Small sample and regression issues

[Aryan Bose]

Dear Stata Experts,

In one of my paper, I have used 30 firms over the year 8 years (total 198 firm-years after excluding missing data) as a sample. Now the reviewer is arguing that the paper does not deal specifically with issues as auto-correlation, heteroscedasticity and multivariate normality in the presence of small sample sizes. I have used clustered robust standard errors by firm for handling the auto-correlation and heteroscedasticity, and it is mentioned in the paper.

I have also applied propensity-score matching (PSM) analysis. The reviewer is also asking the validity of using two-stage regression procedures applied to a very small sample sizes.

Can you please give your suggestion in this regard and help me?

Regards,

Aryan

[Carlo Lazzaro]

Aryan:
you do not give enough details about your queries.
As usual, the best approach is to share what you typed and what Stata gave you back via CODE deliiters (as per FAQ).
That said:
1) I'm not clear about the need for testing multivariate normality (of what)?
2) I'm not clear with what you mean by two.stage regerssion. Did you experience endogeneity issues in your panel data regression?
Please help interested listers to hel you in turn. Thanks.

[Aryan Bose]

Hi Carlo,

Many thanks for your response.

1. Multivariate normality of the regression model variables (I think) because the reviewer's write the following line only:
"the paper does not deal specifically with issues as auto-correlation, heteroscedasticity and multivariate normality in the presence of small sample sizes."

2. Propensity- score-matching (PSM) analysis (which is two-stage) was run for handling the observable selection bias in the findings.

3. I did not find any issue with running the regression with the Stata. Stata produces everything in a right way.

Regards,

Sudipta

[Carlo Lazzaro]

Sudipta:
1) did you address in the method section of the paper that you performed postestimation tests aimed at checking for heteroskedsticity, autocorrelation (and , I would add, model misspecification)? If that were the case, I would simply reply to the reviewer that what she/he asks for has been already detailed in the first submission of the paper:
2) normality is a (weak) requirement for residual distribution only;
3) small sample size limits the number of predictors that you can plug in the right-hand side of your regression equation (see https://projecteuclid.org/euclid.aos/1349196389).
4) glad that you did not detect endogeneity issue in your regression model.

[Aryan Bose]

Thanks Carlo.

I have written how I have handled heteroscedasticity and autocorrelation in the method section. I have only three predictors in the model. My only concern is 198 observations? Is it really a small sample size for applying those tests?

[Carlo Lazzaro]

Sudipta:
as usual, the issue is to give a fair and true view of the data generating process.
If you cannot increase your sample size, you have to live with it.
More substantively: have you checked your model for potential misspecification of the functional form of the regressand?