instrumental variables Flashcards
Yi-Ybar=
(B0+B1Xi+Ui) - (B0+B1Xbar+Ubar)
= B1(Xi-Xbar) + (Ui-Ubar)
B1hat
E(Xi-Xbar)
B1hat zcm adapted
E(B1) + E( (Xi-Xbar)^2(Ui-Ubar)
—————————–
E(Xi-Xbar)^2
Three general steps for ZCM assumption
Substitute for Y
Rearrange
Take expectations :
Two OLS assumptions - x and u independent, expected value of u = 0
How do we get rid of E(
E(Xi-Xbar)^2(Ui-Ubar)
—————————–
E(Xi-Xbar)^2 )
Assumptions - x and u are independent from each other. Therefore you can split up the equation to be left with only the variation in u over x.
Then the expected value of u is zero, therefore all of that goes away.
Other names for omitted variable bias
uncontrolled endogeneity
endogeneity
unobserved heterogeneity
How to determine whether the estimate is biased or not
Take expectations
Would the bias disappear to zero if we had a large enough sample? How do we go about it
To test it we find the probability limit of the estimate (plim)
plim (xu) =
plim(x) x plim(u)
plim(B1hat) =
B1 + Cov(x,u)
———–
Var(x)
or B1 - B1 Var w
—————–
Var z + Var w
Measurement error
Where our data on an explanatory term has been measured wrong
What do we do to solve measurement error
Sub in x-w for z value.
What does measurement error do to the regression line
Bias the coefficient towards zero, therefore flattens out the line.
Measurement error in dependent variable equations
y = q + r
y = B0 + B1hat + u
where u = v + r
What happens with measurement error in dependent variable
x is unrelated to v and r, so x is uncorrelated with u.
Standard errors are correct but inefficient. T tests are still valid
