On the Use of the Harmonic Mean Estimator for Selecting the Hypothetical Income Distribution from Grouped Data

It is known that the harmonic mean estimator is a consistent estimator of the marginal likelihood and is easy to implement, but it has severe biases and does not change as much as the prior distribution changes. In this study, we investigate the use of the harmonic mean estimator to select the hypothetical income distribution from grouped data through Monte Carlo simulations and apply it to real data in Japan. From the results, we confirm that there are significant biases, but it can be reliably used to select an appropriate model only when the sample size is large enough under appropriate prior settings.