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Quarter Summer 2008-S1
Course Econ 120C
Date
August 2, 2008
Instructor
Professor Yongil Jeon
Student ID#
Print Name
Signature
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HW #2, ECO 120C, Summer 2008 S2 Name: _________________________ Student ID#: _________________________
Economics 120C Professor Yongil Jeon Summer 2008-2
Homework #2 Summer 2008-Session 2, Econ 120C (Final Exam, Summer 2008-Session 1, Econ 120C) Answer all questions on separate paper. This problem set should be handed in to your TA at the beginning of your review session on Wednesday, September 3rd, 2008. Problem sets may not be handed in once solutions have been distributed. Please write down your name and PID clearly. Good luck!
Multiple Choices 1. (3 points) Panel data is also called a. longitudinal data. b. cross-sectional data. c. time series data. d. experimental data. Answer:
2. (3 points) 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. Answer:
3. (3 points) Time Fixed Effects regression are useful in dealing with omitted variables a. b. c. d. even if you only have a cross-section of data available. if these omitted variables are constant across entities but vary over time. when there are more than 100 observations. if these omitted variables are constant across time but not over entities.
Answer:
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HW #2, ECO 120C, Summer 2008 S2
4. (3 points) A repeated cross-sectional data set a. is also referred to as panel data. b. is a collection of cross-sectional data sets, where each cross-sectional data set corresponds to a different time period. c. samples identical entities at least twice. d. is typically used for estimating the following regression model Yit = 0 + 1 X it + 2W1,it + ... + 1+ rWr ,it + uit Answer:
5. (3 points). The time interval between observations can be all of the following with the exception of data collected a. b. c. d. daily. by decade. bi-weekly. across firms.
Answer:
6. (3 points). The AR(p) model a. is defined as Yt = 0 + pYt - p + ut . b. represents Yt as a linear function of p of its lagged values. c. can be represented as follows: Yt = 0 + 1 X t + pYt - p + ut . d. can be written as Yt = 0 + 1Yt -1 + ut - p . Answer:
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HW #2, ECO 120C, Summer 2008 S2
7. (10 points) Consider the following panel data regression with a single explanatory variable
Yit = 1Xit + i+ t + uit. This model also can be written as the time and entity fixed effect model with a single explanatory variable Yit = 0 + 1Xit + 2D2i + . . . + nDni + 2B2t + . . . + TBTt + uit,
where B2t=1 if t=2 and 0 otherwise, D2i=1 if i=2 and 0 otherwise, and so forth. How are the coefficients (0,2, . . . ,n, 2, . . . ,T) related to the coefficients (1, . . ., n, 1, . . ., T)?
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HW #2, ECO 120C, Summer 2008 S2
8. (17 points) 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, omits this 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 = 0 + 1Lit + 2 M i + uit
where i is an index for the baseball team, and t indexes time and all variables are in logs. (a) (10 points) 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 underestimate 1 ?
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HW #2, ECO 120C, Summer 2008 S2 (7 points) If you had data for two years, indicate the transformation, which allows you to obtain a consistent estimator for 1 .
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HW #2, ECO 120C, Summer 2008 S2
9. (15 points) 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 = 0 + 1 (Mit /Wit ) + 2D2i + . . . + nD51i + 2B2t + . . . + TB13t + 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) (5 points) Briefly discuss the advantage of using panel data in this situation rather than pure cross sections or time series.
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HW #2, ECO 120C, Summer 2008 S2 (10 points) Estimating the model by OLS but including only time fixed effects results in the following output
E it = 0 0.33 (Mit /Wit ) + 0.35 ( SHYit ) 1.53 uramit ; R 2 = 0.20 (0.08) (0.28) (0.13)
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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?
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HW #2, ECO 120C, Summer 2008 S2
10. (10 points) Consider the model Yt = 0.1 + 0.9Yt -1 + ut , where u t ~ iid (0,1) . Find the mean and variance of Yt .
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HW #2, ECO 120C, Summer 2008 S2
11. (10 points) The moving average model of order 1 has the form Yt = 0 + et + b1et -1 a. (5 points) Show that E (Yt ) = 0 . where et is a serially uncorrelated random variable with mean 0 and variance e2 .
b. (5 points) Show that the variance of Yt is var (Yt ) = e2 (1 + b12 ) .
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HW #2, ECO 120C, Summer 2008 S2
12. (10 points) A distributed lag model is used with only current and past values of Xt1 coupled with an AR(1) error model to derive a quasi-difference model, where the error term was uncorrelated. Instead use a static model Yt = 0 + 1 X t + ut here, where the error term follows an AR(1). Derive the quasi difference form. Explain why in the case of the infeasible GLS estimators you could easily estimate the s by OLS.
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HW #2, ECO 120C, Summer 2008 S2
13. (10 points) Define the difference operator = (1 - L) , where L is the lag operator, such that LjYt = Yt - j . In general, ij = (1 - Lj )i , where i and j are typically omitted when they take the value of 1. Show the expressions in Y only when applying the difference operator to the following expressions, and give the resulting expression an economic interpretation, assuming that you are working with quarterly data:
(a) (5 points) 4Yt
(b) (5 points) 2Yt