Econ 120B Ramu RamanathanSpring 1998 Final exam (35%)Your name ______________________________________Your Id No. (NOT Soc. Sec. no.) ______________________Make sure that all pages (1 through 4) are there. The maximum number of points for the exam is80. Read the questions carefully and make sure that you do not misunderstand them. If there isany ambiguity ask for clarification. Don’t provide the answer to one part somewhere else. Youwon’t get credit for it.I. (10 points)Consider the simple regression model CATCHt= αα + ββ BOATSt+ut, where CATCH = the totalfish catch in thousands of pounds and BOATS = the number of BOATS that went fishing on day t. IfBOATS = 0, then CATCH should be zero also, indicating that the true value of αα is zero. Thus thetrue model is CATCHt= ββ BOATSt+vt. Suppose, however, you kept the constant term in themodel and estimated a constant term and a slope term.What is the nature of the misspecification you are making here; is it adding an irrelevant variableor omitting a relevant variable?Are the estimates biased?Are they consistent?Are they efficient?Are the hypothesis tests valid?II. (10 points)"When it comes to the properties of unbiasedness, consistency, and efficiency of the OLS estimatorsof parameters, adding an irrelevant variable (that is, one that has a truly zero coefficient) to a modelhas the same effect as high multicollinearity." Carefully explain in the next page whether thisstatement is valid. If it is only partly valid, indicate which parts they are.- 2 -III.Consider the following model relating the gain in salary due to a MBA degree to a number of itsdeterminants (for simplicity, the t subscript is omitted):SLRYGAIN = ββ1+ ββ2TUITION + ββ3Z1 + ββ4Z2 + ββ5Z3 + ββ6Z4 + ββ7Z5 + uZ1 = MBA skills graded by recruiters in being analysts (1-4, 1 is best)Z2 = MBA skills graded by recruiters in being team players (1-4, 1 is best)Z3 = MBA skills graded by recruiters in having a global view (1-4, 1 is best)Z4 = Teaching evaluation by MBAs (1-4, 1 is best)Z5 = Curriculum evaluation by MBAs (1-4, 1 is best)Using data for 25 top business schools gathered by Business Week, the coefficients were estimated asfollows:Coefficient Standard Test Retain orerror Statistic Omitβˆ160.899 22.513 Skip this Skip thisβˆ20.314 0.750βˆ3- 3.948 2.756βˆ4- 2.016 2.165βˆ5- 2.402 2.948βˆ6- 0.613 3.062βˆ7- 5.325 3.773R2= 0.461 R__2= 0.282 ESS = 1288.214III.1To carry out a test for the null hypothesis ββi= 0 (i = 2, 3, ...., 7) against a two-sided alternative, writedown in the table above the numerical values of the test statistic for each of the above coefficients,excluding the constant term (6 points).- 3 -State the statistical distribution of the test statistics, including the degrees of freedom, and thecritical value (or range) for a 10 percent test (4 points).In each case, write down (in the table) whether the variable is a candidate for omission or retention(6 points).III.2Test the model for overall significance at the 10 percent level by carrying out the following steps.State the null and alternative hypotheses (3 points).Write down an expression for the test statistic and compute its value (2 + 2 points).State its distribution under the null including the d.f. (2 points).State the criterion for rejection of the null (at the 10 percent level) and apply it (3 points).What is your conclusion about the overall goodness of fit (3 points)?Is there a conflict between your conclusion here and that in question III.1? (2 points). If yes, canyou suggest possible explanation(s) (3 points)?III.3Another model was estimated after omitting some variables. The estimated model is the followingwith p-values in parentheses.SLRYGAINˆ= 62.438 - 6.398 Z1 - 5.516 Z5(< 0.01) (0.006) (0.052)- 4 -Error sum of squares = 1494.512 R____2= 0.318Using the first model as the unrestricted model and the second model as the restricted model, test arelevant joint________ hypothesis at the 10 percent level by carrying out the following steps.State the null and alternative hypotheses (3 points).Write down an expression for the test statistic and compute its value (3 + 2 points).State its distribution under the null including the d.f. (3 points).State the criterion for rejection of the null (at the 10 percent level) and apply it (3 points).Does your test here confirm the individual tests done in III.1 or does it contradict it? (2 points)?III.4In the two models, do the signs of the regression coefficients agree with your intuition or do youthink that some of the signs are wrong? If the latter, which ones? (3 points)III.5Considering the goodness of fit, the tests you have done, the conclusions you have drawn from them,and the significance of the regression coefficients, evaluate the adequacy of the model specification(5