Topic 10: Specification and Data Issues

Question 1

Why would you need a proxy variable?

Answer 1

A proxy variable can be used in place of an unobserved variable, If you think you might have omitted variable bias from leaving out the unobserved variable.

Question 2

What is a proxy variable?

Answer 2

An observed variable that is closely correlated with, but not identical to an unobserved explanatory variable.

Question 3

What is functional form misspecification?

Answer 3

When there is biased caused by omitting variables that are functions of other variables (like excluded x^2).

Question 4

How would you test for functional form misspecification?

Answer 4

By using the Ramsey RESET test.

Question 5

What kind of bias occurs when a model does not properly account for the relationship between the dependent and independent variables because the correct explanatory variable is not observed?

Answer 5

Omitted variable bias.

Question 6

How does Classical measurement error in the dependent error affect the bias and variance of an OLS estimator?

Answer 6

It does not cause bias, but does increase the variance of the OLS estimator.

Question 7

What is classical measurement error?

Answer 7

When the respondent’s answer is erroneous, which causes noise in the regression (e) not providing information about the individual, cov(e,x)=0 and cov(e, u)=0 where x is not observed.

Question 8

What is attenuation bias?

Answer 8

When the bias in an estimator is biased towards zero, thus the expected value is less than the absolute value of the parameter. Occurs from measurement error in the independent variable.

Question 9

What is the form of inconsistency in the OLS estimator under the assumption of classical measurement error in the explanatory variable?

Answer 9

As beta1^ reaches it’s probability limit, it is equal to beta1 times the quantity of 1 minus the fraction of the variation in e divided by the variation in x* plus the variation in e.

Question 10

What are the assumptions needed to have a good proxy variable?

Answer 10

Where x3 is the proxy variable for unobserved x3*:

Cov(x, v) = 0 or very close.
x3 and x3* need to have some correlation, represented by delta1.
Cov (u, x3) = 0 (but not necessary)

Question 11

How do you run a Ramsey RESET test?

Answer 11

Run the necessary regression, then predict the fitted values (predict varname, xb), generate the square and cube of the fitted value, run the original regression included these squared and cubed variables, then joint F test the squared and cubed terms.

Question 12

What is the null hypothesis in the Ramsey RESET test?

Answer 12

The null hypothesis is that the model is correctly specified, or that delta1=0 and delta2=0 (the coefficients on the fitted squared and cubed variables). A small p value is strong evidence to reject the current specification, a large p value fails to reject the specification.

Question 13

When a model does not properly account for the relationship between the dependent and explanatory variables because the correct explanatory variable is not observed, what kind of bias occurs?

Answer 13

Omitted variable bias.

Question 14

Can the Ramsey RESET test be used to test for general omitted variable bias?

Answer 14

No.

Question 15

If the inclusion of one or more proxy variables for an unobserved omitted variable causes the coefficient estimate of the key variable to be lower, what would our conclusion be?

Answer 15

Their inclusion tells us that the return to the true key variable is lower than we would think, because of omitted variable bias.

Question 16

Why might you not want to include certain proxy variables or multiple proxy variables for an unobserved variable?

Answer 16

If they are not good proxies, they could still be causing upward bias, and the introduced multicollinearity could cause more problems with large variances than the omitted variable bias.

Question 17

What is the Davidson-Mackinnon test used for?

Answer 17

Non-nested models that might need a log or level function.

Question 18

What is measurement error?

Answer 18

The difference between the observed value and actual value.

Question 19

What does measurement error in the dependent error cause?

Answer 19

Larger error variances and thus larger variances and standard errors in OLS estimators, but not bias.

Question 20

How do you perform the Davidson-Mackinnon test?

Answer 20

For a level functional form model, estimate the log model, save the fitted values (yhat). Estimate the level model and include the yhat from the log model. A small p value on the yhat is a rejection of level model.

Question 21

How does attenuation bias effect positive and negative estimates?

Answer 21

Positive estimates will be too low and negative estimates will be too high.

Question 22

How does measurement error differently affect the outcome when in the dependent or explanatory variable?

Answer 22

When in the explanatory variable, measurement error causes attenuation bias, when in the dependent variable, it causes larger variances and less precise estimates.