So we've just seen the regression estimates of the causal effect
of test score on house prices, but what did those coefficients mean?
What exactly, how do we interpret them? Here she's listed those
coefficients once again just for reference and on this table she's
converted these coefficients into economically meaningful numbers.
So over here is what she calls the basic hedonic regression, that's
including all of our houses in the sample, where we don't worry
about the regression's continuity, we include everything.
So this is a confounded estimate here, but let's just see Just to
see if it was the truth, what would it mean?
Well, if we took test scores and increased them by 5%, then this
estimate suggests that we get a 5% increase in our house price.
Or if you took a house that was $188,000 it would get about a $9000
increase
in it's value due to a 5% change in test score.
But we know that we don't really believe this number because this
includes all those confounding effects.
We're not using the RDD idea here.
Over here you see 0.35 sample, that's the distance to the border,
0.20 sample, that's the distance to the border, so these
estimates are all using the RDD idea, and we're getting 0.016, 0.013,
0.015.
So here, the coefficients are about half, and the interpretation
also cuts down by about half.
If we increase test scores by about 5% then Then instead of getting
a 5% increase in house price, we only get around a 2% increase in
house price and that translates to if you took a house that was
$188,000, something around a $4,000-ish increase in its overall
value, so
that's the main way that we interpret economically what these coefficients
mean and we can see that if we don't use the RDD to control for
all these confounders we get an effect that's more than twice as
large as once we actually do control to these confounders using
the RDD analysis.
And even though the estimate may get smaller this is still quite
a large number.
So that's a pretty interesting finding.
So that's the main results from this paper by Sandra Block on the
effect of school test scores on policy prices.
Let's conclude by just thinking about how we check the validity
of our assumption needed to apply the RDD analysis.
Well what was that assumption again?
It's that houses just North of this border are basically the same
as houses just south of the border so the only difference between
them, is that one of them has a high quality school and one of them
has a low quality school.
Everything else is the same.
So
RDD analysis looks very similar to randomized experiments.
We've got our treatment group these houses and our control group
these houses.
So just like in randomized experiments and natural experiments we
can do a balance check.
We can look at other variables, other co-variants of interest for
these houses and compare the average values of those
variables for the houses in the control with the houses in the treatment
group, and they should be the same, they should be balanced, that's
what a balance check does.
So, for example, we can look at the average income of houses very
close to the border and compare to the average income of houses
north of the border, they should be the same, if they are not that
suggests that actually this isn't a good comparison.
For example maybe this is a major road that's dividing two very
different neighborhoods.
Maybe up here it's more wealthy and here it's less wealthy.
And so actually that would be a confounding variable.
That even though we're looking very closely
to the border the border was drawn that way for a reason
maybe, maybe it's some kind of jerry mandarin for school districts.
This is something that we have to worry about, and check to make
sure that we are actually getting a good comparison, a good treatment
and a control group, but the only difference is school quality and
not some other confounding. So that's one main thing that a lot of
these papers are gonna spend time on, checking these assumptions,
showing that they're valid and we can actually draw a good causal
inference from this kind of analysis.
[MUSIC]