Compare estiamtes of full and subsample after ivreg

[Kerstin Schmidt]

Dear Statalist community,

I am trying to compare the estimates of an IV regression of the full sample vs. the subsample. I found some examples (https://www.stata.com/statalist/arch.../msg00487.html, https://www.stata.com/statalist/arch.../msg00373.html) but have problems adjusting them to my context.

What I have is the following:

global X x1 x2 x3 x4 x5

*full sample
xtivreg2 Y $X (x_endo = z), fe first endog(x_endo)
est store FS1

*subsample
xtivreg2 Y $X (x_endo = z) if gender==1, fe first endog(x_endo)
est store SS1

Now I would like to statistically compare the estimates of x_endo and x1 in both regressions.

Trying the following produced an error:

testnl [FS1_Y]x_endo=[SS1_]x_endo

equation [FS1_Consumption] not found
r(303);

What can I do instead?

Thanks!

[Andrew Musau]

Tests over overlapping samples can be difficult to interpret. It's akin to claiming that London's GDP per capita is higher than Britain's, despite London being part of Britain. Nevertheless, you can duplicate the data and proceed in the same way as you would with disjoint samples. See https://www.statalist.org/forums/for...ferent-samples.

[Kerstin Schmidt]

Hey Andrew,

Thank you for your answer.

As I am using a Fixed Effects estimation and my gender variable is time-invariant, it is dropped from the model. Therefore, it seems best to run two separate regressions:

xtivreg2 Y x1  $x (x_endo = Z) if gender==1, fe cluster(hhid) first
est sto W1

xtivreg2 Y x1  $x (x_endo = Z) if gender==0, fe cluster(hhid) first
est sto W0

test [W1_Y]x_endo=[W0_Y]x_endo

Results in: equation [W1_Y] not found
r(303);

What can I do here?

[Andrew Musau]

Translating the example in https://www.statalist.org/forums/for...ferent-samples to your setting is as simple as:

webuse hsng2, clear
*create subsample
gen subsample= _n<26

*FULL SAMPLE
ivregress 2sls rent pcturban (hsngval = faminc i.region), robust
*SUBSAMPLE
ivregress 2sls rent pcturban (hsngval = faminc i.region) if subsample, robust


*JOINT REGRESSION (interact variables with group variable). Note with 2 constant terms, we create our own
expand 2 if subsample, gen(sub)

lab def `:val lab sub' 0 "Full sample" 1 "Subsample", modify

gen cons=1
ivregress 2sls rent c.pcturban#i.sub c.cons#i.sub (c.hsngval#i.sub = (c.faminc i.region)#i.sub), nocons robust

*Now compare coefficients across groups, e.g.,
test 0.sub#c.hsngval=  1.sub#c.hsngval

Res.:

. *FULL SAMPLE

. 
. ivregress 2sls rent pcturban (hsngval = faminc i.region), robust

Instrumental variables (2SLS) regression          Number of obs   =         50
                                                  Wald chi2(2)    =      44.98
                                                  Prob > chi2     =     0.0000
                                                  R-squared       =     0.5989
                                                  Root MSE        =     22.166

------------------------------------------------------------------------------
             |               Robust
        rent | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
     hsngval |   .0022398    .000672     3.33   0.001     .0009227    .0035569
    pcturban |    .081516   .4445938     0.18   0.855     -.789872    .9529039
       _cons |   120.7065   15.25546     7.91   0.000     90.80636    150.6067
------------------------------------------------------------------------------
Instrumented:  hsngval
Instruments:   pcturban faminc 2.region 3.region 4.region

. 
. *SUBSAMPLE

. 
. ivregress 2sls rent pcturban (hsngval = faminc i.region) if subsample, robust

Instrumental variables (2SLS) regression          Number of obs   =         25
                                                  Wald chi2(2)    =      22.11
                                                  Prob > chi2     =     0.0000
                                                  R-squared       =     0.5444
                                                  Root MSE        =     27.437

------------------------------------------------------------------------------
             |               Robust
        rent | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
     hsngval |   .0023382   .0009395     2.49   0.013     .0004968    .0041795
    pcturban |  -.3853024   .9975224    -0.39   0.699     -2.34041    1.569806
       _cons |   147.9727   34.01539     4.35   0.000     81.30382    214.6417
------------------------------------------------------------------------------
Instrumented:  hsngval
Instruments:   pcturban faminc 2.region 3.region 4.region

. 
. 
. 
. 
. 
. *JOINT REGRESSION (interact variables with group variable). Note with 2 constant terms, we create our own

. 
. expand 2 if subsample, gen(sub)
(25 observations created)

. 
. 
. 
. lab def `:val lab sub' 0 "Full sample" 1 "Subsample", modify

. 
. 
. 
. gen cons=1

. 
. ivregress 2sls rent c.pcturban#i.sub c.cons#i.sub (c.hsngval#i.sub = (c.faminc i.region)#i.sub), nocons robust
note: 4.region#1.sub omitted because of collinearity.

Instrumental variables (2SLS) regression          Number of obs   =         75
                                                  Wald chi2(6)    =          .
                                                  Prob > chi2     =          .
                                                  R-squared       =          .
                                                  Root MSE        =     24.051

--------------------------------------------------------------------------------
               |               Robust
          rent | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
---------------+----------------------------------------------------------------
 sub#c.hsngval |
  Full sample  |   .0022398    .000672     3.33   0.001     .0009227    .0035569
    Subsample  |   .0023382   .0009395     2.49   0.013     .0004968    .0041795
               |
sub#c.pcturban |
  Full sample  |    .081516   .4445938     0.18   0.855     -.789872    .9529039
    Subsample  |  -.3853024   .9975224    -0.39   0.699     -2.34041    1.569806
               |
    sub#c.cons |
  Full sample  |   120.7065   15.25546     7.91   0.000     90.80636    150.6067
    Subsample  |   147.9727   34.01539     4.35   0.000     81.30382    214.6417
--------------------------------------------------------------------------------
Instrumented:  0b.sub#c.hsngval 1.sub#c.hsngval
Instruments:   0b.sub#c.pcturban 1.sub#c.pcturban 0b.sub#c.cons 1.sub#c.cons
               0b.sub#c.faminc 1.sub#c.faminc 1b.region#1.sub 2.region#0b.sub
               2.region#1.sub 3.region#0b.sub 3.region#1.sub 4.region#0b.sub

. 
. 
. 
. *Now compare coefficients across groups, e.g.,

. 
. test 0.sub#c.hsngval=  1.sub#c.hsngval

 ( 1)  0b.sub#c.hsngval - 1.sub#c.hsngval = 0

           chi2(  1) =    0.01
         Prob > chi2 =    0.9322

[Kerstin Schmidt]

Hey Andrew,

I can fully replicate your example but applying it to a simplified model specification in my data shows a new error: "0b.subsample included in both exogenous and endogenous variable lists."

Here is my code:

gen subsample = (gender==1)

*JOINT REGRESSION (interact variables with group variable). Note with 2 constant terms, we create our own
expand 2 if subsample, gen(sub)
lab def `:val lab sub' 0 "Full sample" 1 "Subsample", modify

gen cons=1

ivregress 2sls Y i.x1##i.sub $x c.cons##i.sub (i.x_endo##i.sub = (c.Z##i.sub)), nocons robust

What is wrong here?

[Andrew Musau]

Without seeing your data and codes for the separate regressions, there is not much that I can comment on. The fixed effects add some extra complications, but there should be ways to handle them.