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Flashcards in instrumental variables Deck (15)
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1
Q

Yi-Ybar=

A

(B0+B1Xi+Ui) - (B0+B1Xbar+Ubar)

= B1(Xi-Xbar) + (Ui-Ubar)

2
Q

B1hat

A
  E(Xi-Xbar)
3
Q

B1hat zcm adapted

A

E(B1) + E( (Xi-Xbar)^2(Ui-Ubar)
—————————–
E(Xi-Xbar)^2

4
Q

Three general steps for ZCM assumption

A

Substitute for Y
Rearrange
Take expectations :
Two OLS assumptions - x and u independent, expected value of u = 0

5
Q

How do we get rid of E(
E(Xi-Xbar)^2(Ui-Ubar)
—————————–
E(Xi-Xbar)^2 )

A

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.

6
Q

Other names for omitted variable bias

A

uncontrolled endogeneity
endogeneity
unobserved heterogeneity

7
Q

How to determine whether the estimate is biased or not

A

Take expectations

8
Q

Would the bias disappear to zero if we had a large enough sample? How do we go about it

A

To test it we find the probability limit of the estimate (plim)

9
Q

plim (xu) =

A

plim(x) x plim(u)

10
Q

plim(B1hat) =

A

B1 + Cov(x,u)
———–
Var(x)

or B1 - B1 Var w
—————–
Var z + Var w

11
Q

Measurement error

A

Where our data on an explanatory term has been measured wrong

12
Q

What do we do to solve measurement error

A

Sub in x-w for z value.

13
Q

What does measurement error do to the regression line

A

Bias the coefficient towards zero, therefore flattens out the line.

14
Q

Measurement error in dependent variable equations

A

y = q + r
y = B0 + B1hat + u
where u = v + r

15
Q

What happens with measurement error in dependent variable

A

x is unrelated to v and r, so x is uncorrelated with u.

Standard errors are correct but inefficient. T tests are still valid