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In this paper, a decomposition method for Tobit-models is derived, which allows the differences in observed outcome variables between two groups to be decomposed into a part that is explained by differences in observed characteristics and a part attributable to differences in the estimated coefficients. Monte Carlo simulations demonstrate that in the case of censored dependent variables this decomposition method produces more reliable results than the conventional Blinder-Oaxaca decomposition for linear regression models. Finally, our method is applied to a decomposition of the gender wage gap using German data.

Sometimes political scientists analyze data where distinctions between data points are unobservable above or below a critical limit. In this case study, we will examine how to address the problems related to this kind of data (broadly known as censored data). The reader will be taken through an example of data that (sometimes) exhibit these feature?feeling thermometers toward candidates in the 2016 U.S. Presidential Election. Particular attention will be paid to the use of Tobit models as a potential solution to censored data.

For a large variety of discrete choice models (or contingency table models) efficientand stable maximum likelihood methods can be constructed basedon the majorization method. The course introduces majorization methods for algorithm construction. We show how to use the majorization principle to reduce complicated optimization problems to sequences of weighted or unweighted least squares problems. Majorization methods are then applied to data analysis techniques used in economics, political science, psychometrics, ecology, sociology, and education.

This paper focuses on a three-dimensional model that combines two different types of spatial interaction effects, i.e. endogenous interaction effects via a spatial lag on the dependent variable and interaction effects among the disturbances via a spatial moving average (SMA) nested random effects errors. A three-stage procedure is proposed to estimate the parameters. In a first stage, the spatial lag panel data model is estimated using an instrumental variable (IV) estimator. In a second stage, a generalized moments (GM) approach is developed to estimate the SMA parameter and the variance components of the disturbance process using IV residuals from the first stage. In a third stage, to purge the equation of the specific structure of the disturbances a Cochrane–Orcutt-type transformation is applied combined with the IV principle. This leads to the GM spatial IV estimator and the regression parameter estimates. Monte Carlo simulations show that our estimators are not very different in terms of root mean square error from those produced by maximum likelihood. The approach is applied to European Union regional employment data for regions nested within countries.

In this paper, we propose a new approach of regularization for the left censored data (Tobit). Specifically, we propose a new Bayesian group Bridge for left-censored regression ( BGBRLC). We developed a new Bayesian hierarchical model and we suggest a new Gibbs sampler for posterior sampling. The results show that the new approach performs very well compared to some existing approaches.

"This is the most recently developed book in Spatial Econometrics which cover important models and estimation methods. Its coverage is rather broad, and some of the topics covered have only been developed in the recent econometric literature in spatial econometrics. The book summarizes our devoted efforts on spatial econometrics that represent joint contributions with former PhD advisees from the Ohio State University in Columbus, Ohio, USA. The coverage is comprehensive and there are a total of sixteen chapters from basic statistics and statistical theory of linear-quadratic forms, law of large numbers (LLN) and central limit theory (CLT) on martingales to nonlinear spatial mixing and spatial near-epoch dependence theories, which can justify the statistic inferences for various spatial models and their estimation. New estimation and testing approaches in empirical likelihood and general empirical likelihood, and Bootstrapping are presented. Model selection is also discussed in this book. In addition to the popular spatial autoregressive models, there are chapters on multivariate SAR models, simultaneous SAR models, and panel dynamic spatial model models. Recent econometric developments on intertemporal spatial models with rational expectations and on flows data in trade theory will also be included. In terms of statistics, classical estimation, testing and inference are the main concerns, and we provide classical inference for the justification of Bayesian simulation approaches."

Political scientists are making increasing use of the Tobit and Heckit models. This paper addresses some common problems in the application and interpretation of these models. Through numerical experiments and reanalysis of data from a study by Romer and Snyder (1994), we illustrate the consequences of using the standard Tobit model, which assumes a censoring point at zero, when the zeros are not due to censoring mechanisms or when actual censoring is not at zero. In the latter case, we also show that Greene's (1981) well-known results on the direction and size of the bias of the OLS estimator in the standard Tobit model do not necessarily hold. Because the Heckit model is often used as an alternative to Tobit, we examine its assumptions and discuss the proper interpretation of the Heckit/Tobit estimation results using Grier and co-workers' (1994) Heckit model of campaign contribution data. Sensitivity analyses of the Heckit estimation results suggest some conclusions rather different from those reached by Grier et al.