Question 1

The "before and after" specification, binary variable specification, and "entity-demeaned" specification produce identical OLS estimates

Accepted Answer

A) as long as there are observations for more than two time periods. 
B) if you use the heteroskedasticity-robust option in your regression program. 
C) for the case of more than 100 observations. 
D) as long as T = 2 and the intercept is excluded from the "before and after" specification. 
A) as long as there are observations for more than two time periods. 
B) if you use the heteroskedasticity-robust option in your regression program. 
C) for the case of more than 100 observations. 
D) as long as T = 2 and the intercept is excluded from the "before and after" specification.

Question 2

You want to investigate the relationship between cumulative GPA scores at graduation and incoming SAT scores of students. For this purpose, you have collected data from a balanced panel of 120 undergraduate colleges and universities in the United States over a ten year period. Discuss some of the entity fixed effects which you potentially capture by allowing for a binary variable for each of the colleges.

Accepted Answer

Students will come up with various possi

Question 3

In Sports Economics, production functions are often estimated by relating the winning percentage of teams (Y)to inputs indicating performance in certain aspects of the game. However, this omits the quality of management. Assume that you could measure the quality of pitching and hitting by a single index L, and that managerial ability is represented by M, which is assumed to be constant over time. The production function would then be specified as follows:
Yit = β0 +β1 Lit + β2Mi + uit
where i is an index for the baseball team, and t indexes time and all variables are in logs.
(a)Assume that managerial ability is unobservable but is positively related, in a linear way, to L. Explain why the OLS estimator $\hat { \beta }$ 1 is inconsistent in the case of a single cross-section, i.e., if you attempt to estimate the above regression for a single year. Do you expect this coefficient to over- or under-estimate β1?
(b)If you had data for two years, indicate the transformation, which allows you to obtain a consistent estimator for β1.

Accepted Answer

(a)Regressing Y on L alone will result i

Question 4

Your textbook suggests an "entity-demeaned" procedure to avoid having to specify a potentially large number of binary variables. While it is somewhat tedious to specify a binary variable for each entity, this can still be handled relatively easily in the case of the 48 contiguous states. Give a few examples where it might be close to impossible to implement specifying such large number of entity binary variables. The idea of the "entity-demeaned" procedure was introduced as a computationally convenient and simplifying procedure. Since there are also time fixed effects, why is there no discussion of using a "time-demeaned" procedure? Using the following equation
Yit = β0 + β1Xit + β3St + uit,
Show how β1 can be estimated by the OLS regression using "time-demeaned" variables.

Accepted Answer

Answers will vary by student with regard

Question 5

It is advisable to use clustered standard errors in panel regressions because

Accepted Answer

A) without clustered standard errors, the OLS estimator is biased 
B) hypothesis testing can proceed in a standard way even if there are few entities (n is small) 
C) they are easier to calculate than homoskedasticity-only standard errors 
D) the fixed effects estimator is asymptotically normally distributed when n is large 
A) without clustered standard errors, the OLS estimator is biased 
B) hypothesis testing can proceed in a standard way even if there are few entities (n is small) 
C) they are easier to calculate than homoskedasticity-only standard errors 
D) the fixed effects estimator is asymptotically normally distributed when n is large

Question 6

Give at least three examples from macroeconomics and five from microeconomics that involve specified equations in a panel data analysis framework. Indicate in each case what the role of the entity and time fixed effects in terms of omitted variables might be.

Accepted Answer

Answers will vary by student. Given the

Question 7

In the panel regression analysis of beer taxes on traffic deaths, the estimation period is 1982-1988 for the 48 contiguous U.S. states. To test for the significance of entity fixed effects, you should calculate the F-statistic and compare it to the critical value from your Fq,∞ distribution, where q equals

Accepted Answer

A) 48. 
B) 54. 
C) 7. 
D) 47. 
A) 48. 
B) 54. 
C) 7. 
D) 47.

Question 8

The difference between an unbalanced and a balanced panel is that

Accepted Answer

A) you cannot have both fixed time effects and fixed entity effects regressions. 
B) an unbalanced panel contains missing observations for at least one time period or one entity. 
C) the impact of different regressors are roughly the same for balanced but not for unbalanced panels. 
D) in the former you may not include drivers who have been drinking in the fatality rate/beer tax study. 
A) you cannot have both fixed time effects and fixed entity effects regressions. 
B) an unbalanced panel contains missing observations for at least one time period or one entity. 
C) the impact of different regressors are roughly the same for balanced but not for unbalanced panels. 
D) in the former you may not include drivers who have been drinking in the fatality rate/beer tax study.

Question 9

Your textbook specifies a simple regression problem for two time periods for the years 1982 and 1988 as follows:
FatalityRatei,1982 = β0 + β1BeerTaxi,1982 + ui,1982
FatalityRatei,1988 = β0 + β1BeerTaxi,1988 + ui,1988
After subtracting the first equation from the second equation, the authors estimate the model and find a negative intercept.
a. Show how you would have to modify the two equations to allow for the presence of an intercept in the differenced model.
b. What would the relative magnitude of the modified model have to be for you to find a negative intercept?

Accepted Answer

a. FatalityRate_i,₁₉₈₂= β₀ +

Question 10

Indicate for which of the following examples you cannot use Entity and Time Fixed Effects: a regression of

Accepted Answer

A) OECD unemployment rates on unemployment insurance generosity for the period 1980-2006 (annual data). 
B) the (log of)earnings on the number of years of education, using the Current Population Survey of 60,000 households for March 2006. 
C) the per capita income level in Canadian Provinces on provincial population growth rates, using decade averages for 1960, 1970, and 1980. 
D) the risk premium of 75 stocks on the market premium for the years 1998-2006. 
A) OECD unemployment rates on unemployment insurance generosity for the period 1980-2006 (annual data). 
B) the (log of)earnings on the number of years of education, using the Current Population Survey of 60,000 households for March 2006. 
C) the per capita income level in Canadian Provinces on provincial population growth rates, using decade averages for 1960, 1970, and 1980. 
D) the risk premium of 75 stocks on the market premium for the years 1998-2006.

Question 11

(Requires Appendix material)When the fifth assumption in the Fixed Effects regression (cov (uit, uis | Xit, Xis)= 0 for t ? s)is violated, then

Accepted Answer

A) using heteroskedastic-robust standard errors is not sufficient for correct statistical inference when using OLS. 
B) the OLS estimator does not exist. 
C) you can use the simple homoskedasticity-only standard errors calculated in your regression package. 
D) you cannot use fixed time effects in your estimation. 
A) using heteroskedastic-robust standard errors is not sufficient for correct statistical inference when using OLS. 
B) the OLS estimator does not exist. 
C) you can use the simple homoskedasticity-only standard errors calculated in your regression package. 
D) you cannot use fixed time effects in your estimation.

Question 12

If Xit is correlated with Xis for different values of s and t, then

Accepted Answer

A) Xit is said to be autocorrelated 
B) the OLS estimator cannot be computed 
C) statistical inference cannot proceed in a standard way even if clustered standard errors are used 
D) this is not of practical importance since these correlations are typically weak in applications 
A) Xit is said to be autocorrelated 
B) the OLS estimator cannot be computed 
C) statistical inference cannot proceed in a standard way even if clustered standard errors are used 
D) this is not of practical importance since these correlations are typically weak in applications

Question 13

Consider a panel regression of unemployment rates for the G7 countries (United States, Canada, France, Germany, Italy, United Kingdom, Japan)on a set of explanatory variables for the time period 1980-2000 (annual data). If you included entity and time fixed effects, you would need to specify the following number of binary variables:

Accepted Answer

A) 21. 
B) 6. 
C) 28. 
D) 26. 
A) 21. 
B) 6. 
C) 28. 
D) 26.

Question 14

You want to study the relationship between weight and height of young children (4th grade to 7th grade). You collect data for more than 400 students and track the progress of these students over the following four years, where you end up with a balanced panel of 400 students (you discard the observations for the students who moved away). Discuss some of the entity fixed effects which you potentially capture by allowing for a binary variable for each of the students. Do you expect significant time fixed effects if you allowed for them?

Accepted Answer

Students will come up with various possi

Question 15

"Empirical studies of economic growth are flawed because many of the truly important underlying determinants, such as culture and institutions, are very hard to measure." Discuss this statement paying particular attention to simple cross-section data and panel data models. Use equations whenever possible to underscore your argument.

Accepted Answer

Although some cultural and institutional

Question 16

In the panel regression analysis of beer taxes on traffic deaths, the estimation period is 1982-1988 for the 48 contiguous U.S. states. To test for the significance of time fixed effects, you should calculate the F-statistic and compare it to the critical value from your Fq,∞ distribution, which equals (at the 5% level)

Accepted Answer

A) 2.01. 
B) 2.10. 
C) 2.80. 
D) 2.64. 
A) 2.01. 
B) 2.10. 
C) 2.80. 
D) 2.64.

Question 17

One of the following is a regression example for which Entity and Time Fixed Effects could be used: a study of the effect of

Accepted Answer

A) minimum wages on teenage employment using annual data from the 48 contiguous states in 2006 . 
B) various performance statistics on the (log of)salaries of baseball pitchers in the American League and the National League in 2005 and 2006. 
C) inflation and inflationary expectations on unemployment rates in the United States, using quarterly data from 1960-2006. 
D) drinking alcohol on the GPA of 150 students at your university, controlling for incoming SAT scores. 
A) minimum wages on teenage employment using annual data from the 48 contiguous states in 2006 . 
B) various performance statistics on the (log of)salaries of baseball pitchers in the American League and the National League in 2005 and 2006. 
C) inflation and inflationary expectations on unemployment rates in the United States, using quarterly data from 1960-2006. 
D) drinking alcohol on the GPA of 150 students at your university, controlling for incoming SAT scores.

Question 18

In the Fixed Effects regression model, you should exclude one of the binary variables for the entities when an intercept is present in the equation

Accepted Answer

A) because one of the entities is always excluded. 
B) because there are already too many coefficients to estimate. 
C) to allow for some changes between entities to take place. 
D) to avoid perfect multicollinearity. 
A) because one of the entities is always excluded. 
B) because there are already too many coefficients to estimate. 
C) to allow for some changes between entities to take place. 
D) to avoid perfect multicollinearity.

Question 19

Consider the time and entity fixed effect model with a single explanatory variable
Yit = β0 + β1Xit + $\gamma _ { 2 }$ D2i + ... + $\gamma _ { n }$ Dni + δ2B2t + ... + δTBTt + uit,
Assume that you had estimated the above equation by OLS. Typically the coefficients for the entity and time binary variables are not reported. Can you think of situations where the pattern of these coefficients might be of interest? What could you do, for example, if you had a strong theoretical justification for believing that a few macroeconomic variables had an effect on Yit?

Accepted Answer

The coefficients pick up the effects of

Question 20

The main advantage of using panel data over cross sectional data is that it

Accepted Answer

A) gives you more observations. 
B) allows you to analyze behavior across time but not across entities. 
C) allows you to control for some types of omitted variables without actually observing them. 
D) allows you to look up critical values in the standard normal distribution. 
A) gives you more observations. 
B) allows you to analyze behavior across time but not across entities. 
C) allows you to control for some types of omitted variables without actually observing them. 
D) allows you to look up critical values in the standard normal distribution.

The "before and after" specification, binary variable specification, and "entity-demeaned" specification produce identical OLS estimates

It is advisable to use clustered standard errors in panel regressions because

Give at least three examples from macroeconomics and five from microeconomics that involve specified equations in a panel data analysis framework. Indicate in each case what the role of the entity and time fixed effects in terms of omitted variables might be.

The difference between an unbalanced and a balanced panel is that

Indicate for which of the following examples you cannot use Entity and Time Fixed Effects: a regression of

(Requires Appendix material)When the fifth assumption in the Fixed Effects regression (cov (u_it, u_is | X_it, X_is)= 0 for t ? s)is violated, then

If X_it is correlated with X_is for different values of s and t, then

One of the following is a regression example for which Entity and Time Fixed Effects could be used: a study of the effect of

In the Fixed Effects regression model, you should exclude one of the binary variables for the entities when an intercept is present in the equation

The main advantage of using panel data over cross sectional data is that it

Economic Questions and Data

Review of Probability

Review of Statistics

Linear Regression With One Regressor

Regression With a Single Regressor: Hypothesis Tests and Confidence Intervals

Linear Regression With Multiple Regressors

Hypothesis Tests and Confidence Intervals in Multiple Regression

Nonlinear Regression Functions

Assessing Studies Based on Multiple Regression

Regression With a Binary Dependent Variable

Instrumental Variables Regression

Experiments and Quasi-Experiments

Introduction to Time Series Regression and Forecasting

Estimation of Dynamic Causal Effects

Additional Topics in Time Series Regression

The Theory of Linear Regression With One Regressor

The Theory of Multiple Regression

Filters

Exam 10: Regression With Panel Data

The "before and after" specification, binary variable specification, and "entity-demeaned" specification produce identical OLS estimates

It is advisable to use clustered standard errors in panel regressions because

Give at least three examples from macroeconomics and five from microeconomics that involve specified equations in a panel data analysis framework. Indicate in each case what the role of the entity and time fixed effects in terms of omitted variables might be.

The difference between an unbalanced and a balanced panel is that

Indicate for which of the following examples you cannot use Entity and Time Fixed Effects: a regression of

(Requires Appendix material)When the fifth assumption in the Fixed Effects regression (cov (uit, uis | Xit, Xis)= 0 for t ? s)is violated, then

If Xit is correlated with Xis for different values of s and t, then

One of the following is a regression example for which Entity and Time Fixed Effects could be used: a study of the effect of

In the Fixed Effects regression model, you should exclude one of the binary variables for the entities when an intercept is present in the equation

The main advantage of using panel data over cross sectional data is that it

Economic Questions and Data

Review of Probability

Review of Statistics

Linear Regression With One Regressor

Regression With a Single Regressor: Hypothesis Tests and Confidence Intervals

Linear Regression With Multiple Regressors

Hypothesis Tests and Confidence Intervals in Multiple Regression

Nonlinear Regression Functions

Assessing Studies Based on Multiple Regression

Regression With a Binary Dependent Variable

Instrumental Variables Regression

Experiments and Quasi-Experiments

Introduction to Time Series Regression and Forecasting

Estimation of Dynamic Causal Effects

Additional Topics in Time Series Regression

The Theory of Linear Regression With One Regressor

The Theory of Multiple Regression

Filters

(Requires Appendix material)When the fifth assumption in the Fixed Effects regression (cov (u_it, u_is | X_it, X_is)= 0 for t ? s)is violated, then

If X_it is correlated with X_is for different values of s and t, then