ak91.Rmd

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output: html_document
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# Quarter of Birth and Returns to Schooling

This replicates Tables 6.4 and 6.5, and Figures 6.1 and 6.2 of *Mastering 'Metrics*.
These present an IV analysis of the returns to schooling using quarters of birth (QOB) as instruments for years of schooling [@AngristKrueger1991].

```{r setup,message=FALSE}
library("AER")
library("sandwich")
library("lmtest")
library("tidyverse")
library("broom")
```

Load `twins` data.
```{r ak91}
data("ak91", package = "masteringmetrics")
```

Some cleaning of the data.
```{r ak91-2}
ak91 <- mutate(ak91,
               qob_fct = factor(qob),
               q4 = as.integer(qob == "4"),
               yob_fct = factor(yob))
```

Table 6.4. IV recipe for returns to schooling using a single QOB instrument.
Regress log wages on 4th quarter.
```{r mod1}
mod1 <- lm(lnw ~ q4, data = ak91)
coeftest(mod1, vcov = sandwich)
```
Regress years of schooling on 4th quarter.
```{r mod2}
mod2 <- lm(s ~ q4, data = ak91)
coeftest(mod2, vcov = sandwich)
```
IV regression of log wages on years of schooling, with 4th quarter as an instrument for years of schooling.
```{r mod3}
mod3 <- ivreg(lnw ~ s | q4, data = ak91)
coeftest(mod3, vcov = sandwich)
```

## Table 6.5

Regression Estimates of Returns to Schooling using Quarter of Birth Instruments

Column 1. OLS
```{r}
mod4 <- lm(lnw ~ s, data = ak91)
coeftest(mod4, vcov = sandwich)
```

Column 2. IV with only the 4th quarter as an instrument.
```{r}
mod5 <- ivreg(lnw ~ s | q4, data = ak91)
summary(mod5, vcov = sandwich, diagnostics = TRUE)
```
The argument `diagnostics = TRUE` will run an F-test on the first stage which is reported as the "Weak instruments" diagnostic.

Column 3. OLS. Controls for year of birth.
```{r}
mod6 <- lm(lnw ~ s + yob_fct, data = ak91)
coeftest(mod6, vcov = sandwich)
```

Column 4. IV reg using only the 4th quarter as an instrument. Controls for year of birth.
```{r}
mod7 <- ivreg(lnw ~ s + yob_fct | q4 + yob_fct, data = ak91)
summary(mod7, vcov = sandwich, diagnostics = TRUE)
```

Column 4. IV reg using all quarters as instruments. Controls for year of birth.
```{r}
mod8 <- ivreg(lnw ~ s + yob_fct | qob_fct + yob_fct, data = ak91)
summary(mod8, vcov = sandwich, diagnostics = TRUE)
```

## Figures

Summarize the average wages by age:
```{r}
ak91_age <- ak91 %>%
  group_by(qob, yob) %>%
  summarise(lnw = mean(lnw), s = mean(s)) %>%
  mutate(q4 = (qob == 4))
```

Average years of schooling by quarter of birth for men born in 1930-39 in the 1980 US Census.
```{r}
ggplot(ak91_age, aes(x = yob + (qob - 1) / 4, y = s)) +
  geom_line() +
  geom_label(mapping = aes(label = qob, color = q4)) +
  theme(legend.position = "none") +
  scale_x_continuous("Year of birth", breaks = 1930:1940) +
  scale_y_continuous("Years of Education", breaks = seq(12.2, 13.2, by = 0.2),
                     limits = c(12.2, 13.2))
```

Average log wages by quarter of birth for men born in 1930-39 in the 1980 US Census.
```{r}
ggplot(ak91_age, aes(x = yob + (qob - 1) / 4, y = lnw)) +
  geom_line() +
  geom_label(mapping = aes(label = qob, color = q4)) +
  scale_x_continuous("Year of birth", breaks = 1930:1940) +
  scale_y_continuous("Log weekly wages") +
  theme(legend.position = "none")
```

## References {-}

-   <http://masteringmetrics.com/wp-content/uploads/2015/02/ReadMe_QOB.txt>
-   <http://masteringmetrics.com/wp-content/uploads/2015/02/ak91.do>