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Final ExamECON 3210 O: Use of Economic DataLaura SalisburyYork UniversityApril 16, 2014This exam contains 7 questions and 12 pages (including this one), for a total of 108 points.Read questions carefully, and answer all questions in the booklets provided.Formulas andtables are provided on the last 5 pages of the exam. You may use a calculator. You have 180minutes. Good luck!1
1. For each of the following, indicate whether the statement is true or false.Explain youranswers(a)(4 pts)Econometric forecasting is more accurate for values of explanatory variablesthat are closer to the sample mean.True. Forecasts based on values ofxthat are far away from the sample mean havea larger variance. Intuitively, we are better able to forecast based on values ofxwehave better information about, i.e. values that are close to the sample mean.(b)(4 pts)Linear regression models are flawed because it is impossible for them tocapture nonlinear relationships between variables.False.It is possible to approximate nonlinear relationships between variable in alinear regression by including polynomial terms or logs.(c)(4 pts)In the presence of heteroskedasticity, least squares estimates are biased.False. In the presence of heteroskedasticity, conventional standard errors for coef-ficient estimates are not appropriate; however, the coefficient estimates themselvesare still unbiased.(d)(4 pts)You are testing a null hypothesis, and the p-value associated with your testis 0.025. You should only reject the null hypothesis if you are willing to accept aprobability of type I error of 2.5% or greater.True. If the p-value is 0.025, you rejectH0for tests at the 2.5% level or greater.The size of the test is exactly the probability of type I error you are willing to accept.2. You are estimating the following regression equation:y=β1+β2x2+β3x3+e2
You are given the following information:R2= 0.4631R2= 0.4233NXi=1(yi-y)2= 1425.68NXi=1x22i= 855.17NXi=1x23i= 1252.33x2= 4.252x3= 86.71r23=-0.676(a)(4 pts)Calculate the sum of squared errors (SSE).You are givenR2= 0.4631, andSST≡∑Ni=1(yi-y)2= 1425.68.So, use theformula forR2and solve for SSE:R2= 1-SSESST⇒0.4631 = 1-SSE1425.68⇒SSE= 765.4476(b)(4 pts)Calculate N.Use the SSE calculated in part (a),R2, and SST to solve for N:R2= 1-SSE/(N-K)SST/(N-1)⇒0.4233 = 1-765.4476/(N-3)1425.68/(N-1)⇒N= 30(c)(4 pts)Calculate the standard error ofb2.You know that∑(x2i-x2)2=∑x22i-Nx22= 855.17-30(4.252)2= 312.785. And,becauser23=-0.676, it follows that1-r223= 1-(-0.676)2= 0.543. Finally, we3
know thatˆσ2=SSEN-K= 765.4476/(30-3) = 28.350. So:\var(b2) =ˆσ2(1-r223)∑(x2i-x2)2=28.3500.543(312.785)= 0.1669Then,se(b2) =q\var(b2) = 0.4086.3. Sean the econometrician is studying the effect of the price of flour on the price of crois-sants. He is also interested in how the price of butter affects the price of croissants. Heestimates the following regression models:CR=β1+β2FL+e(1)CR=β1+β2FL+β3BU+e(2)CR is the price of croissants (in dollars), FL is the price per pound of flour (in cents),and BU is the price per pound of butter (in dollars). Sean obtains the following results,