This paper is labeled as "W" and has no issue number. Issue number 0 is used for chronological purposes.

A statistical definition of the natural unemployment rate hypothesis is advanced and tested. A particular illustrative structural macroeconomic model satisfying the definition is set forth and estimated. The model has "classical" policy implications, implying a number of neutrality propositions asserting the invariance of the conditional means of real variables with respect to the feedback rule for the money supply. The aim is to test how emphatically the data reject a model incorporating rather severe "classical" hypotheses.

No abstract available.

No abstract available.

A dynamic linear demand schedule for labor is estimated and tested. The hypothesis of rational expectations and assumptions about the orders of the Markov processes governing technology impose over-identifying restrictions on a vector autoregression for straight-time employment, overtime employment, and the real wage. The model is estimated by the full information maximum likelihood method. The model is used as a vehicle for re-examining some of the paradoxical cyclical behavior of real wages described in the famous Dunlop-Tarshis-Keynes exchange.

No abstract available.

Preliminary version of WP 43.

Paper prepared for seminar on New Methods in Business Cycle Research, Federal Reserve Bank of Minneapolis, November 13-14, 1975.

This paper explores some of the implications for econometric practice of the principle that people’s observed behavior will change when their constraints change. In dynamic contexts, a proper definition of people’s constraints includes among them laws of motion that describe the evolution of the taxes they must pay and the prices of the goods that they buy and sell. Changes in agents’ perceptions of these laws of motion (or constraints) will in general produce changes in the schedules that describe the choices they make as a function of the information that they possess. Until very recently, received dynamic econometric practice ignored this principle. The practice of dynamic econometrics should be changed so that it is consistent with the principle that people’s rules of choice are influenced by their constraints. This is a substantial undertaking, and involves major adjustments in the ways that we formulate, estimate, and simulate econometric models.

This paper describes methods for estimating the parameters of continuous time linear stochastic rational expectations models from discrete time observations. The economic models that we study are continuous time, multiple variable, stochastic, linear-quadratic rational expectations models. The paper shows how such continuous time models can properly be used to place restrictions on discrete time data. Various heuristic procedures for deducing the implications for discrete time data of these models, such as replacing derivatives with first differences, can sometimes give rise to very misleading conclusions about parameters. The idea is to express the restrictions imposed by the rational expectations model on the continuous time process of the observable variables. Then the likelihood function of a discrete-time sample of observations from this process is obtained. Estimators are obtained by maximizing the likelihood function with respect to the free parameters of the continuous time model.

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 discrete time models.

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 about “money-supply” and price-level behavior under the real bills regime are valid. In particular, both the price level and an asset total that quantity theorists would identify as money fluctuate more under a real bills regime than under a regime with restrictions like those favored by quantity theorists. Despite this, the Pareto criterion does not support the quantity-theory position.

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.

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.

This paper describes how to specify and estimate rational expectations models in which there are exact linear relationships among variables and expectations of variables that the econometrician observes.

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 the time series data.

This paper shows how the cross-equation restrictions implied by dynamic rational expectations models can be used to resolve the aliasing identification problem. Using a continuous time, linear-quadratic optimization environment, this paper describes how the resulting restrictions are sufficient to identify the parameters of the underlying continuous time process when it is known that the true continuous time process has a rational spectral density matrix.

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 as replacing derivatives with first differences, can sometimes give rise to very misleading conclusions about parameters. Our proposal is to express the restrictions imposed by the rational expectations model on the continuous time process generating the observable variables. Then the likelihood function of a discrete time sample of observations from this process is obtained. Parameter estimates are computed by maximizing the likelihood function with respect to the free parameters of the continuous time model.

This paper surveys recent issues in macroeconomics from the viewpoint of dynamic economic theory. The need to look beyond demand and supply curves and the insights that come from doing so are emphasized. Examples of issues in debt management and fiscal policy are analyzed.

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 quantity-theory predictions for commodity money systems; (iii) the circumstances under which one commodity emerges naturally as the commodity money; (iv) the role of inside money (money backed by private debt) in commodity money systems; and (v) the circumstances under which a government can choose the commodity to serve as the commodity money.

Remarks prepared for the Minnesota Economics Association Meeting, November 4, 1977.