Topic 11: Instrumental Variables Estimation

Question 1

What makes an explanatory variable endogenous?

Answer 1

When it is correlated with the error term.

Question 2

Suppose you have an endogenous explanatory variable with beta1, how would you obtain a consistent estimate of beta1?

Answer 2

By using an instrumental variable in place of the endogenous variable.

Question 3

What is an instrumental variable?

Answer 3

A variable correlated with an endogenous explanatory variable, exogenous in that it is not correlated with the error term and does not directly affect the dependent variable. IV is used when x and u might be correlated, so MLR4 doesn’t hold.

Question 4

Do x and u need to be uncorrelated in order to use z as a valid instrument for x?

Answer 4

No.

Question 5

Do z and u need to be uncorrelated to use z as a valid instrument for x?

Answer 5

Yes.

Question 6

Do z and x need to be uncorrelated to use z as a valid instrument for x?

Answer 6

No, z needs to be related to x

Question 7

If z is correlated with y, can it be a valid instrument?

Answer 7

Yes, as long as it’s not directly correlated.

Question 8

What is the instrumental variable estimator for beta1 where z is an instrument for x?

Answer 8

beta^1IV = [sum(zi-zbar)yi] / [sum(zi-zbar)(xi-xbar)

Question 9

How do you interpret a binary explanatory variable?

Answer 9

It is the effect of that variable =1 compared to when it =0 on the y variable.

Question 10

Stata: How do you find the number of observations in a dataset?

Answer 10

The command “sum” will give you the number of observations for each variable.

Question 11

When are percent’s to be used in the interpretation of estimators?

Answer 11

When the units of the variable are in percent or there is a log functional form.

Question 12

If x is an endogenous variable, what does it mean about the relationship between x and u?

Answer 12

X and u are correlated.

Question 13

How are proxy and instrumental variables different in their relationships to x?

Answer 13

A proxy variable uses a direct relationship between z and x, whereas an instrumental variable looks at the indirect relationship between z and x.

Question 14

Stata: what command should you use to determine how many observations there are for varying values of a binary variable?

Answer 14

Use the command “sum if ==0” to know how many observations there are for that variable. If you need multiple parameters, use “&” between them.

Question 15

How are OLS and IV estimates of a coefficient different?

Answer 15

The OLS estimates of a model that requires an IV estimate will be biased, but precise, while the IV estimate will be consistent, but the standard errors incorrect. This is because the IV estimates variance is based only on the variation in the IV.

Question 16

What is the elasticity of demand?

Answer 16

The % change in Quantity demanded over % change in Price.

Question 17

What is the elasticity of supply?

Answer 17

The % change in Quantity supplied over the % change in Price.

Question 18

What was Phillip Wright trying to figure out?

Answer 18

He had an elasticity, but wasn’t sure if it was supply or demand elasticity, so he needed a factor that affected only supply and not demand, and price needs to affect demand, but be uncorrelated with other demand-affecting factors. He needed an instrument variable.

Question 19

How would you set up the instrument diagram for Wright’s problem?

Answer 19

Z (rain) has no effect on Quantity demanded, but is related to Price by theta. Price affects Quantity demanded, by beta.

Question 20

When is a IV estimator consistent?

Answer 20

When it is a valid instrument, such that Cov(z, u) = 0, making any additional bias added to beta1 0.

Question 21

What is the variance of the IV estimator?

Answer 21

Var(beta1^IV) = Sigma^2 / [n * sigma^2 * rhoxz^2

Question 22

How is the IV variance related to the OLS estimator?

Answer 22

The IV variance is larger than the OLS estimator

Question 23

Why would we want to use an IV estimator?

Answer 23

A valid IV estimator provides a consistent estimate without MLR4. So you have to balance the bias from an omitted variable with OLS versus the larger variance of an IV estimator (which increases as correlation between x and z lessens).