Simar and Wilson two-stage efficiency analysis for Stata

Abstract

When one analyzes the determinants of production efficiency, regressing efficiency scores estimated by data envelopment analysis on explanatory variables has much intuitive appeal. Simar and Wilson (2007, Journal of Econometrics 136: 31–64) show that this conventional two-stage estimation procedure suffers from severe flaws that render its results, and particularly statistical inference based on them, questionable. They additionally propose a statistically grounded bootstrap-based two-stage estimator that eliminates the above-mentioned weaknesses of its conventional predecessors and comes in two variants. In this article, we introduce the new command simarwilson, which implements either variant of the suggested estimator in Stata. The command allows for various options and extends the original procedure in some respects. For instance, it allows for analyzing both outputand input-oriented efficiency. To demonstrate the capabilities of simarwilson, we use data from the Penn World Tables and the Global Competitiveness Report by the World Economic Forum to perform a cross-country empirical study about the importance of quality of governance in a country for its efficiency of output production.

Measuring Efficiency of Generating Electric Processes

“…Thus, ranking countries will be more specific if the further research applies a super-SBM model into computing the scores. Moreover, estimating the efficiency change of each country will more specific, and future research should use models such as Windows, Malmquist Productivity Index, or bootstrap DEA [37].…”

Measuring the Meta Efficiency and Its Determinants on Efficiency in the Korean Coffee Shop Franchise

“…They construct an underlying data generating process that is consistent with a two-stage estimation procedure, which implies a truncated rather than censored regression model. Moreover, they develop a parametric bootstrap procedure that is consistent with the assumed data generating process to yield estimated standard errors and confidence intervals that do not suffer from bias due to estimated efficiency scores being correlated [25].…”

“…In an attempt to rationalize studies where second-stage regressions have been estimated but no statistical model has been specified, Simar and Wilson [13,14] introduced assumptions that led to a truncated regression in the second stage which can be estimated consistently using the maximum likelihood (ML) method. This study employs Simar and Wilson's bootstrap algorithm as suggested by Badunenko and Tauchmann [25] and Barros and Assaf [26]. The main assumption is that the original efficiency score is given byθ i = ψ(β , z i ) + ε i ≥ 1 and can be translated into the following regression specification:θ…”

“…Essentially, conventional DEA models rely primarily on the assumption that all DMUs have a set of DMUs sharing homogeneous technology. However, significant operating size disparities such as resource limitation, operational strategies, and management level in Korean coffee shop franchises provide a realistic basis for studying the franchisor's operation efficiency in the presence of heterogeneity, which can be implemented by conducting a metafrontier analysis [22,25]. In particular, Korean coffee shop franchisors can be classified into three groups according to their number of franchisees (N), such as large coffee shop chains (N ≥ 300), medium coffee shop chains (100 ≤ N < 300), and small coffee shop chains (N < 100).…”

“…, β n are coefficients of technical ME determinants in Korean coffee shop franchisor operating environments, and ε i is the error term (statistical noise). Following Badunenko and Tauchmann [25], we employ a STATA 14 program to obtain unbiased coefficients and confidence intervals with 2000 replications. A set of exogenous covariates affecting CRS-and VRS-based ME scores were developed for the second-stage regression analysis, which represents the operating environments of a coffee shop franchisor in Korea, i.e., Franchise History (His i ), Total Franchise Fee (Fee i ), Advertisement and Promotion (Adv i ), Franchisor's Management Control (Con i ), Growth Rate of Franchisor (GR i ), Return on Equity of Franchisor (ROE i ) and Franchise Turnover/Failure Rates (Fail i ) [29,30].…”