Large shocks vs. small shocks. (Or does size matter? May be so.)

What are the shocks that drive economic fluctuations? The answer to this question requires as a first step solving the shock identification issue. This paper proposes a new identification scheme based on two aspects: the long-run effect of the shock (permanent or transitory), and the size of the shock (Large or small). This is done by using a threshold integrated moving average model (TIMA) previously introduced in the literature by the authors. Based on this model we develop a testing strategy to determine whether Large and small shocks have different long-run effects, as well as whether one of them is purely transitory. The paper analyzes the impulse response function of both types of shocks, and provides the asymptotic results sufficient to implement the above testing strategy. Based on these results we develop a new nonlinear permanent-transitory decomposition, that is applied to US stock prices to analyze the quality of the stock market, and to US GNP to investigate the asymmetric behavior of its shocks.