Fitting Dynamically Misspecified Models: An Optimal Transportation Approach

TL;DR

This paper introduces an optimal transportation-based method for filtering and estimation in potentially misspecified state-space models, ensuring model consistency and improving interpretability.

Contribution

It develops a novel sequential optimal transportation approach and a closed-form filtering algorithm for linear processes, with theoretical properties and empirical applications.

Findings

Generated samples are model-consistent and improve interpretability.

The optimal transport estimator has well-defined large sample properties.

Empirical applications demonstrate the method's effectiveness in various models.

Abstract

This paper considers filtering, parameter estimation, and testing for potentially dynamically misspecified state-space models. When dynamics are misspecified, filtered values of state variables often do not satisfy model restrictions, making them hard to interpret, and parameter estimates may fail to characterize the dynamics of filtered variables. To address this, a sequential optimal transportation approach is used to generate a model-consistent sample by mapping observations from a flexible reduced-form to the structural conditional distribution iteratively. Filtered series from the generated sample are model-consistent. Specializing to linear processes, a closed-form Optimal Transport Filtering algorithm is derived. Minimizing the discrepancy between generated and actual observations defines an Optimal Transport Estimator. Its large sample properties are derived. A specification test determines if the model can reproduce the sample path, or if the discrepancy is statistically significant. Empirical applications to DSGE models, affine term structure models, and trend-cycle decomposition illustrate the methodology and the results.