The equilibrium of a typical dynamic rational expectations model, is a covariance stationary (n x 1) vector stochastic process z(t). This stochastic process determines the manner in which random shocks to the environment impinge over time on -agents’ decisions and ultimately upon market prices and quantities. Surprises, Le., random shocks to agents’ information sets, prompt revisions in their contingency plans, thereby impinging on equilibrium prices and quantities.
Research Topic: Econometrics
Exact Linear Rational Expectations Models: Specification and Estimation
A distinguishing characteristic of econometric models that incorporate rational expectations is the presence of restrictions across the parameters of different equations. These restrictions emerge because people’s decisions are supposed to depend on the stochastic environment which they confront. Consequently, equations describing variables af- fected by people’s decisions inherit parameters from the equations that describe the environment. As it turns out, even for models that are linear in the variables, these cross-equation restrictions on the parameters can be complicated and often highly nonlinear.
A Note on First Degree Stochastic Dominance
A link is established between stochastic dominance and a different dominance relationship which we call pointwise dominance. This provides the basis for making several comparisons of expected values of non-decreasing functions of random variables. We discuss economic problems for which the application of stochastic dominance results depends on this link.
Linear Rational Expectations Models for Dynamically Interrelated Variables
A Note on Wiener-Kolmogorov Prediction Formulas for Rational Expectations Models
A prediction formula for geometrically declining sums of future forcing variables is derived for models in which the forcing variables are generated by a vector autoregressive-moving average process. This formula is useful in deducing and characterizing cross-equation restrictions implied by linear rational expectations models.
Instrumental Variables Procedures for Estimating Linear Rational Expectations Models
This paper illustrates how to use instrumental variables procedures to estimate the parameters of a linear rational expectations model. These procedures are appropriate when disturbances are serially correlated and the instrumental variables are not exogenous. We compare our procedures to some alternative estimators that estimate free parameters from restrictions implied by the Euler equations. The procedures are applicable to a variety of linear rational expectations models, several examples of which we cite.
Risk Averse Speculation in the Forward Foreign Exchange Market: An Econometric Analysis of Linear Models
In this paper we study the determination of forward foreign exchange rates. An exchange rate is the price of one currency in terms of another currency, and a forward rate is a contractual exchange rate established at a point in time for a transaction that will take place at the maturity date on the contract in the future. Well-organized forward markets exist for all major currencies of the world for various maturities, with the most active contract lengths being one, three, six, and twelve months.
The Dimensionality of the Aliasing Problem in Models with Rational Spectral Densities
This paper reconsiders the aliasing problem of identifying the parameters of a continuous time stochastic process from discrete time data. It analyzes the extent to which restricting attention to processes with rational spectral density matrices reduces the number of observationally equivalent models. It focuses on rational specifications of spectral density matrices since rational parameterizations are commonly employed in the analysis of time series data.
Aggregation Over Time and the Inverse Optimal Predictor Problem for Adaptive Expectations in Continuous Time
This paper describes the continuous time stochastic process for money and inflation under which Cagan’s adaptive expectations model is optimal. It then analyzes how data formed by sampling money and prices at discrete points in time would behave.