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The instrumental variable quantile regression (IVQR) model (Chernozhukov and Hansen (2005)) is a popular tool for estimating causal quantile effects with endogenous covariates. However, estimation is complicated by the nonsmoothness and nonconvexity of the IVQR GMM objective function. This paper shows that the IVQR estimation problem can be decomposed into a set of conventional quantile regression subproblems which are convex and can be solved efficiently. This reformulation leads to new identification results and to fast, easy to implement, and tuning-free estimators that do not require the availability of high-level \"black box\" optimization routines.

In the regression-discontinuity (RD) design, units are assigned to treatment based on whether their value of an observed covariate exceeds a known cutoff. In this design, local polynomial estimators are now routinely employed to construct confidence intervals for treatment effects. The performance of these confidence intervals in applications, however, may be seriously hampered by their sensitivity to the specific bandwidth employed. Available bandwidth selectors typically yield a \"large\" bandwidth, leading to data-driven confidence intervals that may be biased, with empirical coverage well below their nominal target. We propose new theory-based, more robust confidence interval estimators for average treatment effects at the cutoff in sharp RD, sharp kink RD, fuzzy RD, and fuzzy kink RD designs. Our proposed confidence intervals are constructed using a bias-corrected RD estimator together with a novel standard error estimator. For practical implementation, we discuss mean squared error optimal bandwidths, which are by construction not valid for conventional confidence intervals but are valid with our robust approach, and consistent standard error estimators based on our new variance formulas. In a special case of practical interest, our procedure amounts to running a quadratic instead of a linear local regression. More generally, our results give a formal justification to simple inference procedures based on increasing the order of the local polynomial estimator employed. We find in a simulation study that our confidence intervals exhibit close-to-correct empirical coverage and good empirical interval length on average, remarkably improving upon the alternatives available in the literature. All results are readily available in R and STATA using our companion software packages described in Calonico, Cattaneo, and Titiunik (2014d, 2014b).

We investigate the choice of the bandwidth for the regression discontinuity estimator. We focus on estimation by local linear regression, which was shown to have attractive properties (Porter, J. 2003, \"Estimation in the Regression Discontinuity Model\" (unpublished, Department of Economics, University of Wisconsin, Madison)). We derive the asymptotically optimal bandwidth under squared error loss. This optimal bandwidth depends on unknown functionals of the distribution of the data and we propose simple and consistent estimators for these functionals to obtain a fully data-driven bandwidth algorithm. We show that this bandwidth estimator is optimal according to the criterion of Li (1987, \"Asymptotic Optimality for C p , C L , Cross-validation and Generalized Cross-validation: Discrete Index Set\", Annals of Statistics, 15, 958–975), although it is not unique in the sense that alternative consistent estimators for the unknown functionals would lead to bandwidth estimators with the same optimality properties. We illustrate the proposed bandwidth, and the sensitivity to the choices made in our algorithm, by applying the methods to a data set previously analysed by Lee (2008, \"Randomized Experiments from Non-random Selection in U.S. House Elections\", Journal of Econometrics, 142, 675–697) as well as by conducting a small simulation study.

This paper provides an introduction and \"user guide\" to Regression Discontinuity (RD) designs for empirical researchers. It presents the basic theory behind the research design, details when RD is likely to be valid or invalid given economic incentives, explains why it is considered a \"quasi-experimental\" design, and summarizes different ways (with their advantages and disadvantages) of estimating RD designs and the limitations of interpreting these estimates. Concepts are discussed using examples drawn from the growing body of empirical research using RD.

In difference-in-differences applications, identification of the key parameter often arises from changes in policy by a small number of groups. In contrast, typical inference assumes that the number of groups changing policy is large. We present an alternative inference approach for a small (finite) number of policy changers, using information from a large sample of nonchanging groups. Treatment effect point estimators are not consistent, but we can consistently estimate their asymptotic distribution under any point null hypothesis about the treatment. Thus, treatment point estimators can be used as test statistics, and confidence intervals can be constructed using test statistic inversion.

This paper documents the pervasiveness of job polarization in 16 Western European countries over the period 1993-2010. It then develops and estimates a framework to explain job polarization using routine-biased technological change and offshoring. This model can explain much of both total job polarization and the split into within-industry and between-industry components.

We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L 2 related norms, with dispersive estimates, which give decay in L ∞ . To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.

Motivated by the question of which point-estimator digits to report in a statistical experiment, we study the probabilistic behavior of the digits as a function of the true performance measure and the point estimator's standard error. We investigate the family of Leading-Digit Rules, which guarantees that every unreported digit has correctness probability below a given threshold. Choosing the threshold to be about 0.198 yields Yoneda's rule. The easy-to-implement rule that reports the point estimate through the leading digit of the standard error has threshold (approximately) 0.117, which is not much larger than the one-in-ten probability of a uniformly distributed random digit being correct.

We review the main identification strategies and empirical evidence on the role of expectations in the New Keynesian Phillips curve, paying particular attention to the issue of weak identification. Our goal is to provide a clear understanding of the role of expectations that integrates across the different papers and specifications in the literature. We discuss the properties of the various limited-information econometric methods used in the literature and provide explanations of why they produce conflicting results. Using a common dataset and a flexible empirical approach, we find that researchers are faced with substantial specification uncertainty, as different combinations of various a priori reasonable specification choices give rise to a vast set of point estimates. Moreover, given a specification, estimation is subject to considerable sampling uncertainty due to weak identification. We highlight the assumptions that seem to matter most for identification and the configuration of point estimates. We conclude that the literature has reached a limit on how much can be learned about the New Keynesian Phillips curve from aggregate macroeconomic time series. New identification approaches and new datasets are needed to reach an empirical consensus.

This paper studies the effect of sentiment on asset prices during the 20th century (1905 to 2005). As a proxy for sentiment, we use the fraction of positive and negative words in two columns of financial news from the New York Times. The main contribution of the paper is to show that, controlling for other well-known time-series patterns, the predictability of stock returns using news' content is concentrated in recessions. A one standard deviation shock to our news measure during recessions predicts a change in the conditional average return on the DJIA of 12 basis points over one day.