I am running a pooled panel Heckman two-step estimation to find determinants of insurance purchases. A signficant effect of the inverse mills ratio (imr1) below indicates a selection problem and that Heckman is preferred over OLS.
Code:
*1st stage probit model probit y_seen x18 i.x19 i.x20 round i.x3 x4 x5 x6 x7 i.x8 x9 i.x10##i.x11 i.x12 x13 x14 /// i.x15##c.x16 x17 [pweight=pweight], vce(cluster HHID) margins, dydx(*) post
Code:
Average marginal effects Number of obs = 574
Model VCE : Robust
Expression : Pr(y_seen), predict()
dy/dx w.r.t. : x18 1.x19 1.x20 round 1.x3 x4 x5 x6 x7 1.x8 x9 1.x10 1.x11 1.x12 x13 x14 1.x15 x16 x17
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| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x18 | .0143955 .0015807 9.11 0.000 .0112974 .0174936
1.x19 | -.0449697 .0218515 -2.06 0.040 -.0877979 -.0021416
1.x20 | -.1017704 .0269623 -3.77 0.000 -.1546156 -.0489252
round | -.0479061 .0173747 -2.76 0.006 -.0819598 -.0138523
1.x3 | -.0209526 .0290927 -0.72 0.471 -.0779732 .0360681
x4 | .0000826 .0000152 5.43 0.000 .0000528 .0001124
x5 | .0042392 .0131803 0.32 0.748 -.0215938 .0300721
x6 | .0052349 .0060947 0.86 0.390 -.0067104 .0171802
x7 | .0043644 .0016943 2.58 0.010 .0010435 .0076852
1.x8 | -.0120274 .0366869 -0.33 0.743 -.0839324 .0598777
x9 | .0508862 .013231 3.85 0.000 .024954 .0768184
1.x10 | .0865615 .0383121 2.26 0.024 .0114712 .1616518
1.x11 | .010413 .0292698 0.36 0.722 -.0469548 .0677807
1.x12 | -.0040397 .0392662 -0.10 0.918 -.0810001 .0729207
x13 | -.0221218 .0120994 -1.83 0.067 -.0458363 .0015927
x14 | .0001126 .000437 0.26 0.797 -.000744 .0009691
1.x15 | -.0348978 .0388583 -0.90 0.369 -.1110588 .0412631
x16 | -.001754 .0004966 -3.53 0.000 -.0027274 -.0007806
x17 | .0290123 .0151913 1.91 0.056 -.000762 .0587867
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Note: dy/dx for factor levels is the discrete change from the base level.Code:
qui probit y_seen x18 i.x19 i.x20 round i.x3 x4 x5 x6 x7 i.x8 x9 i.x10##i.x11 i.x12 x13 x14 /// i.x15##c.x16 x17 [pweight=pweight], vce(cluster HHID) predict p1, xb //calculates predicted value of \beta*X from selection regression replace p1=-p1 //calculates -Z_i\gamma generate phi = (1/sqrt(2*_pi))*exp(-(p1^2/2)) //normal distribution density function generate capphi = normal(p1) //cumulative density function generate imr1 = phi/(1-capphi) //calculates Inverse Mills ratio *2nd stage Heckman model: truncated and pooled OLS reg y x1 x2 round i.x3 x4 x5 x6 x7 i.x8 x9 i.x10##i.x11 i.x12 x13 x14 i.x15##c.x16 x17 imr1 /// [pweight=pweight], vce(cluster HHID)
Code:
Linear regression Number of obs = 472
F(21, 124) = 64.07
Prob > F = 0.0000
R-squared = 0.4332
Root MSE = .58905
(Std. Err. adjusted for 125 clusters in HHID)
------------------------------------------------------------------------------
| Robust
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | 1.086289 .0920832 11.80 0.000 .9040309 1.268548
x2 | -1.285324 1.143381 -1.12 0.263 -3.548395 .9777475
round | -.103336 .0590195 -1.75 0.082 -.2201521 .0134801
1.x3 | -.083443 .0714037 -1.17 0.245 -.224771 .057885
x4 | -.000065 .0000324 -2.00 0.047 -.0001292 -8.20e-07
x5 | -.0466427 .023452 -1.99 0.049 -.0930609 -.0002246
x6 | .0381533 .0112903 3.38 0.001 .0158066 .0605
x7 | .0170921 .0034209 5.00 0.000 .0103212 .023863
1.x8 | -.0287251 .0753869 -0.38 0.704 -.1779369 .1204868
x9 | -.0255863 .0329273 -0.78 0.439 -.0907586 .039586
1.x10 | -.1244701 .1442971 -0.86 0.390 -.4100745 .1611344
1.x11 | .0221183 .1491671 0.15 0.882 -.2731251 .3173617
|
x10#x11 |
1 1 | .188353 .1639117 1.15 0.253 -.1360742 .5127803
|
1.x12 | .2493369 .069622 3.58 0.000 .1115354 .3871384
x13 | .0115066 .0247547 0.46 0.643 -.0374899 .0605032
x14 | .001514 .0008878 1.71 0.091 -.0002433 .0032712
1.x15 | .155291 .2137375 0.73 0.469 -.2677555 .5783375
x16 | -.004325 .0031301 -1.38 0.170 -.0105205 .0018704
|
x15#c.x16 |
1 | .003758 .0035941 1.05 0.298 -.0033558 .0108718
|
x17 | .0196864 .0373166 0.53 0.599 -.0541735 .0935464
imr1 | .2430458 .1113475 2.18 0.031 .0226579 .4634338
_cons | 13.41441 12.27384 1.09 0.277 -10.87896 37.70777
------------------------------------------------------------------------------(1) Is the selection equation only based on the truncated sample with y>0? Why? This does not make any sense as there is no variation in y!?
(2) Can this explain why the inverse mills ratio (selection effect) is here not significantly different from zero as indicated by the Wald test that cannot reject the null hypothesis of rho=0?
Code:
heckman y x1 x2 round i.x3 x4 x5 x6 x7 i.x8 x9 i.x10##i.x11 i.x12 x13 x14 i.x15##c.x16 x17 /// [pweight=pweight], /// select(y_seen=x18 i.x19 i.x20 round i.x3 x4 x5 x6 x7 i.x8 x9 i.x10##i.x11 i.x12 x13 x14 /// i.x15##c.x16 x17) vce(cluster HHID)
Code:
Heckman selection model Number of obs = 574
(regression model with sample selection) Selected = 472
Nonselected = 102
Wald chi2(20) = 1384.02
Log pseudolikelihood = -519.9681 Prob > chi2 = 0.0000
(Std. Err. adjusted for 126 clusters in HHID)
------------------------------------------------------------------------------
| Robust
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
y |
x1 | 1.079878 .0870764 12.40 0.000 .9092117 1.250545
x2 | -1.146409 1.003011 -1.14 0.253 -3.112275 .8194557
round | -.1038978 .0547836 -1.90 0.058 -.2112717 .003476
1.x3 | -.0767749 .073642 -1.04 0.297 -.2211107 .0675608
x4 | -.0000586 .0000311 -1.89 0.059 -.0001196 2.31e-06
x5 | -.0532746 .0271382 -1.96 0.050 -.1064644 -.0000848
x6 | .0335714 .0143009 2.35 0.019 .0055421 .0616007
x7 | .0169975 .0032445 5.24 0.000 .0106384 .0233566
1.x8 | -.0426975 .0950499 -0.45 0.653 -.2289919 .143597
x9 | -.0154203 .0327672 -0.47 0.638 -.0796428 .0488022
1.x10 | -.0930904 .1506446 -0.62 0.537 -.3883484 .2021676
1.x11 | .0727406 .1849587 0.39 0.694 -.2897718 .4352531
|
x10#x11 |
1 1 | .165025 .1665951 0.99 0.322 -.1614954 .4915454
|
1.x12 | .2292365 .0845575 2.71 0.007 .0635068 .3949662
x13 | -.0052651 .0451982 -0.12 0.907 -.093852 .0833218
x14 | .0015364 .0009399 1.63 0.102 -.0003058 .0033786
1.x15 | .1121501 .2073449 0.54 0.589 -.2942384 .5185386
x16 | -.0061802 .0047053 -1.31 0.189 -.0154025 .003042
|
x15#c.x16 |
1 | .0056411 .0053074 1.06 0.288 -.0047612 .0160434
|
x17 | .0331053 .0396846 0.83 0.404 -.0446752 .1108857
_cons | 11.9172 10.75137 1.11 0.268 -9.155095 32.9895
-------------+----------------------------------------------------------------
y_seen |
x18 | .0954856 .023458 4.07 0.000 .0495088 .1414624
1.x19 | -.4510818 .1957512 -2.30 0.021 -.834747 -.0674166
1.x20 | -.5628401 .4688995 -1.20 0.230 -1.481866 .356186
round | -.3500378 .1178559 -2.97 0.003 -.5810312 -.1190445
1.x3 | -.0514181 .2962523 -0.17 0.862 -.6320619 .5292257
x4 | .0006573 .0001697 3.87 0.000 .0003247 .0009898
x5 | -.0264533 .1181423 -0.22 0.823 -.2580079 .2051012
x6 | .0606577 .0973045 0.62 0.533 -.1300557 .251371
x7 | .0344755 .012954 2.66 0.008 .0090862 .0598649
1.x8 | -.1359341 .3216742 -0.42 0.673 -.766404 .4945357
x9 | .4386742 .1225535 3.58 0.000 .1984737 .6788748
1.x10 | .1281608 .3533009 0.36 0.717 -.5642962 .8206178
1.x11 | -.1410168 .6800977 -0.21 0.836 -1.473984 1.19195
|
x10#x11 |
1 1 | .4539155 .889635 0.51 0.610 -1.289737 2.197568
|
1.x12 | -.2686829 .5875363 -0.46 0.647 -1.420233 .882867
x13 | -.1141443 .230882 -0.49 0.621 -.5666646 .338376
x14 | .0013928 .0038212 0.36 0.715 -.0060966 .0088822
1.x15 | -.1661187 .6020005 -0.28 0.783 -1.346018 1.013781
x16 | -.0155677 .0053069 -2.93 0.003 -.025969 -.0051663
|
x15#c.x16 |
1 | .0027121 .0076237 0.36 0.722 -.0122302 .0176543
|
x17 | .2812853 .1835776 1.53 0.125 -.0785201 .6410908
_cons | -7.998821 1.645493 -4.86 0.000 -11.22393 -4.773715
-------------+----------------------------------------------------------------
/athrho | 1.003006 1.329345 0.75 0.451 -1.602462 3.608475
/lnsigma | -.5072924 .1124413 -4.51 0.000 -.7276732 -.2869115
-------------+----------------------------------------------------------------
rho | .7628539 .5557379 -.9220383 .998533
sigma | .6021237 .0677035 .4830316 .7505781
lambda | .4593324 .3766132 -.2788158 1.197481
------------------------------------------------------------------------------
Wald test of indep. eqns. (rho = 0): chi2(1) = 0.57 Prob > chi2 = 0.4505Code:
margins, dydx(*) expression(normal(predict(xbsel))) //for AMEs of selection equation
Code:
Average marginal effects Number of obs = 472
Model VCE : Robust
Expression : normal(predict(xbsel))
dy/dx w.r.t. : x1 x2 round 1.x3 x4 x5 x6 x7 1.x8 x9 1.x10 1.x11 1.x12 x13 x14 1.x15 x16 x17 x18 1.x19 1.x20
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | 0 (omitted)
x2 | 0 (omitted)
round | -.0344662 .0111654 -3.09 0.002 -.05635 -.0125823
1.x3 | -.0051114 .0298637 -0.17 0.864 -.0636432 .0534204
x4 | .0000647 .0000153 4.22 0.000 .0000347 .0000948
x5 | -.0026047 .0115287 -0.23 0.821 -.0252005 .0199911
x6 | .0059726 .0093806 0.64 0.524 -.0124131 .0243583
x7 | .0033946 .0012834 2.64 0.008 .0008791 .0059101
1.x8 | -.0128698 .0297024 -0.43 0.665 -.0710854 .0453457
x9 | .0431937 .0113826 3.79 0.000 .0208843 .0655031
1.x10 | .0406141 .0486084 0.84 0.403 -.0546566 .1358847
1.x11 | .0174241 .0212462 0.82 0.412 -.0242176 .0590658
1.x12 | -.0264907 .0569879 -0.46 0.642 -.138185 .0852036
x13 | -.0112391 .0229835 -0.49 0.625 -.056286 .0338078
x14 | .0001371 .000378 0.36 0.717 -.0006037 .000878
1.x15 | -.006072 .0457602 -0.13 0.894 -.0957605 .0836164
x16 | -.0013274 .0004467 -2.97 0.003 -.0022029 -.0004518
x17 | .0276965 .0172296 1.61 0.108 -.0060728 .0614658
x18 | .0094019 .0026424 3.56 0.000 .004223 .0145808
1.x19 | -.0441527 .0200581 -2.20 0.028 -.0834659 -.0048395
1.x20 | -.0544046 .0450362 -1.21 0.227 -.142674 .0338648
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Note: dy/dx for factor levels is the discrete change from the base level.Any help is highly appreciated!
Thanks
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