/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

On robust estimation of the location parameter

We consider statistical inference for regression when data are grouped into clus- ters, with regression model errors independent across clusters but correlated within clusters. Examples include data on individuals with clustering on village or region or other category such as industry, and state-year dierences-in-dierences studies with clustering on state. In such settings default standard errors can greatly overstate es- timator precision. Instead, if the number of clusters is large, statistical inference after OLS should be based on cluster-robust standard errors. We outline the basic method as well as many complications that can arise in practice. These include cluster-specic �xed eects, few clusters, multi-way clustering, and estimators other than OLS.

/pdf/a-practitioner-s-guide-to-cluster-robust-inference-1xbcejtio0.pdf

A Practitioner’s Guide to Cluster-Robust Inference

Many empirical questions in economics and other social sciences depend on causal effects of programs or policies. In the last two decades, much research has been done on the econometric and statistical analysis of such causal effects. This recent theoreti- cal literature has built on, and combined features of, earlier work in both the statistics and econometrics literatures. It has by now reached a level of maturity that makes it an important tool in many areas of empirical research in economics, including labor economics, public finance, development economics, industrial organization, and other areas of empirical microeconomics. In this review, we discuss some of the recent developments. We focus primarily on practical issues for empirical research- ers, as well as provide a historical overview of the area and give references to more technical research.

/pdf/recent-developments-in-the-econometrics-of-program-42vjewfvjw.pdf

Recent developments in the econometrics of program evaluation

In this article, we review quantile models with endogeneity. We focus on models that achieve identification through the use of instrumental variables and discuss conditions under which partial and point identification are obtained. We discuss key conditions, which include monotonicity and full-rank-type conditions, in detail. In providing this review, we update the identification results of Chernozhukov & Hansen (2005). We illustrate the modeling assumptions through economically motivated examples. We also briefly review the literature on estimation and inference.

/pdf/quantile-models-with-endogeneity-72pynhdv8j.pdf

Quantile models with endogeneity

The paper develops estimation and inference methods for econometric models with partial identification, focusing on models defined by moment inequalities and equalities. Main applications of this framework include analysis of game-theoretic models, regression with missing and mismeasured data, bounds in structural quantile models, and bounds in asset pricing, among others.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID909666_code229587.pdf?abstractid=909666&mirid=1

Instrumental Variable Quantile Regression

https://www.ifs.org.uk/uploads/cemmap/wps/cwp381616.pdf

Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings

We propose new concepts of statistical depth, multivariate quantiles, ranks and signs, based on canonical transportation maps between a distribution of interest on $R^d$ and a reference distribution on the $d$-dimensional unit ball. The new depth concept, called Monge-Kantorovich depth, specializes to halfspace depth in the case of spherical distributions, but, for more general distributions, differs from the latter in the ability for its contours to account for non convex features of the distribution of interest. We propose empirical counterparts to the population versions of those Monge-Kantorovich depth contours, quantiles, ranks and signs, and show their consistency by establishing a uniform convergence property for empirical transport maps, which is of independent interest.

Monge-Kantorovich Depth, Quantiles, Ranks, and Signs

Quantile regression (QR) methods fit a linear model for conditional quantiles, just as ordinary least squares (OLS) regression estimates a linear model for conditional means. An attractive feature of the OLS estimator is that it gives a minimum mean square error approximation to the conditional expectation function even when the linear model is mis-specified. Empirical research on quantile regression with discrete covariates suggests that QR has a similar property, but the exact nature of the linear approximation has remained elusive. In this paper, we show that QR can be interpreted as minimizing a weighted mean-squared error loss function for the specification error. We derive the weighting function and show that it is approximately equal to the conditional density of QR residuals. The paper goes on to derive the limiting distribution of QR estimators under very general conditions allowing for mis-specification of the conditional quantile function. Finally, we develop methods for the use of QR as a modelling tool for the entire conditional distribution of a random variable. Testable hypotheses include location-scale models, proportional heteroscedasticity, and stochastic dominance. These ideas are illustrated with a human capital earnings function

Victor Chernozhukov

Papers

Quantile models with endogeneity

Instrumental Variable Quantile Regression

Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings

Monge-Kantorovich Depth, Quantiles, Ranks, and Signs

Quantile Regression under Misspecification