Instrumental Variables
Ralf Martin
Returns to education again
library(AER)
library(dplyr)
df=read.csv("https://www.dropbox.com/s/diecbkq03gfid0p/card1993.csv?dl=1")
#from https://davidcard.berkeley.edu/data_sets.html
lm(wage76 ~ ed76, data = df) %>% summary()##
## Call:
## lm(formula = wage76 ~ ed76, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -623.6 -173.7 -33.3 128.3 1687.9
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 183.934 23.160 7.942 2.78e-15 ***
## ed76 29.566 1.712 17.274 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 251.7 on 3015 degrees of freedom
## (596 observations deleted due to missingness)
## Multiple R-squared: 0.09006, Adjusted R-squared: 0.08976
## F-statistic: 298.4 on 1 and 3015 DF, p-value: < 2.2e-16library(ggplot2)
ggplot(data=df, aes(x=ed76,y=wage76)) + geom_point() + theme_minimal()## Warning: Removed 596 rows containing missing values (geom_point).
# library(ggplot2)
# ggplot(data=CollegeDistance, aes(x=distance)) + geom_histogram() + theme_minimal() first=lm(ed76~nearc4a, data = df)
first %>% summary()##
## Call:
## lm(formula = ed76 ~ nearc4a, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.6575 -1.6575 -0.6575 2.3425 5.1935
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.80654 0.06343 201.911 <2e-16 ***
## nearc4a 0.85094 0.09041 9.412 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.717 on 3611 degrees of freedom
## Multiple R-squared: 0.02394, Adjusted R-squared: 0.02367
## F-statistic: 88.58 on 1 and 3611 DF, p-value: < 2.2e-16iv=ivreg(wage76 ~ ed76 | nearc4a, data=df)
iv %>% summary()##
## Call:
## ivreg(formula = wage76 ~ ed76 | nearc4a, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -941.253 -211.663 -6.304 204.517 1683.696
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -943.77 198.71 -4.749 2.13e-06 ***
## ed76 114.59 14.97 7.652 2.64e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 339.4 on 3015 degrees of freedom
## Multiple R-Squared: -0.6547, Adjusted R-squared: -0.6552
## Wald test: 58.56 on 1 and 3015 DF, p-value: 2.639e-14iv=ivreg(wage76 ~ ed76+factor(region)+nearc4b+nearc2 | nearc4a+nearc4b+nearc2+factor(region)
, data=df )
iv %>% summary()##
## Call:
## ivreg(formula = wage76 ~ ed76 + factor(region) + nearc4b + nearc2 |
## nearc4a + nearc4b + nearc2 + factor(region), data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -853.100 -198.498 -6.864 187.265 1630.953
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -729.039 291.987 -2.497 0.01258 *
## ed76 98.811 20.916 4.724 2.42e-06 ***
## factor(region)2 -126.976 40.111 -3.166 0.00156 **
## factor(region)3 -36.559 34.319 -1.065 0.28683
## factor(region)4 -21.313 42.946 -0.496 0.61974
## factor(region)5 -14.037 38.400 -0.366 0.71474
## factor(region)6 -62.001 30.296 -2.047 0.04079 *
## factor(region)7 17.031 24.201 0.704 0.48166
## factor(region)8 -11.016 23.908 -0.461 0.64499
## factor(region)9 -19.767 35.121 -0.563 0.57360
## nearc4b -8.513 15.013 -0.567 0.57075
## nearc2 27.357 12.357 2.214 0.02691 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 311.4 on 3005 degrees of freedom
## Multiple R-Squared: -0.3884, Adjusted R-squared: -0.3935
## Wald test: 17.66 on 11 and 3005 DF, p-value: < 2.2e-16 first=lm(ed76~nearc4a+factor(region)+nearc4b+nearc2, data = df)
first %>% summary()##
## Call:
## lm(formula = ed76 ~ nearc4a + factor(region) + nearc4b + nearc2,
## data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.3438 -1.6767 -0.2662 2.0324 5.9761
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.41923 0.18020 74.469 < 2e-16 ***
## nearc4a 0.66714 0.10785 6.186 6.88e-10 ***
## factor(region)2 0.25742 0.29739 0.866 0.3868
## factor(region)3 -0.88954 0.20580 -4.322 1.58e-05 ***
## factor(region)4 -1.39531 0.21202 -6.581 5.35e-11 ***
## factor(region)5 -1.31319 0.18230 -7.204 7.11e-13 ***
## factor(region)6 -0.17377 0.22849 -0.761 0.4470
## factor(region)7 -0.15300 0.18226 -0.839 0.4013
## factor(region)8 -0.15192 0.18456 -0.823 0.4105
## factor(region)9 -0.54352 0.25847 -2.103 0.0355 *
## nearc4b 0.25475 0.13183 1.932 0.0534 .
## nearc2 0.03420 0.09664 0.354 0.7234
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.662 on 3601 degrees of freedom
## Multiple R-squared: 0.06556, Adjusted R-squared: 0.0627
## F-statistic: 22.97 on 11 and 3601 DF, p-value: < 2.2e-16 linearHypothesis(first,c("nearc4a=0"))## Linear hypothesis test
##
## Hypothesis:
## nearc4a = 0
##
## Model 1: restricted model
## Model 2: ed76 ~ nearc4a + factor(region) + nearc4b + nearc2
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 3602 25791
## 2 3601 25520 1 271.15 38.261 6.882e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 reduced=lm(wage76~nearc4a+factor(region)+nearc4b+nearc2, data = df)
reduced %>% summary()##
## Call:
## lm(formula = wage76 ~ nearc4a + factor(region) + nearc4b + nearc2,
## data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -631.80 -164.44 -37.61 120.43 1735.20
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 600.144 18.934 31.697 < 2e-16 ***
## nearc4a 65.301 11.192 5.835 5.97e-09 ***
## factor(region)2 -79.575 31.983 -2.488 0.01290 *
## factor(region)3 -122.686 21.488 -5.709 1.24e-08 ***
## factor(region)4 -152.045 22.014 -6.907 6.03e-12 ***
## factor(region)5 -142.303 19.136 -7.436 1.34e-13 ***
## factor(region)6 -72.354 24.341 -2.973 0.00298 **
## factor(region)7 -1.002 19.112 -0.052 0.95819
## factor(region)8 -25.757 19.240 -1.339 0.18075
## factor(region)9 -75.947 26.576 -2.858 0.00430 **
## nearc4b 18.110 13.632 1.329 0.18409
## nearc2 29.110 9.963 2.922 0.00351 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 252.2 on 3005 degrees of freedom
## (596 observations deleted due to missingness)
## Multiple R-squared: 0.08978, Adjusted R-squared: 0.08644
## F-statistic: 26.94 on 11 and 3005 DF, p-value: < 2.2e-16The effect of subsidies on unemployment
library(haven)
library(AER)
df=read.csv( "https://www.dropbox.com/s/8pdffaq268v7m8o/unempprep.csv?dl=1")
#names(df)
summary(df$DDDNGE)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.30000 0.00000 0.00000 -0.01505 0.00000 0.35000Simple OLS
regOLS=lm( DDDln1Punemp ~ DDDNGE ,df)
summary(regOLS)##
## Call:
## lm(formula = DDDln1Punemp ~ DDDNGE, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.5451 -0.1907 0.0165 0.2109 2.8601
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.462220 0.003648 -126.703 < 2e-16 ***
## DDDNGE -0.221062 0.036012 -6.138 8.62e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3743 on 10762 degrees of freedom
## Multiple R-squared: 0.003489, Adjusted R-squared: 0.003396
## F-statistic: 37.68 on 1 and 10762 DF, p-value: 8.624e-10IV
List of historic deprivation controls
controls=c("gdp91","manufshare_1991","popdens_1981","current_unemprate1991","actrate_1991","resid_emp_rate92")
fff=paste(controls, collapse ="+")
fff## [1] "gdp91+manufshare_1991+popdens_1981+current_unemprate1991+actrate_1991+resid_emp_rate92"Now run iv:
fffiv =paste0( "DDDln1Punemp ~ DDDNGE+ ",fff, "| DDDxnivav +",fff)
fffiv## [1] "DDDln1Punemp ~ DDDNGE+ gdp91+manufshare_1991+popdens_1981+current_unemprate1991+actrate_1991+resid_emp_rate92| DDDxnivav +gdp91+manufshare_1991+popdens_1981+current_unemprate1991+actrate_1991+resid_emp_rate92" summary(ivreg( fffiv ,data=df))##
## Call:
## ivreg(formula = fffiv, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.52984 -0.18444 0.01339 0.20575 2.74181
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.7851275 0.0820543 -9.568 < 2e-16 ***
## DDDNGE -0.4546888 0.1131435 -4.019 5.89e-05 ***
## gdp91 0.0030923 0.0003235 9.559 < 2e-16 ***
## manufshare_1991 0.5714105 0.0481121 11.877 < 2e-16 ***
## popdens_1981 0.0004555 0.0004222 1.079 0.281
## current_unemprate1991 -2.1341897 0.4972815 -4.292 1.79e-05 ***
## actrate_1991 0.4900480 0.0628717 7.794 7.07e-15 ***
## resid_emp_rate92 -0.3915193 0.0876794 -4.465 8.08e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3666 on 10756 degrees of freedom
## Multiple R-Squared: 0.04475, Adjusted R-squared: 0.04413
## Wald test: 84.77 on 7 and 10756 DF, p-value: < 2.2e-16Check first stage
ffffs =paste0( "DDDNGE~DDDxnivav+ ",fff)
regFS=lm( ffffs ,df)
summary(regFS) ##
## Call:
## lm(formula = ffffs, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.38214 -0.01537 0.00344 0.02657 0.43048
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.210e-01 2.303e-02 -9.599 < 2e-16 ***
## DDDxnivav 1.015e+00 2.932e-02 34.627 < 2e-16 ***
## gdp91 -4.575e-04 8.145e-05 -5.617 2.00e-08 ***
## manufshare_1991 -1.038e-01 1.146e-02 -9.059 < 2e-16 ***
## popdens_1981 1.969e-04 1.070e-04 1.839 0.06592 .
## current_unemprate1991 1.061e+00 1.372e-01 7.732 1.16e-14 ***
## actrate_1991 -4.786e-02 1.592e-02 -3.007 0.00265 **
## resid_emp_rate92 3.674e-01 2.482e-02 14.803 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.09356 on 10756 degrees of freedom
## Multiple R-squared: 0.1284, Adjusted R-squared: 0.1278
## F-statistic: 226.3 on 7 and 10756 DF, p-value: < 2.2e-16 linearHypothesis(regFS,"DDDxnivav=0")## Linear hypothesis test
##
## Hypothesis:
## DDDxnivav = 0
##
## Model 1: restricted model
## Model 2: DDDNGE ~ DDDxnivav + gdp91 + manufshare_1991 + popdens_1981 +
## current_unemprate1991 + actrate_1991 + resid_emp_rate92
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 10757 104.652
## 2 10756 94.156 1 10.496 1199 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Reduced Form:
fffrf =paste0( "DDDln1Punemp~DDDxnivav+ ",fff)
summary(lm( fffrf ,df))##
## Call:
## lm(formula = fffrf, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.5300 -0.1834 0.0138 0.2023 2.7342
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.6846189 0.0898471 -7.620 2.75e-14 ***
## DDDxnivav -0.4616909 0.1144068 -4.036 5.49e-05 ***
## gdp91 0.0033003 0.0003178 10.386 < 2e-16 ***
## manufshare_1991 0.6185964 0.0446947 13.840 < 2e-16 ***
## popdens_1981 0.0003659 0.0004176 0.876 0.381
## current_unemprate1991 -2.6164480 0.5352012 -4.889 1.03e-06 ***
## actrate_1991 0.5118111 0.0621070 8.241 < 2e-16 ***
## resid_emp_rate92 -0.5585603 0.0968272 -5.769 8.21e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.365 on 10756 degrees of freedom
## Multiple R-squared: 0.0527, Adjusted R-squared: 0.05209
## F-statistic: 85.49 on 7 and 10756 DF, p-value: < 2.2e-16