By Randall Munroe, xkcd.com Econometrics: The Search for Causal Relationships

Parents should consider limiting their teen's exposure to sexual content on TV, said the study's lead author, Anita Chandra, a behavioral scientist at RAND, a nonprofit research organization. Television producers should consider more realistic depictions of the consequences of sex in their scripts... Sexual Content on TV is linked to teen pregnancy LA Times, 11/3/08 Teenagers who watch a lot of television programs that contain sexual content are more than twice as likely to be involved in a pregnancy, according to a study published today in the journal Pediatrics. study published today in the journal Pediatrics The teens who watched the most sexual content on TV (the 90th percentile) were twice as likely to have become pregnant or caused a pregnancy compared to the teens who watched the least amount of sexual content on TV (the 10th percentile).

Lasting Effects Found From Spanking Children: Antisocial Behavior Is Increased, Study Says Washington Post, August 15, 1997, page A3 Spanking children is apt to cause more long-term behavioral problems than most parents who use that approach to discipline may realize, a new study reports. Children who get spanked regularly are more likely over time to cheat or lie, to be disobedient at school and to bully others, and have less remorse for what they do wrong, according to the study by researchers at the University of New Hampshire. It is being published this month in the medical journal Archives of Pediatrics and Adolescent Medicine. "When parents use corporal punishment to reduce antisocial behavior, the long- term effect tends to be the opposite," the study concludes.

How can we identify causal effects? Angrist & Pischke’s 5 tools Ideal case: randomized trial Easiest (but least persuasive?): regression Natural experiments: Instrumental variables Regression discontinuity Differences-in-differences

1. Randomized, Controlled Trials (RCTs) Good benchmark Increasingly popular in economics, especially development (“randomistas”) and behavioral.

Question to always ask: What is the point of this table?

Treatment and Control Groups Treatment group receives the intervention you want to study (Ex: health insurance, new drug, bed nets) Control group should be statistically identical to treatment group except they don’t get treated Study participants are randomly assigned to the groups.

The Math Where n ≡ number in group Y i ≡ outcome for person i (health) D i ≡ treatment status for i (=1 if insurance, 0 otherwise) Y 1i ≡ i‘s outcome if treated Y 0i ≡ i‘s outcome if not treated (can only observe one of these)

The Math What we want to know is Avg n [Y 1i – Y 0i ]. Suppose health insurance improves everyone’s health by k. Then equation 1.2 becomes: The true causal effect The “selection” effect—the difference in health between the insured & uninsured groups if nobody had insurance.

The Math Table 1.1 suggests that the selection effect in this case would probably be positive. So selection would cause us to overstate the effect of having insurance. Note: Law of large numbers implies that Avg n [Y i ] = E[Y i ] as n goes to infiniti.

The Math What does random assignment do for us? Sets E[Y 0i │D i =1] = E[Y 0i │D i =0] (fix notes!) So, no selection effect, and the differences in groups is the pure causal effect we want (if groups are large enough).

Question to always ask: What is the point of this table?

A well-constructed randomized trial can identify causal effects very well. So why don’t we always use this method? Expensive Time consuming (and outcome may not be realized for years) Ethical concerns Logistically difficult External validity

2. Regression Analysis Relationship between college rank and earnings:

2. Regression Analysis Want to draw a line through those points that describes the relationship. y i = α + βx i + e i wage i = α + βrank i + e i Parameters without hats are the true population values. With hats are sample estimates. α is the intercept (wage if rank = 0) β is the slope—how much wage increases with a one- unit increase in rank.

2. Regression Analysis e i is the error term, or how individual i’s wage is different from what we would predict for them based on the values of α and β and their college rank.

2. Regression Analysis We use statistical software packages to estimate α and β, like Stata, R, or SAS. With Ordinary Least Squares Regression (OLS), the software chooses α and β to minimize the sum of the (squared) e i ’s.

2. Regression Analysis How are kids who go to more highly ranked schools different from those who don’t? Ex: Family income (FI), gender, intelligence When we have something in the error term (like FI) that is correlated with x, our estimates of β are biased. This means that E[β-hat] ≠ β. We can’t expect to get the right answer.

2. Regression Analysis Compare the regression model with and without FI: wage i = α + β 1 rank i + β 2 F i + e i wage i = α + β 1 rank i + e i

Econ Prof. Buckles21 Summary of Direction of Bias Corr(x 1, x 2 ) > 0Corr(x 1, x 2 ) < 0  2 > 0 Positive biasNegative bias  2 < 0 Negative biasPositive bias

2. Regression Analysis Compare the regression model with and without FI: wage i = α + β 1 rank i + β 2 F i + e i wage i = α + β 1 rank i + e i Since corr(FI, rank) > 0, β 2 > 0, expect positive bias in our estimate of β 1. Ex. 2: Family size. Ex. 3: Gender

2. Regression Analysis Solution: Include the omitted variable in the model. This gives us the “ceteris paribus” interpretation we’re after. We “hold constant” family income. Then β 1 gives us the effect of rank for people with the same family income.

2. Regression Analysis What this looks like:

Question to always ask: What is the point of this table?