QE 5: Endogeneity Flashcards
What is the omitted variable bias formula? Why is it useful?
c1 = b1 + b2p1. If we think we might have omitted a variable that is positively correlated with X1 and Y, c1 is likely to be an overestimate of b1.
Why does measurement error in the outcome variable not cause problems for causal analysis?
X1 remains orthogonal to u.
Why does (classical) measurement error in explanatory variables lead to attenuation bias?
X1 is no longer orthogonal to u - our estimate will be attenuated towards zero.
What is a valid proxy variable? Why might we include one?
We might want to control for some characteristic that is hard to measure, such as parental wealth. Free school meals is often used as a proxy for this. The part of X2 unexplained by W1 must not be correlated with X1.
What is simultaneous determination? Why does it cause problems for causal analysis?
Some economic variables are ‘jointly’ determined, such as demand and supply. The quantity of a good that is sold is affected by lots of things, including its price. However, price is also affected by lots of things, including the quantity available. Therefore, it is impossible for exogeneity to hold.
What is a randomised controlled trial? How does it solve the endogeneity problem?
An RCT randomly assigns treatment status, such that the treatment is not correlated with the error term by construction.
Why might we still include control variables in a RCT?
We can reduce the standard errors and gain more precise estimates of causal effects. We do this by making the model fit better, which reduces var(u).
Can we test whether random assignment was plausible?
Yes. We can test for balancedness, either by testing for differences in means between treated and untreated groups, or by regressing the treatment dummy on other characteristics, and F-testing that the other characteristics can’t predict class size.
Can we estimate different treatment effects for different sub-populations in an RCT?
Yes, by including interaction terms.
What is conditional random assignment?
Some treatments are randomly assigned conditional on some other variable. If there is evidence of this, controlling for this other variable will eliminate endogeneity.
What is a ‘bad’ control?
If we control for characteristics that are post-treatment (eg mid-year test scores), we reintroduce some endogeneity and fail to consistently estimate the true causal effect. All characteristics we control for must in principle be able to be observed pre-treatment.
What is the difference between the ATE and the TOT?
The ATE is the estimated average effect across the whole population. The TOT is the average effect across those who choose to be treated. These may be very different.
What is a natural experiment?
In a natural experiment, nature ‘partly replicates’ an RCT, creating circumstances such that X is ‘as if’ randomly assigned. Common cases include natural phenomena, policy/legislative cutoffs, etc. We can analyse them (and test their validity) like RCTs.
What is internal validity? What are the main threats to it?
A study is internally valid if it makes credible inferences for the population it studies. The main threats to it are:
- Endogeneity. Have we included/proxied for the major determinants of Y? Have we included potential nonlinearities? Does OR hold?
- Was treatment randomly assigned?
- Was compliance perfect?
- Were there attrition problems?
- Were there Hawthorne or placebo effects?
What is external validity?
A study is externally valid if its inferences can be generalised to other populations.
- Is this population different to the sample population in a way that matters for the determination of outcomes?
- Are there general equilibrium effects that are not captured in a small study?
