Econometrics for dummies
Ralf Martin
Dummies
A binary variable capturing a qualitative state in the data; e.g. female where we set the variable to 1 for women
wage1 <- read.csv("https://www.dropbox.com/s/9agc2vmamfztlel/WAGE1.csv?dl=1")
r1 <- lm(wage ~ female, wage1)
r1 %>% summary()##
## Call:
## lm(formula = wage ~ female, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.5995 -1.8495 -0.9877 1.4260 17.8805
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.0995 0.2100 33.806 < 2e-16 ***
## female -2.5118 0.3034 -8.279 1.04e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.476 on 524 degrees of freedom
## Multiple R-squared: 0.1157, Adjusted R-squared: 0.114
## F-statistic: 68.54 on 1 and 524 DF, p-value: 1.042e-15How can we interpret the coefficients?
\[Wage=\beta_0+\beta_1\times FEMALE+\epsilon\]
As before: by how much we can expect the dependent variable to change if we move one unit in the explanatory variable. Here this means if we go from a man to a women (or from a women to a man). In this case: women earn on average $2.51 less.
Note that
wage1 %>% group_by(female) %>% summarize(mean(wage))## # A tibble: 2 x 2
## female `mean(wage)`
## <int> <dbl>
## 1 0 7.10
## 2 1 4.59Notice, that the intercept (\(\beta_0\)) is the average wage for men. To get the average wage for women we need to add the coefficient: \[ E\{wage| Women\}=\beta_0+\beta_1=4.587...\] where \(E\{wage| Women\}\) is a mathematical way of saying the average (or expected) wage for women.
summary(r1)##
## Call:
## lm(formula = wage ~ female, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.5995 -1.8495 -0.9877 1.4260 17.8805
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.0995 0.2100 33.806 < 2e-16 ***
## female -2.5118 0.3034 -8.279 1.04e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.476 on 524 degrees of freedom
## Multiple R-squared: 0.1157, Adjusted R-squared: 0.114
## F-statistic: 68.54 on 1 and 524 DF, p-value: 1.042e-15 summary(lm(wage ~ 0+educ, wage1))##
## Call:
## lm(formula = wage ~ 0 + educ, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.142 -2.246 -1.066 1.154 16.528
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## educ 0.47266 0.01146 41.25 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.381 on 525 degrees of freedom
## Multiple R-squared: 0.7642, Adjusted R-squared: 0.7637
## F-statistic: 1701 on 1 and 525 DF, p-value: < 2.2e-16 rows=nrow(wage1)
wage1["one"]<-rep(1,rows)
head(wage1) ## X wage educ exper tenure nonwhite female married numdep smsa northcen south
## 1 1 3.10 11 2 0 0 1 0 2 1 0 0
## 2 2 3.24 12 22 2 0 1 1 3 1 0 0
## 3 3 3.00 11 2 0 0 0 0 2 0 0 0
## 4 4 6.00 8 44 28 0 0 1 0 1 0 0
## 5 5 5.30 12 7 2 0 0 1 1 0 0 0
## 6 6 8.75 16 9 8 0 0 1 0 1 0 0
## west construc ndurman trcommpu trade services profserv profocc clerocc
## 1 1 0 0 0 0 0 0 0 0
## 2 1 0 0 0 0 1 0 0 0
## 3 1 0 0 0 1 0 0 0 0
## 4 1 0 0 0 0 0 0 0 1
## 5 1 0 0 0 0 0 0 0 0
## 6 1 0 0 0 0 0 1 1 0
## servocc lwage expersq tenursq one
## 1 0 1.131402 4 0 1
## 2 1 1.175573 484 4 1
## 3 0 1.098612 4 0 1
## 4 0 1.791759 1936 784 1
## 5 0 1.667707 49 4 1
## 6 0 2.169054 81 64 1 summary(lm(wage ~ 0+educ+one, wage1))##
## Call:
## lm(formula = wage ~ 0 + educ + one, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.3396 -2.1501 -0.9674 1.1921 16.6085
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## educ 0.54136 0.05325 10.167 <2e-16 ***
## one -0.90485 0.68497 -1.321 0.187
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.378 on 524 degrees of freedom
## Multiple R-squared: 0.765, Adjusted R-squared: 0.7641
## F-statistic: 852.7 on 2 and 524 DF, p-value: < 2.2e-16 summary(lm(wage ~ educ+one, wage1))##
## Call:
## lm(formula = wage ~ educ + one, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.3396 -2.1501 -0.9674 1.1921 16.6085
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.90485 0.68497 -1.321 0.187
## educ 0.54136 0.05325 10.167 <2e-16 ***
## one NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.378 on 524 degrees of freedom
## Multiple R-squared: 0.1648, Adjusted R-squared: 0.1632
## F-statistic: 103.4 on 1 and 524 DF, p-value: < 2.2e-16 summary(lm(wage ~one, wage1))##
## Call:
## lm(formula = wage ~ one, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.3661 -2.5661 -1.2461 0.9839 19.0839
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.896 0.161 36.62 <2e-16 ***
## one NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.693 on 525 degrees of freedom summary(wage1$wage)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.530 3.330 4.650 5.896 6.880 24.980 summary(lm(wage ~ female, wage1))##
## Call:
## lm(formula = wage ~ female, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.5995 -1.8495 -0.9877 1.4260 17.8805
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.0995 0.2100 33.806 < 2e-16 ***
## female -2.5118 0.3034 -8.279 1.04e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.476 on 524 degrees of freedom
## Multiple R-squared: 0.1157, Adjusted R-squared: 0.114
## F-statistic: 68.54 on 1 and 524 DF, p-value: 1.042e-15 aggregate(wage1$wage, list(wage1$female), mean)## Group.1 x
## 1 0 7.099489
## 2 1 4.587659 aggregate(wage1$wage, list(wage1$female), mean)## Group.1 x
## 1 0 7.099489
## 2 1 4.587659 wage1["male"]<-1-wage1$female
summary(lm(wage ~ male +female, wage1))##
## Call:
## lm(formula = wage ~ male + female, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.5995 -1.8495 -0.9877 1.4260 17.8805
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.5877 0.2190 20.950 < 2e-16 ***
## male 2.5118 0.3034 8.279 1.04e-15 ***
## female NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.476 on 524 degrees of freedom
## Multiple R-squared: 0.1157, Adjusted R-squared: 0.114
## F-statistic: 68.54 on 1 and 524 DF, p-value: 1.042e-15 summary(lm(wage ~ female+male , wage1)) ##
## Call:
## lm(formula = wage ~ female + male, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.5995 -1.8495 -0.9877 1.4260 17.8805
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.0995 0.2100 33.806 < 2e-16 ***
## female -2.5118 0.3034 -8.279 1.04e-15 ***
## male NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.476 on 524 degrees of freedom
## Multiple R-squared: 0.1157, Adjusted R-squared: 0.114
## F-statistic: 68.54 on 1 and 524 DF, p-value: 1.042e-15 summary(lm(wage ~ 0+male +female, wage1)) ##
## Call:
## lm(formula = wage ~ 0 + male + female, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.5995 -1.8495 -0.9877 1.4260 17.8805
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## male 7.099 0.210 33.81 <2e-16 ***
## female 4.588 0.219 20.95 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.476 on 524 degrees of freedom
## Multiple R-squared: 0.7512, Adjusted R-squared: 0.7502
## F-statistic: 790.9 on 2 and 524 DF, p-value: < 2.2e-16Dummies and categorical variables
wage1= wage1 %>% mutate(educats=0,
educats=ifelse(educ==12,1,educats),
educats=ifelse(educ>12,2,educats))
wage1 %>% group_by(educats) %>% summarize(n())## # A tibble: 3 x 2
## educats `n()`
## <dbl> <int>
## 1 0 116
## 2 1 198
## 3 2 212summary(lm(wage~educats,wage1))##
## Call:
## lm(formula = wage ~ educats, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.2933 -2.2542 -0.9292 1.2301 17.6867
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.8751 0.2765 14.016 <2e-16 ***
## educats 1.7091 0.1961 8.717 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.455 on 524 degrees of freedom
## Multiple R-squared: 0.1267, Adjusted R-squared: 0.125
## F-statistic: 75.99 on 1 and 524 DF, p-value: < 2.2e-16Making a set of dummy variables
wage1=wage1 %>% mutate(edu_low=educats==0,
edu_normal=educats==1,
edu_high=educats==2)
reg=lm(wage~edu_low+edu_normal+edu_high,wage1)
reg %>% summary()##
## Call:
## lm(formula = wage ~ edu_low + edu_normal + edu_high, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.393 -2.119 -1.033 1.245 17.587
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.3926 0.2372 31.165 < 2e-16 ***
## edu_lowTRUE -3.3359 0.3989 -8.363 5.56e-16 ***
## edu_normalTRUE -2.0213 0.3413 -5.922 5.78e-09 ***
## edu_highTRUE NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.454 on 523 degrees of freedom
## Multiple R-squared: 0.1287, Adjusted R-squared: 0.1254
## F-statistic: 38.64 on 2 and 523 DF, p-value: 2.236e-16Testing for a linear relationship
library(car)
summary(lm(wage ~ edu_low+edu_normal+edu_high, wage1))##
## Call:
## lm(formula = wage ~ edu_low + edu_normal + edu_high, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.393 -2.119 -1.033 1.245 17.587
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.3926 0.2372 31.165 < 2e-16 ***
## edu_lowTRUE -3.3359 0.3989 -8.363 5.56e-16 ***
## edu_normalTRUE -2.0213 0.3413 -5.922 5.78e-09 ***
## edu_highTRUE NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.454 on 523 degrees of freedom
## Multiple R-squared: 0.1287, Adjusted R-squared: 0.1254
## F-statistic: 38.64 on 2 and 523 DF, p-value: 2.236e-16 reg=lm(wage ~ edu_low+edu_high, wage1)
linearHypothesis(reg,c("edu_lowTRUE=-edu_highTRUE"))## Linear hypothesis test
##
## Hypothesis:
## edu_lowTRUE + edu_highTRUE = 0
##
## Model 1: restricted model
## Model 2: wage ~ edu_low + edu_high
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 524 6253.5
## 2 523 6238.6 1 14.888 1.2481 0.2644Factor variables
wage1 =wage1 %>% mutate(educatsf=factor(educats,label=c("low","normal","high")))Compare:
wage1 %>% group_by(educatsf) %>% summarise(n())## # A tibble: 3 x 2
## educatsf `n()`
## <fct> <int>
## 1 low 116
## 2 normal 198
## 3 high 212wage1 %>% group_by(educats) %>% summarise(n())## # A tibble: 3 x 2
## educats `n()`
## <dbl> <int>
## 1 0 116
## 2 1 198
## 3 2 212Running the same regression again:
reg2=lm(wage ~ educatsf, wage1)
reg2 %>% summary()##
## Call:
## lm(formula = wage ~ educatsf, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.393 -2.119 -1.033 1.245 17.587
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.0567 0.3207 12.651 < 2e-16 ***
## educatsfnormal 1.3146 0.4038 3.255 0.00121 **
## educatsfhigh 3.3359 0.3989 8.363 5.56e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.454 on 523 degrees of freedom
## Multiple R-squared: 0.1287, Adjusted R-squared: 0.1254
## F-statistic: 38.64 on 2 and 523 DF, p-value: 2.236e-16Dummies as dependent variable
bm=read.csv("https://www.dropbox.com/s/e4w6pjm6b4wz9do/bm.csv?dl=1")
summary(lm(call~ofjobs+computerskills+education,bm))##
## Call:
## lm(formula = call ~ ofjobs + computerskills + education, data = bm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.10351 -0.07902 -0.07626 -0.07607 0.92788
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.101742 0.022776 4.467 8.11e-06 ***
## ofjobs 0.001381 0.003287 0.420 0.674
## computerskills -0.020734 0.010194 -2.034 0.042 *
## education -0.002569 0.005586 -0.460 0.646
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.272 on 4866 degrees of freedom
## Multiple R-squared: 0.0008958, Adjusted R-squared: 0.0002798
## F-statistic: 1.454 on 3 and 4866 DF, p-value: 0.225 summary(lm(call~education,bm))##
## Call:
## lm(formula = call ~ education, data = bm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.08841 -0.08185 -0.07966 -0.07966 0.92034
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.088407 0.020117 4.395 1.13e-05 ***
## education -0.002187 0.005454 -0.401 0.688
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2721 on 4868 degrees of freedom
## Multiple R-squared: 3.304e-05, Adjusted R-squared: -0.0001724
## F-statistic: 0.1608 on 1 and 4868 DF, p-value: 0.6884summary(lm(call~black,bm))##
## Call:
## lm(formula = call ~ black, data = bm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.09651 -0.09651 -0.06448 -0.06448 0.93552
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.096509 0.005505 17.532 < 2e-16 ***
## black -0.032033 0.007785 -4.115 3.94e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2716 on 4868 degrees of freedom
## Multiple R-squared: 0.003466, Adjusted R-squared: 0.003261
## F-statistic: 16.93 on 1 and 4868 DF, p-value: 3.941e-05library(ggplot2)
agg=bm %>% group_by(black) %>% summarise(call=mean(call))
ggplot(agg,aes(x=black,y=call))+geom_bar(stat="identity")+theme_minimal()
What about continous explanatory variables?
(linear0 <- lm(call ~ yearsexp , data = bm)) %>% summary()##
## Call:
## lm(formula = call ~ yearsexp, data = bm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.20030 -0.08101 -0.07439 -0.06776 0.94218
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0545046 0.0071949 7.575 4.26e-14 ***
## yearsexp 0.0033136 0.0007716 4.295 1.78e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2716 on 4868 degrees of freedom
## Multiple R-squared: 0.003774, Adjusted R-squared: 0.00357
## F-statistic: 18.44 on 1 and 4868 DF, p-value: 1.784e-05(linear1 <- lm(call ~ factor(yearsexp), data = bm)) %>% summary()##
## Call:
## lm(formula = call ~ factor(yearsexp), data = bm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.25000 -0.08194 -0.07246 -0.05998 0.97059
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0666667 0.0404239 1.649 0.0992 .
## factor(yearsexp)2 -0.0041667 0.0429301 -0.097 0.9227
## factor(yearsexp)3 -0.0202749 0.0448679 -0.452 0.6514
## factor(yearsexp)4 0.0152700 0.0420835 0.363 0.7167
## factor(yearsexp)5 0.0043393 0.0421797 0.103 0.9181
## factor(yearsexp)6 -0.0066911 0.0415222 -0.161 0.8720
## factor(yearsexp)7 0.0109673 0.0420715 0.261 0.7943
## factor(yearsexp)8 0.0059977 0.0419680 0.143 0.8864
## factor(yearsexp)9 0.0276730 0.0457883 0.604 0.5456
## factor(yearsexp)10 0.0487179 0.0469013 1.039 0.2990
## factor(yearsexp)11 0.0373796 0.0453778 0.824 0.4101
## factor(yearsexp)12 0.0057971 0.0519596 0.112 0.9112
## factor(yearsexp)13 0.1021645 0.0459520 2.223 0.0262 *
## factor(yearsexp)14 0.0004474 0.0461260 0.010 0.9923
## factor(yearsexp)15 -0.0372549 0.0616186 -0.605 0.5455
## factor(yearsexp)16 0.0929078 0.0491566 1.890 0.0588 .
## factor(yearsexp)17 -0.0666667 0.1616955 -0.412 0.6801
## factor(yearsexp)18 0.0242424 0.0508830 0.476 0.6338
## factor(yearsexp)19 0.0855072 0.0568565 1.504 0.1327
## factor(yearsexp)20 0.1333333 0.0611152 2.182 0.0292 *
## factor(yearsexp)21 0.0609929 0.0565566 1.078 0.2809
## factor(yearsexp)22 0.1833333 0.1040473 1.762 0.0781 .
## factor(yearsexp)23 -0.0666667 0.0990179 -0.673 0.5008
## factor(yearsexp)25 -0.0666667 0.1101769 -0.605 0.5451
## factor(yearsexp)26 0.0391026 0.0483854 0.808 0.4190
## factor(yearsexp)44 -0.0666667 0.2741681 -0.243 0.8079
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2712 on 4844 degrees of freedom
## Multiple R-squared: 0.01179, Adjusted R-squared: 0.006685
## F-statistic: 2.311 on 25 and 4844 DF, p-value: 0.0002247Student Question: A stepwise linear model?
bm= bm %>% mutate(moret10=yearsexp>10,
moret10Xyearsexp=moret10*yearsexp,
dev=ifelse(moret10==T, yearsexp-10,yearsexp))
lm(call ~ yearsexp , data = bm) %>% summary()##
## Call:
## lm(formula = call ~ yearsexp, data = bm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.20030 -0.08101 -0.07439 -0.06776 0.94218
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0545046 0.0071949 7.575 4.26e-14 ***
## yearsexp 0.0033136 0.0007716 4.295 1.78e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2716 on 4868 degrees of freedom
## Multiple R-squared: 0.003774, Adjusted R-squared: 0.00357
## F-statistic: 18.44 on 1 and 4868 DF, p-value: 1.784e-05lm(call ~ yearsexp+moret10 , data = bm) %>% summary()##
## Call:
## lm(formula = call ~ yearsexp + moret10, data = bm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.15966 -0.07550 -0.07223 -0.06896 0.93594
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.062423 0.008940 6.982 3.3e-12 ***
## yearsexp 0.001634 0.001365 1.197 0.231
## moret10TRUE 0.025329 0.016979 1.492 0.136
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2716 on 4867 degrees of freedom
## Multiple R-squared: 0.00423, Adjusted R-squared: 0.003821
## F-statistic: 10.34 on 2 and 4867 DF, p-value: 3.314e-05res=lm(call ~ yearsexp+moret10+moret10Xyearsexp , data = bm)
res %>% summary()##
## Call:
## lm(formula = call ~ yearsexp + moret10 + moret10Xyearsexp, data = bm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.12465 -0.07921 -0.07269 -0.06617 0.94360
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.053137 0.012612 4.213 2.56e-05 ***
## yearsexp 0.003259 0.002070 1.574 0.1155
## moret10TRUE 0.054572 0.032757 1.666 0.0958 .
## moret10Xyearsexp -0.002874 0.002753 -1.044 0.2966
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2716 on 4866 degrees of freedom
## Multiple R-squared: 0.004453, Adjusted R-squared: 0.003839
## F-statistic: 7.255 on 3 and 4866 DF, p-value: 7.469e-05lm(call ~ yearsexp+moret10Xyearsexp , data = bm) %>% summary()##
## Call:
## lm(formula = call ~ yearsexp + moret10Xyearsexp, data = bm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.19595 -0.07734 -0.07331 -0.06928 0.93676
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.061226 0.011642 5.259 1.51e-07 ***
## yearsexp 0.002014 0.001931 1.043 0.297
## moret10Xyearsexp 0.001048 0.001427 0.734 0.463
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2716 on 4867 degrees of freedom
## Multiple R-squared: 0.003885, Adjusted R-squared: 0.003476
## F-statistic: 9.491 on 2 and 4867 DF, p-value: 7.696e-05\[ y=\beta_1 + \beta_2 exper + \beta_3 MT10 + \beta_4 MT10 \times exper\]
say we are at 15 years
\[ y=\beta_1+ \beta_3 + (\beta_2 + \beta_4 )exper \]
bm=bm %>% mutate(hat=res$coefficients[[1]] +
res$coefficients[[2]] * yearsexp+
res$coefficients[[3]] * moret10 +
res$coefficients[[4]] * moret10Xyearsexp )
ggplot(bm, aes(x=yearsexp,y=hat))+geom_point()
agg2=agg=bm %>% group_by(yearsexp) %>% summarise(call=mean(call))
ggplot(bm,aes(x=yearsexp,y=call) ) + geom_jitter()+
geom_smooth(method="lm")+
geom_bar(data=agg2,aes(x=yearsexp,y=call),
stat="identity",color="orange",
fill="orange",alpha=0.3)+
theme_minimal()
summary(lm(call~yearsexp,bm))##
## Call:
## lm(formula = call ~ yearsexp, data = bm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.20030 -0.08101 -0.07439 -0.06776 0.94218
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0545046 0.0071949 7.575 4.26e-14 ***
## yearsexp 0.0033136 0.0007716 4.295 1.78e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2716 on 4868 degrees of freedom
## Multiple R-squared: 0.003774, Adjusted R-squared: 0.00357
## F-statistic: 18.44 on 1 and 4868 DF, p-value: 1.784e-05 summary(linear2 <- lm(call ~ black, data = bm))##
## Call:
## lm(formula = call ~ black, data = bm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.09651 -0.09651 -0.06448 -0.06448 0.93552
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.096509 0.005505 17.532 < 2e-16 ***
## black -0.032033 0.007785 -4.115 3.94e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2716 on 4868 degrees of freedom
## Multiple R-squared: 0.003466, Adjusted R-squared: 0.003261
## F-statistic: 16.93 on 1 and 4868 DF, p-value: 3.941e-05 summary(linear1 <- lm(call ~ yearsexp, data = bm))##
## Call:
## lm(formula = call ~ yearsexp, data = bm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.20030 -0.08101 -0.07439 -0.06776 0.94218
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0545046 0.0071949 7.575 4.26e-14 ***
## yearsexp 0.0033136 0.0007716 4.295 1.78e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2716 on 4868 degrees of freedom
## Multiple R-squared: 0.003774, Adjusted R-squared: 0.00357
## F-statistic: 18.44 on 1 and 4868 DF, p-value: 1.784e-05 library(aod)
library(margins)
summary(logit1 <- glm(call ~ yearsexp, data = bm, family = "binomial"))##
## Call:
## glm(formula = call ~ yearsexp, family = "binomial", data = bm)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.7780 -0.4075 -0.3924 -0.3779 2.3598
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.75960 0.09620 -28.687 < 2e-16 ***
## yearsexp 0.03908 0.00918 4.257 2.07e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2726.9 on 4869 degrees of freedom
## Residual deviance: 2710.2 on 4868 degrees of freedom
## AIC: 2714.2
##
## Number of Fisher Scoring iterations: 5 summary(linear1)##
## Call:
## lm(formula = call ~ yearsexp, data = bm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.20030 -0.08101 -0.07439 -0.06776 0.94218
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0545046 0.0071949 7.575 4.26e-14 ***
## yearsexp 0.0033136 0.0007716 4.295 1.78e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2716 on 4868 degrees of freedom
## Multiple R-squared: 0.003774, Adjusted R-squared: 0.00357
## F-statistic: 18.44 on 1 and 4868 DF, p-value: 1.784e-05 margins(logit1)## Average marginal effects## glm(formula = call ~ yearsexp, family = "binomial", data = bm)## yearsexp
## 0.002881 log(100)## [1] 4.60517Note that the linear model is fairly close to the average marginal effect
summary(logit2 <- glm(call ~ black, data = bm, family = "binomial"))##
## Call:
## glm(formula = call ~ black, family = "binomial", data = bm)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.4505 -0.4505 -0.3651 -0.3651 2.3416
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.23663 0.06863 -32.590 < 2e-16 ***
## black -0.43818 0.10732 -4.083 4.45e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2726.9 on 4869 degrees of freedom
## Residual deviance: 2709.9 on 4868 degrees of freedom
## AIC: 2713.9
##
## Number of Fisher Scoring iterations: 5 #summary(linear2)
margins(logit2)## Average marginal effects## glm(formula = call ~ black, family = "binomial", data = bm)## black
## -0.03232 summary(logit3 <- glm(call ~ black+yearsexp, data = bm, family = "binomial"))##
## Call:
## glm(formula = call ~ black + yearsexp, family = "binomial", data = bm)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.7008 -0.4318 -0.4006 -0.3496 2.4537
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.560532 0.105784 -24.205 < 2e-16 ***
## black -0.438409 0.107523 -4.077 4.56e-05 ***
## yearsexp 0.039089 0.009199 4.249 2.14e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2726.9 on 4869 degrees of freedom
## Residual deviance: 2693.2 on 4867 degrees of freedom
## AIC: 2699.2
##
## Number of Fisher Scoring iterations: 5 summary(linear3<- lm(call ~ black+ yearsexp, data = bm))##
## Call:
## lm(formula = call ~ black + yearsexp, data = bm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.18403 -0.09148 -0.07715 -0.05843 0.95810
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0705426 0.0081743 8.630 < 2e-16 ***
## black -0.0319446 0.0077711 -4.111 4.01e-05 ***
## yearsexp 0.0033052 0.0007703 4.291 1.82e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2712 on 4867 degrees of freedom
## Multiple R-squared: 0.007221, Adjusted R-squared: 0.006813
## F-statistic: 17.7 on 2 and 4867 DF, p-value: 2.19e-08 margins(logit3)## Average marginal effects## glm(formula = call ~ black + yearsexp, family = "binomial", data = bm)## black yearsexp
## -0.03221 0.002872 margins(linear3)## Average marginal effects## lm(formula = call ~ black + yearsexp, data = bm)## black yearsexp
## -0.03194 0.003305 #test=lm(call~ yearsexp*education,bm)
#mar=margins(test,type="response")
plot(plogis,-5 ,5, )
plogis(2)## [1] 0.8807971 bm["callstar1"] = plogis(-2.7+bm$yearsexp * .3)
bm["callstar2"] = plogis( -2.7+bm$yearsexp * 0.06)
bm["callstar3"] = plogis( -5+bm$yearsexp * 0.06)
bm["callstar4"] = plogis(-1 +bm$yearsexp*.8 )
summary(bm$callstar1)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.08317 0.23148 0.28905 0.40104 0.50000 0.99997 bm=bm[order(bm$yearsexp),]
bm["yearsexp_rand"]=bm$yearsexp+runif( nrow(bm),min = -0.1, max = .1)
bm["call_rand"]=bm$call+runif( nrow(bm),min = -0.02, max = .02)
plot(bm$yearsexp_rand, bm$call_rand, main="",
xlab="Experience", ylab="Call", pch=1)
lines(bm$yearsexp, bm$callstar1 ,col=2)
lines(bm$yearsexp, bm$callstar2 ,col=3)
lines(bm$yearsexp, bm$callstar3 ,col=4)
lines(bm$yearsexp, bm$callstar4 ,col=5)
Nonlinear
wage1=wage1 %>% mutate(educ2 =educ^2)
summary(lm(wage ~ educ+educ2, wage1))##
## Call:
## lm(formula = wage ~ educ + educ2, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.8722 -2.0002 -0.7472 1.2642 17.0159
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.40769 1.45886 3.707 0.000232 ***
## educ -0.60750 0.24149 -2.516 0.012181 *
## educ2 0.04907 0.01007 4.872 1.46e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.307 on 523 degrees of freedom
## Multiple R-squared: 0.201, Adjusted R-squared: 0.198
## F-statistic: 65.79 on 2 and 523 DF, p-value: < 2.2e-16 library(ggplot2)
ggplot(wage1, aes(x=educ, y=wage))+geom_point()+theme_minimal()+
geom_smooth(method=lm,se=FALSE,formula=y ~ poly(x, 2))
`
log linear
library(ggplot2)
z=seq(-.1,.1,.001)
ln1Pz=log(1+z)
df=data.frame(z,ln1Pz)
ggplot(df,aes(x=z))+geom_line(aes(y=ln1Pz),color="green")+
geom_line(aes(y=z),color="red") + theme_minimal() + ylab("ln(1+z)")
Many dummies as control
library(dplyr)
prod=read.csv("https://www.dropbox.com/s/v1j4xzkaado8zlz/prod_balanced.csv?dl=1")
prod=prod %>% mutate(lnl=log(l),lnva=log(va))
prod=prod %>% arrange(id,year) %>% select(id,year,va,l,k,lnk,lnl,lnva)
reg1<-lm(lnva~lnl+lnk,prod)
reg1 %>% summary()##
## Call:
## lm(formula = lnva ~ lnl + lnk, data = prod)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.8415 -0.4453 0.0326 0.4820 3.0979
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.423770 0.034256 99.95 <2e-16 ***
## lnl 0.950352 0.010352 91.81 <2e-16 ***
## lnk 0.304229 0.005801 52.45 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7568 on 14501 degrees of freedom
## Multiple R-squared: 0.7483, Adjusted R-squared: 0.7482
## F-statistic: 2.155e+04 on 2 and 14501 DF, p-value: < 2.2e-16reg2<-lm(lnva~lnl+lnk+factor(year),prod)
reg2 %>% summary()##
## Call:
## lm(formula = lnva ~ lnl + lnk + factor(year), data = prod)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9437 -0.4423 0.0321 0.4801 3.0727
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.400842 0.038004 89.486 < 2e-16 ***
## lnl 0.949582 0.010386 91.428 < 2e-16 ***
## lnk 0.303976 0.005813 52.296 < 2e-16 ***
## factor(year)80 0.057615 0.025075 2.298 0.0216 *
## factor(year)81 0.130706 0.025077 5.212 1.89e-07 ***
## factor(year)82 0.049363 0.025085 1.968 0.0491 *
## factor(year)83 -0.031615 0.025081 -1.260 0.2075
## factor(year)84 0.010665 0.025076 0.425 0.6706
## factor(year)85 -0.055827 0.025090 -2.225 0.0261 *
## factor(year)86 0.062352 0.025121 2.482 0.0131 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7549 on 14494 degrees of freedom
## Multiple R-squared: 0.7496, Adjusted R-squared: 0.7495
## F-statistic: 4821 on 9 and 14494 DF, p-value: < 2.2e-16reg2<-lm(lnva~lnl+lnk+factor(year)+factor(id),prod)
reg2 %>% summary()##
## Call:
## lm(formula = lnva ~ lnl + lnk + factor(year) + factor(id), data = prod)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.5554 -0.2349 0.0323 0.2767 3.2121
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.6053565 0.2142689 26.160 < 2e-16 ***
## lnl 0.7302864 0.0191514 38.132 < 2e-16 ***
## lnk 0.0832028 0.0144970 5.739 9.72e-09 ***
## factor(year)80 0.0775959 0.0171329 4.529 5.98e-06 ***
## factor(year)81 0.1594889 0.0171602 9.294 < 2e-16 ***
## factor(year)82 0.0471271 0.0171524 2.748 0.006013 **
## factor(year)83 -0.0429621 0.0171425 -2.506 0.012217 *
## factor(year)84 0.0061375 0.0171152 0.359 0.719903
## factor(year)85 -0.0543233 0.0171777 -3.162 0.001568 **
## factor(year)86 0.0725690 0.0173079 4.193 2.77e-05 ***
## factor(id)81 1.4392760 0.2608948 5.517 3.52e-08 ***
## factor(id)99 -0.1671771 0.2580364 -0.648 0.517073
## factor(id)117 0.8002776 0.2582686 3.099 0.001948 **
## factor(id)135 -0.0069199 0.2578253 -0.027 0.978588
## factor(id)162 1.5912130 0.2632387 6.045 1.54e-09 ***
## factor(id)171 1.0838099 0.2594566 4.177 2.97e-05 ***
## factor(id)198 -0.6712341 0.2578931 -2.603 0.009258 **
## factor(id)342 0.5866663 0.2610479 2.247 0.024635 *
## factor(id)396 0.1227912 0.2579268 0.476 0.634033
## factor(id)414 1.5716587 0.2578788 6.095 1.13e-09 ***
## factor(id)558 -0.6740037 0.2575815 -2.617 0.008890 **
## factor(id)648 0.5636927 0.2583559 2.182 0.029139 *
## factor(id)729 -0.3576507 0.2576500 -1.388 0.165123
## factor(id)819 1.5474498 0.2731501 5.665 1.50e-08 ***
## factor(id)891 -0.1705523 0.2577757 -0.662 0.508220
## factor(id)981 1.2012318 0.2612698 4.598 4.31e-06 ***
## factor(id)1152 2.5132660 0.2755971 9.119 < 2e-16 ***
## factor(id)1224 1.5204115 0.2601218 5.845 5.19e-09 ***
## factor(id)1278 1.4528151 0.2577798 5.636 1.78e-08 ***
## factor(id)1287 0.0813430 0.2576937 0.316 0.752268
## factor(id)1314 1.3744719 0.2578788 5.330 9.99e-08 ***
## factor(id)1341 -0.3129771 0.2577263 -1.214 0.224626
## factor(id)1458 -0.2892183 0.2582628 -1.120 0.262794
## factor(id)1485 1.5617484 0.2712359 5.758 8.71e-09 ***
## factor(id)1548 -0.1528757 0.2581165 -0.592 0.553678
## factor(id)1584 -0.1817287 0.2575900 -0.705 0.480515
## factor(id)1656 -0.6440409 0.2576363 -2.500 0.012439 *
## factor(id)1665 -0.3132619 0.2577664 -1.215 0.224277
## factor(id)1728 0.3898441 0.2582572 1.510 0.131191
## factor(id)1755 -0.1757968 0.2580292 -0.681 0.495691
## factor(id)1764 0.2506937 0.2576516 0.973 0.330574
## factor(id)1773 -0.6745368 0.2577635 -2.617 0.008884 **
## factor(id)1854 0.2580016 0.2594085 0.995 0.319961
## factor(id)1872 -0.3059760 0.2576493 -1.188 0.235026
## factor(id)2052 2.1571661 0.2612985 8.256 < 2e-16 ***
## factor(id)2061 -0.4319763 0.2575558 -1.677 0.093525 .
## factor(id)2169 -0.1298966 0.2580013 -0.503 0.614641
## factor(id)2223 1.2859217 0.2629495 4.890 1.02e-06 ***
## factor(id)2241 -0.1630382 0.2580493 -0.632 0.527522
## factor(id)2286 0.4990979 0.2603165 1.917 0.055226 .
## factor(id)2295 0.9852219 0.2611796 3.772 0.000163 ***
## factor(id)2331 0.8541909 0.2580046 3.311 0.000933 ***
## factor(id)2349 0.1338416 0.2580956 0.519 0.604067
## factor(id)2403 0.5777349 0.2591303 2.230 0.025797 *
## factor(id)2421 -0.0061601 0.2575429 -0.024 0.980918
## factor(id)2448 0.0964410 0.2580097 0.374 0.708568
## factor(id)2475 1.4355043 0.2631320 5.455 4.98e-08 ***
## factor(id)2673 0.0144194 0.2583855 0.056 0.955498
## factor(id)2709 -0.1662128 0.2577322 -0.645 0.519000
## factor(id)2727 -0.0147164 0.2627237 -0.056 0.955331
## factor(id)2889 -0.3866347 0.2576176 -1.501 0.133430
## factor(id)2907 0.1298096 0.2578423 0.503 0.614660
## factor(id)3033 0.2009196 0.2576569 0.780 0.435526
## factor(id)3069 0.2682161 0.2585572 1.037 0.299589
## factor(id)3105 1.0558392 0.2617694 4.033 5.53e-05 ***
## factor(id)3114 -0.2437408 0.2595274 -0.939 0.347660
## factor(id)3123 -0.6826611 0.2579146 -2.647 0.008135 **
## factor(id)3159 -0.3801967 0.2576666 -1.476 0.140093
## factor(id)3402 -0.3274581 0.2576417 -1.271 0.203758
## factor(id)3429 -0.1124442 0.2587536 -0.435 0.663889
## factor(id)3492 -0.5328434 0.2576081 -2.068 0.038620 *
## factor(id)3501 0.4488308 0.2612827 1.718 0.085858 .
## factor(id)3609 0.5740498 0.2579775 2.225 0.026086 *
## factor(id)3636 1.9612776 0.2706823 7.246 4.55e-13 ***
## factor(id)3987 -0.2724541 0.2577776 -1.057 0.290561
## factor(id)4023 -0.0332804 0.2579733 -0.129 0.897354
## factor(id)4509 -0.1502970 0.2578681 -0.583 0.560008
## factor(id)4599 0.2285003 0.2577492 0.887 0.375353
## factor(id)4653 0.1672693 0.2580586 0.648 0.516878
## factor(id)4842 -0.1946538 0.2575439 -0.756 0.449778
## factor(id)4896 -0.5156019 0.2575777 -2.002 0.045335 *
## factor(id)4923 2.5063944 0.2670160 9.387 < 2e-16 ***
## factor(id)4968 -0.0867783 0.2576741 -0.337 0.736292
## factor(id)4986 0.5715317 0.2584749 2.211 0.027042 *
## factor(id)5094 0.1015499 0.2585121 0.393 0.694456
## factor(id)5112 -0.0020624 0.2579723 -0.008 0.993621
## factor(id)5211 0.2337764 0.2578588 0.907 0.364632
## factor(id)5265 -0.0748174 0.2577130 -0.290 0.771582
## factor(id)5301 -0.1092679 0.2579184 -0.424 0.671826
## factor(id)5346 -0.1151677 0.2575644 -0.447 0.654781
## factor(id)5589 1.0769387 0.2594258 4.151 3.33e-05 ***
## factor(id)5607 -0.6144993 0.2580085 -2.382 0.017248 *
## factor(id)5661 1.4233706 0.2625286 5.422 6.01e-08 ***
## factor(id)5724 -0.4413269 0.2575495 -1.714 0.086634 .
## factor(id)5733 1.0410181 0.2577489 4.039 5.40e-05 ***
## factor(id)5832 -0.0733566 0.2578258 -0.285 0.776016
## factor(id)5868 -0.2832355 0.2580221 -1.098 0.272349
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## factor(id)76239 0.4852471 0.2580516 1.880 0.060073 .
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## factor(id)85059 0.4701586 0.2581579 1.821 0.068599 .
## factor(id)85086 0.5329817 0.2588599 2.059 0.039519 *
## factor(id)85167 0.0087186 0.2576077 0.034 0.973002
## factor(id)85248 -0.4954272 0.2576447 -1.923 0.054514 .
## factor(id)85311 1.0124612 0.2595683 3.901 9.65e-05 ***
## factor(id)85374 -0.2110539 0.2576777 -0.819 0.412767
## factor(id)85392 0.5671706 0.2577145 2.201 0.027770 *
## factor(id)85428 0.3394587 0.2579377 1.316 0.188181
## factor(id)85491 -0.9142074 0.2575521 -3.550 0.000387 ***
## factor(id)85527 0.4473084 0.2575814 1.737 0.082487 .
## factor(id)85572 -0.0098638 0.2577020 -0.038 0.969468
## factor(id)85734 0.1289049 0.2583928 0.499 0.617878
## factor(id)85779 1.2672725 0.2622917 4.832 1.37e-06 ***
## factor(id)85914 0.5537526 0.2603077 2.127 0.033414 *
## factor(id)85941 0.3168445 0.2583766 1.226 0.220113
## factor(id)86103 -0.0609887 0.2599647 -0.235 0.814520
## factor(id)86211 0.5838600 0.2587494 2.256 0.024058 *
## factor(id)86229 0.4346935 0.2607854 1.667 0.095566 .
## factor(id)86247 1.0191228 0.2591790 3.932 8.46e-05 ***
## factor(id)86274 0.2576502 0.2578240 0.999 0.317656
## factor(id)86292 -0.4864104 0.2583340 -1.883 0.059740 .
## factor(id)86346 -0.6825321 0.2577348 -2.648 0.008102 **
## factor(id)86517 0.4809988 0.2579632 1.865 0.062260 .
## factor(id)86571 1.3730966 0.2605078 5.271 1.38e-07 ***
## factor(id)86751 1.9925903 0.2656214 7.502 6.72e-14 ***
## factor(id)86796 1.9076046 0.2610110 7.309 2.86e-13 ***
## factor(id)86859 0.2897880 0.2575855 1.125 0.260603
## factor(id)86868 -0.0544135 0.2577192 -0.211 0.832785
## factor(id)86913 0.6028199 0.2577115 2.339 0.019344 *
## factor(id)86985 1.0401270 0.2577881 4.035 5.50e-05 ***
## factor(id)87003 0.9371051 0.2592758 3.614 0.000302 ***
## factor(id)87147 0.4107676 0.2583315 1.590 0.111842
## factor(id)87156 -0.2449959 0.2575914 -0.951 0.341570
## factor(id)87192 0.3959167 0.2581175 1.534 0.125088
## factor(id)87201 1.4971049 0.2608792 5.739 9.76e-09 ***
## factor(id)87237 0.9439780 0.2606902 3.621 0.000295 ***
## factor(id)87264 0.6647741 0.2583848 2.573 0.010099 *
## factor(id)87273 1.2038403 0.2585323 4.656 3.25e-06 ***
## factor(id)87282 0.9251270 0.2594118 3.566 0.000363 ***
## factor(id)87336 0.1620678 0.2576368 0.629 0.529324
## factor(id)87408 1.0639271 0.2604046 4.086 4.42e-05 ***
## factor(id)87453 1.2631399 0.2631397 4.800 1.60e-06 ***
## factor(id)87516 -0.7290798 0.2575779 -2.831 0.004655 **
## factor(id)87579 1.2580659 0.2623371 4.796 1.64e-06 ***
## factor(id)87606 1.0699510 0.2615765 4.090 4.33e-05 ***
## factor(id)87642 1.9657801 0.2593897 7.578 3.74e-14 ***
## factor(id)87651 0.6933751 0.2582223 2.685 0.007258 **
## factor(id)87687 1.2158985 0.2628485 4.626 3.77e-06 ***
## factor(id)87714 1.4565534 0.2614974 5.570 2.60e-08 ***
## factor(id)87723 1.6791396 0.2671529 6.285 3.38e-10 ***
## factor(id)87741 2.5742576 0.2731234 9.425 < 2e-16 ***
## factor(id)87759 0.8860105 0.2583886 3.429 0.000608 ***
## factor(id)87777 2.7160916 0.2689668 10.098 < 2e-16 ***
## factor(id)87804 1.2363999 0.2621093 4.717 2.42e-06 ***
## factor(id)87813 0.5087874 0.2580244 1.972 0.048648 *
## factor(id)87849 1.2257644 0.2582878 4.746 2.10e-06 ***
## factor(id)87858 0.7626522 0.2656985 2.870 0.004107 **
## factor(id)87876 1.3796153 0.2597685 5.311 1.11e-07 ***
## factor(id)87921 2.5827759 0.2630396 9.819 < 2e-16 ***
## factor(id)87939 1.4937030 0.2584467 5.780 7.67e-09 ***
## factor(id)87984 0.3168918 0.2616032 1.211 0.225786
## factor(id)88002 1.3163010 0.2586850 5.088 3.66e-07 ***
## factor(id)88047 1.6301019 0.2607455 6.252 4.19e-10 ***
## factor(id)88083 0.7853075 0.2615200 3.003 0.002680 **
## factor(id)88155 0.5155198 0.2578237 2.000 0.045575 *
## factor(id)88164 -0.3689001 0.2577429 -1.431 0.152377
## factor(id)88173 1.0498293 0.2576881 4.074 4.65e-05 ***
## factor(id)88209 0.1473896 0.2576697 0.572 0.567325
## factor(id)88218 1.2408499 0.2609672 4.755 2.01e-06 ***
## factor(id)88227 1.4558196 0.2578186 5.647 1.67e-08 ***
## factor(id)88236 2.9191316 0.2760976 10.573 < 2e-16 ***
## factor(id)88245 0.3384258 0.2599562 1.302 0.192989
## factor(id)88254 1.2392870 0.2718956 4.558 5.21e-06 ***
## factor(id)88317 1.8794386 0.2685510 6.998 2.72e-12 ***
## factor(id)88407 0.8936550 0.2613275 3.420 0.000629 ***
## factor(id)88434 0.6963526 0.2584940 2.694 0.007072 **
## factor(id)88497 0.3398834 0.2576338 1.319 0.187109
## factor(id)88533 -0.0806552 0.2576142 -0.313 0.754221
## factor(id)88587 0.0317383 0.2575788 0.123 0.901936
## factor(id)88605 1.4250879 0.2604684 5.471 4.55e-08 ***
## factor(id)88641 1.9423935 0.2588474 7.504 6.60e-14 ***
## factor(id)88659 1.9224117 0.2618282 7.342 2.23e-13 ***
## factor(id)88668 0.5168427 0.2610885 1.980 0.047774 *
## factor(id)88695 -0.2327780 0.2576802 -0.903 0.366352
## factor(id)88722 1.0569594 0.2675614 3.950 7.85e-05 ***
## factor(id)88785 0.9959510 0.2595202 3.838 0.000125 ***
## factor(id)88794 -0.9443197 0.2590011 -3.646 0.000267 ***
## factor(id)88821 0.5058040 0.2576279 1.963 0.049632 *
## factor(id)88866 1.0823482 0.2599553 4.164 3.15e-05 ***
## factor(id)88938 0.1023710 0.2575585 0.397 0.691030
## factor(id)88983 0.2046648 0.2600879 0.787 0.431351
## factor(id)89019 1.3619894 0.2766755 4.923 8.64e-07 ***
## factor(id)89055 0.8691553 0.2643976 3.287 0.001014 **
## factor(id)89082 1.1145866 0.2621791 4.251 2.14e-05 ***
## factor(id)89181 0.7669371 0.2579706 2.973 0.002955 **
## factor(id)89199 2.1833951 0.2622375 8.326 < 2e-16 ***
## factor(id)89244 0.9105354 0.2575476 3.535 0.000409 ***
## factor(id)89253 0.8028419 0.2586714 3.104 0.001915 **
## factor(id)89271 1.4223329 0.2647958 5.371 7.95e-08 ***
## factor(id)89379 0.7403087 0.2577119 2.873 0.004078 **
## factor(id)89406 -0.1465898 0.2578965 -0.568 0.569770
## factor(id)89424 1.7462470 0.2591762 6.738 1.68e-11 ***
## factor(id)89433 1.2315512 0.2642539 4.660 3.19e-06 ***
## factor(id)89514 -0.4660893 0.2592468 -1.798 0.072223 .
## factor(id)89532 0.1564811 0.2577444 0.607 0.543784
## factor(id)89577 0.2083435 0.2576205 0.809 0.418690
## factor(id)89586 0.0210524 0.2576814 0.082 0.934887
## factor(id)89649 0.3554937 0.2601297 1.367 0.171774
## factor(id)89676 0.2667485 0.2582490 1.033 0.301665
## factor(id)89721 0.8341158 0.2596039 3.213 0.001317 **
## factor(id)89865 -0.1008379 0.2587885 -0.390 0.696799
## factor(id)89892 -0.0792915 0.2575989 -0.308 0.758232
## factor(id)89937 0.1814181 0.2577648 0.704 0.481562
## factor(id)89946 -0.6063731 0.2575450 -2.354 0.018566 *
## factor(id)90045 2.6802991 0.2608880 10.274 < 2e-16 ***
## factor(id)90063 0.4821381 0.2593599 1.859 0.063057 .
## factor(id)90198 0.7229879 0.2604004 2.776 0.005504 **
## factor(id)90225 1.3136963 0.2585253 5.081 3.80e-07 ***
## factor(id)90243 0.2002066 0.2576638 0.777 0.437169
## factor(id)90279 -0.2209290 0.2577541 -0.857 0.391389
## factor(id)90306 0.6992883 0.2613107 2.676 0.007458 **
## factor(id)90315 0.6832602 0.2589915 2.638 0.008346 **
## factor(id)90351 1.0263208 0.2682317 3.826 0.000131 ***
## factor(id)90369 1.7827878 0.2678655 6.656 2.94e-11 ***
## factor(id)90432 0.1892960 0.2585348 0.732 0.464068
## factor(id)90441 0.5085938 0.2576695 1.974 0.048424 *
## factor(id)90504 0.5445689 0.2587908 2.104 0.035373 *
## factor(id)90522 1.0348931 0.2592396 3.992 6.59e-05 ***
## factor(id)90531 1.2768330 0.2601525 4.908 9.31e-07 ***
## factor(id)90558 0.5703615 0.2604390 2.190 0.028542 *
## factor(id)90585 0.2509196 0.2576633 0.974 0.330161
## factor(id)90612 1.5908099 0.2697708 5.897 3.80e-09 ***
## factor(id)90639 1.0505318 0.2607759 4.028 5.65e-05 ***
## factor(id)90684 1.3942808 0.2613865 5.334 9.76e-08 ***
## factor(id)90711 0.7816866 0.2582008 3.027 0.002471 **
## factor(id)90819 0.4041932 0.2581114 1.566 0.117382
## factor(id)90864 0.0509994 0.2577137 0.198 0.843133
## factor(id)90882 0.2747534 0.2576110 1.067 0.286198
## factor(id)90891 1.0132094 0.2593597 3.907 9.41e-05 ***
## factor(id)90927 0.9138812 0.2613558 3.497 0.000473 ***
## factor(id)91062 0.7320529 0.2584589 2.832 0.004628 **
## factor(id)91071 -0.2027616 0.2577185 -0.787 0.431439
## factor(id)91143 -0.0026153 0.2577047 -0.010 0.991903
## factor(id)91197 0.0498879 0.2577294 0.194 0.846518
## factor(id)91278 0.1427736 0.2576178 0.554 0.579447
## factor(id)91287 1.4155342 0.2600290 5.444 5.31e-08 ***
## factor(id)91296 0.3460384 0.2614609 1.323 0.185699
## factor(id)91368 0.4525841 0.2577221 1.756 0.079097 .
## factor(id)91404 0.0499710 0.2576110 0.194 0.846196
## factor(id)91629 -0.5770886 0.2584308 -2.233 0.025563 *
## factor(id)91674 0.7227741 0.2588541 2.792 0.005243 **
## factor(id)91728 -0.0669176 0.2577032 -0.260 0.795123
## factor(id)91782 2.1215044 0.2582984 8.213 2.36e-16 ***
## factor(id)91854 0.4445050 0.2580085 1.723 0.084943 .
## factor(id)91908 0.0453901 0.2582662 0.176 0.860494
## factor(id)91926 0.5528037 0.2579142 2.143 0.032103 *
## factor(id)92088 0.8863254 0.2620216 3.383 0.000720 ***
## factor(id)92106 0.0959411 0.2587140 0.371 0.710764
## factor(id)92169 0.8281973 0.2577404 3.213 0.001315 **
## factor(id)92223 -0.0808388 0.2577115 -0.314 0.753770
## factor(id)92232 0.1457932 0.2577854 0.566 0.571703
## factor(id)92538 -0.6547045 0.2589332 -2.528 0.011468 *
## factor(id)92565 -0.4708960 0.2576677 -1.828 0.067643 .
## factor(id)92592 -0.2753193 0.2586138 -1.065 0.287079
## factor(id)92646 0.9280656 0.2620215 3.542 0.000399 ***
## factor(id)92655 -0.2507903 0.2577685 -0.973 0.330607
## factor(id)92736 -0.0577293 0.2578697 -0.224 0.822862
## factor(id)92979 0.2105130 0.2579502 0.816 0.414459
## factor(id)93015 0.0641361 0.2576282 0.249 0.803405
## factor(id)93087 0.9366642 0.2578407 3.633 0.000282 ***
## factor(id)93105 -1.3691998 0.2576439 -5.314 1.09e-07 ***
## factor(id)93186 0.0839955 0.2601716 0.323 0.746817
## factor(id)93195 0.8412455 0.2586597 3.252 0.001148 **
## factor(id)93276 1.7997708 0.2590794 6.947 3.92e-12 ***
## factor(id)93303 0.8591375 0.2576610 3.334 0.000857 ***
## factor(id)93438 0.6637936 0.2576042 2.577 0.009983 **
## factor(id)93447 0.6543407 0.2584532 2.532 0.011361 *
## factor(id)93519 -0.0259064 0.2576213 -0.101 0.919901
## factor(id)93627 -0.0024528 0.2580711 -0.010 0.992417
## factor(id)93636 0.3768219 0.2609351 1.444 0.148730
## factor(id)93645 0.0018211 0.2598049 0.007 0.994407
## factor(id)93726 0.2431416 0.2585700 0.940 0.347065
## factor(id)93861 -0.6948281 0.2577207 -2.696 0.007026 **
## factor(id)93897 0.5816273 0.2588073 2.247 0.024636 *
## factor(id)93933 -0.8315932 0.2576702 -3.227 0.001253 **
## factor(id)93942 0.3911868 0.2575781 1.519 0.128860
## factor(id)94059 1.1990810 0.2577838 4.651 3.33e-06 ***
## factor(id)94158 -0.5645742 0.2576336 -2.191 0.028442 *
## factor(id)94275 0.4994221 0.2578174 1.937 0.052753 .
## factor(id)94392 0.9876897 0.2589362 3.814 0.000137 ***
## factor(id)94518 -0.8581159 0.2575465 -3.332 0.000865 ***
## factor(id)94572 1.3283396 0.2602127 5.105 3.36e-07 ***
## factor(id)94626 -0.3540091 0.2581048 -1.372 0.170221
## factor(id)94662 1.6298265 0.2594459 6.282 3.45e-10 ***
## factor(id)94707 -0.5376160 0.2590865 -2.075 0.038003 *
## factor(id)94752 0.0032215 0.2576878 0.013 0.990026
## factor(id)94761 0.5210282 0.2575745 2.023 0.043112 *
## factor(id)94932 -0.8350614 0.2576210 -3.241 0.001192 **
## factor(id)94986 0.3450263 0.2579127 1.338 0.180997
## factor(id)95148 0.1211833 0.2575577 0.471 0.637999
## factor(id)95175 -0.2195476 0.2576301 -0.852 0.394129
## factor(id)95274 0.5730695 0.2588867 2.214 0.026875 *
## factor(id)95283 0.5154619 0.2577602 2.000 0.045546 *
## factor(id)95355 0.6967064 0.2591407 2.689 0.007186 **
## factor(id)95616 0.0456025 0.2576069 0.177 0.859493
## factor(id)95625 -0.3553529 0.2579903 -1.377 0.168416
## factor(id)95706 -0.7711806 0.2580982 -2.988 0.002814 **
## factor(id)95751 -0.6885778 0.2575969 -2.673 0.007525 **
## factor(id)95787 1.3470695 0.2599817 5.181 2.24e-07 ***
## factor(id)95796 0.3204207 0.2577282 1.243 0.213798
## factor(id)95805 0.1735194 0.2577934 0.673 0.500899
## factor(id)95877 -0.3667293 0.2576273 -1.423 0.154619
## factor(id)95922 0.6963033 0.2579633 2.699 0.006959 **
## factor(id)95994 0.2514171 0.2576262 0.976 0.329133
## factor(id)96012 3.0021487 0.2829598 10.610 < 2e-16 ***
## factor(id)96102 2.2048199 0.2665329 8.272 < 2e-16 ***
## factor(id)96183 0.9872760 0.2577854 3.830 0.000129 ***
## factor(id)96201 1.8590222 0.2675665 6.948 3.89e-12 ***
## factor(id)96273 0.7863726 0.2598452 3.026 0.002481 **
## factor(id)96282 0.9117549 0.2640392 3.453 0.000556 ***
## factor(id)96309 -0.0151066 0.2582038 -0.059 0.953346
## factor(id)96336 0.8390718 0.2576002 3.257 0.001128 **
## factor(id)96381 0.2948155 0.2576293 1.144 0.252504
## factor(id)96399 1.2232669 0.2609031 4.689 2.78e-06 ***
## factor(id)96426 1.8606575 0.2694878 6.904 5.28e-12 ***
## factor(id)96444 -1.2586193 0.2575959 -4.886 1.04e-06 ***
## factor(id)96507 -0.3365902 0.2575890 -1.307 0.191340
## factor(id)96552 0.1711091 0.2576216 0.664 0.506582
## factor(id)96561 1.4833057 0.2578796 5.752 9.03e-09 ***
## factor(id)96606 1.7079845 0.2667450 6.403 1.58e-10 ***
## factor(id)96615 0.7991558 0.2658791 3.006 0.002655 **
## factor(id)96678 0.1278236 0.2577334 0.496 0.619936
## factor(id)96858 -0.2541745 0.2575639 -0.987 0.323740
## factor(id)96885 2.4036185 0.2737264 8.781 < 2e-16 ***
## factor(id)97011 2.6209944 0.2784125 9.414 < 2e-16 ***
## factor(id)97047 1.1776985 0.2592819 4.542 5.62e-06 ***
## factor(id)97119 -0.1755319 0.2577475 -0.681 0.495870
## factor(id)97128 0.0648066 0.2585439 0.251 0.802081
## factor(id)97146 2.6923408 0.2648287 10.166 < 2e-16 ***
## factor(id)97182 0.0116636 0.2576030 0.045 0.963887
## factor(id)97254 -0.1336066 0.2575728 -0.519 0.603969
## factor(id)97353 1.0168029 0.2577442 3.945 8.02e-05 ***
## factor(id)97407 0.1706421 0.2576863 0.662 0.507850
## factor(id)97533 -1.0092892 0.2582781 -3.908 9.36e-05 ***
## factor(id)97884 1.6438909 0.2617162 6.281 3.47e-10 ***
## factor(id)98037 -0.5930641 0.2576007 -2.302 0.021337 *
## factor(id)98064 0.2633950 0.2577385 1.022 0.306826
## factor(id)98082 -0.0609252 0.2575782 -0.237 0.813024
## factor(id)98154 0.5986119 0.2587960 2.313 0.020735 *
## factor(id)98172 -1.4181527 0.2577495 -5.502 3.83e-08 ***
## factor(id)98199 -0.0374161 0.2575439 -0.145 0.884492
## factor(id)98235 0.6721102 0.2601298 2.584 0.009784 **
## factor(id)98253 0.4059026 0.2579295 1.574 0.115583
## factor(id)98262 -0.1860572 0.2576201 -0.722 0.470175
## factor(id)98271 0.6199254 0.2579593 2.403 0.016267 *
## factor(id)98298 -0.0001219 0.2578764 0.000 0.999623
## factor(id)98379 0.2130492 0.2575812 0.827 0.408188
## factor(id)98406 -0.0873709 0.2576008 -0.339 0.734486
## factor(id)98415 1.6953215 0.2576117 6.581 4.86e-11 ***
## factor(id)98424 0.3421246 0.2575852 1.328 0.184136
## factor(id)98433 -0.1014787 0.2577082 -0.394 0.693755
## factor(id)98451 -0.3724707 0.2579693 -1.444 0.148804
## factor(id)98577 0.1744732 0.2577333 0.677 0.498449
## factor(id)98595 -0.5561313 0.2575473 -2.159 0.030843 *
## factor(id)98712 1.2366744 0.2618530 4.723 2.35e-06 ***
## factor(id)98721 0.6819706 0.2607496 2.615 0.008922 **
## factor(id)98739 0.3526775 0.2580664 1.367 0.171770
## factor(id)98748 0.2156309 0.2592094 0.832 0.405493
## factor(id)98802 -0.4555266 0.2578125 -1.767 0.077270 .
## factor(id)98829 0.6663334 0.2605136 2.558 0.010546 *
## factor(id)98838 0.2911006 0.2578358 1.129 0.258913
## factor(id)98847 0.9481148 0.2632603 3.601 0.000318 ***
## factor(id)98865 0.3777183 0.2591205 1.458 0.144950
## factor(id)98901 -0.1841137 0.2610630 -0.705 0.480670
## factor(id)98928 0.4126263 0.2575670 1.602 0.109177
## factor(id)98991 1.9005065 0.2600551 7.308 2.87e-13 ***
## factor(id)99009 1.7272211 0.2661302 6.490 8.90e-11 ***
## factor(id)99045 1.2097829 0.2585447 4.679 2.91e-06 ***
## factor(id)99054 0.8253133 0.2615657 3.155 0.001607 **
## factor(id)99234 1.0294638 0.2646706 3.890 0.000101 ***
## factor(id)99288 0.0336045 0.2576687 0.130 0.896238
## factor(id)99297 0.7089696 0.2595976 2.731 0.006322 **
## factor(id)99306 0.1508402 0.2579751 0.585 0.558754
## factor(id)99396 0.6682148 0.2631717 2.539 0.011126 *
## factor(id)99423 -0.3184972 0.2577820 -1.236 0.216657
## factor(id)99477 -0.3349972 0.2576502 -1.300 0.193556
## factor(id)99513 -0.1729115 0.2576466 -0.671 0.502157
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5151 on 12682 degrees of freedom
## Multiple R-squared: 0.898, Adjusted R-squared: 0.8834
## F-statistic: 61.32 on 1821 and 12682 DF, p-value: < 2.2e-16Heteroskedasticity
# load necessary packages for importing the function
library(RCurl)
# import the function from repository
url_robust <- "https://raw.githubusercontent.com/IsidoreBeautrelet/economictheoryblog/master/robust_summary.R"
eval(parse(text = getURL(url_robust, ssl.verifypeer = FALSE)),
envir=.GlobalEnv)
r_hetero<-lm(wage ~ educatsf*exper, wage1)
summary(r_hetero)
r_hetero<-lm(wage ~ educatsf*exper, wage1)
summary(r_hetero, robust=T)