Paper # Author Title
This paper studies the averaging generalized method of moments (GMM) estimator that combines a conservative GMM estimator based on valid moment conditions and an aggressive GMM estimator based on both valid and possibly misspecified moment conditions, where the weight is the sample analog of an infeasible optimal weight. It is an alternative to pre-test estimators that switch between the conservative and aggressive estimators based on model specification tests. This averaging estimator is robust in the sense that it uniformly dominates the conservative estimator by reducing the risk under any degree of misspecification, whereas the pre-test estimators reduce the risk in parts of the parameter space and increase it in other parts. To establish uniform dominance of one estimator over another, we establish asymptotic theories on uniform approximations of the finite-sample risk differences between two estimators. These asymptotic results are developed along drifting sequences of data generating processes (DGPs) that model various degrees of local misspecification as well as global misspecification. Extending seminal results on the James-Stein estimator, the uniform dominance is established in non-Gaussian semiparametric nonlinear models. The proposed averaging estimator is applied to estimate the human capital production function in a life-cycle labor supply model. Download Paper
The paper studies inference in nonlinear models where identification loss presents in multiple parts of the parameter space. For uniform inference, we develop a local limit theory that models mixed identification strength. Building on this non-standard asymptotic approximation, we suggest robust tests and confidence intervals in the presence of non-identified and weakly identified nuisance parameters. In particular, this covers applications where some nuisance parameters are non-identified under the null (Davies (1977, 1987)) and some nuisance parameters are subject to a full range of identification strength. The asymptotic results involve both inconsistent estimators that depend on a localization parameter and consistent estimators with different rates of convergence. A sequential argument is used to peel the criterion function based on identification strength of the parameters. The robust test is uniformly valid and non-conservative. Download Paper
This paper studies the selection of valid and relevant moments for the generalized method of moments (GMM) estimation. For applications with many candidate moments, our asymptotic analysis accommodates a diverging number of moments as the sample size increases. The proposed procedure achieves three objectives in one-step: (i) the valid and relevant moments are distinguished from the invalid or irrelevant ones; (ii) all desired moments are selected in one step instead of in a stepwise manner; (iii) the parameters of interest are automatically estimated with all selected moments as opposed to a post-selection estimation. The new method performs moment selection and efficient estimation simultaneously via an information-based adaptive GMM shrinkage estimation, where an appropriate penalty is attached to the standard GMM criterion to link moment selection to shrinkage estimation. The penalty is designed to signal both moment validity and relevance for consistent moment selection. We develop asymptotic results for the high-dimensional GMM shrinkage estimator, allowing for non-smooth sample moments and weakly dependent observations. For practical implementation, this one-step procedure is computationally attractive. Download Paper
This paper considers forecast combination with factor-augmented regression. In this framework, a large number of forecasting models are available, varying by the choice of factors and the number of lags. We investigate forecast combination across models using weights that minimize the Mallows and the leave-h-out cross validation criteria. The unobserved factor regressors are estimated by principle components of a large panel with N predictors over T periods. With these generated regressors, we show that the Mallows and leave-h-out cross validation criteria are asymptotically unbiased estimators of the one-step-ahead and multi-step-ahead mean squared forecast errors, respectively, provided that N, T → ∞. (However, the paper does not establish any optimality properties for the methods.) In contrast to well-known results in the literature, this result suggests that the generated-regressor issue can be ignored for forecast combination, without restrictions on the relation between N and T. Simulations show that the Mallows model averaging and leave-h-out cross-validation averaging methods yield lower mean squared forecast errors than alternative model selection and averaging methods such as AIC, BIC, cross validation, and Bayesian model averaging. We apply the proposed methods to the U.S. macroeconomic data set in Stock and Watson (2012) and find that they compare favorably to many popular shrinkage-type forecasting methods. Download Paper
This paper considers forecast combination with factor-augmented regression. In this framework, a large number of forecasting models are available, varying by the choice of factors and the number of lags. We investigate forecast combination using weights that minimize the Mallows and the leave-h-out cross validation criteria. The unobserved factor regressors are estimated by principle components of a large panel with N predictors over T periods. With these generated regressors, we show that the Mallows and leave-h-out cross validation criteria are approximately unbiased estimators of the one-step-ahead and multi-step-ahead mean squared forecast errors, respectively, provided that N, T —› ∞. In contrast to well-known results in the literature, the generated-regressor issue can be ignored for forecast combination, without restrictions on the relation between N and T. Simulations show that the Mallows model averaging and leave-h-out cross-validation averaging methods yield lower mean squared forecast errors than alternative model selection and averaging methods such as AIC, BIC, cross validation, and Bayesian model averaging. We apply the proposed methods to the U.S. macroeconomic data set in Stock and Watson (2012) and find that they compare favorably to many popular shrinkage-type forecasting methods. Download Paper
This paper considers the selection of valid and relevant moments for the generalized method of moments (GMM) estimation. For applications with many candidate moments, our asymptotic analysis ccommodates a diverging number of moments as the sample size increases. The proposed procedure achieves three objectives in one-step: (i) the valid and relevant moments are selected simultaneously rather than sequentially; (ii) all desired moments are selected together instead of in a stepwise manner; (iii) the parameter of interest is automatically estimated with all selected moments as opposed to a post-selection estimation. The new moment selection method is achieved via an information-based adaptive GMM shrinkage estimation, where an appropriate penalty is attached to the standard GMM criterion to link moment selection to shrinkage estimation. The penalty is designed to signal both moment validity and relevance for consistent moment selection and efficient estimation. The asymptotic analysis allows for non-smooth sample moments and weakly dependent observations, making it generally applicable. For practical implementation, this one-step procedure is computationally attractive. Download Paper