Dear All,
Consider estimation of ATE and ATET in an endogenous treatment regression with continuous response variable. Could someone help me to understand the difference between eteffects and etregress with the poutcomes cfunction options?
The etregress model is fitted as:
. webuse drugexp
. etregress lndrug chron age lninc, treat(ins=age married lninc work) poutcomes cfunction
Iteration 0: GMM criterion Q(b) = 2.279e-15
Iteration 1: GMM criterion Q(b) = 6.041e-30
Linear regression with endogenous treatment Number of obs = 6,000
Estimator: Control function
------------------------------------------------------------------------------
| Robust
| Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
lndrug |
chron | .4671725 .0319731 14.61 0.000 .4045064 .5298387
age | .1021359 .00292 34.98 0.000 .0964128 .1078589
lninc | .0550672 .0225036 2.45 0.014 .0109609 .0991735
1.ins | -.8598836 .3483648 -2.47 0.014 -1.542666 -.1771011
_cons | 1.665539 .2527527 6.59 0.000 1.170153 2.160925
-------------+----------------------------------------------------------------
ins |
age | .021142 .0022961 9.21 0.000 .0166416 .0256424
married | .084631 .0359713 2.35 0.019 .0141286 .1551334
lninc | .1023032 .0225009 4.55 0.000 .0582022 .1464041
work | .288418 .0372281 7.75 0.000 .2154522 .3613837
_cons | -.622993 .108795 -5.73 0.000 -.8362273 -.4097587
-------------+----------------------------------------------------------------
/athrho0 | .4035094 .1724539 2.34 0.019 .0655059 .7415129
/lnsigma0 | .3159269 .0500476 6.31 0.000 .2178353 .4140184
/athrho1 | .7929459 .2986601 2.66 0.008 .2075829 1.378309
/lnsigma1 | .1865347 .0613124 3.04 0.002 .0663646 .3067048
-------------+----------------------------------------------------------------
rho0 | .3829477 .1471637 .0654124 .6300583
sigma0 | 1.37153 .0686418 1.243382 1.512885
lambda0 | .5252243 .226367 .0815532 .9688954
rho1 | .6600746 .1685343 .2046518 .880572
sigma1 | 1.205066 .0738855 1.068616 1.35894
lambda1 | .7954338 .2513036 .3028878 1.28798
------------------------------------------------------------------------------
Wald test of indep. (rho0 = rho1 = 0): chi2(2) = 8.88 Prob > chi2 = 0.0118
. margins r.ins, vce(unconditional)
Contrasts of predictive margins Number of obs = 6,000
Expression: Linear prediction, predict()
------------------------------------------------
| df chi2 P>chi2
-------------+----------------------------------
ins | 1 6.09 0.0136
------------------------------------------------
--------------------------------------------------------------
| Unconditional
| Contrast std. err. [95% conf. interval]
-------------+------------------------------------------------
ins |
(1 vs 0) | -.8598836 .3483939 -1.542723 -.1770442
--------------------------------------------------------------
. margins, vce(unconditional) predict(cte) subpop(if ins==1)
Predictive margins Number of obs = 6,000
Subpop. no. obs = 4,556
Expression: Conditional treatment effect, predict(cte)
------------------------------------------------------------------------------
| Unconditional
| Margin std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
_cons | -.7522552 .3826993 -1.97 0.049 -1.502332 -.0021783
------------------------------------------------------------------------------
And the eteffects model is fit as follows:
. eteffects (lndrug chron age lninc) (ins age married lninc work)
Iteration 0: EE criterion = 2.481e-18
Iteration 1: EE criterion = 2.146e-31
Endogenous treatment-effects estimation Number of obs = 6,000
Outcome model: linear
Treatment model: probit
------------------------------------------------------------------------------
| Robust
lndrug | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
ATE |
ins |
(1 vs 0) | -.9089342 .5579228 -1.63 0.103 -2.002443 .1845745
-------------+----------------------------------------------------------------
POmean |
ins |
0 | 6.212021 .5431801 11.44 0.000 5.147408 7.276635
------------------------------------------------------------------------------
. eteffects (lndrug chron age lninc) (ins age married lninc work), atet
Iteration 0: EE criterion = 2.481e-18
Iteration 1: EE criterion = 4.145e-31
Endogenous treatment-effects estimation Number of obs = 6,000
Outcome model: linear
Treatment model: probit
------------------------------------------------------------------------------
| Robust
lndrug | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
ATET |
ins |
(1 vs 0) | -.8529128 .7140559 -1.19 0.232 -2.252437 .546611
-------------+----------------------------------------------------------------
POmean |
ins |
0 | 6.503372 .7138809 9.11 0.000 5.104192 7.902553
------------------------------------------------------------------------------
Notice that point estimates for ATE and ATET and the SEs are not quite the same across commands. Can you help me to understand why it are different?
Consider estimation of ATE and ATET in an endogenous treatment regression with continuous response variable. Could someone help me to understand the difference between eteffects and etregress with the poutcomes cfunction options?
The etregress model is fitted as:
. webuse drugexp
. etregress lndrug chron age lninc, treat(ins=age married lninc work) poutcomes cfunction
Iteration 0: GMM criterion Q(b) = 2.279e-15
Iteration 1: GMM criterion Q(b) = 6.041e-30
Linear regression with endogenous treatment Number of obs = 6,000
Estimator: Control function
------------------------------------------------------------------------------
| Robust
| Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
lndrug |
chron | .4671725 .0319731 14.61 0.000 .4045064 .5298387
age | .1021359 .00292 34.98 0.000 .0964128 .1078589
lninc | .0550672 .0225036 2.45 0.014 .0109609 .0991735
1.ins | -.8598836 .3483648 -2.47 0.014 -1.542666 -.1771011
_cons | 1.665539 .2527527 6.59 0.000 1.170153 2.160925
-------------+----------------------------------------------------------------
ins |
age | .021142 .0022961 9.21 0.000 .0166416 .0256424
married | .084631 .0359713 2.35 0.019 .0141286 .1551334
lninc | .1023032 .0225009 4.55 0.000 .0582022 .1464041
work | .288418 .0372281 7.75 0.000 .2154522 .3613837
_cons | -.622993 .108795 -5.73 0.000 -.8362273 -.4097587
-------------+----------------------------------------------------------------
/athrho0 | .4035094 .1724539 2.34 0.019 .0655059 .7415129
/lnsigma0 | .3159269 .0500476 6.31 0.000 .2178353 .4140184
/athrho1 | .7929459 .2986601 2.66 0.008 .2075829 1.378309
/lnsigma1 | .1865347 .0613124 3.04 0.002 .0663646 .3067048
-------------+----------------------------------------------------------------
rho0 | .3829477 .1471637 .0654124 .6300583
sigma0 | 1.37153 .0686418 1.243382 1.512885
lambda0 | .5252243 .226367 .0815532 .9688954
rho1 | .6600746 .1685343 .2046518 .880572
sigma1 | 1.205066 .0738855 1.068616 1.35894
lambda1 | .7954338 .2513036 .3028878 1.28798
------------------------------------------------------------------------------
Wald test of indep. (rho0 = rho1 = 0): chi2(2) = 8.88 Prob > chi2 = 0.0118
. margins r.ins, vce(unconditional)
Contrasts of predictive margins Number of obs = 6,000
Expression: Linear prediction, predict()
------------------------------------------------
| df chi2 P>chi2
-------------+----------------------------------
ins | 1 6.09 0.0136
------------------------------------------------
--------------------------------------------------------------
| Unconditional
| Contrast std. err. [95% conf. interval]
-------------+------------------------------------------------
ins |
(1 vs 0) | -.8598836 .3483939 -1.542723 -.1770442
--------------------------------------------------------------
. margins, vce(unconditional) predict(cte) subpop(if ins==1)
Predictive margins Number of obs = 6,000
Subpop. no. obs = 4,556
Expression: Conditional treatment effect, predict(cte)
------------------------------------------------------------------------------
| Unconditional
| Margin std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
_cons | -.7522552 .3826993 -1.97 0.049 -1.502332 -.0021783
------------------------------------------------------------------------------
And the eteffects model is fit as follows:
. eteffects (lndrug chron age lninc) (ins age married lninc work)
Iteration 0: EE criterion = 2.481e-18
Iteration 1: EE criterion = 2.146e-31
Endogenous treatment-effects estimation Number of obs = 6,000
Outcome model: linear
Treatment model: probit
------------------------------------------------------------------------------
| Robust
lndrug | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
ATE |
ins |
(1 vs 0) | -.9089342 .5579228 -1.63 0.103 -2.002443 .1845745
-------------+----------------------------------------------------------------
POmean |
ins |
0 | 6.212021 .5431801 11.44 0.000 5.147408 7.276635
------------------------------------------------------------------------------
. eteffects (lndrug chron age lninc) (ins age married lninc work), atet
Iteration 0: EE criterion = 2.481e-18
Iteration 1: EE criterion = 4.145e-31
Endogenous treatment-effects estimation Number of obs = 6,000
Outcome model: linear
Treatment model: probit
------------------------------------------------------------------------------
| Robust
lndrug | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
ATET |
ins |
(1 vs 0) | -.8529128 .7140559 -1.19 0.232 -2.252437 .546611
-------------+----------------------------------------------------------------
POmean |
ins |
0 | 6.503372 .7138809 9.11 0.000 5.104192 7.902553
------------------------------------------------------------------------------
Notice that point estimates for ATE and ATET and the SEs are not quite the same across commands. Can you help me to understand why it are different?
