Deck 10: Regression With Panel Data

Question 1

cov $\left( u _ { i t } , u _ { i s } \mid X _ { i t } , X _ { i s } \right) = 0 \text { for } t \neq s$
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.

Answer 1

conditional on the regressors, the errors are uncorrelated over time.

Question 2

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.

Answer 2

B

Question 3

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.

Answer 3

D

Question 4

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 5

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 6

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 7

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 8

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 9

The notation for panel data is $\left( X _ { i t } , Y _ { i t } \right) , i = 1 , \ldots , n \text { and } t = 1 , \ldots , T$
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.

Question 10

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.

Question 11

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

Question 12

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

Question 13

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 14

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 15

(Requires Appendix material) When the fifth assumption in the Fixed Effects regression $\left( \operatorname { cov } \left( u _ { i t } , u _ { i s } \mid X _ { i i } , X _ { i s } \right) = 0 \text { for } t \neq s \right)$ 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 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

Panel data is also called

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

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 time fixed effects, you should calculate the F -statistic and compare it to the critical value from your $F _ { q , \infty }$ distribution, where q equals

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

Question 19

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 20

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 $F _ { q , \infty }$ distribution, where q equals

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

Question 21

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 22

'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 23

Consider the case of time fixed effects only, i.e., following equation 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 24

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 (a)

Question 25

Consider the time and entity fixed effect model with a single explanatory variable

Question 26

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 27

Consider the following panel data regression with a single explanatory variable 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.).

Question 28

(Requires Matrix Algebra)Consider the time and entity fixed effect model with a single
explanatory variable

Question 29

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 30

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: where i is an index for the baseball team, and t indexes time and all variables are in logs.
(a)

Question 31

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 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.

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: Interpret the results.Is there indication of unconditional convergence? What critical
value did you use?

Question 33

(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?

Question 34

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

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

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?

Question 37

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 38

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.

Question 39

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.

Question 40

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 $F _ { q , \infty }$ distribution, which equals (at the 5 % level)

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