This post recreates this post with proper formatting, syntax highlighting, etc.

First we’ll load the data (download if necessary). I just started playing around with skimr::skim() to generate nice summaries. (digits doesn’t seem to do anything, though?)

data_file = '../_data/did_data.dta'
if (!file.exists(data_file)) {
destfile = data_file)
}

skim(dataf, work, year, children) %>%
skimr::kable(digits = 0)

## Skim summary statistics
##  n obs: 13746
##  n variables: 11
##
## Variable type: numeric
##
##  variable    missing    complete      n       mean       sd      p0     p25     p50     p75     p100      hist
## ----------  ---------  ----------  -------  ---------  ------  ------  ------  ------  ------  ------  ----------
##  children       0        13746      13746     1.19      1.38     0       0       1       2       9      ▇▂▁▁▁▁▁▁
##    work         0        13746      13746     0.51      0.5      0       0       1       1       1      ▇▁▁▁▁▁▁▇
##    year         0        13746      13746    1993.35    1.7     1991    1992    1993    1995    1996    ▇▇▁▇▇▁▆▆


Following the old post, we need to construct dummy variables for (a) before-and-after the EITC takes effect in 1994 and (b) the treatment group (1 or more children). We’ll keep these as logicals (rather than the numerics in the old post).

dataf = dataf %>%
mutate(post93 = year >= 1994,
anykids = children >= 1)


The regression equation is

The “difference-in-differences coefficient” is $\delta_1$, which indicates how the effect of kids changed after the EITC went into effect. Let’s take a second to plot this.

ggplot(dataf, aes(post93, work, color = anykids)) +
geom_jitter() +
theme_minimal()


Okay, so the scatterplot version, like, isn’t perspicuous. How about the un-dummied variables, and just the mean?

ggplot(dataf, aes(year, work, color = anykids)) +
stat_summary(geom = 'line') +
geom_vline(xintercept = 1994) +
theme_minimal()

## No summary function supplied, defaulting to mean_se()


The parallel trends assumption looks good, at least qualitatively. (Remember this only applies prior to the intervention.) However, the parallel trends are nonlinear, which maybe is why the example uses the dummied variable.

Anyway, on to the regression. Which, hey, is a linear probability model because econometricians are funny like that.

model = lm(work ~ anykids*post93, data = dataf)
summary(model)

##
## Call:
## lm(formula = work ~ anykids * post93, data = dataf)
##
## Residuals:
##     Min      1Q  Median      3Q     Max
## -0.5755 -0.4908  0.4245  0.5092  0.5540
##
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)
## (Intercept)             0.575460   0.008845  65.060  < 2e-16 ***
## anykidsTRUE            -0.129498   0.011676 -11.091  < 2e-16 ***
## post93TRUE             -0.002074   0.012931  -0.160  0.87261
## anykidsTRUE:post93TRUE  0.046873   0.017158   2.732  0.00631 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4967 on 13742 degrees of freedom
## Multiple R-squared:  0.0126,	Adjusted R-squared:  0.01238
## F-statistic: 58.45 on 3 and 13742 DF,  p-value: < 2.2e-16


This indicates that the EITC increased work` (workforce participation? whether someone was employed?) by 5% among families with at least 1 child. In the second plot, the blue line goes from about 45% prior to 1994 to about 50% afterwards.