On the Ranking Uncertainty of Labor Market Wage Gaps

This paper uses multiple comparison methods to perform inference on labor market wage gap estimates from a regression model of wage determination. The regression decomposes a sample of workers' wages into a human capital component and a gender specific component; the gender component is called the gender differential or wage gap and is sometimes interpreted as a measure of sexual discrimination. Using data on fourteen industry classifications (e.g. retail sales, agriculture), a new relative estimator of the wage gap is calculated for each industry. The industries are then ranked based on the magnitude of these estimators, and inference experiments are performed using "multiple comparisons with the best" and "multiple comparisons with a control". The inference indicates that differences in gender discrimination across industry classifications is statistically insignificant at the 95% confidence level and that previous studies which have failed to perform inference on gender wage gap order statistics may be misleading.Labor economics, discrimination, wage differentials, multiple comparisons with the best

Selection Procedures for Order Statistics in Empirical Economic Studies

In a presentation to the American Economics Association, McCloskey (1998) argued that "statistical significance is bankrupt" and that economists' time would be "better spent on finding out How Big Is Big". This brief survey is devoted to methods of determining "How Big Is Big". It is concerned with a rich body of literature called selection procedures, which are statistical methods that allow inference on order statistics and which enable empiricists to attach confidence levels to statements about the relative magnitudes of population parameters (i.e. How Big Is Big). Despite their prolonged existence and common use in other fields, selection procedures have gone relatively unnoticed in the field of economics, and, perhaps, their use is long overdue. The purpose of this paper is to provide a brief survey of selection procedures as an introduction to economists and econometricians and to illustrate their use in economics by discussing a few potential applications. Both simulated and empirical examples are provided.Ranking and selection, multiple comparisons, hypothesis testing

On Ranking and Selection from Independent Truncated Normal Distributions

This paper develops probability statements and ranking and selection rules for independent truncated normal populations. An application to a broad class of parametric stochastic frontier models is considered, where interest centers on making probability statements concerning unobserved firm-level technical ineffciency. In particular, probabilistic decision rules allow subsets of firms to be deemed relatively effcient or ineffcient at pre-specified probabilities. An empirical example is provided.Ranking and Selection, Truncated Normal, Stochastic Frontier

Technical Efficiency of Australian Wool Production: Point and Confidence Interval Estimates

A balanced panel of data is used to estimate technical efficiency, employing a fixed-effects stochastic frontier specification for wool producers in Australia. Both point estimates and confidence intervals for technical efficiency are reported. The confidence intervals are constructed using the Multiple Comparisons with the Best (MCB) procedure of Horrace and Schmidt (2000). The confidence intervals make explicit the precision of the technical efficiency estimates and underscore the dangers of drawing inferences based solely on point estimates. Additionally, they allow identification of wool producers that are statistically efficient and those that are statistically inefficient. The data reveal at the 95% confidence level that twenty-one of the twenty-six wool farms analyzed may be efficient.Wool, Technical Efficiency, MCB, MCC

Generalized Moments Estimation for Spatial Panel Data: Indonesian Rice Farming

We consider estimation of a panel data model where disturbances are spatially correlated in the cross-sectional dimension, based on geographic or economic proximity. When the time dimension of the data is large, spatial correlation parameters may be consistently estimated. When the time dimension is small (the usual panel data case), we develop an estimator that extends the cross-sectional model of Kelejian and Prucha. This approach is applied in a stochastic frontier framework to a panel of Indonesian rice farms where spatial correlations represent productivity shock spillovers, based on geographic proximity and weather. These spillovers affect farm-level efficiency estimation and ranking.autocorrelation, Moran I, productivity, stochastic frontier, spatial dependence

Confidence Statements for Efficiency Estimates from Stochastic Frontier Models

This paper is an empirical study of the uncertainty associated with estimates from stochastic frontier models. We show how to construct confidence intervals for estimates of technical efficiency levels under different sets of assumptions ranging from the very strong to the relatively weak. We demonstrate empirically how the degree of uncertainty associated with these estimates relates to the strength of the assumptions made and to various features of the data.Confidence intervals, stochastic frontier models, efficiency measurement

Technical Efficiency of Australian Wool Production: Point and Confidence Interval Estimates

A balanced panel of data is used to estimate technical efficiency, employing a fixed-effects stochastic frontier specification for wool producers in Australia. Both point estimates and confidence intervals for technical efficiency are reported. The confidence intervals are constructed using the multiple comparisons with the best (MCB) procedure of Horrace and Schmidt (1996, 2000). The confidence intervals make explicit the precision of the technical efficiency estimates and underscore the dangers of drawing inferences based solely on point estimates. Additionally, they allow identification of wool producers that are statistically efficient and those that are statistically inefficient. The data reveal at the 95% level that twenty-one of the twenty-six wool farms analyzed may be efficient

Some Results on the Multivariate Truncated Normal Distribution

This note formalizes some analytical results on the n-dimensional multivariate truncated normal distribution where truncation is one-sided and at an arbitrary point. Results on linear transformations, marginal and conditional distributions, and independence are provided. Also, results on log-concavity, A-unimodality and the MTP_2 property are derived

On Ranking and Selection from Independent Truncated Normal Distributions

This paper develops probability statements and ranking and selection rules for independent truncated normal populations. An application to a broad class of parametric stochastic frontier models is considered, where interest centers on making probability statements concerning unobserved firm-level technical inefficiency. In particular, probabilistic decision rules allow subsets of firms to be deemed relatively efficient or inefficient at prespecified probabilities. An empirical example is provided

On the Ranking Uncertainty of Labor Market Wage Gaps

This paper uses multiple comparison methods to perform inference on labor market wage gap estimates from a regression model of wage determination. The regression decomposes a sample of workers\u27 wages into a human capital component and a gender specific component; the gender component is called the gender differential or wage gap and is sometimes interpreted as a measure of sexual discrimination. Using data on fourteen industry classifications (e.g. retail sales, agriculture), a new relative estimator of the wage gap is calculated for each industry. The industries are then ranked based on the magnitude of these estimators, and inference experiments are performed using multiple comparisons with the best and multiple comparisons with a control . The inference indicates that differences in gender discrimination across industry classifications is statistically insignificant at the 95% confidence level and that previous studies which have failed to perform inference on gender wage gap order statistics may be misleading