Weak (Proxy) Factors Robust Hansen-Jagannathan Distance For Linear Asset Pricing Models
Abstract: The Hansen-Jagannathan (HJ) distance statistic is one of the most dominant measures of model misspecification. However, the conventional HJ specification test procedure has poor finite sample performance, and we show that it can be size distorted even in large samples when (proxy) factors exhibit small correlations with asset returns. In other words, applied researchers are likely to reject a model even when it is correctly specified falsely. We provide two alternatives for the HJ statistic and two corresponding novel procedures for model specification tests, which are robust against the presence of weak (proxy) factors, and we also offer a novel robust risk premia estimator. Simulation exercises support our theory. Our empirical application documents the non-reliability of the traditional HJ test as it may produce counter-intuitive results, when comparing nested models, by rejecting a four-factor model but not the reduced three-factor model, while our proposed methods are practically more appealing and show support for a four-factor model for Fama French portfolios.
Identification Robust Testing of Risk Premia in Finite Samples
(conditionally accepted: Journal of Financial Econometrics )
co-authored with Frank Kleibergen and Zhaoguo Zhan
Abstract: The reliability of tests on risk premia in linear factor models is threatened by limited sample sizes and weak identification of risk premia frequently encountered in applied work. We propose novel tests on the risk premia that are robust to both limited sample sizes and the identification strength of the risk premia as reflected by the quality of the risk factors. These tests are appealing for empirically relevant settings, and lead to confidence sets of the risk premia that can substantially different from conventional ones. To show the latter, we revisit two high-profile empirical applications.
Weak (And Over) Identification In Affine Term Structure Models
Abstract: Affine term structure models explore the factor structures in a set of bonds with various maturities. Tractability of affine models comes at the cost of restrictive structural assumptions, induced by the no-arbitrage requirement. Two main issues arise from these structural assumptions: weak identification due to small-βs factors, factors weakly correlated with returns and thus less informative for the identification, and misspecification due to the highly parametric setting. In this thesis, we focus on the reduced rank restrictions in the form of D=βλ. This thesis investigates a regression-based estimator proposed by Adrian et al.  for a general class of affine term structure models. We show that statistical inference on the estimated risk premia based on the regression-based estimator might be misleading with small-βs factors. We propose robust tests against bad-behaved factors, and check the validity of reduced rank restrictions in the affine term structure models.