Using ppmlhdfe with control function approach and boottest

[Umar Boodoo]

Hello. I have quite a large dataset. Difficult and impractical to post a sample using dataex to get anything meaningful at this stage.
Essentially, I have firm-level investment data in foreign countries: Panel data, triple-indexed at the firm-target country-year level. Lots of true zeros in this data, with 5000 firms times 150 target countries times 10 years.

I am using ppmlhdfe (Joao Santos Silva, Sergio Correia ) to estimate investment counts at time t as a function of firm-level financial constraints (continuous), target country financial development index (continuous), and institutional distance between firm country and target country, all at time t-1. Problem is the financial constraints even at time t-1 might be endogenous. Hence, I have tried to combine Jeff Wooldridge's Control function approach to instrument the t-1 financial constraints with its t-2 equivalent. Finishing up with David Roodman boottest.

reg constraints_t1 constraints_t2, vce(bootstrap, seed(1234) reps(500))
predict vhat, residuals

eststo: ppmlhdfe investment_count c.constraints_t1##c.inst_dist c.vhat##c.inst_dist financialdev i.home_country, vce(cluster firm_targetcountry) absorb(industry_year_fixed_effect)
estadd local cmd = "reghdfe", replace
estadd scalar converged=., replace

boottest constraints_t1, nograph reps(100)

Here are the results:

Variable	Coef.	Std	Z	LCI	UCI
Constraints	-0.798	0.025	-31.93	-0.85	-0.75
Financial Dev.	0.520	0.023	22.20	0.47	0.57
Institutional Distance	-0.369	0.020	-18.46	-0.41	-0.33
Interaction: Constraints X Institutional Distance	-0.208	0.019	-11.07	-0.24	-0.17
vhat	0.267	0.038	7.05	0.19	0.34
Interaction: vhat X Institutional Distance	0.102	0.030	3.38	0.04	0.16

Signs of coefficients are as expected.

Questions:
1. Jeff Wooldridge, given the size of the data, the z-stat on vhat is almost likely to always be statistically significant. If my understanding is correct, is the coefficient that I now get on the t-1 financial constraints (-0.798) somehow corrected for endogeneity?
2. David Roodman Joao Santos Silva Sergio Correia am I correctly using boottest after ppmlhdfe? I am getting stuff that I cannot comprehend. See output below.

boottest constraints_t1, nograph reps(100)
Wild bootstrap-t, null imposed, 100 replications, Wald test, bootstrap clustering by pair, Rademacher weights:
                               z =   -29.1569
                        Prob>|z| =     0.0000
95% confidence set for null hypothesis expression: [-.0008602, -.0007525]

The z-stat here is close to what the table shows. Good. But the 95% confidence set is certainly problematic, isn't it?
Not sure how to interpret this.

The bigger problem: when I boottest the interaction term between constraints and institutional distance, I get:

Wild bootstrap-t, null imposed, 100 replications, Wald test, bootstrap clustering by pair, Rademacher weights:
                               z =    14.2234
                        Prob>|z| =     0.0000
95% confidence set for null hypothesis expression: [.0003346, .0004338]

The sign now changes. What am I doing wrong here? Perhaps more apt: what am I doing right here, if at all? Btw, I tried the 999 replications, but it seems that I would need a computer with more than 96GB Ram to run that with my data.

[David Roodman]

boottest does not support ppmlhdfe.