Question 1

Which of the following assumptions is required for obtaining unbiased fixed effect estimators?
A)The errors are heteroskedastic.
B)The errors are serially correlated.
C)The explanatory variables are strictly exogenous.
D)The unobserved effect is correlated with the explanatory variables.

Accepted Answer

Obtaining unbiased fixed effect estimators requires the assumption of strictly exogenous explanatory variables, which means that the unobserved effect is not correlated with the explanatory variables. Heteroskedasticity or serial correlation of errors does not necessarily affect the unbiasedness of fixed effect estimators.

Question 2

A data set is called an unbalanced panel if it has missing years for at least some cross-sectional units in the sample.

Accepted Answer

An unbalanced panel data set refers to a data set in which missing observations exist for some cross-sectional units over time. Therefore, the statement is true.

Question 3

Which of the following is a property of dummy variable regression?
A)This method is best suited for panel data sets with many cross-sectional observations.
B)The R-squared obtained from this method is lower than that obtained from regression on time-demeaned data.
C)The degrees of freedom cannot be computed directly with this method.
D)The major statistics obtained from this method are identical to that obtained from regression on time-demeaned data.

Accepted Answer

Dummy variable regression allows for the analysis of categorical data within a regression model by incorporating dummy variables (also known as indicator variables). These variables take on the value of 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome. The major statistics (such as coefficients, standard errors, t-statistics, and the F-statistic) obtained from a regression that includes dummy variables to account for fixed effects are identical to those obtained from a regression on time-demeaned data in the context of panel data analysis. This is because both approaches effectively control for unobserved heterogeneity that is constant over time within each cross-sectional unit.

Question 4

A pooled OLS estimator that is based on the time-demeaned variables is called the _____.
A)random effects estimator
B)fixed effects estimator
C)least absolute deviations estimator
D)instrumental variable estimator

Accepted Answer

The time-demeaned variables are a characteristic of the fixed effects estimator, which is also known as the within estimator. The within estimator eliminates the time-invariant unobserved heterogeneity by subtracting the mean of each individual's variable from its observations. Therefore, the pooled OLS that is based on time-demeaned variables is a fixed effects estimator.

Question 5

Which of the following statements is true?
A)Fixed effects estimation is not suitable when the unobserved cluster effect is correlated with one or more explanatory variables.
B)Fixed effects approach is not applicable if the key explanatory variables change only at the level of the cluster.
C)The ordinary least squares standard errors are incorrect when there is cluster effect.
D)Random effects estimation can be applied to a cluster sample only if the unobserved cluster effect is correlated with one or more explanatory variables.

Accepted Answer

The ordinary least squares standard errors assume that observations are independent, which is not the case when there is clustering. The correct standard errors should account for this correlation, or else they will be overstated and confidence intervals will be too narrow. Both fixed and random effects estimations attempt to solve this problem by accounting for the clustering, but fixed effects estimation will be biased if the unobserved cluster effect is correlated with the explanatory variables, while random effects estimation assumes that the unobserved cluster effect is uncorrelated with the explanatory variables. The fact that the key explanatory variables change only at the level of the cluster does not affect the applicability of the fixed effects approach. Finally, random effects estimation can be applied to a cluster sample regardless of whether the unobserved cluster effect is correlated with the explanatory variables.

Question 6

In the correlated random effects approach, the regression model includes _____.
A)time averages as separate explanatory variables
B)at least one dummy variable
C)more than one endogenous explanatory variable
D)an instrumental variable

Accepted Answer

The correlated random effects approach includes time averages as separate explanatory variables in the regression model. This is to control for unobserved time-invariant heterogeneity across individuals or entities in the data. The other options (B, C, and D) are not necessarily included in the correlated random effects approach.

Question 7

An economist wants to study the effect of income on savings. He collected data on 120 identical twins. Which of the following methods of estimation is the most suitable method, if income is correlated with the unobserved family effect?
A)Random effects estimation
B)Fixed effects estimation
C)Ordinary least squares estimation
D)Weighted Least squares estimation

Accepted Answer

Since the economist collected data on identical twins, there could be unobserved family effects that are correlated with income and savings. Fixed effects estimation is particularly useful in controlling for unobserved characteristics that do not vary over time, such as genetic background or family environment. Therefore, fixed effects estimation would be the most suitable method for studying the effect of income on savings in this scenario. Random effects estimation assumes that unobserved factors are uncorrelated with the explanatory variable of interest, which may not hold in this case. Ordinary least squares estimation would not account for unobserved heterogeneity, leading to biased estimates. Weighted least squares estimation is generally used when there is heteroscedasticity in the data, which is not a concern in this scenario.

Question 8

The random effects approach _____.
A)cannot be used if the key explanatory variable is constant over time
B)is preferred to pooled OLS because RE is generally more efficient
C)is suitable if the Hausman test rejects the assumption that the unobserved effect is uncorrelated with the explanatory variables
D)is more convincing than fixed effects for policy analysis using aggregate data

Accepted Answer

The random effects (RE) model is generally more efficient than pooled OLS because it accounts for the unobserved heterogeneity across entities.

Question 9

What should be the degrees of freedom (df) for fixed effects estimation if the data set includes 'N' cross sectional units over 'T' time periods and the regression model has 'k' independent variables?
A)N-kT
B)NT-k
C)NT-N-k
D)N-T-k

Accepted Answer

The degrees of freedom for fixed effects estimation are calculated as (NT - N - k). NT represents the total number of observations, N represents the number of cross-sectional units and T represents the number of time periods, and k represents the number of independent variables. The term N represents the number of fixed effects in the model, and subtracting it from the total number of observations (NT) gives us the within-group degrees of freedom. Finally, we subtract the number of independent variables (k) to account for the parameters being estimated in the model. Therefore, the correct formula for degrees of freedom for fixed effects estimation is (NT - N - k).

Question 10

A manufacturing company is sampled from a population of manufacturing companies, and then the data on at least two employees are recorded. This is an example of:
A)​matched pair samples.
B)​random samples.
C)​cluster samples.
D)​nonrandom samples.

Accepted Answer

This is an example of cluster sampling, where a group (or cluster) of subjects (in this case, a company) is selected, and then data is collected from all or a sample of subjects within that group (employees).

Question 11

Which of the following assumptions is required for obtaining unbiased random effect estimators?
A)The idiosyncratic errors are heteroskedastic.
B)The unobserved effect is independent of all explanatory variables in all time periods.
C)The idiosyncratic errors are serially correlated.
D)The unobserved effect is correlated with the explanatory variables.

Accepted Answer

In order to obtain unbiased random effect estimators, the unobserved effect (or individual-specific effect) must be independent of all explanatory variables in all time periods. This is because if there is correlation between the unobserved effect and the explanatory variables, the random effect estimator will be biased. The other assumptions listed (heteroskedastic errors and serial correlation) do not affect the bias of the random effect estimator.

Question 12

To obtain an estimator that reproduces the fixed effects estimates on the time-varying explanatory variables, _____.
A)​one must check whether the time-demeaning allows one to interpret the estimates
B)​one must check whether time-constant variables can be included in the fixed effects
C)​one must be able to interpret the time variations
D)​one must be careful in constructing the time averages

Accepted Answer

To obtain an estimator that reproduces the fixed effects estimates on the time-varying explanatory variables, one must be careful in constructing the time averages. This is because the time averages must be constructed in such a way that they remove any time-invariant heterogeneity across individuals, allowing the resulting estimator to isolate the effect of the time-varying explanatory variables on the outcome.

Question 13

Which of the following is true of the correlated random effects approach (CRE)?
A)The CRE approach assumes that the unobserved effect is uncorrelated with the observed explanatory variables.
B)The CRE approach cannot be used if the regression model includes a time-constant explanatory variable.
C)The CRE approach considers that the unobserved effect is correlated with the average level of explanatory variables.
D)The CRE estimate equals the random effects estimate.

Accepted Answer

The correlated random effects approach (CRE) assumes that the unobserved effect is correlated with the average level of explanatory variables. This approach can be used even if the regression model includes time-constant explanatory variables. The CRE estimate is different from the random effects estimate. Therefore, options A, B, and D are incorrect.

Question 14

Which of the following is a reason for using the correlated random effects approach?
A)It provides unbiased and consistent estimators when the idiosyncratic errors are serially correlated.
B)It provides unbiased and consistent estimators when the idiosyncratic errors are heteroskedastic.
C)It provides a more efficient estimate than the fixed effects approach.
D)It provides a way to include time-constant explanatory variables in a fixed effects analysis.

Accepted Answer

The correlated random effects approach allows for the inclusion of time-constant explanatory variables in a fixed effects analysis. This is helpful when there are important explanatory variables that are constant over time, but cannot be included in a fixed effects model as they are perfectly collinear with the individual-specific intercepts. By allowing for random effects to be correlated with these time-constant explanatory variables, the correlated random effects model provides a way to estimate their effects on the outcome variable.

Question 15

Which of the following is a difference between a fixed effects estimator and a first-difference estimator?
A)The fixed effects estimators are always larger than the first difference estimators in a two-period panel data analysis.
B)The fixed effects estimator is more efficient than the first-difference estimator when the idiosyncratic errors are serially uncorrelated.
C)The first difference estimator is more sensitive to nonnormality and heteroskedasticity.
D)The bias in the first difference estimator depends on the time period (T) of analysis while the bias in the fixed effect does not depend on T.

Accepted Answer

The fixed effects estimator is more efficient than the first-difference estimator when the idiosyncratic errors are serially uncorrelated because it utilizes within-individual variation over time, assuming that the error term does not autocorrelate. This makes it more efficient under these conditions compared to the first-difference estimator, which might be less efficient due to losing one observation per individual when differencing.

Question 16

The appropriate time average of {y_it} is , where T_i is: A)the dummy variable, which equals one when a complete set of data is observed. B)the total number of time periods for cross-sectional observation i. C)the total number of complete time periods for cross-sectional observation i. D)the explanatory variable for cross-sectional observation i.

Accepted Answer

The time average of a variable is the average value of the variable over time. The denominator of this average should represent the total number of time periods for which data is available. Option C is the only choice that provides the appropriate denominator for a time average. Option A refers to a dummy variable, which does not give us any information about the time periods. Option B is the total number of time periods but not the complete ones, and option D refers to an explanatory variable, which is not relevant for calculating the time average.

Question 17

The estimator obtained through regression on quasi-demeaned data is called the _____.
A)random effects estimator
B)fixed effects estimator
C)hetroskedasticity-robust OLS estimator
D)instrumental variables estimator

Accepted Answer

The random effects estimator is obtained through regression on quasi-demeaned data, which involves transforming the data to remove the effects that are constant across entities but vary over time, under the assumption that the entity-specific effect is uncorrelated with the independent variables.

Question 18

In a random effects model, we assume that the unobserved effect is correlated with each explanatory variable.

Accepted Answer

In a random effects model, we assume that the unobserved effect is uncorrelated with the explanatory variables, unlike in a fixed effects model where the unobserved effect may be correlated with the explanatory variables.

Question 19

Which of the following types of variables cannot be included in a fixed effects model?
A)Dummy variable
B)Discrete dependent variable
C)Time-varying independent variable
D)Time-constant independent variable

Accepted Answer

Time-constant independent variables cannot be included in a fixed effects model because the model controls for all time-invariant characteristics of the individuals, effectively differencing out any variable that does not change over time.

Question 20

The random effects estimate is identical to the fixed effects estimate if the estimated transformation parameter ,  , in generalized least squares estimation that eliminates serial correlation between error terms is, _____.
A)less than zero
B)equal to zero
C)equal to one
D)greater than one

Accepted Answer

The answer of The random effects estimate is identical to...

Quiz 14: Advanced Panel Data Methods

Which of the following assumptions is required for obtaining unbiased fixed effect estimators?

A data set is called an unbalanced panel if it has missing years for at least some cross-sectional units in the sample.

Which of the following is a property of dummy variable regression?

A pooled OLS estimator that is based on the time-demeaned variables is called the _____.

Which of the following statements is true?

In the correlated random effects approach, the regression model includes _____.

An economist wants to study the effect of income on savings. He collected data on 120 identical twins. Which of the following methods of estimation is the most suitable method, if income is correlated with the unobserved family effect?

The random effects approach _____.

What should be the degrees of freedom (df) for fixed effects estimation if the data set includes 'N' cross sectional units over 'T' time periods and the regression model has 'k' independent variables?

A manufacturing company is sampled from a population of manufacturing companies, and then the data on at least two employees are recorded. This is an example of:

Which of the following assumptions is required for obtaining unbiased random effect estimators?

To obtain an estimator that reproduces the fixed effects estimates on the time-varying explanatory variables, _____.

Which of the following is true of the correlated random effects approach (CRE) ?

Which of the following is a reason for using the correlated random effects approach?

Which of the following is a difference between a fixed effects estimator and a first-difference estimator?

The appropriate time average of {y_it} is , where T_i is:

The estimator obtained through regression on quasi-demeaned data is called the _____.

In a random effects model, we assume that the unobserved effect is correlated with each explanatory variable.

Which of the following types of variables cannot be included in a fixed effects model?

The random effects estimate is identical to the fixed effects estimate if the estimated transformation parameter , , in generalized least squares estimation that eliminates serial correlation between error terms is, _____.

Quiz 14: Advanced Panel Data Methods

Which of the following assumptions is required for obtaining unbiased fixed effect estimators?

A data set is called an unbalanced panel if it has missing years for at least some cross-sectional units in the sample.

Which of the following is a property of dummy variable regression?

A pooled OLS estimator that is based on the time-demeaned variables is called the _____.

Which of the following statements is true?

In the correlated random effects approach, the regression model includes _____.

An economist wants to study the effect of income on savings. He collected data on 120 identical twins. Which of the following methods of estimation is the most suitable method, if income is correlated with the unobserved family effect?

The random effects approach _____.

What should be the degrees of freedom (df) for fixed effects estimation if the data set includes 'N' cross sectional units over 'T' time periods and the regression model has 'k' independent variables?

A manufacturing company is sampled from a population of manufacturing companies, and then the data on at least two employees are recorded. This is an example of:

Which of the following assumptions is required for obtaining unbiased random effect estimators?

To obtain an estimator that reproduces the fixed effects estimates on the time-varying explanatory variables, _____.

Which of the following is true of the correlated random effects approach (CRE) ?

Which of the following is a reason for using the correlated random effects approach?

Which of the following is a difference between a fixed effects estimator and a first-difference estimator?

The appropriate time average of {yit} is​ , where Ti is:

The estimator obtained through regression on quasi-demeaned data is called the _____.

In a random effects model, we assume that the unobserved effect is correlated with each explanatory variable.

Which of the following types of variables cannot be included in a fixed effects model?

The random effects estimate is identical to the fixed effects estimate if the estimated transformation parameter , , in generalized least squares estimation that eliminates serial correlation between error terms is, _____.

The appropriate time average of {y_it} is , where T_i is: