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Alternative Panel Data Estimators for Stochastic Frontier Models

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Nội dung chi tiết: Alternative Panel Data Estimators for Stochastic Frontier Models

Alternative Panel Data Estimators for Stochastic Frontier Models

Alternative Panel Data Estimators for Stochastic Frontier Modelswilliam Greene’Department of Economics, Stern School of Business, New York University.

Alternative Panel Data Estimators for Stochastic Frontier Models.September 1,2002AbstractReceived analyses based on stochastic frontier modeling with panel data have relied primarily on results from traditional lin

ear fixed and random effects models. This paper examines several extensions of these models that employ nonlinear techniques. The fixed effects model Alternative Panel Data Estimators for Stochastic Frontier Models

is extended to the stochastic frontier model using results that specifically employ the nonlinear specification. Based on Monte Carlo results, we find

Alternative Panel Data Estimators for Stochastic Frontier Models

that in spite of the well documented incidental parameters problem, the fixed effects estimator appears to be no less effective than traditional appi

Alternative Panel Data Estimators for Stochastic Frontier Modelswilliam Greene’Department of Economics, Stern School of Business, New York University.

Alternative Panel Data Estimators for Stochastic Frontier Models the latent class model. Both of these forms allow generalizations of the model beyond the familiar normal distribution framework.Keywords: Panel data

, fixed effects, random effects, random parameters, latent class, computation. Monte Carlo, technical efficiency, stochastic frontier.JEL classificati Alternative Panel Data Estimators for Stochastic Frontier Models

on: Ci, C4• 44 West 4* St.. New York, NY 10012. USA. Telephone: 001-212-998-0876: fax: 01-212-995-4218: e-mail: wgreenegstem.nvu.edu. URL www.stern.nv

Alternative Panel Data Estimators for Stochastic Frontier Models

u.edu'-wgreene. This paper has been prepared for the conference on “Current Developments in Productivity and Efficiency Measurement,” University of Ge

Alternative Panel Data Estimators for Stochastic Frontier Modelswilliam Greene’Department of Economics, Stern School of Business, New York University.

Alternative Panel Data Estimators for Stochastic Frontier Modelsnce on Efficiency and Productivity in July. 2002. discussions at University of Leicester and Binghamton University and ongoing conversations with Mike

Tsionas, Subal, Kumbhakar and Knox Lovell.1IntroductionAigner, Lovell and Schmidt proposed the normal-half normal stochastic frontier in their pionee Alternative Panel Data Estimators for Stochastic Frontier Models

ring work in 1977. A stream of research over the succeeding 25 years has produced a number of innovations in specification and estimation of their mod

Alternative Panel Data Estimators for Stochastic Frontier Models

el. Panel data treatments have kept pace with other types of developments in the literature. However, with few exceptions, these estimators have been

Alternative Panel Data Estimators for Stochastic Frontier Modelswilliam Greene’Department of Economics, Stern School of Business, New York University.

Alternative Panel Data Estimators for Stochastic Frontier Modelsdeling heterogeneity in panel data in the stochastic frontier model. The motivation is to produce specifications which can appropriately isolate firm

heterogeneity while preserving the mechanism in the stochastic frontier that produces estimates of technical or cost inefficiency. The received applic Alternative Panel Data Estimators for Stochastic Frontier Models

ations have effectively blended these two characteristics in a single feature in the model.This study will build to some extent on analyses tlrat have

Alternative Panel Data Estimators for Stochastic Frontier Models

already appeared in other literatures. Section 2 will review some of the terminology of the stochastic frontier model. Section 3 considers fixed effe

Alternative Panel Data Estimators for Stochastic Frontier Modelswilliam Greene’Department of Economics, Stern School of Business, New York University.

Alternative Panel Data Estimators for Stochastic Frontier Modelsd the inefficiency separately, which has not been done previously. This section considers two issues, the practical problem of computing the fixed eff

ects estimator, and the bias and inconsistency of the fixed effects estimator due to the incidental parameters problem. A Monte Carlo study based on a Alternative Panel Data Estimators for Stochastic Frontier Models

large panel from the U.S. banking industry is used to study the incidental parameters problem and its influence on inefficiency estimation. Section 4

Alternative Panel Data Estimators for Stochastic Frontier Models

presents results for random effects and random parameters models. The development here will follow along similar lines as in Section 3. We first reco

Alternative Panel Data Estimators for Stochastic Frontier Modelswilliam Greene’Department of Economics, Stern School of Business, New York University.

Alternative Panel Data Estimators for Stochastic Frontier Models then propose a modification of the random effects model which disentangles these temis. This section will include development of the simulation based

estimator that Is then used to extend the random effects model to a full random parameters specification. The random parameters model is a far more f Alternative Panel Data Estimators for Stochastic Frontier Models

lexible, general specification than the simple random effects specification. We will continue the analysis of the banking industry application In the

Alternative Panel Data Estimators for Stochastic Frontier Models

random parameters model. Section 5 then turns to the latent class specification. The latent class model can be Interpreted as a discrete mixture model

Alternative Panel Data Estimators for Stochastic Frontier Modelswilliam Greene’Department of Economics, Stern School of Business, New York University.

Alternative Panel Data Estimators for Stochastic Frontier Modelson in the data set. Section 5 will develop the model, then apply It to the data on the banking industry considered In the preceding two sections. Some

conclusions are drawn in Section 6.22The Stochastic Frontier ModelThe stochastic frontier model may be writteny,. = /r(x„.z.) + V, ± uit - P'x„ ♦ Jl' Alternative Panel Data Estimators for Stochastic Frontier Models

fc I Vi, ± Uu,where the sign of the last term depends on whether the frontier describes costs (positive) or production (negative). This has the appear

Alternative Panel Data Estimators for Stochastic Frontier Models

ance of a (possibly nonlinear) regression equation, though the error term in the model has (wo parts. The function /(•) denotes the theoretical produc

Alternative Panel Data Estimators for Stochastic Frontier Modelswilliam Greene’Department of Economics, Stern School of Business, New York University.

Alternative Panel Data Estimators for Stochastic Frontier Modelscond component, u.r represents tec hnical or cost inefficiency, and must be positive. The base case stochastic frontier model as originally proposed b

y Aigner, Lovell and Schmidt (1077) adds the distributional assumptions to create an empirical mcxlel; the "composed error'* is the sum of a symmetric Alternative Panel Data Estimators for Stochastic Frontier Models

, normally distributed variable (the idiosync rasy) and the absolute of a normally distributed variable (the inefficiency):Vi, ~ N[0, a?jUá = |ư..| w

Alternative Panel Data Estimators for Stochastic Frontier Models

here 14*’ N[0. try].The model is usually specified in (natural) logs, so the inefficiency term. (/,• can be interpreted as the percentage deviation of

Alternative Panel Data Estimators for Stochastic Frontier Modelswilliam Greene’Department of Economics, Stern School of Business, New York University.

Alternative Panel Data Estimators for Stochastic Frontier Modelsfor this function, so we will generally usey» = P'x„ + Vi ± Uato denote the lull model as well, subsuming (he time invariant effects in Xi,.The analys

is of Inefficiency in (his modeling framework consists ol two (or three s(eps). Al (he first, we will obtain estimates of (he technology' parameters, Alternative Panel Data Estimators for Stochastic Frontier Models

p. This estimation step also produces estimates of the parameters of the distributions of the error terms in the model, <ĩu and Ơ.. In the analysis of

Alternative Panel Data Estimators for Stochastic Frontier Models

inefficiency, these structural parameters may or may not hold any intrinsic interest for the analyst. With the parameter estimates in hand, it is pos

Alternative Panel Data Estimators for Stochastic Frontier Modelswilliam Greene’Department of Economics, Stern School of Business, New York University.

Alternative Panel Data Estimators for Stochastic Frontier Modelsrameters. But. the objective is usually estimation of till, not Ex. which contains the film specific heterogeneity. Jondrow, Lovell, Matcrov, and Schm

idt (1982) (JLMS) have devised a method of disentangling these effects. Their estimator of U;r isE[Ur Exl -<7/. 0 Alternative Panel Data Estimators for Stochastic Frontier Models

T’À. = ơu/ơ,Ou = ±EltX/ơOía*) = the standard normal density evaluated at ữ,t

Alternative Panel Data Estimators for Stochastic Frontier Modelswilliam Greene’Department of Economics, Stern School of Business, New York University.