Lab7: Nonlinear Regression and OB Decomposition in R

Lab7: Nonlinear Regression and OBDecomposition in R

Introduction to Econometrics,Fall 2021

Feifan Wang

Nanjing University

11/04/2021

Feifan Wang (Nanjing University) Lab7: Nonlinear Regression and OB Decomposition in R11/04/2021 1 / 44

1 Introduction

2 Probit Regression

3 Logit Regression

4 Oaxaca-Blinder Decomposition


library(tidyverse)library(magrittr)library(haven)library(ggplot2)library(AER) # package of Applied Econonometrics in Rlibrary(stargazer)


Section 1

Introduction


Regression with a Binary Dependent Variable

Type Population regression function(I) LPM 𝑃(𝑌𝑖 = 1|𝑋𝑖) = 𝛽0 + 𝛽1𝑋𝑖 + 𝑢𝑖(II) Probit 𝐸(𝑌 |𝑋) = 𝑃 (𝑌 = 1|𝑋) = Φ(𝛽0 + 𝛽1𝑋)(III) Logit 𝐸(𝑌 |𝑋) = 𝑃 (𝑌 = 1|𝑋) = 𝐹(𝛽0 + 𝛽1𝑋)


Data: HMDAFollowing the book, we start by loading the data set HMDA whichprovides data that relate to mortgage applications filed in Boston inthe year of 1990.

data(HMDA)head(HMDA)

## deny pirat hirat lvrat chist mhist phist unemp selfemp insurance condomin## 1 no 0.221 0.221 0.8000000 5 2 no 3.9 no no no## 2 no 0.265 0.265 0.9218750 2 2 no 3.2 no no no## 3 no 0.372 0.248 0.9203980 1 2 no 3.2 no no no## 4 no 0.320 0.250 0.8604651 1 2 no 4.3 no no no## 5 no 0.360 0.350 0.6000000 1 1 no 3.2 no no no## 6 no 0.240 0.170 0.5105263 1 1 no 3.9 no no no## afam single hschool## 1 no no yes## 2 no yes yes## 3 no no yes## 4 no no yes## 5 no no yes## 6 no no yes


Data: HMDAstr(HMDA)

## 'data.frame': 2380 obs. of 14 variables:## $ deny : Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 2 1 ...## $ pirat : num 0.221 0.265 0.372 0.32 0.36 ...## $ hirat : num 0.221 0.265 0.248 0.25 0.35 ...## $ lvrat : num 0.8 0.922 0.92 0.86 0.6 ...## $ chist : Factor w/ 6 levels "1","2","3","4",..: 5 2 1 1 1 1 1 2 2 2 ...## $ mhist : Factor w/ 4 levels "1","2","3","4": 2 2 2 2 1 1 2 2 2 1 ...## $ phist : Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 1 1 ...## $ unemp : num 3.9 3.2 3.2 4.3 3.2 ...## $ selfemp : Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 1 1 ...## $ insurance: Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 2 1 ...## $ condomin : Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 2 1 1 1 ...## $ afam : Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 1 1 ...## $ single : Factor w/ 2 levels "no","yes": 1 2 1 1 1 1 2 1 1 2 ...## $ hschool : Factor w/ 2 levels "no","yes": 2 2 2 2 2 2 2 2 2 2 ...

summary(HMDA)

## deny pirat hirat lvrat chist## no :2095 Min. :0.0000 Min. :0.0000 Min. :0.0200 1:1353## yes: 285 1st Qu.:0.2800 1st Qu.:0.2140 1st Qu.:0.6527 2: 441## Median :0.3300 Median :0.2600 Median :0.7795 3: 126## Mean :0.3308 Mean :0.2553 Mean :0.7378 4: 77## 3rd Qu.:0.3700 3rd Qu.:0.2988 3rd Qu.:0.8685 5: 182## Max. :3.0000 Max. :3.0000 Max. :1.9500 6: 201## mhist phist unemp selfemp insurance condomin## 1: 747 no :2205 Min. : 1.800 no :2103 no :2332 no :1694## 2:1571 yes: 175 1st Qu.: 3.100 yes: 277 yes: 48 yes: 686## 3: 41 Median : 3.200## 4: 21 Mean : 3.774## 3rd Qu.: 3.900## Max. :10.600## afam single hschool## no :2041 no :1444 no : 39## yes: 339 yes: 936 yes:2341########

#HMDA<- HMDA %>% filter(pirat<=1)


Data: HMDA

The variable we are interested in is deny, an indicator for whether anapplicant’s mortgage application has been accepted (deny = "no")or denied (deny = "yes").

A regressor that ought to have power in explaining whether amortgage application has been denied is pirat, which is the ratio ofthe payment to household income.

𝑑𝑒𝑛𝑦 = 𝛽0 + 𝛽1 × 𝑃/𝐼 𝑟𝑎𝑡𝑖𝑜 + 𝑢 (1)


Data: HMDA

The variable we are interested in is deny, an indicator for whether anapplicant’s mortgage application has been accepted (deny = "no")or denied (deny = "yes").A regressor that ought to have power in explaining whether amortgage application has been denied is pirat, which is the ratio ofthe payment to household income.

𝑑𝑒𝑛𝑦 = 𝛽0 + 𝛽1 × 𝑃/𝐼 𝑟𝑎𝑡𝑖𝑜 + 𝑢 (1)


Data: HMDA# convert 'deny' to numericHMDA$deny <- as.numeric(HMDA$deny)-1

# estimate a simple linear probability modeldenymod1 <- lm(deny ~ pirat, data = HMDA)summary(denymod1)

#### Call:## lm(formula = deny ~ pirat, data = HMDA)#### Residuals:## Min 1Q Median 3Q Max## -0.73070 -0.13736 -0.11322 -0.07097 1.05577#### Coefficients:## Estimate Std. Error t value Pr(>|t|)## (Intercept) -0.07991 0.02116 -3.777 0.000163 ***## pirat 0.60353 0.06084 9.920 < 2e-16 ***## ---## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#### Residual standard error: 0.3183 on 2378 degrees of freedom## Multiple R-squared: 0.03974, Adjusted R-squared: 0.03933## F-statistic: 98.41 on 1 and 2378 DF, p-value: < 2.2e-16Feifan Wang (Nanjing University) Lab7: Nonlinear Regression and OB Decomposition in R11/04/2021 9 / 44

Predicted Probability

# plot the dataplot(x = HMDA$pirat,

y = HMDA$deny,xlab = "P/I ratio",ylab = "Deny",pch = 20,ylim = c(-0.4, 1.4),cex.main = 0.8)

# add horizontal dashed lines and textabline(h = 1, lty = 2, col = "darkred")abline(h = 0, lty = 2, col = "darkred")text(2.5, 0.9, cex = 0.8, "Mortgage denied")text(2.5, -0.1, cex= 0.8, "Mortgage approved")

# add the estimated regression lineabline(denymod1,

lwd = 1.8,col = "red")



0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0

0.5

1.0

Scatterplot Mortgage Application Denial and the Payment−to−Income Ratio

P/I ratio

Den

y

Mortgage denied

Mortgage approved


Linear probabilty model: Black v.s White

# estimate a simple linear probability modeldenymod2 <- lm(deny ~ pirat+afam,data = HMDA)coeftest(denymod2, vcov. = vcovHC, type = "HC1")

#### t test of coefficients:#### Estimate Std. Error t value Pr(>|t|)## (Intercept) -0.090514 0.028600 -3.1649 0.001571 **## pirat 0.559195 0.088666 6.3067 3.387e-10 ***## afamyes 0.177428 0.024946 7.1124 1.502e-12 ***## ---## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Section 2

Probit Regression


Probit Regression

In Probit regression, the cumulative standard normal distributionfunction Φ(⋅) is used to model the regression function when thedependent variable is binary

𝐸(𝑌 |𝑋) = 𝑃 (𝑌 = 1|𝑋) = Φ(𝛽0 + 𝛽1𝑋)


Probit Regression

denyprobit <- glm(deny ~ pirat,family = binomial(link = "probit"),data = HMDA)

coeftest(denyprobit, vcov. = vcovHC, type = "HC1")

#### z test of coefficients:#### Estimate Std. Error z value Pr(>|z|)## (Intercept) -2.19415 0.18901 -11.6087 < 2.2e-16 ***## pirat 2.96787 0.53698 5.5269 3.259e-08 ***## ---## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1



# plot dataplot(x = HMDA$pirat,

y = HMDA$deny,main = "Probit Model of the Probability of Denial, Given P/I Ratio",xlab = "P/I ratio",ylab = "Deny",pch = 20,ylim = c(-0.4, 1.4),cex.main = 0.85)


# add estimated regression linex <- seq(0, 3, 0.01)y <- predict(denyprobit, list(pirat = x), type = "response")

lines(x, y, lwd = 1.5, col = "steelblue")



0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0

0.5

1.0

Probit Model of the Probability of Denial, Given P/I Ratio

P/I ratio

Den

y

Mortgage denied

Mortgage approved


Prediction differences

# 1. compute predictions for P/I ratio = 0.3, 0.4predictions <- predict(denyprobit,

newdata = data.frame("pirat" = c(0.3, 0.4)),type = "response")

# 2. Compute difference in probabilitiesdiff(predictions)

## 2## 0.06081433


Probit Regression:Black v.s White

denyprobit2 <- glm(deny ~ pirat + afam,family = binomial(link = "probit"),data = HMDA)

coeftest(denyprobit2, vcov. = vcovHC, type = "HC1")

#### z test of coefficients:#### Estimate Std. Error z value Pr(>|z|)## (Intercept) -2.258787 0.176608 -12.7898 < 2.2e-16 ***## pirat 2.741779 0.497673 5.5092 3.605e-08 ***## afamyes 0.708155 0.083091 8.5227 < 2.2e-16 ***## ---## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Black v.s White

# 1. compute predictions for P/I ratio = 0.3predictions <- predict(denyprobit2,

newdata = data.frame("afam" = c("no", "yes"),"pirat" = c(0.3, 0.3)),type = "response")

# 2. compute difference in probabilitiesdiff(predictions)

## 2## 0.1578117


Section 3

Logit Regression


Logit Regression

In Logit regression, the cumulative logistic distribution function 𝐹(⋅)is used to model the regression function when the dependent variableis binary

𝐸(𝑌 |𝑋) = 𝑃(𝑌 = 1|𝑋) = 𝐹(𝛽0 + 𝛽1𝑋)


Logit Regression

denylogit <- glm(deny ~ pirat,family = binomial(link = "logit"),data = HMDA)

coeftest(denylogit, vcov. = vcovHC, type = "HC1")

#### z test of coefficients:#### Estimate Std. Error z value Pr(>|z|)## (Intercept) -4.02843 0.35898 -11.2218 < 2.2e-16 ***## pirat 5.88450 1.00015 5.8836 4.014e-09 ***## ---## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Predicted Probability# plot dataplot(x = HMDA$pirat,

y = HMDA$deny,main = "Probit and Logit Models Model of the Probability of Denial, Given P/I Ratio",xlab = "P/I ratio",ylab = "Deny",pch = 20,ylim = c(-0.4, 1.4),cex.main = 0.9)


# add estimated regression line of Probit and Logit modelsx <- seq(0, 3, 0.01)y_probit <- predict(denyprobit, list(pirat = x), type = "response")y_logit <- predict(denylogit, list(pirat = x), type = "response")

lines(x, y_probit, lwd = 1.5, col = "steelblue")lines(x, y_logit, lwd = 1.5, col = "black", lty = 2)

# add a legendlegend("topleft",

horiz = TRUE,legend = c("Probit", "Logit"),col = c("steelblue", "black"),lty = c(1, 2))



0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0

0.5

1.0

Probit and Logit Models Model of the Probability of Denial, Given P/I Ratio

P/I ratio

Den

y

Mortgage denied

Mortgage approved

Probit Logit


Logit Regression: White vs Black

# estimate a Logit regression with multiple regressorsdenylogit2 <- glm(deny ~ pirat + afam,

family = binomial(link = "logit"),data = HMDA)

coeftest(denylogit2, vcov. = vcovHC, type = "HC1")

#### z test of coefficients:#### Estimate Std. Error z value Pr(>|z|)## (Intercept) -4.12556 0.34597 -11.9245 < 2.2e-16 ***## pirat 5.37036 0.96376 5.5723 2.514e-08 ***## afamyes 1.27278 0.14616 8.7081 < 2.2e-16 ***## ---## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Logit Regression: White vs Black

# 1. compute predictions for P/I ratio = 0.3predictions <- predict(denylogit2,

newdata = data.frame("afam" = c("no", "yes"),"pirat" = c(0.3, 0.3)),type = "response")

predictions

## 1 2## 0.07485143 0.22414592

# 2. Compute difference in probabilitiesdiff(predictions)

## 2## 0.1492945


Table 11.2

# estimate all 6 models for the denial probability

lpm_HMDA <- lm(deny ~ afam + pirat + hirat + lvrat + chist + mhist + phist+ insurance + selfemp, data = HMDA)

logit_HMDA <- glm(deny ~ afam + pirat + hirat + lvrat + chist + mhist + phist+ insurance + selfemp,family = binomial(link = "logit"),data = HMDA)

probit_HMDA_1 <- glm(deny ~ afam + pirat + hirat + lvrat + chist + mhist + phist+ insurance + selfemp,family = binomial(link = "probit"),data = HMDA)


Table 11.2

probit_HMDA_2 <- glm(deny ~ afam + pirat + hirat + lvrat + chist + mhist + phist+ insurance + selfemp + single + hschool + unemp,family = binomial(link = "probit"),data = HMDA)

probit_HMDA_3 <- glm(deny ~ afam + pirat + hirat + lvrat + chist + mhist+ phist + insurance + selfemp + single + hschool + unemp + condomin+ I(mhist==3) + I(mhist==4) + I(chist==3) + I(chist==4) + I(chist==5)+ I(chist==6), family = binomial(link = "probit"),data = HMDA)

probit_HMDA_4 <- glm(deny ~ afam * (pirat + hirat) + lvrat + chist + mhist + phist+ insurance + selfemp + single + hschool + unemp,family = binomial(link = "probit"),data = HMDA)


Table 11.2

rob_se <- list(sqrt(diag(vcovHC(lpm_HMDA, type = "HC1"))),sqrt(diag(vcovHC(logit_HMDA, type = "HC1"))),sqrt(diag(vcovHC(probit_HMDA_1, type = "HC1"))),sqrt(diag(vcovHC(probit_HMDA_2, type = "HC1"))),sqrt(diag(vcovHC(probit_HMDA_3, type = "HC1"))),sqrt(diag(vcovHC(probit_HMDA_4, type = "HC1"))))

stargazer(lpm_HMDA, logit_HMDA, probit_HMDA_1,probit_HMDA_2, probit_HMDA_3, probit_HMDA_4,digits = 3,type = "latex",header = FALSE,se = rob_se,model.numbers = FALSE,column.labels = c("(1)", "(2)", "(3)", "(4)", "(5)", "(6)"))


Table 11.2Mortgage Denial Regressions

Dependent Variable: deny=1 if application is denied,=0 if acceptedOLS logistic probit(1) (2) (3) (4) (5) (6)

afamyes 0.087∗∗∗ 0.684∗∗∗ 0.386∗∗∗ 0.374∗∗∗ 0.380∗∗∗ 0.284(0.022) (0.177) (0.097) (0.098) (0.099) (0.492)

pirat 0.483∗∗∗ 5.135∗∗∗ 2.648∗∗∗ 2.644∗∗∗ 2.653∗∗∗ 2.756∗∗∗(0.115) (1.358) (0.677) (0.659) (0.658) (0.726)

hirat −0.077 −0.666 −0.442 −0.522 −0.546 −0.738(0.111) (1.338) (0.709) (0.705) (0.705) (0.762)

lvrat 0.090∗∗ 1.776∗∗∗ 0.754∗∗ 0.780∗∗ 0.784∗∗ 0.775∗∗(0.037) (0.623) (0.339) (0.336) (0.335) (0.337)

chist2 0.040∗∗∗ 0.708∗∗∗ 0.324∗∗∗ 0.324∗∗∗ 0.322∗∗∗ 0.324∗∗∗(0.015) (0.209) (0.105) (0.106) (0.107) (0.106)

chist3 0.051 0.882∗∗∗ 0.449∗∗∗ 0.434∗∗ 0.432∗∗ 0.435∗∗(0.032) (0.327) (0.173) (0.175) (0.175) (0.174)

chist4 0.142∗∗∗ 1.581∗∗∗ 0.793∗∗∗ 0.764∗∗∗ 0.769∗∗∗ 0.755∗∗∗(0.044) (0.317) (0.173) (0.182) (0.182) (0.182)

chist5 0.106∗∗∗ 1.207∗∗∗ 0.602∗∗∗ 0.609∗∗∗ 0.608∗∗∗ 0.610∗∗∗(0.028) (0.233) (0.122) (0.120) (0.120) (0.120)

chist6 0.159∗∗∗ 1.491∗∗∗ 0.778∗∗∗ 0.799∗∗∗ 0.800∗∗∗ 0.803∗∗∗(0.032) (0.236) (0.128) (0.129) (0.129) (0.130)

mhist2 0.027∗∗ 0.426∗∗ 0.221∗∗ 0.165 0.166 0.166(0.012) (0.201) (0.102) (0.105) (0.105) (0.105)

mhist3 0.042 0.549 0.279 0.209 0.207 0.210(0.061) (0.502) (0.271) (0.271) (0.272) (0.273)

mhist4 0.033 0.578 0.272 0.234 0.231 0.240(0.081) (0.607) (0.339) (0.353) (0.353) (0.354)

phistyes 0.204∗∗∗ 1.268∗∗∗ 0.723∗∗∗ 0.724∗∗∗ 0.724∗∗∗ 0.726∗∗∗(0.035) (0.201) (0.114) (0.115) (0.115) (0.114)

insuranceyes 0.713∗∗∗ 4.565∗∗∗ 2.551∗∗∗ 2.576∗∗∗ 2.574∗∗∗ 2.581∗∗∗(0.044) (0.582) (0.304) (0.299) (0.299) (0.300)

selfempyes 0.061∗∗∗ 0.670∗∗∗ 0.352∗∗∗ 0.337∗∗∗ 0.337∗∗∗ 0.339∗∗∗(0.021) (0.213) (0.113) (0.115) (0.115) (0.115)

singleyes 0.230∗∗∗ 0.237∗∗∗ 0.227∗∗∗(0.081) (0.085) (0.082)

hschoolyes −0.552∗∗ −0.558∗∗ −0.560∗∗(0.239) (0.239) (0.239)

unemp 0.031∗ 0.031∗ 0.031∗(0.018) (0.018) (0.018)

condominyes −0.035(0.094)

I(mhist == 3)

I(mhist == 4)

I(chist == 3)

I(chist == 4)

I(chist == 5)

I(chist == 6)

afamyes:pirat −0.634(1.545)

afamyes:hirat 1.177(1.737)

Constant −0.191∗∗∗ −6.471∗∗∗ −3.298∗∗∗ −2.936∗∗∗ −2.922∗∗∗ −2.905∗∗∗(0.030) (0.617) (0.321) (0.395) (0.399) (0.406)

Observations 2,380 2,380 2,380 2,380 2,380 2,380Adjusted R2 0.254Log Likelihood −636.641 −639.472 −631.707 −631.633 −631.455Akaike Inf. Crit. 1,305.282 1,310.944 1,301.415 1,303.265 1,304.909Residual Std. Error 0.280

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01Robust S.E. are shown in the parentheses


Section 4

Oaxaca-Blinder Decomposition


Oaxaca-Blinder Decomposition: difference in mean

The difference in mean of 𝑌𝑖 of group A and B is

𝑌𝐴 − 𝑌𝐵 = 𝛽𝐴��′𝐴 − 𝛽𝐵��′

𝐵

A small trick: plus and minus a term 𝛽𝐵��′𝐴,then

𝑌𝐴 − 𝑌𝐵 = 𝛽𝐴��′𝐴 − 𝛽𝐵��′

𝐵

= 𝛽𝐴��′𝐴 − 𝛽𝐵��′

𝐴 + 𝛽𝐵��′𝐴 − 𝛽𝐵��′

𝐵

= ( 𝛽𝐴 − 𝛽𝐵)��′𝐴 + 𝛽𝐵(��′

𝐴 − ��′𝐵)

Then the second term is characteristics effect which describes howmuch the difference of outcome, 𝑌 , in mean is due to differences inthe levels of explanatory variables(characteristics).the first term is coefficients effect which describes how much thedifference of outcome, 𝑌 , in mean is due to differences in themagnitude of regression coefficients.




𝑌𝐴 − 𝑌𝐵 = 𝛽𝐴��′𝐴 − 𝛽𝐵��′

𝐵


𝑌𝐴 − 𝑌𝐵 = 𝛽𝐴��′𝐴 − 𝛽𝐵��′

𝐵

= 𝛽𝐴��′𝐴 − 𝛽𝐵��′

𝐴 + 𝛽𝐵��′𝐴 − 𝛽𝐵��′

𝐵

= ( 𝛽𝐴 − 𝛽𝐵)��′𝐴 + 𝛽𝐵(��′

𝐴 − ��′𝐵)





𝑌𝐴 − 𝑌𝐵 = 𝛽𝐴��′𝐴 − 𝛽𝐵��′

𝐵


𝑌𝐴 − 𝑌𝐵 = 𝛽𝐴��′𝐴 − 𝛽𝐵��′

𝐵

= 𝛽𝐴��′𝐴 − 𝛽𝐵��′

𝐴 + 𝛽𝐵��′𝐴 − 𝛽𝐵��′

𝐵

= ( 𝛽𝐴 − 𝛽𝐵)��′𝐴 + 𝛽𝐵(��′

𝐴 − ��′𝐵)

Then the second term is characteristics effect which describes howmuch the difference of outcome, 𝑌 , in mean is due to differences inthe levels of explanatory variables(characteristics).

the first term is coefficients effect which describes how much thedifference of outcome, 𝑌 , in mean is due to differences in themagnitude of regression coefficients.




𝑌𝐴 − 𝑌𝐵 = 𝛽𝐴��′𝐴 − 𝛽𝐵��′

𝐵


𝑌𝐴 − 𝑌𝐵 = 𝛽𝐴��′𝐴 − 𝛽𝐵��′

𝐵

= 𝛽𝐴��′𝐴 − 𝛽𝐵��′

𝐴 + 𝛽𝐵��′𝐴 − 𝛽𝐵��′

𝐵

= ( 𝛽𝐴 − 𝛽𝐵)��′𝐴 + 𝛽𝐵(��′

𝐴 − ��′𝐵)



Oaxaca-Blinder Decomposition: a general framework

Then the difference of the potential outcomes between two groupscan then be decomposed as follows

𝑌𝐴 − 𝑌𝐵 = ��′𝐴 𝛽𝐴 − ��′

𝐵 𝛽𝐵

= ��′𝐴 𝛽𝐴 − ��′

𝐴 𝛽∗ + ��′𝐴 𝛽∗−��′

𝐵 𝛽∗ + ��′𝐵 𝛽∗−��′

𝐵 𝛽𝐵

= (��′𝐴 − ��′

𝐵) 𝛽∗ + [��′𝐴( 𝛽𝐴 − 𝛽∗) + ��′

𝐵( 𝛽∗− 𝛽𝐵)]



The first term, (��′𝐴 − ��′

𝐵) 𝛽∗ is the explained part as usual

characteristics effectendownment effectcomposition effect

The second term, the unexplained part can further be subdividedinto

1 “discrimination” in favor of group A(such as Men)

��′𝐴( 𝛽𝐴 − 𝛽∗)

2 “discrimination” against group B(such as Women)

��′𝐵( 𝛽∗ − 𝛽𝐵)




𝐵) 𝛽∗ is the explained part as usualcharacteristics effect

endownment effectcomposition effect



��′𝐴( 𝛽𝐴 − 𝛽∗)


��′𝐵( 𝛽∗ − 𝛽𝐵)




𝐵) 𝛽∗ is the explained part as usualcharacteristics effectendownment effect

composition effectThe second term, the unexplained part can further be subdividedinto


��′𝐴( 𝛽𝐴 − 𝛽∗)


��′𝐵( 𝛽∗ − 𝛽𝐵)




𝐵) 𝛽∗ is the explained part as usualcharacteristics effectendownment effectcomposition effect



��′𝐴( 𝛽𝐴 − 𝛽∗)


��′𝐵( 𝛽∗ − 𝛽𝐵)







��′𝐴( 𝛽𝐴 − 𝛽∗)


��′𝐵( 𝛽∗ − 𝛽𝐵)







��′𝐴( 𝛽𝐴 − 𝛽∗)


��′𝐵( 𝛽∗ − 𝛽𝐵)







��′𝐴( 𝛽𝐴 − 𝛽∗)


��′𝐵( 𝛽∗ − 𝛽𝐵)


Install Packages

#install.packages("oaxaca")library(oaxaca)



Native v.s Foreign

#library(oaxaca)data("chicago")



Native v.s Foreign

# restore the log(wage) to wagechicago$real.wage <- exp(chicago$ln.real.wage)

# oaxaca decomposition

results <- oaxaca(formula = real.wage ~ age + female+ LTHS + some.college + college + advanced.degree| foreign.born |+ LTHS + some.college + college + advanced.degree,data = chicago)


Oaxaca-Blinder DecompositionOverall Decomposition in twofolds

results$twofold$overall

## group.weight coef(explained) se(explained) coef(unexplained)## [1,] 0.0000000 1.6165339 0.5521838 1.399040## [2,] 1.0000000 0.1822482 0.6093042 2.833326## [3,] 0.5000000 0.8993911 0.4341385 2.116183## [4,] 0.4309309 0.9984559 0.4426210 2.017118## [5,] -1.0000000 1.3557222 0.4350426 1.659852## [6,] -2.0000000 0.9525717 0.4269861 2.063003## se(unexplained) coef(unexplained A) se(unexplained A) coef(unexplained B)## [1,] 0.9675607 1.399040e+00 9.675607e-01 0.0000000## [2,] 0.8662929 0.000000e+00 0.000000e+00 2.8333261## [3,] 0.8328958 6.995202e-01 4.837804e-01 1.4166630## [4,] 0.8268878 7.961506e-01 4.169518e-01 1.2209678## [5,] 0.6761292 9.445705e-01 3.853026e-01 0.7152816## [6,] 0.8443550 4.840572e-14 3.849658e-14 2.0630026## se(unexplained B)## [1,] 0.0000000## [2,] 0.8662929## [3,] 0.4331464## [4,] 0.4929805## [5,] 0.2939783## [6,] 0.8443550Feifan Wang (Nanjing University) Lab7: Nonlinear Regression and OB Decomposition in R11/04/2021 39 / 44

Oaxaca-Blinder DecompositionOverall Decomposition in twofolds

results$twofold$overall

## group.weight coef(explained) se(explained) coef(unexplained)## [1,] 0.0000000 1.6165339 0.5521838 1.399040## [2,] 1.0000000 0.1822482 0.6093042 2.833326## [3,] 0.5000000 0.8993911 0.4341385 2.116183## [4,] 0.4309309 0.9984559 0.4426210 2.017118## [5,] -1.0000000 1.3557222 0.4350426 1.659852## [6,] -2.0000000 0.9525717 0.4269861 2.063003## se(unexplained) coef(unexplained A) se(unexplained A) coef(unexplained B)## [1,] 0.9675607 1.399040e+00 9.675607e-01 0.0000000## [2,] 0.8662929 0.000000e+00 0.000000e+00 2.8333261## [3,] 0.8328958 6.995202e-01 4.837804e-01 1.4166630## [4,] 0.8268878 7.961506e-01 4.169518e-01 1.2209678## [5,] 0.6761292 9.445705e-01 3.853026e-01 0.7152816## [6,] 0.8443550 4.840572e-14 3.849658e-14 2.0630026## se(unexplained B)## [1,] 0.0000000## [2,] 0.8662929## [3,] 0.4331464## [4,] 0.4929805## [5,] 0.2939783## [6,] 0.8443550Feifan Wang (Nanjing University) Lab7: Nonlinear Regression and OB Decomposition in R11/04/2021 40 / 44

Oaxaca-Blinder DecompositionDetailed Decomposition in twofolds

results$twofold$variables

## [[1]]## group.weight coef(explained) se(explained) coef(unexplained)## (Intercept) 0 0.00000000 0.0000000 -4.26374940## age 0 -0.51677529 0.1942235 6.32615876## female 0 -0.27265166 0.1587495 -1.41569495## LTHS 0 2.17644672 0.4047570 0.01973059## some.college 0 -0.78533521 0.3981989 0.19816994## college 0 -0.07907587 0.1081671 0.91805037## advanced.degree 0 0.70631440 0.3476113 -0.59276551## (Base) 0 0.38761084 0.1929361 0.20914055## se(unexplained) coef(unexplained A) se(unexplained A)## (Intercept) 2.5027463 -4.26374940 2.5027463## age 1.7737915 6.32615876 1.7737915## female 0.7161933 -1.41569495 0.7161933## LTHS 0.1950737 0.01973059 0.1950737## some.college 0.7565703 0.19816994 0.7565703## college 0.4307505 0.91805037 0.4307505## advanced.degree 0.4160289 -0.59276551 0.4160289## (Base) 0.5461521 0.20914055 0.5461521## coef(unexplained B) se(unexplained B)## (Intercept) 0 0## age 0 0## female 0 0## LTHS 0 0## some.college 0 0## college 0 0## advanced.degree 0 0## (Base) 0 0#### [[2]]## group.weight coef(explained) se(explained) coef(unexplained)## (Intercept) 1 0.0000000 0.0000000 -4.26374940## age 1 -1.7491472 0.4394072 7.55853070## female 1 -0.5230820 0.2850904 -1.16526457## LTHS 1 2.1315790 0.3672828 0.06459830## some.college 1 -0.6561142 0.2782319 0.06894895## college 1 0.2565104 0.1716329 0.58246411## advanced.degree 1 0.3828740 0.1598105 -0.26932512## (Base) 1 0.3396283 0.2081567 0.25712310## se(unexplained) coef(unexplained A) se(unexplained A)## (Intercept) 2.5027463 0 0## age 2.1870992 0 0## female 0.5578858 0 0## LTHS 0.6372269 0 0## some.college 0.2716997 0 0## college 0.2579248 0 0## advanced.degree 0.1961789 0 0## (Base) 0.6575533 0 0## coef(unexplained B) se(unexplained B)## (Intercept) -4.26374940 2.5027463## age 7.55853070 2.1870992## female -1.16526457 0.5578858## LTHS 0.06459830 0.6372269## some.college 0.06894895 0.2716997## college 0.58246411 0.2579248## advanced.degree -0.26932512 0.1961789## (Base) 0.25712310 0.6575533#### [[3]]## group.weight coef(explained) se(explained) coef(unexplained)## (Intercept) 0.5 0.00000000 0.00000000 -4.26374940## age 0.5 -1.13296126 0.25431565 6.94234473## female 0.5 -0.39786685 0.20786399 -1.29047976## LTHS 0.5 2.15401287 0.31581236 0.04216444## some.college 0.5 -0.72072472 0.24026635 0.13355945## college 0.5 0.08871727 0.07873703 0.75025724## advanced.degree 0.5 0.54459421 0.23716962 -0.43104531## (Base) 0.5 0.36361957 0.19043804 0.23313182## se(unexplained) coef(unexplained A) se(unexplained A)## (Intercept) 2.5027463 -2.131874701 1.25137313## age 1.9784199 3.163079379 0.88689573## female 0.6340766 -0.707847475 0.35809667## LTHS 0.4152481 0.009865293 0.09753686## some.college 0.5126889 0.099084970 0.37828515## college 0.3341499 0.459025187 0.21537527## advanced.degree 0.2980705 -0.296382754 0.20801445## (Base) 0.6010982 0.104570274 0.27307604## coef(unexplained B) se(unexplained B)## (Intercept) -2.13187470 1.25137313## age 3.77926535 1.09354959## female -0.58263229 0.27894288## LTHS 0.03229915 0.31861347## some.college 0.03447448 0.13584983## college 0.29123205 0.12896239## advanced.degree -0.13466256 0.09808947## (Base) 0.12856155 0.32877663#### [[4]]## group.weight coef(explained) se(explained) coef(unexplained)## (Intercept) 0.4309309 0.00000000 0.00000000 -4.26374940## age 0.4309309 -1.04784248 0.27635967 6.85722595## female 0.4309309 -0.38056985 0.21742106 -1.30777675## LTHS 0.4309309 2.15711184 0.31414347 0.03906547## some.college 0.4309309 -0.72964989 0.23080922 0.14248462## college 0.4309309 0.06553863 0.08775204 0.77343587## advanced.degree 0.4309309 0.56693394 0.22358609 -0.45338504## (Base) 0.4309309 0.36693368 0.19174156 0.22981771## se(unexplained) coef(unexplained A) se(unexplained A)## (Intercept) 2.5027463 -2.42636790 1.0785108## age 2.0070336 3.60002128 0.7643816## female 0.6231482 -0.80562821 0.3086299## LTHS 0.4458650 0.01122807 0.0840633## some.college 0.4791278 0.11277238 0.3260295## college 0.3220402 0.52243407 0.1856237## advanced.degree 0.2826180 -0.33732452 0.1792797## (Base) 0.6088164 0.11901542 0.2353538## coef(unexplained B) se(unexplained B)## (Intercept) -1.83738150 1.4242355## age 3.25720467 1.2446105## female -0.50214855 0.3174755## LTHS 0.02783741 0.3626261## some.college 0.02971224 0.1546159## college 0.25100180 0.1467770## advanced.degree -0.11606052 0.1116394## (Base) 0.11080230 0.3741932#### [[5]]## group.weight coef(explained) se(explained) coef(unexplained)## (Intercept) -1 0.0000000 0.0000000 -4.26374940## age -1 -0.9077617 0.1889496 6.71714514## female -1 -0.3765153 0.1924727 -1.31183132## LTHS -1 2.2842920 0.3395741 -0.08811472## some.college -1 -0.6457845 0.2298420 0.05861926## college -1 0.1184423 0.1020764 0.72053222## advanced.degree -1 0.5247323 0.2098660 -0.41118338## (Base) -1 0.3583171 0.1890215 0.23843424## se(unexplained) coef(unexplained A) se(unexplained A)## (Intercept) 2.5027463 -2.79648002 1.37592503## age 1.9117128 4.31910081 1.23066863## female 0.6495781 -0.82854887 0.43750585## LTHS 0.4543170 0.06715558 0.09887232## some.college 0.4566300 -0.01584134 0.30285648## college 0.3194437 0.37770759 0.18035670## advanced.degree 0.2718542 -0.25998201 0.15930891## (Base) 0.6070087 0.08145872 0.26198287## coef(unexplained B) se(unexplained B)## (Intercept) -1.4672694 1.3393762## age 2.3980443 0.8476843## female -0.4832824 0.2455140## LTHS -0.1552703 0.3887881## some.college 0.0744606 0.1762796## college 0.3428246 0.1456698## advanced.degree -0.1512014 0.1156621## (Base) 0.1569755 0.3812108#### [[6]]## group.weight coef(explained) se(explained) coef(unexplained)## (Intercept) -2 0.000000e+00 0.000000e+00 -4.2637494## age -2 -1.022467e+00 2.109268e-01 6.8318508## female -2 -3.827757e-01 2.023125e-01 -1.3055709## LTHS -2 7.719266e-01 1.816907e-01 1.4242507## some.college -2 5.306534e-01 2.375042e-01 -1.1178187## college -2 3.494225e-01 1.992421e-01 0.4895520## advanced.degree -2 7.058122e-01 2.777488e-01 -0.5922633## (Base) -2 -1.110223e-16 1.114487e-16 0.5967514## se(unexplained) coef(unexplained A) se(unexplained A)## (Intercept) 2.5027463 1.8071336 1.3836825## age 1.9310723 3.7302801 1.1410953## female 0.6452018 -0.7931584 0.4145636## LTHS 0.5226847 -0.5979074 0.1458423## some.college 0.5018208 -1.8199959 0.3957505## college 0.3145956 -0.2541760 0.1693892## advanced.degree 0.3071787 -0.5918452 0.2203823## (Base) 0.5917146 -1.4803309 0.3355536## coef(unexplained B) se(unexplained B)## (Intercept) -6.0708830237 1.8621860## age 3.1015706708 0.8977154## female -0.5124125091 0.2527662## LTHS 2.0221581467 0.4993462## some.college 0.7021772181 0.2579598## college 0.7437280111 0.2002168## advanced.degree -0.0004181581 0.1041770## (Base) 2.0770822578 0.5012035


Oaxaca-Blinder DecompositionNative v.s Foreign

plot(results, decomposition = "twofold", group.weight = -2)

## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =## "none")` instead.

Unexplained

Explained

−10 −5 0 5 10

(Base)

advanced.degree

college

some.college

LTHS

female

age

(Intercept)

(Base)

advanced.degree

college

some.college

LTHS

female

age

(Intercept)


Oaxaca-Blinder Decompositionprint(results)

## $beta## $beta$beta.A## (Intercept) age female LTHS some.college## 13.5813773 0.2640051 -6.1497192 -7.9124405 -2.6016154## college advanced.degree## 5.4431146 10.0692349#### $beta$beta.B## (Intercept) age female LTHS some.college## 17.84512667 0.07799874 -3.20548407 -8.07898985 -3.11400069## college advanced.degree## -1.67797882 18.57541990#### $beta$beta.diff## (Intercept) age female LTHS some.college## -4.2637494 0.1860063 -2.9442351 0.1665494 0.5123853## college advanced.degree## 7.1210934 -8.5061850#### $beta$beta.R## (Intercept) age female LTHS some.college## [1,] 0.0000000 17.84513 0.07799874 -3.205484 -8.078990 -3.114001## [2,] 1.0000000 13.58138 0.26400505 -6.149719 -7.912440 -2.601615## [3,] 0.5000000 15.71325 0.17100190 -4.677602 -7.995715 -2.857808## [4,] 0.4309309 16.00775 0.15815462 -4.474246 -8.007219 -2.893198## [5,] -1.0000000 16.37786 0.13701172 -4.426578 -8.479313 -2.560656## [6,] -2.0000000 11.77424 0.15432465 -4.500180 -2.865398 2.104140## college advanced.degree## [1,] -1.677979 18.57542## [2,] 5.443115 10.06923## [3,] 1.882568 14.32233## [4,] 1.390721 14.90984## [5,] 2.513329 13.79998## [6,] 7.414696 18.56221###### $call## oaxaca(formula = real.wage ~ age + female + LTHS + some.college +## college + advanced.degree | foreign.born | +LTHS + some.college +## college + advanced.degree, data = chicago)#### $n## $n$n.A## [1] 287#### $n$n.B## [1] 379#### $n$n.pooled## [1] 666###### $R## [1] 100#### $reg## $reg$reg.A#### Call:## NULL#### Coefficients:## (Intercept) age female LTHS## 8.583 0.264 -6.150 -2.914## some.college college advanced.degree## 2.397 10.441 15.068###### $reg$reg.B#### Call:## NULL#### Coefficients:## (Intercept) age female LTHS## 12.141 0.078 -3.205 -2.375## some.college college advanced.degree## 2.590 4.026 24.280###### $reg$reg.pooled.1#### Call:## NULL#### Coefficients:## (Intercept) age female LTHS## 11.105 0.137 -4.427 -3.206## some.college college advanced.degree## 2.713 7.787 19.073###### $reg$reg.pooled.2#### Call:## NULL#### Coefficients:## (Intercept) age female LTHS## 11.7742 0.1543 -4.5002 -2.8654## some.college college advanced.degree foreign.born## 2.1041 7.4147 18.5622 -2.0630######## $threefold## $threefold$overall## coef(endowments) se(endowments) coef(coefficients) se(coefficients)## 1.6165339 0.5521838 2.8333261 0.8662929## coef(interaction) se(interaction)## -1.4342857 0.7735712#### $threefold$variables## coef(endowments) se(endowments) coef(coefficients)## (Intercept) 0.00000000 0.0000000 -4.26374940## age -0.51677529 0.1942235 7.55853070## female -0.27265166 0.1587495 -1.16526457## LTHS 2.17644672 0.4047570 0.06459830## some.college -0.78533521 0.3981989 0.06894895## college -0.07907587 0.1081671 0.58246411## advanced.degree 0.70631440 0.3476113 -0.26932512## (Base) 0.38761084 0.1929361 0.25712310## se(coefficients) coef(interaction) se(interaction)## (Intercept) 2.5027463 0.00000000 0.0000000## age 2.1870992 -1.23237194 0.4504410## female 0.5578858 -0.25043038 0.2003149## LTHS 0.6372269 -0.04486771 0.4455334## some.college 0.2716997 0.12922099 0.4909572## college 0.2579248 0.33558627 0.2398288## advanced.degree 0.1961789 -0.32344039 0.2602851## (Base) 0.6575533 -0.04798255 0.1266511###### $twofold## $twofold$overall## group.weight coef(explained) se(explained) coef(unexplained)## [1,] 0.0000000 1.6165339 0.5521838 1.399040## [2,] 1.0000000 0.1822482 0.6093042 2.833326## [3,] 0.5000000 0.8993911 0.4341385 2.116183## [4,] 0.4309309 0.9984559 0.4426210 2.017118## [5,] -1.0000000 1.3557222 0.4350426 1.659852## [6,] -2.0000000 0.9525717 0.4269861 2.063003## se(unexplained) coef(unexplained A) se(unexplained A) coef(unexplained B)## [1,] 0.9675607 1.399040e+00 9.675607e-01 0.0000000## [2,] 0.8662929 0.000000e+00 0.000000e+00 2.8333261## [3,] 0.8328958 6.995202e-01 4.837804e-01 1.4166630## [4,] 0.8268878 7.961506e-01 4.169518e-01 1.2209678## [5,] 0.6761292 9.445705e-01 3.853026e-01 0.7152816## [6,] 0.8443550 4.840572e-14 3.849658e-14 2.0630026## se(unexplained B)## [1,] 0.0000000## [2,] 0.8662929## [3,] 0.4331464## [4,] 0.4929805## [5,] 0.2939783## [6,] 0.8443550#### $twofold$variables## $twofold$variables[[1]]## group.weight coef(explained) se(explained) coef(unexplained)## (Intercept) 0 0.00000000 0.0000000 -4.26374940## age 0 -0.51677529 0.1942235 6.32615876## female 0 -0.27265166 0.1587495 -1.41569495## LTHS 0 2.17644672 0.4047570 0.01973059## some.college 0 -0.78533521 0.3981989 0.19816994## college 0 -0.07907587 0.1081671 0.91805037## advanced.degree 0 0.70631440 0.3476113 -0.59276551## (Base) 0 0.38761084 0.1929361 0.20914055## se(unexplained) coef(unexplained A) se(unexplained A)## (Intercept) 2.5027463 -4.26374940 2.5027463## age 1.7737915 6.32615876 1.7737915## female 0.7161933 -1.41569495 0.7161933## LTHS 0.1950737 0.01973059 0.1950737## some.college 0.7565703 0.19816994 0.7565703## college 0.4307505 0.91805037 0.4307505## advanced.degree 0.4160289 -0.59276551 0.4160289## (Base) 0.5461521 0.20914055 0.5461521## coef(unexplained B) se(unexplained B)## (Intercept) 0 0## age 0 0## female 0 0## LTHS 0 0## some.college 0 0## college 0 0## advanced.degree 0 0## (Base) 0 0#### $twofold$variables[[2]]## group.weight coef(explained) se(explained) coef(unexplained)## (Intercept) 1 0.0000000 0.0000000 -4.26374940## age 1 -1.7491472 0.4394072 7.55853070## female 1 -0.5230820 0.2850904 -1.16526457## LTHS 1 2.1315790 0.3672828 0.06459830## some.college 1 -0.6561142 0.2782319 0.06894895## college 1 0.2565104 0.1716329 0.58246411## advanced.degree 1 0.3828740 0.1598105 -0.26932512## (Base) 1 0.3396283 0.2081567 0.25712310## se(unexplained) coef(unexplained A) se(unexplained A)## (Intercept) 2.5027463 0 0## age 2.1870992 0 0## female 0.5578858 0 0## LTHS 0.6372269 0 0## some.college 0.2716997 0 0## college 0.2579248 0 0## advanced.degree 0.1961789 0 0## (Base) 0.6575533 0 0## coef(unexplained B) se(unexplained B)## (Intercept) -4.26374940 2.5027463## age 7.55853070 2.1870992## female -1.16526457 0.5578858## LTHS 0.06459830 0.6372269## some.college 0.06894895 0.2716997## college 0.58246411 0.2579248## advanced.degree -0.26932512 0.1961789## (Base) 0.25712310 0.6575533#### $twofold$variables[[3]]## group.weight coef(explained) se(explained) coef(unexplained)## (Intercept) 0.5 0.00000000 0.00000000 -4.26374940## age 0.5 -1.13296126 0.25431565 6.94234473## female 0.5 -0.39786685 0.20786399 -1.29047976## LTHS 0.5 2.15401287 0.31581236 0.04216444## some.college 0.5 -0.72072472 0.24026635 0.13355945## college 0.5 0.08871727 0.07873703 0.75025724## advanced.degree 0.5 0.54459421 0.23716962 -0.43104531## (Base) 0.5 0.36361957 0.19043804 0.23313182## se(unexplained) coef(unexplained A) se(unexplained A)## (Intercept) 2.5027463 -2.131874701 1.25137313## age 1.9784199 3.163079379 0.88689573## female 0.6340766 -0.707847475 0.35809667## LTHS 0.4152481 0.009865293 0.09753686## some.college 0.5126889 0.099084970 0.37828515## college 0.3341499 0.459025187 0.21537527## advanced.degree 0.2980705 -0.296382754 0.20801445## (Base) 0.6010982 0.104570274 0.27307604## coef(unexplained B) se(unexplained B)## (Intercept) -2.13187470 1.25137313## age 3.77926535 1.09354959## female -0.58263229 0.27894288## LTHS 0.03229915 0.31861347## some.college 0.03447448 0.13584983## college 0.29123205 0.12896239## advanced.degree -0.13466256 0.09808947## (Base) 0.12856155 0.32877663#### $twofold$variables[[4]]## group.weight coef(explained) se(explained) coef(unexplained)## (Intercept) 0.4309309 0.00000000 0.00000000 -4.26374940## age 0.4309309 -1.04784248 0.27635967 6.85722595## female 0.4309309 -0.38056985 0.21742106 -1.30777675## LTHS 0.4309309 2.15711184 0.31414347 0.03906547## some.college 0.4309309 -0.72964989 0.23080922 0.14248462## college 0.4309309 0.06553863 0.08775204 0.77343587## advanced.degree 0.4309309 0.56693394 0.22358609 -0.45338504## (Base) 0.4309309 0.36693368 0.19174156 0.22981771## se(unexplained) coef(unexplained A) se(unexplained A)## (Intercept) 2.5027463 -2.42636790 1.0785108## age 2.0070336 3.60002128 0.7643816## female 0.6231482 -0.80562821 0.3086299## LTHS 0.4458650 0.01122807 0.0840633## some.college 0.4791278 0.11277238 0.3260295## college 0.3220402 0.52243407 0.1856237## advanced.degree 0.2826180 -0.33732452 0.1792797## (Base) 0.6088164 0.11901542 0.2353538## coef(unexplained B) se(unexplained B)## (Intercept) -1.83738150 1.4242355## age 3.25720467 1.2446105## female -0.50214855 0.3174755## LTHS 0.02783741 0.3626261## some.college 0.02971224 0.1546159## college 0.25100180 0.1467770## advanced.degree -0.11606052 0.1116394## (Base) 0.11080230 0.3741932#### $twofold$variables[[5]]## group.weight coef(explained) se(explained) coef(unexplained)## (Intercept) -1 0.0000000 0.0000000 -4.26374940## age -1 -0.9077617 0.1889496 6.71714514## female -1 -0.3765153 0.1924727 -1.31183132## LTHS -1 2.2842920 0.3395741 -0.08811472## some.college -1 -0.6457845 0.2298420 0.05861926## college -1 0.1184423 0.1020764 0.72053222## advanced.degree -1 0.5247323 0.2098660 -0.41118338## (Base) -1 0.3583171 0.1890215 0.23843424## se(unexplained) coef(unexplained A) se(unexplained A)## (Intercept) 2.5027463 -2.79648002 1.37592503## age 1.9117128 4.31910081 1.23066863## female 0.6495781 -0.82854887 0.43750585## LTHS 0.4543170 0.06715558 0.09887232## some.college 0.4566300 -0.01584134 0.30285648## college 0.3194437 0.37770759 0.18035670## advanced.degree 0.2718542 -0.25998201 0.15930891## (Base) 0.6070087 0.08145872 0.26198287## coef(unexplained B) se(unexplained B)## (Intercept) -1.4672694 1.3393762## age 2.3980443 0.8476843## female -0.4832824 0.2455140## LTHS -0.1552703 0.3887881## some.college 0.0744606 0.1762796## college 0.3428246 0.1456698## advanced.degree -0.1512014 0.1156621## (Base) 0.1569755 0.3812108#### $twofold$variables[[6]]## group.weight coef(explained) se(explained) coef(unexplained)## (Intercept) -2 0.000000e+00 0.000000e+00 -4.2637494## age -2 -1.022467e+00 2.109268e-01 6.8318508## female -2 -3.827757e-01 2.023125e-01 -1.3055709## LTHS -2 7.719266e-01 1.816907e-01 1.4242507## some.college -2 5.306534e-01 2.375042e-01 -1.1178187## college -2 3.494225e-01 1.992421e-01 0.4895520## advanced.degree -2 7.058122e-01 2.777488e-01 -0.5922633## (Base) -2 -1.110223e-16 1.114487e-16 0.5967514## se(unexplained) coef(unexplained A) se(unexplained A)## (Intercept) 2.5027463 1.8071336 1.3836825## age 1.9310723 3.7302801 1.1410953## female 0.6452018 -0.7931584 0.4145636## LTHS 0.5226847 -0.5979074 0.1458423## some.college 0.5018208 -1.8199959 0.3957505## college 0.3145956 -0.2541760 0.1693892## advanced.degree 0.3071787 -0.5918452 0.2203823## (Base) 0.5917146 -1.4803309 0.3355536## coef(unexplained B) se(unexplained B)## (Intercept) -6.0708830237 1.8621860## age 3.1015706708 0.8977154## female -0.5124125091 0.2527662## LTHS 2.0221581467 0.4993462## some.college 0.7021772181 0.2579598## college 0.7437280111 0.2002168## advanced.degree -0.0004181581 0.1041770## (Base) 2.0770822578 0.5012035######## $x## $x$x.mean.A## (Intercept) age female LTHS some.college## 1.00000000 34.01045296 0.48083624 0.11846690 0.38675958## college advanced.degree## 0.12891986 0.06968641#### $x$x.mean.B## (Intercept) age female LTHS some.college## 1.00000000 40.63588391 0.39577836 0.38786280 0.13456464## college advanced.degree## 0.08179420 0.03166227#### $x$x.mean.diff## (Intercept) age female LTHS some.college## 0.00000000 -6.62543094 0.08505787 -0.26939590 0.25219494## college advanced.degree## 0.04712567 0.03802414###### $y## $y$y.A## [1] 17.58282#### $y$y.B## [1] 14.56725#### $y$y.diff## [1] 3.015574###### attr(,"class")## [1] "oaxaca"


Oaxaca-Blinder Decomposition: Exercise

Calculate the share of overall endowment effect to wage gapbetween natives and foreign borns

Calculate the share of overall price effect to wage gap betweennatives and foreign bornCalculate shares of detailed endownment effects(every independentvariable) to wage gap between natives and foreign bornsCalculate the share of detailed price effect(every independentvariable plus constant) to wage gap between natives and foreign bornsShow all desirable results above in a table using Stargazer or Kablepackages



Calculate the share of overall endowment effect to wage gapbetween natives and foreign bornsCalculate the share of overall price effect to wage gap betweennatives and foreign born

Calculate shares of detailed endownment effects(every independentvariable) to wage gap between natives and foreign bornsCalculate the share of detailed price effect(every independentvariable plus constant) to wage gap between natives and foreign bornsShow all desirable results above in a table using Stargazer or Kablepackages



Calculate the share of overall endowment effect to wage gapbetween natives and foreign bornsCalculate the share of overall price effect to wage gap betweennatives and foreign bornCalculate shares of detailed endownment effects(every independentvariable) to wage gap between natives and foreign borns

Calculate the share of detailed price effect(every independentvariable plus constant) to wage gap between natives and foreign bornsShow all desirable results above in a table using Stargazer or Kablepackages



Calculate the share of overall endowment effect to wage gapbetween natives and foreign bornsCalculate the share of overall price effect to wage gap betweennatives and foreign bornCalculate shares of detailed endownment effects(every independentvariable) to wage gap between natives and foreign bornsCalculate the share of detailed price effect(every independentvariable plus constant) to wage gap between natives and foreign borns

Show all desirable results above in a table using Stargazer or Kablepackages



Calculate the share of overall endowment effect to wage gapbetween natives and foreign bornsCalculate the share of overall price effect to wage gap betweennatives and foreign bornCalculate shares of detailed endownment effects(every independentvariable) to wage gap between natives and foreign bornsCalculate the share of detailed price effect(every independentvariable plus constant) to wage gap between natives and foreign bornsShow all desirable results above in a table using Stargazer or Kablepackages


Documents

Lab7: Nonlinear Regression and OB Decomposition in R