[MUSIC] Next we're going to talk about what has been, what is and what always will be
the most important statistical technique ever: Regression.
Almost every analysis you will read or see uses regression in some way or another.
So let's talk about that.
Now there're two ways of viewing regression: one is descriptive and the second is causal.
So we're going to start with the descriptive approach.
That’s simply regression is a way of viewing correlations in the data.
So let's look at an example.
Let's think about the effect of property rights on economic development: what's the causal
effect?
So here I'm asking if I were to intervene today and go to every country and increase
their property rights somehow, make their property rights stronger, what would be the
average change in economic development?
For example, would GDP go up everywhere?
This question is what Acemoglu, Johnson and Robinson looked at in 2001 in their paper
in the American Economic Review.
Now this paper is very well known, and it's mainly an application of instrumental variables,
which we'll talk about later on, but here I want to just start by seeing how they use
regression as a description of their data.
So in their data, each unit is a country.
So each country is going to have a different level of property rights and of economic growth.
They're going to measure property rights with a variable called “Protection Against Expropriation
Risk."
This variable is going to take on the value 0, 1, 2, 3 etc. up to 10, where 10 is having
strong property rights, so there's a lot of protection against your property being expropriated
from you by the government or somebody else, and 0 is going to be very weak rights, meaning
you don't have a lot of protection against your property being expropriated from you.
That's how they're going to measure property rights.
Second, they are going to measure economic development by GDP, Gross Domestic Product,
per capita or per person.
So let's look at the data.
So here they've plotted all the data, each point here is a different country.
So up here you see we've got USA, Canada, Australia, and New Zealand, down here we have
Sudan, Haiti and Mali.
On the vertical axis, we have log GDP per Capita 1995 - so that's economic growth, that's
what's being measured on the vertical axis.
On the horizontal axis, it says, Average Expropriation Risk, 1985 through 95 - editorial typo here,
they really mean Average Protection Against Expropriation Risk, so higher numbers are
stronger property rights like I just talked about earlier, lower numbers are lower property
rights.
So over here, we have a lot of very high property rights and then up here we have very high
economic growth.
So that's USA, Canada, Australia for example, have high economic growth and high property
rights.
Down here, we have countries with lower property rights and lower economic growth, countries
like Sudan and Haiti.
And you can see that there seems to be this relationship: countries with higher economic
growth have more property rights.
And then here in this one little line, we've drawn something called the Regression Line,
and that just summarizes what we see visually with the data.
There seems to be this relationship between having high property rights and having high
economic development.
Now formally, we could say that the regression of GDP per Capita on Expropriation Risk shows
a positive relationship: the more protection you have of your property rights, the higher
your GDP per capita is.
A different way of saying this is that a regression of GDP per Capita on Protection Against Expropriation
yields a positive coefficient on Protection Against Expropriation, or on property rights.
So basically we're just saying that we've got some data on countries, on their outcome
variable and on their treatment variable, and in the data of these two variables are
positively correlated.
That's all regression is telling us, we're describing the correlations in the data.
Now, we all know from the earlier modules that correlation doesn't necessarily imply
causation, so although we see in the data by doing regression analysis that there is
this correlation, it doesn't tell us that if we were to intervene and increase in property
rights in countries that that would cause GDP to increase.
And why is that?
The same reasons we've talked about before: there could be a confounding variable, there
could be another variable that's actually having a causal effect on economic development
and happens to be correlated with property rights, and the correlation we're seeing in
our regression analysis in the data is just picking up this confounder.
For example, maybe what matters is how leaders are chosen.
So suppose that democratic countries have higher economic development than dictatorships.
Well, if democracy is also correlated with having high property rights, then this relationship
we see in the data might not be a causal effect of property rights and economic development,
it might be reflecting a causal effect of democracy on economic development, but we
haven't included that confounding variable in the analysis.
So that could be driving everything we're seeing in the regression.
Now there is another new possibility that we haven't talked about before.
So we've talked about cofounders, but another possibility here is something called Reverse
Causality.
What if strong property rights are actually a consequence of high economic development?
So it's not that having property rights increases domestic development - it's the other way
around: having strong economic development makes/increases property rights.
For example, maybe rich countries can afford to protect property rights to pay the police
and the judicial system, etc., to make sure that people are securing what they own.
If this is a problem, then again we can't figure out the direction of causality from
just looking at the data from the regression analysis, from just this correlation we see
between property rights and economic development.
A more general problem that’s even more difficult is that we may have something called
simultaneity: this happens when both directions of causality are happening at the same time.
Not only are property rights affecting economic development, but economic development is affecting
property rights - both directions.
Now this is a difficult problem and to tackle it, we'll have to use a different technique
later on.
But here I just want to say that regression is a way to summarize the data and to just
look at the correlations we see.
That's the descriptive approach to use in regression.
[MUSIC].