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# INTR TO ECONOMETRICS ECON 4630

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This 10 page Class Notes was uploaded by Bethany Conn on Tuesday October 13, 2015. The Class Notes belongs to ECON 4630 at Louisiana State University taught by R. Hill in Fall. Since its upload, it has received 26 views. For similar materials see /class/223030/econ-4630-louisiana-state-university in Economcs at Louisiana State University.

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Date Created: 10/13/15

Econ 4630 Exam 1 Fall 2010 Appendix A B and Chapter 2 in Principles of Econometrics 3e 1 Answer each question in the space provided 2 In order to receive full credit you must answer fully and show all work 3 You may use simple calculators but no other electronic devices 4 There are 100 points possible Name 2 3 1 8g 1 A person s wages are affected by many factors Here we focus on the effect of experience More educated people earn higher wages so let us focus only on people with college degrees 16 years of education De ne EXPER30 EXPER730 where EXPER is years of education Let WAGE hourly wage rate In Exhibit 1 is the result of a regression of WAGE on EXPERSO The data are from 2008 20 la Interpret the estimated equation Page 3 15 lb For a person with exactly 30 years of experience EWAGE Bl Assume that m N Nb1 2653327 W S4121 T 0456264Z Calculate the probability that a randomly selected worker with 30 years experience will have WAGE gt 2700 per hour Draw a sketch illustrating the basis of your calculation 4 Page 15 1c The least squares estimator of the model described is not BLUE if the effect of experience on the expected wage rate is not the same for all levels of experience True or false Explain 5 3 i 1 8g 15 1d In Exhibit 2 are the least squares residuals from the tted regression in Exhibit 1 The center of the residuals is traced out using an adaptive curve Based on these residuals and your general knowledge of economics discuss the suitability of the model WAGE Bl BZEXPER30 8 Explain your reasoning and suggest any alternative models and why they might be better speci cations 6 3 1 8g 2 Chicken of the Sea and Bumble Bee are brands of canned tuna During a week a certain amount of advertising appears for these products There may be no advertising one form of advertising newspaper coupon or two forms coupon and a special store display Let C denote the level of advertising for Chicken of the Sea It can take the values c 0 l or 2 Let B denote the level of advertising of Bumble Bee B can take the values 17 0 l or 2 Suppose the following table represents the joint probability distribution of the advertising levels for these two brands of canned tuna B 0 1 2 0 05 05 05 C l 05 20 15 2 05 15 15 2a What is the eXpected value of C Show your work 7 Page 20 2b What is the conditional expectation of C given that 31 Show your work Discuss Why the concept of conditional expectation is so impo ant to econometiicians The Rules of Summation XX1XZ xw iana 4 mix y x 23 fan byaix Mix Zabx nabx H g x yjUMMfeyzfXy3 fxpytfxpyzfxpyz fxpytfxpyzfxjvyz Expected Values amp Variances Expectations Variances amp Covariances covX Y EX 7EXY7EY ZZXEXyEYfXv x y covX Y P W W EC XCZY C EXCZEY EX YEXEY varaXbYcZa2 varXb2 varYc2 varZ 2abcovXY ZaccovXZ 2bccovYZ IfX Y and Z are independent or uncorrelated random variables then the covariance terms are zero and varaXbYcZ a2 rarXb2 varY c2 varZ Normal Probabilities EXXfax2fx2 mm a wsz mankggn n Erg x g lt20 mg m 1 mm guvmampmnn EgxEgzX Ecc ECXCEX EacXacEX varX 52 EX7EX2 EX27 Em varacX EacXrEacXz c2 varX Marginal and Conditional Distributions x Zfxy for each valueX can take y fy Z x y for each value Y can take f X y PX Y fxy A y y If Y are independent random variables then fx y fxfy for each and every pair of values x and y The converse is also true X and Y are independent random variables then the conditional probability density inction of X given that Yy 39 f X f 00f y M ygt y f y values x andy The converse is also true f x for each and every pair of X N N01 U IfXNNp 51 then Z IfXNNUL oz anda is a constant then PX2aPzza 5 IfXNNu oz anda and b are constants then PangP gzbl U U Assumptions of the Simple Linear Regression Model S T e value of y for each value of x is y 3 32x e SR2 The average value ofthe random error e is Ee 0 since We assume that Ey 3 32x SR3 The variance of the random error e is vare oz vary SR4 The covariance between any pair of random errors 2 and e is coveeJ covyyJ 0 SR5 The variable x is not random and must take at least two different values SR6 optional The values of e are normally dimibuted about their mean 2 N N0 57 Least Squares Estimation Ifbl and b2 are the least squares estimates then 9 b bzx y 9 y 1 4 The Normal Equations Nb Zxbz Zy 2m 2 2w Least Squares Estimators b zltx mo 77 2 20 5 7 53927 Elasticity 7 percentage change inyi Ayy i i 7 percentage change inxi Axx 7 Ax y n AEyEy AEy x Axx Ax Ey L E y Least Squares Expressions Useful for Theory 122 a 2 we w Z X 7 2ma Zna JZMV2M35 Properties of the Least Squares Estimators varltbgtcz L2 may NEW 2 L 20 7 cov b b oz I Z x I GaussiMarkov Theorem Under the assumptions SRlSRS of the linear regression model the estimators b1 and b2 have the smallest variance of all linear and unbiased estimators of 31 and 2 They are the est Linear aniased Estimators BLUE of 31 and a IfWe make the normality assumption assumption SR6 about the r term then e least squares estimators are normally distributed 2 2 2 b NN mix 7 bZNN 3275 2 NZ x e x Z x 7 7 Estimated Error Variance g3 N72 Estimator Standard Errors seb varb sea W tidistribution If assumptions SRlSR 6 of the simple linear regression model hold then i4 k 12 sea lter v Interval Estimates Pb2 itcseb2 g 32 b2 tcseb2 1 r a Hypothesis Testing Components of Hypothesis Tests A null hypothesis Hg An alternative hypothesis H A test statistic A rejection region Ifthe null hypothesis Hg 32 c is true then b 7c t2 Nt 564 OH Rejection rule for a twoitail test Ifthe value of the test statistic falls in the rejection region either tail ofthe tdistribution then We reject the null hypothesis and accept the alternative Type I errorThe null hypothesis is true and We decide to reject it Type II errorThe null hypothesis is false and We decide not to reject it Rejection rule for a twoitail test When theyvalue of a hypothesis test is smaller than the chosen value of a then the test procedure leads to rejection of the null hypothesis Prediction ya liw zxweu n 5 52 farm in WEIL sef1viaf N Emix 2 A lugtlt100 con dence interval or prediction interval for yu t sef yuic Goodness of Ht 204 n W ZOI 7 2 SST SSR SSE SSR SSE A R2 li corryy2 LogiLinear Model lny 3 13 1RD b 19 32 2 percentage change in y given oneunit change in x 3 exp b bzx f1 exp b bzx exp 692 Prediction interval expW r tcse expW tcsef A 2 Generalized Goodness of t measure R corry yW Assumptions of the Multiple Regression Model MR1 yi31i32 2 Hiya MR2 EyBlBZXZ quotWAKQWQFO MM vary vare oz MR4 covy yj cove ej 0 MRS The values ofxk are not random and are not exact linear inctions of the other explanatory variables MR6 yNNB32xZ 3KgkozltgteNN0oz Least Squares Estimates in MR Model Least squares estimates bb2 bk minimize 303va 74302101 r r quot kxm Estimated Error Variance and Estimator Standard Errors 2 28 m sea varltbkgt Example PZ173 c1gt173 9582 Table 1 Cumulative Probabilities for the Standard Normal Distribution ltIgtzPZ z z 000 001 002 003 004 005 006 007 008 009 00 05000 05040 05080 05120 05160 05199 05239 05279 05319 05359 01 0 5398 0 5438 0 5478 0 5517 0 5557 0 5596 0 5636 0 5675 0 5714 0 5753 02 05793 05832 05871 05910 05948 05987 06026 06064 06103 06141 0 3 0 6179 0 6217 0 6255 0 6293 0 6331 0 6368 0 6406 0 6443 0 6480 0 6517 04 0 6554 0 6591 0 6628 0 6664 0 6700 0 6736 0 6772 0 6808 0 6844 0 6879 05 06915 06950 06985 07019 07054 07088 07123 07157 07190 07224 06 07257 07291 07324 07357 07389 07422 07454 07486 07517 07549 07 07580 07611 07642 07673 07704 07734 07764 07794 07823 07852 08 07881 07910 07939 07967 07995 08023 08051 08078 08106 08133 0 9 0 8159 0 8186 0 8212 0 8238 0 8264 0 8289 0 8315 0 8340 0 8365 0 8389 10 0 8413 0 8438 0 8461 0 8485 0 8508 0 8531 0 8554 0 8577 0 8599 0 8621 11 0 8643 0 8665 0 8686 0 8708 0 8729 0 8749 0 8770 0 8790 0 8810 0 8830 12 0 8849 0 8869 0 8888 0 8907 0 8925 0 8944 0 8962 0 8980 0 8997 0 9015 13 09032 09049 09066 09082 09099 09115 09131 09147 09162 09177 14 0 9192 0 9207 0 9222 0 9236 0 9251 0 9265 0 9279 0 9292 0 9306 0 9319 15 0 9332 0 9345 0 9357 0 9370 0 9382 0 9394 0 9406 0 9418 0 9429 0 9441 16 0 9452 0 9463 0 9474 0 9484 0 9495 0 9505 0 9515 0 9525 0 9535 0 9545 17 0 9554 0 9564 0 9573 0 9582 0 9591 0 9599 0 9608 0 9616 0 9625 0 9633 18 0 9641 0 9649 0 9656 0 9664 0 9671 0 9678 0 9686 0 9693 0 9699 0 9706 19 0 9713 0 9719 0 9726 0 9732 0 9738 0 9744 0 9750 0 9756 0 9761 0 9767 2 0 0 9772 0 9778 0 9783 0 9788 0 9793 0 9798 0 9803 0 9808 0 9812 0 9817 21 0 9821 0 9826 0 9830 0 98M 0 9838 0 9842 0 9846 0 9850 0 9854 0 9857 2 2 0 9861 0 9864 0 9868 0 9871 0 9875 0 9878 0 9881 0 9884 0 9887 0 9890 23 09893 09896 09898 09901 09904 09906 09909 09911 09913 09916 24 0 9918 0 9920 0 9922 0 9925 0 9927 0 9929 0 9931 0 9932 0 9934 0 9936 2 5 0 9938 0 9940 0 9941 0 9943 0 9945 0 9946 0 9948 0 9949 0 9951 0 9952 2 6 0 9953 0 9955 0 9956 0 9957 0 9959 0 9960 0 9961 0 9962 0 9963 0 9964 27 0 9965 0 9966 0 9967 0 9968 0 9969 0 9970 0 9971 0 9972 0 9973 0 9974 2 8 0 9974 9975 0 997 9977 0 9977 0 9978 0 9979 0 9979 0 9980 0 9981 2 9 0 9981 0 9982 0 9982 0 9983 0 9984 0 9984 0 9985 0 9985 0 9986 0 9986 0 9988 0 9989 0 9989 0 9989 0 9990 0 9990 3 0 0 9987 0 9987 0 9987 0 9988 Source This table was generatedusmg the SAS fund on PROBNORM

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