Nonparametric Estimation and Inference on Conditional Quantile Processes , (with Jungmo Yoon) March 24, 2011; This version: May 18, 2012.

This paper develops estimation method and asymptotic theory for the analysis of a nonparametrically specified conditional quantile process. For estimation, a simple estimator is proposed which builds on a family of local linear regressions and maintains quantile monotonicity through inequality constraints. As an important feature, the bandwidth parameter is allowed to vary across quantiles to adapt to the data sparsity. For inference, three sets of results are established. First, a uniform Bahadur representation is obtained for the estimator. Second, it is shown that the estimator converges weakly to a continuous Gaussian process, whose critical values can be estimated via simulations by exploiting the fact that it is conditionally pivotal. Third, it is proven that the above asymptotic theory is applicable to quantile processes estimated using rearrangement. We discuss how to apply these results to study quantile dependent treatment effects, to test for conditional stochastic dominance and to evaluate causal effects under the sharp regression discontinuity design. As an empirical illustration, we consider a data set from an experiment known as Project STAR (Student-Teacher Achievement Ratio). The results deliver two new findings benefiting from modeling distributional effects in a flexible nonparametric setting.

Inference and Specification Testing in DSGE Models with Possible Weak Identification, April, 2011; this version: November 2011.

This paper considers inference and model diagnostics for log-linearized DSGE models allowing an unknown subset of parameters to be weakly (including un-) identified. The framework allows for latent state variables, measurement errors and also permits analysis using only part of the spectrum, say at the business cycle frequencies. The latter is important because DSGE models are often designed to explain business cycle movements, not very long-run or very short-run fluctuations. For inference, we first characterize weak identification from a frequency domain perspective and propose a score test for the structural parameters based on the frequency domain maximum likelihood. The construction heavily exploits the structures of the DSGE solution, the score function and the information matrix. In particular, we show that the test statistic can be represented as the explained sum of squares from a complex-valued multivariate linear regression, where weak identification surfaces as (imperfectly) multicollinear regressors. Then, we prove that asymptotically valid inference can be carried out by inverting this test statistic and using Chi-square critical values. Next, we suggest procedures to construct uniform confidence bands for the impulse response function, the time path of the variance decomposition, the individual spectrum and the absolute coherency. For model diagnostics, we propose a family of frequency domain misspecification tests that are robust to weak identification. They can be used to test for misspecification in the mean, in the spectrum as well as misspecification within a band of frequencies. A simulation experiment using a calibrated model suggests that the tests have adequate size even in relatively small samples. It also suggests that it is possible to have informative confidence sets in DSGE models with unidentified parameters, particularly regarding the impulse responses functions. Although the paper focuses on DSGE models, the methods developed are potentially applicable to other dynamic models with well defined spectra, such as the stationary (factor-augmented) structural vector autoregression.

Local and Global Parameter Identification in DSGE Models Allowing for Indeterminacy, May 2013.