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.

Macroeconomics

SEVERAL ECONOMISTS2 have argued that if individuals correctly perceive the rate of inflation so that their expectations are rational, then deterministic models of money and economic growth are unstable. In this view, points on the steady state equilibrium paths examined by Tobin [9] and others are saddlepoints, there being a tendency to diverge more and more from such a path as time elapses if the system is not initially on the path. The source of instability is understood most easily in the context of a model in which money is neutral, with real growth and capital accumulation both being exogenous with respect to the money supply and price level and, moreover, with both equaling zero. Time is continuous. The price level P and money supply M are assumed at each moment to satisfy the demand function for real balances

We measure price-level uncertainty and instability in the United States over the period 1850 to 2012. Major outbreaks of price-level uncertainty and instability occur both before and after World War II, alternating with three price-level moderations: one near the turn of the twentieth century, another under Bretton Woods, and a third in the 1990s. There is no evidence that the price level was systematically more stable or less uncertain before or after World War II. Moderations sometimes involved links to gold, but the experience of the 1990s proves that a well-managed fiat regime can achieve the same outcome.

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.

Alternative monetary policies are analyzed in an ad hoc macroeconomic model in which the public's expectations about prices are rational. The ad hoc model is one in which there is long-run neutrality, since it incorporates the aggregate supply schedule proposed by Lucas. Following Poole, the paper studies whether pegging the interest rate or pegging the money supply period by period minimizes an ad hoc quadratic loss function. It turns out that the probility distribution of output--dispersion as well as mean--is independent of the particular deterministic money supply rule in effect, and that under an interest rate rule the price level is indeterminate.

We compare market prices of risk in economies with identical patterns of endowments, priors, and information flows, but two different market structures, one with complete markets, another in which consumers can trade only a single risk-free bond. We study how opportunities to speculate, uncommon priors, and learning affect market prices of risk. Two types of consumers have diverse beliefs about the law of motion for a random exogenous endowment. One type knows the true law of motion while the other type learns about it via Bayes' theorem. Less-well-informed consumers are pessimistic, initially overestimating the probability of a catastrophic state. Learning dynamics and the wealth dynamics that they drive contribute to differences in evolutions of market prices of risk across market structures.