Checking the power of the Econometric method presented in A Random Attention Model with a special case

Abstract

Abstract

I test the power of the econometric method presented in Masatlioglu et al. (2018) using simulation. The choice dataset is generated by the model presented in Aguiar (2017), RCG model, which is a special case of the model presented in Masatlioglu et al. (2018), RAM model. The observable choice dataset satisfying the RCG model reveals no preference relation according to RAM model. I question if the econometric method can still verify the underlying true preference order as compatible and correctly reject the false preference orders. I show that the econometric method presented in RAM has trivial power in the special case since the construction of the dataset admits the test statistics to exist on the boundary of the moment inequality. However, the method relatively performs well when there exist few alternatives in the choice problem, narrowing down the candidates for the underlying preference order that are compatible with the given dataset. On the other hand, when many alternatives exist, the method fails to give any information about what the true underlying preference might be. When this boundary issue is anticipated, I suggest a one-sided hypothesis test to circumvent this problem and provide simulation evidence to support it. The evidence shows that the one-sided hypothesis test has higher power and gives information about what the true preference order might be in this special case.