Sample Split reghdfe and pweight

[Rob Vo]

Dear all,
I have a question using the reghdfe command and pweight using Stata 16. I run an interaction analysis, and I am interested in the effect of VAR1 dependent on VAR2. I use a weighting, as this makes sense in my question. That works fine.

gen VAR1_VAR2 = VAR1*VAR2

reghdfe ///
ln_gross_investment_total ///
VAR1 VAR2 ///
VAR1_VAR2 ///
[pweight = WEIGHT], cluster(CLUSTER) a(FE) keepsingleton

Then, I perform a sample split in which I split my sample according to a dummy variable SPLIT into high (=1) and low (=0) values for that variable

reghdfe ///
ln_gross_investment_total ///
VAR1 VAR2 ///
VAR1_VAR2 ///
if SPLIT==1 [pweight = WEIGHT], cluster(CLUSTER) a(FE) keepsingleton

reghdfe ///
ln_gross_investment_total ///
VAR1 VAR2 ///
VAR1_VAR2 ///
if SPLIT==0 [pweight = WEIGHT], cluster(CLUSTER) a(FE) keepsingleton

Again, this also works fine. I get reasonable results. Now the problem begins: When I then estimate my whole sample again, using an interaction with SPLIT to test the significance of the difference. I get a different SPLIT_VAR1_VAR2 estimator than if I would compute the difference manually.

gen SPLIT_VAR1 = SPLIT*VAR1
gen SPLIT_VAR2 = SPLIT*VAR2
gen SPLIT_VAR1_VAR2 = SPLIT*VAR1_VAR2

reghdfe ///
ln_gross_investment_total ///
VAR1 VAR2 ///
VAR1_VAR2 ///
SPLIT_VAR1 ///
SPLIT_VAR2 ///
SPLIT_VAR1_VAR2 ///
[pweight = WEIGHT], cluster(CLUSTER) a(FE) keepsingleton

Natally, SPLIT_VAR1_VAR2 should yield the same as VAR1_VAR2 (if SPLIT==1) - VAR1_VAR2 (if SPLIT==0)

When I exclude the weighting from my analysis, this holds true. When I employ pweigh, this is no longer the case. Can it be true, that pweigth somehow biases my results in any direction? I thought that pweight would work also well in subsamples.

Thanks for your answers. I hope I have not forgotten anything. Let me know if you need further information.

Best,
Robert

[FernandoRios]

Hi Robert
The problem is not the weights, but the interaction
When you run these models

reg y x1 x2 x3 i.id if split==0
reg y x1 x2 x3 i.id if split==1

Is as if you are interacting x1, x2, x3 and i.id with split.
However, when you run this model:

reghdfe y split##c.(x1 x2 x3) , abs(id)

is as if you are doing this:

reg y split##c.(x1 x2 x3) i.id

This assumes id is not being interacted with Split. This is why your results are not matching as you were expecting.

HTH
Fernando