Time-varying parameters in the almost ideal demand system and the Rotterdam model: will the best specification please stand up?

We use Monte Carlo simulations to assess the ability of the Rotterdam model and the three versions of the almost ideal demand system (AIDS) to recover the time-varying elasticities of a true demand system and to satisfy theoretical regularity. We find that the Rotterdam model performs better at recovering the signs of all the time-varying elasticities. More importantly, the RM has the ability to track the paths of time-varying income elasticities, even when the true values are very high. The linear-approximate AIDS, not only performs poorly at recovering the time-varying elasticities but also badly approximates the nonlinear AIDS.