In an article in this Review, Christopher Sims presented an innovative statistical technique to determine the direction of causality, then applied this methodology to money and nominal income in the United States. He concluded: main empirical finding is that the hypothesis that causality is unidirectional from money to income agrees with the postwar U.S. data, whereas the hypothesis that causality is unidirectional from income to money is rejected (p. 540). In a more recent paper in this Review, David Williams, C. A. E. Goodhart, and D. H. Gowland applied Sims' statistical methodology to the United Kingdom and concluded: found for the U.K. some evidence of unidirectional causality running from nominal incomes to money but also some evidence of unidirectional causality running from money to prices. Taken together, this evidence suggests, perhaps, a more complicated causal relationship between money and incomes in which both are determined simultaneously (p. 423). Furthermore, Williams, Goodhart, and Gowland suggest some general possibilities for the differences between the United States and the United Kingdom, and they are careful to note that: Because of the various differences in context the finding that in the United Kingdom the relationship between money and income appears different from that found by Sims for the United States in no way casts any doubt on the validity of Sims' own (p. 417). The purpose of this paper is to present a concise model which draws together the findings of Sims for the United States and Williams, Goodhart, and Gowland for the United Kingdom. To accomplish this, a fixed exchange rate system is modeled in which one country, the United States, serves as the primary reserve currency country, while other countries, the United Kingdom in this case, hold a substantial portion of their international reserves denominated in terms of the reserve currency.' Particular attention is paid to the asymmetrical nature of the system with respect to money's influence on nominal income and vice versa. Indeed, the ability of the reserve currency country to create international reserve assets plays the primary role in explaining the asymmetrical nature of the system and the empirical results of Sims, and Williams, Goodhart, and Gowland. The model is couched in a world in which asset reallocations are viewed as adjustments toward maintaining general equilibrium. This equilibrium is based on a stable set of preferences regarding the structure of individual portfolios, broadly defined in terms of holdings of real consumption goods, real interest bearing financial assets, real money balances, and leisure time. The assumption of equilibrium conditions in all markets allows attention to focus directly on the money market to isolate the process of portfolio adjustment in international markets. As in similar models based on the monetary approach to *Economists, Chase Manhattan Bank, N.A. The views expressed in this paper are solely our own and do not necessarily represent those of the Chase Manhattan Bank. We wish to thank David T. King, the managing editor of this Review, J. Richard Zecher, J. E. Tanner, Walton T. Wilford, C. A. E. Goodhart, and Marc A. Miles for their comments on earlier drafts. 1One may note that for the Commonwealth countries the British pound acted as a reserve currency. However, the pound's relative world influence vis-avis the U.S. dollar was small during the Bretton Woods period.

The authors extend the ''Coase Theorem'' by analyzing the effects of one firm's activities on another firm in cases of uncertain externality, legal liability, and resource allocation. A mathematical model is used to examine, in terms of risk acceptance and profit maximizing, a merger of two firms and the ensuing bargaining over one firm's pollution output. This costless bargaining is generally accepted as determining the socially optimal level of resource allocation and is independent of liability assignment. However, the authors conclude that liability rules in an uncertain world can determine resource allocation as much as bargaining skills. Government intervention in the form of tax and subsidy incentives can intervene in favor of increased output. 14 references.