Measurement: Causal Inference Bootcamp

[MUSIC] So the goal of these modules is to
do a quantitative analysis of causality. So to do that, we’re going to have to measure
any variables that we want to understand. Now a variable is just some characteristic
of the Unit of Analysis. And what I mean by unit of analysis is things like countries,
city blocks, people, villages, firms. So these are the units of analysis, the things that
we’re going to analyze, the things that are in our data sets. So we have data on different
people, data on different countries, data on different villages. So the collection of all these units is called
the Population. The population of firms, the population of villages, this is the set of
all the people in the United States, for example, or all the villages in Nigeria, etc. There are two main variables that we have
to measure, the first is the Outcome Variable. This describes the characteristic that we
want to affect, the characteristic that we want to change. For example, how healthy you
are in your old age. The second variable we want to measure is
the Policy Variable, or the Treatment Variable. This describes the characteristic of a unit
of analysis that we are going to use to change the outcome variable. So if our outcome variable
is health, then our treatment variable might be whether you have health insurance or not. And these are both characteristics of a unit
of analysis, for example, a person. A person has a value of how healthy they are, and a
value of whether they have the treatment or not, whether they have health insurance. So there are lots of examples from public
policy besides healthcare. For example, if our outcome variable is a measure of economic
development, our policy variable is a measure of how strong property rights are. Or our
outcome variable could be the amount of crime on a city block, and the treatment variable
would be how many police are stationed to that city block. So more concretely, when we actually do the
analysis, we’re going to have to pick exactly how we’re going to measure these guys. So
the amount of crime is an abstract concept. We’re going to have to pick exactly how we’re
going to measure crime. So for example, we could say the number of car thefts on a city
block. That’s something you can just count and look up in your data. Then to measure
treatment, how many police are stationed there, you could, for example, see did a city block
get extra police or not relative to the average level in the city? For property rights, suppose you want to measure
the effective property rights on economic development. Well there the outcome variable
is economic development. It’s a pretty abstract concept, so in order to do a quantitative
analysis, we’re going to have to figure out how do we measure that? So one way is to just
to use GDP, gross domestic product. That’s a number, you can look it up, how it’s defined. Then the treatment variable, this is the thing
that we want to affect economic development, that we have to measure too. So here it’s
property rights. So how do we measure probably rights? Well, we could define a number that
tells us the risk of expropriation by a foreign government. So what this means is if you are
a company and you invest in some country, how likely is it that that country’s government
is going to just take away what you own there? Take away your oil rigs, your manufacture
plants, etc. If it is not likely at all, then there are strong property rights. If it’s
very likely that they’re going to take what you own, then there is weak property rights,
okay, and people figure out how to measure these things quantitatively. Now it’s not always easy to measure what we
want, and a huge part of research is often figuring out exactly how to do this, exactly
how do you measure difficult things? So for example, think about how do we measure
hope? Why would we want to do that? Well, suppose we were interested in knowing whether
poor children who have hope have better outcomes than children without hope, for example. Do
children with hope get more education? So how do you measure hope? Pretty vague concept,
right? But there’s a paper from 2013, what they did
is they asked children to draw a picture of yourself in the rain. And then they used characteristics
of the drawings, like whether the child has a mouth or not, whether it’s holding an umbrella
or not, etc., to define a quantitative measure of hope. So I’ve a few of those pictures here.
So here’s one picture: this kid is standing here, he is smiling, he’s got a block face,
he’s got an umbrella here, and he’s got his hand up. Look how happy he is, this guy is
so happy, right? Now here is another picture: this person is standing in the rainstorm,
soaked, doesn’t have an umbrella, is frowning, doesn’t look very happy. Well, based on their quantitative measure
of hope, this person is at the 93rd percentile of hope. That means they have a lot of hope,
they’re very high up there. The second picture, this person is near the bottom, they are in
the 15th percentile of hope. They basically have nothing. So there are very, very creative and innovative
ways that people have made to measure difficult concepts like hope. Now for these modules
we’re going to assume that this stuff has already been done, that someone has already
figured out how to measure what we want to look at, and the only question is how do we
determine from data on the policy variable, how much hope there is and from the outcome
variable, how much education a poor child gets, how do we determine from data on that
what the causal effects are? Whether having hope actually does increase the amount of
education you may have. [MUSIC].

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