Detecting Unobserved Heterogeneity in Efficient Prices via Classifier-Lasso

This article proposes a new measure of efficient price as a weighted average of bid and ask prices, where the weights are constructed from the bid-ask long-run relationships in a panel error-correction model (ECM). To allow for heterogeneity in the long-run relationships, we consider a panel ECM with latent group structures so that all the stocks within a group share the same long-run relationship and do not otherwise. We extend the Classifier-Lasso method to the ECM to simultaneously identify the individual’s group membership and estimate the group-specific long-run relationship. We establish the uniform classification consistency and good asymptotic properties of the post-Lasso estimators under some regularity conditions. Empirically, we find that more than 30% of the Standard & Poor’s (S&P) 1500 stocks have estimated efficient prices significantly deviating from the midpoint—a conventional measure of efficient price. Such deviations explored from our data-driven method can provide dynamic information on the extent and direction of informed trading activities.