Martingale-Like Behavior of Prices

Asset prices set in a competitive market need not be martingales; that is, it need not be true that the best predictor of future prices is the current price. Nonetheless, statistical tests for this property are sometimes treated as tests for the proper functioning of an asset market; asset prices often seem to have the property to a close approximation, and it is sometimes supposed that the martingale ought to be imposed on econometric models of asset markets and forecasts made from them. This paper shows that under general conditions, which allow among other things for risk aversion among market participants, competitive asset prices ought to be locally -- over small units of time -- martingale-like. This implies that tests of proper functioning of the market ought to be conducted with data at fine time intervals; results of such tests should not be used to justify imposing the martingale property on a model's long-term projections of asset prices.

The Role of Models and Probabilities in the Monetary Policy Process

macroeconomics, Role of Models, Probabilities, Monetary Policy Process

Comparison of Interwar and Postwar Business Cycles: Monetarism Reconsidered

When monthly data on production, prices, and the money stock are interpreted, via a vector autoregression, as generated by dynamic responses to "surprises" in each of the variables, a remarkable similarity in dynamics between interwar and postwar business cycles emerges, though the size of the "surprises" is much larger in the interwar period. Furthermore, the money stock emerges as firmly causally prior, in Granger's sense, in both periods and accounts for a substantial fraction of variance in production in both periods. When a short interest rate is added to the vector autoregression, the remarkable similarity in dynamics between periods persists, but the central role of the money stock surprises evaporates for the postwar period. While there are potential monetarist explanations for such an observation, none of them seem to fit comfortably the estimated dynamics. A non-monetarist explanation of the dynamics, based on the role of expectations in investment behavior, seems to fit the estimated dynamics better. That this explanation, which is consistent with a passive role for money, could account for so much of the observed postwar relation between money stock and income may raise doubts about the monetarist interpretation even of the interwar data.

Explicit integration of differential equations

Explicit integration of differential equation

Output and Labor Input in Manufacturing

macroeconomics, labor, manufacturing

Improving Monetary Policy Models

If macroeconomic models are to be useful in policy-making, where uncertainty is pervasive, the models must be treated as probability models, whether formally or informally. Use of explicit probability models allows us to learn systematically from past mistakes, to integrate model-based uncertainty with uncertain subjective judgment, and to bind data-bassed forecasting together with theory-based projection of policy effects. Yet in the last few decades policy models at central banks have steadily shed any claims to being believable probability models of the data to which they are fit. Here we describe the current state of policy modeling, suggest some reasons why we have reached this state, and assess some promising directions for future progress.