When the endogenous variable enters the structural equation non-parametrically the linear Instrumental Variable (IV) estimator is no longer consistent. Non-parametric IV (NPIV) can be used but it requires one to impose restrictions during estimation to make the problem well-posed. The...

Recent empirical work in several economic fields, particularly environmental and energy economics, has adapted the regression discontinuity (RD) framework to applications where time is the running variable and treatment begins at a particular threshold in time. In this guide for practitioners,...

Let Y be an outcome of interest, X a vector of treatment measures, and W a vector of pre-treatment control variables. Here X may include (combinations of) continuous, discrete, and/or non-mutually exclusive “treatments”. Consider the linear regression of Y onto X in a subpopulation...

The canonical difference-in-differences (DD) model contains two time periods, “pre” and “post”, and two groups, “treatment” and “control”. Most DD applications, however, exploit variation across groups of units that receive treatment at different times. This paper derives an...

The conventional heteroskedasticity-robust (HR) variance matrix estimator for cross-sectional regression (with or without a degrees of freedom adjustment), applied to the fixed effects estimator for panel data with serially uncorrelated errors, is inconsistent if the number of time periods T is...

The popular quantile regression estimator of Koenker and Bassett (1978) is biased if there is an additive error term. Approaching this problem as an errors-in-variables problem where the dependent variable suffers from classical measurement error, we present a sieve maximum-likelihood approach...

In a seminal paper Abadie et al (2010) develop the synthetic control procedure for estimating the effect of a treatment, in the presence of a single treated unit and a number of control units, with pre-treatment outcomes observed for all units. The method constructs a set of weights such that...

It is common in regression discontinuity analysis to control for high order (third, fourth, or higher) polynomials of the forcing variable. We argue that estimators for causal effects based on such methods can be misleading, and we recommend researchers do not use them, and instead use...

Count data regressions are an important tool for empirical analyses ranging from analyses of patent counts to measures of health and unemployment. Along with negative binomial, Poisson panel regressions are a preferred method of analysis because the Poisson conditional fixed effects maximum...