Question 1

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

Accepted Answer

A) because the first time period must always excluded from your data set. 
B) because there are already too many coefficients to estimate. 
C) to avoid perfect multicollinearity. 
D) to allow for some changes between time periods to take place. 
A) because the first time period must always excluded from your data set. 
B) because there are already too many coefficients to estimate. 
C) to avoid perfect multicollinearity. 
D) to allow for some changes between time periods to take place.

Question 2

cov (uit,uis   Xit,Xis = 0 for t ≠ s means that

Accepted Answer

A) there is no perfect multicollinearity in the errors. 
B) division of errors by regressors in different time periods is always zero. 
C) there is no correlation over time in the residuals. 
D) conditional on the regressors,the errors are uncorrelated over time. 
A) there is no perfect multicollinearity in the errors. 
B) division of errors by regressors in different time periods is always zero. 
C) there is no correlation over time in the residuals. 
D) conditional on the regressors,the errors are uncorrelated over time.

Question 3

Consider the following panel data regression with a single explanatory variable
Yit = β0 + β1Xit + uit.
In each of the examples below,you will be adding entity and time fixed effects.Indicate the total number of coefficients that need to be estimated.
(a)The effect of beer taxes on the fatality rate,annual data,1982-1988,nine U.S.regions (New England,Pacific,Mid-Atlantic,East North Central,etc. ).
(b)The effect of the minimum wage on teenage employment,annual data,1963-2000,five Canadian Regions (Atlantic Provinces,Quebec,Ontario,Prairies,British Columbia).
(c)The effect of savings rates on per capita income,data for three decades (1960-1969,1970-1979,1980-1989;one observation per decade),104 countries of the world.
(d)The effect of pitching quality in baseball (as measured by the Team ERA)on the winning percentage,annual data,1998-1999 season,1999-2000 season,30 teams.

Accepted Answer

(a)16 coefficients (6 time fixed effects

Question 4

You want to find the determinants of suicide rates in the United States.To investigate the issue,you collect state level data for ten years.Your first idea,suggested to you by one of your peers from Southern California,is that the annual amount of sunshine must be important.Stacking the data and using no fixed effects,you find no significant relationship between suicide rates and this variable.(This is good news for the people of Seattle. )However,sorting the suicide rate data from highest to lowest,you notice that those states with the lowest population density are dominating in the highest suicide rate category.You run another regression,without fixed effect,and find a highly significant relationship between the two variables.Even adding some economic variables,such as state per capita income or the state unemployment rate,does not lower the t-statistic for the population density by much.Adding fixed entity and time effects,however,results in an insignificant coefficient for population density.
(a)What do you think is the cause for this change in significance? Which fixed effect is primarily responsible? Does this result imply that population density does not matter?
(b)Speculate as to what happens to the coefficients of the economic variables when the fixed effects are included.Use this example to make clear what factors entity and time fixed effects pick up.
(c)What other factors might play a role?

Accepted Answer

(a)Population density only changes slowl

Question 5

Assume that for the T = 2 time periods case,you have estimated a simple regression in changes model and found a statistically significant positive intercept.This implies

Accepted Answer

A) a negative mean change in the LHS variable in the absence of a change in the RHS variable since you subtract the earlier period from the later period 
B) that the panel estimation approach is flawed since differencing the data eliminates the constant (intercept)in a regression 
C) a positive mean change in the LHS variable in the absence of a change in the RHS variable 
D) that the RHS variable changed between the two subperiods 
A) a negative mean change in the LHS variable in the absence of a change in the RHS variable since you subtract the earlier period from the later period 
B) that the panel estimation approach is flawed since differencing the data eliminates the constant (intercept)in a regression 
C) a positive mean change in the LHS variable in the absence of a change in the RHS variable 
D) that the RHS variable changed between the two subperiods

Question 6

Consider the regression example from your textbook,which estimates the effect of beer taxes on fatality rates across the 48 contiguous U.S.states.If beer taxes were set nationally by the federal government rather than by the states,then

Accepted Answer

A) it would not make sense to use state fixed effect. 
B) you can test state fixed effects using homoskedastic-only standard errors. 
C) the OLS estimator will be biased. 
D) you should not use time fixed effects since beer taxes are the same at a point in time across states. 
A) it would not make sense to use state fixed effect. 
B) you can test state fixed effects using homoskedastic-only standard errors. 
C) the OLS estimator will be biased. 
D) you should not use time fixed effects since beer taxes are the same at a point in time across states.

Question 7

Consider the time and entity fixed effect model with a single explanatory variable
Yit = β0 + β1Xit +   D2i + ...+   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 8

A study,published in 1993,used U.S.state panel data to investigate the relationship between minimum wages and employment of teenagers.The sample period was 1977 to 1989 for all 50 states.The author estimated a model of the following type:   where E is the employment to population ratio of teenagers,M is the nominal minimum wage,and W is average hourly earnings in manufacturing.In addition,other explanatory variables,such as the adult unemployment rate,the teenage population share,and the teenage enrollment rate in school,were included.
(a)Name some of the factors that might be picked up by time and state fixed effects.
(b)The author decided to use eight regional dummy variables instead of the 49 state dummy variables.What is the implicit assumption made by the author? Could you test for its validity? How?
(c)The results,using time and region fixed effects only,were as follows:   = -0.182 × ln(Mit /Wit )+ ... ;R2= 0.727
(0.036)
Interpret the result briefly.
(d)State minimum wages do not exceed federal minimum wages often.As a result,the author decided to choose the federal minimum wage in his specification above.How does this change your interpretation? How is the original equation   affected by this?

Accepted Answer

(a)Time effects will pick up the effect

Question 9

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 10

(Requires Matrix Algebra)Consider the time and entity fixed effect model with a single explanatory variable
Yit = β0 + β1Xit +   D2i + ...+   Dni + δ2B2t + ...+ δTBTt + uit,
For the case of n = 4 and T = 3,write this model in the form Y = Xβ + U,where,in general,
Y =   ,U =   ,X =   =   ,and β =   How would the X matrix change if you added two binary variables,D1 and B1? Demonstrate that in this case the columns of the X matrix are not independent.Finally show that elimination of one of the two variables is not sufficient to get rid of the multicollinearity problem.In terms of the OLS estimator,   = (   X)-1   Y,why does perfect multicollinearity create a problem?

Accepted Answer

For the case of n = 4 and T = 3,the gene

Question 11

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   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 12

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 13

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 14

Consider the case of time fixed effects only,i.e. ,
Yit = β0 + β1Xit + β3St + uit,
First replace β0 + β3St with φt.Next show the relationship between the φt and δt in the following equation
Yit = β0 + β1Xit + δ2B2t + ...+ δTBTt + uit,
where each of the binary variables B2,…,BT indicates a different time period.Explain in words why the two equations are the same.Finally show why there is perfect multicollinearity if you add another binary variable B1.What is the intuition behind the fact that the OLS estimator does not exist in this case? Would that also be the case if you dropped the intercept?

Accepted Answer

Yit = β1Xit + φt + uit.The relationship

Question 15

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 16

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 17

Time Fixed Effects regression are useful in dealing with omitted variables

Accepted Answer

A) even if you only have a cross-section of data available. 
B) if these omitted variables are constant across entities but vary over time. 
C) when there are more than 100 observations. 
D) if these omitted variables are constant across entities but not over time. 
A) even if you only have a cross-section of data available. 
B) if these omitted variables are constant across entities but vary over time. 
C) when there are more than 100 observations. 
D) if these omitted variables are constant across entities but not over time.

Question 18

A pattern in the coefficients of the time fixed effects binary variables may reveal the following in a study of the determinants of state unemployment rates using panel data:

Accepted Answer

A) macroeconomic effects,which affect all states equally in a given year. 
B) attitude differences towards unemployment between states. 
C) there is no economic information that can be retrieved from these coefficients. 
D) regional effects,which affect all states equally,as long as they are a member of that region. 
A) macroeconomic effects,which affect all states equally in a given year. 
B) attitude differences towards unemployment between states. 
C) there is no economic information that can be retrieved from these coefficients. 
D) regional effects,which affect all states equally,as long as they are a member of that region.

Question 19

Two authors published a study in 1992 of the effect of minimum wages on teenage employment using a U.S.state panel.The paper used annual observations for the years 1977-1989 and included all 50 states plus the District of Columbia.The estimated equation is of the following type
(Eit )= β0 + β1 (Mit /Wit )+   D2i + ...+   D51i +   B2t + ...+   B13t + uit,
where E is the employment to population ratio of teenagers,M is the nominal minimum wage,and W is average wage in the state.In addition,other explanatory variables,such as the prime-age male unemployment rate,and the teenage population share were included.
(a)Briefly discuss the advantage of using panel data in this situation rather than pure cross sections or time series.
(b)Estimating the model by OLS but including only time fixed effects results in the following output   it =   0 - 0.33 × (Mit /Wit )+ 0.35(SHYit)- 1.53 × uramit;R2 = 0.20
(0.08)(0.28)(0.13)
where SHY is the proportion of teenagers in the population,and uram is the prime-age male unemployment rate.Coefficients for the time fixed effects are not reported.Numbers in parenthesis are homoskedasticity-only standard errors.
Comment on the above results.Are the coefficients statistically significant? Since these are level regressions,how would you calculate elasticities?
(c)Adding state fixed effects changed the above equation as follows:   it =   0 + 0.07 × (Mit /Wit )- 0.19 × (SHYit)- 0.54 × uramit;   2 = 0.69
(0.10)(0.22)(0.11)
Compare the two results.Why would the inclusion of state fixed effects change the coefficients in this way?
(d)The significance of each coefficient decreased,yet   2 increased.How is that possible? What does this result tell you about testing the hypothesis that all of the state fixed effects can be restricted to have the same coefficient? How would you test for such a hypothesis?

Accepted Answer

(a)There are likely to be omitted variab

Question 20

Consider the special panel case where T = 2.If some of the omitted variables,which you hope to capture in the changes analysis,in fact change over time,then the estimator on the included change regressor

Accepted Answer

A) will be unbiased only when allowing for heteroskedastic-robust standard errors. 
B) may still be unbiased. 
C) will only be unbiased in large samples. 
D) will always be unbiased. 
A) will be unbiased only when allowing for heteroskedastic-robust standard errors. 
B) may still be unbiased. 
C) will only be unbiased in large samples. 
D) will always be unbiased.

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

cov (uit,uis Xit,Xis = 0 for t ≠ s means that

Assume that for the T = 2 time periods case,you have estimated a simple regression in changes model and found a statistically significant positive intercept.This implies

Consider the regression example from your textbook,which estimates the effect of beer taxes on fatality rates across the 48 contiguous U.S.states.If beer taxes were set nationally by the federal government rather than by the states,then

The difference between an unbalanced and a balanced panel is that

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

Time Fixed Effects regression are useful in dealing with omitted variables

A pattern in the coefficients of the time fixed effects binary variables may reveal the following in a study of the determinants of state unemployment rates using panel data:

Consider the special panel case where T = 2.If some of the omitted variables,which you hope to capture in the changes analysis,in fact change over time,then the estimator on the included change regressor

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

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Exam 10: Regression With Panel Data

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

cov (uit,uis Xit,Xis = 0 for t ≠ s means that

Assume that for the T = 2 time periods case,you have estimated a simple regression in changes model and found a statistically significant positive intercept.This implies

Consider the regression example from your textbook,which estimates the effect of beer taxes on fatality rates across the 48 contiguous U.S.states.If beer taxes were set nationally by the federal government rather than by the states,then

The difference between an unbalanced and a balanced panel is that

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

Time Fixed Effects regression are useful in dealing with omitted variables

A pattern in the coefficients of the time fixed effects binary variables may reveal the following in a study of the determinants of state unemployment rates using panel data:

Consider the special panel case where T = 2.If some of the omitted variables,which you hope to capture in the changes analysis,in fact change over time,then the estimator on the included change regressor

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