L21 - Two Stage Least Squares Flashcards

1
Q

Under two-stage least squares, what happens when we have more instruments than we need?

A
  • Any linear combination of Z1 and Z2 will also be a valid instrument –> there are an infinite number of weighted averages of the two instruments
  • This suggests a strategy – instead of choosing one instrument or the other – form a linear combination which minimises the variance of the estimator.
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2
Q

How do you define the Two-Stage Least Squares Estimator?

A
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3
Q

What will be the properties of the two-stage least squares estimator?

A
  • The more instruments we use the better fit we get in the first stage regression, and due to the increase in the number of parameters, R2 will also increase –> more efficient
  • The standard Instrument Variable estimator is a TSLS estimator with only one variable.
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4
Q

What happens to R2 when using two-stage least squares?

A
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5
Q

What is the equation for TSS for the two-stage least squares estimator and why is it difficult to interpret R2?

A
  • Unlike under OLS, there is no guarantee that Σ(Xt - X(bar))ut(hat) will be equal to zero and the term will drop out
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