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.

在收集用于估计离散选择模型的数据时，研究人员经常会在观测中遇到缺失的信息。此外，只要误差项与观察变量无关，就会发生内生性。这两个问题都导致模型参数的估计值不一致。如果例如部分缺失的价格信息与另一个遗漏变量相关联，则可能会在数据中的同一变量中出现信息缺失和内生性的问题。当误差项与具有缺失信息的变量相关时，诸如离散函数模型之类的修正内在性的现存方法无法解决该问题。同样，用于解决丢失信息的方法（例如多重插补方法）也无法处理内生性问题。为了应对这一挑战，通过结合多重插补和控制函数的方法，提出了一种新颖的混合算法。我们在蒙特卡洛实验中验证了该算法，并将其应用于来自新加坡的重型商用车停车的真实数据。在此案例研究中，在缺少价格信息的情况下，我们能够对价格内生性进行实质性校正。