Question about subsample analysis vs interaction for group comparison in non-linear regression model with fixed effects

[Chungyool Kim]

Hi All,

I am using Stata15 to run a non-linear regression model (Poisson pseudo maximum likelihood model(ppmlhdfe command)) to examine my research question.

I have a panel dataset of following setting.
- Panel dataset with 84,000 firm-day observations
- I'm doing Poisson pseudo maximum likelihood model with fixed effect regression with ppmlhdfe, trying to predict whether the Event has an influence on my dependent variable # of disclosures.
- My model is PPML model with industry, year, and month fixed effects and has many control variables (18 variables).

In equation, I run the following model with ppmlhdfe command.

# of disclosure = b0+ b1*Event + b3*controls + industry f.e. + year f.e. +month f.e. + u (Here, Event is the main variable that I am focused on)

In a code format:
ppmlhdfe #_of_disclosure Event controls, absorb(industry year month) vce(cluster firm)

For one of my analysis I want to compare whether the main effect shows up among only one "gender."

I can think of 3 different ways to test this.

(suggestion 1) Run the PPML regression separately for male and female subgroups and test whether two coefficients on Event is significantly different. gender = 1 if male and 2 if female

ppmlhdfe #_of_disclosure Event controls if gender ==1, absorb(industry year month) vce(cluster firm)
est store m1

ppmlhdfe #_of_disclosure Event controls if gender ==2, absorb(industry year month) vce(cluster firm)
est store m2
suest m1 m2 test [m1_mean]Event = [m2_mean]Event (suggestion 2) Run the PPML regression with interaction term of Event and gender (gender not fully interacted with all the controls)

ppmlhdfe #_of_disclosure Event gender i.Event#i.gendercontrols, absorb(industry year month) vce(cluster firm)

(suggestion 3) Run the PPML regression with interaction term of Event and gender (gender fully interacted with all the controls)

ppmlhdfe #_of_disclosure Event gender i.Event#i.gendercontrolsi.gender#c.controls, absorb(industry year month) vce(cluster firm)

My first question is whether my suggestions number 2 and 3 is still valid way to test group comparison for non-linear models such as PPML. I know that under linear regression suggestions number 1 and number 3 are supposed to give you the same coefficients. I am unsure whether the same applies to PPML model. For some reasons my results do not give me the same coefficients (maybe something to do with having fixed effects?)

My second question is what is the reason to prefer suggestion number 3 over suggestion number 2? I know that in suggestion number 2, I restrict the coefficients on controls to not vary among different gender and suggestions number 2 is not the same as suggestion number 1. But, since my model include many control variables with high dimensional fixed effects, I am concerned that if I run fully interacted model (suggestion number 3), there are too many parameters to estimate which may be problematic. Would there be a reason to favor suggestion number 2?

My third question is whether there are reasons to favor suggestion number 1 over suggestion number 3?

My final question is what would be the best way to test group comparison effects for non-linear model such as PPML models.

Thank you for reading a long question!

Your advice would be most appreciated!

[Joao Santos Silva]

Dear Chungyool Kim,

I never used the suest command, but I believe Suggestion 1 will do what you want. As you say, Suggestion 3 should give you the same results if you also interact the fixed effects with gender; this approach may give you more flexibility about how to cluster the standard errors, but I am not sure of that. Suggestion 2 does something totally different and it is up to you to decide if this approach answers your question. If your sample is large enough to estimate the models by gender, then you can certainly use the third option as it it identical to the first one.

Best wishes,

Joao

[Chungyool Kim]

Thank you Joao!

[Aparajita Agarwal]

Prof. Joao Santos Silva : Can you please say a bit more about how one can do joint estimation tests and compare the coefficients from sub-group analyses (e.g. comparing effects for men vs. women) after running ppml? It seems suest doesn't run as a post estimation command post after ppml

Also, in general is it better to run interactions or sub-group analyses with non-linear models like ppml? i will appreciate any advice around this.

[Joao Santos Silva]

Dear Aparajita Agarwal,

To use your example, the way to do it is to estimate the model with the full dataset (i.e., with men and women) and interact all variables (including fixed effects) with the gender indicator. You can then test the significance of the relevant interactions.

Best wishes,

Joao