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Posts Tagged ‘statistics’

Programming an estimation command in Stata: A map to posted entries

I have posted a series of entries about programming an estimation command in Stata. They are best read in order. The comprehensive list below allows you to read them from first to last at your own pace.

  1. Programming estimators in Stata: Why you should

    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.

  2. Programming an estimation command in Stata: Where to store your stuff

    I discuss the difference between scripts and commands, and I introduce some essential programming concepts and constructions that I use to write the scripts and commands.

  3. Programming an estimation command in Stata: Global macros versus local macros

    I discuss a pair of examples that illustrate the differences between global macros and local macros.

  4. Programming an estimation command in Stata: A first ado-command

    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 Read more…

Programming an estimation command in Stata: An OLS command using Mata

I discuss a command that computes ordinary least-squares (OLS) results in Mata, paying special attention to the structure of Stata programs that use Mata work functions.

This command builds on several previous posts; at a minimum, you should be familiar with Programming an estimation command in Stata: A first ado-command using Mata and Programming an estimation command in Stata: Computing OLS objects in Mata.

This is the fifteenth 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.

An OLS command with Mata computations

The Stata command myregress11 computes the results in Mata. The syntax of the myregress11 command is

myregress11 depvar [indepvars] [if] [in] [, noconstant]

where indepvars can contain factor variables or time-series variables.

In the remainder of this post, I discuss the code for myregress11.ado. I recommend that you click on the file name to download the code. To avoid scrolling, view the code in the do-file editor, or your favorite text editor, to see the line numbers.

I do not discuss Read more…

probit 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 easy to interpret. Ultimately, estimates from both models produce similar results, and using one or the other is a matter of habit or preference.

I show that the estimates from a probit and logit model are similar for the computation of a set of effects that are of interest to researchers. I focus on the effects of changes in the covariates on the probability of a positive outcome for continuous and discrete covariates. I evaluate these effects on average and at the mean value of the covariates. In other words, I study the average marginal effects (AME), the average treatment effects (ATE), the marginal effects at the mean values of the covariates (MEM), and the treatment effects at the mean values of the covariates (TEM).

First, I present the results. Second, I discuss the code used for the simulations.

Results

In Table 1, I present the results of a simulation with 4,000 replications when the true data generating process (DGP) satisfies the assumptions of a probit model. I show the Read more…

Programming an estimation command in Stata: Computing OLS objects in Mata

\(\newcommand{\epsilonb}{\boldsymbol{\epsilon}}
\newcommand{\ebi}{\boldsymbol{\epsilon}_i}
\newcommand{\Sigmab}{\boldsymbol{\Sigma}}
\newcommand{\betab}{\boldsymbol{\beta}}
\newcommand{\eb}{{\bf e}}
\newcommand{\xb}{{\bf x}}
\newcommand{\xbit}{{\bf x}_{it}}
\newcommand{\xbi}{{\bf x}_{i}}
\newcommand{\zb}{{\bf z}}
\newcommand{\zbi}{{\bf z}_i}
\newcommand{\wb}{{\bf w}}
\newcommand{\yb}{{\bf y}}
\newcommand{\ub}{{\bf u}}
\newcommand{\Xb}{{\bf X}}
\newcommand{\Mb}{{\bf M}}
\newcommand{\Xtb}{\tilde{\bf X}}
\newcommand{\Wb}{{\bf W}}
\newcommand{\Vb}{{\bf V}}\)I present the formulas for computing the ordinary least-squares (OLS) estimator and show how to compute them in Mata. This post is a Mata version of Programming an estimation command in Stata: Using Stata matrix commands and functions to compute OLS objects. I discuss the formulas and the computation of independence-based standard errors, robust standard errors, and cluster-robust standard errors.

This is the fourteenth 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.

OLS formulas

Recall that the OLS point estimates are given by

\[
\widehat{\betab} =
\left( \sum_{i=1}^N \xb_i’\xb_i \right)^{-1}
\left(
\sum_{i=1}^N \xb_i’y_i
\right)
\]

where \(\xb_i\) is the \(1\times k\) vector of independent variables, \(y_i\) is the dependent variable for each of the \(N\) sample observations, and the model for \(y_i\) is

\[
y_i = \xb_i\betab’ + \epsilon_i
\]

If the \(\epsilon_i\) are independently and identically distributed (IID), we estimate Read more…

Programming an estimation command in Stata: A first ado-command using Mata

I discuss a sequence of ado-commands that use Mata to estimate the mean of a variable. The commands illustrate a general structure for Stata/Mata programs. This post builds on Programming an estimation command in Stata: Mata 101, Programming an estimation command in Stata: Mata functions, and Programming an estimation command in Stata: A first ado-command.

This is the thirteenth 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.

Using Mata in ado-programs

I begin by reviewing the structure in mymean5.ado, which I discussed Read more…

Programming an estimation command in Stata: Mata functions

I show how to write a function in Mata, the matrix programming language that is part of Stata. This post uses concepts introduced in Programming an estimation command in Stata: Mata 101.

This is the twelfth 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.

Mata functions

Commands do work in Stata. Functions do work in Mata. Commands operate on Stata objects, like variables, and users specify options to alter the behavior. Mata functions accept arguments, operate on the arguments, and may return a result or alter the value of an argument to contain a result.

Consider myadd() defined below.

Code block 1: myadd()

mata:
function myadd(X, Y)
{
    A = X + Y
    return(A)
}
end

myadd() accepts two arguments, X and Y, puts the sum of X and Y into A, and returns A. For example, Read more…

Programming an estimation command in Stata: Mata 101

I introduce Mata, the matrix programming language that is part of Stata.

This is the eleventh 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…

Programming an estimation command in Stata: Using a subroutine to parse a complex option

I make two improvements to the command that implements the ordinary least-squares (OLS) estimator that I discussed in Programming an estimation command in Stata: Allowing for options. First, I add an option for a cluster-robust estimator of the variance-covariance of the estimator (VCE). Second, I make the command accept the modern syntax for either a robust or a cluster-robust estimator of the VCE. In the process, I use subroutines in my ado-program to facilitate the parsing, and I discuss some advanced parsing tricks.

This is the tenth 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…

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, analogous to maximum likelihood (ML). GMM uses assumptions about specific moments of the random variables instead of assumptions about the entire distribution, which makes GMM more robust than ML, at the cost of some efficiency. The assumptions are called moment conditions.

GMM generalizes the method of moments (MM) by allowing the number of moment conditions to be greater than the number of parameters. Using these extra moment conditions makes GMM more efficient than MM. When there are more moment conditions than parameters, the estimator is said to be overidentified. GMM can efficiently combine the moment conditions when the estimator is overidentified.

We illustrate these points by estimating the mean of a \(\chi^2(1)\) by MM, ML, a simple GMM estimator, and an efficient GMM estimator. This example builds on Efficiency comparisons by Monte Carlo simulation and is similar in spirit to the example in Wooldridge (2001). Read more…

Programming an estimation command in Stata: Allowing for options

I make three improvements to the command that implements the ordinary least-squares (OLS) estimator that I discussed in Programming an estimation command in Stata: Allowing for sample restrictions and factor variables. First, I allow the user to request a robust estimator of the variance-covariance of the estimator (VCE). Second, I allow the user to suppress the constant term. Third, I store the residual degrees of freedom in e(df_r) so that test will use the \(t\) or \(F\) distribution instead of the normal or \(\chi^2\) distribution to compute the \(p\)-value of Wald tests.

This is the ninth 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…