Random utility models have become standard econometric tools, allowing parameter inference for individual-level categorical choice data. Such models typically presume that changes in observed choices over time can be attributed to changes in either covariates or unobservables. We study how choice dynamics can be captured more faithfully by also directly modeling temporal changes in parameters, using a vector autoregressive process and Bayesian estimation. This approach offers a number of advantages for theorists and practitioners, including improved forecasts, prediction of long-run parameter levels, and correction for potential aggregation biases. We illustrate the method ...