Estimating bid-auction models of residential location using census data with imputed household income

Modeling residential location as a key component of the land-use system is essential to understanding the relationship between land use and transport. The increasing availability of censuses such as the German Zensus 2011 has enabled residential location to be modeled with a large number of observations, presenting both opportunities and challenges. Censuses are statistically highly representative; however, they often lack variables such as income or mobility-related attributes as in the case of Zensus 2011. This is particularly problematic if missing variables define utility or willingness-to-pay functions that characterize choice options in a location model. One example of this is household income, which is an indispensable variable in land-use models because it influences household location preferences and defines affordable location options. For estimating bid-auction location models for different income groups, we impute household income in census data applying an ordered regression model. We find that location models considering this imputation perform sufficiently well as they reveal reasonable and expected aspects of the location patterns. In general, imputing choice variables should thus be considered in the estimation of residential location models but is also promising for other decision problems. Comparing results for two imputation methods, we also show that while applying the deterministic first preference imputation could yield misleading results, the probabilistic Monte Carlo simulation is the correct imputation approach.