Iam a bit lost in understanding what is going wrong with my model.
Here is what I 've done:
I want to test the effect of pollution on an outcome Y. Due to endogeneity issue, I opted for an IV for the air pollution.
The IV is a governmental policy that is expected to have reduced pollution.
So I run the following code
ivprobit Y (pollution = postXtreat ) other controls i.provinceXyear i.coun, cluster( coun) first
i.coun is county fixed effects
i.provinceXyear is province by year of birth (year of exposure to pollution for each individual) fixed effects.
I have a cross section of individuals born in different years before and after the policy in different counties where the policy was implemented and where it was not (so individuals are not the same in different years but the counties are the same over years).
The problem is that the 2SLS estimation does not work as it is
error:
Code:
could not find initial values
Low T per N: (I indeed don't have an observation in each year for a given county) I tried to use a minimum of 6 observations per county: gives me weird results: not the expected signs for the coefficients of interest (compared to the literature) and very high levels of wald chi2 test.
So I tried to run first step on its own: effect of policy on pollution
the policy significantly decreases pollution if I only include county fixed effects and drop province by year fixed effects
the policy significantly increases pollution if I only include province by year fe and drop county fe.
the policy decreases (not significantly) pollution when I include both fe.
Here are the results from my 2SLS estimation:
Code:
Probit model with endogenous regressors Number of obs = 768
Wald chi2(80) = 5.87e+09
Log pseudolikelihood = -326.26393 Prob > chi2 = 0.0000
(Std. Err. adjusted for 79 clusters in coun)
-------------------------------------------------------------------------------------
| Robust
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------+----------------------------------------------------------------
Y |
Pollution | 3.086005 1.116393 2.76 0.006 .8979144 5.274096
other controls here |
provinceXyear |
111996 | -.08387 .828575 -0.10 0.919 -1.707847 1.540107
111997 | 2.066071 1.069159 1.93 0.053 -.0294413 4.161584
111998 | 6.428071 2.221574 2.89 0.004 2.073867 10.78228
111999 | 18.07829 5.652187 3.20 0.001 7.000211 29.15638
141995 | 42.00588 13.57904 3.09 0.002 15.39145 68.6203
141996 | 38.74168 12.66577 3.06 0.002 13.91723 63.56613
141997 | 37.37595 12.43752 3.01 0.003 12.99886 61.75305
141998 | 41.52244 13.64751 3.04 0.002 14.77381 68.27108
141999 | 0 (empty)
211995 | 0 (empty)
211996 | 0 (empty)
211998 | 0 (empty)
321995 | -32.23833 14.00117 -2.30 0.021 -59.68011 -4.796539
321996 | -31.52024 13.4896 -2.34 0.019 -57.95937 -5.081113
321997 | -26.51056 12.34954 -2.15 0.032 -50.71522 -2.305899
321998 | -26.32549 12.32459 -2.14 0.033 -50.48124 -2.169732
321999 | -23.63543 11.11902 -2.13 0.034 -45.4283 -1.842555
341995 | 12.08086 4.487632 2.69 0.007 3.285265 20.87646
341996 | 13.10474 4.618495 2.84 0.005 4.052655 22.15682
341997 | 13.69676 4.88849 2.80 0.005 4.115499 23.27803
341998 | 14.60849 4.863234 3.00 0.003 5.076727 24.14025
341999 | 22.42444 6.500338 3.45 0.001 9.684009 35.16487
411995 | -24.06416 11.05308 -2.18 0.029 -45.72779 -2.400532
411996 | -29.79043 12.73007 -2.34 0.019 -54.7409 -4.839957
411997 | -23.94578 10.78602 -2.22 0.026 -45.08599 -2.805564
411998 | -19.83655 9.896316 -2.00 0.045 -39.23298 -.4401309
411999 | -14.94796 8.330533 -1.79 0.073 -31.2755 1.379587
421995 | 53.82698 18.06005 2.98 0.003 18.42992 89.22404
421996 | 53.06059 17.55104 3.02 0.003 18.66118 87.45999
421997 | 54.54114 18.21225 2.99 0.003 18.84579 90.23649
421998 | 51.97626 17.78062 2.92 0.003 17.12689 86.82563
421999 | 0 (empty)
431995 | 17.97994 5.693734 3.16 0.002 6.820429 29.13946
431996 | 18.92911 5.711715 3.31 0.001 7.734358 30.12387
431997 | 19.31405 5.941527 3.25 0.001 7.668875 30.95923
431998 | 17.58278 5.738822 3.06 0.002 6.334895 28.83066
431999 | 22.75633 7.077011 3.22 0.001 8.88564 36.62701
441995 | 32.94615 10.52149 3.13 0.002 12.32441 53.56789
441996 | 35.76192 11.01219 3.25 0.001 14.17843 57.34541
441997 | 35.80182 10.57486 3.39 0.001 15.07548 56.52817
441998 | 0 (empty)
441999 | 0 (empty)
501995 | 47.14885 15.48771 3.04 0.002 16.7935 77.50421
501996 | 46.78181 15.27741 3.06 0.002 16.83863 76.72499
501997 | 48.1747 15.80058 3.05 0.002 17.20612 79.14327
501998 | 46.87172 15.59802 3.00 0.003 16.30016 77.44327
501999 | 0 (empty)
511995 | 1.721935 3.484826 0.49 0.621 -5.108198 8.552068
511996 | 1.658739 3.239828 0.51 0.609 -4.691207 8.008685
511997 | 3.218198 3.062402 1.05 0.293 -2.784001 9.220396
511998 | 4.442272 3.175146 1.40 0.162 -1.780901 10.66544
531995 | 63.19297 21.46472 2.94 0.003 21.12288 105.2631
531996 | 63.69529 21.0668 3.02 0.002 22.40512 104.9855
531997 | 64.06481 21.24237 3.02 0.003 22.43054 105.6991
531998 | 63.09008 21.21096 2.97 0.003 21.51737 104.6628
621995 | 53.87442 18.24744 2.95 0.003 18.11009 89.63875
621996 | 54.03442 18.35838 2.94 0.003 18.05265 90.01619
621997 | 54.51972 18.2503 2.99 0.003 18.74979 90.28966
621998 | 55.14101 18.60595 2.96 0.003 18.67401 91.60801
621999 | 56.31056 18.85423 2.99 0.003 19.35694 93.26417
|
coun |
110102 | 0 (empty)
110106 | -13.09354 4.934306 -2.65 0.008 -22.7646 -3.42248
110112 | -28.25414 10.68418 -2.64 0.008 -49.19476 -7.313527
110114 | -17.15601 7.642494 -2.24 0.025 -32.13503 -2.177
110117 | -8.157569 3.539463 -2.30 0.021 -15.09479 -1.220348
110229 | 0 (omitted)
140106 | 0 (empty)
140181 | -10.47059 3.848517 -2.72 0.007 -18.01355 -2.927638
140202 | -2.08105 1.762413 -1.18 0.238 -5.535315 1.373216
140302 | 0 (empty)
140303 | 0 (empty)
140802 | -25.92042 8.303874 -3.12 0.002 -42.19572 -9.64513
140902 | -8.621005 2.574202 -3.35 0.001 -13.66635 -3.575662
140925 | 0 (omitted)
140926 | 0 (empty)
210281 | 0 (empty)
210681 | 0 (empty)
320106 | 5.242644 1.620017 3.24 0.001 2.067469 8.417819
320324 | 28.17655 10.15529 2.77 0.006 8.272558 48.08055
320506 | -9.89474 3.724395 -2.66 0.008 -17.19442 -2.59506
320602 | 19.40026 7.038686 2.76 0.006 5.604693 33.19583
320802 | 30.50033 10.8443 2.81 0.005 9.245899 51.75477
320922 | 52.77043 18.79556 2.81 0.005 15.9318 89.60906
321002 | 0 (empty)
321003 | 0 (omitted)
340621 | -26.86266 9.671252 -2.78 0.005 -45.81797 -7.907354
340823 | 0 (empty)
340826 | -2.259944 1.222119 -1.85 0.064 -4.655254 .1353656
341021 | 9.824597 3.735512 2.63 0.009 2.503127 17.14607
341222 | 0 (empty)
341622 | -28.56904 9.765208 -2.93 0.003 -47.7085 -9.429587
341702 | .7764585 1.157949 0.67 0.503 -1.493081 3.045998
341723 | 0 (omitted)
410105 | -5.759551 4.047172 -1.42 0.155 -13.69186 2.17276
410224 | 5.387618 1.717888 3.14 0.002 2.020619 8.754617
410725 | -8.221678 3.736771 -2.20 0.028 -15.54561 -.8977407
410804 | 0 (empty)
410821 | -6.021951 2.427631 -2.48 0.013 -10.78002 -1.263881
410902 | 3.171023 1.820221 1.74 0.081 -.396545 6.738591
411081 | 4.254515 1.369178 3.11 0.002 1.570975 6.938056
411421 | 6.240048 2.245017 2.78 0.005 1.839895 10.6402
411626 | 0 (empty)
411681 | 9.350898 3.518704 2.66 0.008 2.454366 16.24743
419001 | 0 (omitted)
420114 | -75.58378 28.44936 -2.66 0.008 -131.3435 -19.82406
420923 | -61.17186 22.75807 -2.69 0.007 -105.7769 -16.56686
421123 | -41.23018 15.58056 -2.65 0.008 -71.76752 -10.69285
421222 | 0 (empty)
422801 | 1.470895 .8623866 1.71 0.088 -.2193515 3.161142
429004 | 0 (omitted)
429006 | 0 (empty)
430203 | 0 (empty)
430412 | 0 (empty)
430481 | 5.574934 1.395489 3.99 0.000 2.839825 8.310042
430602 | 1.109517 1.117361 0.99 0.321 -1.08047 3.299505
430681 | -1.982857 1.460608 -1.36 0.175 -4.845596 .879883
430722 | -2.010796 1.191164 -1.69 0.091 -4.345434 .3238421
430726 | 22.6113 7.288642 3.10 0.002 8.325827 36.89678
430821 | 21.28617 6.902019 3.08 0.002 7.758462 34.81388
431081 | 22.27484 7.042788 3.16 0.002 8.471231 36.07845
431102 | 19.67963 6.294948 3.13 0.002 7.341755 32.0175
431382 | 0 (omitted)
440903 | 0 (empty)
441283 | -27.0436 9.766924 -2.77 0.006 -46.18642 -7.900779
441481 | .1222263 .6380388 0.19 0.848 -1.128307 1.372759
441882 | 4.874451 1.955997 2.49 0.013 1.040768 8.708133
445281 | -15.15457 4.963472 -3.05 0.002 -24.88279 -5.426342
445381 | 0 (omitted)
500102 | -7.83161 3.05731 -2.56 0.010 -13.82383 -1.839392
500110 | -14.2077 5.446549 -2.61 0.009 -24.88273 -3.532656
500112 | -8.656853 3.18219 -2.72 0.007 -14.89383 -2.419874
500118 | -40.62365 14.91713 -2.72 0.006 -69.86068 -11.38661
500226 | -43.58252 15.88888 -2.74 0.006 -74.72416 -12.44088
500234 | 0 (omitted)
510108 | 0 (empty)
510112 | 3.459886 1.381993 2.50 0.012 .7512298 6.168542
510411 | 0 (empty)
510421 | 54.74082 19.12786 2.86 0.004 17.2509 92.23074
510904 | 0 (empty)
510921 | 0 (empty)
510922 | 8.710109 2.957502 2.95 0.003 2.913511 14.50671
511303 | 0 (empty)
511923 | 35.16372 11.98724 2.93 0.003 11.66915 58.65828
512021 | 0 (omitted)
530103 | -7.249693 2.86106 -2.53 0.011 -12.85727 -1.642119
530111 | -6.859282 3.030257 -2.26 0.024 -12.79848 -.9200863
530402 | -2.91392 2.890143 -1.01 0.313 -8.578496 2.750657
530821 | 1.564858 .4002959 3.91 0.000 .7802929 2.349424
530921 | 1.037258 .7277906 1.43 0.154 -.3891855 2.463701
532621 | -1.262446 .6773748 -1.86 0.062 -2.590076 .0651841
532901 | -1.059275 1.514925 -0.70 0.484 -4.028474 1.909924
532926 | 0 (omitted)
620102 | -12.39494 3.767134 -3.29 0.001 -19.77839 -5.011498
620402 | -14.29236 5.463535 -2.62 0.009 -25.00069 -3.584026
620502 | -1.702812 1.134908 -1.50 0.134 -3.927191 .5215665
620522 | -3.187792 .3398281 -9.38 0.000 -3.853843 -2.521742
620524 | 2.321082 1.305137 1.78 0.075 -.23694 4.879105
620902 | 9.024004 3.345744 2.70 0.007 2.466466 15.58154
620921 | 11.23223 3.62328 3.10 0.002 4.130728 18.33373
621021 | 0 (empty)
621022 | -2.876322 1.882069 -1.53 0.126 -6.56511 .8124653
621121 | 0 (omitted)
|
_cons | -73.00119 25.63254 -2.85 0.004 -123.24 -22.76233
--------------------+----------------------------------------------------------------
Pollution |
Other controls here|
provinceXyear |
coun |
postXtreat | .2023854 .1374779 1.47 0.141 -.0670663 .4718372
_cons | 22.86447 2.841963 8.05 0.000 17.29432 28.43462
--------------------+----------------------------------------------------------------
/athrho | -1.038874 .5649298 -1.84 0.066 -2.146116 .0683683
/lnsigma | -1.491382 .0945231 -15.78 0.000 -1.676644 -1.30612
--------------------+----------------------------------------------------------------
rho | -.7774429 .2234763 -.9730202 .0682619
sigma | .2250614 .0212735 .1870005 .2708689
-------------------------------------------------------------------------------------
Instrumented: Pollution
Instruments: other controls 111996.provinceXyear
111997.provinceXyear 111998.provinceXyear 111999.provinceXyear
141995.provinceXyear 141996.provinceXyear 141997.provinceXyear
141998.provinceXyear 321995.provinceXyear 321996.provinceXyear
321997.provinceXyear 321998.provinceXyear 321999.provinceXyear
341995.provinceXyear 341996.provinceXyear 341997.provinceXyear
341998.provinceXyear 341999.provinceXyear 411995.provinceXyear
411996.provinceXyear 411997.provinceXyear 411998.provinceXyear
411999.provinceXyear 421995.provinceXyear 421996.provinceXyear
421997.provinceXyear 421998.provinceXyear 431995.provinceXyear
431996.provinceXyear 431997.provinceXyear 431998.provinceXyear
431999.provinceXyear 441995.provinceXyear 441996.provinceXyear
441997.provinceXyear 501995.provinceXyear 501996.provinceXyear
501997.provinceXyear 501998.provinceXyear 511995.provinceXyear
511996.provinceXyear 511997.provinceXyear 511998.provinceXyear
531995.provinceXyear 531996.provinceXyear 531997.provinceXyear
531998.provinceXyear 621995.provinceXyear 621996.provinceXyear
621997.provinceXyear 621998.provinceXyear 621999.provinceXyear
110106.coun 110112.coun 110114.coun 110117.coun 140181.coun
140202.coun 140802.coun 140902.coun 320106.coun 320324.coun
320506.coun 320602.coun 320802.coun 320922.coun 340621.coun
340826.coun 341021.coun 341622.coun 341702.coun 410105.coun
410224.coun 410725.coun 410821.coun 410902.coun 411081.coun
411421.coun 411681.coun 420114.coun 420923.coun 421123.coun
422801.coun 430481.coun 430602.coun 430681.coun 430722.coun
430726.coun 430821.coun 431081.coun 431102.coun 441283.coun
441481.coun 441882.coun 445281.coun 500102.coun 500110.coun
500112.coun 500118.coun 500226.coun 510112.coun 510421.coun
510922.coun 511923.coun 530103.coun 530111.coun 530402.coun
530821.coun 530921.coun 532621.coun 532901.coun 620102.coun
620402.coun 620502.coun 620522.coun 620524.coun 620902.coun
620921.coun 621022.coun postXtreat
-------------------------------------------------------------------------------------
Wald test of exogeneity (/athrho = 0): chi2(1) = 3.38 Prob > chi2 = 0.0659
.PS- I dropped values from first step because of the number of characters allowed in a post.
0 Response to ivprobit - very high wald chi2 - not the expected signs
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