Marno Verbeek

Testing for Selectivity Bias in Panel Data Models

The authors discuss several tests to check for the presence of selectivity bias in estimators based on panel data. One approach to test for selectivity bias is to specify the selection mechanism explicitly and estimate it jointly with the model of interest. Alternatively, one can derive the asymptotically efficient Lagrange multiplier test. Both approaches are computationally demanding. In this paper, the authors propose the use of simple variable addition and (quasi-) Hausman tests for selectivity bias that do not require any knowledge of the response process. They compare the power of these tests with the asymptotically efficient test using Monte Carlo methods. Copyright 1992 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Can cohort data be treated as genuine panel data

If repeated observations on the same individuals are not available it is not possible to capture unobserved individual characteristics in a linear model by using the standard fixed effects estimator. If large numbers of observations are available in each period one can use cohorts of individuals with common characteristics to achieve the same goal, as shown by Deaton (1985). It is tempting to analyze the observations on cohort averages as if they are observations on individuals which are observed in consecutive time periods. In this paper we analyze under which conditions this is a valid approach. Moreover, we consider the impact of the construction of the cohorts on the bias in the standard fixed effects estimator. Our results show that the effects of ignoring the fact that only a synthetic panel is available will be small if the cohort sizes are sufficiently large (100, 200 individuals) and if the true means within each cohort exhibit sufficient time variation.

Two-step estimation of panel data models with censored endogenous variables and selection bias

This paper presents some two-step estimators for a wide range of parametric panel data models with censored endogenous variables and sample selection bias. Our approach is to derive estimates of the unobserved heterogeneity responsible for the endogeneity/selection bias to include as additional explanatory variables in the primary equation. These are obtained through a decomposition of the reduced form residuals. The panel nature of the data allows adjustment, and testing, for two forms of endogeneity and/or sample selection bias. Furthermore, it incorporates roles for dynamics and state dependence in the reduced form. Finally, we provide an empirical illustration which features our procedure and highlights the ability to test several of the underlying assumptions.

Estimating and Interpreting Models With Endogenous Treatment Effects

This article examines the relationship between two alternative approaches, instrumental variables and control function procedures, for estimating the impact of endogenous treatment effects. Although it is well known that the two approaches generate comparable estimates, the relationship between the estimators and their accompanying endogeneity tests appears not to be well understood. We show that the two procedures are closely related. We also examine the implications of the two procedures for the underlying economic sorting behavior.

Selecting Copulas for Risk Management

Copulas offer financial risk managers a powerful tool to model the dependence between the different elements of a portfolio and are preferable to the traditional, correlation-based approach. In this paper we show the importance of selecting an accurate copula for risk management. We extend standard goodness-of-fit tests to copulas. Contrary to existing, indirect tests, these tests can be applied to any copula of any dimension and are based on a direct comparison of a given copula with observed data. For a portfolio consisting of stocks, bonds and real estate, these tests provide clear evidence in favour of the Students t copula, and reject both the correlation-based Gaussian copula and the extreme value-based Gumbel copula. In comparison with the Students t copula, we find that the Gaussian copula underestimates the probability of joint extreme downward movements, while the Gumbel copula overestimates this risk. Similarly we establish that the Gaussian copula is too optimistic on diversification benefits, while the Gumbel copula is too pessimistic. Moreover, these differences are significant.

Incomplete Panels and Selection Bias

In this chapter attention will be paid to selection bias in panel data. In case of selection bias a rule other than simple random sampling determines how sampling from the underlying population takes place. This selection rule may distort the representation of the true population and consequently distort inferences based on the observed data using standard methods. Distorting selection rules may be the outcome of self—selection decisions of agents, non-response decisions of agents or decisions of sample survey statisticians. Many existing panel data sets suffer from missing observations due to nonresponse of agents or design decisions of survey statisticians. Both sources of missing observations may imply a non—random selection rule. Additionally, in many economic applications decisions of individual agents imply a distorting selection rule. Examples of these types of self—selection are the endogenous decisions to join the labor force or to participate in some social program.

Estimating Dynamic Models from Repeated Cross-Sections

An important feature of panel data is that it allows the estimation of parameters characterizing dynamics from individual level data. Several authors argue that such parameters can also be identified from repeated cross-section data and present estimators to do so. This paper reviews the identification conditions underlying these estimators. As grouping data to obtain a pseudo-panel is an application of instrumental variables (IV), identification requires that standard IV conditions are met. This paper explicitly discuss the implications of these conditions for empirical analyses. We also propose a computationally attractive instrumental variables estimator that is consistent under a relatively weak set of conditions. A Monte Carlo study indicates that this estimator may work well in practice.

Whose wages do unions raise? A dynamic model of unionism and wage rate determination for young men

We estimate the union premium for young men over a period of declining unionization (1980-87) through a procedure which identifies the alternative sources of the endogeneity of union status. While we estimate the average increase in wages resulting from union employment to be in excess of 20% we find that the return to unobserved heterogeneity operating through union status is substantial and that the union premium is highly variable. We also find that the premium is sensitive to the form of sorting allowed in estimation. Moreover, the data are consistent with comparative advantage sorting. Our results suggest that the unobserved heterogeneity which positively contributes to the likelihood of union membership is associated with higher wages. We are unable, however, to determine whether this is due to the ability of these workers to extract monopoly rents or whether it reflects the more demanding hiring standards of employers faced by union wages.

Minimum MSE estimation of a regression model with fixed effects from a series of cross-sections

If panel data are not available but repeated cross-sections are, the parameters in a regression model with fixed individual effects can be estimated consistently using the cohort approach proposed by Deaton (1985). In this paper we show that Deatons estimator is inconsistent if the number of time periods is small, even if the number of cohorts tends to infinity. Moreover, we propose an alternative estimator which does not suffer from a bias due to a small number of sampling periods and we introduce a new class of estimators, containing both estimators mentioned above. We discuss minimum mean squared error estimation within this class. Our results show that it may be optimal to eliminate only part of the measurement error in the cohort averages, since the implied bias is offset by a smaller variance.

Pseudo-Panels and Repeated Cross-Sections

In many countries there is a lack of genuine panel data where specific individuals or firms are followed over time. However, repeated cross-sectional surveys may be available, where a random sample is taken from the population at consecutive points in time. In this paper we discuss the identification and estimation of panel data models from repeated cross sections. In particular, attention will be paid to linear models with fixed individual effects, to models containing lagged dependent variables and to discrete choice models.