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# st: rbounds Hodges-Lehmann point estimates and ATT estimates

 From Richard Palmer-Jones To statalist@hsphsun2.harvard.edu Subject st: rbounds Hodges-Lehmann point estimates and ATT estimates Date Thu, 1 Jul 2010 17:06:34 +0100

```Dear Readers

When  I run rbounds after psmatch2 I find that the Hodges-Lehman
minimum and maximum point estimates of impact are (generally)
substantially different to the estimated ATT when the Gamma =1. Could
someone explain this?

. use lalonde.dta

. psmatch2 t age age2 educ educ2 black hisp marr re74 u74 re74 re75 ,
outcome(re78)
note: re74 dropped because of collinearity

Probit regression                                 Number of obs   =       2675
LR chi2(10)     =     882.99
Prob > chi2     =     0.0000
Log likelihood =  -231.1534                       Pseudo R2       =     0.6564

------------------------------------------------------------------------------
t |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
age |    .165835   .0597947     2.77   0.006     .0486395    .2830305
age2 |  -.0031243   .0009159    -3.41   0.001    -.0049195    -.001329
educ |   .4034187   .1637615     2.46   0.014      .082452    .7243854
educ2 |  -.0233423   .0081187    -2.88   0.004    -.0392546   -.0074299
black |   1.179666   .1692016     6.97   0.000     .8480369    1.511295
hisp |   1.200164   .3092023     3.88   0.000     .5941388     1.80619
marr |  -1.000713   .1456276    -6.87   0.000    -1.286138    -.715288
re74 |  -.0000509   .0000141    -3.62   0.000    -.0000784   -.0000233
u74 |    .326188   .1842919     1.77   0.077    -.0350175    .6873935
re75 |   -.000103   .0000205    -5.03   0.000    -.0001431   -.0000629
_cons |  -4.082649   1.221929    -3.34   0.001    -6.477585   -1.687713
------------------------------------------------------------------------------
Note: 659 failures and 0 successes completely determined.
There are observations with identical propensity score values.
The sort order of the data could affect your results.
Make sure that the sort order is random before calling psmatch2.
----------------------------------------------------------------------------------------
Variable     Sample |    Treated     Controls   Difference
S.E.   T-stat
----------------------------+-----------------------------------------------------------
re78  Unmatched | 6349.14537   21553.9213  -15204.7759
1154.61435   -13.17
ATT | 6349.14537   5387.78028   961.365096
1420.27513     0.68
----------------------------+-----------------------------------------------------------
Note: S.E. for ATT does not take into account that the propensity
score is estimated.

| psmatch2:
psmatch2: |   Common
Treatment |  support
assignment | On suppor |     Total
-----------+-----------+----------
Untreated |     2,490 |     2,490
Treated |       185 |       185
-----------+-----------+----------
Total |     2,675 |     2,675

. gen diff =  re78- _re78
(2490 missing values generated)

. rbounds diff, gamma(1(.2)3)

Rosenbaum bounds for diff (N = 185 matched pairs)

Gamma           sig+      sig-    t-hat+    t-hat-       CI+       CI-
----------------------------------------------------------------------
1        .203558   .203558    498.13    498.13  -618.815   1671.48
1.2        .594682   .028425  -109.352   1108.27  -1261.98   2361.57
1.4        .873746   .002358   -622.61   1680.15  -1795.44   2936.95
1.6        .973397   .000138   -1113.6   2160.85  -2305.18   3440.96
1.8        .995808   6.3e-06   -1507.8    2567.3  -2722.57   3920.69
2        .999467   2.4e-07  -1811.98    2961.7  -3098.75    4317.7
2.2        .999942   8.3e-09  -2171.23      3265  -3463.81   4741.49
2.4        .999995   2.6e-10  -2410.04   3622.82  -3749.03   5057.69
2.6              1   7.3e-12  -2717.38   3919.67  -4063.75   5380.66
2.8              1   2.0e-13  -2960.24      4167  -4308.32   5657.37
3              1   5.1e-15  -3195.96   4413.54  -4566.85    5982.9

* gamma  - log odds of differential assignment due to unobserved factors
sig+   - upper bound significance level
sig-   - lower bound significance level
t-hat+ - upper bound Hodges-Lehmann point estimate
t-hat- - lower bound Hodges-Lehmann point estimate
CI+    - upper bound confidence interval (a=  .95)
CI-    - lower bound confidence interval (a=  .95)

.
end of do-file

My problem is:

ATT = 961
Gammat-hat+    t-hat-
1       498.13    498.13
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```