Adaptive Shrinkage Estimation of High Dimensional Moment Condition Model with Smooth Structural Changes

Abstract

Structural change is a long-standing problem in time series econometrics and macroeconomics, and financial time series are likely to be affected by structural instability due to changes in preferences, technologies, policies, etc. Most of the existing literature on moment condition models assumed that structural parameters were fixed over the entire sample period. To allow for time-varying structural parameters in the high dimensional moment condition models, this paper proposes a shrinkage local generalized method of moment (SLGMM) which simultaneously achieves parameter estimation and moment selection. We show that our method consistently selects the correct moment conditions and the SLGMM estimator possesses the oracle property, that is, it is as efficient as the time-varying GMM estimator based on all valid moment conditions. Moreover, we establish the consistency and asymptotic normality of the SLGMM estimator. A Monte Carlo simulation and an empirical application on asset pricing are conducted to show the merits of the newly proposed method.