Second moments of asset returns are important for risk management and portfolio selection. The problem of estimating second moments can be approached from two angles: time series and the cross-section. In time series, the key is to account for conditional heteroskedasticity; a favored model is Dynamic Conditional Correlation (DCC), derived from the ARCH/GARCH family started by Engle (1982). In the cross-section, the key is to correct in-sample biases of sample covariance matrix eigenvalues; a favored model is nonlinear shrinkage, derived from Random Matrix Theory (RMT). The present paper marries these two strands of literature in order to deliver improved estimation of large dynamic covariance matrices.
These days, it is common practice to base inference about the coefficients in a hetoskedastic linear model on the ordinary least squares estimator in conjunction with using heteroskedasticity consistent standard errors. Even when the true form of heteroskedasticity is unknown, heteroskedasticity consistent standard errors can also used to base valid inference on a weighted least squares estimator and using such an estimator can provide large gains in efficiency over the ordinary least squares estimator. However, intervals based on asymptotic approximations with plug-in standard errors often have coverage that is below the nominal level, especially for small sample sizes. Similarly, tests can have null rejection probabilities that are above the nominal level. In this paper, it is shown that under unknown hereroskedasticy, a bootstrap approximation to the sampling distribution of the weighted least squares estimator is valid, which allows for inference with improved finite-sample properties. For testing linear constraints, permutations tests are proposed which are exact when the error distribution is symmetric and is asymptotically valid otherwise. Another concern that has discouraged the use of weighting is that the weighted least squares estimator may be less efficient than the ordinary least squares estimator when the model used to estimate the unknown form of the heteroskedasticity is misspecified. To address this problem, a new estimator is proposed that is asymptotically at least as efficient as both the ordinary and the weighted least squares estimator. Simulation studies demonstrate the attractive finite-sample properties of this new estimator as well as the improvements in performance realized by bootstrap confidence intervals.
This paper constructs a novel equilibrium in the chopstick auction of Szentes and Rosenthal (Games and Economic Behavior, 2003a, 2003b). In contrast to the existing solution, the identified equilibrium strategy allows a simple and intuitive characterization. Moreover, its best-response set has the same Hausdorff dimension as its support, which may be seen as a robustness property. The analysis also reveals some new links to the literature on Blotto games.
We show that a one-off incentive to bias advice has persistent effects. In an experiment, advisers were paid a bonus to recommend a lottery which only risk-seeking individuals should choose to a less informed client. Afterwards, they had to choose for themselves and make a second recommendation to another client, without any bonus. These advisers choose the risky lottery and recommend it a second time up to six times more often than advisers in a control group who were never offered a bonus. These results are consistent with a theory we present which is based on advisers' image concerns of appearing incorruptible.
