The Mroz87 data frame contains data about 753 married women. These data are collected within the "Panel Study of Income Dynamics" (PSID). Of the 753 observations, the first 428 are for women with positive hours worked in 1975, while the remaining 325 observations are for women who did not work for pay in 1975. A more complete discussion of the data is found in Mroz (1987) . It also includes the following explanatory variables:
lfp: Dummy variable for labor-force participation.
hours: Wife's hours of work in 1975.
kids5: Number of children 5 years old or younger.
kids618: Number of children 6 to 18 years old.
Age: Wife's age.
Educ: Wife's educational attainment, in years.
wage: Wife's average hourly earnings, in 1975 dollars.
repwage: Wife's wage reported at the time of the 1976 interview.
hushrs: Husband's hours worked in 1975.
husage: Husband's age.
huseduc: Husband's educational attainment, in years.
huswage: Husband's wage, in 1975 dollars.
faminc: Family income, in 1975 dollars.
mtr: Marginal tax rate facing the wife.
motheduc: Wife's mother's educational attainment, in years.
fatheduc: Wife's father's educational attainment, in years.
unem: Unemployment rate in county of residence, in percentage points.
city: Dummy variable = 1 if live in large city, else 0.
exper: Actual years of wife's previous labor market experience.
nwifeinc: Non-wife income.
wifecoll: Dummy variable for wife's college attendance.
huscoll: Dummy variable for husband's college attendance.
Mroz87An object of class data.frame with 753 rows and 22 columns.
PSID Staff, The Panel Study of Income Dynamics, Institute for Social ResearchPanel Study of Income Dynamics, University of Michigan, https://psidonline.isr.umich.edu/
Thomas A Mroz (1987). “The sensitivity of an empirical model of married women's hours of work to economic and statistical assumptions.” Econometrica: Journal of the Econometric Society, 765--799. Mikhail Zhelonkin, Marc G. Genton, Elvezio Ronchetti (2019). ssmrob: Robust Estimation and Inference in Sample Selection Models. R package version 0.7, https://CRAN.R-project.org/package=ssmrob. Ott Toomet, Arne Henningsen (2008). “Sample Selection Models in R: Package sampleSelection.” Journal of Statistical Software, 27(7). https://www.jstatsoft.org/article/view/v027i07. Jeffrey M Wooldridge (2016). Introductory econometrics: A modern approach. Nelson Education.
# Wooldridge(2016): page 247
data(Mroz87)
attach(Mroz87)
#> The following objects are masked from MEPS2001 (pos = 3):
#>
#> age, educ
#> The following objects are masked from MEPS2001 (pos = 4):
#>
#> age, educ
#> The following objects are masked from MEPS2001 (pos = 5):
#>
#> age, educ
#> The following objects are masked from Mroz87 (pos = 6):
#>
#> age, city, educ, exper, faminc, fatheduc, hours, husage, huscoll,
#> huseduc, hushrs, huswage, kids5, kids618, lfp, motheduc, mtr,
#> nwifeinc, repwage, unem, wage, wifecoll
#> The following objects are masked from MEPS2001 (pos = 7):
#>
#> age, educ
#> The following objects are masked from MEPS2001 (pos = 8):
#>
#> age, educ
#> The following objects are masked from MEPS2001 (pos = 9):
#>
#> age, educ
#> The following objects are masked from MEPS2001 (pos = 10):
#>
#> age, educ
selectEq <- lfp ~ nwifeinc + educ + exper + I(exper^2) + age + kids5 + kids618
outcomeEq <- log(wage) ~ educ + exper + I(exper^2)
outcomeS <- cbind(educ, exper)
outcomeC <- cbind(educ, exper)
outcomeBS <- wage ~ educ + exper + I(exper^2)
outcomeBS <- wage ~ educ + exper + I(exper^2)
HeckmanCL(selectEq, outcomeEq, data = Mroz87)
#> $coefficients
#> (Intercept) nwifeinc educ exper I(exper^2) age
#> 0.270073573 -0.012023770 0.130903996 0.123347160 -0.001887289 -0.052852446
#> kids5 kids618 (Intercept) educ exper I(exper^2)
#> -0.868324675 0.036005607 -0.578102306 0.109065489 0.043887302 -0.000859097
#> sigma rho
#> 0.663799475 0.048601124
#>
#> $value
#> [1] -832.8978
#>
#> $loglik
#> [1] 832.8978
#>
#> $counts
#> gradient
#> 1
#>
#> $hessian
#> XS(Intercept) XSnwifeinc XSeduc XSexper
#> XS(Intercept) -3.841431e+02 -7.801652e+03 -4.690202e+03 -3.930787e+03
#> XSnwifeinc -7.801652e+03 -2.090808e+05 -9.834592e+04 -7.473540e+04
#> XSeduc -4.690202e+03 -9.834592e+04 -5.911411e+04 -4.780152e+04
#> XSexper -3.930787e+03 -7.473540e+04 -4.780152e+04 -6.333871e+04
#> XSI(exper^2) -6.321051e+04 -1.123608e+06 -7.630328e+05 -1.317075e+06
#> XSage -1.639732e+04 -3.355287e+05 -1.995606e+05 -1.774652e+05
#> XSkids5 -9.101045e+01 -1.755805e+03 -1.183796e+03 -7.214715e+02
#> XSkids618 -5.336924e+02 -1.094389e+04 -6.442923e+03 -4.130979e+03
#> XO(Intercept) 1.500566e+01 2.956320e+02 1.856870e+02 1.724166e+02
#> XOeduc 1.856871e+02 3.773567e+03 2.376064e+03 2.121908e+03
#> XOexper 1.724166e+02 3.187171e+03 2.121908e+03 2.927987e+03
#> XOI(exper^2) 2.927972e+03 5.072790e+04 3.568018e+04 6.264582e+04
#> sigma 6.426914e-02 1.290896e+01 -1.059846e+00 3.803792e-02
#> rho 6.757277e+00 -1.127708e+00 1.019434e+02 4.108881e+01
#> XSI(exper^2) XSage XSkids5 XSkids618
#> XS(Intercept) -6.321051e+04 -1.639732e+04 -91.0104538 -5.336924e+02
#> XSnwifeinc -1.123608e+06 -3.355287e+05 -1755.8048883 -1.094389e+04
#> XSeduc -7.630328e+05 -1.995606e+05 -1183.7955517 -6.442923e+03
#> XSexper -1.317075e+06 -1.774652e+05 -721.4714573 -4.130979e+03
#> XSI(exper^2) -3.250851e+07 -3.003639e+06 -8126.2360442 -4.838512e+04
#> XSage -3.003639e+06 -7.246758e+05 -3156.2793510 -2.110235e+04
#> XSkids5 -8.126236e+03 -3.156279e+03 -117.3955653 -1.450579e+02
#> XSkids618 -4.838512e+04 -2.110235e+04 -145.0579212 -1.425219e+03
#> XO(Intercept) 2.926868e+03 6.371433e+02 2.8586698 2.080913e+01
#> XOeduc 3.569400e+04 7.863720e+03 38.0828492 2.538479e+02
#> XOexper 6.258583e+04 7.751901e+03 23.9624977 1.761839e+02
#> XOI(exper^2) 1.560624e+06 1.384080e+05 281.4923278 2.179570e+03
#> sigma -5.279017e+00 5.164078e+00 -0.2710216 3.907176e-01
#> rho 5.516245e+02 2.636675e+02 6.8164411 6.380234e+00
#> XO(Intercept) XOeduc XOexper XOI(exper^2)
#> XS(Intercept) 15.00566 1.856871e+02 172.4166 2.927972e+03
#> XSnwifeinc 295.63196 3.773567e+03 3187.1712 5.072790e+04
#> XSeduc 185.68703 2.376064e+03 2121.9076 3.568018e+04
#> XSexper 172.41662 2.121908e+03 2927.9868 6.264582e+04
#> XSI(exper^2) 2926.86768 3.569400e+04 62585.8346 1.560624e+06
#> XSage 637.14330 7.863720e+03 7751.9013 1.384080e+05
#> XSkids5 2.85867 3.808285e+01 23.9625 2.814923e+02
#> XSkids618 20.80913 2.538479e+02 176.1839 2.179570e+03
#> XO(Intercept) -972.43572 -1.230963e+04 -12676.3172 -2.282062e+05
#> XOeduc -12309.63323 -1.608894e+05 -160192.2177 -2.867601e+06
#> XOexper -12676.31723 -1.601922e+05 -228206.2493 -4.985108e+06
#> XOI(exper^2) -228206.24811 -2.867601e+06 -4985108.4243 -1.242963e+08
#> sigma -25.01817 -3.038649e+02 -251.8162 -3.997888e+03
#> rho -342.38510 -4.164895e+03 -3445.0338 -5.475566e+04
#> sigma rho
#> XS(Intercept) 6.426914e-02 6.757277
#> XSnwifeinc 1.290896e+01 -1.127708
#> XSeduc -1.059846e+00 101.943398
#> XSexper 3.803792e-02 41.088807
#> XSI(exper^2) -5.279017e+00 551.624480
#> XSage 5.164078e+00 263.667498
#> XSkids5 -2.710216e-01 6.816441
#> XSkids618 3.907176e-01 6.380234
#> XO(Intercept) -2.501817e+01 -342.385099
#> XOeduc -3.038649e+02 -4164.895260
#> XOexper -2.518162e+02 -3445.033829
#> XOI(exper^2) -3.997888e+03 -54755.656407
#> sigma -1.942498e+03 20.715129
#> rho 2.071513e+01 -199.287133
#>
#> $fisher_infoHC
#> XS(Intercept) XSnwifeinc XSeduc XSexper
#> XS(Intercept) 2.594991e-01 2.718850e-04 -7.789529e-03 -1.640174e-03
#> XSnwifeinc 2.718850e-04 2.373249e-05 -4.309163e-05 3.922394e-06
#> XSeduc -7.789529e-03 -4.309163e-05 6.438223e-04 -1.945572e-05
#> XSexper -1.640174e-03 3.922394e-06 -1.945572e-05 3.632435e-04
#> XSI(exper^2) 6.346992e-05 1.156980e-07 3.251721e-07 -1.079852e-05
#> XSage -3.337445e-03 -6.513168e-06 2.068130e-05 -5.466997e-06
#> XSkids5 -1.899580e-02 2.033978e-05 -3.948289e-04 -1.808508e-05
#> XSkids618 -1.008835e-02 -1.000235e-05 1.158510e-04 6.871686e-05
#> XO(Intercept) 6.022574e-03 9.236679e-05 -4.871064e-04 7.546264e-05
#> XOeduc -2.300538e-04 -2.629779e-06 1.916973e-05 -3.334309e-06
#> XOexper -2.113263e-04 -3.814569e-06 1.562376e-05 1.508822e-06
#> XOI(exper^2) 4.446188e-06 7.898120e-08 -3.198640e-07 -8.261317e-08
#> sigma -5.822507e-05 -1.128188e-06 4.711254e-06 -1.412136e-06
#> rho -3.851831e-03 -7.967870e-05 3.344543e-04 -8.973288e-05
#> XSI(exper^2) XSage XSkids5 XSkids618
#> XS(Intercept) 6.346992e-05 -3.337445e-03 -1.899580e-02 -1.008835e-02
#> XSnwifeinc 1.156980e-07 -6.513168e-06 2.033978e-05 -1.000235e-05
#> XSeduc 3.251721e-07 2.068130e-05 -3.948289e-04 1.158510e-04
#> XSexper -1.079852e-05 -5.466997e-06 -1.808508e-05 6.871686e-05
#> XSI(exper^2) 3.798656e-07 -4.990624e-07 -2.743623e-07 -3.082357e-07
#> XSage -4.990624e-07 7.192480e-05 4.549849e-04 1.276900e-04
#> XSkids5 -2.743623e-07 4.549849e-04 1.409431e-02 6.297921e-04
#> XSkids618 -3.082357e-07 1.276900e-04 6.297921e-04 1.889229e-03
#> XO(Intercept) -9.882218e-07 -5.538153e-05 -1.305286e-03 1.092054e-04
#> XOeduc 5.942579e-08 1.603208e-06 3.620852e-05 -2.860859e-06
#> XOexper -1.009607e-07 2.186112e-06 5.295525e-05 -5.224609e-06
#> XOI(exper^2) 4.229821e-09 -4.419860e-08 -1.072319e-06 1.124489e-07
#> sigma 2.395838e-08 7.484541e-07 1.752961e-05 -1.270694e-06
#> rho 1.504750e-06 4.582844e-05 1.120394e-03 -8.701059e-05
#> XO(Intercept) XOeduc XOexper XOI(exper^2)
#> XS(Intercept) 6.022574e-03 -2.300538e-04 -2.113263e-04 4.446188e-06
#> XSnwifeinc 9.236679e-05 -2.629779e-06 -3.814569e-06 7.898120e-08
#> XSeduc -4.871064e-04 1.916973e-05 1.562376e-05 -3.198640e-07
#> XSexper 7.546264e-05 -3.334309e-06 1.508822e-06 -8.261317e-08
#> XSI(exper^2) -9.882218e-07 5.942579e-08 -1.009607e-07 4.229821e-09
#> XSage -5.538153e-05 1.603208e-06 2.186112e-06 -4.419860e-08
#> XSkids5 -1.305286e-03 3.620852e-05 5.295525e-05 -1.072319e-06
#> XSkids618 1.092054e-04 -2.860859e-06 -5.224609e-06 1.124489e-07
#> XO(Intercept) 6.663591e-02 -3.220597e-03 -2.101249e-03 4.677659e-05
#> XOeduc -3.220597e-03 2.197739e-04 2.074961e-05 -2.830950e-07
#> XOexper -2.101249e-03 2.074961e-05 2.200181e-04 -5.885013e-06
#> XOI(exper^2) 4.677659e-05 -2.830950e-07 -5.885013e-06 1.738280e-07
#> sigma -4.320090e-04 1.204950e-05 1.799837e-05 -3.720779e-07
#> rho -2.389701e-02 6.652017e-04 9.972370e-04 -2.062457e-05
#> sigma rho
#> XS(Intercept) -5.822507e-05 -3.851831e-03
#> XSnwifeinc -1.128188e-06 -7.967870e-05
#> XSeduc 4.711254e-06 3.344543e-04
#> XSexper -1.412136e-06 -8.973288e-05
#> XSI(exper^2) 2.395838e-08 1.504750e-06
#> XSage 7.484541e-07 4.582844e-05
#> XSkids5 1.752961e-05 1.120394e-03
#> XSkids618 -1.270694e-06 -8.701059e-05
#> XO(Intercept) -4.320090e-04 -2.389701e-02
#> XOeduc 1.204950e-05 6.652017e-04
#> XOexper 1.799837e-05 9.972370e-04
#> XOI(exper^2) -3.720779e-07 -2.062457e-05
#> sigma 5.204977e-04 3.373580e-04
#> rho 3.373580e-04 2.075767e-02
#>
#> $prop_sigmaHC
#> XS(Intercept) XSnwifeinc XSeduc XSexper XSI(exper^2)
#> 0.5094105161 0.0048716003 0.0253736528 0.0190589484 0.0006163324
#> XSage XSkids5 XSkids618 XO(Intercept) XOeduc
#> 0.0084808490 0.1187194404 0.0434652577 0.2581393215 0.0148247744
#> XOexper XOI(exper^2) sigma rho
#> 0.0148330060 0.0004169268 0.0228144176 0.1440752278
#>
#> $level
#> [1] "0" "1"
#>
#> $nObs
#> [1] 753
#>
#> $nParam
#> [1] 14
#>
#> $N0
#> [1] 325
#>
#> $N1
#> [1] 428
#>
#> $NXS
#> [1] 8
#>
#> $NXO
#> [1] 4
#>
#> $df
#> [1] 739
#>
#> $aic
#> [1] 1693.796
#>
#> $bic
#> [1] 1758.532
#>
#> $initial.value
#> XS(Intercept) XSnwifeinc XSeduc XSexper XSI(exper^2)
#> 0.2700735726 -0.0120236370 0.1309039692 0.1233471675 -0.0018870674
#> XSage XSkids5 XSkids618 XO(Intercept) XOeduc
#> -0.0528524416 -0.8683246795 0.0360056106 -0.5781023058 0.1090654909
#> XOexper XOI(exper^2) sigma rho
#> 0.0438873010 -0.0008591134 0.6637994802 0.0486011464
#>
#> attr(,"class")
#> [1] "HeckmanCL" "list"
HeckmanBS(selectEq, outcomeBS, data = Mroz87)
#> $coefficients
#> (Intercept) nwifeinc educ exper I(exper^2)
#> 1.0572557181 -0.0147278022 0.1681025891 0.1593054823 -0.0024351869
#> age kids5 kids618 (Intercept) educ
#> -0.0684422196 -1.1249025687 0.0458617934 -0.4607747704 0.1092064320
#> exper I(exper^2) sigma rho
#> 0.0469100554 -0.0008813633 3.4295872561 0.1973192668
#>
#> $value
#> [1] -1375.13
#>
#> $loglik
#> [1] 1375.13
#>
#> $counts
#> gradient
#> 29
#>
#> $hessian
#> XS(Intercept) XSnwifeinc XSeduc XSexper
#> XS(Intercept) -238.083749 -4865.42142 -2904.88466 -2509.54248
#> XSnwifeinc -4865.421418 -135063.24692 -61206.28222 -46849.26031
#> XSeduc -2904.884657 -61206.28222 -36643.63222 -30751.26907
#> XSexper -2509.542480 -46849.26031 -30751.26907 -41957.75843
#> XSI(exper^2) -42851.466743 -744867.68344 -524234.05860 -922233.93003
#> XSage -10164.913362 -209321.43916 -123559.77600 -112841.25630
#> XSkids5 -56.132815 -1130.25127 -725.51697 -420.84153
#> XSkids618 -332.769995 -6893.76670 -4016.79185 -2677.41552
#> XO(Intercept) 45.203570 886.15188 560.37533 521.82236
#> XOeduc 560.377529 11306.46919 7178.28589 6447.60223
#> XOexper 521.829446 9512.68568 6447.65681 8949.98670
#> XOI(exper^2) 9024.120817 153929.16179 110554.85630 194413.71287
#> sigma 2.669478 47.09007 33.78183 31.99792
#> rho 12.370817 152.64164 153.43393 24.48918
#> XSI(exper^2) XSage XSkids5 XSkids618
#> XS(Intercept) -42851.467 -10164.9134 -56.1328147 -332.769995
#> XSnwifeinc -744867.683 -209321.4392 -1130.2512675 -6893.766699
#> XSeduc -524234.059 -123559.7760 -725.5169684 -4016.791846
#> XSexper -922233.930 -112841.2563 -420.8415264 -2677.415517
#> XSI(exper^2) -24415590.913 -2031228.7263 -4739.8363156 -32993.660516
#> XSage -2031228.726 -449427.0826 -1957.8752339 -13143.220120
#> XSkids5 -4739.836 -1957.8752 -72.3171438 -94.919677
#> XSkids618 -32993.661 -13143.2201 -94.9196766 -903.074054
#> XO(Intercept) 8892.995 1918.1436 8.6099758 63.253575
#> XOeduc 108911.241 23729.4232 113.5922838 774.150771
#> XOexper 190480.877 23384.4720 68.3396231 543.418659
#> XOI(exper^2) 4805269.187 425408.2505 790.1306309 6877.654653
#> sigma 556.450 111.6992 0.5836707 3.714711
#> rho -131.443 507.3594 10.7166028 19.309263
#> XO(Intercept) XOeduc XOexper XOI(exper^2)
#> XS(Intercept) 4.520357e+01 560.3775 5.218294e+02 9.024121e+03
#> XSnwifeinc 8.861519e+02 11306.4692 9.512686e+03 1.539292e+05
#> XSeduc 5.603753e+02 7178.2859 6.447657e+03 1.105549e+05
#> XSexper 5.218224e+02 6447.6022 8.949987e+03 1.944137e+05
#> XSI(exper^2) 8.892995e+03 108911.2408 1.904809e+05 4.805269e+06
#> XSage 1.918144e+03 23729.4232 2.338447e+04 4.254083e+05
#> XSkids5 8.609976e+00 113.5923 6.833962e+01 7.901306e+02
#> XSkids618 6.325358e+01 774.1508 5.434187e+02 6.877655e+03
#> XO(Intercept) -8.657102e+02 -10980.3842 -1.058246e+04 -1.933234e+05
#> XOeduc -1.098038e+04 -143609.1500 -1.341087e+05 -2.433149e+06
#> XOexper -1.058246e+04 -134108.7395 -1.851892e+05 -4.235504e+06
#> XOI(exper^2) -1.933234e+05 -2433148.7038 -4.235504e+06 -1.147060e+08
#> sigma -4.404924e+01 -563.8503 -5.632749e+02 -1.029695e+04
#> rho -3.262976e+02 -3981.5125 -3.179036e+03 -5.063642e+04
#> sigma rho
#> XS(Intercept) 2.669478e+00 12.37082
#> XSnwifeinc 4.709007e+01 152.64164
#> XSeduc 3.378183e+01 153.43393
#> XSexper 3.199792e+01 24.48918
#> XSI(exper^2) 5.564500e+02 -131.44297
#> XSage 1.116992e+02 507.35936
#> XSkids5 5.836707e-01 10.71660
#> XSkids618 3.714711e+00 19.30926
#> XO(Intercept) -4.404924e+01 -326.29756
#> XOeduc -5.638503e+02 -3981.51251
#> XOexper -5.632749e+02 -3179.03556
#> XOI(exper^2) -1.029695e+04 -50636.41535
#> sigma -2.041875e+01 -29.64021
#> rho -2.964021e+01 -234.79415
#>
#> $fisher_infoBS
#> XS(Intercept) XSnwifeinc XSeduc XSexper
#> XS(Intercept) 4.163452e-01 3.724328e-04 -1.231614e-02 -2.476946e-03
#> XSnwifeinc 3.724328e-04 3.341683e-05 -5.809189e-05 1.405027e-05
#> XSeduc -1.231614e-02 -5.809189e-05 9.773869e-04 -6.114682e-05
#> XSexper -2.476946e-03 1.405027e-05 -6.114682e-05 4.630791e-04
#> XSI(exper^2) 9.401491e-05 -1.166546e-08 7.235139e-07 -1.274078e-05
#> XSage -5.419957e-03 -1.107658e-05 4.610968e-05 4.328911e-06
#> XSkids5 -3.061410e-02 3.455536e-06 -4.793473e-04 2.026045e-04
#> XSkids618 -1.538756e-02 -1.389451e-05 1.668090e-04 8.767279e-05
#> XO(Intercept) 1.276996e-02 5.690601e-05 -6.891985e-04 1.340770e-04
#> XOeduc -7.463711e-04 -2.285162e-06 5.058765e-05 -1.053630e-05
#> XOexper -2.059426e-04 -1.281458e-06 8.149283e-07 1.453030e-05
#> XOI(exper^2) 3.271104e-06 1.936811e-08 5.020224e-09 -4.197141e-07
#> sigma 3.104563e-03 2.791095e-05 -6.157169e-05 1.535370e-04
#> rho -3.954513e-03 -5.074544e-05 1.323307e-04 -2.133469e-04
#> XSI(exper^2) XSage XSkids5 XSkids618
#> XS(Intercept) 9.401491e-05 -5.419957e-03 -3.061410e-02 -1.538756e-02
#> XSnwifeinc -1.166546e-08 -1.107658e-05 3.455536e-06 -1.389451e-05
#> XSeduc 7.235139e-07 4.610968e-05 -4.793473e-04 1.668090e-04
#> XSexper -1.274078e-05 4.328911e-06 2.026045e-04 8.767279e-05
#> XSI(exper^2) 4.290347e-07 -1.038487e-06 -5.491239e-06 -3.334788e-08
#> XSage -1.038487e-06 1.121030e-04 6.743485e-04 1.980049e-04
#> XSkids5 -5.491239e-06 6.743485e-04 2.243445e-02 7.860470e-04
#> XSkids618 -3.334788e-08 1.980049e-04 7.860470e-04 2.919259e-03
#> XO(Intercept) -2.003566e-06 -1.252026e-04 -2.432971e-03 6.279688e-05
#> XOeduc 1.811467e-07 4.956054e-06 8.239857e-05 -9.110411e-07
#> XOexper -4.012678e-07 2.865076e-06 6.592801e-05 -5.557346e-06
#> XOI(exper^2) 1.342042e-08 -3.620876e-08 -9.315197e-07 1.205061e-07
#> sigma -2.774219e-06 -7.855799e-05 -1.635099e-03 2.104829e-05
#> rho 3.953770e-06 9.658813e-05 2.144538e-03 -2.300693e-05
#> XO(Intercept) XOeduc XOexper XOI(exper^2)
#> XS(Intercept) 1.276996e-02 -7.463711e-04 -2.059426e-04 3.271104e-06
#> XSnwifeinc 5.690601e-05 -2.285162e-06 -1.281458e-06 1.936811e-08
#> XSeduc -6.891985e-04 5.058765e-05 8.149283e-07 5.020224e-09
#> XSexper 1.340770e-04 -1.053630e-05 1.453030e-05 -4.197141e-07
#> XSI(exper^2) -2.003566e-06 1.811467e-07 -4.012678e-07 1.342042e-08
#> XSage -1.252026e-04 4.956054e-06 2.865076e-06 -3.620876e-08
#> XSkids5 -2.432971e-03 8.239857e-05 6.592801e-05 -9.315197e-07
#> XSkids618 6.279688e-05 -9.110411e-07 -5.557346e-06 1.205061e-07
#> XO(Intercept) 5.856782e-02 -3.397233e-03 -1.213138e-03 2.345059e-05
#> XOeduc -3.397233e-03 2.511506e-04 1.705903e-06 1.639702e-07
#> XOexper -1.213138e-03 1.705903e-06 1.614609e-04 -4.094126e-06
#> XOI(exper^2) 2.345059e-05 1.639702e-07 -4.094126e-06 1.191256e-07
#> sigma 8.997609e-03 -4.063090e-04 -4.068092e-04 7.184043e-06
#> rho -1.365395e-02 4.605938e-04 4.045037e-04 -6.508920e-06
#> sigma rho
#> XS(Intercept) 3.104563e-03 -3.954513e-03
#> XSnwifeinc 2.791095e-05 -5.074544e-05
#> XSeduc -6.157169e-05 1.323307e-04
#> XSexper 1.535370e-04 -2.133469e-04
#> XSI(exper^2) -2.774219e-06 3.953770e-06
#> XSage -7.855799e-05 9.658813e-05
#> XSkids5 -1.635099e-03 2.144538e-03
#> XSkids618 2.104829e-05 -2.300693e-05
#> XO(Intercept) 8.997609e-03 -1.365395e-02
#> XOeduc -4.063090e-04 4.605938e-04
#> XOexper -4.068092e-04 4.045037e-04
#> XOI(exper^2) 7.184043e-06 -6.508920e-06
#> sigma 6.240435e-02 -9.616911e-03
#> rho -9.616911e-03 1.268997e-02
#>
#> $prop_sigmaBS
#> XS(Intercept) XSnwifeinc XSeduc XSexper XSI(exper^2)
#> 0.6452482042 0.0057807292 0.0312631871 0.0215192725 0.0006550074
#> XSage XSkids5 XSkids618 XO(Intercept) XOeduc
#> 0.0105878722 0.1497813481 0.0540301683 0.2420079012 0.0158477318
#> XOexper XOI(exper^2) sigma rho
#> 0.0127067251 0.0003451458 0.2498086234 0.1126497757
#>
#> $level
#> [1] "0" "1"
#>
#> $nObs
#> [1] 753
#>
#> $nParam
#> [1] 14
#>
#> $N0
#> [1] 325
#>
#> $N1
#> [1] 428
#>
#> $NXS
#> [1] 8
#>
#> $NXO
#> [1] 4
#>
#> $df
#> [1] 739
#>
#> $aic
#> [1] 2778.261
#>
#> $bic
#> [1] 2842.997
#>
#> $initial.value
#> XS(Intercept) XSnwifeinc XSeduc XSexper XSI(exper^2)
#> 0.2700735726 -0.0120236370 0.1309039692 0.1233471675 -0.0018870674
#> XSage XSkids5 XSkids618 XO(Intercept) XOeduc
#> -0.0528524416 -0.8683246795 0.0360056106 -0.5781023058 0.1090654909
#> XOexper XOI(exper^2) sigma rho
#> 0.0438873010 -0.0008591134 0.6637994802 0.0486011464
#>
#> attr(,"class")
#> [1] "HeckmanBS" "list"
HeckmanSK(selectEq, outcomeEq, data = Mroz87, lambda = 1)
#> $coefficients
#> (Intercept) nwifeinc educ exper I(exper^2)
#> 0.2663350384 -0.0121320482 0.1313398741 0.1232814605 -0.0018862461
#> age kids5 kids618 (Intercept) educ
#> -0.0528283462 -0.8673963062 0.0358745816 -0.5553913893 0.1083498518
#> exper I(exper^2) sigma rho lambda
#> 0.0428353751 -0.0008373951 0.6633956023 0.0265869564 0.0051435224
#>
#> $value
#> [1] -832.8851
#>
#> $loglik
#> [1] 832.8851
#>
#> $counts
#> gradient
#> 31
#>
#> $hessian
#> XS(Intercept) XSnwifeinc XSeduc XSexper
#> XS(Intercept) -3.839434e+02 -7.799189e+03 -4.687737e+03 -3.928680e+03
#> XSnwifeinc -7.799189e+03 -2.090237e+05 -9.831712e+04 -7.473170e+04
#> XSeduc -4.687737e+03 -9.831712e+04 -5.908392e+04 -4.777597e+04
#> XSexper -3.928680e+03 -7.473170e+04 -4.777597e+04 -6.330552e+04
#> XSI(exper^2) -6.317501e+04 -1.123750e+06 -7.626059e+05 -1.316495e+06
#> XSage -1.638825e+04 -3.354107e+05 -1.994462e+05 -1.773594e+05
#> XSkids5 -9.096065e+01 -1.754743e+03 -1.183143e+03 -7.209231e+02
#> XSkids618 -5.333519e+02 -1.093638e+04 -6.438298e+03 -4.127602e+03
#> XO(Intercept) 8.205715e+00 1.617611e+02 1.015385e+02 9.429380e+01
#> XOeduc 1.015386e+02 2.064831e+03 1.299319e+03 1.160448e+03
#> XOexper 9.429380e+01 1.744692e+03 1.160447e+03 1.601411e+03
#> XOI(exper^2) 1.601409e+03 2.777785e+04 1.951460e+04 3.427190e+04
#> sigma 4.936320e-02 7.275883e+00 -3.085468e-01 4.978053e-01
#> rho 2.202930e+00 -1.010889e+02 4.657854e+01 3.858208e+00
#> -3.801678e+00 -7.983124e+01 -4.570128e+01 -3.343441e+01
#> XSI(exper^2) XSage XSkids5 XSkids618
#> XS(Intercept) -6.317501e+04 -1.638825e+04 -90.9606464 -5.333519e+02
#> XSnwifeinc -1.123750e+06 -3.354107e+05 -1754.7434109 -1.093638e+04
#> XSeduc -7.626059e+05 -1.994462e+05 -1183.1428466 -6.438298e+03
#> XSexper -1.316495e+06 -1.773594e+05 -720.9230946 -4.127602e+03
#> XSI(exper^2) -3.249887e+07 -3.001815e+06 -8118.4314413 -4.833259e+04
#> XSage -3.001815e+06 -7.242440e+05 -3154.4414820 -2.108984e+04
#> XSkids5 -8.118431e+03 -3.154441e+03 -117.3355831 -1.449819e+02
#> XSkids618 -4.833259e+04 -2.108984e+04 -144.9819147 -1.424244e+03
#> XO(Intercept) 1.600706e+03 3.484004e+02 1.5615110 1.137736e+01
#> XOeduc 1.952090e+04 4.299773e+03 20.8026166 1.387688e+02
#> XOexper 3.423534e+04 4.239097e+03 13.0848409 9.630804e+01
#> XOI(exper^2) 8.540126e+05 7.569543e+04 153.6748441 1.190990e+03
#> sigma 6.820745e+00 3.456450e+00 -0.1504175 2.254802e-01
#> rho -3.287902e+00 6.476978e+01 5.2320221 -2.378987e-01
#> -4.929680e+02 -1.632514e+02 -1.1030797 -5.292520e+00
#> XO(Intercept) XOeduc XOexper XOI(exper^2)
#> XS(Intercept) 8.205715e+00 1.015386e+02 9.429380e+01 1.601409e+03
#> XSnwifeinc 1.617611e+02 2.064831e+03 1.744692e+03 2.777785e+04
#> XSeduc 1.015385e+02 1.299319e+03 1.160447e+03 1.951460e+04
#> XSexper 9.429380e+01 1.160448e+03 1.601411e+03 3.427190e+04
#> XSI(exper^2) 1.600706e+03 1.952090e+04 3.423534e+04 8.540126e+05
#> XSage 3.484004e+02 4.299773e+03 4.239097e+03 7.569543e+04
#> XSkids5 1.561511e+00 2.080262e+01 1.308484e+01 1.536748e+02
#> XSkids618 1.137736e+01 1.387688e+02 9.630804e+01 1.190990e+03
#> XO(Intercept) -9.728654e+02 -1.231529e+04 -1.268311e+04 -2.283376e+05
#> XOeduc -1.231529e+04 -1.609660e+05 -1.602810e+05 -2.869308e+06
#> XOexper -1.268311e+04 -1.602810e+05 -2.283376e+05 -4.988045e+06
#> XOI(exper^2) -2.283376e+05 -2.869308e+06 -4.988045e+06 -1.243695e+08
#> sigma -1.768870e+01 -2.169920e+02 -1.899467e+02 -3.128105e+03
#> rho -3.421641e+02 -4.160352e+03 -3.444595e+03 -5.474556e+04
#> -5.146964e+02 -6.515510e+03 -6.710456e+03 -1.208136e+05
#> sigma rho
#> XS(Intercept) 0.0493632 2.202930e+00 -3.801678e+00
#> XSnwifeinc 7.2758833 -1.010889e+02 -7.983124e+01
#> XSeduc -0.3085468 4.657854e+01 -4.570128e+01
#> XSexper 0.4978053 3.858208e+00 -3.343441e+01
#> XSI(exper^2) 6.8207445 -3.287902e+00 -4.929680e+02
#> XSage 3.4564504 6.476978e+01 -1.632514e+02
#> XSkids5 -0.1504175 5.232022e+00 -1.103080e+00
#> XSkids618 0.2254802 -2.378987e-01 -5.292520e+00
#> XO(Intercept) -17.6887048 -3.421641e+02 -5.146964e+02
#> XOeduc -216.9920470 -4.160352e+03 -6.515510e+03
#> XOexper -189.9466568 -3.444595e+03 -6.710456e+03
#> XOI(exper^2) -3128.1051277 -5.474556e+04 -1.208136e+05
#> sigma -1945.5691531 8.950718e+00 -5.135650e+00
#> rho 8.9507181 -1.966555e+02 -1.810612e+02
#> -5.1356500 -1.810612e+02 -2.728446e+02
#>
#> $fisher_infoSK
#> XS(Intercept) XSnwifeinc XSeduc XSexper
#> XS(Intercept) 2.607742e-01 2.707460e-04 -7.787429e-03 -1.649631e-03
#> XSnwifeinc 2.707460e-04 2.378824e-05 -4.327614e-05 3.842568e-06
#> XSeduc -7.787429e-03 -4.327614e-05 6.441054e-04 -1.916256e-05
#> XSexper -1.649631e-03 3.842568e-06 -1.916256e-05 3.631697e-04
#> XSI(exper^2) 6.368457e-05 1.171386e-07 3.187663e-07 -1.079667e-05
#> XSage -3.336645e-03 -6.448504e-06 2.056440e-05 -5.296766e-06
#> XSkids5 -1.894548e-02 2.122565e-05 -3.975518e-04 -1.555675e-05
#> XSkids618 -1.009446e-02 -9.874134e-06 1.161743e-04 6.906245e-05
#> XO(Intercept) 3.587688e-02 9.996349e-05 -4.635215e-04 7.042070e-05
#> XOeduc -1.685233e-04 -2.824948e-06 1.602191e-05 -2.629876e-06
#> XOexper -1.777005e-04 -4.114119e-06 1.663565e-05 -3.406032e-07
#> XOI(exper^2) 3.713389e-06 8.504490e-08 -3.418884e-07 -2.115870e-08
#> sigma -1.537409e-04 -6.340256e-07 2.587376e-06 -5.844552e-07
#> rho -3.419609e-03 -8.619460e-05 3.529992e-04 -7.367988e-05
#> -5.870822e-02 -5.764860e-07 1.831933e-06 -1.422438e-06
#> XSI(exper^2) XSage XSkids5 XSkids618
#> XS(Intercept) 6.368457e-05 -3.336645e-03 -1.894548e-02 -1.009446e-02
#> XSnwifeinc 1.171386e-07 -6.448504e-06 2.122565e-05 -9.874134e-06
#> XSeduc 3.187663e-07 2.056440e-05 -3.975518e-04 1.161743e-04
#> XSexper -1.079667e-05 -5.296766e-06 -1.555675e-05 6.906245e-05
#> XSI(exper^2) 3.797807e-07 -5.027593e-07 -3.260366e-07 -3.141368e-07
#> XSage -5.027593e-07 7.189071e-05 4.537903e-04 1.276206e-04
#> XSkids5 -3.260366e-07 4.537903e-04 1.407745e-02 6.287437e-04
#> XSkids618 -3.141368e-07 1.276206e-04 6.287437e-04 1.890101e-03
#> XO(Intercept) -9.800692e-07 -3.615505e-05 -1.063092e-03 1.222271e-04
#> XOeduc 4.464710e-08 1.037913e-06 2.953418e-05 -3.313035e-06
#> XOexper -3.775544e-08 1.420247e-06 4.301682e-05 -5.416606e-06
#> XOI(exper^2) 1.954121e-09 -2.878579e-08 -8.761149e-07 1.143331e-07
#> sigma 9.565656e-09 2.488932e-07 7.180079e-06 -7.576980e-07
#> rho 1.192653e-06 2.989167e-05 9.097625e-04 -1.012726e-04
#> 2.437359e-08 5.591326e-07 1.248089e-05 -1.022437e-06
#> XO(Intercept) XOeduc XOexper XOI(exper^2)
#> XS(Intercept) 3.587688e-02 -1.685233e-04 -1.777005e-04 3.713389e-06
#> XSnwifeinc 9.996349e-05 -2.824948e-06 -4.114119e-06 8.504490e-08
#> XSeduc -4.635215e-04 1.602191e-05 1.663565e-05 -3.418884e-07
#> XSexper 7.042070e-05 -2.629876e-06 -3.406032e-07 -2.115870e-08
#> XSI(exper^2) -9.800692e-07 4.464710e-08 -3.775544e-08 1.954121e-09
#> XSage -3.615505e-05 1.037913e-06 1.420247e-06 -2.878579e-08
#> XSkids5 -1.063092e-03 2.953418e-05 4.301682e-05 -8.761149e-07
#> XSkids618 1.222271e-04 -3.313035e-06 -5.416606e-06 1.143331e-07
#> XO(Intercept) 8.430479e-01 -3.260040e-03 -2.151335e-03 4.780054e-05
#> XOeduc -3.260040e-03 2.208403e-04 2.220832e-05 -3.126330e-07
#> XOexper -2.151335e-03 2.220832e-05 2.214467e-04 -5.912323e-06
#> XOI(exper^2) 4.780054e-05 -3.126330e-07 -5.912323e-06 1.743236e-07
#> sigma -3.416738e-03 6.527188e-06 9.670545e-06 -1.998369e-07
#> rho -2.514657e-02 6.987428e-04 1.034672e-03 -2.137560e-05
#> -1.464421e+00 4.591159e-06 1.283234e-05 -2.977488e-07
#> sigma rho
#> XS(Intercept) -1.537409e-04 -3.419609e-03 -5.870822e-02
#> XSnwifeinc -6.340256e-07 -8.619460e-05 -5.764860e-07
#> XSeduc 2.587376e-06 3.529992e-04 1.831933e-06
#> XSexper -5.844552e-07 -7.367988e-05 -1.422438e-06
#> XSI(exper^2) 9.565656e-09 1.192653e-06 2.437359e-08
#> XSage 2.488932e-07 2.989167e-05 5.591327e-07
#> XSkids5 7.180079e-06 9.097625e-04 1.248090e-05
#> XSkids618 -7.576980e-07 -1.012726e-04 -1.022437e-06
#> XO(Intercept) -3.416738e-03 -2.514657e-02 -1.464421e+00
#> XOeduc 6.527188e-06 6.987428e-04 4.591159e-06
#> XOexper 9.670545e-06 1.034672e-03 1.283234e-05
#> XOI(exper^2) -1.998369e-07 -2.137560e-05 -2.977488e-07
#> sigma 5.286648e-04 1.820265e-04 6.011182e-03
#> rho 1.820265e-04 2.164031e-02 4.055325e-04
#> 6.011182e-03 4.055325e-04 2.766304e+00
#>
#> $prop_sigmaSK
#> XS(Intercept) XSnwifeinc XSeduc XSexper XSI(exper^2)
#> 0.5106605347 0.0048773185 0.0253792318 0.0190570106 0.0006162635
#> XSage XSkids5 XSkids618 XO(Intercept) XOeduc
#> 0.0084788387 0.1186484409 0.0434752885 0.9181764031 0.0148606968
#> XOexper XOI(exper^2) sigma rho
#> 0.0148810852 0.0004175207 0.0229927113 0.1471064574 1.6632210988
#>
#> $level
#> [1] "0" "1"
#>
#> $nObs
#> [1] 753
#>
#> $nParam
#> [1] 15
#>
#> $N0
#> [1] 325
#>
#> $N1
#> [1] 428
#>
#> $NXS
#> [1] 8
#>
#> $NXO
#> [1] 4
#>
#> $df
#> [1] 738
#>
#> $aic
#> [1] 1695.77
#>
#> $bic
#> [1] 1765.131
#>
#> $initial.value
#> XS(Intercept) XSnwifeinc XSeduc XSexper XSI(exper^2)
#> 0.2700735726 -0.0120236370 0.1309039692 0.1233471675 -0.0018870674
#> XSage XSkids5 XSkids618 XO(Intercept) XOeduc
#> -0.0528524416 -0.8683246795 0.0360056106 -0.5781023058 0.1090654909
#> XOexper XOI(exper^2) sigma rho
#> 0.0438873010 -0.0008591134 0.6637994802 0.0486011464 1.0000000000
#>
#> attr(,"class")
#> [1] "HeckmanSK" "list"
HeckmantS(selectEq, outcomeEq, data = Mroz87, df=5)
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> $coefficients
#> (Intercept) nwifeinc educ exper I(exper^2)
#> 0.4978609360 -0.0119468890 0.1395750239 0.1496618759 -0.0022845408
#> age kids5 kids618 (Intercept) educ
#> -0.0642790009 -1.0438382682 0.0344075726 -0.2524442781 0.1084650789
#> exper I(exper^2) sigma rho df
#> 0.0251406451 -0.0004567222 0.4437009922 -0.3825537027 3.0611213085
#>
#> $value
#> [1] -788.0048
#>
#> $loglik
#> [1] 788.0048
#>
#> $counts
#> gradient
#> 23
#>
#> $hessian
#> XS(Intercept) XSnwifeinc XSeduc XSexper
#> XS(Intercept) -276.279889 -5676.89800 -3370.17261 -2745.78741
#> XSnwifeinc -5676.897996 -152129.18872 -71581.70592 -54076.69840
#> XSeduc -3370.172614 -71581.70592 -42424.72414 -33188.52498
#> XSexper -2745.787406 -54076.69840 -33188.52498 -42778.40650
#> XSI(exper^2) -42409.625635 -783271.72339 -506697.63501 -866851.38998
#> XSage -11808.440930 -244825.97584 -143597.72247 -124432.56229
#> XSkids5 -64.189661 -1198.67593 -838.69899 -549.19385
#> XSkids618 -377.064256 -7769.45217 -4533.27928 -2790.41094
#> XO(Intercept) -123.631966 -2455.25564 -1535.38653 -1428.43246
#> XOeduc -1535.329286 -31841.27646 -19621.99579 -17644.23223
#> XOexper -1428.306982 -27455.03826 -17643.51185 -24243.46636
#> XOI(exper^2) -22514.180044 -413077.85500 -275652.74970 -464145.01948
#> sigma 41.564271 848.93668 477.45835 145.17510
#> rho -33.248443 -858.65335 -387.63244 -327.09601
#> -5.291253 -90.14072 -66.73986 -86.32669
#> XSI(exper^2) XSage XSkids5 XSkids618
#> XS(Intercept) -4.240963e+04 -11808.4409 -64.1896612 -377.064256
#> XSnwifeinc -7.832717e+05 -244825.9758 -1198.6759299 -7769.452170
#> XSeduc -5.066976e+05 -143597.7225 -838.6989926 -4533.279283
#> XSexper -8.668514e+05 -124432.5623 -549.1938456 -2790.410941
#> XSI(exper^2) -2.065509e+07 -2021786.9256 -6419.7179662 -31083.726758
#> XSage -2.021787e+06 -522088.1862 -2216.3303243 -14985.014873
#> XSkids5 -6.419718e+03 -2216.3303 -81.8098089 -91.095572
#> XSkids618 -3.108373e+04 -14985.0149 -91.0955722 -980.878858
#> XO(Intercept) -2.383508e+04 -5243.9968 -22.7479482 -169.136936
#> XOeduc -2.910894e+05 -64987.7790 -298.3629265 -2059.997034
#> XOexper -5.029150e+05 -64592.8359 -219.2311093 -1387.282345
#> XOI(exper^2) -1.062248e+07 -1058417.2988 -2846.1763689 -16543.637657
#> sigma -1.021381e+02 1794.6487 21.3015373 69.263258
#> rho -5.601655e+03 -1466.8375 -7.4992960 -48.007271
#> -1.691839e+03 -223.1172 0.1008317 -7.400591
#> XO(Intercept) XOeduc XOexper XOI(exper^2)
#> XS(Intercept) -1.236320e+02 -1535.3293 -1428.3070 -2.251418e+04
#> XSnwifeinc -2.455256e+03 -31841.2765 -27455.0383 -4.130779e+05
#> XSeduc -1.535387e+03 -19621.9958 -17643.5118 -2.756527e+05
#> XSexper -1.428432e+03 -17644.2322 -24243.4664 -4.641450e+05
#> XSI(exper^2) -2.383508e+04 -291089.3860 -502915.0381 -1.062248e+07
#> XSage -5.243997e+03 -64987.7790 -64592.8359 -1.058417e+06
#> XSkids5 -2.274795e+01 -298.3629 -219.2311 -2.846176e+03
#> XSkids618 -1.691369e+02 -2059.9970 -1387.2823 -1.654364e+04
#> XO(Intercept) -1.603049e+03 -20225.7308 -21948.5227 -3.656782e+05
#> XOeduc -2.022573e+04 -263234.3212 -276185.6292 -4.578532e+06
#> XOexper -2.194852e+04 -276185.6292 -399817.8712 -7.711990e+06
#> XOI(exper^2) -3.656782e+05 -4578531.7428 -7711990.1335 -1.549952e+08
#> sigma 3.640734e+01 320.6567 -175.8686 -4.252300e+03
#> rho -3.733093e+02 -4533.1794 -3949.9510 -6.345921e+04
#> -8.901774e+00 -118.6308 -124.2653 -1.970930e+03
#> sigma rho
#> XS(Intercept) 41.56427 -33.248443 -5.2912530
#> XSnwifeinc 848.93668 -858.653347 -90.1407190
#> XSeduc 477.45835 -387.632441 -66.7398624
#> XSexper 145.17510 -327.096006 -86.3266925
#> XSI(exper^2) -102.13813 -5601.655257 -1691.8385443
#> XSage 1794.64866 -1466.837458 -223.1172273
#> XSkids5 21.30154 -7.499296 0.1008317
#> XSkids618 69.26326 -48.007271 -7.4005910
#> XO(Intercept) 36.40734 -373.309330 -8.9017744
#> XOeduc 320.65666 -4533.179426 -118.6308043
#> XOexper -175.86861 -3949.951008 -124.2652960
#> XOI(exper^2) -4252.30003 -63459.211467 -1970.9298784
#> sigma -1024.21124 -65.572109 52.6782735
#> rho -65.57211 -160.708893 4.7831234
#> 52.67827 4.783123 -7.0565100
#>
#> $fisher_infotS
#> XS(Intercept) XSnwifeinc XSeduc XSexper
#> XS(Intercept) 3.788323e-01 4.300820e-04 -1.126833e-02 -2.446954e-03
#> XSnwifeinc 4.300820e-04 3.465533e-05 -6.662903e-05 -1.401856e-05
#> XSeduc -1.126833e-02 -6.662903e-05 9.595737e-04 4.867902e-05
#> XSexper -2.446954e-03 -1.401856e-05 4.867902e-05 7.451617e-04
#> XSI(exper^2) 9.607302e-05 7.033272e-07 -1.193874e-06 -2.260065e-05
#> XSage -4.879588e-03 -6.887225e-06 1.304668e-05 -4.248193e-05
#> XSkids5 -2.973245e-02 8.714184e-05 -8.552571e-04 -6.644081e-04
#> XSkids618 -1.557904e-02 -1.679540e-05 2.020970e-04 1.386587e-04
#> XO(Intercept) -6.771346e-03 3.006379e-05 6.049990e-04 -3.415546e-04
#> XOeduc 6.723054e-04 -4.547400e-06 -3.944619e-05 1.305610e-05
#> XOexper -4.036150e-04 1.120199e-05 -4.116268e-05 2.708583e-07
#> XOI(exper^2) 1.710373e-05 -4.566285e-07 1.649845e-06 1.444797e-07
#> sigma -6.749056e-04 1.217992e-05 -1.072031e-04 -1.997086e-04
#> rho -1.443353e-03 -8.395560e-05 2.517242e-04 4.972278e-04
#> -1.232842e-02 1.072962e-04 -1.186627e-03 -1.943165e-03
#> XSI(exper^2) XSage XSkids5 XSkids618
#> XS(Intercept) 9.607302e-05 -4.879588e-03 -2.973245e-02 -1.557904e-02
#> XSnwifeinc 7.033272e-07 -6.887225e-06 8.714184e-05 -1.679540e-05
#> XSeduc -1.193874e-06 1.304668e-05 -8.552571e-04 2.020970e-04
#> XSexper -2.260065e-05 -4.248193e-05 -6.644081e-04 1.386587e-04
#> XSI(exper^2) 7.842362e-07 1.522063e-07 1.544261e-05 -1.465862e-06
#> XSage 1.522063e-07 1.123224e-04 8.307862e-04 1.910053e-04
#> XSkids5 1.544261e-05 8.307862e-04 2.268361e-02 1.261896e-03
#> XSkids618 -1.465862e-06 1.910053e-04 1.261896e-03 2.830404e-03
#> XO(Intercept) 1.381655e-05 -2.836660e-06 4.597487e-05 -2.839333e-05
#> XOeduc -4.068438e-07 -3.571677e-06 -5.706934e-05 3.151376e-06
#> XOexper -2.667300e-07 1.527107e-05 2.322106e-04 -4.131314e-07
#> XOI(exper^2) -1.302426e-09 -6.204294e-07 -9.467217e-06 4.312753e-08
#> sigma 4.218231e-06 6.619023e-05 1.133724e-03 6.176752e-06
#> rho -1.815825e-05 -5.140153e-05 -9.770105e-04 -9.749775e-05
#> 2.932867e-05 7.940525e-04 1.368609e-02 -3.915545e-04
#> XO(Intercept) XOeduc XOexper XOI(exper^2)
#> XS(Intercept) -6.771346e-03 6.723054e-04 -4.036150e-04 1.710373e-05
#> XSnwifeinc 3.006379e-05 -4.547400e-06 1.120199e-05 -4.566285e-07
#> XSeduc 6.049990e-04 -3.944619e-05 -4.116268e-05 1.649845e-06
#> XSexper -3.415546e-04 1.305610e-05 2.708583e-07 1.444797e-07
#> XSI(exper^2) 1.381655e-05 -4.068438e-07 -2.667300e-07 -1.302426e-09
#> XSage -2.836660e-06 -3.571677e-06 1.527107e-05 -6.204294e-07
#> XSkids5 4.597487e-05 -5.706934e-05 2.322106e-04 -9.467217e-06
#> XSkids618 -2.839333e-05 3.151376e-06 -4.131314e-07 4.312753e-08
#> XO(Intercept) 1.686422e-02 -1.787067e-03 1.551650e-03 -6.348620e-05
#> XOeduc -1.787067e-03 1.386079e-04 -1.695025e-05 8.238775e-07
#> XOexper 1.551650e-03 -1.695025e-05 -1.884593e-04 6.722046e-06
#> XOI(exper^2) -6.348620e-05 8.238775e-07 6.722046e-06 -2.230080e-07
#> sigma 3.856769e-05 -5.328380e-05 1.462318e-04 -5.809670e-06
#> rho -1.877314e-03 3.509341e-04 -1.221758e-03 5.009474e-05
#> -1.850548e-03 -1.936741e-04 1.627219e-04 -3.880025e-06
#> sigma rho
#> XS(Intercept) -6.749056e-04 -1.443353e-03 -1.232842e-02
#> XSnwifeinc 1.217992e-05 -8.395560e-05 1.072962e-04
#> XSeduc -1.072031e-04 2.517242e-04 -1.186627e-03
#> XSexper -1.997086e-04 4.972278e-04 -1.943165e-03
#> XSI(exper^2) 4.218231e-06 -1.815825e-05 2.932867e-05
#> XSage 6.619023e-05 -5.140153e-05 7.940525e-04
#> XSkids5 1.133724e-03 -9.770105e-04 1.368609e-02
#> XSkids618 6.176752e-06 -9.749775e-05 -3.915545e-04
#> XO(Intercept) 3.856769e-05 -1.877314e-03 -1.850548e-03
#> XOeduc -5.328380e-05 3.509341e-04 -1.936741e-04
#> XOexper 1.462318e-04 -1.221758e-03 1.627219e-04
#> XOI(exper^2) -5.809670e-06 5.009474e-05 -3.880025e-06
#> sigma 1.692617e-03 -2.545606e-04 1.307093e-02
#> rho -2.545606e-04 1.163042e-02 9.733140e-03
#> 1.307093e-02 9.733140e-03 2.610326e-01
#>
#> $prop_sigmatS
#> XS(Intercept) XSnwifeinc XSeduc XSexper XSI(exper^2)
#> 0.6154935149 0.0058868774 0.0309769866 0.0272976502 0.0008855711
#> XSage XSkids5 XSkids618 XO(Intercept) XOeduc
#> 0.0105982265 0.1506108063 0.0532015371 0.1298623109 0.0117731861
#> XOexper XOI(exper^2) sigma rho
#> NaN NaN 0.0411414228 0.1078444373 0.5109135270
#>
#> $level
#> [1] "0" "1"
#>
#> $nObs
#> [1] 753
#>
#> $nParam
#> [1] 15
#>
#> $N0
#> [1] 325
#>
#> $N1
#> [1] 428
#>
#> $NXS
#> [1] 8
#>
#> $NXO
#> [1] 4
#>
#> $df
#> [1] 738
#>
#> $aic
#> [1] 1606.01
#>
#> $bic
#> [1] 1675.371
#>
#> $initial.value
#> XS(Intercept) XSnwifeinc XSeduc XSexper XSI(exper^2)
#> 0.2700735726 -0.0120236370 0.1309039692 0.1233471675 -0.0018870674
#> XSage XSkids5 XSkids618 XO(Intercept) XOeduc
#> -0.0528524416 -0.8683246795 0.0360056106 -0.5781023058 0.1090654909
#> XOexper XOI(exper^2) sigma rho
#> 0.0438873010 -0.0008591134 0.6637994802 0.0486011464 5.0000000000
#>
#> attr(,"class")
#> [1] "HeckmantS" "list"
HeckmanGe(selectEq, outcomeEq, outcomeS, outcomeC, data = Mroz87)
#> $coefficients
#> (Intercept) nwifeinc educ exper I(exper^2)
#> 0.3083446512 -0.0108256215 0.1288475059 0.1213859436 -0.0018564658
#> age kids5 kids618 (Intercept) educ
#> -0.0531769095 -0.8485347564 0.0262167847 -0.8001492248 0.1461329093
#> exper I(exper^2) interceptS educ exper
#> 0.0191510501 -0.0002680912 -0.3911809963 0.0180533864 -0.0199367566
#> interceptC educ exper
#> 1.4413106688 -0.1333918941 0.0064362287
#>
#> $value
#> [1] -818.5952
#>
#> $loglik
#> [1] 818.5952
#>
#> $counts
#> gradient
#> 33
#>
#> $hessian
#> (Intercept) nwifeinc educ exper
#> (Intercept) -398.551080 -8.204773e+03 -4890.50447 -4.066634e+03
#> nwifeinc -8204.773050 -2.259989e+05 -104444.34984 -7.796831e+04
#> educ -4890.504470 -1.044443e+05 -62149.08415 -4.951590e+04
#> exper -4066.633838 -7.796831e+04 -49515.89890 -6.534474e+04
#> I(exper^2) -65274.034940 -1.166368e+06 -785755.22235 -1.359202e+06
#> age -16985.839303 -3.517924e+05 -207425.72688 -1.833351e+05
#> kids5 -97.233757 -1.930903e+03 -1283.49167 -7.581414e+02
#> kids618 -547.060304 -1.144307e+04 -6637.77093 -4.197408e+03
#> (Intercept) -35.797611 -1.113305e+03 -683.32312 -2.304140e+02
#> educ -683.322940 -1.921839e+04 -11563.55198 -5.989302e+03
#> exper -230.419589 -9.306608e+03 -5989.34015 -4.491184e+02
#> I(exper^2) -621.027325 -1.028417e+05 -67999.02688 5.337552e+04
#> interceptS 1.341774 3.226102e+01 -10.44589 -3.650596e+00
#> educ -10.455900 -1.528122e+02 -451.48188 -4.151298e+02
#> exper -3.666178 -5.648848e+02 -415.20649 -1.035252e+01
#> interceptC -11.996483 -6.425779e+02 -229.86996 -5.468326e+01
#> educ -229.855324 -1.024875e+04 -3843.54775 -1.214391e+03
#> exper -54.674544 -4.461255e+03 -1214.44571 -5.547303e-01
#> I(exper^2) age kids5 kids618
#> (Intercept) -6.527403e+04 -1.698584e+04 -97.233757 -547.060304
#> nwifeinc -1.166368e+06 -3.517924e+05 -1930.902865 -11443.067948
#> educ -7.857552e+05 -2.074257e+05 -1283.491668 -6637.770925
#> exper -1.359202e+06 -1.833351e+05 -758.141396 -4197.407696
#> I(exper^2) -3.364361e+07 -3.097877e+06 -8442.699915 -48912.865482
#> age -3.097877e+06 -7.495459e+05 -3362.538412 -21617.569209
#> kids5 -8.442700e+03 -3.362538e+03 -125.705555 -151.913491
#> kids618 -4.891287e+04 -2.161757e+04 -151.913491 -1458.294931
#> (Intercept) -6.247448e+02 -1.355571e+03 -16.922933 -49.785181
#> educ -6.793196e+04 -2.729628e+04 -270.673631 -849.002371
#> exper 5.324676e+04 -7.827096e+03 -135.797924 -389.972049
#> I(exper^2) 2.580724e+06 1.299966e+04 -1455.206897 -4356.606907
#> interceptS 3.447092e+01 7.014813e+01 1.313179 7.361349
#> educ -6.286345e+03 -1.658559e+02 12.926206 77.140279
#> exper 7.440769e+03 1.761447e+02 17.745501 45.822980
#> interceptC 3.089743e+02 -4.852040e+02 -9.548804 -19.574461
#> educ -5.982054e+03 -9.388902e+03 -169.400404 -306.692928
#> exper 6.193264e+03 -9.140686e+02 -61.064351 -107.881597
#> (Intercept) educ exper I(exper^2)
#> (Intercept) -35.79761 -683.3229 -2.304196e+02 -6.210273e+02
#> nwifeinc -1113.30525 -19218.3894 -9.306608e+03 -1.028417e+05
#> educ -683.32312 -11563.5520 -5.989340e+03 -6.799903e+04
#> exper -230.41397 -5989.3019 -4.491184e+02 5.337552e+04
#> I(exper^2) -624.74478 -67931.9582 5.324676e+04 2.580724e+06
#> age -1355.57113 -27296.2827 -7.827096e+03 1.299966e+04
#> kids5 -16.92293 -270.6736 -1.357979e+02 -1.455207e+03
#> kids618 -49.78518 -849.0024 -3.899720e+02 -4.356607e+03
#> (Intercept) -1108.51126 -13823.4203 -1.758825e+04 -3.686964e+05
#> educ -13823.42025 -178878.6520 -2.173520e+05 -4.511726e+06
#> exper -17588.25447 -217352.0356 -3.686497e+05 -9.090340e+06
#> I(exper^2) -368696.35171 -4511725.6079 -9.090340e+06 -2.492372e+08
#> interceptS 23.47509 508.0138 4.770057e+01 -4.000514e+02
#> educ 508.10304 8519.1350 4.522912e+03 6.898470e+04
#> exper 47.52839 4521.4703 -2.567228e+03 -1.678541e+05
#> interceptC -319.65106 -3822.9037 -3.565225e+03 -6.682114e+04
#> educ -3822.93903 -47392.4321 -4.218923e+04 -7.675729e+05
#> exper -3565.20571 -42189.4617 -6.179399e+04 -1.538446e+06
#> interceptS educ exper interceptC
#> (Intercept) 1.341774 -10.45590 -3.666178e+00 -11.996483
#> nwifeinc 32.261016 -152.81216 -5.648848e+02 -642.577852
#> educ -10.445889 -451.48188 -4.152065e+02 -229.869963
#> exper -3.650596 -415.12978 -1.035252e+01 -54.683258
#> I(exper^2) 34.470923 -6286.34465 7.440769e+03 308.974261
#> age 70.148126 -165.85591 1.761447e+02 -485.204008
#> kids5 1.313179 12.92621 1.774550e+01 -9.548804
#> kids618 7.361349 77.14028 4.582298e+01 -19.574461
#> (Intercept) 23.475094 508.10304 4.752839e+01 -319.651057
#> educ 508.013844 8519.13499 4.521470e+03 -3822.903725
#> exper 47.700571 4522.91228 -2.567228e+03 -3565.224912
#> I(exper^2) -400.051421 68984.69771 -1.678541e+05 -66821.139518
#> interceptS -868.818800 -10986.88215 -1.129482e+04 -28.317283
#> educ -10986.882154 -143119.43838 -1.423573e+05 -452.919732
#> exper -11294.815498 -142357.28120 -2.161494e+05 -235.501586
#> interceptC -28.317283 -452.91973 -2.355016e+02 -169.712551
#> educ -452.850421 -7060.81448 -4.304506e+03 -1973.286726
#> exper -235.352522 -4303.37553 -1.838144e+03 -1234.054328
#> educ exper
#> (Intercept) -229.8553 -5.467454e+01
#> nwifeinc -10248.7472 -4.461255e+03
#> educ -3843.5478 -1.214446e+03
#> exper -1214.3908 -5.547303e-01
#> I(exper^2) -5982.0536 6.193264e+03
#> age -9388.9022 -9.140686e+02
#> kids5 -169.4004 -6.106435e+01
#> kids618 -306.6929 -1.078816e+02
#> (Intercept) -3822.9390 -3.565206e+03
#> educ -47392.4321 -4.218946e+04
#> exper -42189.2324 -6.179399e+04
#> I(exper^2) -767572.9156 -1.538446e+06
#> interceptS -452.8504 -2.353525e+02
#> educ -7060.8145 -4.303376e+03
#> exper -4304.5059 -1.838144e+03
#> interceptC -1973.2867 -1.234054e+03
#> educ -23807.0100 -1.413797e+04
#> exper -14137.9709 -1.991912e+04
#>
#> $fisher_infoHG
#> (Intercept) nwifeinc educ exper
#> (Intercept) 2.603676e-01 4.344265e-04 -7.935599e-03 -1.747633e-03
#> nwifeinc 4.344265e-04 3.180715e-05 -7.433471e-05 3.544360e-06
#> educ -7.935599e-03 -7.433471e-05 6.958936e-04 -1.585502e-05
#> exper -1.747633e-03 3.544360e-06 -1.585502e-05 3.646826e-04
#> I(exper^2) 6.802001e-05 2.557944e-07 -2.308316e-07 -1.066377e-05
#> age -3.392467e-03 -6.153114e-06 2.633900e-05 -5.427745e-06
#> kids5 -1.735109e-02 1.295733e-04 -7.182041e-04 -4.650714e-05
#> kids618 -1.014705e-02 -1.380988e-05 1.329252e-04 9.090650e-05
#> (Intercept) 2.315337e-02 1.993647e-03 -6.457762e-03 1.238171e-03
#> educ -3.237517e-04 -4.211509e-05 1.250750e-04 -6.410923e-05
#> exper -1.488057e-03 -1.160957e-04 3.835710e-04 -4.169231e-05
#> I(exper^2) 4.009754e-05 2.767688e-06 -9.174747e-06 9.661756e-07
#> interceptS -7.707261e-03 -6.150549e-04 1.971320e-03 -3.873692e-05
#> educ 8.633239e-04 6.585313e-05 -2.129236e-04 5.108854e-06
#> exper -1.430005e-04 -1.027442e-05 3.330627e-05 -3.991563e-06
#> interceptC 1.186882e-02 -4.880488e-04 1.524963e-03 -2.648500e-03
#> educ -1.537696e-03 -5.174707e-05 1.571378e-04 1.980368e-04
#> exper -1.708242e-03 -6.402566e-05 2.194319e-04 -6.321165e-06
#> I(exper^2) age kids5 kids618
#> (Intercept) 6.802001e-05 -3.392467e-03 -1.735109e-02 -1.014705e-02
#> nwifeinc 2.557944e-07 -6.153114e-06 1.295733e-04 -1.380988e-05
#> educ -2.308316e-07 2.633900e-05 -7.182041e-04 1.329252e-04
#> exper -1.066377e-05 -5.427745e-06 -4.650714e-05 9.090650e-05
#> I(exper^2) 3.721558e-07 -4.997887e-07 1.643267e-06 -9.428348e-07
#> age -4.997887e-07 7.158041e-05 4.553776e-04 1.250069e-04
#> kids5 1.643267e-06 4.553776e-04 1.475623e-02 5.743327e-04
#> kids618 -9.428348e-07 1.250069e-04 5.743327e-04 1.848135e-03
#> (Intercept) 5.139493e-06 -6.578000e-05 1.581651e-02 8.984588e-04
#> educ 5.822582e-07 6.127358e-06 -1.759993e-04 -4.502597e-05
#> exper -8.686285e-07 9.034131e-07 -1.047899e-03 -3.011847e-05
#> I(exper^2) 2.354161e-08 -1.147500e-07 2.422392e-05 5.887100e-07
#> interceptS -9.033616e-06 -9.475953e-06 -6.006745e-03 -1.243908e-04
#> educ 9.209892e-07 7.386249e-07 6.408295e-04 1.106387e-05
#> exper -6.598222e-08 4.462253e-07 -8.649722e-05 -2.299114e-06
#> interceptC 4.985871e-05 7.525703e-05 3.803715e-03 -2.811501e-03
#> educ -4.857417e-06 -1.660003e-05 -1.265148e-03 2.031383e-04
#> exper -1.094985e-06 1.545757e-05 -4.817376e-04 1.685328e-05
#> (Intercept) educ exper I(exper^2)
#> (Intercept) 2.315337e-02 -3.237517e-04 -1.488057e-03 4.009754e-05
#> nwifeinc 1.993647e-03 -4.211509e-05 -1.160957e-04 2.767688e-06
#> educ -6.457762e-03 1.250750e-04 3.835710e-04 -9.174747e-06
#> exper 1.238171e-03 -6.410923e-05 -4.169231e-05 9.661756e-07
#> I(exper^2) 5.139493e-06 5.822582e-07 -8.686285e-07 2.354161e-08
#> age -6.578000e-05 6.127358e-06 9.034131e-07 -1.147500e-07
#> kids5 1.581651e-02 -1.759993e-04 -1.047899e-03 2.422392e-05
#> kids618 8.984588e-04 -4.502597e-05 -3.011847e-05 5.887100e-07
#> (Intercept) 5.088791e-01 -1.503322e-02 -2.610571e-02 6.215133e-04
#> educ -1.503322e-02 6.028516e-04 6.114560e-04 -1.469930e-05
#> exper -2.610571e-02 6.114560e-04 1.539787e-03 -3.690323e-05
#> I(exper^2) 6.215133e-04 -1.469930e-05 -3.690323e-05 8.974179e-07
#> interceptS -1.270050e-01 3.238028e-03 6.721062e-03 -1.609833e-04
#> educ 1.347412e-02 -3.312055e-04 -7.327796e-04 1.753561e-05
#> exper -2.287959e-03 5.816112e-05 1.276389e-04 -3.067672e-06
#> interceptC -3.150998e-01 1.321302e-02 1.270930e-02 -3.038808e-04
#> educ 6.903637e-03 -6.585675e-04 3.720231e-05 -1.768544e-07
#> exper -1.299927e-02 3.324039e-04 7.139309e-04 -1.782301e-05
#> interceptS educ exper interceptC
#> (Intercept) -7.707261e-03 8.633239e-04 -1.430005e-04 1.186882e-02
#> nwifeinc -6.150549e-04 6.585313e-05 -1.027442e-05 -4.880488e-04
#> educ 1.971320e-03 -2.129236e-04 3.330627e-05 1.524963e-03
#> exper -3.873692e-05 5.108854e-06 -3.991563e-06 -2.648500e-03
#> I(exper^2) -9.033616e-06 9.209892e-07 -6.598222e-08 4.985871e-05
#> age -9.475953e-06 7.386249e-07 4.462253e-07 7.525703e-05
#> kids5 -6.006745e-03 6.408295e-04 -8.649722e-05 3.803715e-03
#> kids618 -1.243908e-04 1.106387e-05 -2.299114e-06 -2.811501e-03
#> (Intercept) -1.270050e-01 1.347412e-02 -2.287959e-03 -3.150998e-01
#> educ 3.238028e-03 -3.312055e-04 5.816112e-05 1.321302e-02
#> exper 6.721062e-03 -7.327796e-04 1.276389e-04 1.270930e-02
#> I(exper^2) -1.609833e-04 1.753561e-05 -3.067672e-06 -3.038808e-04
#> interceptS 8.157542e-02 -7.135222e-03 4.050405e-04 4.977729e-02
#> educ -7.135222e-03 6.688778e-04 -6.405069e-05 -5.200294e-03
#> exper 4.050405e-04 -6.405069e-05 2.542208e-05 1.171812e-03
#> interceptC 4.977729e-02 -5.200294e-03 1.171812e-03 4.928443e-01
#> educ 1.238237e-03 -1.463538e-04 -3.415627e-06 -3.191357e-02
#> exper 4.089712e-03 -4.253878e-04 6.471656e-05 4.999540e-03
#> educ exper
#> (Intercept) -1.537696e-03 -1.708242e-03
#> nwifeinc -5.174707e-05 -6.402566e-05
#> educ 1.571378e-04 2.194319e-04
#> exper 1.980368e-04 -6.321165e-06
#> I(exper^2) -4.857417e-06 -1.094985e-06
#> age -1.660003e-05 1.545757e-05
#> kids5 -1.265148e-03 -4.817376e-04
#> kids618 2.031383e-04 1.685328e-05
#> (Intercept) 6.903637e-03 -1.299927e-02
#> educ -6.585675e-04 3.324039e-04
#> exper 3.720231e-05 7.139309e-04
#> I(exper^2) -1.768544e-07 -1.782301e-05
#> interceptS 1.238237e-03 4.089712e-03
#> educ -1.463538e-04 -4.253878e-04
#> exper -3.415627e-06 6.471656e-05
#> interceptC -3.191357e-02 4.999540e-03
#> educ 2.838775e-03 4.531140e-05
#> exper 4.531140e-05 5.362827e-04
#>
#> $prop_sigmaHG
#> (Intercept) nwifeinc educ exper I(exper^2) age
#> 0.5102623139 0.0056397828 0.0263797951 0.0190966653 0.0006100457 0.0084605205
#> kids5 kids618 (Intercept) educ exper I(exper^2)
#> 0.1214752278 0.0429899420 0.7133576442 0.0245530362 0.0392401172 0.0009473214
#> interceptS educ exper interceptC educ exper
#> 0.2856141132 0.0258626711 0.0050420311 0.7020287094 0.0532801600 0.0231577786
#>
#> $level
#> [1] "0" "1"
#>
#> $nObs
#> [1] 753
#>
#> $nParam
#> [1] 18
#>
#> $N0
#> [1] 325
#>
#> $N1
#> [1] 428
#>
#> $NXS
#> [1] 8
#>
#> $NXO
#> [1] 4
#>
#> $df
#> [1] 735
#>
#> $aic
#> [1] 1673.19
#>
#> $bic
#> [1] 1756.424
#>
#> $initial.value
#> (Intercept) nwifeinc educ exper I(exper^2)
#> 0.2700735726 -0.0120236370 0.1309039692 0.1233471675 -0.0018870674
#> age kids5 kids618 (Intercept) educ
#> -0.0528524416 -0.8683246795 0.0360056106 -0.5781023058 0.1090654909
#> exper I(exper^2) interceptS educ exper
#> 0.0438873010 -0.0008591134 0.6637994802 1.0000000000 1.0000000000
#> interceptC educ exper
#> 0.0486011464 0.0000000000 0.0000000000
#>
#> $NE
#> [1] 3
#>
#> $NV
#> [1] 3
#>
#> attr(,"class")
#> [1] "HeckmanGe" "list"