[MUSIC] So we've just looked at the graphs for the effects of whether you're Protestant
relative to being Catholic on your preferences for leisure, redistribution, and government
intervention.
In a usual academic paper, you're going to have graphs like that and you're going to
have all the results formally in table form.
So now we're going to look at the same result but in the table.
That's what I've got right here.
So Table 3 says Reduced Form Results - remember, “reduced form” just is another way of
saying regression.
So they are doing a regression here, and they've got five different columns for five different
outcome variables for Preferences For Leisure, Redistribution, Intervention (that's what
we looked at before), and then two other outcome variables, Mean Income and Income Inequality.
So we didn't look at the plots for those.
Now if you look at just this first column, we come down here and we see “observations
133,” so they’re doing the same thing that Sandra Black did in her paper, they're
going to just restrict our sample size down to the observations that are close to the
border, namely within about 5.01 kilometers to the border.
So then, just for those municipalities, they're going to do a regression of the outcome variable
on what side of the border you are on (that's what this T is), how close you are from the
border, an interaction term between whether you’re on one side of the border and how
far you are, and then a constant.
So that's what these numbers here are.
So what is our finding?
First, the constant here tells us the preferences for the Catholics, because T means being on
the Protestant side.
So this is 48% Preferences For Leisure for being Catholics, then being on the Protestant
side drops your preferences down by 9%.
So that's exactly the same number we saw in the picture, now just in table form.
And here we see the standard errors are in parenthesis (2.22) and this is a highly statistically
significant effect.
So this is not just due to random sampling noise.
It's an actual causal effect.
Over here in column 2, we change the outcome variable, do the same regression analysis,
and we find the causal effect of being Protestant is -3.4.
That's also roughly what we saw in table form -sorry- in the figure, and for Catholics it
was 43% and for the Protestants the effect was -3.4%, so the overall preference was about
40% for Protestants.
Just this number minus that.
Our third outcome variable was Preferences For Government Intervention, and again over
here in this first row we see the same thing we saw in the picture: -4% treatment effect
for being Protestant.
And relative to Catholics having a baseline of about 52%.
Now if we look at these final two columns, these we didn't see the pictures of, but these
are other outcome variables to analyze.
So Mean Income: it looks like being on the Protestant side actually increases your average
income, although the effect’s just a little bit marginally statistically significant (so
this is a pretty big standard error).
And the Income Inequality is also higher on the Protestant side in 1996.
So that suggests that being Protestant has a causal effect on increasing income inequality,
increasing average income, lowering your preferences for government intervention, for redistribution,
and for leisure.
Okay, there is one big problem though with all of these numbers, and that's that this
is a Fuzzy RDD design.
There is a non-compliance problem: being on the Protestant side of the border does not
mean everyone is Protestant, there are some Catholics and likewise being on the Catholic
side of the border doesn't mean you're Catholic, there are some Protestants over there.
So this is very similar to the non-compliance problem.
So how we are going to solve that?
Well, we are going to solve it using instrumental variables.
So here's what we are going to do: let's just look at this first outcome variable.
Then in Table 4 of the paper they call it Second Stage Results.
Okay, so in Table 4 it’s labeled “second stage” - that's a keyword to let you know
that we're doing instrumental variables analysis.
Remember two stage least squares: two stages, the second stage.
So this is the second stage results.
So here's what they've got.
They're going to do exactly the same kind of analysis, but using two stage least squares
instead of ordinary linear regression.
They're going to use the same number of municipalities, 133 villages or cities or towns, as they did
in the regression analysis.
So now we have the same variables as controls, and now instead of labeling T here, which
is which side of the border you're on, they're going to label the variable The Share Of Protestants.
Okay so now we're looking at the actual causal effect of Protestant on preference for leisure,
as opposed to just the causal effect of which side of the border are you on.
So the main finding is that the effect increases.
It goes from -9 down to -13.
So actually once we adjust for the non-compliance problem, because we’ve got a fuzzy RDD,
our estimate of the causal effect gets larger.
Okay, so relative to Catholics, Protestants have an even stronger preference against leisure.
Now we can do the same thing for all the other outcome variables.
So here's our original table, that had the intention-to-treat problem, and now let's
compare it to the second stage results using two stage least squares.
So this is the comparison we just saw.
We saw that once we adjusted for this non-compliance problem, the Preference For Leisure causal
effect increased (went from -9 to -13).
The same thing happens for the other outcome variables: for Redistribution it goes from
-3.4 up to -5; Intervention, -4 up to -6; Mean Income, 2 up to 4; and Income Inequality,
0.08 up to 0.13.
Now, that's exactly the same thing we saw when we analyzed the Oregon Healthcare Experiment.
We saw that the problem was these effects are made smaller because of the non-compliance,
because there's some muddling of our treatment and control groups.
There are actually Catholics in the Protestant areas and Protestants in the Catholic areas.
So if there is an actual causal effect then that's getting lost a little bit because of
that non-compliance, and once we fix it we see that the magnitudes of the effects get
larger.
So this table here, this last table, Table 4, the Second Stage Results, these are the
main results in the paper.
This is what they're going to conclude.
They're going to say, because we have a RDD we have a good idea that we're getting a real
causal effect of being Protestant on these different outcomes.
And they're going to claim this actually is quantitative evidence from Max Weber’s famous
thesis that there is a Protestant work ethic.
Protestants actually cause you to have higher income inequality, higher mean income, less
preference for the government to intervene, less preferences for redistribution and less
preferences for leisure or more preference for work.
That's the main finding of this paper, we think we believe it because it's an RDD analysis
and that's what they find.
[MUSIC]