nlcom after two GMMs, suest not working

[Nona Karalashvili]

Hello,

I need a nonlinear combinations of parameter estimates from two GMM models, call them model1 and GMM2.
I do the following:

gmm ($eq1-var1) ($eq2 - var2), winitial(identity) from(a 0.5 b 0.5)
estimates store model1
gmm ($eq3-var3) ($eq4 - var4) ($eq5 - var5) ($q6-var6), winitial(identity) from(c 0.5 d 0.5 e 0.5 f 0.5)
estimates store model2
suest model1 model2, vce(cluster clustervar)

at which point I get a message:
model1 was estimated with a nonstandard vce (robust)
r(322);

After suest, I would want the following:
nlcom (comb: [model1]_b[/a]/ [model2]_b[/d] )

I tried GMM's with various vce types, including "unadjusted", Stata always gives me the same error message, with the change that instead of vce (robust) it tells me whichever vce I used (e.g. vce (unadjusted)).

I also tried retrieving estimates without suest but it does not work.

Please let me know how can I do the above without Mata. I am very rusty in Mata and would strongly prefer to use the usual Stata language.

Many thanks,
Best wishes,
Nona

[Jeff Pitblado (StataCorp)]

This error message is not as specific as it could be; suest does not
work with gmm estimation results.

Nona could actually combine the two gmm model specifications into
a single call to gmm and then use nlcom.

Here is an example using the auto data that shows the point estimates
in the combined model are the same as the separate gmm fits.

sysuse auto

gmm     (mpg - {xb:gear_ratio turn} - {b0})                             ///
        ,                                                               ///
        instruments(gear_ratio turn)                                    ///
        winit(identity)                                                 ///
        derivative(/xb = -1)                                            ///
        derivative(/b0 = -1)                                            ///
        vce(unadjusted)
estimates store mpg

gmm     (price - {zb:headroom displacement foreign} - {a0})             ///
        ,                                                               ///
        instruments(headroom displacement foreign)                      ///
        winit(identity)                                                 ///
        derivative(/zb = -1)                                            ///
        derivative(/a0 = -1)                                            ///
        vce(unadjusted) 
estimates store price

gmm     (mpg:mpg - {xb:gear_ratio turn} - {b0})                         ///
        (price:price - {zb:headroom displacement foreign} - {a0})       ///
        ,                                                               ///
        instruments(mpg:gear_ratio turn)                                ///
        instruments(price:headroom displacement foreign)                ///
        winit(identity)                                                 ///
        derivative(mpg/xb = -1)                                         ///
        derivative(mpg/b0 = -1)                                         ///
        derivative(price/zb = -1)                                       ///
        derivative(price/a0 = -1)

estimates table mpg price ., b se

Here is the output I got from estimates table:

-----------------------------------------------------
    Variable |    mpg         price        active    
-------------+---------------------------------------
xb_gear_ra~o |
       _cons |  3.0328836                 3.0328836  
             |  1.3448594                 1.5016643  
-------------+---------------------------------------
xb_turn      |
       _cons | -.73305019                -.73305019  
             |  .13948458                   .117972  
-------------+---------------------------------------
b0           |
       _cons |  41.218012                 41.218012  
             |  8.8065809                 8.3967394  
-------------+---------------------------------------
zb_headroom  |
       _cons |              -534.78093   -534.78093  
             |               337.54132    271.96603  
-------------+---------------------------------------
zb_displac~t |
       _cons |               29.368237    29.368237  
             |               3.7645843    4.2083208  
-------------+---------------------------------------
zb_foreign   |
       _cons |               3620.5118    3620.5118  
             |               691.86449    658.46219  
-------------+---------------------------------------
a0           |
       _cons |               895.34402    895.34402  
             |               1125.1362    897.25673  
-----------------------------------------------------
                                         legend: b/se

[Nona Karalashvili]

Jeff, this is a great idea! Thanks you!

I did try doing that before posting my question here, but the problem I encounter there is that parameters a and b in my post do not get standard errors. I really have no explanation of why that happens. Because they do not come with standard errors, nlcom thinks they are just numbers so the standard error on the combination comes up too low.

To be more specific, here is my combined gmm (where my parameter a in the previous post corresponds to wn, and b corresponds to gn, the equations are defined as the corresponding globals):

global inaive "{wn}"
global snaive "{wn}*{gn}"
...
gmm ($nmeanx-x) ($nxx-x*x) ($meansstar-infpayn) ($meaninteractions - interactions) ($inaive - interactionsnaive) ($snaive-infpaynnaive), winitial(identity) vce(cluster strata) from(g 0.5 q 0.5 r 0.5 w 0.5 wn 0.5 gn 0.5)

and this is what I get:

Number of parameters = 6
Number of moments = 6
Initial weight matrix: Identity Number of obs = 780
GMM weight matrix: Cluster (strata)

(Std. Err. adjusted for 103 clusters in strata)

Robust
Coef. Std. Err. z P>z [95% Conf. Interval]

/g .0868321 .0182984 4.75 0.000 .0509679 .1226962
/r .5134686 .0445523 11.53 0.000 .4261476 .6007896
/q .7561935 .0329366 22.96 0.000 .6916389 .8207481
/w .9137773 .053899 16.95 0.000 .8081371 1.019417
/wn .5589744 . . . . .
/gn .0733945 . . . . .

the estimates of wn and gn are "correct" in the sense that when I run those two as a separate gmm it gives me the exact same estimates, BUT I do get standard errors, unlike in the above.

Any ideas of what is going on and how to fix it?

Thanks a lot!
Best wishes,
Nona

[Jeff Pitblado (StataCorp)]

Maybe if you gave us the full specification of your gmm model and a dataset that reproduces
this behavior, one of us might have some further insight.

[Nona Karalashvili]

I will ask my co-authors.

Thanks again!
Nona

[Nona Karalashvili]

Please see the data attached.
Here is the gmm model.

scalar nnn = 7
local phi = 1
local psi = 0
global inaive "{wn}"
global snaive "{wn}*{gn}"
global meaninteractions "{w}*((1-{r}*{q}))^(`phi')+({w}*{r}*(1-{g})*{q})*(`psi')"
global nmeanx "(nnn/2)*(1+{g})*(1-{r}*{q})"
global nxx "(nnn/2)*(1+{g})*(1-{r}*{q})+(nnn-1)*nnn*(1/2*(1+{g}))^2*(1-2*{r}*{q}+{r}*{q}^2)"
global meansstar "{w}*{g}*(1-{r}*{q}-`phi'*{r}*{q}*(1-{q}))"

gmm ($nmeanx-x) ($nxx-x*x) ($meansstar-infpayn) ($meaninteractions - interactions) ($inaive - interactions) ($snaive-infpayn), winitial(identity) vce(cluster strata) from(g 0.5 q 0.5 r 0.5 w 0.5 wn 0.5 gn 0.5)
nlcom (behav: (_b[/wn])/ (_b[/w]) * 1 / (1-(_b[/r])*(_b[/q]) -`phi'*(_b[/r])*(_b[/q])*(1-(_b[/q])) ) ) (goverg: (_b[/g])/ (_b[/gn]) )

As you will see, {wn} and {gn} come out without standard errors, which is why nlcom's output is incorrect (see goverg's standard error in comparison with g's)

Any insight on how to fix the problem would be much appreciated. The alternative is to simply bootstrap the linear combination's standard errors, but I would rather use a more conventional route.

Thanks again!
Best wishes,
Nona

[Jeff Pitblado (StataCorp)]

It looks like the last two moment equations for the variables
interactions and infpayn are in conflict with moment
equations 3 and 4, also for variables interaction and infpayn.

[Nona Karalashvili]

I do have the same sense, but I fail to see any reason.
At the same time, if I copy those variables and name differently, so that I have two sets of variables which are copies of each other (so that there is no conflict due to sharing of variables), this does not solve the problem either. It could be that this perfect correlation is the reason, but I fail to see the underlying logic.

Thanks again!
Nona

[Nona Karalashvili]

So, here is what helped. I created a new dummy with exact same number of 1 as interactions but with different order, and I used that instead of interactions in the fifth moment condition. I got the standard errors for wn this way.. So it was the use of the same, or perfectly correlated variables that made Stata stumble. Though there is no theoretical problem with the model.
Thanks again! Your input really helped me get to the bottom of this! I really appreciate your time!

Nona

[Nona Karalashvili]

well, the problem with my solution however is that I can no longer estimate clusterred standard errors because of that re-ordering that was necessary to kill off the perfect correlation. This is a real problem. I guess the only thing I can do is to bootrstap and get the standard error of that combination of estimates that I need. Please let me know if there are other solutions.

Thanks again!
Nona

[Michael Wittry]

Hi there,

I am getting the same error message when using suest. I'm trying to compare coefficients between two models with high dimensional fixed effects. Here is what I am trying to run.

reghdfe y x, absorb(fe1 fe2 fe3)
est store eq1
reghdfe y x z, absorb(fe1 fe2 fe3)
est store eq2

suest eq1 eq2, vce(cl cluster1)

This is where I'm getting the error about nonstandard vce. Is there anyway to get around this problem and estimate a SUR when using these high dimensional fixed effects.

Thanks!

Mike

[Sergio Correia]

Hi Michael,

So far I see a few reasons for why this will not work

• suest doesn't support -areg- and since -reghdfe- (SSC) is basically -areg- on steroids, this hints that they are not compatible. Delving further into this, the problem is that in areg and reghdfe you don't get the residuals with "e = y - xb", but you need the additional fixed effects (i.e. "e = y-xb-d" in stata notation)
• The second problem, and the one -suest- complained about, is that reghdfe uses e(vce)="unadjusted" instead of the usual e(vce)="ols" for the default case (even though they are the same thing). I don't remember well the reason behind that, but I think that "unadjusted" is more general than just "ols" (e.g. in the iv case).

Finally, I'm not entirely sure of the reasons for using -suest- in this case. I'm not familiar with the command though so I might be missing something.

Best,
Sergio

[Michael Wittry]

Hi Sergio,

Thanks for the response. Mainly, I want to test for significant differences between coefficients in a full model and a nested model. The only way I know how to do this is with a seemingly unrelated equations framework. The full and nested models I want to use are estimated with reghdfe (I actually cluster my SE's but the suest command told me to cluster with suest).

I'm not sure if that clears up what I'm trying to do, but in any case, it seems like I won't be able to use suest for this task. If you have any suggestions on the SUR methodology with reghdfe, please let me know.

Thanks,
Mike

[Sergio Correia]

Ok, I think I found your solution. You can run the -test varlist- command after reghdfe, with varlist being equal to the additional variables in the full model.
Now, do not run this after a regression with unadjusted/ols errors, as the results of -test- will be wrong. They seem to work fine with clustered errors, as shown in the proof of concept below:

Best,
Sergio

cls
clear all
sysuse auto
gen n = _n
local vce cluster n 

reghdfe price length weight displacement, absorb(turn) vce(cluster n )
di e(df_r)
di e(df_a)
di e(df_m)
test length weight

areg price length weight displacement, absorb(turn) vce(cluster n)
di e(df_r)
di e(df_a)
di e(df_m)
test length weight

qui regress price length weight displacement i.turn, vce(cluster n)
test length weight

[Michael Wittry]

Hi Sergio,

I really appreciate the help, but I don't see how I can test coefficients across two different models. For example, with your code example from above, I would want to do something like the following. Let me know if that doesn't make sense. I know suest does this for reg commands (as well as probit, logit, etc).

Thanks again,
Mike

cls
clear all
sysuse auto
gen n = _n
local vce cluster n

reghdfe price length, absorb(turn) vce(cluster n) // This is model1
reghdfe price length weight displacement, absorb(turn) vce(cluster n) // This is model2

test length(model1) = length(model2)