Question 1

If N is the number of individuals observed in each of T time periods,what is generally true of a "long,narrow" panel? A)T > N B)N > T C)N = T D)N^1/2< T²

Accepted Answer

A "long, narrow" panel refers to a panel dataset where the number of time periods (T) is greater than the number of individuals/units (N). This type of panel is commonly used in longitudinal studies where the focus is on changes over time within a smaller group of individuals or units.

Question 2

In which model are coefficient estimates determined by variation within individuals rather than variation across individuals?
A)pooled model
B)fixed effects
C)random effects
D)none of these

Accepted Answer

Coefficient estimates in fixed effects models are determined by variation within individuals rather than variation across individuals. In contrast, the pooled model combines variation across individuals and within individuals, while random effects models allow for both within-individual and between-individual variation but assume that the between-individual variation is random. Therefore, the correct answer is B (fixed effects).

Question 3

Which type of model does not have a coefficient that varies with t or i ?
A)a pooled model
B)fixed effects
C)random effects
D)none of these

Accepted Answer

In a pooled model, there is only one set of coefficients that apply to all individuals or units in the data. The coefficients do not vary with time or other individual-specific characteristics. Both fixed effects and random effects models allow for individual-specific coefficients that can vary with time or other individual-specific characteristics.

Question 4

If you perform a Hausman test on a random effects model and have a test statistic that exceeds your critical value,which of the following is not correct?
A)at least one of the regressors in the RE model is endogenous
B)none of the common coefficient estimates in the RE model will be significantly different in the FE model
C)FE may be the preferred estimation technique
D)this model may be better estimated using the Hausman-Taylor estimator

Accepted Answer

The answer of If you perform a Hausman test on...

Question 5

What is the primary advantage of using panel data rather than a large cross- section data set collected over time?
A)it allow you to control for individual heterogeneity
B)it allows the effects of legislation to be estimated
C)it gives you more degrees of freedom
D)it allow coefficients to vary over time

Accepted Answer

Panel data allows for the control of individual heterogeneity by observing the same individuals over time, whereas a large cross-section data set only captures individuals at a single point in time and does not allow for individual-specific controls. Therefore, the primary advantage of using panel data is to control for individual heterogeneity.

Question 6

Which of these assumptions indicates homoskedasticity? A)E(e_it)= 0 B)var(e_it)= E(e²_it)= $\sigma$ ² C)cov(e_it,e_js)= E(e_it,e_js)= 0 for i j or t s D)cov(e_it,x_2it)= 0,cov(e_it,x_3it)

Accepted Answer

Homoskedasticity refers to the assumption that the variance of the error terms in a regression model is constant across all levels of the independent variable. Choice B, despite its complex notation, is the only one that directly addresses the variance of error terms being constant, which is the definition of homoskedasticity.

Question 7

Which model is also called an error components model?
A)pooled model
B)fixed effects
C)random effects
D)none of these

Accepted Answer

The random effects model is also known as the error components model because it assumes that the error term in the model is composed of two components: the random effects component and the residual error component.

Question 8

Which type of model has coefficients that vary with i and t?
A)pooled model
B)fixed effects
C)random effects
D)none of these

Accepted Answer

The answer of Which type of model has coefficients that...

Question 9

Which of these assumptions means all error terms are uncorrelated? A)E(e_it)= 0 B)var(e_it)= E(e²_it)= $\sigma$ ² C)cov(e_it,e_js)= E(e_it,e_js)= 0 for i j or t s D)cov(e_it,x_2it)= 0,cov(e_it,x_3it)

Accepted Answer

Option C specifies that the covariance between the error terms is zero, which implies that all error terms are uncorrelated. A and B do not specify the same, while D is talking about the covariance between the error terms and the covariates, not among the error terms themselves.

Question 10

Which of the following assumptions must be made in order to use the pooled least squares estimator,but is relaxed in the cluster robust model? A)E(e_it)= 0 B)var(e_it)= E(e²_it)= $\sigma$ ² C)cov(e_it,e_js)= E(e_it,e_js)= 0 for i j or t s D)cov(e_it,x_2it)= 0,cov(e_it,x_3it)

Accepted Answer

The assumption that cov(e_it,e_js)=0 for i,j or t,s must be made in order to use the pooled least squares estimator. However, this assumption is relaxed in the cluster robust model, which allows for within-cluster correlation between errors.

Question 11

Which of the following is not a reason random effects (RE)results may be preferred to fixed effects (FE)?
A)RE accounts for the random sampling process that generated the data
B)RE is a GLS estimator so in large samples it has a smaller variance than FE which is a least squares estimator
C)RE produces a coefficient for race,gender,or other individual characteristics that are constant over time
D)RE estimates are more robust in the case of endogenous regressors

Accepted Answer

Random effects estimates are not more robust in the case of endogenous regressors; in fact, they can be biased if there is endogeneity.

Question 12

Which of the following is not an estimation technique utilizing panel data?
A)a pooled model
B)fixed effects
C)random effects
D)probit

Accepted Answer

Probit is not an estimation technique utilizing panel data. It is a type of regression model used for binary dependent variables. A pooled model, fixed effects, and random effects are all commonly used estimation techniques for panel data.

Question 13

When should the Hausman-Taylor estimator be used?
A)when a RE model has some endogenous regressors
B)when FE is statistically insignificant
C)when you do not have any information as to which regressors are endogenous
D)when you want to estimate RE on a long,narrow data set

Accepted Answer

The Hausman-Taylor estimator should be used when a random effects model has some endogenous regressors. This estimator is specifically designed to address endogeneity issues in panel data models with random effects.

Question 14

If N is the number of individuals observed in each of T time periods,what is generally true of a "short,wide" panel? A)T > N B)N > T C)N = T D)N^1/2< T²

Accepted Answer

A "short, wide" panel refers to a dataset where the number of individuals observed (N) is greater than the number of time periods (T). This means that each individual is observed in multiple time periods, but not necessarily consecutively. This type of panel is characterized by having a large cross-sectional dimension (i.e. many individuals) and a small time dimension (i.e. few time periods).

Question 15

Which type of model has coefficients that vary with i,but are constant with t?
A)pooled model
B)fixed effects
C)random effects
D)none of these

Accepted Answer

In fixed effects model, the coefficients vary across individuals (i) but are constant across time (t). This means that the model controls for individual-level heterogeneity and focuses on within-individual variation over time. Pooled model assumes that all individuals have the same coefficients, while random effects model allows the coefficients to vary randomly across individuals and time. However, fixed effects model is preferred when individual-level heterogeneity is a concern and when we want to estimate the effect of a variable on the outcome within individuals over time.

Question 16

For a random effects model the least squares estimator is unbiased and consistent.The errors can be corrected for potential heterogeneity using _________________,but the estimator with minimum variance is _______________.
A)cluster-robust standard errors,GLS
B)White's correction,ML
C)2SLS,fixed effects
D)cluster-robust standard errors,pooled

Accepted Answer

Cluster-robust standard errors can correct for potential heterogeneity, and the estimator with minimum variance in the context of a random effects model is Generalized Least Squares (GLS).

Question 17

Which of these assumptions means the errors are uncorrelated with all x's? A)E(e_it)= 0 B)var(e_it)= E(e²_it)= $\sigma$ ² C)cov(e_it,e_js)= E(e_it,e_js)= 0 for i j or t s D)cov(e_it,x_2it)= 0,cov(e_it,x_3it)

Accepted Answer

The correct assumption that means the errors are uncorrelated with all x's is that the covariance between the errors and each independent variable (x) is zero. This is directly stated in option D, where the covariance between the error term and different x variables is equal to zero, indicating that the errors are uncorrelated with the independent variables.

Question 18

How do you test for endogenous regressors,or correlation between the error term and any regressor in a random effects model?
A)estimate coefficients with RE and FE,then perform a Hausman test of equality
B)estimate the model capturing estimated residuals,then regress residuals on all regressors and perform an F-test
C)estimate RE model capturing estimated residuals,then estimate coefficients of correlation with each regressor
D)estimate RE and FE models and perform an F test on each model individually.If the difference between the F statistics is significant,conclude endogeneity.

Accepted Answer

The Hausman test is used to test for the presence of endogenous regressors in panel data models by comparing the coefficients of the Random Effects (RE) model and the Fixed Effects (FE) model. If the difference in coefficients is statistically significant, it suggests that the regressors are correlated with the error term, indicating endogeneity.

Question 19

If you perform a Hausman test on a random effects model and have a test statistic that exceeds your critical value,what should you conclude?
A)all of the regressors in the RE model are exogenous
B)none of the common RE and FE coefficients are significantly different
C)at least one of the coefficients is significantly different from zero
D)at least one of the regressors in the RE model is endogenous

Accepted Answer

If the Hausman test statistic exceeds the critical value, it means that the null hypothesis (random effects are consistent) is rejected in favor of the alternative hypothesis (the random effects model is inconsistent and the fixed effects model should be used instead). This suggests that at least one of the regressors in the random effects model is endogenous, meaning it is correlated with the error term. Therefore, we should conclude that choice D is the correct answer.

Question 20

What is the difference between balanced and unbalanced panels?
A)unbalanced panels have some observations missing,balanced do not
B)balanced panels are demographically representative of the population being studied,unbalanced are not
C)balanced panels have an equal number of observations above and below the mean of the dependent variable,unbalanced panels are skewed
D)a balanced panel has T = N,an unbalanced panel has N>T or N<T

Accepted Answer

Balanced panels have all individuals (or entities) observed at each time period, meaning no observations are missing. Unbalanced panels, on the other hand, have some observations missing for certain individuals (or entities) at some time periods.

Quiz 16: Panel Data Models

If N is the number of individuals observed in each of T time periods,what is generally true of a "long,narrow" panel?

In which model are coefficient estimates determined by variation within individuals rather than variation across individuals?

Which type of model does not have a coefficient that varies with t or i ?

If you perform a Hausman test on a random effects model and have a test statistic that exceeds your critical value,which of the following is not correct?

What is the primary advantage of using panel data rather than a large cross- section data set collected over time?

Which of these assumptions indicates homoskedasticity?

Which model is also called an error components model?

Which type of model has coefficients that vary with i and t?

Which of these assumptions means all error terms are uncorrelated?

Which of the following assumptions must be made in order to use the pooled least squares estimator,but is relaxed in the cluster robust model?

Which of the following is not a reason random effects (RE) results may be preferred to fixed effects (FE) ?

Which of the following is not an estimation technique utilizing panel data?

When should the Hausman-Taylor estimator be used?

If N is the number of individuals observed in each of T time periods,what is generally true of a "short,wide" panel?

Which type of model has coefficients that vary with i,but are constant with t?

For a random effects model the least squares estimator is unbiased and consistent.The errors can be corrected for potential heterogeneity using ___,but the estimator with minimum variance is _.

Which of these assumptions means the errors are uncorrelated with all x's?

How do you test for endogenous regressors,or correlation between the error term and any regressor in a random effects model?

If you perform a Hausman test on a random effects model and have a test statistic that exceeds your critical value,what should you conclude?

What is the difference between balanced and unbalanced panels?