The stock market is said to be a leading indicator for GDP growth. Because the stock market prices the expectations of future earnings, a bullish market may predict future economic growth and vice versa. Let Y1, be GDP growth and Xt, be SP500 returns, (both series collected at the quarterly frequency as in the previous exercise). Run OLS for the following models:
a. Yt = β0 + β1X1 + ut (contemporaneous correlation).
b. Yt, = β0 + β 1xt–1 + ut, (one-quarter leading indicator).
c. Y1 = β0 + β1Xt–1 + β 2Xt–2 + β3Xt–3 + β4Xt–4 + ut (four-quarter leading indicator).
d. Y1 = β0 + β1Xt–1 + β2Xt–2 + β3Xt–3 + β4Xt–4 + ut (leading indica-tor tor with GDP inertia).
For each model, assess the R-squared and the adjusted R-squared. Which model do you prefer?