Philipp Ketz, Paris School of Economics – University of Copenhagen

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Philipp Ketz, Paris School of Economics

"A Simple Solution to Invalid Inference in the Random Coefficients Logit Model"

Abstract

We show that the standard approach to inference in the random coefficients logit model suffers from size distortions. The problem arises due to boundary issues and is aggravated when the model is parameterized with respect to standard deviations, which constitutes common practice. For example, in case of a single random coefficient, the asymptotic size of the nominal 95% confidence interval, which is obtained by inverting the two-sided t-test for the standard deviation, equals 83.65%. In seeming contradiction, we also find that standard errors can be unreasonably large. The proposed solution is to perform inference with respect to variances rather than standard deviations. This alleviates the problem of unreasonably large standard errors and, in combination with the estimator proposed in Ketz (2017a), allows the construction of confidence intervals that (uniformly) control asymptotic size.

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Link to paper

Contact person: Rasmus Søndergaard Pedersen