We investigate conditions sufficient for identification of average treatment effects using instrumental variables. First we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect. We then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument. Finally we derive the probability limit of the standard IV estimator under these conditions. It is seen to be a weighted average of local average treatment effects.

Evolution and Rationality Some Recent Game-Theoretic Results. Identification and Estimation of Local Average Treatment Effects

http://people.stern.nyu.edu/wgreene/FrontierModeling/Reference-Papers/Greene-JE2005-Heterogeneity.pdf

Reconsidering heterogeneity in panel data estimators of the stochastic frontier model

This paper uses the concept of a metafrontier to compare the technical efficiencies of firms that may be classified into different groups. The paper presents the basic analytical framework necessary for the definition of a metafrontier, shows how a metafrontier can be estimated using non-parametric and parametric methods, and presents an empirical application using cross-country agricultural sector data. The paper also explores the issues of technological change, time-varying technical inefficiency, multiple outputs, different efficiency orientations, and firm heterogeneity.

/pdf/metafrontier-frameworks-for-the-study-of-firm-level-59ca3drmoy.pdf

Metafrontier frameworks for the study of firm-level efficiencies and technology ratios

The Econometrics of Panel DataSpringer Handbook of Science and Technology IndicatorsPanel Data EconometricsThe Econometrics of Panel DataA Practitioner's Guide to Stochastic Frontier Analysis Using StataBenchmarking for Performance EvaluationEssays on Microeconomics and Industrial OrganisationHealth System EfficiencyInternational Journal of Production EconomicsEconometric Analysis of Model Selection and Model TestingInternational Applications of Productivity and Efficiency AnalysisAdvanced Robust and Nonparametric Methods in Efficiency AnalysisEconometrics and the Philosophy of EconomicsThe Measurement of Productive EfficiencyMeasuring Efficiency in Health CareFinancial, Macro and Micro Econometrics Using REconometric Analysis of Cross Section and Panel DataApplied EconometricsProductivity and Efficiency AnalysisEconometric Model SelectionProductivity and Efficiency AnalysisStochastic Frontier AnalysisThe Oxford Handbook of Health EconomicsThe Measurement of Productive Efficiency and Productivity GrowthNew Directions in Productivity Measurement and Efficiency AnalysisA Primer on Efficiency Measurement for Utilities and Transport RegulatorsPanel Data EconometricsProduction and Efficiency Analysis with RApplications of Modern Production TheoryThe Measurement of Productive EfficiencyNonparametric Econometric Methods and ApplicationAn Introduction to Efficiency and Productivity AnalysisHealth, the Medical Profession, and RegulationThe Analysis of Household SurveysData Envelopment AnalysisProgramming Collective IntelligenceEfficiency AnalysisProductivity and Efficiency AnalysisMeasurement of Productivity and EfficiencyProduction Frontiers

The Econometric Approach to Efficiency Analysis

A DEA-based stochastic frontier estimation framework is presented to evaluate contextual variables affecting productivity that allows for both one-sided inefficiency deviations as well as two-sided random noise. Conditions are identified under which a two-stage procedure consisting of DEA followed by ordinary least squares (OLS) regression analysis yields consistent estimators of the impact of contextual variables. Conditions are also identified under which DEA in the first stage followed by maximum likelihood estimation (MLE) in the second stage yields consistent estimators of the impact of contextual variables. This requires the contextual variables to be independent of the input variables, but the contextual variables may be correlated with each other. Monte Carlo simulations are carried out to compare the performance of our two-stage approach with one-stage and two-stage parametric approaches. Simulation results indicate that DEA-based procedures with OLS, maximum likelihood, or even Tobit estimation in the second stage perform as well as the best of the parametric methods in the estimation of the impact of contextual variables on productivity. Simulation results also indicate that DEA-based procedures perform better than parametric methods in the estimation of individual decision-making unit (DMU) productivity. Overall, the results establish DEA as a nonparametric stochastic frontier estimation (SFE) methodology.

Evaluating Contextual Variables Affecting Productivity Using Data Envelopment Analysis

Consider a stochastic frontier model with one-sided inefficiency u, and suppose that the scale of u depends on some variables (firm characteristics) z. A “one-step” model specifies both the stochastic frontier and the way in which u depends on z, and can be estimated in a single step, for example by maximum likelihood. This is in contrast to a “two-step” procedure, where the first step is to estimate a standard stochastic frontier model, and the second step is to estimate the relationship between (estimated) u and z. In this paper we propose a class of one-step models based on the “scaling property” that u equals a function of z times a one-sided error u
* whose distribution does not depend on z. We explain theoretically why two-step procedures are biased, and we present Monte Carlo evidence showing that the bias can be very severe. This evidence argues strongly for one-step models whenever one is interested in the effects of firm characteristics on efficiency levels.

https://pages.stern.nyu.edu/~wgreene/FrontierModeling/Reference-Papers/Wang-Schmidt-JPA2002-One_Two_Step.pdf

One-step and two-step estimation of the effects of exogenous variables on technical efficiency levels

Consider a stochastic frontier model with one-sided inefficiency u, and suppose that the scale of u depends on some variables (firm characteristics) z. A one-step model specifies both the stochastic frontier and the way in which u depends on z, and can be estimated in a single step, for example by maximum likelihood. This is in contrast to a two-step procedure, where the first step is to estimate a standard stochastic frontier model, and the second step is to estimate the relationship between (estimated) u and z. In this paper we propose a class of one-step models based on the scaling property that u equals a function of z times a one-sided error u * whose distribution does not depend on z. We explain theoretically why two-step procedures are biased, and we present Monte Carlo evidence showing that the bias can be very severe. This evidence argues strongly for one-step models whenever one is interested in the effects of firm characteristics on efficiency levels.

We consider a model that provides flexible parameterizations of the exogenous influences on inefficiency. In particular, we demonstrate the model's unique property of accommodating non-monotonic efficiency effect. With this non-monotonicity, production efficiency no longer increases or decreases monotonically with the exogenous influence; instead, the relationship can shifts within the sample. Our empirical example shows that variables can indeed have non-monotonic effects on efficiency. Furthermore, ignoring non-monotonicity is shown to yield an inferior estimation of the model, which sometimes results in opposite predictions concerning the data.

Heteroscedasticity and non-monotonic efficiency effects of a stochastic frontier model

Heteroscedasticity and Non-Monotonic Efficiency Effects of a Stochastic Frontier Model

A Practitioner's Guide to Stochastic Frontier Analysis Using Stata provides practitioners in academia and industry with a step-by-step guide on how to conduct efficiency analysis using the stochastic frontier approach. The authors explain in detail how to estimate production, cost, and profit efficiency and introduce the basic theory of each model in an accessible way, using empirical examples that demonstrate the interpretation and application of models. This book also provides computer code, allowing users to apply the models in their own work, and incorporates the most recent stochastic frontier models developed in academic literature. Such recent developments include models of heteroscedasticity and exogenous determinants of inefficiency, scaling models, panel models with time-varying inefficiency, growth models, and panel models that separate firm effects and persistent and transient inefficiency. Immensely helpful to applied researchers, this book bridges the chasm between theory and practice, expanding the range of applications in which production frontier analysis may be implemented.

/pdf/a-practitioner-s-guide-to-stochastic-frontier-analysis-using-31j0qb13hh.pdf

Hung-Jen Wang

Papers

One-step and two-step estimation of the effects of exogenous variables on technical efficiency levels

One-step and two-step estimation of the effects of exogenous variables on technical efficiency levels

Heteroscedasticity and non-monotonic efficiency effects of a stochastic frontier model

Heteroscedasticity and Non-Monotonic Efficiency Effects of a Stochastic Frontier Model

A Practitioner's Guide to Stochastic Frontier Analysis Using Stata