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Chernozhukov et al. (2016) provide a generic double/de-biased machine learning (ML) approach for obtaining valid inferential statements about focal parameters, using Neyman-orthogonal scores and cross-fitting, in settings where nuisance parameters are estimated using ML methods. In this note, we illustrate the application of this method in the context of estimating average treatment effects and average treatment effects on the treated using observational data.

Program evaluation methods are widely applied in economics to assess the effects of policy interventions and other treatments of interest. In this article, we describe the main methodological frameworks of the econometrics of program evaluation. In the process, we delineate some of the directions along which this literature is expanding, discuss recent developments, and highlight specific areas where new research may be particularly fruitful.

We introduce a flexible parametric family of matrix-valued covariance functions for multivariate spatial random fields, where each constituent component is a Matérn process. The model parameters are interpretable in terms of process variance, smoothness, correlation length, and colocated correlation coefficients, which can be positive or negative. Both the marginal and the cross-covariance functions are of the Matérn type. In a data example on error fields for numerical predictions of surface pressure and temperature over the North American Pacific Northwest, we compare the bivariate Matérn model to the traditional linear model of coregionalization.

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.

This paper presents genetic matching, a method of multivariate matching that uses an evolutionary search algorithm to determine the weight each covariate is given. Both propensity score matching and matching based on Mahalanobis distance are limiting cases of this method. The algorithm makes transparent certain issues that all matching methods must confront. We present simulation studies that show that the algorithm improves covariate balance and that it may reduce bias if the selection on observables assumption holds. We then present a reanalysis of a number of data sets in the LaLonde (1986) controversy.

Many environmental processes exhibit weakening spatial dependence as events become more extreme. Well-known limiting models, such as max-stable or generalized Pareto processes, cannot capture this, which can lead to a preference for models that exhibit a property known as asymptotic independence. However, weakening dependence does not automatically imply asymptotic independence, and whether the process is truly asymptotically (in)dependent is usually far from clear. The distinction is key as it can have a large impact upon extrapolation, that is, the estimated probabilities of events more extreme than those observed. In this work, we present a single spatial model that is able to capture both dependence classes in a parsimonious manner, and with a smooth transition between the two cases. The model covers a wide range of possibilities from asymptotic independence through to complete dependence, and permits weakening dependence of extremes even under asymptotic dependence. Censored likelihood-based inference for the implied copula is feasible in moderate dimensions due to closed-form margins. The model is applied to oceanographic datasets with ambiguous true limiting dependence structure. Supplementary materials for this article are available online.

Since Quetelet's work in the nineteenth century, social science has iconified the average man, that hypothetical man without qualities who is comfortable with his head in the oven and his feet in a bucket of ice. Conventional statistical methods since Quetelet have sought to estimate the effects of policy treatments for this average man. However, such effects are often quite heterogeneous: Medical treatments may improve life expectancy but also impose serious short-term risks; reducing class sizes may improve the performance of good students but not help weaker ones, or vice versa. Quantile regression methods can help to explore these heterogeneous effects. Some recent developments in quantile regression methods are surveyed in this review.

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.

Understanding and characterizing treatment effect variation in randomized experiments has become essential for going beyond the \"black box\" of the average treatment effect. Nonetheless, traditional statistical approaches often ignore or assume away such variation. In the context of randomized experiments, this article proposes a framework for decomposing overall treatment effect variation into a systematic component explained by observed covariates and a remaining idiosyncratic component. Our framework is fully randomization-based, with estimates of treatment effect variation that are entirely justified by the randomization itself. Our framework can also account for noncompliance, which is an important practical complication. We make several contributions. First, we show that randomization-based estimates of systematic variation are very similar in form to estimates from fully interacted linear regression and two-stage least squares. Second, we use these estimators to develop an omnibus test for systematic treatment effect variation, both with and without noncompliance. Third, we propose an R 2 -like measure of treatment effect variation explained by covariates and, when applicable, noncompliance. Finally, we assess these methods via simulation studies and apply them to the Head Start Impact Study, a large-scale randomized experiment. Supplementary materials for this article are available online.

Functions to calculate measures of spatial association, especially measures of spatial autocorrelation, have been made available in many software applications. Measures may be global, applying to the whole data set under consideration, or local, applying to each observation in the data set. Methods of statistical inference may also be provided, but these will, like the measures themselves, depend on the support of the observations, chosen assumptions, and the way in which spatial association is represented; spatial weights are often used as a representational technique. In addition, assumptions may be made about the underlying mean model, and about error distributions. Different software implementations may choose to expose these choices to the analyst, but the sets of choices available may vary between these implementations, as may default settings. This comparison will consider the implementations of global Moran’s I, Getis–Ord G and Geary’s C, local \\[I_i\\] and \\[G_i\\], available in a range of software including Crimestat, GeoDa, ArcGIS, PySAL and R contributed packages.