Simon M. Potter

IMPULSE RESPONSE ANALYSIS IN NONLINEAR MULTIVARIATE MODELS

Abstract This paper presents a unified approach to impulse response analysis which can be used for both linear and nonlinear multivariate models. After discussing the advantages and disadvantages of traditional impulse response functions for nonlinear models, we introduce the concept of a generalized impulse response function which, we argue, is applicable to both linear and nonlinear models. We develop measures of shock persistence and asymmetric effects of shocks derived from the generalized impulse response function. We illustrate the use of these measures for a nonlinear bivariate model of US output and the unemployment rate.

A floor and ceiling model of US output

Abstract Building on previous nonlinear time-series models we further examine the form of nonlinearity in US output. We develop a model of US output that allows for floor and ceiling effects to alter the dynamics of output growth. The model estimated on post-Korean War quarterly data, displays features similar to nonlinear trade cycle models of the 1940s and 1950s. Thus, as predicted by many of the earlier theoretical models, our empirical results suggest that the turning points of the business cycle provide new initial conditions for the ensuing growth process. We also find important asymmetries in the responses of output to positive and negative shocks. This history and shock dependence property is not present in linear or approximately linear models of the type that arise in the standard implementations of Real Business Cycle theory.

Dynamic Asymmetries in U.S. Unemployment

We examine dynamic asymmetries in U.S. unemployment using nonlinear time series models and Bayesian methods. We find strong statistical evidence in favor of a two-regime threshold auto-regressive model. Empirical results indicate that, once we take into account both parameter and model uncertainty, there are economically interesting asymmetries in the unemployment rate. One finding of particular interest is that shocks that lower the unemployment rate tend to have a smaller effect than shocks that raise the unemployment rate. This finding is consistent with unemployment rises being sudden and falls gradual.

Forecasting Recessions Using the Yield Curve

We compare forecasts of recessions using four different specifications of the probit model: a time invariant conditionally independent version; a business cycle specific conditionally independent model; a time invariant probit with autocorrelated errors; and a business cycle specific probit with autocorrelated errors. The more sophisticated versions of the model take into account some of the potential underlying causes of the documented predictive instability of the yield curve. We find strong evidence in favour of the more sophisticated specification, which allows for multiple breakpoints across business cycles and autocorrelation. We also develop a new approach to the construction of real time forecasting of recession probabilities. Copyright

Nonlinear impulse response functions

The standard linear technique of impulse response function analysis is extended to the nonlinear case by defining a generalized impulse response function. Measures of persistence and asymmetry in response are constructed for a wide class of time series.

Bayes factors and nonlinearity: Evidence from economic time series

This paper argues in favor of a Bayesian approach to evaluating evidence of nonlinearity in economic time series over the classical approach that has been dominant in the applied literature. An application is presented concerning nonlinearity in US GNP.

Dynamic Hierarchical Factor Models

This paper uses multilevel factor models to characterize within- and between-block variations as well as idiosyncratic noise in large dynamic panels. Block-level shocks are distinguished from genuinely common shocks, and the estimated block-level factors are easy to interpret. The framework achieves dimension reduction and yet explicitly allows for heterogeneity between blocks. The model is estimated using an MCMC algorithm that takes into account the hierarchical structure of the factors. The importance of block-level variations is illustrated in a four-level model estimated on a panel of 445 series related to different categories of real activity in the United States.

Are Apparent Findings of Nonlinearity Due to Structural Instability in Economic Time Series

Many modelling issues and policy debates in macroeconomics depend on whether macroeconomic times series are best characterized as linear or nonlinear. If departures from linearity exist, it is important to know whether these are endogenously generated (as in, e.g., a threshold autoregressive model) or whether they merely reflect changing structure over time. We advocate a Bayesian approach and show how such an approach can be implemented in practice. An empirical exercise involving several macroeconomic time series shows that apparent findings of threshold type nonlinearities could be due to structural instability.

Predicting A Recession: Evidence From The Yield Curve In The Presence Of Structural Breaks

A probit model is used to examine the stability of the predictive content of the term structure in forecasting U.S. recessions. In particular, we compare forecasts of a recession under different assumptions regarding the presence of a structural break. We find strong evidence of the existence of a structural break in the U.S. economy, but there is considerable uncertainty about its exact location. Further, recession predictions - including for the year 2001 - are very sensitive to the location of breakpoints.

Recent Changes in the US Business Cycle

The US business cycle expansion that started in March 1991 is the longest on record. In this paper we use statistical techniques to examine whether this expansion is a one-time unique event or whether its length is a result of a change in the stability of the US economy. Bayesian methods are used to estimate a common factor model that allows for structural breaks in the dynamics of a wide range of macroeconomic variables. We find strong evidence that a reduction in volatility is common to the series examined. Further, the reduction in volatility implies that future expansions will be considerably longer than the historical record. Copyright 2001 by Blackwell Publishers Ltd and The Victoria University of Manchester