Cross-sectional GMM estimation under a common data shock

A GMM estimation approach is developed for a stylized cross-sectional model with a non-localized common data shock. Common shocks are often encountered in economics and finance. Thus, their implications for estimation are of substantial interest. Other researchers investigated properties of OLS estimator under localized and non-localized shocks and proposed a GMM estimator for cross-sectional data with localized shocks. However, cross-sectional GMM estimation under non-localized shocks received little attention. We fill in the gap by developing an estimation framework in this setting. We propose one- and two-step GMM estimators and prove that they are consistent and asymptotically mixed normal under specified regularity conditions. The asymptotic mixed normality of our estimators differentiates them from usual asymptotically normal GMM estimators and necessitates a further investigation of statistical inference and specification testing. We show that despite the estimators' asymptotic mixed normality, conventional Wald tests can still be employed. We also prove that the OIR test retains its usual chi-squared asymptotic distribution. We investigate finite-sample performance of the method using Monte Carlo simulations of a financial model featuring a market-wide systematic risk. The approach allows us to estimate instantaneous market volatility, average instantaneous idiosyncratic volatility, and idiosyncratic risk-premium using only a cross-section of stock returns.