A stochastic frontier model with correction for sample selection

Abstract

Heckman's (1979) sample selection model has been employed in three decades of applications of linear regression studies. The formal extension of the method to nonlinear models, however, is of more recent vintage. A generic solution for nonlinear models is proposed in Terza (1998). We have developed simulation based approach in Greene (2006). This paper builds on this framework to obtain a sample selection correction for the stochastic frontier model. We first show a surprisingly simple way to estimate the familiar normal-half normal stochastic frontier model (which has a closed form log likelihood) using maximum simulated likelihood. The next step is to extend the technique to a stochastic frontier model with sample selection. Here, the log likelihood does not exist in closed form, and has not previously been analyzed. We develop a simulation based estimation method for the stochastic frontier model. In an application that seems superficially obvious, the method is used to revisit the World Health Organization data [WHO (2000), Tandon et al. (2000)] where the sample partitioning is based on OECD membership. The original study pooled all 191 countries. The OECD members appear to be discretely different from the rest of the sample. We examine the difference in a sample selection framework.JEL classification: C14; C23; C25

Technical efficiency analysis correcting for biases from observed and unobserved variables: an application to a natural resource management project

“…The combination of efficiency estimation and sample selection appears in a few studies which have generally dealt with selectivity bias by relying on the Heckman approach, a procedure that is unsuitable for nonlinear models such as the SPF (Greene 2010). Bradford et al (2001) studied patient-specific costs for cardiac revascularization in a large hospital.…”

“…To deal with biases from unobserved variables (e.g., managerial ability) within an SPF formulation, we use the model recently introduced by Greene (2010). This model assumes that the unobserved characteristics in the selection equation are correlated with the noise in the stochastic frontier model; hence, Greene's contribution can be seen as a significant improvement of Heckman's self-selection specification for the linear regression model.…”

“…The Murphy and Topel (2002) correction is used to adjust the standard errors in essentially the same fashion as Heckman's correction of the canonical selection model. Greene (2010) goes on to argue that the non-selected observations (i.e., when d i = 0) do not contribute information about the parameters to the simulated log likelihood and thus the function to be maximized becomes:…”

“…It should be noted that the approach gives a strikingly similar answer to the JLMS plug in result [see Sect. 2.4 in Greene (2010) for details].…”

“…Thus, we first need to establish a group of beneficiaries and a control group that should have been very similar at the baseline, according to a vector of time invariant observable attributes. In addition, we need to address possible self-selection in the context of a stochastic production frontier (SPF) model, an issue we deal with by using the model recently introduced by Greene (2010). A contribution of this article is to narrow the gap between significant methodological advances that have been made in the estimation of SPF models (Greene 2008), which has lead to a sizable number of farm level TE studies (Bravo-Ureta et al 2007), and the rapidly evolving impact evaluation literature (Khandker et al 2010).…”