1Causal inference is an exercise in counterfactual thinking, full of what if questions about the road not taken. We ask ourselves these questions all the time. What would have happened if I had taken that job? Said yes instead of no? How would life be different today?

2A counterfactual is the hypothetical state of a what if question. With counterfactual thinking, there is what actually happened, and then there is the hypothetical counterfactual of what would have happened, counter to fact, under the alternative scenario. The difference between what did happen and what would have happened is known as the causal effect. Robert Frost fans see the problem. Two roads diverged in a yellow wood, and sorry I could not travel both and be one traveler.

3Robert has to choose one road. He can't take both simultaneously. He can either take the road more traveled, a decision we'll call X equals zero, or he can take the road less traveled, a decision we'll call X equals one.

4In some ways it might be easier to refer to Robert's decision as the variable road, or R, and set the values of road to more traveled or less traveled, representing his two choices. But instead I'm referring to his decision as X, and to the values of X as zero and one. Why? Often we refer to potential causes as X and to response variables as Y. And typically, when the treatment, or exposure, X can take two levels, such as treated and not treated, we label treated one, and not treated zero.

5In this example, I imagine Robert looking left and then looking right. Observing that the second path was grassy and wanted wear, he decided to go right, taking the one less traveled by. Frost claims that his decision to take the uncommon path made all the difference, so I'm labeling that path, the road less traveled, as the treatment. X equals one.

6Robert's two choices correspond to two potential outcomes, or states of the world, that he could experience. There is the potential outcome that results from taking the road more traveled, and the potential outcome that results from taking the road less traveled. We'll call these Y if X equals zero, what happens if he takes the road more traveled, and Y if X equals one, what happens if he takes the road less traveled.

7So what does he do? He famously takes the road less traveled. Robert's factual outcome is what happens after making that choice. His other potential outcome will never be observed. Taking the road more traveled is now the counterfactual. He can only wonder what would have happened, counter to fact, if he had taken the beaten path.

8And yet, Robert boldly claims that taking the road less traveled made all the difference. How can he know for sure? We defined causal effects as the difference between what did happen and what would have happened, but we only observed what happened, not what would have. So we have a missing data problem.

9This is what's often called the fundamental problem of causal inference. We only get to observe one potential outcome for any given person, or unit, more generally. The causal effect of taking the road less traveled is the difference in the two potential outcomes, Y if X equals one minus Y if X equals zero. But Y if X equals zero is missing. So we can't measure this effect for Robert.

10We can, however, compare groups of people like Robert who take one road or the other and estimate the average treatment effect, or A T E. I'm emphasizing estimate, because truly calculating the average treatment effect would require knowing both potential outcomes for each person, or unit, like classrooms or schools. We can only observe one potential outcome for any given person. But let's ignore that for a moment, to understand the true average treatment effect.

11While we're pretending, let's imagine that the response variable Robert writes about in his poem is happiness later in life, and happiness, our Y, is measured on a scale of zero to ten, where zero is not at all happy and ten is very happy. The left panel here shows fictional happiness data for a sample of twelve people, including Robert, under both potential outcomes. Notice how each person has two values: the happiness that would result if they took the road less traveled, and the happiness that would result if they took the road more traveled. Some people, like the first traveler on the left, would be happiest taking the road more traveled. Other people, such as Robert, who is number eleven, would find greater happiness on the road less traveled.

12As shown in the right panel, the average treatment effect is calculated as the difference between the group averages, which is equivalent to the average of the travelers' individual causal effects. In this example, where we are all knowing, the average treatment effect is one point five. Taking the road less traveled increases happiness on average by one point five points on a scale of zero to ten. Remember, we're pretending here. We never observe both potential outcomes.

13We're not all knowing, of course, and we only get to observe one potential outcome for each person. This means we have to estimate the average treatment effect by comparing people like Robert who take the road less traveled to people who take the road more traveled. But how do people come to take one road versus the other?

14This figure shows two scenarios, of an infinite number. On the left, in panel A, travelers are randomly assigned to a road. Imagine that they come to the fork in the road and pull directions out of a hat. Half are assigned to the road less traveled, and half to the road more traveled. In both panels, the grey dots represent the unobserved counterfactuals. Notice that under perfect randomization, on the left, the estimated average treatment effect of one point five is equal to the true, but unknowable, average treatment effect.

15On the right, in panel B, travelers choose a road themselves. Imagine that they go with their gut and all happen to pick the road that maximizes their individual happiness. Here the estimate is four point seven. That does not line up with the true average treatment effect, because the estimate includes bias. And remember that bias is anything that takes us away from the truth.

16Why does the estimate go wrong in panel B? The answer is selection bias, systematic differences between groups that distort our comparison. When travelers chose their own road, the optimistic people, who would have been happier regardless of which road they took, selected into the road less traveled. So when we compare average happiness across roads, we're not just seeing the effect of the road. We're also seeing the effect of optimism.

17As we will see in later chapters, randomization can be a very effective way to neutralize selection bias, but randomization is not always possible or maintained. Most research is non-experimental, or what many would call observational. Selection bias will remain a threat in many cases, and unfortunately we can't simply calculate it and subtract it away, because the exact quantity is typically unknowable. That leaves us with research design and statistical adjustment as our only defense.

18Cunningham has argued that the entire enterprise of causal inference is about developing a reasonable strategy for negating the role that selection bias is playing in estimated causal effects.

19There are different causal inference methods for addressing selection bias, and which one a researcher chooses tends to be heavily influenced by their context and discipline. Clinical researchers, biostatisticians, and behavioral interventionists often prefer to use experimental designs that randomly allocate people, or units, to different treatment arms. Folks in this camp might refer to themselves as clinical trialists. There is also a rich tradition of experimentation in the social sector among economists and public policy scholars. Three economists won the twenty nineteen Nobel Prize in Economics for their experimental approach to alleviating global poverty. Where randomization is not available, the work has to be non-experimental.

20Many research questions in global health are not amenable to experimentation, and the approach to causal inference must be rooted in non-experimental, or observational, data. These non-experimental approaches divide into two main buckets: confounder-control and instrument-based. Confounder-control is characterized by the use of statistical adjustment to make groups more comparable. You'll find many examples of confounder-control in epidemiology and public health journals. Instrument-based studies, sometimes called quasi-experimental designs, estimate treatment effects by finding and leveraging arbitrary reasons why some people are more likely to be treated or exposed. Instrument-based studies are quite common in economics and psychology.

21Both families of approaches exist to answer the same problem. Confounder-control uses statistical adjustment to make groups more comparable. Instrument-based studies find and leverage arbitrary reasons why some people are more likely to be treated. The chapter introduces each approach in turn, and so do the videos that follow.