Shrinkage Estimation, Model Selection and Uniform Inference in Possibly Nonstationary SVARs with External Instruments

Description

Structural vector autoregressive (SVAR) models are widely applied to estimate impulse response functions (IRFs), which describe the dynamic impacts of an economic shock on a system of variables. In recent years, SVARs with external instrumental variables (SVAR-IV) have become more popular to uncover the unobserved effects of economic shocks. Existing theory for SVAR-IVs is usually developed under a crucial assumption called stationarity. However, practitioners often include highly persistent time series into SVARs, so the stationarity assumption is likely to be violated in many empirical applications. Motivated by the gap between the theory and common practice, this project mainly concerns two theoretical problems when we allow for possible nonstationarity in SVAR-IV models.First, we will consider how to select useful (lagged) variables in SVAR-IV models via a shrinkage method called adaptive Lasso. This method has selection consistency, that is, it is able to keep relevant variables and eliminate irrelevant variables under the assumption of stationarity. In nonstationary cases, its properties are less explored in the literature. We plan to extend the theory of adaptive Lasso to nonstationary SVARs and design data dependent penalty terms so that adaptive Lasso can achieve selection consistency without requiring the knowledge about which variables are nonstationary.Second, this project plans to develop a statistical inference method that is uniformly valid over the parameter space. Our previous study develops a pointwise approximation for inference. Pointwise results may perform poorly when parameters take certain values in the parameter space. In contrast, the uniformity means that the inferential theory works for all values in the parameter space. That is, uniformly valid inference methods will work well when parameters take the least favorable values. We plan to find the conditions under which our previous pointwise result can achieve uniformity.