No 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.

Closed forms for the distribution of some conventional statistics are given as a prelude to deriving their asymptotic power functions as unit root tests. In the process, an important distinction is drawn between two classes of statistics: one which relies on deterministic normalizations and the other which uses stochastic normalizations. When the data follow a driftless autoregression, a t test (which belongs to the second class) for a unit root is found to perform better than the other tests in small to moderate effective samples.

Matrix Algebra is the first volume of the Econometric Exercises Series. It contains exercises relating to course material in matrix algebra that students are expected to know while enrolled in an (advanced) undergraduate or a postgraduate course in econometrics or statistics. The book contains a comprehensive collection of exercises, all with full answers. But the book is not just a collection of exercises; in fact, it is a textbook, though one that is organized in a completely different manner than the usual textbook. The volume can be used either as a self-contained course in matrix algebra or as a supplementary text.

No abstract