Limited dependent variable

Abstract: Models designed for limited dependent variables are increasingly common in political science. Researchers estimating such models often give little attention to the coefficient estimates and instead focus on marginal effects, predicted probabilities, predicted counts, etc. Since the models are nonlinear, the estimated effects are sensitive to how one generates the predictions. The most common approach involves estimating the effect for the “average case.” But this approach creates a weaker connection between the results and the larger goals of the research enterprise and is thus less preferable than the observed-value approach. That is, rather than seeking to understand the effect for the average case, the goal is to obtain an estimate of the average effect in the population. In addition to the theoretical argument in favor of the observed-value approach, we illustrate via an empirical example and Monte Carlo simulations that the two approaches can produce substantively different results.

Abstract: This chapter focuses on two of the developments in panel data econometrics since the Handbook chapter by Chamberlain (1984). The first objective of this chapter is to provide a review of linear panel data models with predetermined variables. We discuss the implications of assuming that explanatory variables are predetermined as opposed to strictly exogenous in dynamic structural equations with unobserved heterogeneity. We compare the identification from moment conditions in each case, and the implications of alternative feedback schemes for the time series properties of the errors. We next consider autoregressive error component models under various auxiliary assumptions. There is a trade-off between robustness and efficiency since assumptions of stationary initial conditions or time series homoskedasticity can be very informative, but estimators are not robust to their violation. We also discuss the identification problems that arise in models with predetermined variables and multiple effects. Concerning inference in linear models with predetermined variables, we discuss the form of optimal instruments, and the sampling properties of GMM and LIML-analogue estimators drawing on Monte Carlo results and asymptotic approximations. A number of identification results for limited dependent variable models with fixed effects and strictly exogenous variables are available in the literature, as well as some results on consistent and asymptotically normal estimation of such models. There are also some results available for models of this type including lags of the dependent variable, although even less is known for nonlinear dynamic models. Reviewing the recent work on discrete choice and selectivity models with fixed effects is the second objective of this chapter. A feature of parametric limited dependent variable models is their fragility to auxiliary distributional assumptions. This situation prompted the development of a large literature dealing with semiparametric alternatives (reviewed in Powell, 1994’s chapter). The work that we review in the second part of the chapter is thus at the intersection of the panel data literature and that on cross-sectional semiparametric limited dependent variable models.

Abstract: This paper presents a survey of the methods used in the estimation of limited dependent variable models with panel data. It first reviews some issues in the analysis of panel data when the dependent variables are continuous. The problems of fixed effects vs. random effects and serious correlation vs. state dependence are discussed with reference to continuous data. The paper then discusses these problems with reference to the panel logit, panel probit, and panel tobit models. The paper presents a comparative assessment of these models.

Abstract: Strategy researchers are increasingly turning their attention from examining the impact of strategic choices on firm performance to examining the factors that determine strategic choices at the firm level. This shift of research orientation has meant that researchers are increasingly faced with a limited dependent variable (LDV) that takes a limited number of usually discrete values, for which LDV methods such as logit or probit are required. Despite their growing popularity, there appears to be widespread problems in the use of LDV methods. This research note complements recent studies that offer general guidelines by presenting and illustrating the practical steps needed to implement the methods essential for analyzing and interpreting the results from LDV models. Copyright © 2009 John Wiley & Sons, Ltd.