Bootstrap standard error control function

[Henry Strawforrd]

I am trying to bootstrap the standard from a control function approach. They are massively off, the non-bootstrapped SE's are much closer to the ivreg2 SEs. Using robust or not does change this.

Anybody has an idea what is going on?

Below an example based on Wooldridge's fish data.

// Programs
*ssc install bcuse
*ssc install ivreg2

bcuse fish, clear

rename lavgprc p
rename ltotqty q
qui su speed2, det
gen stormy = (speed2 > r(p50))

capture program drop cf
program define cf
    capture drop resid
    qui reg q stormy i.mon i.tues i.wed i.thurs
    predict resid, resid
    reg p q i.mon i.tues i.wed i.thurs resid
end


// 1. 2SLS
ivreg2 p i.mon i.tues i.wed i.thurs (q = stormy)

// 2. Control Function
cf

// 3. Bootstrapped Control Function
bootstrap, reps(1000) seed(12345) : cf

[Henry Strawforrd]

.

[Felix Bittmann]

I am not really sure if this is a valid comparison. As far as I see you have a main function of interest, which is:

 ivreg2 p i.mon i.tues i.wed i.thurs (q = stormy)

Why dont you bootstrap this, something like?

bootstrap: ivreg2 p i.mon i.tues i.wed i.thurs (q = stormy)

Then you can compare analytic and bootstrap SEs for the exact same command. What you show in the example looks like you compare two different approaches / commands.

[Henry Strawforrd]

Usually, control function estimation techniques are used when there is no closed form 2sls solution. Imagine for example your first stage is a ppml model. In that case, we want to use the bootstrap to approximate the 2sls solution. If that procedure is legitimate, then it should give similar results for the linear case (where we know the solution).