Introduction to treatment effects in Stata: Part 2
This post was written jointly with David Drukker, Director of Econometrics, StataCorp. In our last post, we introduced the concept of treatment effects and demonstrated four of the treatment-effects...
View ArticleMaximum likelihood estimation by mlexp: A chi-squared example
Overview In this post, I show how to use mlexp to estimate the degree of freedom parameter of a chi-squared distribution by maximum likelihood (ML). One example is unconditional, and another example...
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Efficiency comparisons by Monte Carlo simulation
Overview In this post, I show how to use Monte Carlo simulations to compare the efficiency of different estimators. I also illustrate what we mean by efficiency when discussing statistical estimators....
View ArticleEstimating parameters by maximum likelihood and method of moments using mlexp...
\(\newcommand{\epsilonb}{\boldsymbol{\epsilon}} \newcommand{\ebi}{\boldsymbol{\epsilon}_i} \newcommand{\Sigmab}{\boldsymbol{\Sigma}} \newcommand{\Omegab}{\boldsymbol{\Omega}}...
View ArticleProbit model with sample selection by mlexp
Overview In a previous post, David Drukker demonstrated how to use mlexp to estimate the degree of freedom parameter in a chi-squared distribution by maximum likelihood (ML). In this post, I am going...
View ArticleFixed Effects or Random Effects: The Mundlak Approach
Today I will discuss Mundlak’s (1978) alternative to the Hausman test. Unlike the latter, the Mundlak approach may be used when the errors are heteroskedastic or have intragroup correlation. What is...
View ArticleUsing mlexp to estimate endogenous treatment effects in a probit model
I use features new to Stata 14.1 to estimate an average treatment effect (ATE) for a probit model with an endogenous treatment. In 14.1, we added new prediction statistics after mlexp that margins can...
View Articlextabond Cheat Sheet
Random-effects and fixed-effects panel-data models do not allow me to use observable information of previous periods in my model. They are static. Dynamic panel-data models use current and past...
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Understanding the generalized method of moments (GMM): A simple example
\(\newcommand{\Eb}{{\bf E}}\)This post was written jointly with Enrique Pinzon, Senior Econometrician, StataCorp. The generalized method of moments (GMM) is a method for constructing estimators,...
View ArticleUsing mlexp to estimate endogenous treatment effects in a heteroskedastic...
I use features new to Stata 14.1 to estimate an average treatment effect (ATE) for a heteroskedastic probit model with an endogenous treatment. In 14.1, we added new prediction statistics after mlexp...
View Articleprobit or logit: ladies and gentlemen, pick your weapon
We often use probit and logit models to analyze binary outcomes. A case can be made that the logit model is easier to interpret than the probit model, but Stata’s margins command makes any estimator...
View Articleregress, probit, or logit?
In a previous post I illustrated that the probit model and the logit model produce statistically equivalent estimates of marginal effects. In this post, I compare the marginal effect estimates from a...
View ArticleBayesian binary item response theory models using bayesmh
This post was written jointly with Yulia Marchenko, Executive Director of Statistics, StataCorp. Table of Contents Overview 1PL model 2PL model 3PL model 4PL model 5PL model Conclusion Overview Item...
View ArticleTesting model specification and using the program version of gmm
This post was written jointly with Joerg Luedicke, Senior Social Scientist and Statistician, StataCorp. The command gmm is used to estimate the parameters of a model using the generalized method of...
View ArticleVector autoregression—simulation, estimation, and inference in Stata
\(\newcommand{\epsb}{{\boldsymbol{\epsilon}}} \newcommand{\mub}{{\boldsymbol{\mu}}} \newcommand{\thetab}{{\boldsymbol{\theta}}} \newcommand{\Thetab}{{\boldsymbol{\Theta}}}...
View ArticleHow to generate random numbers in Stata
Overview I describe how to generate random numbers and discuss some features added in Stata 14. In particular, Stata 14 includes a new default random-number generator (RNG) called the Mersenne Twister...
View ArticleFitting distributions using bayesmh
This post was written jointly with Yulia Marchenko, Executive Director of Statistics, StataCorp. As of update 03 Mar 2016, bayesmh provides a more convenient way of fitting distributions to the outcome...
View ArticleA simulation-based explanation of consistency and asymptotic normality
Overview In the frequentist approach to statistics, estimators are random variables because they are functions of random data. The finite-sample distributions of most of the estimators used in applied...
View ArticleARMA processes with nonnormal disturbances
Autoregressive (AR) and moving-average (MA) models are combined to obtain ARMA models. The parameters of an ARMA model are typically estimated by maximizing a likelihood function assuming independently...
View ArticleUnderstanding omitted confounders, endogeneity, omitted variable bias, and...
Initial thoughts Estimating causal relationships from data is one of the fundamental endeavors of researchers. Ideally, we could conduct a controlled experiment to estimate causal relations. However,...
View ArticleGelman–Rubin convergence diagnostic using multiple chains
Overview MCMC algorithms used for simulating posterior distributions are indispensable tools in Bayesian analysis. A major consideration in MCMC simulations is that of convergence. Has the simulated...
View ArticleTests of forecast accuracy and forecast encompassing
\(\newcommand{\mub}{{\boldsymbol{\mu}}} \newcommand{\eb}{{\boldsymbol{e}}} \newcommand{\betab}{\boldsymbol{\beta}}\)Applied time-series researchers often want to compare the accuracy of a pair of...
View ArticleMultiple equation models: Estimation and marginal effects using gsem
Starting point: A hurdle model with multiple hurdles In a sequence of posts, we are going to illustrate how to obtain correct standard errors and marginal effects for models with multiple steps. Our...
View ArticleMultiple equation models: Estimation and marginal effects using mlexp
We continue with the series of posts where we illustrate how to obtain correct standard errors and marginal effects for models with multiple steps. In this post, we estimate the marginal effects and...
View ArticleUnit-root tests in Stata
\(\newcommand{\mub}{{\boldsymbol{\mu}}} \newcommand{\eb}{{\boldsymbol{e}}} \newcommand{\betab}{\boldsymbol{\beta}}\)Determining the stationarity of a time series is a key step before embarking on any...
View ArticleFlexible discrete choice modeling using a multinomial probit model, part 1
\(\newcommand{\xb}{{\bf x}} \newcommand{\betab}{\boldsymbol{\beta}} \newcommand{\zb}{{\bf z}} \newcommand{\gammab}{\boldsymbol{\gamma}}\)We have no choice but to choose We make choices every day, and...
View ArticleFlexible discrete choice modeling using a multinomial probit model, part 2
Overview In the first part of this post, I discussed the multinomial probit model from a random utility model perspective. In this part, we will have a closer look at how to interpret our estimation...
View ArticleEffects of nonlinear models with interactions of discrete and continuous...
I want to estimate, graph, and interpret the effects of nonlinear models with interactions of continuous and discrete variables. The results I am after are not trivial, but obtaining what I want using...
View ArticleDoctors versus policy analysts: Estimating the effect of interest
\(\newcommand{\Eb}{{\bf E}}\)The change in a regression function that results from an everything-else-held-equal change in a covariate defines an effect of a covariate. I am interested in estimating...
View ArticleProbability differences and odds ratios measure conditional-on-covariate...
\(\newcommand{\Eb}{{\bf E}} \newcommand{\xb}{{\bf x}} \newcommand{\betab}{\boldsymbol{\beta}}\)Differences in conditional probabilities and ratios of odds are two common measures of the effect of a...
View ArticleMultiple-equation models: Estimation and marginal effects using gmm
We estimate the average treatment effect (ATE) for an exponential mean model with an endogenous treatment. We have a two-step estimation problem where the first step corresponds to the treatment model...
View ArticleVector autoregressions in Stata
Introduction In a univariate autoregression, a stationary time-series variable \(y_t\) can often be modeled as depending on its own lagged values: \begin{align} y_t = \alpha_0 + \alpha_1 y_{t-1} +...
View ArticleExact matching on discrete covariates is the same as regression adjustment
I illustrate that exact matching on discrete covariates and regression adjustment (RA) with fully interacted discrete covariates perform the same nonparametric estimation. Comparing exact matching with...
View ArticleGroup comparisons in structural equation models: Testing measurement invariance
When fitting almost any model, we may be interested in investigating whether parameters differ across groups such as time periods, age groups, gender, or school attended. In other words, we may wish to...
View ArticleTwo faces of misspecification in maximum likelihood: Heteroskedasticity and...
For a nonlinear model with heteroskedasticity, a maximum likelihood estimator gives misleading inference and inconsistent marginal effect estimates unless I model the variance. Using a robust estimate...
View ArticleCointegration or spurious regression?
\(\newcommand{\betab}{\boldsymbol{\beta}}\)Time-series data often appear nonstationary and also tend to comove. A set of nonstationary series that are cointegrated implies existence of a long-run...
View ArticleAn ordered-probit inverse probability weighted (IPW) estimator
teffects ipw uses multinomial logit to estimate the weights needed to estimate the potential-outcome means (POMs) from a multivalued treatment. I show how to estimate the POMs when the weights come...
View ArticleStructural vector autoregression models
\(\def\bfy{{\bf y}} \def\bfA{{\bf A}} \def\bfB{{\bf B}} \def\bfu{{\bf u}} \def\bfI{{\bf I}} \def\bfe{{\bf e}} \def\bfC{{\bf C}} \def\bfsig{{\boldsymbol \Sigma}}\)In my last post, I discusssed...
View ArticleQuantile regression allows covariate effects to differ by quantile
Quantile regression models a quantile of the outcome as a function of covariates. Applied researchers use quantile regressions because they allow the effect of a covariate to differ across conditional...
View ArticleEstimating covariate effects after gmm
In Stata 14.2, we added the ability to use margins to estimate covariate effects after gmm. In this post, I illustrate how to use margins and marginsplot after gmm to estimate covariate effects for a...
View ArticleSolving missing data problems using inverse-probability-weighted estimators
We discuss estimating population-averaged parameters when some of the data are missing. In particular, we show how to use gmm to estimate population-averaged parameters for a probit model when the...
View ArticleLong-run restrictions in a structural vector autoregression
\(\def\bfA{{\bf A}} \def\bfB{{\bf }} \def\bfC{{\bf C}}\)Introduction In this blog post, I describe Stata’s capabilities for estimating and analyzing vector autoregression (VAR) models with long-run...
View ArticleIntroduction to Bayesian statistics, part 1: The basic concepts
In this blog post, I’d like to give you a relatively nontechnical introduction to Bayesian statistics. The Bayesian approach to statistics has become increasingly popular, and you can fit Bayesian...
View ArticleIntroduction to Bayesian statistics, part 2: MCMC and the Metropolis–Hastings...
In this blog post, I’d like to give you a relatively nontechnical introduction to Markov chain Monte Carlo, often shortened to “MCMC”. MCMC is frequently used for fitting Bayesian statistical models....
View ArticleUnderstanding truncation and censoring
Truncation and censoring are two distinct phenomena that cause our samples to be incomplete. These phenomena arise in medical sciences, engineering, social sciences, and other research fields. If we...
View ArticleEstimation under omitted confounders, endogeneity, omitted variable bias, and...
Initial thoughts Estimating causal relationships from data is one of the fundamental endeavors of researchers, but causality is elusive. In the presence of omitted confounders, endogeneity, omitted...
View ArticleStata 15 announced, available now
We announced Stata 15 today. It’s a big deal because this is Stata’s biggest release ever. I posted to Statalist this morning and listed sixteen of the most important new features. Here on the blog I...
View ArticleNonparametric regression: Like parametric regression, but not
Initial thoughts Nonparametric regression is similar to linear regression, Poisson regression, and logit or probit regression; it predicts a mean of an outcome for a set of covariates. If you work with...
View ArticleEstimating the parameters of DSGE models
Introduction Dynamic stochastic general equilibrium (DSGE) models are used in macroeconomics to model the joint behavior of aggregate time series like inflation, interest rates, and unemployment. They...
View ArticleBayesian logistic regression with Cauchy priors using the bayes prefix
Introduction Stata 15 provides a convenient and elegant way of fitting Bayesian regression models by simply prefixing the estimation command with bayes. You can choose from 45 supported estimation...
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