A dummy variable equal to 1 if the nearby school is in regular session and 0 otherwise;

Transcription

1 Lehrstuhl für Betrebswrtschaftslehre, Emprsche Wrtschaftsforschung Otto-von-Guercke-Unverstät Magdeburg, Postfach 410, Magdeburg Prof. Dr. Dr. Bodo Vogt Otto-von-Guercke-Unverstät Magdeburg Fakultät für Wrtschaftswssenschaft Vlfredo-Pareto-Gebäude (G), A-344 Unverstätsplatz Magdeburg Telefon: +49-(0) Telefax: +49-(0) Fnancal Econometrcs Summer Semester 01 Exercse Sheet I Hypotheses Testng Problem 1: Develop approprate hypotheses for each slope coeffcent n the followng equaton, and then calculate t-scores and test the null hypothess at 5% sgnfcance level (standard errors are reported n parentheses): Yˆ t t t t 15.1 (0.7) (0) (108) (138.3) N=9 =0.78 Y Number of yogurts sold durng perod t; t Average temperature durng perod t; 1t t 3t Prce of a yogurt; A dummy varable equal to 1 f an ad s posted n the newspaper and 0 otherwse; A dummy varable equal to 1 f the nearby school s n regular sesson and 0 otherwse;

2 Choosng the Independent Varables Problem : Assume you want to study the determnants of smokng behavor n the US and that you estmate the followng cross-sectonal model based on data from 1988 for all 50 states (standard errors n parentheses): Cˆ 100 9E I 0.04T 3V 1.5 t (3) (1) (0.04) (1) (0.5) t-score: =0.50 N=50 (states) C The number of cgarettes consumed per day per person n the -th state; E The average number of years of educaton for persons over 1 n the -th state; I The average ncome n the -th state (thousands of dollars); T The tax per package of cgarettes n the -th state (cents), V The number of vdeo ads aganst smokng ared on the three major networks n the -th state; The number of rado ads aganst smokng ared on the fve largest rado networks n the -th state, a) Develop and test (at 5 percent level) approprate hypotheses for the coeffcents of the varables n ths equaton. b) Do you appear to have any rrelevant and/or omtted varables? Explan your answer. c) Let s assume that your answer to part b was yes to both. Whch problem s more mportant to solve frst, rrelevant varables or omtted varables? Why? d) One of the purposes of runnng the equaton was to determne the effectveness of antsmokng advertsng on televson and rado. What s your concluson? e) You decde that tax rates are rrelevant to cgarette smokng and you therefore drop t from the equaton. Gven the followng results, use the four specfcaton crtera to decde whether tax rates are ndeed rrelevant. Explan your reasonng. Cˆ E I 3.5V 1.6 (3) (0.9) (1) (0.5) =0.50 N=50 (states)

3 Problem 3: The managers of a fast food company want to run a regresson n order to decde where to buld ther next fast food store. They collect nformaton from the 30 exstng stores and run a regresson on the sales of each of the stores as a functon of several factors characterzng locaton n order to predct whch of the consdered locatons for the new store wll maxmze ther sales. The followng equaton s estmated (standard errors n parentheses): Yˆ (0.0) (0.01) (10) (1) Y Average daly sales (n hundreds of dollars) of the -th store; The number of cars that pass the -th locaton per hour; 1 Average ncome n the area of the -th store; The number of tables n the -th store; 3 The number of competng shops n the area of the -th store; 4 a) Hypothesze expected sgns, calculate the correct t-scores, and test the sgnfcance at the 1 percent level for each of the coeffcents. b) What problems appear to exst n the equaton? What evdence of these problems do you have? c) What suggeston would you make for a possble second run of ths admttedly hypothetcal equaton? (Hnt: Before recommendng the ncluson of a potentally left-out varable, consder whether the excluson of the varable could possbly have caused any observed bas). Problem 4: Assume you are a manager of an nstant oatmeal company and you have to decde whether to rase prces for next year. You decde to buld a model of the mpact of prce on sales, and you estmate the followng equaton (standard errors n parentheses): Yˆ t 1t t 3t (0) (6) (10) (0.0005) t-score: =0.78 N=9 (annual model) Y t Sales of nstant oatmeal produced by your company n year t; Prce of nstant oatmeal produced by your company n year t; 1t Prce of the competng nstant oatmeal n year t; t Advertsng of your nstant oatmeal; 3t Dsposable ncome n year t; 3

4 a) Create and test approprate hypotheses about the slope coeffcents of ths equaton at the 5 percent level. b) What econometrc problems, f any, appear to be n the equaton? Do you see any ndcatons that there s an rrelevant varable? Explan. c) If you could add one varable to ths equaton, what would t be? Explan your answer. d) Suddenly you realze that you have made a mstake. What s t? Multcollnearty Problem 5: You want to reduce damage done to dorms by rowdy students and you therefore buld a crosssectonal model of last term s dorms damage to each dorm as a functon of the attrbutes of that dorm (standard errors n parentheses). Yˆ (53) (0.75) (1.4) =0.84 N=33 Y The amount of damage (n dollars) done to the -th dorm last term; The percentage of the -th dorm resdents who are frst-semester students; 1 The number of students who lve n the -th dorm; 3 The number of ncdents nvolvng alcohol n the -th dorm last term (ncdents nvolvng alcohol may or may not nvolve damage to the dorm); a) Hypothesze sgns, calculate t-scores, and test hypotheses for ths result (5 percent level). b) What problems (omtted varables, rrelevant varables, or multcollnearty) appear to exst n ths equaton? Why? c) Suppose you were now told that the smple correlaton coeffcent between and 0.94; would that change your answer? How? d) Is t possble that the unexpected sgn of Why? 3 was ˆ could have been caused by multcollnearty? Problem 6: A cross-sectonal regresson was run on a sample of 44 states n an effort to understand federal defense spendng by state (standard errors n parentheses): Yˆ (0.07) (0.1664) (0.009) Y Annual spendng (mllons of dollars) on defense n the -th state; 4

5 1 Contracts (mllons of dollars) awarded n the -th state per year; Annual payroll (mllons of dollars) for workers n defense-orented ndustres n the -th state; The number of cvlans employed n defense-orented ndustres n the -th state; 3 a) Hypothesze sgns, calculate t-scores, and test hypotheses for ths result (5 percent level). b) The VIFs for ths equaton are all above 0, and those for 1 and are above 30. What concluson does ths nformaton allow you to draw? c) What recommendaton would you make for a rerun of ths equaton wth a dfferent specfcaton? Explan your answer. Problem 7: Calculatng VIFs (varance nflaton factors) typcally nvolves runnng sets of auxlary regressons, one regresson for each ndependent varable n an equaton. a) Consder the followng regresson model: Y ˆ Wrte each ndependent varable as a functon of the other ndependent varables (create three auxlary regressons).. Assume that the coeffcents of determnaton equatons are as follows: 1 =1.46, =0.6, (=1,, 3) for each of the three auxlary 3 = Calculate the correspondng VIFs.. Analyze the degree of multcollnearty by evaluatng the sze of VIF( ˆ ). b) Calculate the VIF for 1 n an equaton where 1 and are the only ndependent varables, gven that the VIF for s 3.8 and N=8. c) Calculate the VIF for 1 n an equaton where t s the only ndependent varable, gven that the smple correlaton coeffcent between 1 and Y s 0.80 and N=15. Seral Correlaton Problem 8: After GLS has been run on an equaton, the ˆ s are stll good estmates of the orgnal (nontrasformed) equaton except for the constant term: a) What must be done to the estmate of the constant term generated by GLS to compare t wth the one estmated by OLS? b) Why s just an adjustment necessary? c) Consder the followng regresson equaton (after GLS): 5

6 Yˆ t 1t t 3t ˆ 0.80 Calculate the ˆ 0 that would be comparable to the one n a nontransformed equaton. d) The two estmates are dfferent. Why? Does such a dfference concern you? Problem 9: Consder the followng equaton for US per capta consumpton of beef (standard errors n parentheses): Yˆ ln t 1t t 3t (7.4) (0.13) (0.1) (4.1) t-score: =0.7 N=8 DW=0.94 Y The annual per capta pounds of beef consumed n the US n year t; t ln The log of real per capta dsposable ncome n the US n 198 dollars n year t; t 3t 1t Average annualzed real wholesale prce of beef n year t (n cents per pound); Average annualzed real wholesale prce of pork n year t (n cents per pound); A dummy varable equal to 1 for years after 1981, 0 otherwse (an attempt to capture the ncreased consumer awareness of the health dangers of red meat); a) Develop and test your own hypotheses wth respect to the ndvdual estmated slope coeffcents. b) Test for seral correlaton usng the Durbn-Watson d test at the 5 percent level. c) What econometrc problem(s) (f any) does the above equaton appear to have? What remedy would you suggest? d) You take your own advce, and apply the GLS to the above equaton, obtanng (standard errors n parentheses): Yˆ ln t 1t t 3t (14.1) (0.10) (0.09) (3.9) t-scores: = N=8 ˆ =0.8 Compare the two equatons. Whch do you prefer? Why? 6