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Efficient Method of Moments (EMM) is used to fit the standard stochastic volatility model and various extensions to several daily financial time series. EMM matches to the score of a model determined by data analysis called the score generator. Discrepancies reveal characteristics of data that stochastic volatility models cannot approximate. The two score generators employed here are "Semiparametric ARCH" and "Nonlinear Nonparametric". With the first, the standard model is rejected, although some extensions are accepted. With the second, all versions are rejected. The extensions required for an adequate fit are so elaborate that nonparametric specifications are probably more convenient. Corresponding author: George Tauchen, Duke University, Department of Economics, Social Science Building, Box 90097, Durham NC 27708-0097 USA, phone 1-919-660-1812, FAX 1-919-684-8974, e-mail get@tauchen.econ.duke.edu. 0 1 Introduction The stochastic volatility model has been proposed as a descripti...

We introduce reprojection as a general purpose technique for characterizing the observable dynamics of a partially observed nonlinear system. System parameters are estimated by method of moments wherein moments implied by the system are matched to moments implied by the transition density for observables that is determined by projecting the data onto its Hermite representation. Reprojection imposes the constraints implied by the system on the transition density and is accomplished by projecting a long simulation of the estimated system onto the Hermite representation. We utilize the technique to assess the dynamics of several diffusion models for the short-term interest rate that have been proposed and compare them to a new model that has feedback from the interest rate into both the drift and diffusion coefficients of a volatility equation. This effort entails the development of new graphical diagnostics.

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This paper models the dynamics of adjustment to long-run PPP over the post-Bretton Woods period in a nonlinear framework consistent with the presence of frictions in international trade. We estimate exponential smooth transition autoregressive (ESTAR) models of deviations from PPP, which are obtained using the Johansen cointegration method, for both CPI- and WPI-based measures and a broad set of U.S. trading partners. In several cases, we find clear evidence of a mean-reverting dynamic process for sizable deviations from PPP, with the equilibrium tendency varying nonlinearly with the magnitude of disequilibrium. Analysis of impulse response functions also supports a nonlinear dynamic structure, but convergence to long-run PPP in the post-Bretton Woods era is very slow.

In this paper we investigate the multi-period forecast performance of a number of empirical selfexciting threshold autoregressive (SETAR) models that have been proposed in the literature for modelling exchange rates and GNP, amongst other variables. We take each of the empirical SETAR models in turn as the DGP to ensure that the `non-linearity' characterises the future, and compare the forecast performance of SETAR and linear autoregressive models on a number of quantitative and qualitative criteria. Our results indicate that non-linear models have an edge in certain states of nature but not in others, and that this can be highlighted by evaluating forecasts conditional upon the regime.

This paper investigates the contribution of monetary policy to the changes in output growth and inflation dynamics in the US. We identify a policy shock and a policy rule in a time-varying coefficients VAR using robust sign restrictions. The transmission of policy shocks has been relatively stable. The variance of the policy shock has decreased over time, but policy shocks account for a small fraction of the level and the variations in inflation and output growth volatility and persistence. Finally we find little evidence of a significant increase in the long run response of the interest rate to inflation.

The effects of changes to the tax rate are studied within a framework where an estimated regime-switching process for the debt-output ratio is embedded in a standard growth model. The regime is a hidden state variable, so agents face a signal extraction problem. Consequently, agents incorporate the possibility of switching to different fiscal regimes when forming expectations over future taxes. Decision rules have additional nonlinearity relative to fixed-regime models. Income allocation and the tax elasticity of investment depend on agents’ inference regarding the regime. Specifically, the tax elasticity can be either positive or negative, depending on whether agents perceive a tax reform as an intra-regime shock or change in regime.