Causal Inference

The Mixtape
Causal Inference
The Mixtape

Scott Cunningham

Yale
UNIVERSITY PRESS
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10 9 8 7 6 5 4 3 2 1
To my son, εiles, one of my favorite people.

I love you. You’ve tagged my head and heart.

Contents

Acknowledgments
Introduction
What Is Causal Inference?
Do Not Confuse Correlation with Causality
Optimization Makes Everything Endogenous
Example: Identifying Price Elasticity of Demand
Conclusion
Probability and Regression Review
Directed Acyclic Graphs
Introduction to DAG Notation
Potential Outcomes Causal Model
Physical Randomization
Randomization Inference
Conclusion
Matching and Subclassification
Subclassification
Exact Matching
Approximate Matching
Regression Discontinuity
Huge Popularity of Regression Discontinuity
Estimation Using an RDD
Challenges to Identification
Replicating a Popular Design: The Close Election
Regression Kink Design
Conclusion
Instrumental Variables
 History of Instrumental Variables: Father and Son
Intuition of Instrumental Variables
Homogeneous Treatment Effects
Parental Methamphetamine Abuse and Foster Care
The Problem of Weak Instruments
Heterogeneous Treatment Effects
Applications
Popular IV Designs
Conclusion
Panel Data
DAG Example
Estimation
Data Exercise: Survey of Adult Service Providers
Conclusion
Difference-in-Differences
John Snow’s Cholera Hypothesis
Estimation
Inference
Providing Evidence for Parallel Trends Through Event Studies and
Parallel Leads
The Importance of Placebos in DD
Twoway Fixed Effects with Differential Timing
Conclusion
Synthetic Control
Introducing the Comparative Case Study
Prison Construction and Black Male Incarceration
Conclusion
Bibliography
Permissions Index
Acknowledgments

Just as it takes a village to raise a child, it takes many people to help me

write a book like this. The people to whom I am indebted range from the
scholars whose work has inspired me—Alberto Abadie, Josh Angrist, Susan
Athey, David Card, Esther Duflo, Guido Imbens, Alan Krueger, Robert
LaLonde, Steven Levitt, Alex Tabarrok, John Snow, and many more—to
friends, mentors, and colleagues.
I am most indebted first of all to my former advisor, mentor, coauthor,
and friend Christopher Cornwell. I probably owe Chris my entire career. He
invested in me and taught me econometrics as well as empirical designs
more generally when I was a grad student at the University of Georgia. I
was brimming with a million ideas and he some-how managed to keep me
focused. Always patient, always holding me to high standards, always
believing I could achieve them, always trying to help me correct fallacious
reasoning and poor knowledge of econometrics. I would also like to thank
Alvin Roth, who has encouraged me over the last decade in my research.
That encouragement has buoyed me throughout my career repeatedly.
Finally, I’d like to thank Judea Pearl for inviting me to UCLA for a day of
discussions around an earlier draft of the Mixtape and helping improve it.
But a book like this is also due to countless conversations with friends
over the years, as well as reading carefully their own work and learning
from them. People like Mark Hoekstra, Rebecca Thornton, Paul Goldsmith-
Pinkham, Mark Anderson, Greg DeAngelo, Manisha Shah, Christine
Durrance, Melanie Guldi, Caitlyn Myers, Bernie Black, Keith Finlay, Jason
Lindo, Andrew Goodman-Bacon, Pedro Sant’anna, Andrew Baker, Rachael
Meager, Nick Papageorge, Grant McDermott, Salvador Lozano, Daniel
Millimet, David Jaeger, Berk Ozler, Erin Hengel, Alex Bartik, Megan
Stevenson, Nick Huntington-Klein, Peter Hull, as well as many many more
on #EconTwitter, a vibrant community of social scientists on Twitter.
I would also like to thank my two students Hugo Rodrigues and Terry
Tsai. Hugo and Terry worked tirelessly to adapt all of my blue collar Stata
code into R programs. Without them, I would have been lost. I would also
like to thank another student, Brice Green, for early trials of the code to
confirm it worked by non-authors. Blagoj Gegov helped create many of the
figures in Tikz. I would like to thank Ben Chidmi for adapting a simulation
from R into Stata, and Yuki Yanai for allowing me to use his R code for a
simulation. Thank you to Zeljko Hrcek for helping make amendments to the
formatting of the LaTeX when I was running against deadline. And thank
you to my friend Seth Hahne for creating several beautiful illustrations in
the book. I would also like to thank Seth Ditchik for believing in this
project, my agent Lindsay Edgecombe for her encouragement and work on
my behalf, and Yale University Press. And to my other editor, Charlie
Clark, who must have personally read this book fifty times and worked so
hard to improve it. Thank you, Charlie. And to the musicians who have
sung the soundtrack to my life, thanks to Chance, Drake, Dr. Dre, Eminem,
Lauryn Hill, House of Pain, Jay-Z, Mos Def, Notorious B.I.G., Pharcyde,
Tupac Shakur, Tribe, Kanye West, Young MC, and many others.
Finally, I’d like to thank my close friends, Baylor colleagues, students,
and family for tolerating my eccentric enthusiasm for causal inference and
economics for years. I have benefited tremendously from many
opportunities and resources, and for that and other things I am very grateful.
This book, and the class it was based on, is a distillation of countless
journal articles, books, as well as classes I have taken in person and studied
from afar. It is also a product of numerous conversations I’ve had with
colleagues, students and teachers for many years. I have attempted to give
credit where credit is due. All errors in this book were caused entirely by
me, not the people listed above.
Causal Inference
Introduction

My path to economics was not linear. I didn’t major in economics, for

instance. I didn’t even take an economics course in college. I majored in
English, for Pete’s sake. My ambition was to become a poet. But then I
became intrigued with the idea that humans can form plausible beliefs about
causal effects even without a randomized experiment. Twenty-five years
ago, I wouldn’t have had a clue what that sentence even meant, let alone
how to do such an experiment. So how did I get here? Maybe you would
like to know how I got to the point where I felt I needed to write this book.
The TL;DR version is that I followed a windy path from English to causal
inference.1 First, I fell in love with economics. Then I fell in love with
empirical research. Then I noticed that a growing interest in causal
inference had been happening in me the entire time. But let me tell the
longer version.
I majored in English at the University of Tennessee at Knoxville and
graduated with a serious ambition to become a professional poet. But, while
I had been successful writing poetry in college, I quickly realized that
finding the road to success beyond that point was probably not realistic. I
was newly married, with a baby on the way, and working as a qualitative
research analyst doing market research. Slowly, I had stopped writing
poetry altogether.2
My job as a qualitative research analyst was eye opening, in part because
it was my first exposure to empiricism. My job was to do “grounded
theory”—a kind of inductive approach to generating explanations of human
behavior based on observations. I did this by running focus groups and
conducting in-depth interviews, as well as through other ethnographic
methods. I approached each project as an opportunity to understand why
people did the things they did (even if what they did was buy detergent or
pick a cable provider). While the job inspired me to develop my own
theories about human behavior, it didn’t provide me a way of falsifying
those theories.
 I lacked a background in the social sciences, so I would spend my
evenings downloading and reading articles from the Internet. I don’t
remember how I ended up there, but one night I was on the University of
Chicago Law and Economics working paper series website when a speech
by Gary Becker caught my eye. It was his Nobel Prize acceptance speech
on how economics applies to all of human behavior [Becker, 1993], and
reading it changed my life. I thought economics was about stock markets
and banks until I read that speech. I didn’t know economics was an engine
that one could use to analyze all of human behavior. This was
overwhelmingly exciting, and a seed had been planted.
But it wasn’t until I read an article on crime by Lott and Mustard [1997]
that I became truly enamored of economics. I had no idea that there was an
empirical component where economists sought to estimate causal effects
with quantitative data. A coauthor of that paper was David Mustard, then an
associate professor of economics at the University of Georgia, and one of
Gary Becker’s former students. I decided that I wanted to study with
Mustard, and so I applied to the University of Georgia’s doctoral program
in economics. I moved to Athens, Georgia, with my wife, Paige, and our
infant son, Miles, and started classes in the fall of 2002.
After passing my first-year comprehensive exams, I took Mustard’s labor
economics field class and learned about a variety of topics that would shape
my interests for years. These topics included the returns to education,
inequality, racial discrimination, crime, and many other fascinating topics in
labor. We read many, many empirical papers in that class, and afterwards I
knew that I would need a strong background in econometrics to do the kind
of research I cared about. In fact, I decided to make econometrics my main
field of study. This led me to work with Christopher Cornwell, an
econometrician and labor economist at Georgia. I learned a lot from Chris,
both about econometrics and about research itself. He became a mentor,
coauthor, and close friend.
Econometrics was difficult. I won’t even pretend I was good at it. I took
all the econometrics courses offered at the University of Georgia, some
more than once. They included classes covering topics like probability and
statistics, cross-sections, panel data, time series, and qualitative dependent
variables. But while I passed my field exam in econometrics, I struggled to
understand econometrics at a deep level. As the saying goes, I could not see
the forest for the trees. Something just wasn’t clicking.
 I noticed something, though, while I was writing the third chapter of my
dissertation that I hadn’t noticed before. My third chapter was an
investigation of the effect of abortion legalization on the cohort’s future
sexual behavior [Cunningham and Cornwell, 2013]. It was a revisiting of
Donohue and Levitt [2001]. One of the books I read in preparation for my
study was Levine [2004], which in addition to reviewing the theory of and
empirical studies on abortion had a little table explaining the difference-in-
differences identification strategy. The University of Georgia had a
traditional econometrics pedagogy, and most of my field courses were
theoretical (e.g., public economics, industrial organization), so I never
really had heard the phrase “identification strategy,” let alone “causal
inference.” Levine’s simple difference-in-differences table for some reason
opened my eyes. I saw how econometric modeling could be used to isolate
the causal effects of some treatment, and that led to a change in how I
approach empirical problems.

What Is Causal Inference?

My first job out of graduate school was as an assistant professor at Baylor
University in Waco, Texas, where I still work and live today. I was restless
the second I got there. I could feel that econometrics was indispensable, and
yet I was missing something. But what? It was a theory of causality. I had
been orbiting that theory ever since seeing that difference-in-differences
table in Levine [2004]. But I needed more. So, desperate, I did what I
always do when I want to learn something new—I developed a course on
causality to force myself to learn all the things I didn’t know.
I named the course Causal Inference and Research Design and taught it
for the first time to Baylor master’s students in 2010. At the time, I couldn’t
really find an example of the sort of class I was looking for, so I cobbled
together a patchwork of ideas from several disciplines and authors, like
labor economics, public economics, sociology, political science,
epidemiology, and statistics. You name it. My class wasn’t a pure
econometrics course; rather, it was an applied empirical class that taught a
variety of contemporary research designs, such as difference-in-differences,
and it was filled with empirical replications and readings, all of which were
built on the robust theory of causality found in Donald Rubin’s work as well
as the work of Judea Pearl. This book and that class are in fact very similar
to one another.3
So how would I define causal inference? Causal inference is the
leveraging of theory and deep knowledge of institutional details to estimate
the impact of events and choices on a given outcome of interest. It is not a
new field; humans have been obsessing over causality since antiquity. But
what is new is the progress we believe we’ve made in estimating causal
effects both inside and outside the laboratory. Some date the beginning of
this new, modern causal inference to Fisher [1935], Haavelmo [1943], or
Rubin [1974]. Some connect it to the work of early pioneers like John
Snow. We should give a lot of credit to numerous highly creative labor
economists from the late 1970s to late 1990s whose ambitious research
agendas created a revolution in economics that continues to this day. You
could even make an argument that we owe it to the Cowles Commission,
Philip and Sewall Wright, and the computer scientist Judea Pearl.
But however you date its emergence, causal inference has now matured
into a distinct field, and not surprisingly, you’re starting to see more and
more treatments of it as such. It’s sometimes reviewed in a lengthy chapter
on “program evaluation” in econometrics textbooks [Wooldridge, 2010], or
even given entire book-length treatments. To name just a few textbooks in
the growing area, there’s Angrist and Pischke [2009], Morgan and Winship
[2014], Imbens and Rubin [2015], and probably a half dozen others, not to
mention numerous, lengthy treatments of specific strategies, such as those
found in Angrist and Krueger [2001] and Imbens and Lemieux [2008]. The
market is quietly adding books and articles about identifying causal effects
with data all the time.
So why does ωausal Inference: The εixtape exist? Well, to put it bluntly,
a readable introductory book with programming examples, data, and
detailed exposition didn’t exist until this one. My book is an effort to fill
that hole, because I believe what researchers really need is a guide that
takes them from knowing almost nothing about causal inference to a place
of competency. Competency in the sense that they are conversant and
literate about what designs can and cannot do. Competency in the sense that
they can take data, write code and, using theoretical and contextual
knowledge, implement a reasonable design in one of their own projects. If
this book helps someone do that, then this book will have had value, and
that is all I can and should hope for.
 But what books out there do I like? Which ones have inspired this book?
And why don’t I just keep using them? For my classes, I mainly relied on
Morgan and Winship [2014], Angrist and Pischke [2009], as well as a
library of theoretical and empirical articles. These books are in my opinion
definitive classics. But they didn’t satisfy my needs, and as a result, I was
constantly jumping between material. Other books were awesome but not
quite right for me either. Imbens and Rubin [2015] cover the potential
outcomes model, experimental design, and matching and instrumental
variables, but not directed acyclic graphical models (DAGs), regression
discontinuity, panel data, or synthetic control. Morgan and Winship [2014]
cover DAGs, the potential outcomes model, and instrumental variables, but
have too light a touch on regression discontinuity and panel data for my
tastes. They also don’t cover synthetic control, which has been called the
most important innovation in causal inference of the last 15 years by Athey
and Imbens [2017b]. Angrist and Pischke [2009] is very close to what I
need but does not include anything on synthetic control or on the graphical
models that I find so critically useful. But maybe most importantly, Imbens
and Rubin [2015], Angrist and Pischke [2009], and Morgan and Winship
[2014] do not provide any practical programming guidance, and I believe it
is in replication and coding that we gain knowledge in these areas.4
This book was written with a few different people in mind. It was written
first and foremost for practitioners, which is why it includes easy-to-
download data sets and programs. It’s why I have made several efforts to
review papers as well as replicate the models as much as possible. I want
readers to understand this field, but as important, I want them to feel
empowered so that they can use these tools to answer their own research
questions.
Another person I have in mind is the experienced social scientist who
wants to retool. Maybe these are people with more of a theoretical bent or
background, or maybe they’re people who simply have some holes in their
human capital. This book, I hope, can help guide them through the modern
theories of causality so common in the social sciences, as well as provide a
calculus in directed acyclic graphical models that can help connect their
knowledge of theory with estimation. The DAGs in particular are valuable
for this group, I think.
A third group that I’m focusing on is the nonacademic person in industry,
media, think tanks, and the like. Increasingly, knowledge about causal
inference is expected throughout the professional world. It is no longer
simply something that academics sit around and debate. It is crucial
knowledge for making business decisions as well as for interpreting policy.
Finally, this book is written for people very early in their careers, be they
undergraduates, graduate students, or newly minted PhDs. My hope is that
this book can give them a jump start so that they don’t have to meander,
like many of us did, through a somewhat labyrinthine path to these
methods.

Do Not Confuse Correlation with Causality

It is very common these days to hear someone say “correlation does not
mean causality.” Part of the purpose of this book is to help readers be able
to understand exactly why correlations, particularly in observational data,
are unlikely to be reflective of a causal relationship. When the rooster
crows, the sun soon after rises, but we know the rooster didn’t cause the sun
to rise. Had the rooster been eaten by the farmer’s cat, the sun still would
have risen. Yet so often people make this kind of mistake when naively
interpreting simple correlations.
But weirdly enough, sometimes there are causal relationships between
two things and yet no observable correlation. Now that is definitely
strange. How can one thing cause another thing without any discernible
correlation between the two things? Consider this example, which is
illustrated in Figure 1. A sailor is sailing her boat across the lake on a windy
day. As the wind blows, she counters by turning the rudder in such a way so
as to exactly offset the force of the wind. Back and forth she moves the
rudder, yet the boat follows a straight line across the lake. A kindhearted yet
naive person with no knowledge of wind or boats might look at this woman
and say, “Someone get this sailor a new rudder! Hers is broken!” He thinks
this because he cannot see any relationship between the movement of the
rudder and the direction of the boat.
Figure 1. No correlation doesn’t mean no causality. Artwork by Seth Hahne © 2020.

But does the fact that he cannot see the relationship mean there isn’t one?
Just because there is no observable relationship does not mean there is no
causal one. Imagine that instead of perfectly countering the wind by turning
the rudder, she had instead flipped a coin—heads she turns the rudder left,
tails she turns the rudder right. What do you think this man would have seen
if she was sailing her boat according to coin flips? If she randomly moved
the rudder on a windy day, then he would see a sailor zigzagging across the
lake. Why would he see the relationship if the movement were randomized
but not be able to see it otherwise? Because the sailor is endogenously
moving the rudder in response to the unobserved wind. And as such, the
relationship between the rudder and the boat’s direction is canceled—even
though there is a causal relationship between the two.
This sounds like a silly example, but in fact there are more serious
versions of it. Consider a central bank reading tea leaves to discern when a
recessionary wave is forming. Seeing evidence that a recession is emerging,
the bank enters into open-market operations, buying bonds and pumping
liquidity into the economy. Insofar as these actions are done optimally,
these open-market operations will show no relationship whatsoever with
actual output. In fact, in the ideal, banks may engage in aggressive trading
in order to stop a recession, and we would be unable to see any evidence
that it was working even though it was!
Human beings engaging in optimal behavior are the main reason
correlations almost never reveal causal relationships, because rarely are
human beings acting randomly. And as we will see, it is the presence of
randomness that is crucial for identifying causal effect.

Optimization Makes Everything Endogenous

Certain presentations of causal inference methodologies have sometimes
been described as atheoretical, but in my opinion, while some practitioners
seem comfortable flying blind, the actual methods employed in causal
designs are always deeply dependent on theory and local institutional
knowledge. It is my firm belief, which I will emphasize over and over in
this book, that without prior knowledge, estimated causal effects are rarely,
if ever, believable. Prior knowledge is required in order to justify any claim
of a causal finding. And economic theory also highlights why causal
inference is necessarily a thorny task. Let me explain.
There’s broadly thought to be two types of data. There’s experimental
data and non-experimental data. The latter is also sometimes called
observational data. Experimental data is collected in something akin to a
laboratory environment. In a traditional experiment, the researcher
participates actively in the process being recorded. It’s more difficult to
obtain data like this in the social sciences due to feasibility, financial cost,
or moral objections, although it is more common now than was once the
case. Examples include the Oregon Medicaid Experiment, the RAND health
insurance experiment, the field experiment movement inspired by Esther
Duflo, Michael Kremer, Abhijit Banerjee, and John List, and many others.
Observational data is usually collected through surveys in a retrospective
manner, or as the by-product of some other business activity (“big data”). In
many observational studies, you collect data about what happened
previously, as opposed to collecting data as it happens, though with the
increased use of web scraping, it may be possible to get observational data
closer to the exact moment in which some action occurred. But regardless
of the timing, the researcher is a passive actor in the processes creating the
data itself. She observes actions and results but is not in a position to
interfere with the environment in which the units under consideration exist.
This is the most common form of data that many of us will ever work with.
Economic theory tells us we should be suspicious of correlations found in
observational data. In observational data, correlations are almost certainly
not reflecting a causal relationship because the variables were endogenously
chosen by people who were making decisions they thought were best. In
pursuing some goal while facing constraints, they chose certain things that
created a spurious correlation with other things. And we see this problem
reflected in the potential outcomes model itself: a correlation, in order to be
a measure of a causal effect, must be based on a choice that was made
independent of the potential outcomes under consideration. Yet if the person
is making some choice based on what she thinks is best, then it necessarily
is based on potential outcomes, and the correlation does not remotely
satisfy the conditions we need in order to say it is causal. To put it as
bluntly as I can, economic theory says choices are endogenous, and
therefore since they are, the correlations between those choices and
outcomes in the aggregate will rarely, if ever, represent a causal effect.
Now we are veering into the realm of epistemology. Identifying causal
effects involves assumptions, but it also requires a particular kind of belief
about the work of scientists. Credible and valuable research requires that we
believe that it is more important to do our work correctly than to try and
achieve a certain outcome (e.g., confirmation bias, statistical significance,
asterisks). The foundations of scientific knowledge are scientific
methodologies. True scientists do not collect evidence in order to prove
what they want to be true or what others want to believe. That is a form of
deception and manipulation called propaganda, and propaganda is not
science. Rather, scientific methodologies are devices for forming a
particular kind of belief. Scientific methodologies allow us to accept
unexpected, and sometimes undesirable, answers. They are process
oriented, not outcome oriented. And without these values, causal
methodologies are also not believable.

Example: Identifying Price Elasticity of Demand

One of the cornerstones of scientific methodologies is empirical analysis.5
By empirical analysis, I mean the use of data to test a theory or to estimate a
relationship between variables. The first step in conducting an empirical
economic analysis is the careful formulation of the question we would like
to answer. In some cases, we would like to develop and test a formal
economic model that describes mathematically a certain relationship,
behavior, or process of interest. Those models are valuable insofar as they
both describe the phenomena of interest and make falsifiable (testable)
predictions. A prediction is falsifiable insofar as we can evaluate, and
potentially reject, the prediction with data.6 A model is the framework with
which we describe the relationships we are interested in, the intuition for
our results, and the hypotheses we would like to test.7
After we have specified a model, we turn it into what is called an
econometric model, which can be estimated directly with data. One clear
issue we immediately face is regarding the functional form of the model, or
how to describe the relationships of the variables we are interested in
through an equation. Another important issue is how we will deal with
variables that cannot be directly or reasonably observed by the researcher,
or that cannot be measured very well, but which play an important role in
our model.
A generically important contribution to our understanding of causal
inference is the notion of comparative statics. Comparative statics are
theoretical descriptions of causal effects contained within the model. These
kinds of comparative statics are always based on the idea of ceteris paribus
—or “all else constant.” When we are trying to describe the causal effect of
some intervention, for instance, we are always assuming that the other
relevant variables in the model are not changing. If they were changing,
then they would be correlated with the variable of interest and it would
confound our estimation.8
To illustrate this idea, let’s begin with a basic economic model: supply
and demand equilibrium and the problems it creates for estimating the price
elasticity of demand. Policy-makers and business managers have a natural
interest in learning the price elasticity of demand because knowing it
enables firms to maximize profits and governments to choose optimal taxes,
and whether to restrict quantity altogether [Becker et al., 2006]. But the
problem is that we do not observe demand curves, because demand curves
are theoretical objects. More specifically, a demand curve is a collection of
paired potential outcomes of price and quantity. We observe price and
quantity equilibrium values, not the potential price and potential quantities
along the entire demand curve. Only by tracing out the potential outcomes
along a demand curve can we calculate the elasticity.
To see this, consider this graphic from Philip Wright’s Appendix B
[Wright, 1928], which we’ll discuss in greater detail later (Figure 2). The
price elasticity of demand is the ratio of percentage changes in quantity to
price for a single demand curve. Yet, when there are shifts in supply and
demand, a sequence of quantity and price pairs emerges in history that
reflect neither the demand curve nor the supply curve. In fact, connecting
the points does not reflect any meaningful or useful object.

Figure 2. Wright’s graphical demonstration of the identification problem. Figure from Wright, P. G.
(1928). The Tariff on Animal and Vegetable τils. The Macmillan Company.

The price elasticity of demand is the solution to the following equation:

But in this example, the change in P is exogenous. For instance, it holds
supply fixed, the prices of other goods fixed, income fixed, preferences
fixed, input costs fixed, and so on. In order to estimate the price elasticity of
demand, we need changes in P that are completely and utterly independent
of the otherwise normal determinants of supply and the other determinants
of demand. Otherwise we get shifts in either supply or demand, which
creates new pairs of data for which any correlation between P and Q will
not be a measure of the elasticity of demand.
The problem is that the elasticity is an important object, and we need to
know it, and therefore we need to solve this problem. So given this
theoretical object, we must write out an econometric model as a starting
point. One possible example of an econometric model would be a linear
demand function:

where α is the intercept, δ is the elasticity of demand, X is a matrix of

factors that determine demand like the prices of other goods or income, γ is
the coefficient on the relationship between X and Qd, and u is the error
term.9
Foreshadowing the content of this mixtape, we need two things to
estimate price elasticity of demand. First, we need numerous rows of data
on price and quantity. Second, we need for the variation in price in our
imaginary data set to be independent of u. We call this kind of
independence exogeneity. Without both, we cannot recover the price
elasticity of demand, and therefore any decision that requires that
information will be based on stabs in the dark.

Conclusion
This book is an introduction to research designs that can recover causal
effects. But just as importantly, it provides you with hands-on practice to
implement these designs. Implementing these designs means writing code
in some type of software. I have chosen to illustrate these designs using two
popular software languages: Stata (most commonly used by economists)
and R (most commonly used by everyone else).
The book contains numerous empirical exercises illustrated in the Stata
and R programs. These exercises are either simulations (which don’t need
external data) or exercises requiring external data. The data needed for the
latter have been made available to you at Github. The Stata examples will
download files usually at the start of the program using the following
command: use
https://github.com/scunning1975/mixtape/raw/master/DATAFILENAME.D
TA, where DATAFILENAME.DTA is the name of a particular data set.
For R users, it is a somewhat different process to load data into memory.
In an effort to organize and clean the code, my students Hugo Sant’Anna
and Terry Tsai created a function to simplify the data download process.
This is partly based on a library called haven, which is a package for
reading data files. It is secondly based on a set of commands that create a
function that will then download the data directly from Github.10
Some readers may not be familiar with either Stata or R but nonetheless
wish to follow along. I encourage you to use this opportunity to invest in
learning one or both of these languages. It is beyond the scope of this book
to provide an introduction to these languages, but fortunately, there are
numerous resources online. For instance, Christopher Baum has written an
excellent introduction to Stata at
https://fmwww.bc.edu/GStat/docs/StataIntro.pdf. Stata is popular among
microeconomists, and given the amount of coauthoring involved in modern
economic research, an argument could be made for investing in it solely for
its ability to solve basic coordination problems between you and potential
coauthors. But a downside to Stata is that it is proprietary and must be
purchased. And for some people, that may simply be too big of a barrier—
especially for anyone simply wanting to follow along with the book. R on
the other hand is open-source and free. Tutorials on Basic R can be found at
https://cran.r-project.org/doc/contrib/Paradis-rdebuts_en.pdf, and an
introduction to Tidyverse (which is used throughout the R programming)
can be found at https://r4ds.had.co.nz. Using this time to learn R would
likely be well worth your time.
Perhaps you already know R and want to learn Stata. Or perhaps you
know Stata and want to learn R. Then this book may be helpful because of
the way in which both sets of code are put in sequence to accomplish the
same basic tasks. But, with that said, in many situations, although I have
tried my best to reconcile results from Stata and R, I was not always able to
do so. Ultimately, Stata and R are different programming languages that
sometimes yield different results because of different optimization
procedures or simply because the programs are built slightly differently.
This has been discussed occasionally in articles in which authors attempt to
better understand what accounts for the differing results. I was not always
able to fully reconcile different results, and so I offer the two programs as
simply alternative approaches. You are ultimately responsible for anything
you do on your own using either language for your research. I leave it to
you ultimately to understand the method and estimating procedure
contained within a given software and package.
In conclusion, simply finding an association between two variables might
be suggestive of a causal effect, but it also might not. Correlation doesn’t
mean causation unless key assumptions hold. Before we start digging into
the causal methodologies themselves, though, I need to lay down a
foundation in statistics and regression modeling. Buckle up! This is going
to be fun.

Notes
1 “Too long; didn’t read.”
2 Rilke said you should quit writing poetry when you can imagine yourself living without it [Rilke,
2012]. I could imagine living without poetry, so I took his advice and quit. Interestingly, when I later
found economics, I went back to Rilke and asked myself if I could live without it. This time, I
decided I couldn’t, or wouldn’t—I wasn’t sure which. So I stuck with it and got a PhD.
3 I decided to write this book for one simple reason: I didn’t feel that the market had provided the
book that I needed for my students. So I wrote this book for my students and me so that we’d all be
on the same page. This book is my best effort to explain causal inference to myself. I felt that if I
could explain causal inference to myself, then I would be able to explain it to others too. Not thinking
the book would have much value outside of my class, I posted it to my website and told people about
it on Twitter. I was surprised to learn that so many people found the book helpful.
4 Although Angrist and Pischke [2009] provides an online data warehouse from dozens of papers,
I find that students need more pedagogical walk-throughs and replications for these ideas to become
concrete and familiar.
5 It is not the only cornerstone, or even necessarily the most important cornerstone, but empirical
analysis has always played an important role in scientific work.
6 You can also obtain a starting point for empirical analysis through an intuitive and less formal
reasoning process. But economics favors formalism and deductive methods.
7 Scientific models, be they economic ones or otherwise, are abstract, not realistic, representations
of the world. That is a strength, not a weakness. George Box, the statistician, once quipped that “all
models are wrong, but some are useful.” A model’s usefulness is its ability to unveil hidden secrets
about the world. No more and no less.
8 One of the things implied by ceteris paribus that comes up repeatedly in this book is the idea of
covariate balance. If we say that everything is the same except for the movement of one variable,
then everything is the same on both sides of that variable’s changing value. Thus, when we invoke
ceteris paribus, we are implicitly invoking covariate balance—both the observable and the
unobservable covariates.
9 More on the error term later.
 10 This was done solely for aesthetic reasons. Often the URL was simply too long for the margins
of the book otherwise.