Deck 10: Regression With Panel Data

Question 1

If you included both time and entity fixed effects in the regression model which includes a constant,then

A)one of the explanatory variables needs to be excluded to avoid perfect multicollinearity.
B)you can use the "before and after" specification even for T > 2.
C)you must exclude one of the entity binary variables and one of the time binary variables for the OLS estimator to exist.
D)the OLS estimator no longer exists.

Answer 1

C

Question 2

The notation for panel data is (Xit,Yit),i = 1,... ,n and t = 1,... ,T because

A)we take into account that the entities included in the panel change over time and are replaced by others.
B)the X's represent the observed effects and the Y the omitted fixed effects.
C)there are n entities and T time periods.
D)n has to be larger than T for the OLS estimator to exist.

Answer 2

C

Question 3

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

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.

Answer 3

B

Question 4

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

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 5

When you add state fixed effects to a simple regression model for U.S.states over a certain time period,and the regression R2 increases significantly,then it is safe to assume that

A)the included explanatory variables,other than the state fixed effects,are unimportant.
B)state fixed effects account for a large amount of the variation in the data.
C)the coefficients on the other included explanatory variables will not change.
D)time fixed effects are unimportant.

Question 6

In the Fixed Effects regression model,using (n - 1)binary variables for the entities,the coefficient of the binary variable indicates

A)the level of the fixed effect of the ith entity.
B)will be either 0 or 1.
C)the difference in fixed effects between the ith and the first entity.
D)the response in the dependent variable to a percentage change in the binary variable.

Question 7

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

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 8

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

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 9

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

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 10

Panel data is also called

A)longitudinal data.
B)cross-sectional data.
C)time series data.
D)experimental data.

Question 11

The difference between an unbalanced and a balanced panel is that

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 12

The Fixed Effects regression model

A)has n different intercepts.
B)the slope coefficients are allowed to differ across entities,but the intercept is "fixed" (remains unchanged).
C)has "fixed" (repaired)the effect of heteroskedasticity.
D)in a log-log model may include logs of the binary variables,which control for the fixed effects.

Question 13

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

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 14

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

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.

Question 15

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,where q equals

A)6.
B)7.
C)48.
D)53.

Question 16

With Panel Data,regression software typically uses an "entity-demeaned" algorithm because

A)the OLS formula for the slope in the linear regression model contains deviations from means already.
B)there are typically too many time periods for the regression package too handle.
C)the number of estimates to calculate can become extremely large when there are a large number of entities.
D)deviations from means sum up to zero.

Question 17

Time Fixed Effects regression are useful in dealing with omitted variables

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

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

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

Question 19

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

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 20

Consider estimating the effect of the beer tax on the fatality rate,using time and state fixed effect for the Northeast Region of the United States (Maine,Vermont,New Hampshire,Massachusetts,Connecticut and Rhode Island)for the period 1991-2001.If Beer Tax was the only explanatory variable,how many coefficients would you need to estimate,excluding the constant?

A)18
B)17
C)7
D)11

Question 21

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?

Question 22

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

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 23

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

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 24

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.

Question 25

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:

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

Question 26

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)

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

Question 27

In panel data,the regression error

A)is likely to be correlated over time within an entity
B)should be calculated taking into account heteroskedasticity but not autocorrelation
C)only exists for the case of T > 2
D)fits all of the three descriptions above

Question 28

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?

Question 29

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?

Question 30

A researcher investigating the determinants of crime in the United Kingdom has data for 42 police regions over 22 years.She estimates by OLS the following regression
ln(cmrt)it = αi + φt + β1unrtmit + β2proythit + β3 ln(pp)it + uit;i = 1,... ,t = 1,... ,22
where cmrt is the crime rate per head of population,unrtm is the unemployment rate of males,proyth is the proportion of youths,pp is the probability of punishment measured as (number of convictions)/(number of crimes reported).α and φ are area and year fixed effects,where αi equals one for area i and is zero otherwise for all i,and φt is one in year t and zero for all other years for t = 2,…,22.φ1 is not included.
(a)What is the purpose of excluding φ1? What are the terms α and φ likely to pick up? Discuss the advantages of using panel data for this type of investigation.
(b)Estimation by OLS using heteroskedasticity and autocorrelation-consistent standard errors results in the following output,where the coefficients of the fixed effects are not reported: = 0.063 × unrtmit + 3.739 × proythit - 0.588 × ln(pp)it ;R2 = 0.904
(0.109)(0.179)(0.024)
Comment on the results.In particular,what is the effect of a ten percent increase in the probability of punishment?
(c)To test for the relevance of the area fixed effects,your restrict the regression by dropping all entity fixed effects and add single constant is added.The relevant F-statistic is 135.28.What are the degrees of freedom? What is the critical value from your F table?
(d)Although the test rejects the hypothesis of eliminating the fixed effects from the regression,you want to analyze what happens to the coefficients and their standard errors when the equation is re-estimated without fixed effects.In the resulting regression, and do not change by much,although their standard errors roughly double.However, is now 1.340 with a standard error of 0.234.Why do you think that is?

Question 31

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

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 32

You learned in intermediate macroeconomics that certain macroeconomic growth models predict conditional convergence or a catch up effect in per capita GDP between the countries of the world.That is,countries which are further behind initially in per-capita GDP will grow faster than the leader.You gather data from the Penn World Tables to test this theory.
(a)By limiting your sample to 24 OECD countries,you hope to have a more homogeneous set of countries in your sample,i.e. ,countries that are not too different with respect to their institutions.To simplify matters,you decide to only test for unconditional convergence.In that case,the laggards catch up even without taking into account differences in some of the driving variables.Your scatter plot and regression for the time period 1975-1989 are as follows: = 0.024 - 0.005 PCGDP75_US;R2= 0.025,SER = 0.006
(0.06)(0.008)
where is the average annual growth rate of per capita GDP from 1975-1989,and PCGDP75_US is per capita GDP relative to the United States in 1975.Numbers in parenthesis are heteroskedasticity-robust standard errors.
Interpret the results.Is there indication of unconditional convergence? What critical value did you use?
(b)Although you are quite discouraged by the result,you think that it might be due to the specific time period used.During this period,there were two OPEC oil price shocks with varying degrees of exposure for the OECD countries.You therefore repeat the exercise for the period 1960-1974,with the following results: = 0.061 - 0.043 PCGDP60_US;R2= 0.613,SER = 0.008
(0.004)(0.007)
where is the average annual growth rate of per capita GDP from 1960-1974,and PCGDP60_US is per capita GDP relative to the United States in 1960.
Compare this regression to the previous one.
(c)You decide to run one more regression in differences.The dependent variable is now the change in the growth rate of per capita GDP from 1960-1974 to 1975-1989 (diffg)and the regressor the difference in the initial conditions (diffinit).This produces the following graph and regression: = -0.006 - 0.096 × diffinit;R2 = 0.468;SER = 0.009
(0.03)(0.021)
Interpret these results.Explain what has happened to unobservable omitted variables that are constant over time.Suggest what some of these variables might be.
(d)Given that there are only two time periods,what other methods could you have employed to generate the identical results? Why do you think that the slope coefficient in this regression is significant given the results over the sub-periods?

Question 33

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?

Question 34

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?

Question 35

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

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 36

HAC standard errors and clustered standard errors are related as follows:

A)they are the same
B)clustered standard errors are one type of HAC standard error
C)they are the same if the data is differenced
D)clustered standard errors are the square root of HAC standard errors

Question 37

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:

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 38

You first encountered growth regression in your intermediate macroeconomics course ("beta-convergence regressions"),that is,conditionally on some initial condition in per capita income,different authors tried to find the determinants of growth.Since growth is a long-run phenomenon,various studies collected data for a panel of numerous countries using 10-year averages,over a time period stretching from 1960 to 2005.For example,a balanced panel might consist of 50 or so odd countries for the time periods 1960-1970,1971-1980,…,2000-2005.Instead of using two-way fixed effects (entity fixed effects and time fixed)authors often only employed time fixed effects.Why do you think that is? What sort of information would be lost if these authors employed entity fixed effects as well?

Question 39

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.

Question 40

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

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.

Question 41

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.

Question 42

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?

Question 43

"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.

Question 44

Your textbook modifies the four assumptions for the multiple regression model by adding a new assumption.This represents an extension of the cross-sectional data case,where errors are uncorrelated across entities.The new assumption requires the errors to be uncorrelated across time,conditional on the regressors as well (cov(uit,uis Xit,Xis)= 0 for t ≠ s. ).
(a)Discuss why there might be correlation over time in the errors when you use U.S.state panel data.Does this mean that you should not use OLS as an estimator?
(b)Now consider pairs of adjacent states such as Indiana and Michigan,Texas and Arkansas,New York and Connecticut,etc.Is it likely that the fifth assumption will hold here,even though the "contemporaneous" errors are correlated? If not,can you still use OLS for estimation?

Question 45

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.

Question 46

(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?

Question 47

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?

Question 48

Your textbook reports the following result from an two-way fixed effects (entity and time fixed effects)regression model: = -0.66 BeerTax + StateFixedEffects + TimeFixedEffects
(0.36)
Where the number in parenthesis is the heteroskedasticity- and autocorrelation-consistent (HAC)standard error.
a.Calculate the t-statistic.Can you reject the null hypothesis that the slope coefficient is zero in the population,using a two-sided test and a 5% significance level?
b.Given that economic theory suggests that the population slope is negative under the alternative hypothesis,is it possible to use a one-sided test here? In that case,does your conclusion change?
c.Using only heteroskedasticity-robust standard errors,but not HAC standard errors,the value in parenthesis becomes 0.25.Repeat the calculations in (a)and report your decision based on a two-sided test.
d.Since the coefficient becomes more statistically significant in (d),should this influence your choice of standard errors? Why or why not?

Question 49

A study attempts to investigate the role of the various determinants of regional Canadian unemployment rates in order to get a better picture of Canadian aggregate unemployment rate behavior.The annual data (1967-1991)is for five regions (Atlantic region,Quebec,Ontario,Prairies,and British Columbia),and four age-gender groups (female and male,adult and young).Focusing on young females,the authors find significant effects for the following variables: the regional relative minimum wage rate (minimum wages divided by average hourly earnings),the regional share of youth in the labor force,the regional share of adult females in the labor force,United States activity shocks (deviations of United States GDP from trend),an indicator of the degree of monetary tightness in Canada,regional union density,and a regional index of unemployment insurance generosity.Explain why the authors only used region fixed effects.How would their specification have to change if they also employed time fixed effects?

Question 50

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.