Econ 120B Ramu RamanathanSpring 1998 Second Midterm (30%)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.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 = 50- 2 -Using quarterly data for ten years (making the number of observations 40), the following model ofdemand for new cars was estimated.NUMCARS = ββ1+ ββ2PRICE + ββ3INCOME + ββ4INTRATE + ββ5UNEMP + utwhere NUMCARS is the number of new car sales per thousand population, PRICE is the new carprice index, INCOME is per capita real disposable income (in actual dollars), INTRATE is theinterest rate, and UNEMP is the unemployment rate. The following table has the estimates of theββ’s for three alternative models (constant term is not presented).(Values in parentheses are standard errors)____________________________________________________________________-----------------------------------------------------------------Variable Model A Model B Model C-----------------------------------------------------------------constant not shown not shown not shownprice -0.071391 -0.079392 -0.024883(0.034730) (0.011022) (0.007366)income 0.003159 0.00356(0.001763) (0.0006266)intrate -0.153699 -0.146651 -0.204769(0.049190) (0.039229) (0.051442)unemp -0.072547(0.298195)-----------------------------------------------------------------ESS 23.510464 23.550222 44.65914ADJ RSQ 0.758 0.764 0.565SGMASQ 0.671728 0.654173 1.207004AIC 0.754701 0.719108 1.29716FPE 0.755693 0.71959 1.297529HQ 0.814563 0.764388 1.35795SCHWARZ 0.932092 0.851414 1.472329SHIBATA 0.734702 0.706507 1.28395GCV 0.767689 0.726859 1.304869RICE 0.783682 0.735944 1.313504-----------------------------------------------------------------In Model A, test the joint hypothesis ββ3= ββ5= 0 by carrying out the following steps.1. (8 points) Write down the formula for the test statistic and compute it.- 3 -2. (3 points) State its distribution and d.f.3. (4 points) State the decision rule (for a 1 percent level) and your conclusion.Next test each of the ββ’s in Model A only__________________________ whether or not it is significantly different from zero bycarrying out the following steps.4. (3 points) Write down the d.f. for the test statistic. ___________5. (3 points) Write down the critical value (or range) for a 10 percent level of significance (don’task me whether the test is one-tailed or two-tailed, you decide what it is based on the informationgiven above).6. (8 points) Use the information in 5 and test whether each coefficient (excluding constant) issignificant or not. Clearly show your work and state your conclusion.For PRICEFor INCOME- 4 -For INTRATEFor UNEMP7. (4 + 4 points) Based on your test in 6, would you recommend any of the variables in Model A beomitted? If yes, which one and why? Also state what the advantages of omitting the variable(s) are.8. (8 points) For each variable in Model A, explain whether the sign of the estimated regressioncoefficients is as you would expect or is it "the wrong sign"? (justify your answers carefully).For PRICE- 5 -For INCOMEFor INTRATEFor UNEMP9. (5 points) Which of the three models is the "best". Explain what criteria you used and why youchoose the model you