Also available in Stata and Python versions
Load libraries
library(wooldridge)
library(stargazer)
library(AER)
library(mfx)
library(sampleSelection)Wage Offer Equation for Married Women
summary(OLS <- lm(lwage ~ educ + exper + expersq, data=mroz))##
## Call:
## lm(formula = lwage ~ educ + exper + expersq, data = mroz)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.08404 -0.30627 0.04952 0.37498 2.37115
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.5220406 0.1986321 -2.628 0.00890 **
## educ 0.1074896 0.0141465 7.598 1.94e-13 ***
## exper 0.0415665 0.0131752 3.155 0.00172 **
## expersq -0.0008112 0.0003932 -2.063 0.03974 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6664 on 424 degrees of freedom
## (325 observations deleted due to missingness)
## Multiple R-squared: 0.1568, Adjusted R-squared: 0.1509
## F-statistic: 26.29 on 3 and 424 DF, p-value: 1.302e-15summary(Heckman <-selection(inlf ~ nwifeinc + educ + exper + expersq + age + kidslt6 + kidsge6, lwage ~ educ + exper + expersq, data=mroz, method="2step"))## --------------------------------------------
## Tobit 2 model (sample selection model)
## 2-step Heckman / heckit estimation
## 753 observations (325 censored and 428 observed)
## 15 free parameters (df = 739)
## Probit selection equation:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.270077 0.508593 0.531 0.59556
## nwifeinc -0.012024 0.004840 -2.484 0.01320 *
## educ 0.130905 0.025254 5.183 2.81e-07 ***
## exper 0.123348 0.018716 6.590 8.34e-11 ***
## expersq -0.001887 0.000600 -3.145 0.00173 **
## age -0.052853 0.008477 -6.235 7.61e-10 ***
## kidslt6 -0.868328 0.118522 -7.326 6.21e-13 ***
## kidsge6 0.036005 0.043477 0.828 0.40786
## Outcome equation:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.5781032 0.3050062 -1.895 0.05843 .
## educ 0.1090655 0.0155230 7.026 4.83e-12 ***
## exper 0.0438873 0.0162611 2.699 0.00712 **
## expersq -0.0008591 0.0004389 -1.957 0.05068 .
## Multiple R-Squared:0.1569, Adjusted R-Squared:0.149
## Error terms:
## Estimate Std. Error t value Pr(>|t|)
## invMillsRatio 0.03226 0.13362 0.241 0.809
## sigma 0.66363 NA NA NA
## rho 0.04861 NA NA NA
## --------------------------------------------summary(HeckmanFull <-selection(inlf ~ nwifeinc + educ + exper + expersq + age + kidslt6 + kidsge6, lwage ~ nwifeinc + educ + exper + expersq + age + kidslt6 + kidsge6, data=mroz, method="2step"))## --------------------------------------------
## Tobit 2 model (sample selection model)
## 2-step Heckman / heckit estimation
## 753 observations (325 censored and 428 observed)
## 19 free parameters (df = 735)
## Probit selection equation:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.270077 0.508593 0.531 0.59556
## nwifeinc -0.012024 0.004840 -2.484 0.01320 *
## educ 0.130905 0.025254 5.183 2.82e-07 ***
## exper 0.123348 0.018716 6.590 8.37e-11 ***
## expersq -0.001887 0.000600 -3.145 0.00173 **
## age -0.052853 0.008477 -6.235 7.63e-10 ***
## kidslt6 -0.868328 0.118522 -7.326 6.24e-13 ***
## kidsge6 0.036005 0.043477 0.828 0.40786
## Outcome equation:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.5602852 0.4587672 -1.221 0.222370
## nwifeinc 0.0038434 0.0044919 0.856 0.392492
## educ 0.1187171 0.0340507 3.486 0.000518 ***
## exper 0.0598358 0.0336730 1.777 0.075987 .
## expersq -0.0010523 0.0006381 -1.649 0.099566 .
## age -0.0111580 0.0134792 -0.828 0.408054
## kidslt6 -0.1880451 0.2308275 -0.815 0.415533
## kidsge6 -0.0122255 0.0296063 -0.413 0.679775
## Multiple R-Squared:0.1649, Adjusted R-Squared:0.1489
## Error terms:
## Estimate Std. Error t value Pr(>|t|)
## invMillsRatio 0.2885 0.4636 0.622 0.534
## sigma 0.6896 NA NA NA
## rho 0.4183 NA NA NA
## --------------------------------------------summary(OLSfull <- lm(lwage ~ educ + exper + expersq + nwifeinc + age + kidslt6 + kidsge6, data=mroz))##
## Call:
## lm(formula = lwage ~ educ + exper + expersq + nwifeinc + age +
## kidslt6 + kidsge6, data = mroz)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.0827 -0.3160 0.0532 0.3810 2.3551
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.3579972 0.3182963 -1.125 0.26135
## educ 0.0998844 0.0150975 6.616 1.13e-10 ***
## exper 0.0407097 0.0133723 3.044 0.00248 **
## expersq -0.0007473 0.0004018 -1.860 0.06358 .
## nwifeinc 0.0056942 0.0033195 1.715 0.08701 .
## age -0.0035204 0.0054145 -0.650 0.51593
## kidslt6 -0.0558725 0.0886034 -0.631 0.52865
## kidsge6 -0.0176484 0.0278910 -0.633 0.52723
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6667 on 420 degrees of freedom
## (325 observations deleted due to missingness)
## Multiple R-squared: 0.1641, Adjusted R-squared: 0.1502
## F-statistic: 11.78 on 7 and 420 DF, p-value: 1.023e-13stargazer(OLS, Heckman, HeckmanFull,OLSfull, no.space=TRUE, type="text", title = "Table 19.1 Wage Offer Equation for Married Women")##
## Table 19.1 Wage Offer Equation for Married Women
## ===============================================================================================
## Dependent variable:
## ---------------------------------------------------------------------------
## lwage
## OLS selection OLS
## (1) (2) (3) (4)
## -----------------------------------------------------------------------------------------------
## nwifeinc 0.004 0.006*
## (0.004) (0.003)
## educ 0.107*** 0.109*** 0.119*** 0.100***
## (0.014) (0.016) (0.034) (0.015)
## exper 0.042*** 0.044*** 0.060* 0.041***
## (0.013) (0.016) (0.034) (0.013)
## expersq -0.001** -0.001* -0.001* -0.001*
## (0.0004) (0.0004) (0.001) (0.0004)
## age -0.011 -0.004
## (0.013) (0.005)
## kidslt6 -0.188 -0.056
## (0.231) (0.089)
## kidsge6 -0.012 -0.018
## (0.030) (0.028)
## Constant -0.522*** -0.578* -0.560 -0.358
## (0.199) (0.305) (0.459) (0.318)
## -----------------------------------------------------------------------------------------------
## Observations 428 753 753 428
## R2 0.157 0.164
## Adjusted R2 0.151 0.150
## rho 0.049 0.418
## Inverse Mills Ratio 0.032 (0.134) 0.288 (0.464)
## Residual Std. Error 0.666 (df = 424) 0.667 (df = 420)
## F Statistic 26.286*** (df = 3; 424) 11.779*** (df = 7; 420)
## ===============================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Education Endogenous and Sample Selection
summary(Probit <- glm(inlf ~ exper + expersq + nwifeinc + age + kidslt6 + kidsge6 + motheduc
+ fatheduc + huseduc, data=mroz, family=binomial(link="probit")))##
## Call:
## glm(formula = inlf ~ exper + expersq + nwifeinc + age + kidslt6 +
## kidsge6 + motheduc + fatheduc + huseduc, family = binomial(link = "probit"),
## data = mroz)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.2193 -0.9413 0.4550 0.8604 2.2870
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.1466683 0.4916633 2.332 0.01969 *
## exper 0.1285092 0.0185409 6.931 4.17e-12 ***
## expersq -0.0019474 0.0005935 -3.281 0.00103 **
## nwifeinc -0.0074295 0.0050157 -1.481 0.13854
## age -0.0527656 0.0085094 -6.201 5.62e-10 ***
## kidslt6 -0.8149250 0.1163696 -7.003 2.51e-12 ***
## kidsge6 0.0241509 0.0436677 0.553 0.58022
## motheduc 0.0295320 0.0186856 1.580 0.11400
## fatheduc 0.0133487 0.0178497 0.748 0.45456
## huseduc 0.0161394 0.0197305 0.818 0.41336
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1029.75 on 752 degrees of freedom
## Residual deviance: 822.64 on 743 degrees of freedom
## AIC: 842.64
##
## Number of Fisher Scoring iterations: 4linearHypothesis(Probit, c("motheduc = 0", "fatheduc =0", "huseduc =0"))## Linear hypothesis test
##
## Hypothesis:
## motheduc = 0
## fatheduc = 0
## huseduc = 0
##
## Model 1: restricted model
## Model 2: inlf ~ exper + expersq + nwifeinc + age + kidslt6 + kidsge6 +
## motheduc + fatheduc + huseduc
##
## Res.Df Df Chisq Pr(>Chisq)
## 1 746
## 2 743 3 8.0245 0.04551 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1IMR <- dnorm(predict(Probit))/pnorm(predict(Probit))
wIMR <- ivreg(lwage ~ educ + exper + expersq + IMR | exper + expersq + IMR +nwifeinc + age + kidslt6 + kidsge6 + motheduc + fatheduc + huseduc, data = mroz)
woutIMR <- ivreg(lwage ~ educ + exper + expersq | exper + expersq + nwifeinc + age + kidslt6 + kidsge6 + motheduc + fatheduc + huseduc, data = mroz)
stargazer(wIMR, woutIMR, no.space=TRUE, type="text")##
## =====================================================
## Dependent variable:
## ---------------------------------
## lwage
## (1) (2)
## -----------------------------------------------------
## educ 0.088*** 0.087***
## (0.021) (0.021)
## exper 0.046*** 0.043***
## (0.017) (0.013)
## expersq -0.001** -0.001**
## (0.0004) (0.0004)
## IMR 0.040
## (0.133)
## Constant -0.325 -0.270
## (0.333) (0.280)
## -----------------------------------------------------
## Observations 428 428
## R2 0.153 0.153
## Adjusted R2 0.145 0.147
## Residual Std. Error 0.669 (df = 423) 0.668 (df = 424)
## =====================================================
## Note: *p<0.1; **p<0.05; ***p<0.01wIMR2 <- ivreg(lwage ~ educ + exper + expersq + IMR | exper + expersq + IMR + motheduc + fatheduc + huseduc, data = mroz)
woutIMR2 <- ivreg(lwage ~ educ + exper + expersq | exper + expersq + motheduc + fatheduc + huseduc, data = mroz)
stargazer(wIMR2, woutIMR2, no.space=TRUE, type="text")##
## =====================================================
## Dependent variable:
## ---------------------------------
## lwage
## (1) (2)
## -----------------------------------------------------
## educ 0.081*** 0.080***
## (0.022) (0.022)
## exper 0.046*** 0.043***
## (0.017) (0.013)
## expersq -0.001** -0.001**
## (0.0004) (0.0004)
## IMR 0.036
## (0.134)
## Constant -0.234 -0.187
## (0.337) (0.285)
## -----------------------------------------------------
## Observations 428 428
## R2 0.150 0.150
## Adjusted R2 0.142 0.144
## Residual Std. Error 0.670 (df = 423) 0.669 (df = 424)
## =====================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Wage Offer Equation for Married Women
summary(Tobit <- tobit(inlf ~ nwifeinc + motheduc + fatheduc + huseduc + exper + expersq + age + kidslt6 + kidsge6 , data=mroz, left = 0 ))##
## Call:
## tobit(formula = inlf ~ nwifeinc + motheduc + fatheduc + huseduc +
## exper + expersq + age + kidslt6 + kidsge6, left = 0, data = mroz)
##
## Observations:
## Total Left-censored Uncensored Right-censored
## 753 325 428 0
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.7832485 0.2644459 2.962 0.00306 **
## nwifeinc -0.0042396 0.0027476 -1.543 0.12283
## motheduc 0.0134540 0.0101337 1.328 0.18429
## fatheduc 0.0082528 0.0096746 0.853 0.39364
## huseduc 0.0112281 0.0105784 1.061 0.28850
## exper 0.0779554 0.0104014 7.495 6.64e-14 ***
## expersq -0.0012600 0.0003276 -3.847 0.00012 ***
## age -0.0287968 0.0045577 -6.318 2.65e-10 ***
## kidslt6 -0.4729478 0.0657462 -7.194 6.31e-13 ***
## kidsge6 0.0216831 0.0233501 0.929 0.35309
## Log(scale) -0.3687450 0.0386299 -9.546 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Scale: 0.6916
##
## Gaussian distribution
## Number of Newton-Raphson Iterations: 4
## Log-likelihood: -690.1 on 11 Df
## Wald-statistic: 201.6 on 9 Df, p-value: < 2.22e-16v2 <- resid(Tobit)
Heckman <-selection(inlf ~ nwifeinc + educ + exper + expersq + age + kidslt6 + kidsge6, lwage ~ educ + exper + expersq + v2, data=mroz, method="2step")
OLSr <- lm(lwage ~ educ + exper + expersq + v2, data=mroz)
OLSur <- lm(lwage ~ educ + exper + expersq + +nwifeinc + age + kidslt6 + kidsge6, data=mroz)
stargazer(Heckman, OLSr, OLSur, no.space=TRUE, type="text")##
## ==================================================================================
## Dependent variable:
## --------------------------------------------------------------
## lwage
## selection OLS
## (1) (2) (3)
## ----------------------------------------------------------------------------------
## educ 0.103*** 0.108*** 0.100***
## (0.020) (0.014) (0.015)
## exper 0.046*** 0.046*** 0.041***
## (0.017) (0.017) (0.013)
## expersq -0.001** -0.001** -0.001*
## (0.0005) (0.0005) (0.0004)
## v2 0.163 0.053
## (0.325) (0.128)
## nwifeinc 0.006*
## (0.003)
## age -0.004
## (0.005)
## kidslt6 -0.056
## (0.089)
## kidsge6 -0.018
## (0.028)
## Constant -0.508 -0.589** -0.358
## (0.336) (0.255) (0.318)
## ----------------------------------------------------------------------------------
## Observations 753 428 428
## R2 0.157 0.164
## Adjusted R2 0.149 0.150
## rho -0.186
## Inverse Mills Ratio -0.125 (0.340)
## Residual Std. Error 0.667 (df = 423) 0.667 (df = 420)
## F Statistic 19.720*** (df = 4; 423) 11.779*** (df = 7; 420)
## ==================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01