This is the third of three volumes containing edited versions of papers and commentaries presented in invited symposium sessions of the Eighth World Congress of the Econometric Society. The papers summarize and interpret recent key developments and discuss future directions in a wide range of topics in economics and econometrics. The papers cover both theory and applications. Written by leading specialists in their fields, these volumes provide a unique survey of progress in the discipline.
Research Topic: Econometrics
Generalized Method of Moments Estimation: A Time Series Perspective (published title “Method of Moments”)
This entry describes empirical methods for estimating dynamic economic systems using time-series data. By design, the methods target specific feature of the dynamic system and do not require a complete specification of the time-series evolution. The resulting generalized-method-of-moments estimation and inference methods use estimating equations implied by some components of a dynamic economic system. This entry describes the statistical methods and some applications of these methods.
Spectral Methods for Identifying Scalar Diffusions
This paper shows how to identify nonparametrically scalar stationary diffusions from discrete-time data. The local evolution of the diffusion is characterized by a drift and diffusion coefficient along with the specification of boundary behavior. We recover this local evolution from two objects that can be inferred directly from discrete-time data: the stationary density and a conveniently chosen eigenvalue–eigenfunction pair of the conditional expectation operator over a unit interval of time. This construction also lends itself to a spectral characterization of the over-identifying restrictions implied by a scalar diffusion model of a discrete-time Markov process.
Short-term Interest Rates As Subordinated Diffusions
In this article we characterize and estimate the process for short-term interest rates using federal funds interest rate data. We presume that we are observing a discrete-time sample of a stationary scalar diffusion. We concentrate on a class of models in which the local volatility elasticity is constant and the drift has a flexible specification. To accommodate missing observations and to break the link between “economic time” and calendar time, we model the sampling scheme as an increasing process that is not directly observed. We propose and implement two new methods for estimation. We find evidence for a volatility elasticity between one and one-half and two. When interest rates are high, local mean reversion is small and the mechanism for inducing stationarity is the increased volatility of the diffusion process.
Bootstrapping the Long Run
We develop and apply bootstrap methods for diffusion models whenfitted to the long run as characterized by the stationarydistribution of the data. To obtain bootstrap refinements tostatistical inference, we simulate candidate diffusion processes. Weuse these bootstrap methods to assess measurements of local meanreversion or pull to the center of the distribution for short-terminterest rates. We also use them to evaluate the fit of the model to the empirical density.
Back To the Future: Generating Moment Implications for Continuous Time Markov-Processes
Continuous-time Markov processes can be characterized conveniently by their infinitesimal generators. For such processes there exist forward and reverse-time generators. We show how to use these generators to construct moment conditions implied by stationary Markov processes. Generalized method of moments estimators and tests can be constructed using these moment conditions. The resulting econometric methods are designed to be applied to discrete-time data obtained by sampling continuous-time Markov processes
Rational Expectations Econometrics
At the core of the rational expectations revolution is the insight that economic policy does not operate independently of economic agents’ knowledge of that policy and their expectations of the effects of that policy. This means that there are very complicated feedback relationships existing between policy and the behaviour of economic agents, and these relationships pose very difficult problems in econometrics when one tries to exploit the rational expectations insight in formal economic modelling.
This volume consists of work by two rational expectations pioneers dealing with the “nuts and bolts” problems of modelling the complications introduced by rational expectations. Each paper deals with aspects of the problem of making inferences about parameters of a dynamic economic model on the basis of time series observations. Each exploits restrictions on an econometric model imposed by the hypothesis that agents within the model have rational expectations.