Discussion of A. Ronald Gallant: “Reflections on the Probability Space Induced by Moment Conditions with Implications for Bayesian Inference”

The paper of Gallant discussed the practicability of Bayesian inference under distributional assertions on the moment functions. It concluded that such inference is possible with a proper prior, if some of the properties of a pivotal statistic are satisfied by the moment functions. Our discussion focuses on the application to the Habit model. We use rolling windows of half the original sample size. This captures the many booms and recessions better than the original sample, covering a rather long period, and it explores the performance of the method with smaller samples. The results demonstrate that when the prior is proper, the approach gives decent performance even with relatively small samples, as the estimations of the curvature parameter with the sub-samples are rather stable among different rolling windows, and are close to those with the original sample. Results also show that an informative prior considerably supplements the decreased amount of information contained in the data, as the posterior standard deviations with sub-samples are similar to those with the original one.