Opening
Host
Welcome back. Today we are on randomized trials and health insurance. People with insurance often report better health. That sounds like a strong argument for expanding coverage. But could the difference have existed before anyone bought a policy?
Economist
That question matters because insurance changes more than a hospital bill. It changes the price people pay when they seek care. It can also protect a household from financial trouble. The RAND experiment tested different levels of coverage. People offered free care used more services. Yet the average physical health improvements were surprisingly limited. Oregon later offered another chance to study insurance through a lottery.
Host
So the puzzle is bigger than whether people visit a doctor. Does health insurance make people healthier? I want to understand how researchers can answer that without confusing insurance with the advantages of people who already have it.
Economist
By the end of this episode, you should be able to explain selection bias using potential outcomes. You should also explain why random assignment makes a comparison credible. Finally, you should interpret insurance experiments together with their statistical uncertainty. We will follow the mind map through The Question, The Investigation, and The Resolution. No diagram is needed to follow the reasoning.
Host
And we will keep asking what the comparison actually measures. An offer of insurance, receiving insurance, visiting a doctor, and becoming healthier sound related. They are still different things.
Economist
Exactly. Keeping those differences clear is the central habit we will practice. We will begin with an ordinary survey comparison. Then we will rebuild that comparison so that it can answer a causal question.
The Question
Host
Let's start with The Question. The central challenge is health insurance and health. Why is a comparison between insured and uninsured people such an attractive starting point?
Economist
We want a comparison that policy can change. In the American setting described in the chapter, health spending was high, yet many people lacked coverage. Insurance might encourage preventive care or help people manage long illnesses. Those are plausible reasons to expect better health. But a plausible mechanism is a starting hypothesis. We still need evidence that separates its effect from other explanations.
Host
My prediction is that insured people will look healthier in a survey. They have help paying for care, so that seems likely. Would that at least establish the direction of the effect?
Economist
The survey does show better reported health among the insured. But that pattern alone cannot establish even the direction of the causal effect. The people who have coverage might have started healthier. Alternatively, people expecting expensive illnesses might seek more insurance. Either kind of selection changes the comparison. We need to ask what the same people would have experienced under a different insurance arrangement.
Host
Let's be precise about the naive survey evidence. Which people were compared, and what counted as health on that 1 to 5 scale? I would rather understand a modest measure properly than treat an impressive average as a complete medical assessment.
Economist
The National Health Interview Survey, or NHIS, asks people to describe their general health. The chapter uses married respondents from 2009, aged 26 to 59, with at least one spouse working. The scale runs from poor health at its lowest score to excellent health at its highest. Higher scores therefore mean better reported health. This is an ordered self-report measure. It is useful, but it is different from a laboratory test or a doctor's examination.
Host
The chapter's companion materials summarize a positive gap. Do we need to distinguish that summary from the exact comparisons in the original analysis?
Economist
Yes. The original analysis reports husbands and wives separately. Among husbands, the insured mean is 4.01 and the uninsured mean is 3.70. Among wives, the corresponding means are 4.02 and 3.62. Those are separate comparisons. We should not combine a mean from one group with a mean from another, or treat a different summary as the same estimate.
Host
Before I give insurance the credit, what else differs between those groups? People do not normally receive insurance through a coin toss. Their employment and family situations probably matter.
Economist
That is the difficulty. The insured respondents are older on average, more educated, richer, and more often employed. Education and income can influence both insurance coverage and health. For example, education may affect health habits as well as employment opportunities. The survey comparison contains all these differences together. A large sample can measure that combined gap precisely without telling us which part insurance caused.
Host
We need some vocabulary for the missing comparison. What exactly is an outcome, what is a treatment, and what is a potential outcome? The words sound more medical than the problem requires.
Economist
An outcome is the result we study, such as reported health. A treatment is the condition whose effect we want, such as a specified insurance policy. It need not be a medicine. A potential outcome is what would happen to a person under a particular treatment condition. For our question, imagine that person's health with coverage and that person's health without coverage, in otherwise comparable circumstances.
Host
So the treatment effect compares two possible outcomes for the same person. It does not begin by comparing different people. But we can observe only the condition that actually happens.
Economist
Right. The unobserved alternative is called the counterfactual. It is the outcome under the condition the person did not experience. Selection bias arises when the people receiving treatment would have had different outcomes even without it. Random assignment means using chance to decide who is offered a treatment. We will see how that helps create a credible comparison group.
Host
Could we just wait and observe the person again without insurance? That might look like a way to recover the missing outcome without needing another person at all.
Economist
A later observation also changes time. The person may be older, have a different job, or face a different illness. We would again need assumptions to separate the treatment from those changes. Potential outcomes are defined for a clear comparison, including a setting and a time period. They help us state the question accurately, even when we cannot observe every answer.
Host
Our first recap is about the question itself. A health gap is visible, but the same person's alternative outcome is missing. Better measured averages do not automatically repair that problem.
Economist
Exactly. We have identified an outcome, a treatment, and a counterfactual. The survey comparison is informative about differences between groups. To interpret those differences as insurance effects, we need a reason that the groups represent comparable alternatives.
The Investigation
Host
Now we enter The Investigation. Let's begin with the selection bias problem. Could a misleading comparison actually suggest that helpful insurance is harmful, rather than merely exaggerating its benefit?
Economist
Yes. Consider the chapter's deliberately hypothetical students, Khuzdar and Maria. Their imagined potential outcomes are a teaching device, not survey findings. Khuzdar would have poorer health without insurance and chooses coverage. Maria expects good health either way and chooses no coverage. If we compare their observed health, Maria can look healthier even though insurance helps Khuzdar. His underlying disadvantage hides the benefit.
Host
I predict that comparing their observed outcomes would blame insurance for Khuzdar's worse health. That conclusion would reverse what the hypothetical example says happens to him. Where does the misleading part enter?
Economist
Your prediction is correct. The comparison mixes a treatment effect with a starting difference. First ask how Khuzdar's health changes with insurance. Then ask how his health without insurance differs from Maria's health without insurance. Adding those components produces the observed gap. The second component is selection bias. It can be large enough to reverse the sign of the observed comparison.
Host
Does that logic survive when we replace these imagined students with many actual people? I might expect a big sample to average away personal differences, including the differences that affect insurance choices.
Economist
Only random differences average away in the way we need. If healthier or richer people systematically select coverage, a larger sample repeats the same sorting pattern. For groups, the observed gap equals the average treatment effect among the treated plus their average untreated disadvantage or advantage. That last part compares untreated potential outcomes across groups. The chapter initially uses a constant effect to simplify the algebra. The basic problem also exists when effects differ across people.
Host
Why say the average effect among the treated? I might otherwise hear the formula as the average effect for everyone, including people who did not choose insurance.
Economist
Because we start with the observed outcomes of people who actually received treatment. We imagine removing their insurance while keeping that group fixed. That gives their average treatment effect. We then compare their untreated potential outcomes with the control group's untreated outcomes. Without additional assumptions, that decomposition does not identify the effect for the entire population. Randomization will give us a stronger connection between the groups.
Host
The map mentions confounders and a back-door path. Can we understand those words without drawing a causal diagram? I suspect they describe the alternative explanations already hiding inside the health gap.
Economist
A confounder is a factor that helps determine both treatment and outcome. Education is a candidate here. It may affect coverage through employment and affect health through behavior or resources. That creates an alternative route linking insurance and health. A back-door path is a diagram's name for such a route. We can understand the problem by asking whether something besides insurance makes the groups different.
Host
If we compare people with the same schooling, have we closed that alternative route? That seems more practical than running a health insurance experiment. What would still worry you?
Economist
Equal schooling removes that particular observed difference. It does not guarantee equal income, health habits, or expectations about future illness. Some important characteristics are unrecorded. Many visible group differences should also make us cautious about hidden differences. This is the fundamental problem of causal inference: we never observe both potential outcomes for an individual. A comparison group must stand in for the missing alternative, and its credibility needs a justification.
Host
Before solving that problem, let's understand the map's regression tool. What does it mean to regress health on a dummy variable? I want to know exactly what the computer adds to a comparison of averages.
Economist
A dummy variable records membership in a group. Here it records whether someone is insured. With an intercept and only that indicator, ordinary least squares regression reproduces the group means. The intercept is the uninsured group's average health. The insurance coefficient is the insured mean minus the uninsured mean. The fitted insured mean adds that coefficient to the intercept. No hidden causal adjustment occurs in this calculation.
Host
Let's work through the husbands' comparison using a single consistent sample. The insured mean is 4.01 and the uninsured mean is 3.70. We subtract the uninsured mean from the insured mean. What does that give us?
Economist
Subtracting gives a gap of 0.31 index points. These are survey-weighted means. The gap also comes from a dummy-only regression using the same survey weights. The coefficient describes an association. Calling it an effect would require a credible reason to dismiss selection bias. The arithmetic cannot supply that reason. Survey weights give people different influence so the estimate reflects the population represented by the survey. Keep those weights and the sample definition consistent.
Host
So regression can organize the same comparison, while uncertainty calculations tell us how stable that comparison is. Neither feature turns the original insurance decision into an experiment. How do we read the standard error beside a coefficient?
Economist
A standard error measures the sampling uncertainty of an estimate. We will develop that idea after the experiments. For now, divide the estimated difference by its standard error. The result is the t-statistic. Under usual large-sample conditions, an absolute t-statistic above about 2 is evidence against a zero population difference. This is a rough statistical rule, not a test of whether selection bias exists.
Host
That helps with the NHIS comparison table. Large differences across education, income, and employment warn that the groups are different. A very precise health gap would still be a precise comparison of unlike groups.
Economist
Exactly. A standard error describes random uncertainty around an estimate. Selection bias describes a systematic problem with what the estimate compares. More observations can shrink the first problem while leaving the second untouched. We need to change the design of the comparison, not merely add more observations to it.
Host
The solution on the map is random assignment. Suppose researchers use chance to offer coverage within a group of eligible people. How does that address both the characteristics we measure and those we cannot measure?
Economist
The assignment rule does not consult income, schooling, or hidden health expectations. Each eligible person has a specified chance of treatment independent of their potential outcomes. Across repeated assignments, treatment and control groups have the same expected mix of people. Their expected untreated health is therefore the same. This removes systematic selection bias from assignment, even though a particular experiment can have chance imbalances.
Host
Is that why a coin toss involving very few people would still be random, but might produce a poor practical comparison? It could place an unusually healthy person in one group just by chance.
Economist
Yes. Randomization is unbiased by design; it does not promise identical observed groups in every small sample. The law of large numbers says that averages become more stable as the amount of independent information grows. With larger randomized groups, chance differences usually become less important. Importantly, random assignment does not make individuals identical. It makes the groups comparable on average, including in unmeasured characteristics.
Host
I also want to separate random assignment from random sampling. If a study recruits volunteers and then randomizes them, its internal comparison can be strong. But volunteers might differ from people outside the study.
Economist
Correct. Random sampling concerns who enters the study from a wider population. Random assignment concerns who receives which condition inside it. Assignment supports a causal comparison for study participants. Generalizing to another population needs further reasoning about eligibility, context, and treatment. Even excellent randomization cannot make a different population experience the same effect automatically.
Host
The history on the map includes James Lind, Peirce and Jastrow, and Fisher. What should we remember from that history without treating every early comparison as a randomized trial?
Economist
Lind compared scurvy remedies among sailors chosen to be similar. That was a controlled comparison, but it did not randomly allocate treatments. Peirce and Jastrow described chance-based allocation in their 1885 work on sensation. Fisher developed the logic of randomized experimental design in work including his 1925 statistics book. The distinction matters more than memorizing dates: choosing similar people and allocating treatment by chance are different procedures.
Host
That brings us to the RAND Health Insurance Experiment. What exactly was assigned, and what was the control condition? I want to avoid hearing free care versus catastrophic coverage as insurance versus absolutely no protection.
Economist
RAND ran from 1974 to 1982 and enrolled roughly 4,000 people. The analysis groups its original plans into four types: catastrophic coverage, a deductible plan, coinsurance plans, and free care. Coinsurance means patients pay a share of each bill. A deductible requires payment before specified coverage begins. All groups had some protection against very high expenses. Catastrophic coverage was the comparison group, an approximation to little coverage rather than complete absence of insurance.
Host
So generosity changed the price people faced when seeking care. Free care removed direct charges, while the less generous plans required more payment until a limit. Before comparing later outcomes, what did researchers check?
Economist
They checked baseline balance: whether groups looked similar before treatment could affect them. They compared characteristics such as age, schooling, income, and initial health. Most differences were small, without a consistent pattern favoring one group. A few unusual differences can occur by chance when a table contains many comparisons. The design and the overall pattern matter; balance is useful evidence, not proof that every hidden difference is exactly zero.
Host
The companion analysis clusters standard errors by family. Why should uncertainty care about family membership if the spreadsheet has a separate row for every person? I might otherwise count all those rows as independent information.
Economist
Family members received the same assigned plan and may share health conditions and behavior. Their observations need not be independent. Family clustering allows estimation errors to be related within families. It avoids treating tightly connected observations as if they were unrelated experimental units. The standard error must respect how the experiment was organized, not simply how many rows the data contain.
Host
Could people leaving the experiment undo that careful beginning? If the original groups were balanced, I might assume the later comparison stays fair even when some participants disappear from follow-up.
Economist
That assumption is unsafe. Many RAND participants dropped out, and dropout rates differed across plans. Fewer people left free care. This is called differential attrition. If leaving is related to potential health or spending, the people still observed may no longer be comparable. Initial random assignment does not automatically correct selective follow-up. The original chapter warns that this could have compromised validity. Keep that concern alongside the reported results.
Host
Now for the results. If free care lowers what patients pay, I would expect more visits. Did the experiment find a modest response or a large one?
Economist
Free care raised face-to-face visits by about 1.7 relative to catastrophic coverage. Total medical spending increased by about 45 percent. Outpatient care responded more strongly than hospital admissions. That pattern is consistent with patients having more discretion over outpatient visits, while doctors often make admission decisions. These comparisons concern the assigned plans. They reveal that demand for care responds to what patients pay.
Host
Economists sometimes call that moral hazard. Does the term accuse patients of bad behavior? A visit that becomes affordable could be medically useful, so the label alone cannot tell us whether the extra care was wasteful.
Economist
Exactly. Here moral hazard describes a response to insurance changing incentives. It is not a moral judgment or a direct measure of waste. To assess the extra care, we need outcomes and costs. RAND measured general health, blood pressure, cholesterol, and mental health. More generous coverage produced little average improvement on those measured outcomes over the study period. The estimates constrain some large average gains, but do not establish that every benefit is exactly zero.
Host
We should also keep the limits visible. Could an average result hide benefits for poorer or sicker patients? What can we safely say about exceptions and other settings?
Economist
An average can hide differing individual effects. The chapter also notes slightly better corrected vision in the free-care group. We should therefore avoid saying that no outcome ever improved. Nor should we extrapolate directly to all uninsured people. RAND excluded some public insurance groups, studied particular families, and gave even controls catastrophic protection. Those features help define its question. They also motivate looking at a different experiment.
Host
The next case is Oregon's Medicaid lottery in 2008. Medicaid is public insurance for eligible people with low incomes. Why did this setting create a credible comparison rather than another ordinary difference between buyers and nonbuyers?
Economist
More people registered than Oregon could cover. A lottery randomly selected people who could apply for expanded coverage. Winning did not guarantee eligibility or completed paperwork. The clean comparison is therefore lottery winners versus lottery losers. The treatment at this stage is the opportunity to apply. It is not simply actual insurance enrollment, and the people who ultimately enrolled were not randomly selected from all winners.
Host
The map's shorthand about a quarter enrolling could confuse that distinction. Was the total enrollment rate among winners actually only 25 percent? Or is that number describing the extra coverage caused by winning?
Economist
It describes the extra coverage, approximately. In the statewide data, about 14 percent of losers had Medicaid during the following year. Winning raised that probability by about 26 percentage points. Thus roughly 40 percent of winners had coverage, rather than only a quarter. Some losers obtained Medicaid through other routes. The key causal change is the difference between those enrollment rates, not the winners' enrollment rate alone.
Host
That distinction also changes how we interpret later outcomes. If we compare winners and losers, what causal effect have we estimated? And why would we resist comparing enrolled winners with people who remained uninsured?
Economist
The winner-loser comparison estimates the intention-to-treat effect, often shortened to ITT. That is the effect of assignment to the opportunity, including people whose coverage did not change. Comparing actual enrollees with nonenrollees reintroduces choices and eligibility differences. To estimate an effect of coverage itself, later methods use the lottery's change in coverage. The adjustment divides the outcome gap by the coverage gap, under additional assumptions.
Host
So this previews instrumental variables. We use an external push toward coverage instead of pretending enrollment itself was random. We will need assumptions that winning affects the outcome through coverage and does not make anyone less likely to enroll.
Economist
Yes, and the resulting effect concerns people whose coverage was changed by that push. It is not automatically the effect for every applicant. We will develop those ideas later. For now, keep assignment and receipt separate. In Oregon, winning increased health service use, including emergency department use. The hope that insurance would simply replace emergency care with cheaper routine care did not describe the observed pattern.
Host
And what happened beyond service use? The point of insurance might include avoiding a frightening bill, even when a blood pressure test changes little. Did Oregon show something that RAND's average physical health results could miss?
Economist
Winners reported some improvement in general health. More detailed interviews suggested improvement in mental health, with little clear measured physical health improvement. Medical debt and the risk of very large medical expenses also fell. Financial protection may help explain the mental health gains, although that mechanism is not separately established by the lottery comparison. These benefits matter even when measured physical outcomes show limited change.
Host
There is a policy lesson here. A program can increase spending and still protect people from financial risk. But we cannot claim it saves emergency care costs when that particular outcome actually increased.
Economist
Right. Policy evaluation needs several outcomes and a clear comparison. RAND primarily varied insurance generosity among people with some protection. Oregon expanded the opportunity to obtain coverage among lower-income applicants. Similar patterns in use and physical health are informative across these settings. They do not make the interventions identical, or make every possible future expansion produce the same results.
Host
Let's finish the investigation with the inference toolkit. We have used standard errors and significance several times. Can you connect those ideas to the appendix without making listeners work through a page of equations?
Economist
Start with the difference between a population and a sample. The population mean is a fixed feature of the population we want to describe. A sample mean changes when different people enter our data. An estimator is a rule for using sample data to estimate a population quantity. An unbiased estimator gets that quantity right on average across repeated samples. It can still miss in a particular sample.
Host
That sounds different from the law of large numbers. Unbiasedness is about the average result of repeating the procedure. The law of large numbers is about getting closer as a sample grows. Neither says an individual estimate is perfect.
Economist
Exactly. Also distinguish standard deviation from standard error. Standard deviation describes variation between people's outcomes. Variance expresses that spread using squared distances from the mean. A standard error describes variation in an estimate across repeated samples. With independent observations, the standard error of a mean falls with the square root of sample size. Dependent observations, including family groups, require an appropriate adjustment.
Host
What makes the familiar large-sample t-statistic useful? Individual medical spending could be very uneven. I do not want to assume every person's outcome follows a neat bell-shaped distribution.
Economist
The central limit theorem concerns the distribution of appropriately standardized averages, not a promise about individual outcomes. With enough independent information and suitable conditions, that distribution becomes approximately bell-shaped. This lets us assess how surprising an estimate would be under a proposed population value. The null hypothesis usually says the treatment effect is zero. The t-statistic compares the estimate's distance from that proposed value with its standard error.
Host
How does a 95 percent confidence interval improve on a simple significant-or-not label? I would like to hear what effects remain compatible with an estimate, rather than only whether a threshold was crossed.
Economist
A large-sample interval extends roughly two standard errors below and above the estimate. A 95 percent confidence procedure covers the true population quantity in about that share of repeated samples. It does not assign a probability to a fixed parameter after we see one interval. The interval helps us assess possible effect sizes. A wide interval containing zero may also contain substantial benefits or harms.
Host
And a narrow interval around zero limits large effects more strongly. But statistical significance still cannot tell us whether an effect is economically or medically important. A precisely measured tiny change may have little practical value.
Economist
Correct. For a difference between independent means, uncertainty comes from both groups. We combine their sampling variances before taking a square root to obtain the standard error. A very small control group can therefore limit precision even with many treated people. We also allow differing outcome variation where appropriate. Sound inference respects the design, the sample, and the question being asked.
Host
To recap the investigation, selection bias explains why the survey comparison is unreliable as a causal answer. Random assignment repairs the assignment mechanism. RAND and Oregon then show how much the treatment definition and the measured outcome matter.
Economist
And statistical uncertainty remains after randomization. We need standard errors and confidence intervals to judge precision. A good causal design answers why the comparison is credible; good inference tells us how much uncertainty remains in its numerical answer.
The Resolution
Host
We have reached The Resolution. Let's play devil's advocate. Someone says, insured people are healthier, so insurance works. Another person says, the experiments found little physical improvement, so insurance is worthless. Which claim survives?
Economist
Neither is justified as stated. The first treats association as causation and ignores selection bias. The second turns particular average outcomes into a judgment about every benefit of insurance. A careful answer asks which people, which coverage, which comparison, which outcomes, and which time period. The experiments provide credible answers within those definitions. They do not remove the need to define what we want to know.
Host
My prediction is that the missing phrase in the second claim is financial protection. Even without a clear measured physical health gain, insurance could reduce debt and anxiety. That would change the policy discussion.
Economist
That is the important correction. Oregon provides evidence of financial protection and improved mental health. Those are outcomes, not excuses for ignoring physical health. At the same time, their value does not prove that every coverage expansion is worth any cost. We must compare the benefits and costs of the particular policy, including who gains and who pays.
Host
A third claim says that no statistically significant effect means no effect. We have already learned to distrust that shortcut. How would you correct it in one careful explanation?
Economist
Ask how wide the confidence interval is and what effects it still allows. A noisy estimate near zero says much less than a tightly estimated one. Even a narrow interval does not prove exact zero for every individual or every outcome. RAND's measured average health changes were small relative to the spending response. That is a useful finding without turning a statistical threshold into a universal claim.
Host
What are our main takeaways? I would begin by asking whether treatment groups would have differed even without treatment. That question seems more valuable than starting with a complicated statistical technique.
Economist
Yes. An observed group difference combines a causal component with a selection component. With differing effects, specify whose average effect you mean. Random assignment makes assignment independent of potential outcomes, in expectation. Check the allocation process and baseline balance, then interpret the observed differences with their uncertainty. A dummy-only regression packages a difference in means; it does not manufacture a credible control group.
Host
And the evidence takeaway is more specific than saying insurance works or fails. RAND reports much greater use under more generous plans, without clear large average improvements in measured health. Its differential attrition limits how confidently we interpret those comparisons. Oregon also shows financial and mental health benefits.
Economist
Keep one further habit: define the control condition out loud. Catastrophic coverage differs from no coverage. A chance to apply differs from receiving coverage. A self-reported health score differs from a clinical measure. Once those distinctions are clear, apparently conflicting findings can become answers to different questions. This helps us compare studies without forcing them into a single oversimplified verdict.
Host
Then the thesis is that random assignment turns a comparison of groups into a causal effect. What qualification should travel with that sentence, so that it stays useful rather than sounding like a guarantee about any experiment?
Economist
Random assignment supports a causal estimate of the assigned intervention when the experiment is properly implemented and outcomes are comparably measured. Finite samples still have uncertainty. Incomplete take-up changes the meaning of the direct comparison to an assignment effect. Results also have a population and a setting. The thesis is powerful because it replaces systematic selection with a known assignment rule, not because it removes every research problem.
Host
Our resolution recap is to keep the causal question and the statistical question separate. First establish why the control group is credible. Then ask which effect was estimated and how precisely it was measured.
Economist
That is the durable lesson. Random assignment makes the comparison informative about causation. Clear definitions, careful measurement, and honest uncertainty make that causal answer useful.
Wrap-up
Host
Let's return to our learning goals. We can explain selection bias with potential outcomes, explain why random assignment helps, and interpret the insurance experiments with uncertainty. What single sentence should we carry into the next topic?
Economist
The thesis to remember is this: random assignment turns a comparison of groups into a causal effect, for the intervention actually assigned. We still check balance, examine selective loss to follow-up, distinguish offers from receipt, and examine confidence intervals. RAND and Oregon teach these habits through concrete policy questions. More use of care is not automatically better physical health, and physical health is not the only outcome that matters.
Host
Here is a final application question. Suppose a new insurance lottery finds that winners use more care than losers. Some winners never enroll, and some losers obtain coverage another way. Is the direct difference the effect of receiving insurance for everyone?
Economist
Pause the episode and think about what the lottery assigned. Identify the treatment group, the comparison group, and the intervention before deciding what the estimated difference means.
Host
My answer is that the direct difference estimates the effect of winning the opportunity. We preserve random assignment by comparing winners and losers. We do not silently replace that comparison with enrollees versus people without coverage.
Economist
Exactly. Estimating a coverage effect requires an additional method and its assumptions. To practice the calculations and balance checks, open the Colab notebook and the lecture slides. Keep the definition of each comparison beside its result. You can then see why the same regression calculation has a descriptive interpretation in the survey and a causal interpretation in a credible experiment.
Host
Next, Chapter 2, Regression, asks whether an elite private college is worth the extra tuition. When random assignment is unavailable, comparing people with similar observed characteristics becomes especially tempting. We will ask what that adjustment can and cannot accomplish. Thanks for listening, and goodbye.