Marco Lippi

Diffusion of technical change and the decomposition of output into trend and cycle

In this paper we argue that modelling the trend component in real GNP as a random walk is inconsistent with its interpretation as productivity growth. As an alternative we specify the trend as an Auto Regressive Integrated Moving Average (ARIMA) process, whose impulse response function follows an S-shaped pattern reflecting the process of diffusion of technical change. Such an ARIMA process is employed to build and estimate an Unobserved Components ARIMA (UCARIMA) model using USA post-war quarterly data. We find that our model, although more parsimonious, fits the data as well as the standard random walk plus AR(2) cycle. Moreover, the cycle has a very low variance relative to the variance of the trend in our model.

On persistence of shocks to economic variables: A common misconception

Abstract Empirical results on U.S. GNP have provided estimates of the Beveridge and Nelsons persistence measure (almost) always greater than unity when using ARIMA models and always smaller than unity when using UCARIMA models. This paper shows that a measure of persistence less than unity is a mathematical consequence of the definition of UCARIMA models and not an independent estimation result. Therefore, ARIMA and UCARIMA estimates of persistence cannot be compared on the same ground.