Volume 7, Issue 4

This paper outlines a bootstrapping approach to the estimation and analysis of macroeconometric models. It integrates for dynamic, nonlinear, simultaneous equation models the bootstrapping approach to evaluating estimators initiated by Efron (1979) and the stochastic simulation approach to evaluating models' properties initiated by Adelman and Adelman (1959). It also estimates for a particular model the gain in coverage accuracy from using bootstrap confidence intervals over asymptotic confidence intervals.

Given the objective of estimating the unknown parameters of a possibly nonlinear dynamic model using a finite (and relatively small) data set, it is common to use a Kalman filter Maximum Likelihood (ML) approach, ML-type estimators or more recently a GMM (Imbens, Spady and Johnson, 1998), BMOM (Zellner 1997), or other information theoretic estimators (e.g., Golan, Judge and Miller, 1996). Except for the BMOM, the above ML-type methods require some distributional assumptions while the moment-type estimators require some assumptions on the moments of the underlying distribution that generated the data. In the BMOM approach however, sampling assumptions underlying most ML and other approaches are not employed for the given data. The error terms are viewed as parameters with unknown values.Based on a generalization of the Maximum Entropy (ME), a semi-parametric, Information-Theoretic (IT) framework for estimating dynamic models with minimal distributional assumptions is formulated here. Like the BMOM approach, under this formulation, one views the errors as another set of unknown parameters to be estimated. Thus, for any data set, the estimation problem is ill-posed (under-determined) where the number of unknowns is always greater than the number of data points. The Information-Theoretic approach is one way to estimate the unknown parameters.After developing the basic IT (entropy) model, a computationally efficient concentrated model is developed where the optimization is done with respect to the Lagrange multipliers associated with each observation. The dual concentrated model is used to contrast this IT approach with the more traditional ML-type estimators. Statistics and inference procedures are developed as well. Monte Carlo results for estimating the parameters of noisy, chaotic systems are presented.

We develop a behavioral exchange rate model with chartists and fundamentalists to study cyclical behavior in foreign exchange markets. Within our model, the market impact of fundamentalists depends on the strength of their belief in fundamental analysis. Estimation of a STAR GARCH model shows that the more the exchange rate deviates from its fundamental value, the more fundamentalists leave the market. In contrast to previous findings, our paper indicates that due to the nonlinear presence of fundamentalists, market stability decreases with increasing misalignments. A stabilization policy such as central bank interventions may help to deflate bubbles.

Many empirical studies find that financial variables possess a predictive power over real economic activity. To examine this relationship, we adopt two time-series techniques: spectral analysis and a newly developed method, wavelet analysis. The major innovation of this paper is to apply wavelet analysis to the investigation of the relationship between various financial variables and real economic activity. Spectral analysis reports that US industrial production and financial variables have a common component in the long run and a varying lead-lag relationship, depending on the cycles. It implies that the relationship between US industrial production and the financial variables is not constant over time. This result is consistently confirmed by wavelet analysis. The lead-lag relationship, in the sense of Granger causality, varies over time, depending on the wavelet time scale.

Linear Vector Autoregression (VAR) models provide a useful starting point for analysing multivariate relationships between economic variables. They are frequently used for empirical macroeconomic modelling, policy analysis and forecasting. However, linear VAR systems fail to capture non-linear dynamics such as regime switching and asymmetric responses to shocks, suggested by the recent theoretical developments in macroeconomic research. In addition, an increasing body of empirical evidence suggests that the linear conditional expectations implied by standard VAR models do not always accord with the observed facts. For example, a significant number of empirical studies document asymmetries in the effects of monetary policy on output growth. This paper employs a more general nonlinear VAR methodology to re-examine previous findings that credit market conditions contribute to economic fluctuations as a propagator of shocks. Unlike linear projections it allows for nonlinear dynamics and asymmetric effects of shocks. We estimate a threshold vector autoregression (TVAR), in which the system's dynamics change back and forth between credit constrained and unconstrained regimes. Using generalised impulse response functions (GIRF) generated from the estimated nonlinear model, we examine the real effects of monetary policy. We find evidence of asymmetry in the effects of monetary policy in the credit constrained and unconstrained regimes as well as different output effects of monetary contractions and expansions.