In his restatement of quantity theory of money, Milton Friedman (1956) argued that physical goods should be regarded as a substitute for and that higher expected rates of inflation should induce a portfolio shift from to physical assets. As Friedman has derived his equation, demand for real balances is a function of expected rate of inflation in addition to nominal rates of interest, wealth and real income (p. 58, equation (11)). This also has been approach of many applied studies. For example, Valentine (1977, p. 747) concludes: the fact that anticipated rate of inflation has an effect on demand for which is additional to its effect through its influence on nominal interest rate provides support for Friedman's view of demand for money (emphasis mine). There is, of course, likely to be some degree of substitution between physical goods and wider definitions of money, which is definition Friedman envisages. It is difficult to believe, however, that demand for narrowly defined (MI) which is used primarily for transactions balances, should be terribly sensitive to moderate expected rates of inflation. Certainly from theoretical considerations, in transactions demand models of Tobin-Baumol variety there is no role for expected rate of inflation, other than via interest rates. Herein lies paradox. Whilst theory and common sense seem to dictate that expected or actual inflation play little role in demand for narrow money, a number of studies for different countries have reported opposite. These include Shapiro (1973) and Goldfeld (1973) for United States, Smith and Winder (1971) for Canada, and Adams and Porter (1976), Juttner and Tuckwell (1974) and Valentine (1977) for Australia. This paper reconciles theory and evidence by showing that with more appropriate specification of previous studies, expected or actual rate of inflation is redundant and not significant. Those models use either a partial adjustment mechanism or an expectations formation mechanism in real terms. It is shown below that this equation is rejected relative to one in which expectations and adjustments are in terms of nominal variables. This nominal specification was pointed out by Goldfeld (1973) and Hafer and Hein (1980), who selected nominal version on basis of within sample errors. Following a description of real adjustment models in next section, section III shows this selection of nominal version more rigorously on basis of a likelihood ratio test. More importantly it is shown that this test of superiority of specification is identical to test that rate of inflation exerts no independent influence on demand for money. These tests are carried out in section IV. Since empirical studies of this question use both actual and expected rates of inflation, results of those authors using expected rate of inflation are examined in section V. In all cases strategy has been to replicate those models as closely as possible to see if their conclusions are upheld under more appropriate specifications; and in all cases these conclusions are not upheld. The aim of paper is not to suggest new or appropriate expectations formations or to exhaust all possible ones but to test those on which previous conclusions are based. The aim is twofold: to point out duality of appropriate real vs. nominal test procedure with test of significance of rate of inflation; and to show that conclusions of previous studies regarding independent effect of rate of inflation on transactions balances are due to an incorrect specification and interpretation.

sumer reliance upon advertising since these mechanisms substitute as sources of product/vendor information. One can predict, therefore, that when relative prices favor consumer reliance upon advertising as information, producers will respond accordingly. This prediction also received empirical verification-advertising intensity by sellers in the mobile Washington, D.C. area greatly exceeded advertising intensity in the relatively stable Baltimore, Maryland area.

This paper explores the consequences of the timing of payments for the demand for money. It is found that if payments are the minimum of the money in the bank account or bills due, the demand for money will respond slowly to changes in income. This prediction disagrees with some formulations of the short-run demand for money (e.g., Irving Fisher's) but agrees with empirical estimates. The demand for money is adjusted to supply by changes in quantities (i.e., payments flows) rather than by changes in prices or interest rates.

In a recent paper (1984), Robert Eisner and Paul Pieper, present new calculations of the real value of the federal debt. Eisner and Pieper correctly take account of fluctuations in the market value of nominal assets and liabilities, and also take account of changes in real values wrought by inflation. They define an adjusted real deficit as the change in the real net debt of the government (liabilities less assets). Defining L(A) as the nominal value of already outstanding government liabilities (assets), P as the price level and P as its rate of change, and D as the conventionally measured deficit, Eisner-Pieper define their adjusted real deficit (D*/P) as

George A. Akerlof, Ross D. Milbourne, New Calculations of Income and Interest Elasticities in Tobin's Model of the Transactions Demand for Money, The Review of Economics and Statistics, Vol. 60, No. 4 (Nov., 1978), pp. 541-546