Frontier production functions,technical efficiency and panel data: With application to paddy farmers in India

Frontier production functions are important for the prediction of technical efficiencies of individual firms in an industry. A stochastic frontier production function model for panel data is presented, for which the firm effects are an exponential function of time. The best predictor for the technical efficiency of an individual firm at a particular time period is presented for this time-varying model. An empirical example is presented using agricultural data for paddy farmers in a village in India.This article is a revision of the Invited Paper presented by the senior author in the Productivity and Efficiency Analysis sessions at the ORSA/TIMS 30th Joint National Meeting, Philadelphia, Pennsylvania, 29–31 October 1990. We have appreciated comments from Martin Beck, Phil Dawson, Knox Lovell and three anonymous referees. We gratefully acknowledge the International Crops Research Institute for the Semi-Arid Tropics (ICRISAT) for making available to us the data obtained from the Village Level Studies in India.     

A general framework for frontier estimation with panel data

The main objective of the paper is to present a general framework for estimating production frontier models with panel data. A sample of firms i = 1, ..., N is observed on several time periods t = 1, ... T. In this framework, nonparametric stochastic models for the frontier will be analyzed. The usual parametric formulations of the literature are viewed as particular cases and the convergence of the obtained estimators in this general framework are investigated. Special attention is devoted to the role of N and of T on the speeds of convergence of the obtained estimators. First, a very general model is investigated. In this model almost no restriction is imposed on the structure of the model or of the inefficiencies. This model is estimable from a nonparametric point of view but needs large values of T and of N to obtain reliable estimates of the individual production functions and estimates of the frontier function. Then more specific nonparametric firm effect models are presented. In these cases, only NT must be large to estimate the common production function; but again both large N and T are needed for estimating individual efficiencies and for estimating the frontier. The methods are illustrated through a numerical example with real data.     

Productive efficiency of French grain producers: A latent variable model

In this article we propose to implement a covariance structure analysis to deal with the estimation of a stochastic frontier production function on panel data and the measurement of a time-varying technical efficiency. First, this method solves the potential problem of correlations between input quantities and individual effects. Second, individual effects and efficiency measures can be recovered as a byproduct of the analysis through the so-called factor scores. We implement this approach by fitting to a balanced panel of French grain producers, a parsimonious version of the Cornwell, Schmidt, and Sickles [1990]'s model where technical efficiencies are individual-specific linear functions of time. A specification search shows that this model is preferred to the traditional production function. Results shed light on the temporal pattern of efficiency in the French grain production sector.The authors thank Jacques Mairesse, Quang Vuong, two referees, the editor, and session participants at the Econometric Society European Meeting, Cambridge, September 1991, at the Second European Workshop on Efficiency and Productivity Analysis, Louvain-la-Neuve, October 1991, at the Conference on Current Issues in Productivity, Newark, December 1991, and at the ENSAE-EHESS seminar, Paris, March 1992, for helpful comments and suggestions.     

Income convergence within the MENA countries: A panel unit root approach

This article aims at testing the convergence hypothesis in MENA region using new tests of a unit root in panel data. Evans and Karras [Evans P., & Karras G. (1996). Convergence revisited. Journal of Monetary Economics, 37, 249–265] and Bernard and Jones [Bernard A., & Jones C. I. (1996). Productivity across industries and countries: Time series theory and evidence. The Review of Economics and Statistics, 135–146] recommend this technique to evaluate the income convergence hypothesis. According to them it avoids econometric problems of the cross-countries growth regressions testing convergence and sample bias of the multivariate cointegration techniques. We test for both absolute and the conditional convergence with panel unit root tests using the Summers and Heston's data 5.6 and 6.1 on the periods of 1960 to 1990 and from 1960 to 2000. The absolute convergence hypothesis use panel unit roots test with no fixed individual effects. The catching-up hypothesis is not rejected for most groups of countries of the region during both periods. If we allow a break in the unit root tests, the hypothesis is not rejected for more groups. The conditional convergence requires panel unit root tests with fixed individual effects. Again, during the whole periods, the conditional convergence is not rejected for the major part of the remaining groups of MENA countries.     

Unknown latent structure and inefficiency in panel stochastic frontier models

Journal of Productivity Analysis - This paper extends the fixed effect panel stochastic frontier models to allow group heterogeneity in the slope coefficients. We propose the first-difference...     

Efficiency and ownership in Swedish electricity retail distribution

This article examines the efficiency of electricity retail distributors in Sweden in a multiple output multiple input framework. Productive efficiency measures are calculated by use of different versions of the non-parametric Data Envelopment Analysis (DEA) method. Comparisons are made between different types of ownership and between different types of service areas.The study indicates a rather low level of technical efficiency, a high level of scale efficiency in urban service areas, but a fairly low level of scale efficiency in rural areas. The results show no significant differences in efficiency between different types of ownership or economic organization.Paper presented at ORSA/TIMS joint national meeting, Productivity and Global Competition, Philadelphia, October 29–31, 1990.     

Estimating Technological Change Using a Stochastic Frontier Production Function Framework: Evidence from U.S. Firm-Level Data

This paper presents a methodology for estimating an index of technological change using firm-level data in a stochastic frontier production function model that takes into account time-varying technical inefficiency. In contrast to the Solow divisia index approach, econometric estimation of the index with panel data allows the researcher to separate technical progress from the stochastic measurement error. Applying the econometric methodology to a panel of 908 publicly-traded U.S. firms from the COMPUSTAT database, we find evidence of a significant downturn in general technological change for the period, 1970– 1989, whereas the divisia index methodology applied to the same data shows stagnation. When the sample is divided into Manufacturing, Services, and Miscellaneous categories we find that estimates of technological change for the three groups display markedly different stochastic behavior and that the Services group is the source of the downturn.     

Scale Efficiency in Canadian Trust Companies

A new method for estimating a relative scale function is derived which does not require the specification or estimation of the firm's cost function. The method is applied to a panel of Canadian trust companies for the years 1985–1988. Results show that the industry scale function is convex with respect to firm size, as measured by the firm's assets. The method avoids a number of shortcomings associated with traditional studies of scale economies in financial institutions.     

Controlling for Burnout in Estimating Mortgage Prepayment Models

Burnout is a consequence of unobservable predictive variables. This paper describes a methodology for estimating mortgage prepayment models which corrects for burnout. The paper generalizes the approach of Deng, Quigley, and Van Order (Econometrica, 68, 275–307, 1998) and Stanton (Rev. Finan. Stud.8, 677–708, 1995) in modeling the impact of unobservable variables as a probability distribution. The estimator is applied to a sample of loan histories and the results compared to a conventional logit analysis of the data. Predictions and simulations from both models are compared to illustrate the properties of the new estimator.     

Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations

This paper examines the technical efficiency of US Federal Reserve check processing offices over 1980–2003. We extend results from Park et al. [Park, B., Simar, L., Weiner, C., 2000. FDH efficiency scores from a stochastic point of view. Econometric Theory 16, 855–877] and Daouia and Simar [Daouia, A., Simar, L., 2007. Nonparametric efficiency analysis: a multivariate conditional quantile approach. Journal of Econometrics 140, 375–400] to develop an unconditional, hyperbolic, α-quantile estimator of efficiency. Our new estimator is fully non-parametric and robust with respect to outliers; when used to estimate distance to quantiles lying close to the full frontier, it is strongly consistent and converges at rate root-n, thus avoiding the curse of dimensionality that plagues data envelopment analysis (DEA) estimators. Our methods could be used by policymakers to compare inefficiency levels across offices or by managers of individual offices to identify peer offices.     

Measurement of Dynamic Efficiency in Production: An Application of Data Envelopment Analysis to Japanese Electric Utilities

The purpose of this paper is to measure productive efficiencies when a firm employs quasi-fixed inputs that cannot be instantaneously adjusted to their optimal levels. To this end, data envelopment analysis (DEA) is extended to a dynamic framework so that investment behavior can be modelled with the efficient production frontier. Based on the work of Nemoto and Goto (1999), we show how the efficiencies of quasi-fixed inputs and their adjustment processes are evaluated. An application to Japanese electric utilities over the 1981–1995 period delivers empirically plausible results and proves the usefulness of the procedure.     

Technical efficiency measures for dairy farms using panel data: A comparison of alternative model specifications

This article examines the impact of fixed effects production functions vis-à-vis stochastic production frontiers on technical efficiency measures. An unbalanced panel consisting of 96 Vermont dairy farmers for the 1971–1984 period was used in the analysis. The models examined incorporated both time-variant and time-invariant technical efficiency. The major source of variation in efficiency levels across models stemmed from the assumption made concerning the distribution of the one-sided term in the stochastic frontiers. In general, the fixed effects technique was found superior to the stochastic production frontier methodology. Despite the fact that the results of various statistical tests revealed the superiority of some specifications over others, the overall conclusion of the study is that the efficiency analysis was fairly consistent throughout all the models considered.     

Labour-use efficiency in Swedish social insurance offices

This paper considers the estimation of frontier production functions in panel data models. It proposes a multi-stage method to obtain estimates of (1) the parameters of a flexible input requirement function and (2) technical inefficiency decomposed into time-invariant (firm-specific), time-varying, and the residual components. The proposed method is used to analyse labour-use efficiency of Swedish local social insurance offices on the basis of a large panel of observations during the time period 1974–84. Empirical results show: (1) substantial variations in labour-use efficiency among these offices, with the mean efficiencies declining over time; (2) presence of economies of scale, thereby meaning that most of the offices were of suboptimal size.     

A two-stage realized volatility approach to estimation of diffusion processes with discrete data

This paper motivates and introduces a two-stage method of estimating diffusion processes based on discretely sampled observations. In the first stage we make use of the feasible central limit theory for realized volatility, as developed in [Jacod, J., 1994. Limit of random measures associated with the increments of a Brownian semiartingal. Working paper, Laboratoire de Probabilities, Universite Pierre et Marie Curie, Paris] and [Barndorff-Nielsen, O., Shephard, N., 2002. Econometric analysis of realized volatility and its use in estimating stochastic volatility models. Journal of the Royal Statistical Society. Series B, 64, 253–280], to provide a regression model for estimating the parameters in the diffusion function. In the second stage, the in-fill likelihood function is derived by means of the Girsanov theorem and then used to estimate the parameters in the drift function. Consistency and asymptotic distribution theory for these estimates are established in various contexts. The finite sample performance of the proposed method is compared with that of the approximate maximum likelihood method of [Aït-Sahalia, Y., 2002. Maximum likelihood estimation of discretely sampled diffusion: A closed-form approximation approach. Econometrica. 70, 223–262].     

Efficiency Measurement With Unbalanced Panel Data: Evidence from Tunisian Textile,Clothing and Leather Industries

This paper is concerned with the estimation of stochastic frontier production functions with unbalanced panel data when unobservable firm efficiency levels are related to explanatory variables. We use the weighted-means Instrumental Variables method acknowledged to R. Gardner (1998) which is a modification of the Hausman-Taylor (1981) procedure adapted for unbalanced panel data. The estimation method is used to examine technical efficiency in Tunisian textile, clothing and leather (TCL) industries during the period 1983–1994. Further, we assume a Translog production frontier where input uses are expressed in efficiency units and adjusted for the age of capital and types of labor. Firm-specific time-invariant technical efficiency is obtained using Schmidt and Sickles (1984) approach. The results suggest that the Instrumental Variables method produces more accurate estimates of the unknown firm level technical efficency. Mean efficency scores resulting from the MHT method is of 66.5%.     

Misspecification Preferred: The Sensitivity of Inefficiency Rankings

Ruggiero (European Journal of Operational Research 115, 555–563. 1999) compared the two popular parametric frontier methods for cross-sectional data—the stochastic frontier and the corrected OLS—in a simulation study. He demonstrated that the inefficiency ranking accuracy of the established stochastic frontier is uniformly inferior to that of the misspecified Corrected OLS (COLS) (which lacks an error term). The reason for his result remains unclear, however. In this paper, a more extensive simulation study is therefore conducted to find out whether the superiority of COLS is simply due to small sample sizes or to poor performance of the inefficiency level estimator.JEL Classification: C1,C2,C5     

Forecasting ultimate resource recovery

This paper considers Hubbert's model for forecasting ultimate resource recovery and its extensions by Kaufmann (1991, Resources and Energy 13, 111–127) and Cleveland and Kaufmann (1991, Energy Journal 12, 17–46). The emphasis of the paper is on econometric and forecasting issues, and it discusses alternative methods of estimating Hubbert's model. Using data on oil production in the U.S. lower 48 states, the paper reports the results of estimating the various specifications of the model and its extensions by the maximum-likelihood method, and provides the implied estimates for ultimate resource recovery and their associated standard errors. When economic factors are taken into account the estimates of ultimate resource recovery become state-dependent, and we find that in this case the estimates are higher than those obtained from the various specifications of Hubbert's original model. Although the accuracy of the estimates of ultimate recoverable reserves cannot be evaluated before oil reserves are actually exhausted, we examine how the various models estimated over the periods 1926–1985 and 1948–1985 perform in predicting oil production over the 1986–1990 period.     

Functional Forms of Stochastic Frontier Production Functions and Models for Technical Inefficiency Effects: A Comparative Study for Wheat Farmers in Pakistan

This paper considers translog and Cobb-Douglas stochastic frontiers in which the technical inefficiency effects are defined by three different models. The models involved are the time-varying inefficiency model, proposed by Battese and Coelli (1992), the inefficiency effects model for panel data, proposed by Battese and Coelli (1995), and the non-neutral frontier model, proposed by Huang and Liu (1994). Technical change is also accounted for in the frontier models. Predicted technical efficiencies of the wheat farmers and estimates of the elasticities of wheat production with respect to the different inputs and the returns-to-scale parameter are compared under the different model specifications.     

A General Method of Deriving the Inefficiencies of Banks from a Profit Function

This article develops a new method of estimating inefficiencies in joint production and shows that unlike the approaches utilized in the previous studies of inefficiency, this method maintains a consistent relationship between the error term of a profit function and the error terms of its price derivatives. A useful by-product of the method is a proof of a Hotelling-like lemma that relates stochastic input demand and output supply functions to stochastic profit functions. While the previous studies fit a single frontier to data on all firms, this paper estimates a frontier unique to every observed firm to allow each one to have a different potential of achieving maximal levels of profit. The new method is applied in the analysis of annual data, 1984–1989, for U.S. commercial banks. Both the analytical and numerical results of the paper show that the residual that the previous studies attribute to inefficiency includes the effects of excluded variables and of inaccuracies in the specified functional forms. Once accurate estimates of these effects are subtracted from the residual, the distortions in the measured inefficiencies should be considerably reduced. Consequently, this article considers how such estimates might be obtained.