Studies of non-linear features in the business cycle

Abstract

Writers on the business cycle often emphasize that non-linear models are needed to account for certain of its features. Thus it is often said that either the asymmetry of the duration of business cycle expansions and contractions or the variability of these quantities demand a non-linear model. Such comments are rarely made precise however and mostly consist of references to such assertions from the past. Thus the asymmetry in the cycle is mostly accompanied by references to Keynes (1936) and Burns and Mitchell (1946). But these authors were looking at what we call today the classical cycle i.e. movements in the level of GDP, and so the fact that there are long expansions and short contractions can arise simply due to the presence of long-run growth in the economy, and it is not obvious that it has much to do with non-linearity. This thesis aims to introduce various statistics that can be used to characterise the specific shape of the non-linearity observed in macroeconomic time series. Chapter 2 introduces a range of statistics and presents the dating algorithm used in this thesis, which is based on the BBQ algorithm of Harding and Pagan (2002). Chapter 3 tests the adequacy of linear models versus the SETAR model of van Dijk and Franses(2003) and the bounceback model of Kim, Morley and Piger (2005) in capturing observed non-linear features of the data. Chapter 4 extends this work by examining the three state Markov model of Hamilton (1989), again using the “bounce-back” model of Kim C., Morley, J. and J. Piger, (2005), and the more complicated “tension” model of DeJong, D., Dharmarajan, H., Liesenfeld, R. and Richard, J., (2005). Chapter 4 also extends Chapter 3 by estimating the above mentioned models on US GDP, Australian non-farm GDP, US investment and Australian dwellings investment. They are then simulated in order to gauge the cycle properties. Chapter 5 analyses the business cycle implications of two related multivariate dynamic factor models presented in papers by Kim and Piger (2001, 2002). Finally Chapter 6 concludes.