Regression

Question 1

What is the equation for a linear regression?

Answer 1

Yi= a + BDi +Ei

Question 2

what are the two potential outcomes?

Answer 2

Y1i= a+b+ei

and

Y0i= a+ei

the beta here is the parameter of interest and is the causal effect of X on Y

Question 3

What is the conditional independence assumption?

Answer 3

Conditional on observable characteristics X, potential outcomes are independent of treatment status D

idea that is a core set of variables are satisfied and are similar in the two groups, the two outcomes are independent on treatment d

make the assumption that based on X we can assume that the error term is 0 - we are more comfortable in identifying the beta and saying it is causal

Question 4

What are the four key questions for non-experimental casual inference?

Answer 4

1. Is beta identified?
2. what assumption on (X, ei) allow for causal inference and are those assumptions credible?i.e. nothing in the error term will effect your outcome conditional on X
3. economic, scientific and institutional knowledge inform this credibility?
4. Turns on comparability of treatment and control groups- how balanced X are between treatment and control groups? If they are similar in the observables it is plausible that they would be similar in the unonservables

Question 5

What proves causation?

Answer 5

• most suggestive is randomised controlled experiment
• regression with a clever controlled strategy can be suggestive but less so than an experiment

Question 6

What are the implications of being too controlling?

Answer 6

more controls are not always better to identify a causal effect

adding regression controls can possibly increase bias - for example when I si also an outcome of D - bad control

Question 7

How do you deal with having many controls

Answer 7

report regression with and without controls and discuss the limitations of the analysis

alternative research with better models eg. instrumental variables may be required?

Question 8

If CIA holds what is the imapct on the error term

Answer 8

If CIA holds, condition on X, treatment D is uncorleated with the error term and it is as good as randomly assigned
beta is causal

Question 9

what is the biggest challenge associated with the regression?

Answer 9

the CIA assumption is the strongest assumption acorss all methods
challenge when there are unobservables in the error term - eg. measuring individual ambition

we can never get rid of the error term you can only ever minimise it