungary, Iceland, Indonesia, India, Iran, Ireland, Israel, Italy, Jamaica, Japan, Jordan, Kenya, Korea, Lesotho,
Acknowledgment
I would like to thank an anonymous referee for helpful comments, and Pierre-Guillaume Méon and Christophe Godlewski for their help.
References (18)
- et al.
Consistency conditions for regulatory analysis of financial institutions: A comparison of frontier efficiency methods
Journal of Economics and Business
(1998) - et al.
Measuring efficiency of decision making units
European Journal of Operations Research
(1978) - et al.
Measuring cost efficiency in banking: Econometric and linear programming evidence
Journal of Econometrics
(1990) - et al.
On the estimation of technical inefficiency in the stochastic frontier production function model
Journal of Econometrics
(1982) Real money balances and production efficiency: A panel-data stochastic production frontier study
Journal of Macroeconomics
(2002)Evaluating the cost-efficiency of the Italian banking system: What can be learned from the joint application of parametric and non-parametric techniques
Journal of Banking and Finance
(1997)- et al.
Institutions, freedom, and technical efficiency
Southern Economic Journal
(2002) - et al.
Some models for estimating technical and scale inefficiencies in data envelopment analysis
Management Science
(1984) - et al.
A model for technical inefficiency effects in a stochastic production frontier for panel data
Empirical Economics
(1995)
Cited by (7)
Does Islamic banking development favor macroeconomic efficiency? Evidence on the Islamic finance-growth nexus
2015, Economic ModellingCitation Excerpt :An alternative technique based on linear programming tools, namely, DEA (Data Envelopment Analysis), could also be applied to estimate the production frontier. However, in the process of comparing the efficiency scores that are obtained using the stochastic frontier approach and DEA at the macroeconomic level, Weill (2006) has shown that the efficiency measures are robust with respect to the choice of the frontier technique. Notably, he shows a very high positive correlation between the rankings of the efficiency scores of both approaches, which supports the view that the choice of the frontier technique should not influence the results of any study looking at the determinants of macroeconomic efficiency.
Cost efficiency of the Chinese banking sector: A comparison of stochastic frontier analysis and data envelopment analysis
2014, Economic ModellingCitation Excerpt :Additionally, we find that there is a smaller difference between the distributional characteristics of the cost efficiency scores estimated by DEA and New DEA than that between any DEA and SFA. In summary, while we observe some differences in the distributional properties of the efficiency scores provided by the three models, such differences may result from the various underlying assumptions on which the methods are based and may not necessarily represent any intrinsic problems with the efficiency scores themselves (Weill, 2006). On the other hand if the different frontier techniques can generate a similar rank order of cost efficiency scores, then the regulatory authorities may be able to draw some important policy conclusions from the analysis of the cost efficiency scores.
Does financial intermediation matter for macroeconomic performance?
2010, Economic ModellingCorruption and total factor productivity: Level or growth effects?
2011, Portuguese Economic JournalFinancial intermediation and macroeconomic efficiency
2010, Applied Financial EconomicsInvestor protection and macroeconomic efficiency
2009, Revue Economique