Robin C. Sickles

Production Frontiers and Panel Data

This article considers estimation of a stochastic frontier production function-the type introduced by Aigner, Lovell, and Schmidt (1977) and Meeusen and van den Broeck (1977). Such a production frontier model consists of a production function of the usual regression type but with an error term equal to the sum of two parts. The first part is typically assumed to be normally distributed and represents the usual statistical noise, such as luck, weather, machine breakdown, and other events beyond the control of the firm. The second part is nonpositive and represents technical inefficiencythat is, failure to produce maximal output, given the set of inputs used. Realized output is bounded from above by a frontier that includes the deterministic part of the regression, plus the part of the error representing noise; so the frontier is stochastic. There also exist socalled deterministic frontier models, whose error term contains only the nonpositive component, but we will not consider them here (e.g., see Greene 1980). Frontier models arise naturally in the problem of efficiency measurement, since one needs a bound on output to measure efficiency. A good survey of such production functions and their relationship to the measurement of productive efficiency was given by F0rsund, Lovell, and Schmidt (1980).

A Comparison of the Performance of Three Flexible Functional Forms

When selecting a functional form for use in empirical work, one is confronted by a choice between forms that exhibit good behavior globally and those that possess flexibility. Relatively simple forms, such as Cobb-Douglas and CES, satisfy certain regularity conditions globally, but the very simplicity that guarantees global good behavior also prevents such forms from modelling very sophisticated technologies. On the other hand, relatively complex forms having the flexibility to model fairly sophisticated technologies have been developed, but their very flexibility prevents them from being well-behaved globally. The current trend is clearly toward the development and use of flexible forms which, although not globally well-behaved, may nonetheless satisfy the desired regularity conditions over a range of observations that contain or intersect the set of sample observations. In light of their inability to satisfy regularity conditions globally, and in light of the substantial econometric sophistication required in their estimation, it is worthwhile investigating just how well various flexible forms do model technology. This can be accomplished in a number of ways. Berndt, Darrough and Diewert [1977] simply fitted three flexible forms translog, generalized Leontief and generalized Cobb-Douglas to postwar Canadian expenditure data, and found the translog model to be preferred on Bayesian grounds a posteriori. Applebaum [1979] and Berndt and Khaled [1979] developed generalized Box-Cox forms that contain the translog, generalized Leontief, and generalized square root quadratic forms as special or limiting cases. Using 1929-1971 U. S. manufacturing data, Applebaum found that the generalized Leontief and generalized square root quadratic forms the best representations for the primal and dual specifications of technology. Using 1947-1971 U. S. manufacturing data, Berndt and Khaled were able to reject the generalized square root quadratic restriction, but unable to reject the generalized Leontief restriction; tests concerning the translog restriction were inconclusive. A difficulty with this empirical approach is that the true technology is unknown. Evaluating the performance of flexible forms on the basis of how well they fit observed data is useful if interest centers on the data, but may be misleading if

Finite sample evidence on the performance of stochastic frontiers and data envelopment analysis using panel data

Abstract In recent years a number of alternative methods have been proposed with which to measure technical efficiency. However, we know little of their comparative performance. In this study we examine the relative strengths of two different methodologies - stochastic frontier models (SF) and data envelopment analysis (DEA) - in estimating firm-specific technical efficiency. To address the limitations of previous studies we utilize Monte Carlo techniques which allow us to control the structure of the underlying technology and the stochastic environment. Most stochastic frontier models have focused on estimating average technical efficiency across all firms. The failure to estimate firm-specific technical efficiency has been regarded as a major limitation of previous stochastic frontier models. To overcome this limitation we estimate firm-specific technical efficiency using panel data. We also examine the performance of stochastic frontier models using panel data for three estimators - maximum likelihood random effects, generalized least squares random effects, and within fixed effects. Our results indicate that for simple underlying technologies the relative performance of the stochastic frontier models vis-a-vis DEA relies on the choice of functional forms. If the employed form is close to the given underlying technology, stochastic frontier models outperform DEA using a number of metrics. As the misspecification of the functional form becomes more serious and as the degree of correlatedness of inefficiency with regressors increases, DEAs appeal becomes more compelling. Our results also indicate that the preferred estimator for the SF model is the within estimator, which addresses two problems common to stochastic frontier models - the possible correlatedness of input levels and technical efficiency and the dependence of stochastic frontier models on distributional assumptions concerning the form of technical inefficiency.

Efficiency and productivity growth comparisons of European and U.S. Air carriers: A first look at the data

In this paper we carry out technical efficiency and productivity growth comparisons among the four largest European carriers and eight of their American counterparts. The time period of our comparisons is 1976 through 1986. This is a particularly interesting period since it begins just after the informal steps toward deregulation in the United States and ends just prior to the introduction of the first wave of reforms by the Council of Ministers in Europe. We also identify the potential efficiency gains of the European liberalization by comparing efficiency differences between the two carrier groups. The reductions in inefficiency describe the amount that inputs can be decreased without altering output.

Airline efficiency differences between Europe and the US: Implications for the pace of EC integration and domestic regulation☆

Abstract In this paper we examine the performance of the eight largest European and the eight largest American airlines during the period 1976–1986. During this period the American industry was deregulated and the European industrys competitive posture was significantly liberalized. Two alternative methodologies for identifying productive efficiency are used - a parametric one using statistical estimation and a nonparametric one using linear programming. We find that were European carriers under deregulation to be as productively efficient as their American counterparts, the European industry would save approximately

Allocative distortions and the regulatory transition of the U.S. airline industry

4 billion per year (in 1986 dollars).

Stochastic panel frontiers: A semiparametric approach

Abstract Our paper develops a model of allocative distortions with which we analyze departures of the U.S. airline industry from efficient resource allocation during the period 1970–1981. Airline technology is assumed to transform capital, labor, energy, and materials into passenger and cargo service whose characteristics are endogeneously determined. A generalized-Leontief system of distorted profit, output supply, input demand, and reduced form output characteristics expressions is estimated by FIML using a multivariate error components model with vector autoregressive disturbances. Our results tend to support the common perception that deregulation reduced both the total cost and relative level of allocative distortions.

The Relationship Between Stock Market Returns and Technical Efficiency Innovations: Evidence from the US Airline Industry

This paper complements the results of Hausman and Taylor (1981) and Cornwell, Schmidt and Sickles (1990) and generalizes Park and Simar (1994) by examining the semiparametric efficient estimation of panel models in which the random effects and the regressors have certain patterns of correlation. A model in which this estimator may have particular promise is the stochastic panel frontier model. In that model inefficiency may be correlated with certain determinants of technology or proxies for heterogeneity in the application of that technology. Generalized least squares or other estimators that fail to address this dependency structure are inconsistent. We examine semiparametric efficient estimation for three different models based on differing dependency structures. Efficiency of the slope parameters and the asymptotic properties of the level of the frontier function are explored. We illustrate our new estimator in an analysis of productive efficiency between selected North American and European airline firms after domestic deregulation in the US and prior to recent European reforms implemented in the course of EC integration.

Estimation of long-run inefficiency levels: a dynamic frontier approach

This paper analyzes the association between two firm performance measures: stock market returns and relative technical efficiency. Using linear programming techniques (Data Envelopment Analysis and Free Disposal Hull), technical efficiencies are calculated for a panel of eleven US airlines observed quarterly from 1970–1990. A relationship, between efficiency news in a quarter and stock market performance in the following two months, is found. A risky arbitrage portfolio strategy, of buying firms with the most positive efficiency news and short-selling those with the worst news during this time frame, results in zero beta risk yet yields annual returns of 17% and 18% for the two methodologies.

A NEW PANEL DATA TREATMENT FOR HETEROGENEITY IN TIME TRENDS

Cornwell, Schmidt, and Sickles (1990) and Kumbhakar (1990), among others, developed stochasticfrontier production models which allow firm specific inefficiency levels to change over time. These studies assumed arbitrary restrictions on the short-run dynamics of efficiency levels which have little theoretical justification. Further, the models are inappropriate for estimation of long-run efficiencies. We consider estimation of an alternative frontier model in which firmspecific technical inefficiency levels are autoregressive. This model is particularly useful to examine a potential dynamic link between technical innovations and production inefficiency levels. We apply our methodology to a panel of US airlines.