Lecture notes 14 Endogeneity Flashcards
What is endogeneity?
When X is correlated with the error term.
Factors impacting both X and Y that are not included in the model.
What are the cases in which endogeneity could arise?
Measurement error
Economic Theory
Omitted variable bias.
What is the implication of endogeneity?
It causes the OLS estimates to be biased.
How does omitted variable bias cause endogeneity?
Two cases:
Misspecification
No observing important variable.
Eg
Y = B0 + B1X + B2X^2 epsilon
but we run Y = B0 + B1X + epsilon
the error term has the B2X^2 included in it which is correlated with the B1X1
So the expectation of epsilon given x is not zero.
How does not including important variables?
if a variable that is important to explain the regression is not included then it goes into the error term and causes bias.
How does measurement error cause endogeneity?
As in the survey u = X* -X
when we try and observe true X there is mismeasurement that when expanded biases as the error term has this extra part
and E(X | epsion) is not equaled to 0
How can economic theory cause endogeneity and what is an example of this?
What is a second example
-Cobb douglas F(K,L) are correlated with epsilon as firms with high A will have more K,L
Assume a demand function with price as a regressor
When demand goes up epsilon goes up which also causes price to go up.
What is endogeneity via simultaneity
When variables have a two way relationhsip at the same time .
How can one solve endogeneity?
Instrumental variable
What is an instrumental variable usually denoted by?
z
What are the two conditions:
Instrument relevance Z and X are correlated
Instrument exogeneity
Z and epsilon are not correlated.
What is an example of an Instrumental variable
How many instrumental variables do you need for endogenous variables?
At least as many IVS as endogenous variables.
What happens to the use of IV if the instrumental relevance is very weak?
What is the issue if the instrument exogeneity condition does not hold?
-It means the IV estimator is very imprecise.
-It means that the IV estimator is biased.
How do you do an IV regression and why is this?
Once you have found instrument that is relevant and exogenous:
Regress X = gamma 0 + gamma 1 Z
Then save X hat from this regression (the part of X that is not correlated with epsilon). As the instrument is not correlated with epsilon.
Y = beta0 +beta1 Xtilda
Thus we regress Y on X tilda to get beta0 and Beta 1 and these are called the IV estimators.
What is IV estimator also called?
Two stage least squares estimator.H
