Using Robust Standard Errors in Stata OLS Regression for Reliable Inference

Desired outcome

Obtain reliable coefficient estimates from a linear OLS model in Stata, especially when heteroskedasticity is present.

Prerequisites

• Stata installed (version 16.0 or later recommended).
• Access to the command window with user permissions.
• Sample dataset; the built‑in `auto` dataset is used for illustration.

Procedure

1. Load the dataset:

   sysuse auto

2. Run the basic OLS regression:

   regress price mpg weight

3. Check for heteroskedasticity with the Breusch‑Pagan test:

   estat breuschpagan

   – a significant p‑value (<0.05) indicates non‑constant variance.
4. If heteroskedasticity is detected, re‑estimate using robust standard errors:

   regress price mpg weight, robust

5. Compare the coefficient table: conventional SEs versus robust SEs.

Verification and recovery

After estimation, examine the output table for:

• Coefficient signs and significance (t‑stat > 1.96 for 5% level).
• Robust standard errors (displayed in parentheses when `robust` option is used).
• Model fit statistics such as R‑squared and F‑statistic.

If the robust model produces implausible results, consider:

• Re‑checking the Breusch‑Pagan test.
• Inspecting residual plots with predict resid and twoway (scatter residual mpg).
• Fitting a heteroskedasticity‑consistent model such as Huber‑White or clustered SEs.

To revert to the original (non‑robust) specification, simply re‑run the basic regress command without the `robust` option.

Limitations

Robust standard errors assume the correct mean‑value regression model; misspecification of the functional form can still bias estimates. They are not suitable for small samples where the asymptotic theory may not hold. Ensure the dataset meets the linear regression assumptions (linearity, no perfect multicollinearity).