Maximum Likelihood in Stata, Step by Step (5-Minute Crash Course)

In this 5-minute tutorial, I walk through the basics of implementing Maximum Likelihood Estimation (MLE) in Stata using a custom likelihood function. If you're a grad student or researcher working with ml, this video will help you get started faster.

I show how to:

Write a likelihood evaluator program
Use ml model and ml maximize
Specify log-likelihoods and transform parameters
The code example is designed to highlight the structure and logic behind MLE in Stata so you can apply it to your own work.

🧠 What’s covered: args, tempvar, log-likelihood coding, using ml model, estimation output.

📂 Full code available here
clear all
set more off
cls


sysuse auto


*********OLS Method
reg price mpg weight



********MLE Method
cap program drop mle_demo
program define mle_demo

*Arguments likelihood function (lnf), coefficient matrix (xb) and variance-covariance matrix (sigma)
args lnf xb v

*Generate variables as temporary variables
tempvar e sig2
gen `e'=$ML_y1-`xb'
gen double `sig2' =`v'^2

*Use likelihood function using normal distribution assumption
replace `lnf'=-0.5*ln(2*_pi) - ln(`v')-0.5*(`e'^2)/`sig2'


end

***Initialize MLE
ml model lf mle_demo (price=mpg weight) /v

***Check It Works/Test It
*ml check

**Run it
ml maximize

**Compare
reg price mpg weight

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