We investigate whether fluctuations in U.S. inflation rates are better described by infrequently occurring large shocks or by frequently occurring small shocks. We estimate a model that encompasses the two hypotheses within the framework of non-Gaussian state-space models. Our results indicate support for infrequently occurring large shocks, but this weakens somewhat once we allow for outliers and conditional heteroskedasticity. It appears that, for the purpose of forecasting monthly U.S. inflation rates, recognizing the distinction between frequent small shocks and infrequent large shocks does not matter much once outliers and conditional heteroskedasticity are allowed for.

We investigate asymmetries in the conditional mean dynamics of U.S. GNP. Because the statistical evidence on nonlinearities in the conditional mean could be influenced by the presence of outliers or by a failure to model conditional heter oske dasticity, we explicitly account for outliers by assuming that the innovations are drawn from the stable family, and model time-varying volatility by a GARCH(1, 1) process. We also allow for the possibility of long memory in the series with fractional differencing. Our results indicate statistically significant nonlinearities in the conditional mean that persist even after accounting for these features in the data.

We explore the effects of fat tails on the equilibrium implications of the long-run risks model of asset pricing by introducing innovations with dampened power law to consumption and dividends growth processes. We estimate the model structural parameters by maximum likelihood. We find that the stochastic volatility model with fat tails can generate implied risk premium, expected risk free rate and their volatilities comparable to the magnitudes observed in data. The model with fat tails leads to a significant increase in implied risk premia over the benchmark Gaussian model, but similar values for other equilibrium quantities of interest.