ARE106SU09HW5KEY

# ARE106SU09HW5KEY - University of California Davis...

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University of California, Davis Managerial Economic(ARE) 106, Summer 2009 Instructor: John H. Constantine KEY —Problem Set #5: Due THURSDAY, September 3, 2009 Problem 1 : You are to run SHAZAM for this problem. Assume α = 0.05 . Annual data on new housing units and their determinants housing = total new housing units started, in thousands pop = U.S. population in millions gnp = gross national product in constant 1982 dollars in billions unemp = unemployment rate in % among all workers intrate = new home mortgage yields, FHLBB, in % sample 1 23 read(are106/DATA4-3) year housing pop gnp unemp intrate ols housing pop gnp unemp intrate stop (a) What is the PRF implied by the SHAZAM command file give above? housing t = β 1 + β 2 pop t + β 3 gnp t + β 4 unemp t + β 5 intrate t + e t . (b) What signs do you expect on each coefficient, a priori. Briefly explain why this is so. β 2 > 0. As population increases, we expect housing starts to increase. β 3 > 0. As GNP, or national income, increases, we expect housing starts to increase. β 4 < 0. As the unemployment rate increases, we expect housing starts to decrease. β 5 < 0. As the interest rate increases, we expect housing starts to decrease. (c) For each right-hand side determinant, you are to conduct a t-test on whether each determinant contributes to new housing starts. Provide a brief interpretation of each determinant’s effect on housing starts. There are four hypothesis tests—H 0 : β K = 0 vs. H 1 : β K 0 for K = 2, …, 5. Only b 5 is statistically significant. The interpretation here is that if interest rates increase by 1%, we expected housing starts to fall by 174,690 units (on average.) The other estimated coefficients are not statistically significant and thus we cannot reject that their corresponding β K = 0. That is, these results imply that population, gross domestic product, and the unemployment do not contribute to housing starts. This is not what one might expect, but it is likely that there is a fair amount of multicollinearity in this model. (e) Test the overall significance of the model. State H 0 , the estimated F and the critical F, and make your conclusion.

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SHAZAM OUTPUT -----------------------------307381472631283 Content-Disposition: form-data; name="IX"; filename="hw5_prob01.txt" FILE UPLOAD (120 CHARS MAX) FOR: Content-Type: text/plain ********************************************************************* Hello/Bonjour/Aloha/Howdy/G Day/Kia Ora/Konnichiwa/Buenos Dias/Nee Hau/Ciao Welcome to SHAZAM - Version 10.0 - JUL 2004 SYSTEM=LINUX PAR= 781 |_sample 1 23 |_read(are106/DATA4-3) year housing pop gnp unemp intrate UNIT 88 IS NOW ASSIGNED TO: are106/DATA4-3 6 VARIABLES AND 23 OBSERVATIONS STARTING AT OBS 1 |_ols housing pop gnp unemp intrate R-SQUARE = 0.4499 R-SQUARE ADJUSTED = 0.3277 VARIANCE OF THE ESTIMATE-SIGMA**2 = 80237. STANDARD ERROR OF THE ESTIMATE-SIGMA = 283.26 SUM OF SQUARED ERRORS-SSE= 0.14443E+07 MEAN OF DEPENDENT VARIABLE = 1601.1 LOG OF THE LIKELIHOOD FUNCTION = -159.683 ANALYSIS OF VARIANCE - FROM MEAN SS DF MS F REGRESSION 0.11814E+07 4. 0.29536E+06 3.681 ERROR 0.14443E+07 18. 80237. P-VALUE TOTAL 0.26257E+07 22. 0.11935E+06 0.023 ANALYSIS OF VARIANCE - FROM ZERO SS DF MS F REGRESSION 0.60142E+08 5. 0.12028E+08 149.911 ERROR 0.14443E+07 18. 80237. P-VALUE TOTAL 0.61587E+08 23. 0.26777E+07 0.000 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 18 DF P-VALUE CORR. COEFFICIENT
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ARE106SU09HW5KEY - University of California Davis...

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