Aggregation, Persistence and Volatility in a Macro Model

Abstract

We introduce firm heterogeneity into the standard monopolistically competitive real business cycle (RBC) model. The fundamental equilibrium path is derived and the time-series properties of aggregate GDP are studied analytically. Although firms' productivities are subject to temporary shocks, the aggregate process displays a surprising novel form of nonlinearity and long memory which had not been built into the model at the outset. This aggregate GDP turns out to have very different properties from log-linear time-series models such as auto-regressive (AR) models and their extensions. It displays very strong persistence, which ends abruptly with a sudden change of tendency, giving its autocorrelation function (ACF) an S-shape. Although persistent, it is mean-reverting, unlike the everlasting memory of unit-root processes. Its volatility is of a greater order of magnitude than that of any of its components, so small micro-shocks can generate large macro fluctuations. It is also characterized by long, asymmetric cycles of random lengths. Increased monopoly power tends to reduce the amplitude and increase the persistence of business cycles. Strikingly, we find that the empirical ACFs constructed from GDP data for the U.K. and the U.S. display this characteristic S-shape.

International output convergence: evidence from an autocorrelation function approach

“…The intermediate cases of slow convergence, denoted as fractionalˇ-convergence by Michelacci and Zaffaroni (2000), imply an ACF that decays at a hyperbolic rate. Furthermore, an S-shaped ACF, as in Abadir and Talmain (2002), would imply that there is a slow tendency towards convergence (fractional convergence) with a persistent and nonlinear pattern.…”

Two estimators of the long-run variance: Beyond short memory

“…see Diebold and Rudebusch (1989), Baillie and Bollerslev (1994), Gil-Alaña and Robinson (1997), Chambers (1998), Cavaliere (2001), Abadir and Talmain (2002). It is therefore of interest to adapt the most popular of these procedures, the Bartlett-kernel heteroskedasticity and autocorrelation consistent (HAC) estimator, to account for the possibility of long memory and antipersistence.…”

The Persistence of Inflation in OECD Countries: A Fractionally Integrated Approach

“…Another way of obtaining FI behavior was proposed by Parke (1999). He considers the cumulation of a 1 1 Some examples are Michelacci and Zaffaroni (2000), Abadir and Talmain (2002), Haubrich and Lo (2001), Byers et al (1997), etc. sequence of shocks that switch to 0 after a random delay. If the probability that a shock survives for k periods, p k , decreases with k at the rate Operationally, a binomial expansion of the operator (1 − L) d is used in order to fractionally differentiate a time series:…”