PP3: Endogeneity and Instrumental Variables Flashcards
Define exogenous variables
relating to or developing from external factors
Define endogenous variables
A variable that’s changed by its relationship with other variables int the model
What can cause endogeneity?
1) Omitted variable bias
2) Simultaneity (reverse causality)
3) Measurement error
How does a measurement error affect the dependent variable? Indepedent variables?
If in the dependent varaible, typically does not lead to bias unless error is correlated with any of the explanatory variables
If in an explanatory variable, if its random, then its attenuation bias. If its correlated with unobservables, then bias is hard to characterize
Define attenuation bias
bias that’s caused by measurement error or noise in your independent variables
What two conditions do instrumental variables need to satsify?
1) it is uncorrelated with u (exclusion restriction)
2) it is uncorrelated with other x’s (inclusion restriction)
What are the steps to Two-Stage Least Squares?
1) regression the endogenous variable on all exogenous variables to get fitted values
2) Use fitted values instead of original endogenous variable in the OLS equation
T/F: R^2 is not useful in IV estimation.
True: it has no natural interpretation and can be negative!
Define consistency for econometrics.
As a sample size becomes very large, B approaches the true B with a very high probability
What are the two theorums of the statistical properies of 2SLS?
1) If 2SLS 1-4 hold, estimator is consistent (MLR 1-4)
2) If 2SLS 1-5 hold, then its efficient in large samples (MLR 1-5)
What happens when we have a weak instrument?
1) Variances can be very large
2) 2SLS esimator can have a large asymptotic bais even if z and u are only moderately correlated
They have F-stats < 10 as well
What is simultaneity bias?
When the y variable affects the x variable and the x variable affects the y variable at the same time.
aka x and y influence each other simultaneously
Given the following output, detemine if there is a strong…
F(2,847) = 23.32
Prob > F = 0.000
first stage correlation between instruments and the endogenous variable
Reject the null, and we have strong inclusion restriction
Given the following output, determine if the regression has endogeneity
var | coef. | p > t
educ | 0.1425 | 0.000
tenure | 0.0106 | 0.000
vhat | -0.0712 | 0.019
vhat indicates there is endogenoueity.
Specifically for educ variable (see slide 38)
