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1 Ecoomcs 3 Professor Spearot Itroducto to Ecoometrcs Fall 007 Fal Eam Name Fal Eam Verso A 80 Pots You must aswer all the questos. The eam s closed book ad closed otes. You ma use calculators, but the must ot be graphg calculators. Do ot use our ow scratch paper. You must show our work to receve full credt You have plet of tme to fsh. Take our tme ad rela. Ad, have a safe ad Happ Holda!. You have four kds that that wegh 50, 60, 70, ad 80 pouds. Ther respectve heghts are, 3, 4, ad 3 ft. a. What s the covarace betwee heght ad weght? (5 pots)

2 b. Suppose I estmate Heght β + Weght + u usg a dfferet sample (ot our aswer from a). The 0 β sample covarace of Heght ad Weght s 0. The sample varace of Weght s. What s the estmate of β? (5 pots). You wsh to predct the effects of educato, eperece, ad teure o wage outcomes. Specfcall, ou estmate the followg specfcato: The results from rug ths regresso are below: log( wage ) β 0 educ teure 3eper + u Source SS df MS Number of obs F( 3, 93) Model Prob > F Resdual R-squared Adj R-squared 0.54 Total Root MSE lwage Coef. Std. Err. t P> t [95% Cof. Iterval] educ teure eper _cos a. Do a two sded t-test at the 5% level to determe f eperece (eper) s a statstcall sgfcat determat of the log wage. Please state the ull ad alteratve hpotheses, ad terpret the result. (5 pots)

3 b. Perhaps ou ve heard the phrase, I was traed the school of hard kocks t s just as good as school. Wrte dow the hpothess that states that educato (educ) ad eperece (eper) have equal effects o the log wage. Also provde a two-sded alteratve. ( Pots) c. Please mapulate the regresso equato (a) so that our ull hpothess (b) ca be tested usg a t-test. Show our work!! (8 Pots)

4 Suppose that I adjust the specfcato (a) as follows, log( wage ) β 0 educ teure 3eper 4eper 5age 6age + u where age s the age of the respodet ( ears). Source SS df MS Number of obs F( 6, 98) 9.7 Model Prob > F Resdual R-squared Adj R-squared 0.53 Total Root MSE lwage Coef. Std. Err. t P> t [99% Cof. Iterval] educ teure eper eper age age _cos d. Please costruct a 99% cofdece terval for the coeffcet o teure, β. (5 pots)

5 e. What s the p-value for the lear eperece term (eper)? Please draw the dstrbuto uder the ull ad compute the two-sded p-value (please gve the rage ad a appromate value). (5 pots) f. Please test the hpothess that addg age, age, ad eper makes o dfferece predctg the log wage. That s, please test whether these varables are jotl sgfcat. Do ths at the 95% level, statg the ull ad alteratve hpotheses. (0 pots)

6 g. Professor Spearot wll be 9 Jauar. He feels old, though s shamelessl hopg that hs wage makes up for t. Assumg that he gas o addtoal eperece ad o addtoal teure, what s the predcted effect o the wage gog from age 8 to age 9? Iterpret brefl. (5 pots) h. At what eperece level s the wage mamzed? Show our work! (5 pots)

7 3. Suppose that I ru the followg regresso predctg the effects of caddate epedtures ad other factors o electo outcomes: votea β 0 lepeda lepedb 3prtstr + u I the regresso equato, lepeda s the log epedtures of caddate A, lepedb s the log epedtures of caddate B, ad prtstr s the relatve stregth of part A The results from rug ths regresso are below:. regress votea lepeda lepedb prtstra Source SS df MS Number of obs F( 3, 69) 5.3 Model Prob > F Resdual R-squared Adj R-squared Total Root MSE votea Coef. Std. Err. t P> t [95% Cof. Iterval] lepeda lepedb prtstra _cos a. Are the varables the model (lepeda, lepedb, ad prtstr) a sgfcat determat of the votes caddate A receves? Please test ths hpothess at the 95% level. Wrte the ull hpothess, the alteratve, ad brefl terpret the result. (5 Pots)

8 b. Suppose that Caddate A s Mke Gravel ad Caddate B s Mtt Rome. Mtt speds much more tha Mke. I wat to predct the outcome of ths hpothetcal race, ad produce cofdece tervals for ths predcto. Please wrte a equato for the predcto f lepeda (Mke), lepedb0 (Mtt), ad prtstra50 (ctzes hate both partes equall!!). Derve a ew estmatg equato to geerate the predcto ad ts stadard error. Please also wrte the ecessar commads to geerate a ew varables STATA. (0 Pots)

9 c. Suppose that as campag epedtures rse, uobserved factors affectg votg outcomes ted to become more varable. What kd of problem s ths? What should be doe about t? (5 Pots) d. Suppose that caddate A speds more moe because he/she has better deas, ad better deas get ou more votes. What assumpto s volated our curret model? I what drecto s β based? (5 Pots)

10 Etra Credt: Look back at the full model problem #. Age dscrmato s perceved to be commoplace Amerca socet. Age dscrmato occurs f there ests a age above whch wages go dow, depedet of other attrbutes (educato, eperece, teure). Usg the results Problem #, brefl dscuss whether there s evdece of age dscrmato. ( pots) Helpful formulas ( ) ( )( ) ( )( ) ( ) ( ) ( ) Fstat R 0 k q SST k R SST u SST R UR UR β β β σ σ σ ρ σ σ