We study the convergence of recursive least-squares learning schemes in economic environments in which there is private information. The presence of private information leads to the presence of hidden state variables from the viewpoint of particular agents. By applying theorems of Ljung, we extend some of our earlier results to characterize conditions under which a system governed by least-squares learning will eventually converge to a rational expectations equilibrium. We apply insights from the learning results to formulate and compute the equilibrium of a version of Townsend's model.

[Two competing monetary policy prescriptions are analyzed within the context of overlapping generations models. The real-bills prescription is for unfettered private intermediation or central bank operations designed to produce the effects of such intermediation. The quantity-theory prescription, in contrast, is for restrictions on private intermediation designed to separate "money" from credit. Although our models are consistent with quantity-theory predictions about money supply and price-level behavior under these two policy prescriptions, the models imply that the quantity-theory prescription is not Pareto optimal and the real-bills prescription is.]

I. Introduction, 212. — II. An income-expenditures model, 214. — III. Conclusions, 224.

I. Introduction, 127. — II. A loanable funds model, 130. — III. Empirical results, 132. — IV. Macauley's criticism reconsidered, 138. — V. Conclusions, 139.

[This paper describes an environment in which government-issued currency is dominated in rate of return and in which there obtains a Modigliani-Miller theorem for government open market operations. Earlier Modigliani-Miller theorems for government finance have been stated for environments in which government-issued currency is not dominated in rate of return in equilibrium. Since government-issued currency is widely observed to be dominated in return, it is useful to study how Modigliani-Miller theorems hinge on absence of rate of return dominance.]

Monetary policy can be constrained by fiscal policy if fiscal deficits grow large enough to require monetization of government debt. That fact implies that the administrative independence of central banks does not by itself imply that monetary policy is independent of the fiscal decisions of governments. This essay describes limitations, possibilities, and suitable goals for monetary policy within the existing pattern of institutional responsibilities. The economic limitations of what can be achieved by monetary policy are summarized in six propositions developed in the paper.

Martin Feldstein and Otto Eckstein (1970) have set out and estimated a model of interest rate determination which they claim represents an integration of Keynes's liquidity preference theory with Irving Fisher's theory of the impact of expected inflation on interest rates. They achieve their integration by first inverting a Keynesian demand function for real balances, solving it for the nominal rate of interest. Then to incorporate Fisher's effect, they simply add to the right side of this equation a distributed lag in current and past actual rates of inflation, the same proxy for expected inflation that Irving used. Feldstein and Eckstein interpret sizable and statistically significant estimated coefficients on the elements of that distributed lag as confirming the presence of an effect of anticipated inflation on the interest rate. It is questionable whether Keynes's and Fisher's theories stand in need of any integration at all, since they are in principle compatible in the first place. The two theories are on very different footings. Keynes's liquidity preference theory is a theory about one particular structural equation relating real money balances, income, and the nominal rate of interest. On the other hand, Fisher's theory is one about how the whole economy is put together; that is, it is a statement about the reduced form equation for the nominal interest rate. In Fisher's theory, an exogenous increase in the anticipated rate of inflation is asserted to work its way through the economy in such a fashion that the nominal interest rate rises by the amount of the increase in anticipated inflation.1 In this note, I suggest that Feldstein and Eckstein's equation does not successfully synthesize Keynes and Fisher. Furthermore, I suggest that Feldstein and Eckstein's econometric procedure is not a good one for estimating the dimensions of the Fisher effect. In particular, the effect may be present in full force but still not be detected by Feldstein and Eckstein's procedure. On the other hand, it is possible to construct examples of economies in which there is really no effect but in which Feldstein and Eckstein's test would point to the presence of one. Finally, I show that in a model that includes both Keynes's liquidity preference schedule and a reduced form for the interest rate like the one posited by Fisher, Feldstein and Eckstein's equation is not statistically identifiable.

ECONOMISTS have recently begun to devote an increasing amount of attention to the relationships among interest rates on various instruments. Rates on instruments which differ with respect to maturity alone, all other features supposedly being held constant, have in particular received a great deal of attention since the publication of Meiselman's [7] work in 1962. While the term structure has certainly received the most concern, import-ant contributions have been made to the broader problem of studying relationships among rates on bonds which differ with respect to features other than maturity.' An especially important aspect of this broader area of research lies in examining the relationships between rates on government and corporate bonds. Knowledge of the characteristics of these relationships is important for an understanding of the paths through which monetary policy affects yields on corporate bonds, and hence, perhaps, expenditures on investment. This paper presents the results of an examination of the relationships among several interest rates on government and corporate bonds for the period January 1951 through December 1960. Monthly data are used, and series for the rates on three-month treasury bills, one, two, three, four, five, ten, and twentyyear government bonds, commercial paper, and Moody's Aaa's and Baa's are studied.2 This list represents an array of instruments ranging over a broad maturity spectrum and featuring various levels of quality. Tools of spectral and cross-spectral analysis are used to study the behavior of the series and the relationships among the series at various important components of oscillation.3 In addition to calculating the standard statistics associated with the spectrum and cross-spectrum, the relatively new tool of complex demodulation is employed to study the seasonal behavior of selected rates.4