II Econometric Analysis Using R

Also available in Stata and Python versions

### Chapter 7. Systems of Equations

#### Example 7.3

library(wooldridge)
library(AER)
library(systemfit)
library(plm)
library(plyr)

SUR System for Wages and Fringe Benefits

system <- list(
Wage =  hrearn ~ educ + exper + expersq + tenure +  tenuresq + union + south + nrtheast + nrthcen + married + white  + male,
Benefit = hrbens ~ educ + exper + expersq + tenure +  tenuresq + union + south + nrtheast + nrthcen + married + white  + male
)
ols <- systemfit(system, method = "OLS", data=fringe)
summary(ols)
##
## systemfit results
## method: OLS
##
##           N   DF     SSR detRCov   OLS-R2 McElroy-R2
## system 1232 1206 11600.6 4.63027 0.208685   0.292642
##
##           N  DF       SSR       MSE     RMSE       R2   Adj R2
## Wage    616 603 11437.037 18.966893 4.355100 0.205093 0.189274
## Benefit 616 603   163.544  0.271217 0.520785 0.398674 0.386708
##
## The covariance matrix of the residuals
##              Wage  Benefit
## Wage    18.966893 0.716847
## Benefit  0.716847 0.271217
##
## The correlations of the residuals
##            Wage Benefit
## Wage    1.00000 0.31606
## Benefit 0.31606 1.00000
##
##
## OLS estimates for 'Wage' (equation 1)
## Model Formula: hrearn ~ educ + exper + expersq + tenure + tenuresq + union +
##     south + nrtheast + nrthcen + married + white + male
##
##                Estimate  Std. Error  t value   Pr(>|t|)
## (Intercept) -2.63212671  1.22832151 -2.14286  0.0325236 *
## educ         0.45881395  0.06912628  6.63733 7.1256e-11 ***
## exper       -0.07584282  0.05734542 -1.32256  0.1864828
## expersq      0.00399449  0.00117795  3.39104  0.0007418 ***
## tenure       0.11008462  0.08380979  1.31351  0.1895122
## tenuresq    -0.00507064  0.00327692 -1.54738  0.1222965
## union        0.80799328  0.40780495  1.98132  0.0480089 *
## south       -0.45662223  0.55170344 -0.82766  0.4081912
## nrtheast    -1.15075861  0.60575425 -1.89971  0.0579478 .
## nrthcen     -0.63626628  0.55604484 -1.14427  0.2529651
## married      0.64238821  0.41779850  1.53756  0.1246820
## white        1.14089121  0.61193899  1.86439  0.0627530 .
## male         1.78470236  0.39800745  4.48409 8.7674e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.3551 on 603 degrees of freedom
## Number of observations: 616 Degrees of Freedom: 603
## SSR: 11437.036645 MSE: 18.966893 Root MSE: 4.3551
## Multiple R-Squared: 0.205093 Adjusted R-Squared: 0.189274
##
##
## OLS estimates for 'Benefit' (equation 2)
## Model Formula: hrbens ~ educ + exper + expersq + tenure + tenuresq + union +
##     south + nrtheast + nrthcen + married + white + male
##
##                 Estimate   Std. Error  t value   Pr(>|t|)
## (Intercept) -0.889747099  0.146883282 -6.05751 2.4342e-09 ***
## educ         0.076792360  0.008266154  9.28997 < 2.22e-16 ***
## exper        0.022564931  0.006857393  3.29060  0.0010581 **
## expersq     -0.000473359  0.000140860 -3.36049  0.0008272 ***
## tenure       0.053555571  0.010022015  5.34379 1.2924e-07 ***
## tenuresq    -0.001163631  0.000391856 -2.96954  0.0031010 **
## union        0.365908540  0.048765513  7.50343 2.2404e-13 ***
## south       -0.022686547  0.065972964 -0.34388  0.7310591
## nrtheast    -0.056746823  0.072436387 -0.78340  0.4336986
## nrthcen     -0.037998394  0.066492111 -0.57147  0.5678925
## married      0.057862604  0.049960547  1.15817  0.2472548
## white        0.090158182  0.073175962  1.23207  0.2184017
## male         0.268338264  0.047593923  5.63808 2.6438e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.520785 on 603 degrees of freedom
## Number of observations: 616 Degrees of Freedom: 603
## SSR: 163.543819 MSE: 0.271217 Root MSE: 0.520785
## Multiple R-Squared: 0.398674 Adjusted R-Squared: 0.386708

HOME

#### Example 7.7

Effects of Job Training Grants on Firm Scrap Rates

summary(lm(lscrap ~ d88 + d89 + grant + grant_1, data=jtrain))
##
## Call:
## lm(formula = lscrap ~ d88 + d89 + grant + grant_1, data = jtrain)
##
## Residuals:
##     Min      1Q  Median      3Q     Max
## -5.2026 -0.8960 -0.0846  1.0242  3.3003
##
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)  0.59743    0.20306   2.942  0.00375 **
## d88         -0.23937    0.31086  -0.770  0.44245
## d89         -0.49652    0.33793  -1.469  0.14375
## grant        0.20002    0.33828   0.591  0.55519
## grant_1      0.04894    0.43607   0.112  0.91079
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.492 on 157 degrees of freedom
##   (309 observations deleted due to missingness)
## Multiple R-squared:  0.01731,    Adjusted R-squared:  -0.007726
## F-statistic: 0.6914 on 4 and 157 DF,  p-value: 0.5989

HOME

#### Example 7.8

Effect of Being in Season on Grade Point Average

summary(lm(trmgpa ~ spring + cumgpa + crsgpa + frstsem + season + sat + verbmath + hsperc + hssize + black + female, data=gpa3))
##
## Call:
## lm(formula = trmgpa ~ spring + cumgpa + crsgpa + frstsem + season +
##     sat + verbmath + hsperc + hssize + black + female, data = gpa3)
##
## Residuals:
##      Min       1Q   Median       3Q      Max
## -1.90608 -0.28531 -0.00412  0.35062  1.56491
##
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.068e+00  3.381e-01  -6.115 1.58e-09 ***
## spring      -1.216e-02  4.648e-02  -0.262    0.794
## cumgpa       3.146e-01  4.049e-02   7.770 2.71e-14 ***
## crsgpa       9.840e-01  9.603e-02  10.247  < 2e-16 ***
## frstsem      7.691e-01  1.204e-01   6.387 3.03e-10 ***
## season      -4.626e-02  4.710e-02  -0.982    0.326
## sat          1.410e-03  1.464e-04   9.628  < 2e-16 ***
## verbmath    -1.126e-01  1.306e-01  -0.862    0.389
## hsperc      -6.601e-03  1.020e-03  -6.475 1.75e-10 ***
## hssize      -5.761e-05  9.937e-05  -0.580    0.562
## black       -2.313e-01  5.433e-02  -4.257 2.35e-05 ***
## female       2.856e-01  5.096e-02   5.603 3.00e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5299 on 720 degrees of freedom
## Multiple R-squared:  0.5191, Adjusted R-squared:  0.5117
## F-statistic: 70.64 on 11 and 720 DF,  p-value: < 2.2e-16
gpa3p <- pdata.frame(gpa3, index = c("id", "term"))

summary(pggls(trmgpa ~ spring + cumgpa + crsgpa + frstsem + season + sat + verbmath + hsperc + hssize + black + female, data=gpa3p, model = "pooling"))
## Oneway (individual) effect General FGLS model
##
## Call:
## pggls(formula = trmgpa ~ spring + cumgpa + crsgpa + frstsem +
##     season + sat + verbmath + hsperc + hssize + black + female,
##     data = gpa3p, model = "pooling")
##
## Balanced Panel: n = 366, T = 2, N = 732
##
## Residuals:
##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max.
## -1.874434 -0.306303 -0.005001  0.000000  0.348366  1.545998
##
## Coefficients:
##                Estimate  Std. Error z-value  Pr(>|z|)
## (Intercept) -2.0339e+00  3.4208e-01 -5.9457 2.753e-09 ***
## spring      -2.9597e-02  4.1460e-02 -0.7139    0.4753
## cumgpa       2.3011e-01  4.0154e-02  5.7308 9.995e-09 ***
## crsgpa       1.0282e+00  9.3076e-02 11.0465 < 2.2e-16 ***
## frstsem      5.5750e-01  1.1799e-01  4.7250 2.302e-06 ***
## season      -5.0952e-02  4.2074e-02 -1.2110    0.2259
## sat          1.5020e-03  1.5893e-04  9.4505 < 2.2e-16 ***
## verbmath    -1.2838e-01  1.4278e-01 -0.8991    0.3686
## hsperc      -6.9640e-03  1.1140e-03 -6.2515 4.065e-10 ***
## hssize      -6.6763e-05  1.0880e-04 -0.6136    0.5395
## black       -2.3395e-01  5.9432e-02 -3.9365 8.268e-05 ***
## female       3.1014e-01  5.5123e-02  5.6264 1.840e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Total Sum of Squares: 420.3
## Residual Sum of Squares: 203.41
## Multiple R-squared: 0.51603

HOME

#### Example 7.9

#library(plyr)
gpa3['uhat'] <- resid(lm(trmgpa ~ spring + cumgpa + crsgpa + frstsem + season + sat + verbmath + hsperc + hssize + black + female, data=gpa3))

gpa3b <- ddply(
gpa3, .(id), transform,
uhat_1 = c(NA, uhat[-length(uhat)])
)

summary(lm(trmgpa ~ cumgpa + crsgpa + season + sat + verbmath + hsperc + hssize + black + female + uhat_1, data=gpa3b))
##
## Call:
## lm(formula = trmgpa ~ cumgpa + crsgpa + season + sat + verbmath +
##     hsperc + hssize + black + female + uhat_1, data = gpa3b)
##
## Residuals:
##      Min       1Q   Median       3Q      Max
## -2.14097 -0.25914  0.01412  0.31478  1.19124
##
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.266e+00  4.247e-01  -5.337 1.69e-07 ***
## cumgpa       3.489e-01  7.203e-02   4.843 1.91e-06 ***
## crsgpa       1.001e+00  1.177e-01   8.503 5.21e-16 ***
## season      -2.710e-02  5.795e-02  -0.468 0.640291
## sat          1.413e-03  1.991e-04   7.094 7.10e-12 ***
## verbmath    -1.137e-01  1.703e-01  -0.668 0.504854
## hsperc      -4.954e-03  1.417e-03  -3.495 0.000535 ***
## hssize      -8.435e-05  1.289e-04  -0.655 0.513191
## black       -2.407e-01  7.068e-02  -3.406 0.000734 ***
## female       2.919e-01  7.326e-02   3.985 8.20e-05 ***
## uhat_1       1.942e-01  6.121e-02   3.173 0.001642 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4854 on 355 degrees of freedom
##   (366 observations deleted due to missingness)
## Multiple R-squared:  0.6155, Adjusted R-squared:  0.6047
## F-statistic: 56.83 on 10 and 355 DF,  p-value: < 2.2e-16
summary(lm(uhat ~  uhat_1, data=gpa3b))
##
## Call:
## lm(formula = uhat ~ uhat_1, data = gpa3b)
##
## Residuals:
##      Min       1Q   Median       3Q      Max
## -2.09519 -0.26626  0.01715  0.30685  1.15824
##
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.913e-17  2.512e-02   0.000        1
## uhat_1       2.122e-01  4.520e-02   4.695 3.79e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4805 on 364 degrees of freedom
##   (366 observations deleted due to missingness)
## Multiple R-squared:  0.05709,    Adjusted R-squared:  0.0545
## F-statistic: 22.04 on 1 and 364 DF,  p-value: 3.788e-06

HOME