A Model for Ordinal Responses with an Application to Policy Interest Rate

Abstract

The decisions to reduce, leave unchanged, or increase (the price, rating, policy interest rate, etc.) are often characterized by abundant no-change outcomes that are generated by different processes. Moreover, the positive and negative responses can also be driven by distinct forces. To capture the heterogeneity of the data-generating process this paper develops a two-stage cross-nested model, combining three ordered probit equations. In the policy rate setting context, the first stage, a policy inclination decision, determines a latent policy stance (loose, neutral or tight), whereas the two latent amount decisions, conditional on a loose or tight stance, fine-tune the rate at the second stage. The model allows for the possible correlation among the three latent decisions. This approach identifies the driving factors and probabilities of three types of zeros: the "neutral" zeros, generated directly by a neutral policy stance, and two kinds of "offset" zeros, the "loose" and "tight" zeros, generated by a loose or tight stance, offset at the second stage. Monte Carlo experiments show good performance in small samples. Both the simulations and empirical applications to the panel data on individual policymakers' votes for the interest rate demonstrate the superiority with respect to the conventional and two-part models.