On the consistency of aggregate production frontiers

Abstract

This paper investigates the consistency of efficiency frontier methods applied at the aggregate level. We estimate eight aggregate production frontiers on a sample of 93 countries, depending on three methodological choices for the specification of the frontier: the choice of the approach technique (stochastic frontier approach or data envelopment analysis), the specification of human capital as an input, and the nature of returns to scale.

We observe some differences on the descriptive statistics of the distributions of the efficiency scores, but also a very high significant and positive correlation between scores rankings regardless of the methodological choices made. Our results tend then to suggest the consistency of the efficiency techniques at the aggregate level.

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.