Econ122B Problem Set 2

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Problem Set 2
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  1 Econ   122B   Problem   Set    2   Name (Print)______________________ Due in class Feb 6 UCI   ID________________ _____________ Multiple - Choice   Questions   (Choose the best answer, and briefly explain your reasoning.) 1. Assume we have a simple linear regression model:        . Given a random sample from the population, which of the following statement is true? a. OLS estimators are biased when BMI    do not vary much in the sample. b. OLS estimators are biased when the sample size is small (say 20 observations). c. OLS estimators are biased when the error u   captures perseverance and self‐control, and you believe that people who are perseverant and have more self‐control are less likely overweight. d. None of the above.   2. Suppose you are interested in the effect of class attendance on college performance, and plan to estimate the following model:        , where colGPA  is current GPA and skipped   is the average number of classes skipped per week. Due to lack of information, students’ motivation is omitted from the regression. Assume that more motive students are less likely skip classes. OLS estimator of the coefficient for skipped   will most likely a) be biased away from zero, so that the impact of skipped   on colGPA  is overestimated. b) be biased toward zero, so that the impact of skipped   on colGPA  is underestimated. c) be unbiased. d) be biased, but not enough information to determine if the impact is overestimated or underestimated. Questions 3‐5 are based on the following information: Consider the following population model for household spending on food:                 , where  food   is food expenditure in dollars, inc  is income, educ   is the education level of household head, hhsize  is the size of a household.  2 3. Suppose a researcher estimates this model, one can a) be certain that the R 2  is greater than 1 b) be certain that the R 2  is equal to 0 c) be certain that the R 2  is between 0 and 1 d) be certain that the R 2  is equal to 1 4. Suppose that the variable for food expenditure is measured with errors, so  food   =  food_c  + e , where  food    is the mismeasured variable,  food_c   is the true    food    expenditure,   e  is the measurement error independent of all    the   other    variables . We would expect that: a) OLS estimators for the coefficients will all be biased b) OLS estimators for the coefficients will all be unbiased c) all the standard errors will be bigger than they would be without the measurement error d) both b) and c) 5. Suppose the data were collected through a telephone survey, and the last 4 digits of the households’ telephone number was accidentally coded as something else and included in the regression. Denote the coefficient as 3  β  . We would expect a) the OLS estimators 123 ˆˆˆ, , and  β β β   are all biased. b) OLS estimator 3 ˆ  β   is invalid, but 12 ˆˆ, and  β β   are valid.  c) the OLS estimators 12 ˆˆ, and  β β   are unbiased, and R 2  will get larger. d) the OLS estimators 12 ˆˆ, and  β β   are unbiased, and R 2  will not change. 6. You have to worry about perfect collinearity in the multiple regression model because a) many economic variables are perfectly correlated. b) the OLS estimator cannot be computed in this situation. c) in real life, economic variables change together all the time. d) with perfect collinearity, R 2  is equal to 1.  3 7. Suppose a researcher is interested in the impact of on‐the‐job training on productivity, and plans to estimate the following model:        , where  prod   is a measure of labor productivity, and training   represents number of hours a worker has spent in a training program. The researcher believes that less efficient or less able workers tend to spend more time on training. If this is true, then OLS estimates of this model will most likely a. be biased, because training  is correlated with efficiency/ability  , which is in the error term. b. be unbiased if using a large enough sample. c. be biased, because the variance of efficienc/ability   depends on training.  d. be unbiased, as long as both  prod   and training  are recorded correctly. 8. Suppose you have the following estimated equation,   500 84  , where Burger   refers to weekly number of burgers sold on average in In&In   Burger   joint and price is in US dollars. What would be your estimate of the slope if  price   were in GB pounds (assuming 1 GB pound = 2 US dollars) AND you use daily number of burgers sold rather than weekly? a. ‐12 b. ‐84 c. ‐168 d. ‐24 9. Using data on 4,137 college students, the following equation was estimated by OLS:   1.392 0.0135  0.00148    4,137,   0.273 where colGPA  is measured on a four‐point scale, hsperc  is the percentile in the high school graduating class (defined so that, for example, hsperc   = 5 means the top 5%  4 of the class), and SAT is the combined math and verbal scores on the student achievement test. 1)   How would you interpret the estimated slope for hsperc ? 2)   How would you interpret the R  2 ? 3)   Suppose that two high school graduates, A and B, graduated in the same percentile from high school, but Student A’s SAT score was 140 points higher (about one standard deviation in the sample). What is the predicted difference in college GPA for these two students? 4)   Holding hsperc  fixed what difference in SAT scores leads to a predicated colGPA  difference of .50, or one‐half of a grade point? 10. A researcher has data for 33 states’ data on soda taxes and obesity rate (percentage of people who are obese), Soda taxes measured in cents, and estimates the following regression (Note that log value of soda tax is used as the independent variable). Standard errors are in parentheses.   25.6 0.005  log  10.0 0.002    0.05 Suppose Soda taxes were measured in dollars instead of cents, 1) What would be the estimated coefficient of log( SodaTax  )? 2) What would be R 2 ?
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