Endogeneity and the IV estimator Flashcards
Sources of Endogeneity(4)
- unobservable omitted variables
- reverse causation
- simultaneous equations
- measurement error bias
Fundamental assumption of least-squares estimators(1)
The model error is unrelated to the regressors
What is the problem with endogeneity?
All estimates of βj become inconsistent
What is the endogenous model?
y=β_0+x_1 β_1+x_2 β_2+…+x_K β_K+u_i
Property of instrument z
Changes in z affect x but not y (although indirectly through x)
What are the conditions to observe a variable, zt, to generate an exogenous form of xt?
When is the Instrumental Variables estimator consistent?
When z is correlated with x and uncorrelated with the error term
Are IV estimators more efficient and consistent than OLS?
They are usually more consistent, but less efficient - especially if instruments are weakly correlated with the variable being instrumented
This will be reflected in increasing standard errors
What is the order condition for IV estimator?
r >= K
where:
r is a number of instruments
K is the number of independent endogenous components
Properties of the Pooled Model
y_it=β_0+x′_it β+u_it “ i”=”1,…,N, t”=”1,…,T.”
Coefficients are Constant
Pooled OLS is consistent when cov[u,x]=0
Panel-corrected standard errors and t-statistics must be used
Pooled OLS is inconsistent if the FE model is appropriate
Fixed Effects Methods
Measures association between individual-specific deviations of regressors from their time-averaged values and individual-specific deviations of the dependent variable from its time-averaged value
What is the variance of the IV estimator equal to? (in terms of OLS estimator variance)
It is equal to the variance of the OLS estimator over the sample correlation coefficient between x and z
What does the 2 stage least squares (2SLS) estimator do?
Takes all of the possible linear instruments for the variable xK and chooses the instruments that is most highly correlated with xK given by the linear projection:
