Adding vce(robust) can change standard errors and intervals without changing coefficients. With data, variables, sample and estimator fixed, the OLS point estimate answers the same question while the uncertainty calculation changes. Fix those conditions before comparison instead of changing samples and controls at the same time.
The heteroskedasticity case uses entirely simulated data. Python computes covariance matrices directly; Stata reads the same CSV and executes conventional and robust regressions. Coefficients, SEs, intervals and p-values were independently compared. Download code, data, figures and actual logs and rerun in a new practice directory.
Make heteroskedasticity a known condition
The model is y = 1 + 2x + (0.3 + 1.2|x|)z, with x Uniform(−2,2), independent standard-normal z and independent observations. Errors have zero conditional mean but variance depending on x. Heteroskedasticity is deliberately generated here; a residual plot does not establish this model for real research.
Seed 42 generates 500 observations. Both regressions include an intercept and use all rows without changing controls or selecting samples. An example request is:
Use the specified simulation, retain identical data and OLS coefficients, and calculate conventional and HC1 SEs, t-reference intervals and p-values. Provide Python and Stata code, all coefficient rows, a residual figure and actual logs. Check sample equality, do not change seeds or samples to obtain significance, and write only in the practice directory.
In Marx Max, inspect actual code and output; connect licensed Stata following the Stata guide first.
What changes between conventional and HC1?
Conventional covariance uses a residual MSE. HC1 uses squared residuals in a sandwich matrix with n/(n−k), where k includes the intercept and equals 2 here. Stata’s official regress manual documents its heteroskedasticity-robust calculation and finite-sample correction.
The slope is about 1.973 with conventional SE 0.066 and HC1 SE 0.084, giving a wider interval. Intercept SEs are almost equal and HC1 is slightly smaller: robust SEs need not all be larger. The slope is significant under both reference calculations; a significance reversal is not a success criterion.
Intervals and p-values use a t reference with n−k degrees of freedom, not an exact finite-sample coverage guarantee under heteroskedasticity. One simulation cannot establish universal superiority. Studying coverage requires a separately specified repeated-simulation comparison.
Rerun the package, then revisit your research question
The complete package contains self-written Python and Stata programs, simulated data, all coefficients, figures, both actual logs and instructions. Retain reference outputs and extract into a new directory. Follow README dependencies and run python analyze.py, or use a new Stata session at the package root and do analysis.do. Stata independently reads the CSV without Python or third-party commands.
Check completion markers, 500 observations and all coefficients before comparing SEs, intervals and p-values. Stata clear all clears session memory and programs overwrite named practice outputs: save existing work first. Use separate full-package copies for new seeds, retaining both results rather than selecting a preferred p-value.
For real research, assess observation dependence, exogeneity and model specification. HC1 does not change coefficients or repair endogeneity, omitted variables, clustering or serial correlation. This exercise isolates heteroskedasticity inference. Review OLS sampling distributions to distinguish repeated-sample coefficient variation from uncertainty estimation in one regression, then choose inference for the research design.