Identification Robust Inference for the Risk Premium in Term Structure Models

TL;DR

This paper develops robust statistical tests for assessing the risk premia in dynamic affine term structure models, addressing identification issues and extending existing tests to multi-factor, time-varying settings.

Contribution

It introduces an extension of the Anderson-Rubin test for models with multiple factors and time-varying risk prices, providing a computationally feasible method for robust inference.

Findings

Some factors influence risk price variation despite being weak.

Weak identification issues are more common in multi-factor models.

Empirical analysis highlights potential pitfalls in inference without full-rank loadings.

Abstract

We propose identification robust statistics for testing hypotheses on the risk premia in dynamic affine term structure models. We do so using the moment equation specification proposed for these models in Adrian et al. (2013). We extend the subset (factor) Anderson-Rubin test from Guggenberger et al. (2012) to models with multiple dynamic factors and time-varying risk prices. Unlike projection-based tests, it provides a computationally tractable manner to conduct identification robust tests on a larger number of parameters. We analyze the potential identification issues arising in empirical studies. Statistical inference based on the three-stage estimator from Adrian et al. (2013) requires knowledge of the factors' quality and is misleading without full-rank beta's or with sampling errors of comparable size as the loadings. Empirical applications show that some factors, though potentially weak, may drive the time variation of risk prices, and weak identification issues are more prominent in multi-factor models.