II Econometric Analysis Using R

### Chapter 18 Count, Fractional, and Other Nonnegative Responses

Also covered using Python and Stata

#### Example 18.1

library(wooldridge)
library(stargazer)
library(AER)
library(mfx)

Effects of Education on Fertility

OLS <- lm(children ~ educ + age + agesq + evermarr + urban + electric + tv, data=fertil2)

Poisson <- glm(children ~ educ + age + agesq + evermarr + urban + electric + tv, data=fertil2, family=poisson)

stargazer(OLS, Poisson, no.space=TRUE, type="text", title = "Table 18.1 OLS and Poisson Estimates of a Fertility Equation")
##
## Table 18.1 OLS and Poisson Estimates of a Fertility Equation
## ========================================================
##                             Dependent variable:
##                     ------------------------------------
##                                   children
##                                OLS             Poisson
##                                (1)               (2)
## --------------------------------------------------------
## educ                        -0.064***         -0.022***
##                              (0.006)           (0.003)
## age                         0.272***           0.337***
##                              (0.017)           (0.010)
## agesq                       -0.002***         -0.004***
##                             (0.0003)           (0.0001)
## evermarr                    0.682***           0.315***
##                              (0.052)           (0.024)
## urban                       -0.228***         -0.086***
##                              (0.046)           (0.022)
## electric                    -0.262***         -0.121***
##                              (0.076)           (0.039)
## tv                          -0.250***         -0.145***
##                              (0.090)           (0.047)
## Constant                    -3.394***         -5.375***
##                              (0.245)           (0.163)
## --------------------------------------------------------
## Observations                  4,358             4,358
## R2                            0.590
## Log Likelihood                                -6,497.060
## Akaike Inf. Crit.                             13,010.120
## Residual Std. Error     1.424 (df = 4350)
## F Statistic         893.910*** (df = 7; 4350)
## ========================================================
## Note:                        *p<0.1; **p<0.05; ***p<0.01
poissonmfx(Poisson, data=fertil2, atmean = F)
## Call:
## poissonmfx(formula = Poisson, data = fertil2, atmean = F)
##
## Marginal Effects:
##                dF/dx   Std. Err.        z     P>|z|
## educ     -0.04912535  0.00662408  -7.4162 1.205e-13 ***
## age       0.76491583  0.02380923  32.1269 < 2.2e-16 ***
## agesq    -0.00933287  0.00034254 -27.2459 < 2.2e-16 ***
## evermarr  0.67533842  0.04986768  13.5426 < 2.2e-16 ***
## urban    -0.19458611  0.04883491  -3.9846 6.760e-05 ***
## electric -0.26136098  0.08052419  -3.2457  0.001171 **
## tv       -0.30907074  0.09527605  -3.2440  0.001179 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## dF/dx is for discrete change for the following variables:
##
## [1] "evermarr" "urban"    "electric" "tv"

#### Example 18.2

Is Education Endogenous in the Fertility Equation?

fertil2 <- subset(fertil2, !is.na(electric))

v2 <- resid(OLS <- lm(educ ~ frsthalf + age + agesq + evermarr + urban + electric + tv, data=fertil2))

Poisson <- glm(children ~ educ + age + agesq + evermarr + urban + electric + tv + v2, data=fertil2, family=poisson)

stargazer(OLS, Poisson, no.space=TRUE, type="text") 
##
## ========================================================
##                             Dependent variable:
##                     ------------------------------------
##                               educ             children
##                                OLS             Poisson
##                                (1)               (2)
## --------------------------------------------------------
## frsthalf                    -0.636***
##                              (0.104)
## educ                                            -0.046
##                                                (0.032)
## age                          -0.070*           0.336***
##                              (0.041)           (0.010)
## agesq                        -0.001           -0.004***
##                              (0.001)           (0.0001)
## evermarr                    -0.802***          0.294***
##                              (0.124)           (0.037)
## urban                       0.864***           -0.065*
##                              (0.109)           (0.035)
## electric                    1.978***            -0.071
##                              (0.179)           (0.076)
## tv                          2.715***            -0.078
##                              (0.211)           (0.100)
## v2                                              0.025
##                                                (0.032)
## Constant                    8.203***          -5.185***
##                              (0.575)           (0.298)
## --------------------------------------------------------
## Observations                  4,358             4,358
## R2                            0.251
## Note:                        *p<0.1; **p<0.05; ***p<0.01