------------------------------------------------------------------------------------------------------ log: c:\Imbook\bwebpage\Section4\mma16p3selection.txt log type: text opened on: 19 May 2005, 13:04:33 . . ********** OVERVIEW OF MMA16P3SELECTION.DO ********** . . * STATA Program . * copyright C 2005 by A. Colin Cameron and Pravin K. Trivedi . * used for "Microeconometrics: Methods and Applications" . * by A. Colin Cameron and Pravin K. Trivedi (2005) . * Cambridge University Press . . * Chapter 16.6 pages 553-5 . * Selection models example . * It provides . * (1) Two-part model estimation (Table 16.1) . * (2) Selection model estimation . * (2A) ML estimates (Table 16.1) . * (2B) Heckman 2-step estimates (Table 16.1) . * (2C) Check for possible collinearity problems in Heckman 2-Step . . * To use this program you need health expenditure data in Stata data set . * randdata.dta . . ********** SETUP ********** . . set more off . version 8.0 . set scheme s1mono /* Used for graphs */ . . ********** DATA DESCRIPTION ********** . . * Essentially same data as in P. Deb and P.K. Trivedi (2002) . * "The Structure of Demand for Medical Care: Latent Class versus . * Two-Part Models", Journal of Health Economics, 21, 601-625 . * except that paper used different outcome (counts rather than $) . . * Each observation is for an individual over a year. . * Individuals may appear in up to five years. . * All available sample is used except only fee for service plans included. . * In analysis here only year 2 is used so panel complications are avoided. . * Clustering of individuals within household is ignored here. . . * Dependent variable is . * MED med Annual medical expenditures in constant dollars . * excluding dental and outpatient mental . * LNMED lnmeddol Ln(Medical expenditures) given meddol > 0 . * Missing otherwise . * DMED binexp 1 if medical expenditures > 0 . . * Regressors are . * - Health insurance measures . * LC logc log(coinsrate+1) where coinsurance rate is 0 to 100 . * IDP idp 1 if individual deductible plan . * LPI lpi 1og(annual participation incentive payment) or 0 if no payment . * FMDE fmde log(max(medical deductible expenditure)) if IDP=1 and MDE>1 or 0 otherw > ise. . * - Health status measures . * NDISEASE disea number of chronic diseases . * PHYSLIM physlm 1 if physical limitation . * HLTHG hlthg 1 if good health . * HLTHF hlthf 1 if good health . * HLTHP hlthp 1 if good health (omitted is excellent) . * - Socioeconomic characteristics . * LINC linc log of annual family income (in $) . * LFAM lfam log of family size . * EDUCDEC educdec years of schooling of decision maker . * AGE xage exact age . * BLACK black 1 if black . * FEMALE female 1 if female . * CHILD child 1 if child . * FEMCHILD fchild 1 if female child . . * If panel data used then clustering is on . * zper person id . . ********** READ DATA ********** . . use randdata.dta, clear . sum Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- plan | 20190 11.17553 3.976751 1 19 site | 20190 3.298811 1.80382 1 6 coins | 20190 26.3056 36.40386 0 100 tookphys | 20190 .5974245 .4904288 0 1 year | 20190 2.420109 1.217141 1 5 -------------+-------------------------------------------------------- zper | 20190 357965.5 180868.1 125024 632167 black | 20190 .1814983 .3827071 0 1 income | 20190 8037.409 4058.371 0 29237.54 xage | 20190 25.72233 16.76945 0 64.27515 female | 20190 .5170381 .499722 0 1 -------------+-------------------------------------------------------- educdec | 20186 11.96681 2.806255 0 25 time | 20190 .9989561 .0259741 .0767123 1 outpdol | 20190 51.12649 94.92627 0 2599.902 drugdol | 20190 13.1687 33.76212 0 706.3979 suppdol | 20190 6.8024 21.39346 0 1009.47 -------------+-------------------------------------------------------- mentdol | 20190 6.870347 58.41298 0 1340.834 inpdol | 20190 100.4694 655.6215 0 38649.81 meddol | 20190 171.5679 698.2015 0 39182.02 totadm | 20190 .1127291 .4111857 0 8 inpmis | 20190 .0039624 .062824 0 1 -------------+-------------------------------------------------------- mentvis | 20190 .4322437 3.430789 0 62 mdvis | 20190 2.860426 4.504365 0 77 notmdvis | 20190 .6855869 3.763543 0 109 num | 20190 3.954235 1.853034 1 14 mhi | 20190 76.55584 12.50224 12.2 100 -------------+-------------------------------------------------------- disea | 20190 11.24449 6.741449 0 58.6 physlm | 20190 .1235003 .3220164 0 1 ghindx | 14967 73.09055 15.99371 3.7 100 mdeoff | 20185 417.8422 384.1199 0 1000 pioff | 20185 446.677 367.466 0 1291.68 -------------+-------------------------------------------------------- child | 20190 .4013373 .4901812 0 1 fchild | 20190 .1937098 .3952139 0 1 lfam | 20190 1.248156 .539301 0 2.639057 lpi | 20190 4.707894 2.69784 0 7.163699 idp | 20190 .2599802 .4386343 0 1 -------------+-------------------------------------------------------- logc | 20190 2.383342 2.041776 0 4.564348 fmde | 20190 4.029524 3.471353 0 8.294049 hlthg | 20190 .3620109 .4805938 0 1 hlthf | 20190 .077266 .2670196 0 1 hlthp | 20190 .0149579 .1213874 0 1 -------------+-------------------------------------------------------- xghindx | 20190 73.2375 14.2332 3.7 100 linc | 20190 8.708265 1.228309 0 10.28324 lnum | 20190 1.248156 .539301 0 2.639057 lnmeddol | 15737 4.109318 1.484654 -.8495329 10.57597 binexp | 20190 .7794453 .414631 0 1 . . /* Describe and summarize the original data. > describe > summarize > * The orignal data are a panel. > * The following summarizes panel features for completeness > iis zper > tis year > xtdes > xtsum meddol lnmeddol binexp > */ . . ********** DATA SELECTION AND TRANSFORMATIONS ********** . . * Use only Year 2 . keep if year==2 (14615 observations deleted) . . * educdec is missing for one observation . drop if educdec==. (1 observation deleted) . . * rename variables . rename meddol MED . rename binexp DMED . rename lnmeddol LNMED . rename linc LINC . rename lfam LFAM . rename educdec EDUCDEC . rename xage AGE . rename female FEMALE . rename child CHILD . rename fchild FEMCHILD . rename black BLACK . rename disea NDISEASE . rename physlm PHYSLIM . rename hlthg HLTHG . rename hlthf HLTHF . rename hlthp HLTHP . rename idp IDP . rename logc LC . rename lpi LPI . rename fmde FMDE . . * Define the regressor list which in commands can refer to as $XLIST . global XLIST LC IDP LPI FMDE PHYSLIM NDISEASE HLTHG HLTHF HLTHP /* > */ LINC LFAM EDUCDEC AGE FEMALE CHILD FEMCHILD BLACK . . * Summarize the dependents and regressors . sum MED DMED LNMED $XLIST Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- MED | 5574 169.7247 802.8303 0 39182.02 DMED | 5574 .7680301 .4221277 0 1 LNMED | 4281 4.069462 1.499372 -.5343859 10.57597 LC | 5574 2.420739 2.043883 0 4.564348 IDP | 5574 .261751 .4396272 0 1 -------------+-------------------------------------------------------- LPI | 5574 4.726834 2.681354 0 7.163699 FMDE | 5574 4.065015 3.450558 0 8.294049 PHYSLIM | 5574 .1242463 .3233768 0 1 NDISEASE | 5574 11.20526 6.788959 0 58.6 HLTHG | 5574 .3649085 .4814477 0 1 -------------+-------------------------------------------------------- HLTHF | 5574 .0782203 .268542 0 1 HLTHP | 5574 .0156082 .123965 0 1 LINC | 5574 8.696929 1.220592 0 10.28324 LFAM | 5574 1.241407 .5403965 0 2.564949 EDUCDEC | 5574 11.9466 2.837492 0 25 -------------+-------------------------------------------------------- AGE | 5574 25.57613 16.73011 .0253251 63.27515 FEMALE | 5574 .5184787 .4997032 0 1 CHILD | 5574 .4050951 .4909545 0 1 FEMCHILD | 5574 .1955508 .3966597 0 1 BLACK | 5574 .1859852 .3860055 0 1 . . * Detailed summary shows that MED>0 very skewed whereas LNMED is not . sum MED LNMED if MED>0, detail medical exp excl outpatient men ------------------------------------------------------------- Percentiles Smallest 1% 2.109705 .5860291 5% 5.752914 .6630728 10% 9.376465 .6770833 Obs 4281 25% 21.31435 .6770833 Sum of Wgt. 4281 50% 52.64357 Mean 220.987 Largest Std. Dev. 909.9021 75% 136.4518 12044.11 90% 453.8059 17465.98 Variance 827921.9 95% 904.328 18641.98 Skewness 24.00829 99% 2666.309 39182.02 Kurtosis 873.379 LNMED ------------------------------------------------------------- Percentiles Smallest 1% .746548 -.5343859 5% 1.749707 -.4108706 10% 2.238203 -.3899609 Obs 4281 25% 3.059381 -.3899609 Sum of Wgt. 4281 50% 3.963544 Mean 4.069462 Largest Std. Dev. 1.499372 75% 4.915971 9.396331 90% 6.11767 9.76801 Variance 2.248116 95% 6.807192 9.833171 Skewness .347695 99% 7.888451 10.57597 Kurtosis 3.28909 . . * Write final data to a text (ascii) file so can use with programs other than Stata . outfile DMED MED LNMED LC IDP LPI FMDE PHYSLIM NDISEASE HLTHG HLTHF HLTHP /* > */ LINC LFAM EDUCDEC AGE FEMALE CHILD FEMCHILD BLACK /* > */ using mma16p3selection.asc, replace . . ****************** CHAPTER 16.6 REGRESSION ANALYSIS ************** . . * The analysis below models log expenditure (lny), not expenditure (y) . * where here y = MED and lny = LNMED. . . * This makes regular tobit difficult as it is not clear . * what the censoring/truncation point is since ln(0) = -infinity . * Also note that some LNMED<0 as 0 0 . * Then E[y] = exp(xb + (s^2)/2) for y > 0 . * and E[y] = Pr[y>0]*exp(xb + (s^2)/2) for all y . . * The models estimated are . * (1) Two-part model using . * (a) probit for whether positive y . * (b) regress with lny as dependent variable . * (2) Sample selection model similar to (3) . * except that inverse Mills ratio appears in (b), estimated by . * (a) MLE . * (b) Heckman 2-step . . * Additionally censored tobit and truncated tobit commands in levels . * are given below for completeness. . . ************ (1) TWO-PART MODEL ************ . . * Two-part model: binary probit and then lognormal for expenditures . . * First part: probit for MED > 0 . probit DMED $XLIST /* global XLIST defined earlier */ Iteration 0: log likelihood = -3019.1326 Iteration 1: log likelihood = -2698.302 Iteration 2: log likelihood = -2690.6146 Iteration 3: log likelihood = -2690.5768 Iteration 4: log likelihood = -2690.5768 Probit estimates Number of obs = 5574 LR chi2(17) = 657.11 Prob > chi2 = 0.0000 Log likelihood = -2690.5768 Pseudo R2 = 0.1088 ------------------------------------------------------------------------------ DMED | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- LC | -.118708 .0269005 -4.41 0.000 -.1714319 -.065984 IDP | -.1279483 .0522351 -2.45 0.014 -.2303272 -.0255693 LPI | .0283091 .0088793 3.19 0.001 .010906 .0457121 FMDE | .0075319 .0161584 0.47 0.641 -.024138 .0392018 PHYSLIM | .2732013 .0743761 3.67 0.000 .1274268 .4189758 NDISEASE | .0224861 .0035958 6.25 0.000 .0154384 .0295338 HLTHG | .0387516 .0438545 0.88 0.377 -.0472016 .1247049 HLTHF | .1920062 .0836688 2.29 0.022 .0280185 .355994 HLTHP | .6397294 .2126322 3.01 0.003 .222978 1.056481 LINC | .0518413 .0168128 3.08 0.002 .0188889 .0847938 LFAM | -.0335599 .041728 -0.80 0.421 -.1153452 .0482253 EDUCDEC | .036307 .0076536 4.74 0.000 .0213062 .0513078 AGE | .0002631 .0021606 0.12 0.903 -.0039715 .0044978 FEMALE | .4451035 .054292 8.20 0.000 .3386932 .5515138 CHILD | .111489 .0808338 1.38 0.168 -.0469424 .2699203 FEMCHILD | -.4512845 .0799219 -5.65 0.000 -.6079284 -.2946405 BLACK | -.6057367 .0523148 -11.58 0.000 -.7082718 -.5032017 _cons | -.271605 .1877345 -1.45 0.148 -.6395579 .0963478 ------------------------------------------------------------------------------ . estimates store twoparta /* version 8 command for later table */ . scalar llprobit = e(ll) /* Log-likelihood */ . predict probsel2part, p /* Pr[y>0] = PHI(x'b) */ . predict xbprobit, xb /* x'b */ . . * Second part: OLS for log of positive values . * Here LNMED where LNMED missing if MED < 0 . regress LNMED $XLIST Source | SS df MS Number of obs = 4281 -------------+------------------------------ F( 17, 4263) = 39.69 Model | 1314.70352 17 77.335501 Prob > F = 0.0000 Residual | 8307.23358 4263 1.94868252 R-squared = 0.1366 -------------+------------------------------ Adj R-squared = 0.1332 Total | 9621.9371 4280 2.24811614 Root MSE = 1.396 ------------------------------------------------------------------------------ LNMED | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- LC | -.0164006 .0312495 -0.52 0.600 -.0776658 .0448647 IDP | -.0789998 .061796 -1.28 0.201 -.2001522 .0421526 LPI | .0027057 .0097138 0.28 0.781 -.0163383 .0217498 FMDE | -.0306123 .0180695 -1.69 0.090 -.0660379 .0048134 PHYSLIM | .2619829 .0687459 3.81 0.000 .1272052 .3967607 NDISEASE | .0198922 .0034441 5.78 0.000 .01314 .0266444 HLTHG | .1438008 .0483778 2.97 0.003 .0489553 .2386464 HLTHF | .3642649 .0881004 4.13 0.000 .1915422 .5369876 HLTHP | .7865099 .1700502 4.63 0.000 .453123 1.119897 LINC | .0931988 .0217849 4.28 0.000 .0504891 .1359085 LFAM | -.1408033 .046203 -3.05 0.002 -.2313852 -.0502214 EDUCDEC | -5.66e-06 .0082599 -0.00 0.999 -.0161993 .016188 AGE | .0055602 .002251 2.47 0.014 .0011471 .0099733 FEMALE | .3442509 .0571573 6.02 0.000 .2321929 .456309 CHILD | -.2677921 .0904307 -2.96 0.003 -.4450833 -.0905009 FEMCHILD | -.3512207 .0896517 -3.92 0.000 -.5269847 -.1754568 BLACK | -.1964412 .0677021 -2.90 0.004 -.3291725 -.0637099 _cons | 3.077182 .2213448 13.90 0.000 2.64323 3.511133 ------------------------------------------------------------------------------ . estimates store twopartb . scalar lllognormal = e(ll) /* Log-likelihood */ . scalar sols = e(rmse) /* Standard error of the regression */ . predict pLNMED, xb /* Predicted mean from OLS */ . predict rLNMED, residuals (1293 missing values generated) . . * Check for normal errors . hettest Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance Variables: fitted values of LNMED chi2(1) = 17.11 Prob > chi2 = 0.0000 . * imtest . sktest LNMED rLNMED Skewness/Kurtosis tests for Normality ------- joint ------ Variable | Pr(Skewness) Pr(Kurtosis) adj chi2(2) Prob>chi2 -------------+------------------------------------------------------- LNMED | 0.000 0.001 . 0.0000 rLNMED | 0.000 0.000 . 0.0000 . . * Create two-part model log-likelihood . scalar lltwopart = llprobit + lllognormal . di "lltwopart = " lltwopart lltwopart = -10184.076 . . * Create predictions of level of expenditures not logs . * E[y] = exp(pLNMED + (s^2)/2) for y > 0 . * and E[y] = Pr[y>0]*exp(xb + (s^2)/2) for all y . gen pMEDpos2part = exp(pLNMED + (sols^2)/2) . gen pMEDall2part = probsel2part*pMEDpos2part . . * Compare predictions to actual for MED > 0 . sum LNMED pLNMED MED pMEDpos2part if MED > 0 Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- LNMED | 4281 4.069462 1.499372 -.5343859 10.57597 pLNMED | 4281 4.069462 .5542326 2.298199 6.482164 MED | 4281 220.987 909.9021 .5860291 39182.02 pMEDpos2part | 4281 183.462 126.0213 26.37827 1731.088 . corr LNMED pLNMED MED pMEDpos2part if MED > 0 (obs=4281) | LNMED pLNMED MED pMEDpo~t -------------+------------------------------------ LNMED | 1.0000 pLNMED | 0.3696 1.0000 MED | 0.4560 0.1576 1.0000 pMEDpos2part | 0.3387 0.9204 0.1669 1.0000 . . * Compare predictions to actual including zeroes . sum MED pMEDall2part DMED probsel2part Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- MED | 5574 169.7247 802.8303 0 39182.02 pMEDall2part | 5574 140.966 120.2022 4.880651 1729.783 DMED | 5574 .7680301 .4221277 0 1 probsel2part | 5574 .7678377 .1457464 .1526731 .999246 . corr MED pMEDall2part DMED probsel2part (obs=5574) | MED pMEDal~t DMED probse~t -------------+------------------------------------ MED | 1.0000 pMEDall2part | 0.1772 1.0000 DMED | 0.1162 0.2158 1.0000 probsel2part | 0.1031 0.6380 0.3467 1.0000 . . ************ (2) SELECTION MODEL ************ . . * Sample selection model for log expenditures . * Selection equation: . * Observe y = y* if I = z'a + u > 0 u ~ N[0,1] . * Regression equation: . * y* = x'b + v v ~ N[0,s^2] and Corr[u,v]=rho . . * (2A) MLE for sample selection model . heckman LNMED $XLIST, select (DMED = $XLIST) Iteration 0: log likelihood = -10183.753 (not concave) Iteration 1: log likelihood = -10183.676 (not concave) Iteration 2: log likelihood = -10183.593 (not concave) Iteration 3: log likelihood = -10183.525 (not concave) Iteration 4: log likelihood = -10183.467 (not concave) Iteration 5: log likelihood = -10183.408 (not concave) Iteration 6: log likelihood = -10183.311 (not concave) Iteration 7: log likelihood = -10183.21 (not concave) Iteration 8: log likelihood = -10179.155 Iteration 9: log likelihood = -10176.799 Iteration 10: log likelihood = -10170.17 Iteration 11: log likelihood = -10170.11 Iteration 12: log likelihood = -10170.11 Heckman selection model Number of obs = 5574 (regression model with sample selection) Censored obs = 1293 Uncensored obs = 4281 Wald chi2(17) = 805.17 Log likelihood = -10170.11 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- LNMED | LC | -.0760236 .0337456 -2.25 0.024 -.1421638 -.0098833 IDP | -.1497199 .0661379 -2.26 0.024 -.2793478 -.020092 LPI | .01493 .0105015 1.42 0.155 -.0056526 .0355127 FMDE | -.023522 .0194745 -1.21 0.227 -.0616913 .0146474 PHYSLIM | .3548628 .0755425 4.70 0.000 .2068023 .5029233 NDISEASE | .0286474 .0037972 7.54 0.000 .0212051 .0360897 HLTHG | .1559173 .0521775 2.99 0.003 .0536513 .2581834 HLTHF | .4451223 .0955263 4.66 0.000 .2578942 .6323505 HLTHP | .9986065 .1878791 5.32 0.000 .6303701 1.366843 LINC | .1214009 .0230845 5.26 0.000 .0761562 .1666457 LFAM | -.1583018 .0497464 -3.18 0.001 -.255803 -.0608005 EDUCDEC | .0175951 .0090183 1.95 0.051 -.0000805 .0352707 AGE | .0057376 .0024426 2.35 0.019 .0009501 .0105251 FEMALE | .5503441 .0633313 8.69 0.000 .4262171 .6744711 CHILD | -.1976875 .097398 -2.03 0.042 -.3885841 -.006791 FEMCHILD | -.5653227 .0975292 -5.80 0.000 -.7564765 -.374169 BLACK | -.5358684 .0749191 -7.15 0.000 -.6827072 -.3890296 _cons | 2.107745 .2442285 8.63 0.000 1.629066 2.586424 -------------+---------------------------------------------------------------- DMED | LC | -.1068027 .0264766 -4.03 0.000 -.1586959 -.0549096 IDP | -.108769 .0509938 -2.13 0.033 -.2087149 -.0088231 LPI | .0294804 .0086214 3.42 0.001 .0125827 .0463781 FMDE | .0007403 .0158738 0.05 0.963 -.0303719 .0318524 PHYSLIM | .2848256 .0722656 3.94 0.000 .1431877 .4264635 NDISEASE | .0210805 .0034967 6.03 0.000 .0142271 .027934 HLTHG | .0576901 .042799 1.35 0.178 -.0261945 .1415747 HLTHF | .2237238 .0814547 2.75 0.006 .0640755 .3833721 HLTHP | .7984291 .2048087 3.90 0.000 .3970114 1.199847 LINC | .0553122 .0166179 3.33 0.001 .0227416 .0878827 LFAM | -.031201 .0402985 -0.77 0.439 -.1101846 .0477827 EDUCDEC | .031499 .0074987 4.20 0.000 .0168018 .0461961 AGE | -.0006072 .0021064 -0.29 0.773 -.0047357 .0035212 FEMALE | .4093059 .0532548 7.69 0.000 .3049283 .5136834 CHILD | .0530643 .0786326 0.67 0.500 -.1010527 .2071813 FEMCHILD | -.3953421 .0783811 -5.04 0.000 -.5489662 -.241718 BLACK | -.5831049 .0520534 -11.20 0.000 -.6851277 -.4810822 _cons | -.2141574 .1842169 -1.16 0.245 -.5752159 .146901 -------------+---------------------------------------------------------------- /athrho | .9408188 .0736303 12.78 0.000 .796506 1.085132 /lnsigma | .4511091 .0177227 25.45 0.000 .4163732 .485845 -------------+---------------------------------------------------------------- rho | .7355982 .0337886 .6620789 .7950943 sigma | 1.570053 .0278256 1.516452 1.625548 lambda | 1.154928 .0702985 1.017145 1.29271 ------------------------------------------------------------------------------ LR test of indep. eqns. (rho = 0): chi2(1) = 27.93 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ . estimates store heckmle . scalar llhecklogs = e(ll) /* Log-likelihood */ . scalar shml = e(sigma) /* s where Var[v]=s^2 */ . . * Save the Stata predictions: . * Distinguish between ystar=E[y*], ypos=E[y|I>0] and yall=E[y] . predict ystarhml, xb /* E[y*] = x'b */ . predict yposhml, ycond /* E[y|I>0] = E[y*|I>0] = x'b+c*lamda(z'a) */ . predict invmillhml, mills /* lamda(z'a) = phi(z'a)/PHI(z'a) */ . predict probselhml, psel /* PHI(z'a) */ . * The following not appropriate here as it sets y=0 if I<0 . * whereas here data is in logs and y=ln(MED)=-infinity if I<0 . predict yallhml, yexpected /* E[y] = PHI(z'a)*E[y|I>0] */ . sum ystarhml yposhml invmillhml probselhml yallhml Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- ystarhml | 5574 3.543161 .7462608 .9570364 6.92732 yposhml | 5574 4.000607 .5482433 2.50515 6.92955 invmillhml | 5574 .396082 .2165116 .0019309 1.476998 probselhml | 5574 .7674107 .1404707 .1737047 .9994534 yallhml | 5574 3.124032 .9125439 .4932862 6.925763 . . * Create predictions of level of expenditures not logs . * E[y] = exp(ypos + (s^2)/2) for y > 0 Var[v]=s^2 . * and E[y] = Pr[y>0]*exp(ypos + (s^2)/2) for all y . gen pMEDposhml = exp(yposhml + (shml^2)/2) . gen pMEDallhml = probselhml*pMEDposhml . . * Compare predictions to actual for MED > 0 . sum LNMED yposhml MED pMEDposhml if MED > 0 Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- LNMED | 4281 4.069462 1.499372 -.5343859 10.57597 yposhml | 4281 4.071295 .5573439 2.50515 6.92955 MED | 4281 220.987 909.9021 .5860291 39182.02 pMEDposhml | 4281 240.4096 185.0424 42.00053 3505.48 . corr LNMED yposhml MED pMEDpos2part if MED > 0 (obs=4281) | LNMED yposhml MED pMEDpo~t -------------+------------------------------------ LNMED | 1.0000 yposhml | 0.3690 1.0000 MED | 0.4560 0.1592 1.0000 pMEDpos2part | 0.3387 0.9343 0.1669 1.0000 . . * Compare predictions to actual including zeroes . sum MED pMEDallhml DMED probselhml Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- MED | 5574 169.7247 802.8303 0 39182.02 pMEDallhml | 5574 184.5571 174.1649 8.814864 3503.564 DMED | 5574 .7680301 .4221277 0 1 probselhml | 5574 .7674107 .1404707 .1737047 .9994534 . corr MED pMEDallhml DMED probselhml (obs=5574) | MED pMEDal~l DMED probse~l -------------+------------------------------------ MED | 1.0000 pMEDallhml | 0.1734 1.0000 DMED | 0.1162 0.2015 1.0000 probselhml | 0.1074 0.6092 0.3468 1.0000 . . * (2B) Heckman 2 step for sample selection model . * Same as MLE execpt add option twostep in heckman command . heckman LNMED $XLIST, select (DMED = $XLIST) twostep Heckman selection model -- two-step estimates Number of obs = 5574 (regression model with sample selection) Censored obs = 1293 Uncensored obs = 4281 Wald chi2(34) = 944.44 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- LNMED | LC | -.0279209 .039754 -0.70 0.482 -.1058373 .0499955 IDP | -.0922898 .0680191 -1.36 0.175 -.2256048 .0410252 LPI | .0052225 .0111057 0.47 0.638 -.0165442 .0269893 FMDE | -.0295212 .0182427 -1.62 0.106 -.0652762 .0062339 PHYSLIM | .2814948 .0804535 3.50 0.000 .1238088 .4391808 NDISEASE | .021617 .0050395 4.29 0.000 .0117398 .0314943 HLTHG | .1474026 .0490497 3.01 0.003 .051267 .2435381 HLTHF | .3821683 .0961284 3.98 0.000 .19376 .5705765 HLTHP | .833294 .1974488 4.22 0.000 .4463015 1.220287 LINC | .0990973 .0251548 3.94 0.000 .0497948 .1483998 LFAM | -.1441358 .0468074 -3.08 0.002 -.2358766 -.052395 EDUCDEC | .0033639 .0109501 0.31 0.759 -.0180979 .0248257 AGE | .0055556 .0022549 2.46 0.014 .0011361 .0099751 FEMALE | .3846323 .1032799 3.72 0.000 .1822074 .5870573 CHILD | -.2565136 .0936771 -2.74 0.006 -.4401173 -.0729098 FEMCHILD | -.392146 .125089 -3.13 0.002 -.637316 -.146976 BLACK | -.2633649 .1577542 -1.67 0.095 -.5725574 .0458276 _cons | 2.882514 .4698969 6.13 0.000 1.961533 3.803495 -------------+---------------------------------------------------------------- DMED | LC | -.118708 .0269005 -4.41 0.000 -.1714319 -.065984 IDP | -.1279483 .0522351 -2.45 0.014 -.2303272 -.0255693 LPI | .0283091 .0088793 3.19 0.001 .010906 .0457121 FMDE | .0075319 .0161584 0.47 0.641 -.024138 .0392018 PHYSLIM | .2732013 .0743761 3.67 0.000 .1274268 .4189758 NDISEASE | .0224861 .0035958 6.25 0.000 .0154384 .0295338 HLTHG | .0387516 .0438545 0.88 0.377 -.0472016 .1247049 HLTHF | .1920062 .0836688 2.29 0.022 .0280185 .355994 HLTHP | .6397294 .2126322 3.01 0.003 .222978 1.056481 LINC | .0518413 .0168128 3.08 0.002 .0188889 .0847938 LFAM | -.0335599 .041728 -0.80 0.421 -.1153452 .0482253 EDUCDEC | .036307 .0076536 4.74 0.000 .0213062 .0513078 AGE | .0002631 .0021606 0.12 0.903 -.0039715 .0044978 FEMALE | .4451035 .054292 8.20 0.000 .3386932 .5515138 CHILD | .111489 .0808338 1.38 0.168 -.0469424 .2699203 FEMCHILD | -.4512845 .0799219 -5.65 0.000 -.6079284 -.2946405 BLACK | -.6057367 .0523148 -11.58 0.000 -.7082718 -.5032017 _cons | -.271605 .1877345 -1.45 0.148 -.6395579 .0963478 -------------+---------------------------------------------------------------- mills | lambda | .2358048 .5018117 0.47 0.638 -.7477282 1.219338 -------------+---------------------------------------------------------------- rho | 0.16833 sigma | 1.4008246 lambda | .23580476 .5018117 ------------------------------------------------------------------------------ . estimates store heck2step . scalar sh2s = e(sigma) /* s where Var[v]=s^2 */ . . * Save the Stata predictions: . * Distinguish between ystar=E[y*], ypos=E[y|I>0] and yall=E[y] . predict ystarh2s, xb /* E[y*] = x'b */ . predict yposh2s, ycond /* E[y|I>0] = E[y*|I>0] = x'b+c*lamda(z'a) */ . predict invmillh2s, mills /* lamda(z'a) = phi(z'a)/PHI(z'a) */ . predict probselh2s, psel /* PHI(z'a) */ . * The following not appropriate here as it sets y=0 if I<0 . * whereas here data is in logs and y=ln(MED)=-infinity if I<0 . predict yallh2s, yexpected /* E[y] = PHI(z'a)*E[y|I>0] */ . sum ystarh2s yposh2s invmillh2s probselh2s yallh2s Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- ystarh2s | 5574 3.904371 .589474 2.005307 6.573941 yposh2s | 5574 3.997637 .5516546 2.337985 6.574553 invmillh2s | 5574 .3955256 .2253329 .002599 1.545223 probselh2s | 5574 .7678377 .1457464 .1526731 .999246 yallh2s | 5574 3.124344 .9213697 .4450346 6.569597 . . * Create predictions of level of expenditures not logs . * E[y] = exp(ypos + (s^2)/2) for y > 0 Var[v]=s^2 . * and E[y] = Pr[y>0]*exp(ypos + (s^2)/2) for all y . gen pMEDposh2s = exp(yposh2s + (sh2s^2)/2) . gen pMEDallh2s = probselh2s*pMEDposh2s . . * Compare predictions to actual for MED > 0 . sum LNMED yposh2s MED pMEDposh2s if MED > 0 Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- LNMED | 4281 4.069462 1.499372 -.5343859 10.57597 yposh2s | 4281 4.069462 .5543231 2.337985 6.574553 MED | 4281 220.987 909.9021 .5860291 39182.02 pMEDposh2s | 4281 184.9993 129.5432 27.63657 1911.624 . corr LNMED yposh2s MED pMEDpos2part if MED > 0 (obs=4281) | LNMED yposh2s MED pMEDpo~t -------------+------------------------------------ LNMED | 1.0000 yposh2s | 0.3697 1.0000 MED | 0.4560 0.1584 1.0000 pMEDpos2part | 0.3387 0.9240 0.1669 1.0000 . . * Compare predictions to actual including zeroes . sum MED pMEDallh2s DMED probselh2s Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- MED | 5574 169.7247 802.8303 0 39182.02 pMEDallh2s | 5574 142.1438 123.2964 5.272963 1910.182 DMED | 5574 .7680301 .4221277 0 1 probselh2s | 5574 .7678377 .1457464 .1526731 .999246 . corr MED pMEDallh2s DMED probselh2s (obs=5574) | MED pMEDa~2s DMED probs~2s -------------+------------------------------------ MED | 1.0000 pMEDallh2s | 0.1772 1.0000 DMED | 0.1162 0.2132 1.0000 probselh2s | 0.1031 0.6298 0.3467 1.0000 . . * (2C) Check for possible collinearity problems in Heckman 2-Step . . * Check variation in inverse mills ratio and related measures . gen zprimea = invnorm(probselh2s) . gen zprimeasq = zprimea*zprimea . sum invmillh2s probselh2s zprimea ystarh2s Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- invmillh2s | 5574 .3955256 .2253329 .002599 1.545223 probselh2s | 5574 .7678377 .1457464 .1526731 .999246 zprimea | 5574 .8217315 .5175712 -1.025036 3.17314 ystarh2s | 5574 3.904371 .589474 2.005307 6.573941 . sum invmillh2s probselh2s zprimea ystarh2s, detail Mills' ratio ------------------------------------------------------------- Percentiles Smallest 1% .0443035 .002599 5% .1081773 .0065964 10% .1479522 .0074306 Obs 5574 25% .2404661 .0111331 Sum of Wgt. 5574 50% .3522253 Mean .3955256 Largest Std. Dev. .2253329 75% .5044507 1.42819 90% .7088638 1.42819 Variance .0507749 95% .863094 1.466996 Skewness 1.105156 99% 1.080771 1.545223 Kurtosis 4.403004 Pr(DMED) ------------------------------------------------------------- Percentiles Smallest 1% .338421 .1526731 5% .4598847 .1769602 10% .5570307 .1900167 Obs 5574 25% .6946899 .1900167 Sum of Wgt. 5574 50% .7984734 Mean .7678377 Largest Std. Dev. .1457464 75% .8717066 .9962835 90% .927941 .9976236 Variance .021242 95% .9502093 .9979156 Skewness -1.048826 99% .9823552 .999246 Kurtosis 3.903288 zprimea ------------------------------------------------------------- Percentiles Smallest 1% -.4167765 -1.025036 5% -.1007243 -.9270119 10% .1434453 -.8778346 Obs 5574 25% .5091883 -.8778346 Sum of Wgt. 5574 50% .8361809 Mean .8217315 Largest Std. Dev. .5175712 75% 1.134495 2.676793 90% 1.460626 2.82333 Variance .2678799 95% 1.646887 2.865093 Skewness -.0298741 99% 2.105021 3.17314 Kurtosis 3.462529 Linear prediction ------------------------------------------------------------- Percentiles Smallest 1% 2.770451 2.005307 5% 3.096997 2.005307 10% 3.248734 2.066777 Obs 5574 25% 3.460358 2.093177 Sum of Wgt. 5574 50% 3.818303 Mean 3.904371 Largest Std. Dev. .589474 75% 4.304362 6.054721 90% 4.68132 6.055911 Variance .3474796 95% 4.946257 6.273092 Skewness .5047628 99% 5.495563 6.573941 Kurtosis 3.235111 . . * Check for Mills ratio linear in zprimea . regress invmillh2s zprimea Source | SS df MS Number of obs = 5574 -------------+------------------------------ F( 1, 5572) =84783.34 Model | 265.518552 1 265.518552 Prob > F = 0.0000 Residual | 17.4500012 5572 .00313173 R-squared = 0.9383 -------------+------------------------------ Adj R-squared = 0.9383 Total | 282.968553 5573 .050774906 Root MSE = .05596 ------------------------------------------------------------------------------ invmillh2s | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- zprimea | -.4217284 .0014484 -291.18 0.000 -.4245677 -.418889 _cons | .7420731 .0014065 527.59 0.000 .7393158 .7448305 ------------------------------------------------------------------------------ . regress invmillh2s zprimea zprimeasq Source | SS df MS Number of obs = 5574 -------------+------------------------------ F( 2, 5571) = . Model | 282.919807 2 141.459904 Prob > F = 0.0000 Residual | .04874607 5571 8.7500e-06 R-squared = 0.9998 -------------+------------------------------ Adj R-squared = 0.9998 Total | 282.968553 5573 .050774906 Root MSE = .00296 ------------------------------------------------------------------------------ invmillh2s | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- zprimea | -.6381933 .0001715 -3720.60 0.000 -.6385296 -.6378571 zprimeasq | .1329635 .0000943 1410.22 0.000 .1327787 .1331484 _cons | .7945547 .0000831 9556.73 0.000 .7943917 .7947177 ------------------------------------------------------------------------------ . * twoway scatter yinvmill probitxb . . * Check R-squared from regress yinvmill on other regressors . regress invmillh2s $XLIST Source | SS df MS Number of obs = 5574 -------------+------------------------------ F( 17, 5556) = 7477.36 Model | 271.118403 17 15.9481414 Prob > F = 0.0000 Residual | 11.85015 5556 .002132856 R-squared = 0.9581 -------------+------------------------------ Adj R-squared = 0.9580 Total | 282.968553 5573 .050774906 Root MSE = .04618 ------------------------------------------------------------------------------ invmillh2s | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- LC | .0529008 .000877 60.32 0.000 .0511815 .0546202 IDP | .0590603 .0017037 34.67 0.000 .0557204 .0624003 LPI | -.0113774 .0002792 -40.75 0.000 -.0119247 -.01083 FMDE | -.0054681 .0005178 -10.56 0.000 -.0064831 -.004453 PHYSLIM | -.0864947 .0021028 -41.13 0.000 -.090617 -.0823724 NDISEASE | -.0077731 .0001032 -75.31 0.000 -.0079754 -.0075707 HLTHG | -.0155696 .0013947 -11.16 0.000 -.0183037 -.0128355 HLTHF | -.0844067 .0025693 -32.85 0.000 -.0894435 -.0793698 HLTHP | -.2164141 .0052914 -40.90 0.000 -.2267872 -.206041 LINC | -.0293205 .0005678 -51.64 0.000 -.0304337 -.0282074 LFAM | .0170455 .0013216 12.90 0.000 .0144545 .0196364 EDUCDEC | -.0152414 .0002405 -63.38 0.000 -.0157128 -.01477 AGE | .0001145 .0000665 1.72 0.085 -.0000158 .0002448 FEMALE | -.1792718 .0016754 -107.00 0.000 -.1825563 -.1759873 CHILD | -.0474152 .0025807 -18.37 0.000 -.0524744 -.042356 FEMCHILD | .1803783 .002565 70.32 0.000 .1753498 .1854067 BLACK | .3020816 .0017915 168.62 0.000 .2985695 .3055937 _cons | .875215 .0061051 143.36 0.000 .8632467 .8871833 ------------------------------------------------------------------------------ . . * Find the condition number with inverse mills ratio included . matrix accum XX = invmillh2s $XLIST (obs=5574) . matrix XXScaled = corr(XX) . matrix symeigen XXSeigvec XXSeigval = XXScaled . scalar rowsXX = rowsof(XX) . scalar condnum1 = sqrt(XXSeigval[1,1]/XXSeigval[1,rowsXX]) . scalar condnum2 = sqrt(XXSeigval[1,1]/XXSeigval[1,(rowsXX-1)]) . . * Find the condition number without inverse mills ratio . matrix accum ZZ = $XLIST (obs=5574) . matrix ZZScaled = corr(ZZ) . matrix symeigen ZZSeigvec ZZSeigval = ZZScaled . scalar rowsZZ = rowsof(ZZ) . scalar condnumnoinvmills1 = sqrt(ZZSeigval[1,1]/ZZSeigval[1,rowsZZ]) . scalar condnumnoinvmills2 = sqrt(ZZSeigval[1,1]/ZZSeigval[1,(rowsZZ-1)]) . . * Condition numbers between 30 and 100 indicate a strong near dependency . scalar list condnum1 condnum2 condnum1 = 82.333696 condnum2 = 24.558474 . scalar list condnumnoinvmills1 condnumnoinvmills2 condnumnoinvmills1 = 36.660119 condnumnoinvmills2 = 20.990872 . . * (2D) Do Heckman 2 step manually (this is unnecessary) . quietly probit DMED $XLIST /* global XLIST defined earlier */ . predict pselmanual, p /* Pr[y>0] = PHI(x'b) */ . predict xbmanual, xb /* x'b */ . gen invmillsmanual = normden(xbmanual)/pselmanual . regress LNMED $XLIST invmillsmanual if MED > 0 Source | SS df MS Number of obs = 4281 -------------+------------------------------ F( 18, 4262) = 37.49 Model | 1315.13292 18 73.06294 Prob > F = 0.0000 Residual | 8306.80418 4262 1.94903899 R-squared = 0.1367 -------------+------------------------------ Adj R-squared = 0.1330 Total | 9621.9371 4280 2.24811614 Root MSE = 1.3961 ------------------------------------------------------------------------------ LNMED | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- LC | -.0279209 .0397381 -0.70 0.482 -.1058282 .0499864 IDP | -.0922898 .067979 -1.36 0.175 -.225564 .0409844 LPI | .0052225 .0110962 0.47 0.638 -.0165318 .0269769 FMDE | -.0295212 .01822 -1.62 0.105 -.065242 .0061996 PHYSLIM | .2814948 .0803424 3.50 0.000 .1239819 .4390076 NDISEASE | .0216171 .0050367 4.29 0.000 .0117426 .0314915 HLTHG | .1474026 .0489869 3.01 0.003 .0513627 .2434424 HLTHF | .3821683 .0960103 3.98 0.000 .1939381 .5703985 HLTHP | .833294 .1971219 4.23 0.000 .4468325 1.219756 LINC | .0990973 .0251514 3.94 0.000 .0497875 .1484071 LFAM | -.1441358 .0467495 -3.08 0.002 -.2357891 -.0524825 EDUCDEC | .0033639 .0109441 0.31 0.759 -.0180922 .0248201 AGE | .0055556 .0022512 2.47 0.014 .001142 .0099692 FEMALE | .3846324 .103291 3.72 0.000 .1821281 .5871366 CHILD | -.2565135 .0935766 -2.74 0.006 -.4399725 -.0730546 FEMCHILD | -.392146 .1250644 -3.14 0.002 -.6373374 -.1469547 BLACK | -.2633649 .1578399 -1.67 0.095 -.5728134 .0460835 invmillsma~l | .235805 .5023784 0.47 0.639 -.7491182 1.220728 _cons | 2.882514 .470116 6.13 0.000 1.960841 3.804186 ------------------------------------------------------------------------------ . predict yposmanual, xb . * Predictions here should equal those from heckman two-step earlier . sum yposh2s yposmanual invmillh2s invmillsmanual probselh2s pselmanual Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- yposh2s | 5574 3.997637 .5516546 2.337985 6.574553 yposmanual | 5574 3.997637 .5516546 2.337985 6.574553 invmillh2s | 5574 .3955256 .2253329 .002599 1.545223 invmillsma~l | 5574 .3955256 .2253329 .002599 1.545223 probselh2s | 5574 .7678377 .1457464 .1526731 .999246 -------------+-------------------------------------------------------- pselmanual | 5574 .7678377 .1457464 .1526731 .999246 . * And put in squared invmills ratio . gen invmillssq = invmillsmanual*invmillsmanual . regress LNMED $XLIST invmillsmanual invmillssq if MED > 0 Source | SS df MS Number of obs = 4281 -------------+------------------------------ F( 19, 4261) = 35.64 Model | 1319.30272 19 69.4369854 Prob > F = 0.0000 Residual | 8302.63438 4261 1.94851781 R-squared = 0.1371 -------------+------------------------------ Adj R-squared = 0.1333 Total | 9621.9371 4280 2.24811614 Root MSE = 1.3959 ------------------------------------------------------------------------------ LNMED | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- LC | -.0793176 .0530386 -1.50 0.135 -.1833009 .0246658 IDP | -.1419148 .075965 -1.87 0.062 -.2908457 .0070161 LPI | .0174224 .0138796 1.26 0.209 -.0097888 .0446337 FMDE | -.0258495 .0183897 -1.41 0.160 -.0619029 .0102039 PHYSLIM | .3867535 .1078448 3.59 0.000 .1753217 .5981854 NDISEASE | .0305019 .0078898 3.87 0.000 .0150337 .0459701 HLTHG | .1652111 .0504705 3.27 0.001 .0662626 .2641596 HLTHF | .4576241 .1089774 4.20 0.000 .2439716 .6712766 HLTHP | 1.056745 .2493566 4.24 0.000 .5678762 1.545614 LINC | .1169339 .027948 4.18 0.000 .0621414 .1717264 LFAM | -.1550441 .0473343 -3.28 0.001 -.2478439 -.0622443 EDUCDEC | .018452 .0150373 1.23 0.220 -.011029 .047933 AGE | .0057227 .0022538 2.54 0.011 .001304 .0101414 FEMALE | .5748999 .1660813 3.46 0.001 .2492941 .9005056 CHILD | -.2096856 .0988886 -2.12 0.034 -.4035587 -.0158125 FEMCHILD | -.5873068 .1828525 -3.21 0.001 -.9457929 -.2288207 BLACK | -.5010232 .2264954 -2.21 0.027 -.9450721 -.0569744 invmillsma~l | 2.159812 1.407886 1.53 0.125 -.6003768 4.920001 invmillssq | -1.043357 .7132265 -1.46 0.144 -2.441653 .3549381 _cons | 1.909849 .8142753 2.35 0.019 .3134454 3.506253 ------------------------------------------------------------------------------ . . ************ (3) DISPLAY RESULTS FOR TABLE 16.1 (page 554) ************ . . * Note for brevity the coefficients for only some of the regressors are reported . . * First two columns of Table 16.1 (page 554) . * Two part estimates: probit for first part and lognormal for second . estimates table twoparta twopartb, t stats(N ll rank aic bic) b(%10.3f) ---------------------------------------- Variable | twoparta twopartb -------------+-------------------------- LC | -0.119 -0.016 | -4.41 -0.52 IDP | -0.128 -0.079 | -2.45 -1.28 LPI | 0.028 0.003 | 3.19 0.28 FMDE | 0.008 -0.031 | 0.47 -1.69 PHYSLIM | 0.273 0.262 | 3.67 3.81 NDISEASE | 0.022 0.020 | 6.25 5.78 HLTHG | 0.039 0.144 | 0.88 2.97 HLTHF | 0.192 0.364 | 2.29 4.13 HLTHP | 0.640 0.787 | 3.01 4.63 LINC | 0.052 0.093 | 3.08 4.28 LFAM | -0.034 -0.141 | -0.80 -3.05 EDUCDEC | 0.036 -0.000 | 4.74 -0.00 AGE | 0.000 0.006 | 0.12 2.47 FEMALE | 0.445 0.344 | 8.20 6.02 CHILD | 0.111 -0.268 | 1.38 -2.96 FEMCHILD | -0.451 -0.351 | -5.65 -3.92 BLACK | -0.606 -0.196 | -11.58 -2.90 _cons | -0.272 3.077 | -1.45 13.90 -------------+-------------------------- N | 5574.000 4281.000 ll | -2690.577 -7493.499 rank | 18.000 18.000 aic | 5417.154 15022.998 bic | 5536.419 15137.513 ---------------------------------------- legend: b/t . di "lltwopart = " lltwopart lltwopart = -10184.076 . . * Last four columns of Table 16.1 (page 554) . * Sample selection estimates: 2step and MLE estimates . set matsize 60 . estimates table heck2step heckmle, t stats(N ll rank aic bic) b(%10.3f) ---------------------------------------- Variable | heck2step heckmle -------------+-------------------------- LNMED | LC | -0.028 -0.076 | -0.70 -2.25 IDP | -0.092 -0.150 | -1.36 -2.26 LPI | 0.005 0.015 | 0.47 1.42 FMDE | -0.030 -0.024 | -1.62 -1.21 PHYSLIM | 0.281 0.355 | 3.50 4.70 NDISEASE | 0.022 0.029 | 4.29 7.54 HLTHG | 0.147 0.156 | 3.01 2.99 HLTHF | 0.382 0.445 | 3.98 4.66 HLTHP | 0.833 0.999 | 4.22 5.32 LINC | 0.099 0.121 | 3.94 5.26 LFAM | -0.144 -0.158 | -3.08 -3.18 EDUCDEC | 0.003 0.018 | 0.31 1.95 AGE | 0.006 0.006 | 2.46 2.35 FEMALE | 0.385 0.550 | 3.72 8.69 CHILD | -0.257 -0.198 | -2.74 -2.03 FEMCHILD | -0.392 -0.565 | -3.13 -5.80 BLACK | -0.263 -0.536 | -1.67 -7.15 _cons | 2.883 2.108 | 6.13 8.63 -------------+-------------------------- DMED | LC | -0.119 -0.107 | -4.41 -4.03 IDP | -0.128 -0.109 | -2.45 -2.13 LPI | 0.028 0.029 | 3.19 3.42 FMDE | 0.008 0.001 | 0.47 0.05 PHYSLIM | 0.273 0.285 | 3.67 3.94 NDISEASE | 0.022 0.021 | 6.25 6.03 HLTHG | 0.039 0.058 | 0.88 1.35 HLTHF | 0.192 0.224 | 2.29 2.75 HLTHP | 0.640 0.798 | 3.01 3.90 LINC | 0.052 0.055 | 3.08 3.33 LFAM | -0.034 -0.031 | -0.80 -0.77 EDUCDEC | 0.036 0.031 | 4.74 4.20 AGE | 0.000 -0.001 | 0.12 -0.29 FEMALE | 0.445 0.409 | 8.20 7.69 CHILD | 0.111 0.053 | 1.38 0.67 FEMCHILD | -0.451 -0.395 | -5.65 -5.04 BLACK | -0.606 -0.583 | -11.58 -11.20 _cons | -0.272 -0.214 | -1.45 -1.16 -------------+-------------------------- mills | lambda | 0.236 | 0.47 -------------+-------------------------- athrho | _cons | 0.941 | 12.78 -------------+-------------------------- lnsigma | _cons | 0.451 | 25.45 -------------+-------------------------- Statistics | N | 5574.000 5574.000 ll | -10170.110 rank | 37.000 38.000 aic | . 20416.221 bic | . 20668.004 ---------------------------------------- legend: b/t . . ************ (4) A LITTLE FURTHER ANALYSIS ********** . . * Predictions . * Compare predictions to actual for MED > 0 . sum MED pMEDpos2part pMEDposhml pMEDposh2s if MED > 0 Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- MED | 4281 220.987 909.9021 .5860291 39182.02 pMEDpos2part | 4281 183.462 126.0213 26.37827 1731.088 pMEDposhml | 4281 240.4096 185.0424 42.00053 3505.48 pMEDposh2s | 4281 184.9993 129.5432 27.63657 1911.624 . corr MED pMEDpos2part pMEDposhml pMEDposh2s if MED > 0 (obs=4281) | MED pMEDpo~t pMEDpo~l pMEDp~2s -------------+------------------------------------ MED | 1.0000 pMEDpos2part | 0.1669 1.0000 pMEDposhml | 0.1617 0.9830 1.0000 pMEDposh2s | 0.1669 0.9994 0.9887 1.0000 . . * Compare predictions to actual including zeroes . sum MED pMEDall2part pMEDallhml pMEDallh2s DMED probsel2part probselhml probselh2s Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- MED | 5574 169.7247 802.8303 0 39182.02 pMEDall2part | 5574 140.966 120.2022 4.880651 1729.783 pMEDallhml | 5574 184.5571 174.1649 8.814864 3503.564 pMEDallh2s | 5574 142.1438 123.2964 5.272963 1910.182 DMED | 5574 .7680301 .4221277 0 1 -------------+-------------------------------------------------------- probsel2part | 5574 .7678377 .1457464 .1526731 .999246 probselhml | 5574 .7674107 .1404707 .1737047 .9994534 probselh2s | 5574 .7678377 .1457464 .1526731 .999246 . corr MED pMEDall2part pMEDallhml pMEDallh2s DMED probsel2part probselhml probselh2s (obs=5574) | MED pMEDal~t pMEDal~l pMEDa~2s DMED probse~t probse~l probs~2s -------------+------------------------------------------------------------------------ MED | 1.0000 pMEDall2part | 0.1772 1.0000 pMEDallhml | 0.1734 0.9861 1.0000 pMEDallh2s | 0.1772 0.9995 0.9909 1.0000 DMED | 0.1162 0.2158 0.2015 0.2132 1.0000 probsel2part | 0.1031 0.6380 0.5939 0.6298 0.3467 1.0000 probselhml | 0.1074 0.6552 0.6092 0.6468 0.3468 0.9980 1.0000 probselh2s | 0.1031 0.6380 0.5939 0.6298 0.3467 1.0000 0.9980 1.0000 . . ********** CLOSE OUTPUT . log close log: c:\Imbook\bwebpage\Section4\mma16p3selection.txt log type: text closed on: 19 May 2005, 13:04:40 ----------------------------------------------------------------------------------------------------