Estimating and Testing Time Variation Modeling Misspecification

Description

There is growing empirical evidence that the structure of economic relationships changes over time. Enabling time variation in econometric models is vital in economic and finance studies, such as when capturing time-varying risk exposures, modeling dynamic volatility estimation, engaging in high-frequency and high-dimensional factor model analysis, and solving for policy functions in dynamic stochastic general equilibrium models. Recent years have witnessed great enthusiasm for developing time-varying econometric models. Unfortunately, existing economic theory does not identify the underlying conditioning or state variables that drive time variation. Hence, all the existing time-varying estimation methods run the risk, to varying degrees, of misspecification. Different dynamic and time-varying econometric methods often produce diverse and even conflicting results. Since all models could be wrong, the primary focus should not be on developing sophisticated test statistics to reject existing models. The more meaningful approach seeks to know and measure the discrepancy between the actual underlying process and a given specification method. However, econometricians and empirical practitioners have long struggled to measure and test the appropriateness of time variation modeling so that they could decide on an appropriate modeling strategy. This project intends to fill the gap and objectively evaluate time-varying misspecification detection and tests. We will develop a novel and first-available methodology for testing and measuring time variation specifications in this project. Misspecification in time-varying modeling can come from various channels, such as omitted variable biases from conditioning variables, failure to include deterministic processes, the existence of latent processes, and so forth. We aim to provide guidance to empirical practitioners regarding the choice of appropriate time variation specification methods and to determine the richness of the conditioning variables used in modeling time variation in economic and financial systems.As a direct application, this project will revisit the stochastic discount factor model with time-varying risk prices. In the literature, there is an ongoing debate about whether the source of time variation in factor prices is a function of time or some stochastic processes. If conditioning variables drive time-varying parameters, is the unsatisfactory improvement in its explanatory power due to the existence of omitted variable biases? This proposal also intends to extend our estimation and testing methodology to high frequency analysis, in which observations are sampled frequently. The literature has documented time variation in factors and factor loadings. We intend to answer whether this variation is due to changes in factors or factor loadings, given the altered high-frequency covariance matrix structure.