A bivariate Granger-causality test on money and output finds statistically significant causality when data are measured in log levels, but not when they are measured in first differences of the logs. Which of these results is right? The answer to that question matters because a finding of no...

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...

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...

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...

On our interpretation, real bills advocates favor unfettered intermediation, while their critics, who we call quantity theorists, favor legal restrictions on intermediation geared to separate “money” from “credit.” We display examples of economies in which quantity-theory assertions...

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.

This paper proposes a method for estimating the parameters of continuous time, stochastic rational expectations models from discrete time observations. The method is important since various heuristic procedures for deducing the implications for discrete time data of continuous time models, such...

This paper shows how the cross-equation restrictions delivered by the hypothesis of rational expectations can serve to solve the aliasing identification problem. It is shown how the rational expectations restrictions uniquely identify the parameters of a continuous time model from statistics of...

Commodity money is modeled as one or two of the capital goods in a one-consumption good and one or two capital-good, overlapping generations model. Among the topics addressed using versions of the model are (i) the nature of the inefficiency of commodity money; (ii) the validity of...