The Great Moderation Gauss file(s) hetero_moderation.g Matlab file(s) hetero_moderation.m This exercise is based on annual data on real U.S. GDP per capita for the period 1946 to 2006. The Great Moderation refers to the decrease in the volatility of U.S. output growth after the early 1980s by comparison with previous volatility levels. This proposition is tested by specifying the following model yt = β0 + β1dt + ut , ut ∼ N(0, σ2 t ) σ 2 t = exp(γ0 + γ1dt), where yt is the growth rate in real GDP and dt is a dummy variable to be defined later.

(a) Compute the growth rate in real GDP yt = 100(ln GDPt − ln GDPt−1).

(b) Compute the sample means and sample variances of yt for the subperiods 1947 to 1983 and 1984 to 2006.

(c) Define the dummy variable dt =  0 : 1947 to 1983 1 : 1984 to 2006 , and estimate the parameters of the model, θ = {β0, β1, γ0, γ1}, by maximum likelihood. Interpret the parameter estimates by comparing the estimates to the descriptive statistics computed in part (b).

(d) The Great Moderation suggests that the U.S. GDP growth rate has become less volatile in the post-1983 period. This requires that γ1 6= 0. Perform LR, Wald and LM tests of this restriction and interpret the results.

(e) The model allows for both the mean and the variance to change. Test the restriction β1 = 0. If the null hypothesis is not rejected, then redo part

(d) subject to the restriction β1 = 0.