University of California at Berkeley Fall Introductory Applied Econometrics Final examination

Transcription

1 SID: EEP 118 / IAS 118 Elsabeth Sadoulet and Daley Kutzman Unversty of Calforna at Berkeley Fall 01 Introductory Appled Econometrcs Fnal examnaton Scores add up to 10 ponts Your name: SID: 1. (15 ponts) Suppose you estmate the followng model: energy = hhsze +.46 ncome +8 stove (3.) (1.6) (1.03) (.6) (standard errors n parentheses) where energy s a household s monthly energy bll (n $), hhsze s the number of members n a household, ncome s a households annual ncome (n $1000), and stove s a dummy varable ndcatng that the household owns a stove. a. Interpret the estmated effect of ncome on energy expendtures b. Rewrte the estmated equaton wth the dependent varable, energy, n unts of $10. (You can fgure out what the estmated coeffcents are wthout runnng a new regresson.) c. Now rewrte the estmated equaton wth the dependent varable, energy, n unts of $10 and ncome n unts of $100.. (15 ponts) An equaton for the revenue of a store s estmated from 35 weekly observatons on revenue (n $1,000) and ts expendtures n advertsng (n $1,000): revenue = ˆβ0 + ˆβ 1 advertsng = advertsng R = 0.55 n = 35 (6.5) (0.44) (standard errors n parentheses) a. Test (at the 5% sgnfcance level) that the coeffcent on advertsng s equal to 1 aganst the alternatve that t s greater than 1. b. What does a coeffcent on advertsng greater than 1 mean n terms of the effcency of advertsng expendtures? c. The return to advertsng sθ = β 1 1. Construct and nterpret a 95 % confdence nterval for the return to advertsng. 3. (15 ponts). Followng are the results of two estmatons for the wage of college students, where lwage s log hourly wage, college s the number of credts completed at college, exper s years of work experence, black =1 f Afrcan-Amercan, hspanc = 1 f Hspanc, and whte =1 f nether Afrcan-Amercan or Hspanc. The output s on page 1 of the exam. a. Test the hypothess at the 5% level that there s no race effect n wage determnaton? b. How do the wages of Hspanc workers compare to the wages of whte workers, and of Afrcan-Amercan workers? c. How would you set up an equaton that wll gve you the standard error on the dfference n predcted wage between Hspanc and Afrcan-Amercan workers of same educaton and experence? 1

2 SID: 4. (5 ponts) Suppose you have a random sample of people n the U.S. wth data on the average number of hours they sleep each week, and ther age n years. You obtan the followng regresson results wth ths data: (1) sleep = ln ( age ) R = 0.1 Instead, a colleague of yours tres a quadratc functonal form and obtans the followng results: () sleep = age +.55age R = 0.39 Your colleague argues that the nformaton above s enough to conclude that her regresson, model (), s a better ft. Is ths correct? Explan why or why not. 5. (10 ponts) If a youth who s less than 18 years old commts an offense, the case s sent to the more lenent juvenle courts. However, f a youth commts an offense after hs/her 18 th brthday, the case s sent to the much harsher adult crmnal court. You have a cross-sectonal data set of youths of ages 16-0 n Florda n 005. Ths data set ncludes the brthday, gender, famly ncome, and whether or not the youth had been arrested for commttng an offense. a. How would you estmate the causal effect of harsher punshments on the probablty of commttng a crme? Be sure to wrte down the exact regresson you would run and defne each varable n your regresson. State whch coeffcent wll gve you the estmated causal effect. (You can use a lnear probablty model here, for smplcty.) b. What key assumpton do you need to make for your regresson n part a. to estmate the causal effect of harsher punshments on the probablty of commttng a crme? 6. (0 ponts) Usng monthly data on the revenue generated by vsts to a regonal park, you estmated the followng model over 4 years of data: Revenue t = 35Jant +15Feb t + 4Mar t + 34Apr t + 43May t + 65Jun t + 75July t + 45Aug t +34Sep t + 7Oct t +15Nov t + 5Dec t 1. p t 0.5p t 1 0.3p t where Revenue t s the revenue n US$1000 and p t s the gasolne prce n $/gallon for the observed months t =1,,..., 48. a. What s the predcted revenue n a month of February when the prce of gasolne s stable at $3/gallon? b. Why do you need to add monthly dummy varables to measure the effect of gasolne prce on revenue? c. Suppose the prce of gasolne suddenly ncreases by 50c n a month of June and then returns to ts ntal level n July. What s the predcted effect on revenues n June, July, August, and September? d. Suppose now that the ncrease n prce s permanent. What s the predcted effect on revenues n June, July August, and September? 7. (10 ponts) The followng two wage equatons have been estmated for textle ndustry workers n Bangladesh: log(wage) = male experence 0.005male*experence (.48) (0.05) (0.005) (0.00) n whch the dependent varable s the log of the hourly wage n US$, and the explanatory varables are a male dummy and years of experence. Numbers n parentheses are standard errors. a. Draw a graph that shows the estmated log(wage) as a functon of experence for male. Add on the same graph the estmated log(wage) as a functon of experence for female. Remember to label your axes as well as all ntercepts and slopes. b. Dscuss the graph,.e., explan how the wages of women compare to the wages of men from the tme they start to work to when they have more experence.

3 SID: 8. (15 ponts) Below (reported on page 13 of the exam) are two logt estmatons on whether a buyer purchased ecolabeled apple. The second estmaton ncludes 4 demographc varables (numlt5 num5_17 num18_64 numgt64) that are not ncluded n the frst equaton. a. Usng the frst equaton, nterpret how the purchase of ecolabeled apples responds to the prces of the regular apples. b. Usng the frst equaton, dscuss how the gender of the buyer nfluences the estmated probablty of the purchase of ecolabeled apples. c. Test for the jont sgnfcance of the four demographc varables. 9. (15 ponts) You want to measure the effect of a school constructon program that took place n some dstrcts (called Treated) but not n other (called Control). You observe the average level of educaton of cohorts that were too old to beneft from the program and that of younger cohorts that were of school age after the completon of the constructon program: Average level of educaton (n years) Treated dstrcts Control dstrcts Older cohorts Younger cohorts a. What does the comparson of the treated and control dstrcts tell you about the placement of the school constructon program? b. Whch method could you use to estmate the mpact of the school constructon program on the level of educaton? What s the key assumpton for ts valdty? c. What s the mpact of the school constructon program on the level of educaton? Wrte an equaton that wll allow you to obtan a standard error on ths estmated mpact. 3

4 Formulae Statstcs and mscellaneous Covarance between two varables n a populaton: = a 1 a cov( x, y) = var x + var y + cov(x, y) cov a 1 x + b 1, a y + b var x + y = 1 ( x x )( y y ) n cov x, y When y s a bnary varable wth probablty prob(y = 1) = p(x), the varance condtonal on x s p(x)(1 p(x)) For small values of x: e ax 1 + ax OLS estmator ˆβ 1 = cov ( x, y ) var x wth var ( ˆβ1 ) = σ SST x wth heteroskedastcty: For multple regresson: var ( ˆβ j ) = var ( ˆβ1 ) = σ SST j 1 R j ( x x ) SST x σ Adjusted R square: R = 1 SSR / n k 1 ˆσ = 1 SST / n 1 SST / n 1 E e log ( y +u ) = elog y e σ / Test statstcs: Loglkelhood rato statstc for q restrctons: LR = ( Loglkelhood UR Loglkelhood R ) ~ χ q F statstc for q restrctons n a regresson done wth n observatons and k exogenous varables: R R ( R UR ) q ( 1 R UR ) n k 1 ~ F ( q,n k 1 ) Chow statstc: F = SSR SSR + SSR P 1 q ( SSR 1 + SSR ) [ n K 1] where SSR p s the sum-square errors of the pooled estmaton, SSR 1 and SSR are sum-square errors of the two separate estmatons. 4

5 Exercse 4.. reg lwage college exper Source SS df MS Number of obs = F(, 197) = Model Prob > F = Resdual R-squared = Adj R-squared = Total Root MSE =.4198 lwage Coef. Std. Err. t P> t [95% Conf. Interval] college exper _cons reg lwage college exper black hspanc Source SS df MS Number of obs = F( 4, 195) = 19.7 Model Prob > F = Resdual R-squared = Adj R-squared = Total Root MSE =.4170 lwage Coef. Std. Err. t P> t [95% Conf. Interval] college exper black hspanc _cons

6 Exercse 8 The varables are: ecobuy =1 f buyer purchased ecolabeled apples regprc prce of regular apples (n $/lb) ecoprc prce of ecolabeled apples (n $/lb) male =1 f buyer s male numlt5 # n household younger than 5 num5_17 # n household 5 to 17 num18_64 # n household 18 to 64 numgt64 # n household older than 64. logt ecobuy regprc ecoprc male Iteraton 0: log lkelhood = Iteraton 1: log lkelhood = Iteraton : log lkelhood = Iteraton 3: log lkelhood = Iteraton 4: log lkelhood = Logstc regresson Number of obs = 660 LR ch(3) = Prob > ch = Log lkelhood = Pseudo R = ecobuy Coef. Std. Err. z P> z [95% Conf. Interval] regprc ecoprc male _cons mfx Margnal effects after logt y = Pr(ecobuy) (predct) = varable dy/dx Std. Err. z P> z [ 95% C.I. ] X regprc ecoprc male* (*) dy/dx s for dscrete change of dummy varable from 0 to 1. logt ecobuy regprc ecoprc numlt5 num5_17 num18_64 numgt64 male Iteraton 0: log lkelhood = Iteraton 1: log lkelhood = Iteraton : log lkelhood = Iteraton 3: log lkelhood = Logstc regresson Number of obs = 660 LR ch(7) = Prob > ch = Log lkelhood = Pseudo R = ecobuy Coef. Std. Err. z P> z [95% Conf. Interval] regprc ecoprc numlt num5_ num18_ numgt male _cons