-1. Dr. Brumm kindly provided us the data he used in his paper. qhich i:

containedin the file brumm.dat.Itc onsistso f 1995d atao n 76 countries.

(a) Estimate the model by least squares and test

(i) the strong joint hypothesis that Br :0, 9z : l, and 9r : -1.

(ii) the weak joint hypothesis 9z: I and B, : -1.

(b) Examinet hel easts quaresre sidualsfo r thep resenceo fheteroskedasticitrye lated to the variable MONEY GROWTH.

(c) Obtain robust standard errors for the model and compare them to the least squares standard errors.

(d) It is argued that OUTPUT GROWTH may be endogenous. Four instrumental variables are proposed, INITIAL : initial level of real GDP, SCHOOL : a measureo f the population'se ducationaal ttainment,I W : &Vrr?g!investment share of GDP, and POPRATE : average population growth rate. Using these instruments obtain instrumental variables QSLS\ estimates of the inflation equation.

(e) Testt he stronga nd weak hypothesesli stedi n

(a) using the lVestimates.I f your software permits make the tests robust to heteroskedasticity.

(0 Use the Hausman test to check the endogeneity of OUTP UT GROWTH. Because the regression errors may be heteroskedastic, use robust standard errors when estimating the auxiliary regression.

(g) Test the validity of the overidentifying restrictions.

(h) Testt he relevanceo f the instrumentsu singa joint F-test asd escribedin Section 10.4.2.If your software permits, use a robust joint test.