Nonlinear dynamics and econometrics: AN introduction

Abstract

The empirical modelling of economic time series is dominated by methods that assume linearity of the underlying dynamic economic system, the so-called Frisch-Slutsky paradigm. The main a priori argument in favour of linearity and the reason for its original adoption is its simplicity: autoregressive models can be estimated using standard regression packages and there is now a wide range of computer software packages available to estimate models with linear moving average components; the dynamics contained in estimated models can be completely characterized by their impulse response functions and directly related to linear models of the macroeconomy. The dominance of the Frisch-Slutsky paradigm is not based on any strong a priori belief that the economic system is linear. Indeed, once curvature is introduced into utility functions and/or production functions, nonlinearity is pervasive in theoretical dynamic models, hence the shortage of 'closed-form' solutions. Nor is it based on any convincing empirical evidence that actual economic time series are best described as linear stochastic processes. The LQ optimization approach (namely Linear constraints and Quadratic objective functions) which underlies most econometric applications (either implicitly or explicitly) is undoubtedly attractive on analytical and computational grounds, but can be highly deficient in areas where economic behaviour is dominated by asymmetric costs of adjustments, irreversibilities, transaction costs or institutional and physical rigidities. The challenge facing applied econometrics in dealing with these issues is truly immense. Reliable statistical techniques are required for detecting dynamic nonlinearities. Stochastic optimization models that are capable of capturing the primary sources of dynamic nonlinearities and are suitable for empirical analysis need to be developed. The possible effects of temporal aggregation, and aggregation across commodities and agents, need to be worked out in the context of nonlinear dynamic models. These are complicated issues, solutions to some of which have eluded us even in the case of linear models, and promise to be far more complicated when we enter the realm of nonlinear dynamic models. It is therefore natural to expect that real progress in the area of nonlinear dynamic econometric models will be slow and hard to come by. Nevertheless, the past two decades have witnessed important advances in the mathematical and statistical analysis of dynamic systems, particularly in physics, epidemiology and meteorology. Many of these developments have already found their way into economics and