I discuss the code for a simple estimation command to focus on the details of how to implement an estimation command. The command that I discuss estimates the mean by the sample average. I begin by reviewing the formulas and a do-file that implements them. I subsequently introduce ado-file programming and discuss two versions of the command. Along the way, I illustrate some of the postestimation features that work after the command.

This is the fourth post in the series Programming an estimation command in Stata. I recommend that you start at the beginning. See Programming an estimation command in Stata: A map to posted entries for a map to all the posts in this series. Read more…

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 use to estimate an ATE.

I am building on a previous post in which I demonstrated how to use mlexp to estimate the parameters of a probit model with sample selection. Our results match those obtained with biprobit; see [R] biprobit for more details. In a future post, I use these techniques to estimate treatment-effect parameters not yet available from another Stata command. Read more…

I discuss a pair of examples that illustrate the differences between global macros and local macros. You can view this post as a technical appendix to the previous post in the #StataProgramming series, which introduced global macros and local macros.

In every command I write, I use local macros to store stuff in a workspace that will not alter a user’s data and to make my code easier to read. A good understanding of the differences between global macros and local macros helps me to write better code. The essential differences between global macros and local macros can be summarized in two points. Read more…

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. Read more…

If you tell me “I program in Stata”, it makes me happy, but I do not know what you mean. Do you write scripts to make your research reproducible, or do you write Stata commands that anyone can use and reuse? In the series #StataProgramming, I will show you how to write your own commands, but I start at the beginning. Discussing the difference between scripts and commands here introduces some essential programming concepts and constructions that I use to write scripts and commands.

This is the second post in the series Programming an estimation command in Stata. I recommend that you start at the beginning. See Programming an estimation command in Stata: A map to posted entries for a map to all the posts in this series. Read more…

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 to use mlexp to estimate the parameters of a probit model with sample selection. I will illustrate how to specify a more complex likelihood in mlexp and provide intuition for the probit model with sample selection. Our results match the heckprobit command; see [R] heckprobit for more details. Read more…

Distributing a Stata command that implements a statistical method will get that method used by lots of people. They will thank you. And, they will cite you!

This post is the first in the series #StataProgramming about programing an estimation command in Stata that uses Mata to do the numerical work. In the process of showing you how to program an estimation command in Stata, I will discuss do-file programming, ado-file programming, and Mata programming. When the series ends, you will be able to write Stata commands.

Stata users like its predictable syntax and its estimation-postestimation structure that facilitates hypothesis testing, specification tests, and parameter interpretation. To help you write Stata commands that people want to use, I illustrate how Stata syntax is predictable and give an overview of the estimation-postestimation structure that you will want to emulate in your programs. Read more…

\(\newcommand{\epsilonb}{\boldsymbol{\epsilon}}
\newcommand{\ebi}{\boldsymbol{\epsilon}_i}
\newcommand{\Sigmab}{\boldsymbol{\Sigma}}
\newcommand{\Omegab}{\boldsymbol{\Omega}}
\newcommand{\Lambdab}{\boldsymbol{\Lambda}}
\newcommand{\betab}{\boldsymbol{\beta}}
\newcommand{\gammab}{\boldsymbol{\gamma}}
\newcommand{\Gammab}{\boldsymbol{\Gamma}}
\newcommand{\deltab}{\boldsymbol{\delta}}
\newcommand{\xib}{\boldsymbol{\xi}}
\newcommand{\iotab}{\boldsymbol{\iota}}
\newcommand{\xb}{{\bf x}}
\newcommand{\xbit}{{\bf x}_{it}}
\newcommand{\xbi}{{\bf x}_{i}}
\newcommand{\zb}{{\bf z}}
\newcommand{\zbi}{{\bf z}_i}
\newcommand{\wb}{{\bf w}}
\newcommand{\yb}{{\bf y}}
\newcommand{\ub}{{\bf u}}
\newcommand{\Gb}{{\bf G}}
\newcommand{\Hb}{{\bf H}}
\newcommand{\thetab}{\boldsymbol{\theta}}
\newcommand{\XBI}{{\bf x}_{i1},\ldots,{\bf x}_{iT}}
\newcommand{\Sb}{{\bf S}} \newcommand{\Xb}{{\bf X}}
\newcommand{\Xtb}{\tilde{\bf X}}
\newcommand{\Wb}{{\bf W}}
\newcommand{\Ab}{{\bf A}}
\newcommand{\Bb}{{\bf B}}
\newcommand{\Zb}{{\bf Z}}
\newcommand{\Eb}{{\bf E}}\) This post was written jointly with Joerg Luedicke, Senior Social Scientist and Statistician, StataCorp.

Overview

We provide an introduction to parameter estimation by maximum likelihood and method of moments using mlexp and gmm, respectively (see [R] mlexp and [R] gmm). We include some background about these estimation techniques; see Pawitan (2001, Casella and Berger (2002), Cameron and Trivedi (2005), and Wooldridge (2010) for more details.

Maximum likelihood (ML) estimation finds the parameter values that make the observed data most probable. The parameters maximize the log of the likelihood function that specifies the probability of observing a particular set of data given a model.

Method of moments (MM) estimators specify population moment conditions and find the parameters that solve the equivalent sample moment conditions. MM estimators usually place fewer restrictions on the model than ML estimators, which implies that MM estimators are less efficient but more robust than ML estimators. Read more…

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.

I wrote this post to continue a dialog with my friend who doubted the usefulness of the sample average as an estimator for the mean when the data-generating process (DGP) is a \(\chi^2\) distribution with \(1\) degree of freedom, denoted by a \(\chi^2(1)\) distribution. The sample average is a fine estimator, even though it is not the most efficient estimator for the mean. (Some researchers prefer to estimate the median instead of the mean for DGPs that generate outliers. I will address the trade-offs between these parameters in a future post. For now, I want to stick to estimating the mean.)

In this post, I also want to illustrate that Monte Carlo simulations can help explain abstract statistical concepts. I show how to use a Monte Carlo simulation to illustrate the meaning of an abstract statistical concept. (If you are new to Monte Carlo simulations in Stata, you might want to see Monte Carlo simulations using Stata.) Read more…

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 models the parameter as a function of covariates. I also show how to generate data from chi-squared distributions and I illustrate how to use simulation methods to understand an estimation technique. Read more…