Weak identification in probit models with endogenous covariates

Political Analysis, 2010

We look at conventional methods for removing endogeneity bias in regression models, including the linear model and the probit model. It is known that the usual Heckman two-step procedure should not be used in the probit model: from a theoretical perspective, it is unsatisfactory, and likelihood methods are superior. However, serious numerical problems occur when standard software packages try to maximize the biprobit likelihood function, even if the number of covariates is small. We draw conclusions for statistical practice. Finally, we prove the conditions under which parameters in the model are identifiable. The conditions for identification are delicate; we believe these results are new.

Journal of Econometrics, 1988

A two-step maximum likelihood procedure is proposed for estimating simultaneous probit models and is compared to alternative limited information estimators. Conditions under which these estimators attain the Cramer-Rao lower bound are stated. Simple tests of exogeneity are proposed and are shown to be asymptotically equivalent to one another and to have the same local asymptotic power as classical tests based on the limitedd information maximum likelihood estimator.

2002

Discussion Papers on Business and Economics, 2006

Sample selection and endogeneity are frequent causes of biases in non-experimental empirical studies. In binary models a standard solution involves complex multivariate models. A simple approximation has been shown to work well in bivariate models. This paper extends the approximation to a trivariate model. Simulations show that the approximation outperforms full maximum likelihood while a least squares approximation may be severely biased. The methods are used to estimate the influence of trust in the parliament and politicians on votingpropensity. No previous studies have allowed for endogeneity of trust on voting and it is shown to severely affect the results.

In the present paper a mixed approach is proposed for the simultaneously estimation of regression and correlation structure parameters in multivariate probit models using generalized estimating equations for the former and pseudo-score equations for the latter. The finite sample properties of the corresponding estimators are compared to estimators proposed by Qu, Williams, Beck and Medendorp (1992) and Qu, Piedmonte and Williams (1994) using generalized estimating equations for both sets of parameters via a Monte Carlo experiment. As a `reference' estimator for an equicorrelation model, the maximum likelihood (ML) estimator of the random effects probit model is calculated. The results show the mixed approach to be the most robust approach in the sense that the number of datasets for which the corresponding estimates converged was largest relative to the other two approaches. Furthermore, the mixed approach led to the most efficient non-ML estimators and to very efficient estimat...

Journal of Time Series Analysis, 2016

For discrete panel data, the dynamic relationship between successive observations is often of interest. We consider a dynamic probit model for short panel data. A problem with estimating the dynamic parameter of interest is that the model contains a large number of nuisance parameters, one for each individual. Heckman proposed to use maximum likelihood estimation of the dynamic parameter, which, however, does not perform well if the individual effects are large. We suggest new estimators for the dynamic parameter, based on the assumption that the individual parameters are random and possibly large. Theoretical properties of our estimators are derived and a simulation study shows they have some advantages compared to Heckman's estimator.

2007

Many economic applications involve the modeling of a binary variable as simultaneously determined with one of its dycotomous regressors. In this paper we deal with a prominent health economics case study, that of cesarean section delivery utilization across public and private hospitals. Estimating the probability of cesarean section in a univariate framework neglecting the potential endogeneity of the hospital type dummy might lead to invalid inference. Since little is known about the exact sampling properties of alternative statistics for testing exogeneity of a dycotomous regressor in probit models, we conduct an extensive Monte Carlo experiment. Equipped with the simulation results we apply a comprehensive battery of tests to an Italian sample of women and find clear evidence against exogeneity of the hospital type dummy. We speculate on the economic implications of these results and discuss the misleading interpretation arising from the adoption of either univariate probit model or seemingly unrelated bivariate probit model.

Journal of Econometrics, 2009

Fixed effects estimators of nonlinear panel models can be severely biased due to the incidental parameters problem. In this paper I find that the most important component of this incidental parameters bias for probit fixed effects estimators of index coefficients is proportional to the true value of these coefficients, using a large-T expansion of the bias. This result allows me to derive a lower bound for this bias, and to show that fixed effects estimates of ratios of coefficients and average marginal effects have zero bias in the absence of heterogeneity, and have negligible bias relative to their true values for a wide variety of distributions of regressors and individual effects.

SSRN Electronic Journal, 2012

We consider the following problem. A structural equation of interest contains two sets of explanatory variables which economic theory predicts may be endogenous. The researcher is interesting in testing the exogeneity of only one of them. Standard exogeneity tests are in general unreliable from the view point of size control to assess such a problem. We develop four alternative tests to address this issue in a convenient way. We provide a characterization of their distributions under both the null hypothesis (level) and the alternative hypothesis (power), with or without identification. We show that the usual χ 2 critical values are still applicable even when identification is weak. So, all proposed tests can be described as robust to weak instruments. We also show that test consistency may still hold even if the overall identification fails, provided partial identification is satisfied. We present a Monte Carlo experiment which confirms our theory. We illustrate our theory with the widely considered returns to education example. The results underscore: (1) how the use of standard tests to assess partial exogeneity hypotheses may be misleading, and (2) the relevance of using our procedures when checking for partial exogeneity.

Oxford Bulletin of Economics and Statistics, 1999

This note points out to applied researchers what adjustments are needed to the coefficient estimates in a random effects probit model in order to make valid comparisons in terms of coefficient estimates and marginal effects across different specifications. These adjustments are necessary because of the normalisation that is used by standard software in order to facilitate easy estimation of the random effects probit model.