This chapter discusses the formal and informal techniques that are commonly used to give quantitative answers in the field of distributional analysis. To this end, it covers subjects including inequality, poverty, and the modeling of income distributions. It also deals with parametric and...

We study the finite-sample properties of tests for overidentifying restrictions in linear regression models with a single endogenous regressor and weak instruments. Under the assumption of Gaussian disturbances, we derive expressions for a variety of test statistics as functions of eight...

Bayesian decisions are observationally identical to decisions with judgment. Decisions with judgment test whether a judgmental decision is optimal and, in case of rejection, move to the closest boundary of the confidence interval, for a given confidence level. The resulting decisions condition...

We study the problem of nonparametric regression when the regressor is endogenous, which is an important nonparametric instrumental variables (NPIV) regression in econometrics and a difficult ill-posed inverse problem with unknown operator in statistics. We first establish a general upper bound...

The Regression Kink (RK) design is an increasingly popular empirical method, with more than 20 studies circulated using RK in the last 5 years since the initial circulation of Card, Lee, Pei and Weber (2012). We document empirically that these estimates, which typically use local linear...

We show that the Anderson-Rubin (AR) statistic is the sum of two independent piv-otal statistics. One statistic is a score statistic that tests location and the other statistictests misspecification. The chi-squared distribution of the location statistic has a degreesof freedom parameter that is...

A decision maker tests whether the gradient of the loss function evaluated at a judgmental decision is zero. If the test does not reject, the action is the judgmental decision. If the test rejects, the action sets the gradient equal to the boundary of the rejection region. This statistical...

In this study, we consider the test statistics that can be written as the sample average of data and derive their limiting distribution under the maximum likelihood (ML) and the quasi-maximum likelihood (QML) frameworks. We first generalize the asymptotic variance formula suggested in Pierce...

We are occupied with a simple example concerning the limit theory of the OLSE when the innovation process of the regression has the form of a martingale transform the i.i.d. part of which lies in the domain of attraction of an \alpha-stable distribution, the scalling sequence has a potentially...

This paper presents a discussion of overdispersed generalized linear regression models. Commonly used estimates of the unknown dispersion parameter are the Pearson statistic or the modification of Farrington (1996), who proposed a first order linear correction term to Pearson's statistic. We...