Econ 120B Ramu RamanathanSpring 1998 First Midterm (20%)Your name (please print it) ___________________________________Your Student Id. (NOT Soc. Sec. no.)____________________________DO NOT TURN THE PAGE UNTIL EVERYONE HAS RECEIVEDTHE EXAM AND YOU ARE GIVEN THE SIGNAL TO START.ALSO, YOU MUST STOP WRITING WHEN YOU ARE ASKEDTO DO SO (YOU WILL BE GIVEN A 2 MINUTE WARNING).TEN POINTS WILL BE DEDUCTED FOR EACH MINUTE OFEXTRA TIME IT TAKES YOU TO STOP WRITING.If you use a pencil, you forfeit the right to complain about gradingUNLESS YOU PICK UP THE EXAM FROM THE TA FROMHIS/HER OFFICE AND LOOK AT THE GRADING BEFORELEAVING THE OFFICE.Make sure that all pages (1 through 5) are there. Read the questionscarefully and make sure that you do not misunderstand them. If youget stuck somewhere, don’t waste time but move on.IN THE HYPOTHESIS TESTING PARTS, DON’T ASK MEWHETHER THE TEST IS ONE-SIDED OR TWO-SIDED. YOUHAVE TO FIGURE THAT OUT FOR YOURSELF FROM THEINFORMATION PROVIDED.I CONSIDER CHEATING AS A VERY SERIOUS MATTER ANDWILL GIVE AN F IN THE COURSE TO ANY ONE CHEATINGAND ALSO REFER HIM/HER TO THE DEAN FORDISCIPLINARY ACTION.MAXIMUM NUMBER OF POINTS = 70- 2 -I.In the simple regression model Yt= αα + ββ Xt+ut, are the following statements correct? Fullyexplain why or why not?I.1 (7 points)If the X-values have a small sample variance, then OLS estimators ααˆand ββˆwill be less preciselyestimated.I.2 (8 points)If the errors utare serially correlated or heteroscedastic, then OLS estimators ααˆand ββˆwill still beunbiased and consistent, but not efficient.II. Suppose you specified the regression model as Yt= ββ Xt+utand estimated ββ as ββˆ=[ΣΣ (XtYt)] / [ΣΣ (Xt2)]. However, the true model has a constant term so that Ytis actually given by Yt= αα + ββ Xt+ut, where uthas zero expectation, X is given, and αα≠≠ 0.- 3 -II.1 (12 points)Carefully derive the true expected value of ββˆand show that it is biased.II.2 (4 points)Derive the condition under which ββˆwill be unbiased (it should not be αα = 0).II.3 (4 points) What is the intuitive interpretation of the condition you just derived?III.Consider the simple regression model Yt= αα + ββ Xt+utin which Ytis total expenditure on traveland Xtis total income for the tthState. Including the District of Columbia, you have data for 51observations. Both variables are measured in billions of dollars. The following is a partialcomputer output for the above data.VARIABLE COEFFICIENT STDERRORconstant 0.49812 0.535515income 0.055573 0.003293Error Sum of Sq (ESS) 417.110335Total sum of Squares (TSS) 2841.33048859- 4 -III.1 (5 points)What is the econometric interpretation of the estimated coefficient for income? Does the numericalvalue appear reasonable?III.2 (14 points)Test individually whether the coefficients for the constant term and income are significantlydifferent from zero at the 5% level. Be sure to state the null and alternative hypotheses, the teststatistic and its distribution, the critical value (or range), and the criterion. What is yourconclusion?III.3 (3 points)Compute the measure of goodness of fit.- 5 -III.4 (5 points)Test the model for goodness of fit at the 1 percent level of significance. Show all your derivations.What is your conclusion?III.5 (8 points)Suppose the data on X and Y are converted to thousands and a new model is estimated as Y*= αα*+ ββ*X*+u*, where the variables with asterisks are the transformed ones. In the table below, fill inthe blanks, indicated by underlined items, that give the values for the transformed model. Showyour derivations.VARIABLE COEFFICIENT STDERRORconstant ___________ ________income* ___________ ________Error Sum of Sq (ESS*) _________Total sum of Squares (TSS*)