econometrics

A statistical analysis is internally valid​ if

the statistical inferences about causal effects are valid for the population studied

Threats to internal validity lead​ to:

failures of one or more of the least squares assumptions.

Comparing the California test scores to test scores in Massachusetts is appropriate for external validity​ if

the institutional settings in California and​ Massachusetts, such as organization in classroom instruction and​ curriculum, were similar in the two states.

The question of​ reliability/unreliability of a multiple regression depends​ on:

internal and external validity.

Internal validity is​ that:

the estimator of the causal effect should be unbiased and consistent.

The true causal effect might not be the same in the population studied and the population of interest​ because

of differences in characteristics of the population.

of geographical differences.

the study is out of date.

What is the​ trade-off when including an extra variable in a​ regression?

An extra variable could control for omitted variable​ bias, but it also increases the variance of other estimated coefficients.

Suppose that a state offered voluntary standardized tests to all its third graders and that these data were used in a study of class size on student performance. Which of the following would generate selection​ bias?

Schools with​ higher-achieving students could be more likely to volunteer to take the test.

A researcher estimates the effect on crime rates of spending on police by using​ city-level data. Which of the following represents simultaneous​ causality?

Cities with high crime rates may need a larger police​ force, and thus more spending. More police​ spending, in​ turn, reduces crime.

A researcher estimates a regression using two different software packages. The first uses the​ homoskedasticity-only formula for standard errors. The second uses the​ heteroskedasticity-robust formula. The standard errors are very different. Which should the researcher​ use?

The ​heteroskedasticity-robust standard errors should be used

Labor economists studying the determinants of​ women's earnings discovered a puzzling empirical result. Using randomly selected employed​ women, they regressed earnings on the​ women's number of children and a set of control variables​ (age, education,​ occupation, and so​ forth). They found that women with more children had higher​ wages, controlling for these other factors. What is most likely causing this​ result?

Sample selection bias

A survey of earnings contains an unusually high fraction of individuals who state their weekly earnings in​ 100s, such as​ 300, 400,​ 500, etc.

This is an example​ of:

errors-in-variables bias.

In the case of​ errors-in-variables bias

the OLS estimator is consistent if the variance in the unobservable variable is relatively large compared to the variance in the measurement error.

In the case of​ errors-in-variables bias, the precise size and direction of the bias depend​ on

the correlation between the measured variable and the measurement error.

Suppose that the linear probability model yields a predicted value of Y that is equal to 1.3. Explain why this is nonsensical.

The predicted value of Y must be between 0 and 1.

One of your friends is using data on individuals to study the determinants of smoking at your university. She is particularly concerned with estimating marginal effects on the probability of smoking at the extremes. She asks you whether she should use a​ probit, logit, or linear probability model. What advice do you give​ her?

She should use the logit or​ probit, but not the linear probability model.

The linear probability model​ is:

the application of the linear multiple regression model to a binary dependent variable.

F​-statistics computed using maximum likelihood​ estimators

can be used to test joint hypotheses

The probit​ model

forces the predicted values to lie between 0 and 1.

In the probit​ regression, the coefficient beta 1 ​indicates:

the change in the the z​-value associated with a unit change in X.

Probit coefficients are typically estimated​ using:

the method of maximum likelihood

Why are the coefficients of probit and logit models estimated by maximum likelihood instead of​ OLS?

OLS cannot be used because the regression function is not a linear function of the regression coefficients.

To measure the fit of the probit​ model, you​ should:

use the​ "fraction correctly​ predicted" or the​ "pseudo R squared​."

Nonlinear least​ squares

solves the minimization of the sum of squared predictive mistakes through sophisticated mathematical so ​ routines, essentially by​ trial-and-error methods.

When testing joint​ hypotheses, you can​ use

either the F​-statistic or the​ chi-squared statistic.