Conditional Maximum Likelihood Estimation for Logistic Panel Data Models with Non-Responses

Abstract

In analyzing most survey data in which the dependent variable is a binary choice variable taking values 1 or 0 for success or failure respectively it is feasible to consider the conditional probabilities of the dependent variable. Under strict exogeneity, this conditional probability equals the expected value of the dependent variable. This treatment calls for a nonlinear function which will ensure that the conditional probability lies between 0 and 1 and such functions yield the probit model and the logit model. For panel data econometrics, such nonlinear panel data models require conditioning the probabilities on the minimal sufficient statistic for the fixed effects so as to curb the incidental parameter problem. Solving the joint probability distribution function by maximum likelihood method yields consistent ‘conditional maximum likelihood estimate’ for the model parameters in cases when the data set is complete (or balanced) with no cases of missing observations. In cases of missing observations in the covariates, researchers employ several imputation techniques to make the data complete. Imputation, however, brings about a bias in the covariate and this bias is propagated to the parameter estimates. This study considers the susceptibility of nonlinear logistic panel data model with single fixed effects to imputation by investigating the bias arising from various imputation methods. The study developed a conditional maximum likelihood estimator for nonlinear binary choice logistic panel data model in the presence of missing observations. A Monte Carlo simulation was designed to determine the magnitude of bias arising from some common imputation techniques and recommend better techniques to be used in order to improve model performance in the presence of missing observations in econometrics panel data analysis. The simulation results show that the parameter estimates for the conditional logistic model are less biased than those from the unconditional logistic model without sacrificing on the precision. Mean imputation and median imputation preserve precision of the parameter estimates better than last value carried forward.