The data set for this problem is Ch.15.Data.xls. It contains quarterly data on real GDP (RGDP) and the federal funds rate (FF) for the sample period 1954Q3 through 2017Q1. For this part of the problem, assume the regressors are exogenous.
a. Estimate a distributed lag model with RGDP as the dependent variable, and the current value plus five lags of FF as the independent variables. Assume the errors are autocorrelated (i.e. correct for this). Use the sample period 1954:Q3 through 2007:Q4.
The impact multiplier is: _______
The multiplier after three periods have gone by is: _______
The long-run or cumulative multiplier is: _______
(All answers to four decimal places.)
For this question, assume strict exogeneity (for this model, both exogeneity and strict exogeneity would be hard to justify since the current value of FF depends, in part, on RGDP through the Taylor rule (or the lag of RGDP), but for the purposes of this problem, make the assumption anyway).
b. Use 1-step GLS to correct for first-order autocorrelation in the model (and sample period) estimated in part a.
The estimated correlation coefficient (?1) is: ________
The impact multiplier is: ______
The long-run multiplier is: _______
(All to four decimal places.)
Again, for this question, assume strict exogeneity, use the model from part a. assuming AR(1) errors, and use the sample period 1954:Q3 through 2007Q4.
c. Estimate the model using iterative GLS (i.e. Cochrane-Orcutt). Use a convergence criterion of .001 (i.e. continue until the absolute value of the difference in rho between successive steps is less than .001).
The final estimate of ?1 is ______(four decimal places):
The estimated impact multiplier is ______(four decimal places)