Econometric Analysis of Nonlinear Dynamic Models with Applications in International Macroeconomics

The project "Econometric Analysis of Nonlinear Dynamic Models with Applications in International Macroeconomics" was an ESRC-funded project (reference number: R00235524) carried out in the Department of Applied Economics at the University of Cambridge and in the Department of Economics at the University of Leicester over the period 1/09/95 31/08/98. In what follows, we describe the aims of the project, and provide a nontechnical summary, a full-report, and a list of papers produced on the project. Summary of aims and objectives of project 1. To investigate the econometric properties of a general class of non-linear dynamic models, emphasising dynamic endogenous switching models and models incorporating rational expectations. 2. To investigate the dynamic properties of such models through the development of measures of persistence of shocks and through the impulse response analysis of dynamic models. 3. To develop testing procedures to compare non-linear models. 4. To investigate the possible asymmetric effects of macroeconomic and other shocks on macroeconomic variables. Non-Technical Summary In recent years, there has been considerable interest in non-linear models in economics. The continuing development of sophisticated theoretical models of economic phenomena has resulted in an increasing dissatisfaction with the approximations that are provided by linear systems. And the growth in computing power experienced in recent years has made it feasible to estimate a very wide range of non-linear models. However, it can be argued that one of the major shortcomings of this growing literature is that estimated non-linear models are not always very closely linked to economic theory. Rather, the models are designed to capture particular non-linear features of the data. Moreover, given the variety of non-linear models that are available, the need for a systematic strategy for model evaluation and selection becomes paramount, and yet this literature is still in its early stages of development. This research project has aimed to develop new techniques for the analysis of non-linear dynamic models and to apply them in the analysis of macroeconomic and international financial markets data. The need for cohesion between a model and the underlying analytic account of how economic agents operate has meant that our research has been restricted to a specific class of models and to a particular set of topics in macroeconomics. Specifically, attention has concentrated on the class of non-linear dynamic models that accommodate the possibility of regime changes (including ‘threshold’ models and ‘endogenous switching regression’ models). We have also considered their application in the study of fluctuations of the outputs of various countries and exchange rate movements (although we have considered models of stock returns also). In terms of the development of econometric methods, attention has focused on the development of testing procedures to compare non-linear models and the development of suitable techniques for the analysis of dynamic properties of non-linear stochastic models. The project has made significant contributions in four main areas. First, it has contributed to the development of the analysis of non-linear dynamic models involving rational expectations models, focusing on two classes of model: namely, models obtained as the outcome of a (finite-horizon) intertemporal optimisation problem and the limited-dependent variable models in which there exist bounds within which the variable of interest is constrained to move. Both classes of models are widely observed in economics and, because they are intrinsically dynamic in nature, the solution of the models is complicated in the presence of Rational Expectations. Efficient computational techniques and estimation methods have been developed in the project for the solution and econometric analysis of these models. Second, appropriate techniques have been derived with which the dynamic properties of non-linear dynamic models can be investigated. Specifically, the impulse response analysis of non-linear dynamic models has been developed in some detail, and the use of these new methods has already become established in the literature. Third, important progress has been made in the area of the evaluation and comparison of non-linear dynamic models, having extended the literature on non-nested testing between non-linear models, and having examined the use of various selection criteria used when choosing between different non-linear models. Fourth, these theoretical developments have been applied successfully in a number of areas and, specifically, in the study of non-linearities in business cycle fluctuations, in the modelling of the exchange rate subject to target zones, and in the analysis of stock returns in financial markets. The work of the project demonstrates the complexity involved in the analysis of non-linear dynamic models and the importance of relating econometric modelling activity to the underlying economic theory. On the other hand, the work also illustrates the power of nonlinear dynamic models in capturing the properties of a wide variety of economic phenomena, and suggests that non-linear dynamic models will become more popular and more extensively used in future years.