Question

The index of industrial production ( t IP ) is a monthly time series that measures the quantity of industrial commodities produced in a given month. Suppose that an analyst has data on this index for the United States. The analyst begins by computing Y subscript t = 1200 X ln IP subscript t / IP subscript t-1 , which gives the monthly percentage change in IP measured in percentage points at an annual rate. The analyst estimates an AR(4) model for industrial production growth and then augments that model with four lagged values of ?Rt , where Rt is the interest rate on three-month U.S. Treasury bills (measured in percentage points at an annual rate). All regressions are estimated over the sample period 1960:1 through 2000:12 (that is, January 1960 through December 2000). (a) The Granger causality F statistic on the four lags of ?Rt is 2.35. Do interest rates help to predict IP growth? Explain your answer. 2 (b) The analyst also regresses ?Rt on a constant, four lags of ?Rt , and four lags of IP growth. The resulting Granger causality F statistic on the four lags of IP growth is 2.87. Does IP growth help to predict interest rates? Explain your answer.

Answer 1

To test the Granger causality, flow from interest rate to Index of Industrial Production (IIP), there must be, past value of IIP has a significant impact on current interest rate and vice-versa. Hence the joint significance of lagged coefficient OF interest rate should be statistically significant for predicting the IIP and vice-versa. Since we have F value for 492 observation (1960:1 through 2000:12) with four lag of independent variable so we have df1 = 4 (four restrictions) and df2 = 492-(8+1)= 483 to get critical F test value. df1 is the degree of freedom which is the number of restrictions (or the number of coefficients being jointly tested). 2(a) It has F value of 2.35, less than 2.39 so we accept null hypothesis of no Granger causality from interest rate to IIP. Not able to predict IIP. (2b), the critical value of F test is 2.39, at 5% level of significance and calculated F value 2.87 is greater than the critical value so it can be said that IIP able to predict interest rate.