statistics

A simulation for OLS model In an observational study, we need to assume we have the functional form to get causal effect estimated correctly, in addtion to the assumption of treatment being exogenous.

In a non-linear model (for example, logit or poisson model), the interpretation of the coefficient on the interaction term is tricky. Ai and Norton (2003) points out that the interaction term coefficient is not the same as people can interpret as in a linear model; that is, how much effect of \(x1\) changes with the value of \(x2\).

Interaction with two binary variables In a regression model with interaction term, people tend to pay attention to only the coefficient of the interaction term. Let’s start with the simpliest situation: \(x_1\) and \(x_2\) are binary and coded 0/1.

Marginal effects in a linear model Stata’s margins command has been a powerful tool for many economists. It can calculate predicted means as well as predicted marginal effects. However, we do need to be careful when we use it when fixed effects are included.

In empirical studies, data sets with a lot of zeros are often hard to model. There are various models to deal with it: zero-inflated Poisson model, Negative Binomial (NB)model, hurdle model, etc.

This post is inspired by diffuse prior Lewbel’s 2012 paper proposed an estimator based on heteroscedasticity to address the problem of endogeneity without an instrument. This problem has been an issue for many (maybe most) empirical researchers with observational data.