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Unformatted text preview: 139Spring 09 FINALName ..................................................................DO NOT TURN OVER UNTIL TOLD TO DO SONotes:1. Use a calculator where necessary.2. Show your work, place your answers in the spaces provided and make use of the cheat sheet.3. If you want to make any additional assumptions to simplify a problem, please state them clearly.4.Keep verbal answers concise(no more than 4 sentences, and bullet points are &ne).Guide:There are 126 points and you have 150 minutes.Q1 and Q2 are short.Q3 is on treatment e/ects and part (e) contains proofs.Q4 is on IV.The questions can be done in any order.Good Luck and Enjoy the Summer.11. [18 points] You are working as an intern for a local bank. As part of a costcutting exercise,they want to know how many minutes it takes a teller to serve a customer. This type of duration datais commonly modeled using an exponential distribution. The pdf for a duration of lengthyiisf(yij&) =1&e&yi&foryi&and& >where&is the single parameter.(a) [4 points] Suppose that&= 1. Sketch the pdf on the axes below, marking the values of thepdf fory= 0; y= 1andy= 2.f(y)y12f(y)y12(b) You want to estimate the parameter&using maximum likelihood and a random sample ofNobservations from local branches.(i) [4 points] What is the joint probability of the observed data given&?2(ii) [4 points] Show that the loglikelihood is&Nlog(&)&PNi=1yi&(iii) [4 points] Derive the ML estimator of&(don&t worry about the secondorder condition).(iv) [2 points]N= 200;PNi=1yi= 424:3;PNi=1y2i= 1985:8. Calculate the ML point estimate of&.32. [16 points] You get data on a sample of students graduating from high school, together withan indicator for whether they will attend college in the Fall. You estimate probit models for whetherthey will go to college, as a function of individual and highschool characteristics. There are two speci&cations: one with high school characteristics and one without. Standard errors are in parentheses.(1)(2)Dep VarGo to CollegeGo to CollegeParental Income:04:03($000s)(0:01)(0:01)Number of Siblings (count)&:42&:27(0:20)(0:14)At least One Parent:95:90Attended College (Dummy)(0:34)(0:31)Private High School:80(Dummy)(0:23)Religious High School&:34(Dummy)(0:15)Constant&2:80&2:75(0:95)(0:85)Loglikelihood&4;300:78&4;280:78(a) [4 points] Based on the speci&cation in column (1) what is the predicted probability of attendingcollege for someone with no siblings, a parental income of $100,000 and parents who attended college.(b) [6 points] Perform a likelihood ratio test for whether the school characteristics are jointlysigni&cant at the 1% level. Show your working (i.e., the test statistic, the distribution used and thecritical value) clearly....
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 Spring '08
 ALESSANDROTAROZZI
 Econometrics, Regression Analysis, Trigraph, ........., Estimation theory, zi

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