Combining multiple imputation and control function methods to deal with missing data and endogeneity in discrete-choice models

While collecting data for estimating discrete-choice models, researchers often encounter missing information in observations. In addition, endogeneity can occur whenever the error term is not independent of the observed variables. Both problems result in inconsistent estimators of the model parameters. The problems of missing information and endogeneity may occur in the same variable in the data, if, e.g., partially missing price information is correlated with another omitted variable. Extant approaches to correct for endogeneity in discrete choice models, such as the control function method, do not address the problem when the error term is correlated with a variable having missing information. Likewise, approaches to address missing information, such as the multiple imputation method, cannot handle endogeneity problems. To address this challenge, we propose a novel hybrid algorithm by combining the methods of multiple imputation and the control function. We validate the algorithm in a Monte-Carlo experiment and apply it to real data of heavy commercial vehicle parking from Singapore. In this case study, we were able to substantially correct for price endogeneity in the presence of missing price information.