OLS, Random Assignment and Selection Bias Flashcards
How to interpret B0 in basic OLS (1 regressor)
The expected number of (outcome) produced/whatever with regressor = 0
How to interpret B1 in basic OLS (1 regressor)
The change in outcome associated with the regressor increasing by 1 on average
How to interpret Ui in basic OLS (1 regressor)
The effect of all factors other than regressors on the outcome
How to interpret B0 in multivariate OLS
Expected outcome if both regressors = 0
How to interpret B1 in multivariate OLS
the change in outcome associated with that regressor increasing by 1 on average, golding fixed other regressors
How to check if random assignment is successful (dont explain why important and how it works in this one, just how to check)
Calculate sample averages of observable variables for treated and control groups.
If sample averages of observable variables are similar, then it is justified that unobservable characteristics are also similar.
This can be tested using a t-test, where the null hypothesis is that the difference in means = 0.
Compare the t-stat to the critical value, reject if absolute value is greater.
If you fail to reject, then random assignment was successfu
Why is random assignment and thus no selection bias important
The difference in means of the outcomes can be decomposed into an ATT and selection bias.
We cannot observe E[Y0i|Di=1] (in the ATT).
If random assignment is true and there is no selection bias, then this unobserved term is the same as the average outcome of the control group
E[Y0i|Di=1] = E[Y0i|Di=0]
Therefore the difference in outcomes is the causal effect of treatment
How is the Law of Large Numbers important
As sample size increases, the sample average converges to the population mean
Thus, sample averages of potential outcomes in the absence of treatment are very similar to the population means which are equal, so they will have a difference of nearly 0
Therefore, there is no selection bias
