EEP 118 / IAS 118 Elisabeth Sadoulet and Tania Barham University of California at Berkeley Fall 2004 Introductory Applied Econometrics Midterm examination Scores add up to 50 Your name:________________________________________ SID:________________ 1. (5 points) Denote by X the number of miles per gallon achieved by cars of a particular model. You are told that X : Nµ= 20,σ2= 4(). What is the probability that for a random sample of 25 cars, the average miles per gallon X will be between 19 and 21? 2. (5 points) What is the definition of homoskedasticity? Briefly explain its meaning. 13. (5 points). A Newsweek poll reported that 47% of the likely voters of the State of Florida are favorable to President Bush, while this number is 44% in the State of Michigan. The poll included 1000 respondents in each state. Is there statistically significant evidence that Michigan is less favorable to President Bush than Florida? Explain. 4. (10 points) A researcher is interested in the effects of household income and mother’s education on child health. Using data from a Demographic and Health Survey in a developing country, the researcher regresses weight/height (called z-score among health specialists, noting that a higher z-score means a healthier child)) of children 3-5 years old on their mother’s education and the household income: zscore =β0+β1motheduc+β2income+u (a) What are the conditions for the OLS estimators and to be unbiased estimators of the effect of mother’s education and household income? ˆ β 1ˆ β 2(b) Knowing that children’s health is strongly influenced by the availability of clean water and sewage, are and biased, and if you think they are biased, are they biased upward or downward? Why? ˆ β 1ˆ β 2 25. (10 points) You have n = 36 quarterly observations on: the imports M of a country, an index of import prices , and real aggregate income GDP. Adding dummy variables Q, and for the 2PM2,Q3Q4nd, 3rd, and 4th quarter of the year, you estimate the model: log M =β0+β1log PM+β2log GDP +β3Q2 +β4Q3 +β5Q4 + uand find the following results: , log Mº= 4.30 − 0.58 log PM+ 1.45log GDP + .15Q2 + .10Q3 + .40Q4Ź(0.13) ŹŹŹŹŹŹŹŹŹŹŹ (0.21) ŹŹŹŹŹŹŹŹŹŹŹ(.10)ŹŹŹŹŹŹ(.05)ŹŹŹŹŹŹ(.12)R2= 0.253n=36 (a) Construct a 95% confidence interval for β1. (b) Test the hypothesis against at the 5% significance level. Interpret this result in economic terms. β2= 1β2≠ 1 36. (15 points) Using data on 4,000 full time workers from the 1998 Current Population Survey, the following wage regressions for average hourly earnings were estimated: wageº= 4.40 + 5.48College− 2.62Female + 0.29 AgeŹ(1.05) (0.21) (0.20) (0.04) R2= 0.190 wageº= 3.75 + 5.44College − 2.62Female + 0.29 Age + 0.69Northeast + 0.60Midwest − 0.27SouthŹ(1.06) (0.21) (0.20) (0.04) (0.30) (0.28)ŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹ(0.26) R2= 0.194where wage is the average hourly earnings (in 1998 dollars), College is a binary variable (1 if college, 0 if high school), Female is a binary variable (1 if female, 0 if male), and Age is the age in years. The U.S. are divided into four regions, Northeast, Midwest, South, and West, each represented by a dummy variable. (a) Is age an important factor in the determination of earnings? Explain. (b) Why is a West dummy variable not included in the model? What would happen if it were? (c) Does there appear to be important regional differences in wages? (Perform a joint test of significance for the 3 regional dummy variables) 4EEP 118 / IAS 118 Elisabeth Sadoulet and Tania Barham University of California at Berkeley Fall 2004 Introductory Applied Econometrics Midterm examination Formulae Statistics Covariance between two variables in a population: cov x, y()=1nxi−x ()yi−y ()i∑ cov a1x + b1,a2y + b2()= a1a2cov x, y() var ax + by()= a2var x + b2var y + 2abcov(x, y) When y is a binary variable with probability prob(y = 1) = p(x), the variance conditional on x is p(x)(1– p(x)) OLS estimator ˆ β 1=cov x, y()varx with varˆ β 1()=σ2SSTx For multiple regression: varˆ β j()=σ2SSTj1 − Rj2() Adjusted R square: R 2= 1 −SSR / n − k −1()SST / n −1()= 1 −ˆ σ 2SST / n − 1() Test statistics: F statistic for q restrictions in a regression done with n observations and k exogenous variables: RUR2− RR2()q1− RUR2()n − k −1()~ Fn− k −1,q()