The business cycle implications of fluctuating long run expectations

I consider a DSGE model where consumption depends on the present discounted value of wage and capital income. The agent is uncertain if these variables are stationary or non-stationary and puts positive probability on both representations. The agent uses Bayesian learning to update his probability weights on each model and these weights vary over time according to how well each model fits the data. The model exhibits an improved fit to the data relative to a no-learning benchmark. It requires half the standard deviation of exogenous shocks to match the volatility of output and still matches the relative volatilities of key business cycle variables. The model lowers the contemporaneous correlation of consumption and wages with output and generates positive autocorrelation in growth rates. Impulse responses exhibit persistent responses and forecast errors are positively serially correlated. Finally, in contrast to the existing literature, the model endogenously generates observed time varying volatility and long run predictability of business cycle variables, especially for investment, without generating counterfactually high serial correlation of forecast errors.