Demand for Money

Demand for Money

Chapter 8 THE DEMAND FOR MONEY STEPHEN M. GOLDFELD Princeton University DANIEL E. SICHEL* Board of Governors of the Federal Reserve System Contents 1. 2. Introduction Overview of empirical difficulties 2. 1. 2. 2. U. S. money demand Money demand: International evidence A brief theoretical overview A variable-by-variable review Money demand and the partial adjustment mechanism Criticisms and modifications of the partial adjustment model Dynamic models that impose long-run relationships Simultaneity, exogeneity, and the nature of the adjustment process . Re-examining the basic specification 3. 1. 3. 2. 300 302 302 306 308 308 4. Econometric issues 4. 1. 4. 2. 4. 3. 4. 4. 5. Concluding remarks References 313 324 325 333 338 341 349 353 * We thank Benjamin Friedman for his comments. The opinions expressed are those of the authors; they do not necessarily reflect the views of the Board of Governors of the Federal Reserve System. Handbook of Monetary Economics, Volume I, Edited by B. M. Friedman and F. H. Hahn © Elsevier Science Publishers B. V. , 1990 300 S. M. Goldfeld and D. E. Sichel I.

Introduction The relation between the demand for money balances and its determinants is a fundamental building block in most theories of macroeconomic behavior. Indeed, most macroeconomic models, whether theoretical or econometric, generally ignore the rich institutional detail of the financial sector and attempt to capture financial factors via the demand and supply of money. Furthermore, the demand for money is a critical component in the formulation of monetary policy and a stable demand function for money has long been perceived as a prerequisite for the use of monetary aggregates in the conduct of policy.

Not surprisingly, then, the demand for money in many countries has been subjected to extensive empirical scrutiny. The evidence that emerged, at least prior to the mid-1970s, suggested that a few variables (essentially income and interest rates, with appropriate allowance for lags) were capable of providing a plausible and stable explanation of money demand. As has been widely documented, especially for the United States but elsewhere as well, matters have been considerably less satisfactory since the mid-1970s.

First, there was the episode of the “missing m o n e y ” when conventional money demand equations systematically overpredicted actual money balances. Moreover, attempts to fit conventional demand functions to a sample that included the missing money period invariably produced parameter estimates with some quite unreasonable properties. Second, in the 1980s, U. S. money demand functions, whether or not fixed up to explain the 1970s, generally exhibited extended periods of underprediction as observed velocity fell markedly.

To be sure, the period since the mid-1970s has been marked by unusual economic conditions in many countries including supply shocks, severe bouts of high and variable inflation, record-high interest rates, and deep recessions. The period also coincided with the widespread adoption of floating exchange rates and, in a number of major industrial countries, with substantial institutional changes brought about by financial innovation and financial deregulation. Where institutional change was particularly marked, it also led to a change in what we think of as ” m o n e y ” .

The period since 1974 thus provided a very severe test of empirical money demand relationships and it is perhaps not so surprising that this period succeeded in exposing a number of shortcomings in existing specifications of money demand functions. 1 lit is perhaps ironic that the emergence of these shortcomings roughly coincided with the adoption by a number of central banks of policies aimed at targeting monetary aggregates. Some have argued that this association is more than mere coincidence.

In any event, given the vested interest of policymakers in the existence of a reliably stable money demand function, it is hardly surprising that employees of central banks were among the most active contributors to the most recent literature on money demand. Ch. 8: The Demand for Money 301 The repeated breakdown of existing empirical models in the face of newly emerging data has fostered a vast industry devoted to examining and improving the demand for money function. This process has been aided by a growing arsenal of econometric techniques that has permitted more sophisticated examinations of dynamics, functional forms, and expectations.

These techniques have also provided researchers with a wide variety of diagnostic tests to evaluate the adequacy of particular specifications. Initially, at least in the United States, this led to two strands of research. The first was what Judd and Scadding (1982a) called “reopening the pre-1973 agenda”. As a practical matter this amounted to re-exploring variables (e. g. measures of transactions), functional forms, or dynamics that seemed to be unnecessary in a more tranquil period.

A second strand of research was devoted to modifying existing specifications to account for changes brought about by financial innovation and deregulation. While these various strands of research have yielded considerable insight, matters are still in a state of flux. Part of the reason is that, perhaps not surprisingly, the modeling of financial innovation and deregulation proved to be a quite difficult task. Some have even gone further, suggesting that instabilities in money demand are to be expected, reflecting structural change in the economic and financial environment.

Spindt (1987) has characterized the unsettled flavor of the literature by noting that researchers either seem to conclude that no explanation is adequate to explain some recent money demand “puzzle” or that “the author’s own, (usually many years old), specification still works just fine, so there isn’t really any puzzle at all” [Spindt (1987, p. 1)]. Spindt goes on to suggest that we may need an alternative paradigm, a call that seems to be echoed in other recent reviews of empirical money demand [Judd and Scadding (1982a), Gordon (1984), Roley (1985)].

The outline of the chapter is as follows. Section 2 documents the nature of the difficulties with conventional demand functions, both in the United States and elsewhere. For the remainder of the chapter, however, when empirical results are presented the focus will be exclusively on the United States. Section 3 begins with a brief review of some underlying theoretical models and uses these as a vehicle to re-examine measurement and specification issues such as the definition of money and the appropriate scale and opportunity cost variables.

Section 4 considers econometric issues starting with estimation issues in the partial adjustment model and then analyzes criticisms and modifications of the partial adjustment model. This section also discusses the estimation of money demand imposing assumed or estimated long-run relationships and considers questions of simultaneity and the so-called buffer-stock approach. The final section considers the recent behavior of money demand functions and summarizes the current state of affairs. 302 2. Overview of empirical difficulties S. M. Goldfeld and D. E. Sichel

As noted above, prior to the mid-1970s relatively simple specifications appeared to yield a stable demand function for money with plausible long-run parameter values. The subsequent misbehavior of the money demand function, both in the United States and elsewhere, has been widely documented [Goldfeld (1976), Judd and Scadding (1982a), Roley (1985), Fair (1987)]. As a consequence, we will be brief and somewhat selective in summarizing the evidence. Our present focus will be on postwar quarterly data for which a partial adjustment model of the following form was once deemed to be quite serviceable: In m~ = b 0 + b 1 In

Yt + b2 In r~ + b3 In mr_ 1 + b47rt + Ut , (2. 1) where m, is real money balances, r, represents one (or more) interest rates, y, is a transactions variable, and 7rt = In(P,/P, 1) is the rate of inflation associated with the price index, P,. The inclusion of 7r, in (2. 1) is meant to encompass the so-called real partial adjustment model ( b 4 = 0) or the nominal partial adjustment model (b 4 = – b3). 2 While not fully appropriate, (2. 1) is commonly estimated by single equation methods, which, however, do correct for the first-order serial correlation typically found in the residuals of (2. 1).

The Cochrane-Orcutt procedure is frequently used for this purpose although some variant of nonlinear least squares or maximum likelihood is generally more appropriate. 3 2. 1. U. S. m o n e y d e m a n d Results of estimating a version of (2. 1) with U. S. data are reported in Table 8. 1 for several sample periods. The data pertain to M1, currency plus checkable deposits, and are measured as seasonally adjusted quarterly averages, while y is measured by real GNP, P by the implicit GNP price deflator, and r is represented by two rates, R C P , the commercial paper rate, and R C B P , the commercial bank passbook rate.

The data reflect the February 1987 revision of the money stock and the major 1985 revision of the national income accounts. The results reported in Table 8. 1 were obtained by Cochrane-Orcutt although the results with full maximum likelihood taking account of the first observation were, for all practical purposes, the same. 2See Section 4 below for a derivation of (2. 1) and a discussion of the two types of adjustment models. 3Section 4 below. Ch. 8: The Demand for Money 303 Table 8. 1 A conventional money demand model Variable Intercept 952:31974:1 0. 381 (1. 7)” 0. 131 (5. 0) -0. 016 (5. 9) 0. 030 (3. 3) 0. 788 (12. 4) -0. 711 (6. 9) 0. 452 0. 0038 1952:31979:3 -0. 313 (2. 6) 0. 039 (5. 0) -0. 013 (5. 0) -0. 002 (0. 4) 1. 007 (47. 9) -0. 889 (9. 5) 0. 367 0. 0042 1952:31986:4 -0. 340 (4. 3) 0. 047 (7. 1) -0. 013 (5. 2) -0. 003 (0. 9) 1. 002 (67. 1) -1. 033 (10. 0) 0. 166 0. 0061 1974:21986:4 -0. 451 (2. 6) 0. 044 (1. 3) -0. 018 (2. 6) 0. 100 (1. 0) 0. 997 (32. 6) -0. 823 (2. 6) 0. 000 0. 0084 y RCP RCBP m, 1 P,/P, i p SEE at-statistics in parentheses. The first column of Table 8. gives the results for the relatively tranquil period ending in 1974:1. The results are generally sensible with significant income and interest effects and plausible long-run elasticities. Moreover, the specification appears stable over the period 1952:3 to 1974:1. This is revealed by formal tests of stability, conditional on an assumed sample split (not reported), or by the informal observation that the same specification estimated through the end of 1962 and simulated until 1974:1 does a good job of tracking the actual data. The static and dynamic simulation paths are portrayed in Figure 8. along with actual path of real balances. Some root mean square 6. 5 m Actual Static /_ • • ~ 6. 4, o 6. 3′ ?? 1 m Dynamic .” .. -“””‘. , . ” .. ‘” • • • •it ,,,,o oO. ””‘”””” mn • = 6. 2. mm~mlwmllmmw am m n • -I 6. 1 63. 1 • ! ! ! ! 68. 1 73. 1 78. 1 83. 1 86. ,4 Figure 8. 1. Log real balances and forecasts. 304 S. M. Goldfeld and D. E. Sichel Table 8. 2 Simulation root mean squared errors a Period t963-66 1967-70 1971-74 1975-76 1977-78 1979-80 1981-82 1983-84 1985-86 Static 0. 0053 0. 0051 0. 0044 0. 0180 0. 0199 0. 0226 0. 0285 0. 0202 0. 114 Dynamic 0. 0126 0. 0130 0. 0066 0. 0510 0. 0723 0. 0830 0. 0100 0. 0765 0. 0453 aErrors are for the specification of Table 8. 1, estimated through 1962:4 and simulated forward as pictured in Figure 8. 1. errors for subsamples of the forecast period for these simulations are given in Table 8. 2. The same underlying simulations are summarized in a different way in Figure 8. 2 which plots actual and simulated velocity. Table 8. 2 and Figures 8. 1 and 8. 2 reveal that the behavior of a conventional specification sharply deteriorates after 1974.

This poor forecasting performance suggests that the money demand equation underwent some sort of structural change after 1974, at least relative to the specification used in Table 8. 1. This is borne out in the last three columns of Table 8. 1 and in the formal stability tests reported in Table 8. 3. The key shortcoming of the results in Table 8. 1 is the fact that the coefficient of the lagged dependent variable is essentially unity, suggesting that we have a misspecified partial adjustment mechanism. This result obtains, even if we restrict the estimation to the post-1974 period.

N • Actual Static 7 O “6 O 4 3 63. 1 I I I I 68. 1 73. 1 78. 1 83. 1 86. 4 Figure 8. 2. Velocity and forecasts. Ch, 8: The Demand for Money 305 Table 8. 3 Parameter constancy tests Sample period Split point 1952:3-1979:3a 1974:1 1952:3-1986:4a 1974:1 1952:3-1986:4b 1979:3 aSpecification of Table 8. 1. bSpecification of first column of Table 8. 4. Significance level for F-test 0. 0004 0. 0364 0. 0011 Moreover, a closer examination of the results suggests that the post-1974 period itself may not readily lend itself to finding a single stable specification.

This speculation is perhaps more plausible when seen in view of the change in the Federal Reserve operating procedure that was introduced in October 1979, and of the substantial degree of financial deregulation after 1980. While we discuss more fully below the reasons for the empirical shortcomings we observe that, briefly put, the immediate post-1974 period of the missing money has been largely attributed to the effects of financial innovation. While the specification of the money demand function can be altered to reflect this in various ways described below, one can also “repair” the money demand function by the use of dummy variables.

Indeed, Haler and Hein (1982) have suggested that one could restore stability of the conventional specification over the period 1952-1978 by use of an intercept dummy, D, which takes the value of zero up to 1974:1 and unity thereafter. A re-examination of this issue suggested that this simple device was not quite adequate to restore stability but that slope dummies for y and R C P along with the intercept dummy were sufficient. 4 The results for this specification are given in Table 8. 4 for the sample period 1952:3 to 1979:3.

While this fix-up of the money demand equation is uninformative as to underlying causes, it does permit an examination of whether the most recent behavior of money demand is consistent with the specification given in Table 8. 4. The formal stability test reported in the last row of Table 8. 3 suggests that the post-1979 behavior is statistically different. While the conventional specification does well prior to 1974, the recent revision of the G N P data released in 1985 has cast some doubt about the adequacy of this specification, even in the pre-1974 period.

The issue is homogeneity with respect to the price level. Homogeneity of money demand, at least in the long run, is generally presumed to be a feature of any wellspecified money demand function. Consequently, rejection of homogeneity is typically taken to be evidence of misspecification. Tests for homogeneity are 4The set of dummies needed to restore stability is somewhat sensitive to the precise sample period, the presumed point of split, and the exact nature of the stability test. 306 S. M. Goldfeld and D. E. Sichel Table 8. Variants of a conventional money demand model 1952:31952:31952:3Variable 1979:3 1979:3 1974:1 Intercept 0. 198 0. 191 0. 296 (1. 0)” (1. 0) (1. 2) y 0. 110 0. 168 0. 178 (4. 5) (4. 8) (4. 7) RCP -0. 016 -0. 016 -0. 016 (5. 8) (6. 3) (6. 1) RCBP -0. 023 -0. 33 -0. 037 (2. 8) (3. 6) (3. 5) m, 1 0. 842 0. 768 0. 740 (14. 5) (11. 7) (9. 7) P,/P,_ ~ -0. 768 -0. 674 -0. 639 (8. 1) (6. 8) (5. 9) Dy -0. 065 -0. 070 (1. 6) (1. 8) DRCP 0. 016 0. 018 (2. 5) (2. 8) D 0. 466 0. 507 (1. 5) (I. 7) P -0. 034 -0. 033 (2. 5) (2. 2) p 0. 377 0. 360 0. 425 (3. 5) (3. 3) (3. 6) SEE 0. 0039 0. 0038 0. 037 “t-statistics in parentheses. typically accomplished by including In Pt in an e q u a t i o n like (2. 1) and doing a t-test to see if the coefficient is significantly different f r o m zero. G e n e r a l l y speaking, at least for s a m p l e periods that avoid the missing m o n e y , such tests have a c c e p t e d h o m o g e n e i t y [see G o l d f e l d (1973) and Spencer (1985)]. T a b l e 8. 4 reports the results of including the variable In Pt in the conventional specification through 1974:1 and in the conventional specification a u g m e n t e d with d u m m i e s for the period to 1979:3.

T h e significance of this variable further serves to call into d o u b t the a d e q u a c y of the partial a d j u s t m e n t model. T a k e n as a whole, the evidence for the U n i t e d States u n m i s t a k a b l y suggests the n e e d to rethink the conventional specification. B e f o r e turning to this we briefly consider results for o t h e r countries. 2. 2. M o n e y d e m a n d : International evidence Fair (1987) contains a good s u m m a r y of the empirical evidence on the d e m a n d for m o n e y in 27 countries. T o facilitate c o m p a r i s o n s across countries, Fair uses Ch. 8: The Demand for Money 307 common specification in which the dependent variable is real balances per capita and the explanatory variables are the lagged dependent variable, per capita real GNP, and a short-term interest rate. Table 8. 5 contains a selection of Fair’s results for OECD countriesJ The results in Table 8. 5 indicate some considerable similarity in money demand functions across OECD countries. Moreover, the “average” long-run income and interest elasticities are similar to those reported for the United States. With the exception of Germany, these OECD countries also share with the United States a penchant for instability in money demand.

Indeed, Fair found such instability present in 13 of the 17 countries tested. 6 Table 8. 5 International money demand; dependent variable: (m/pop)~ “b Country Canada Japan France Germany Italy U. K. Average Sample 1962:1-1985:4 1966:1-1985:4 1964:1-1985:4 1969:1-1985:4 1971:1-1985:3 1958:1-1986:1 Y/pop 0. 071 (2. 9) c 0. 084 (1. 3) 0. 094 (3. 5) 0. 343 (4. 8) 0. 130 (1. 8) 0. 118 (7. 0) 0. 140 R -0. 004 (2. 4) -0. 005 (3. 3) -0. 002 (1. 7) -0. 005 (6. 0) -0. 004 (2. 6) -0. 005 (4. 9) -0. 004 ~r -1. 66 (3. 3) -0. 29 (0. 6) – 0. 49 (1. 1) -0. 74 (2. 4) -0. 79 (2. 4) -0. 69 (4. 2) 0. 8 (m/pop),_~ 0. 94 0. 90 0. 25 0. 71 0. 86 0. 44 0. 68 SEE 0. 028 0. 023 0. 022 0. 013 0. 019 0. 022 0. 021 STAB d 19. 1″ 59. 4* 45. 3″ 5. 8 17. 0” aAll variables are in log form except for R, which is in levels. ~AII estimates are obtained with 2SLS. Only the estimates for the United Kingdom required serial correlation correction. The first-order serial correlation coefficient for the United Kingdom is -0. 377 with a t-statistic of 4. 3. Ct-statistics in parentheses. aThe value of the chi-squared statistic for rejecting parameter constancy with sample split following 1972:4.

For Germany, the sample split is 1975:4. *Significant at the 5 percent level. 5The results presented are a reparameterization of Fair’s to make them comparable with the U. S. specification. In particular, if z 1 and z2 are the coefficients on real and nominal balances in Fair’s table 1, these can be reparameterized so that (~-1+ “r2) and r 2 are the coefficients on real balances and inflation, respectively. Unfortunately, given the information presented by Fair, it is not possible to obtain standard errors for lagged money under this reparameterization. For a similar set of findings, see Boughton (1981). Curiously enough, using flow of funds data Fair reports a stable demand function for the United States. In attempting to replicate Fair’s results for the United States, we discovered that his stability finding depends somewhat on the exclusion of a rate such as RCBP and on the choice of the sample period. Furthermore, it should be noted that the extra noise in the flow of funds data tends to make it harder to reject parameter constancy. 308 S. M. Goldfeld and D. E. Sichel 3. Re-examining the basic specification

As should be apparent from the previous section, conventional specifications of money demand have exhibited substantial shortcomings over the last 15 years. As we shall see, attempts to repair these specifications have led to a reexamination of a wide variety of issues. Some of these issues can best be motivated with reference to the underlying theoretical models so it is to a brief review of these that we now turn. 3. 1. A b r i e f theoretical o v e r v i e w One early approach to the demand for money is the quantity theory of money. An example of this starts with the identity: MV~ PT , (3. 1) here M is the quantity of money, V is the velocity of circulation, P is the price level, and T is the volume of transactions. The assumption that V, being determined by technological a n d / o r institutional factors, is relatively constant allows one to recast (3. 1) as a demand function for money. Keynes modified this simple story and, in so doing, distinguished among three motives for holding m o n e y – t r a n s a c t i o n s , precautionary, and speculative. Overall, the main empirical legacy of Keynes in this area was the introduction of the interest rate into the demand for money, primarily via the speculative motive. 3. . 1. Transactions demand Most subequent developments amplified on the Keynesian motives in various ways. Baumol (1952) and Tobin (1956) both applied inventory-theoretic considerations to the transactions motive. In the simplest of these models, individuals are paid (in bonds) an amount Y at the beginning of a period and spend this amount uniformly over the period. This leads to the so-called square-root law with average money holdings given by M = ( 2 b Y ~ r ) 1/2 , (3. 2) where r is the interest rate on bonds and b is the brokerage charge or fixed transactions cost for converting bonds into cash. While the simplicity of (3. ) has appealed to many empirical researchers, it should be noted that the precise form of (3. 2) is highly dependent on the assumed payments mechanism. More particularly, under alternative assumptions proportional brokerage charges may be relevant and there may be nonconstant interest and income elasticities. Ch. 8: The Demand for Money 309 Yet another application of inventory theory to the transactions demand for money is the work of Miller and Orr (1966), which can also be interpreted as a model of the precautionary motive for money holding since there is a minimum allowable money holding below which a penalty must be paid.

As in the B a u m o l – T o b i n ( B – T ) framework, Miller and Orr ( M – O ) consider two assets and transactions costs which are fixed per transaction. The key difference is that M – O take cash flows to be stochastic. In the simplest version of their model, cash flows follow a random walk without drift in which in a given time interval (say 1/t of a day), there is an equal probability of a positive or negative cash flow of m dollars. Given a lower bound below which money balances cannot drop (normalized to zero), the optimal policy consists of an upper bound, h, and a return level, z.

Whenever money balances reach the lower bound, z dollars of bonds are converted to cash; whenever the upper bound is reached, h – z dollars of cash are converted to bonds. Minimizing the sum of expected per-day transactions and opportunity costs yields the optimal return level: z* = [(3b/4r)o-211/3 , (3. 3) where cr 2 is the daily variance of changes in cash balances (o-2 = m2t). In addition, M – O show that h* = 3z* and that the optimal size of average cash balances is given by M* = 4 z * / 3 . Thus, like the B – T approach, the M – O model yields a constant interest elasticity, although the value is 1/3 rather than 1/2.

The income or transactions elasticity is a bit more ambiguous since the only “scale” variable is o-2 which is the product of m 2 and t. If one thinks in terms of m, the size of each cash flow, then the scale elasticity is 2/3; however, if one thinks in terms of t, the rate of transactions, then the scale elasticity is 1/3. This ambiguity concerning the scale variable has meant that the M – O model is rarely estimated directly. Nevertheless, as we shall see, the M – O model is extremely useful for analyzing the consequences of innovation in cash management techniques. 3. 1. 2. Portfolio d e m a n d

Along with the transactions and precautionary motives, Keynes’ speculative motive has also been reformulated – largely in terms of portfolio theory [Tobin (1958)]. In the two-asset version of this approach, the individual wealth-holder allocates his portfolio between money, treated as a riskless asset, and an asset with an uncertain rate of return. Under the assumption of expected utility maximization, the optimal portfolio mix can be shown to depend on wealth and on the properties of the utility function and the distribution function for the return on the risky asset. Of particular relevance are the degree of risk 10 S. M. Goldfeld and D. E. Sichel aversion and the mean and variance of the return on the risky asset. In the general multi-asset case, the demand functions for each asset in the portfolio, including money, depend on all the expected returns and on the variances and covariances of these returns. From a theoretical point of view, with the usual caveat about income effects, the analysis yields a negative interest elasticity for the demand for money, providing another rationalization of Keynes’ liquidity preference hypothesis. From an empirical point of view, however, matters are less satisfactory.

To be sure, given specific utility and distribution functions, one can derive estimable asset demand functions. 7 However, given the menu of assets available in most countries, the portfolio approach actually undermines the speculative demand for money. The reason is that if money pays a zero return and if there is a riskless asset paying a positive rate of return (e. g. a savings deposit), then money is a dominated asset and will not be held. s In such a setting, to resurrect an asset demand for money one needs to combine the portfolio approach with transaction costs.

Friedman’s (1956) restatement of the quantity theory parallels Tobin’s portfolio approach in regarding the primary role of money as a form of wealth. Friedman dispenses with the separate motives posited by Keynes, and treats money as an asset yielding a flow of services to the holder. Wealth, both human and nonhuman, is thus one of the major determinants of money demand. However, to circumvent the empirical difficulties with nonhuman wealth, Friedman, reasoning from the fact that wealth is capitalized income, motivates the use of permanent income in a money demand function.

Furthermore, as in the Keynesian analysis of the speculative motive, Friedman posits that one aspect of the opportunity cost of holding money is the expected return on bonds. However, since there exist assets other than money and bonds that individuals may hold (e. g. equities or physical goods), Friedman considers the rates of return on these assets as part of the opportunity cost as well. Since the expected rate of return on physical goods can be measured by the expected rate of inflation, this variable also plays a role in Friedman’s theoretical analysis. 3. 1. 3.

Combining transactions and portfolio demand While suggestive, Friedman’s approach sidesteps the explicit role of money in the transactions process and also ignores problems of uncertainty. More recent 7The absence of data on variances and covariances is a potential stumbling block, especially in a world where these change over time. See Subsection 3. 2. 3. 8Obviously the result holds when m o n e y pays a positive return as long as the alternative asset has a higher yield. Also, in the presence of inflation, both m o n e y and the saving deposit will be risky assets but m o n e y will still he dominated.

Ch. 8: The Demand for Money 311 work has, in fact, emphasized one or both of these aspects, although a fully general treatment of uncertainty in the presence of transactions costs has yet to be developed. 9 The work of Ando and Shell (1975) represents one partial attempt. They consider a world with three assets, one risky and two, money and savings deposits, with certain nominal returns, r S and r m. They also treat the price level as uncertain and view individuals as maximizing expected utility where utility is given by U(C~, C2) and C i is the consumption in the ith period.

The role of money in the transactions process is captured in a real transactions cost function, T ( M , C 1), where holding higher money balances reduces transaction costs and thus, other things equal, raises C 2. Ando and Shell then assume that C 1 is determined independently of portfolio choice and show that the appropriate marginal condition for maximizing expected utility is given by r s – r m = T m ( M , C1) • (3. 4) Equation (3. 4) can be inverted to give money demand as a function of C1, (r s – rm), and the parameters of T.

More particularly, the demand for money is seen to be independent of the rate of return on the risky asset and of the expected price level and of wealth as well. To the extent they are robust, these results obviously dramatically simplify empirical work. One possible lack of generality stems from the assumption that C 1 is determined independently of the portfolio decision. The role of this assumption can be seen in the work of McCallum and Goodfriend (1987) who also deal in a three-asset world consisting of money, bonds, and capital.

McCallum and Goodfriend first consider the case of certainty, and start with an intertemporal household utility function of the form: U(C,, L , ) + fiU(C~+~, L,+I) + f i Z u ( C , + z , L,+z) + – – – , where C, and L, are consumption and leisure. The household has a production technology as well as initial real stocks of money (m,_~), bonds (b,_l) , and capital (k,_l). Somewhat analogous to the Ando-Shell setup, the role of money is captured by a “shopping time” function S, = 0((2,, m , ) , where shopping time, S,, subtracts from leisure.

As McCallum and Goodfriend show, maximizing utility results in a demand for money which can be written as m, =f(m,_l, k , _ l , b, 1, R , , R,+~ …. 7r,, ~,+1… ) , (3. 5) 9See Buiter and Armstrong (1978). 312 s. M. Goldfeld and D. E. Sichel where R, and 7r, are the nominal interest rate and the inflation rate, respectively, and where variables dated after t are anticipated values. 1° Equation (3. 5) is hardly a conventional-looking money demand function but the model does imply such a representation. Indeed, after some manipulation, McCallum and Goodfriend show that (3. 5) can be transformed to m t = g(Ct, R,). (3. 6)

The rather conventional-looking equation (3. 6) results from the fact that the structure of the McCallum-Goodfriend model is such that the use of the choice variable, C,, in (3. 6) allows one to eliminate everything but R t from (3. 5). Of particular interest is the role of initial wealth, which appears in (3. 5) via m , _ l , bt 1, and kt_ 1 but which has no role in (3. 6). As (3. 6) and (3. 4) are very close in spirit, the remaining issue is the robustness of (3. 6) to alternative assumptions. As McCallum and Goodfriend indicate, on this score there is good news and bad news. First, if we allow for the fact that future variables (e. . Rt+l, 7Tt+l) are not known with certainty, then it is quite likely that no closed form solution analogous to (3. 5) will exist. However, as McCallum and Goodfriend show after some further manipulation, (3. 6) will continue to be valid. Where the validity of (3. 6) is lost is if the intertemporal utility function is not time-separable. While this provides some comfort, the absence of a general portfolio/transactions model is particularly unfortunate, given that financial innovation and deregulation in the United States have increasingly offered to consumers a menu of financial assets that combine portfolio and transactions features.

While we make no pretense at having provided a comprehensive theoretical overview, it nevertheless appears that the bulk of empirical work on money demand has been motivated by one or more of the simple theories we have sketched. Taken as a group, the various theories we have discussed suggest many possible modifications to the conventional specification. For example, both the quantity theory and portfolio approaches suggest the use of a considerably broader range of opportunity cost variables as well as of a measure of wealth.

Portfolio theory also suggests the use of measures of uncertainty for the opportunity cost variabes. The transactions approach raises the issue of how the volume of transactions is to be measured and leads one to question the appropriateness of the implicit assumption of a constant real transaction cost embodied in the conventional specification. This latter assumption is particularly suspect in the light of the numerous innovations in financial markets and in the face of the substantial deregulation that evolved, at least in t°Equation (3. ) follows the simplifying assumption in McCallum and Goodfriend that labor is inelastically supplied. Otherwise, the wage rate would appear in (3. 5). Ch. 8: The Demand for Money 313 the United States. These issues, however, are best discussed as part of a more systematic review of the specification of money demand. 3. 2. A variable-by-variable review In re-evaluating the performance of the conventional specification, it is useful to consider the measurement and specification issues on a variable-by-variable basis. We begin with the dependent variable, money. . 2. 1. Definition of money Rather obviously, a first issue in the empirical estimation of money demand is the selection of an explicit measure of money. This choice is typically guided by some particular theoretical framework, but even so such choices are often less than clear-cut. Moreover, what passes for money can be readily altered by changing financial institutions. In the United States, at least, such changes, prompted by private financial innovation and deregulation, have had major implications for the definition of money.

In general, theories based on a transactions approach provide the most guidance and lead to a narrow definition of money that includes currency and checkable deposits. In some institutional settings a plausible measure of checkable deposits is readily apparent. In other settings there may well be a spectrum of checkable assets without any clear-cut dividing line. For example, a deposit account may limit the number of checks per month or may have a minimum check size. Other accounts may permit third-party transfers only if regular periodic payments are involved or may permit check-writing only with substantial service charges.

When such deposit accounts should be included in a transactions-based definition of money is not obvious. Once one moves away from a transactions view of the world, the appropriate empirical definition of money is even less clear. A theory that simply posits that money yields some unspecified flow of services must confront the fact that many assets may yield these services in varying degrees. Such theories have typically relied on a relatively broad definition of money but the definitions utilized are inevitably somewhat arbitrary.

To make these issues more concrete, we focus on measures of the money stock for the United States. 3. 2. 1. 1. Traditional aggregates. Table 8. 6 reports various official measures and key components. The official narrow definition of money, M1, presently includes currency, traveler’s checks, demand deposits at commercial banks, and other checkable deposits (OCDs). OCDs primarily consist of negotiable order of withdrawal ( N O W ) account. NOWs provide an insured interest- 314 S. M. Goldfeld and D. E. Sichel Table 8. 6 Various U. S. oney stock measures and components a (December 1986) Aggregate and component M1 Currency Traveler’s checks Demand deposits Other checkable deposits M2 M1 Overnight RPs plus overnight Eurodollars Money market mutual fund balancesb Money market deposit accountsb Savings deposits Small-denomination time deposits M3 M2 Large time deposits Term RPs and term Eurodollars b Institutional money market mutual funds Amount $ 730. 5 183. 5 6. 4 308. 3 232. 3 2,799. 7 730. 5 77. 3 207. 6 571. 3 366. 2 853. 2 3,488. 8 2,799. 7 447. 0 165. 2 84. 1 “Data are in billions and seasonally adjusted, except as noted. bNot seasonally adjusted.

Due to the use of unadjusted data the components of M2 and M3 do not precisely sum to the seasonally adjusted value of M2 and M3. b e a r i n g t r a n s a c t i o n s a c c o u n t a n d are available at several types of d e p o s i t o r y i n s t i t u t i o n s ( c o m m e r c i a l b a n k s , savings b a n k s , a n d savings a n d loan associations). 1~ B o t h of these features are a d e p a r t u r e from the earlier definition of M1 which, aside from c u r r e n c y , only c o u n t e d zero-yielding d e m a n d deposits available at a single d e p o s i t o r y i n s t i t u t i o n , c o m m e r c i a l b a n k s .

A s suggested earlier, e v e n with a t r a n s a c t i o n s – b a s e d m e a s u r e w h e r e to draw the line is n o t always evident. M o r e particularly, it can be a r g u e d that o n e or m o r e of the following c o m p o n e n t s of M2, which are e x c l u d e d from M1, b e l o n g in a t r a n s a c t i o n s m e a s u r e . (i) M o n e y m a r k e t deposit accounts ( M M D A s ) – i n s u r e d i n t e r e s t – b e a r i n g accounts at d e p o s i t o r y i n s t i t u t i o n s that p e r m i t u n l i m i t e d transfers to o t h e r accounts b u t only a small n u m b e r of checks per m o n t h . ii) M o n e y m a r k e t m u t u a l f u n d s ( M M M F s ) – u n i n s u r e d i n t e r e s t – b e a r i n g 11NOW accounts were, in fact, introduced by an innovative savings bank in Massachusetts in 1972 but only became available nationally in 1981. During the transition period the old definition of M1 became increasingly outmoded, a problem that has been repeated other times with other financial innovations. While it may be possible to sort these issues out after the fact, as they are occurring they may present thorny problems for the monetary authorities. Ch. 8: The Demand for Money 15 accounts that currently can generally function as a checkable account although there were previous restrictions on use (e. g. a minimum check size). (iii) Repurchase agreements ( R P s ) – a security sale with an agreement to repurchase it at a specified time and price. MMMFs rose in the mid-1970s, about the same time as NOWs, and for the same reason: high interest rates stimulated financial institutions to introduce and promote substitutes for demand deposits. MMDAs were a regulatory creation designed to enable depository institutions to compete more easily with MMMFs.

While the MMDAs and MMMFs clearly can be used to make transactions, their exclusion from M1 rests on the view that their features make them less appropriate for such purposes. Indeed, this is borne out by the pattern of use of these accounts which have lower rates of turnover as compared with instruments included in M1. Since the rationale for including RPs in M1 is at first blush unclear, a word of elaboration is called for, especially since a number of authors have argued that redefining narrow money to include RPs could solve the missing money puzzle of the 1970s.

In the 1970s RPs emerged as a popular device for corporate cash management, especially via overnight RPs, which provided, via the differential between sale and purchase prices, a way of converting a zero yielding demand deposit into an earning asset. 12 This suggested to some that RPs and demand deposits were essentially perfect substitutes and that M1 should be redefined to include some types of RPs. Moreover, rough attempts to do this appeared to lead to dramatic improvements in the forecasting of money demand for 1974-76.

Subsequent evidence, however, has cast doubt on these findings. 13 For one, transactions costs on RPs appear high enough to question the perfect substitutability assumption. Viewed in this light, RPs become just one of the numerous instruments used by corporate cash managers. Moreover, other institutional features of the market suggest there are substantial limits on using RPs to reduce demand deposits. Finally, even including RPs in M1 does not work all that well after 1976.

As should be evident, defining money may involve some hard choices. Determining what constitutes checkable deposits, for example, involves deciding where one draws the line in a spectrum of transactions-type assets that are substitutable in varying degrees. As to the choice between narrow and broad definitions, given the continued empirical difficulties with narrow definitions and the blurred lines between transactions and portfolio considerations, it is *2Moreover there were no reserve requirements on RPs.

We should also note that even without RPs the prohibition of the p a y m e n t of explicit interest on d e m a n d deposits, of course, did not prohibit the implicit p a y m e n t of interest on such deposits via the provision of “free” services. 13For a discussion of the issues and some empirical results, see Judd and Scadding (1982a). 316 S. M. Goldfeld and D. E. Sichel not surprising that some researchers have advocated the use of a concept like M2 for estimation purposes.

In addition to problems of determining which components belong in which aggregate, conventional broad monetary measures obtained by simply adding together quantities of different assets have been criticized for improper aggregation of assets with differing degrees of “liquidity” or as, it is sometimes put, which offer differing degrees of monetary services. Weighting the various components of money by the degree of “moneyness” is an idea that has been advocated over the years, but has experienced a resurgence at the hands of Barnett (1980) and Spindt (1985).

The work of Barnett and Spindt relies on index number and aggregation theory to develop aggregate money indices. For the United States a variety of these indices are now constructed and reported monthly by the Federal Reserve. The aggregates are calculated by the Fisher ideal index number formula given by 3. 2. 1. 2. Alternative aggregation approaches. M, . .F . Z . mitait L ~-t-i X? ~ mitait 1 “] 1/2 ‘ I (3. 7) Z mi, lai, Z mi,_lait_l_ 1 where mit is the component quantity of the ith asset and the air is the associated weight. Barnett and Spindt differ in their choice of the ai,.

Barnett’s work aggregates the components of money according to their characteristics as assets in a portfolio, while Spindt aggregate these components according to their characteristics as a transactions medium. In Barnett’s original approach, following Friedman (1956), monetary assets are viewed as durable goods rendering a flow of monetary services. In this framework, the a , ‘ s measure the opportunity or “user” cost for asset i, which is the interest forgone by holding asset i as opposed to an alternative higher-yielding nonmonetary asset. One immediate problem is how these user costs are to be calculated.

A first issue concerns the own rate where there are obvious measurement difficulties created by the payment of implicit interest via the provision of services and the existence of explicit service charges. The lack of data make it hard to evaluate the seriousness of these difficulties. More is known, however, as to the consequences of the benchmark yield on the nonmonetary asset. Current practice is to use a corporate bond rate as the benchmark rate, except when one of the own rates on some mi, is higher, and this rate is then used as the benchmark rate.

This means that the user cost of this highly liquid asset is zero and the implied monetary services are therefore unreasonably regarded as nil. Even in less extreme situations, the evidence suggests that Ch. 8: The Demand for Money 317 interest rate movements can produce anomalous variations in user costs. Put another way, the resulting monetary service indices are sensitive to the choice of the benchmark yield. Furthermore, at least as now constructed, the monetary service indices appear to behave somewhat oddly in various parts of the 1980s [see Lindsey and Spindt (1986)].

This has turned interest to an alternative approach to monetary aggregates due to Spindt (1985). In contrast to aggregation by asset characteristics used by Barnett, Spindt has developed a money stock index based on transaction-theoretic considerations in which the component assets are viewed as differing in the volume of transactions financed per dollar of asset. In terms of the equation of exchange we have: E miui -= P Q , where v i is the net turnover rate or velocity of the ith asset. It is then the u i that are used as the weights in (3. 7).

One implementation of this approach is embodied in the series MQ published by the Federal Reserve. MQ includes those assets in M1 plus money market deposit accounts and money market mutual funds. 14 As with the case of the monetary services index, there are some nasty measurement problems here as well. In the first instance, gross turnover rates are not available for some assets (currency, money market mutual funds). Furthermore, even where available, gross turnover rates reflect a large volume of payments for transactions not reflected in GNP such as financial transactions and payments for intermediate goods.

To go from gross turnover to net turnover therefore requires many assumptions. Nevertheless, there is some evidence that the growth rate of MQ “appears fairly robust to variations of most of these assumptions within plausible ranges” [Lindsey and Spindt (1986, p. C-4)]. While the problems in constructing MQ thus appear to be surmountable, when the finished product, MQ, is used in a money demand function, it appears to suffer several disruptions in the 1980s) 5 Nevertheless, the proponents of MQ regard the results as sufficiently promising that two refinements are being pursued.

The first is to relax the not realistic assumption that all holders of a given asset necessarily have the same turnover rate (e. g. contrast business and household use of demand deposits). A second refinement is to define velocities in (3. 7) with reference to a broader measure of transactions 14Despite the apparent circularity in using velocity to define the aggregate, MQ will not change if the components m e remain the same and the v i change. This can readily be seen by examining (3. 7). 15Data on M Q are currently only available beginning in 1970 so they cannot easily be used to shed light on the “missing money” period. 18 S. M. Goldfeld and D. E. Sichel than real GNP. The first step here is to define such a measure and some progress on this has been reported in Corrado and Spindt (1986). Of course, as is discussed below, such a measure of transactions could be used with any measure of money. Overall, it would thus appear that the jury is still out on the virtues of applying index theory to yield measures of money. 16 3. 2. 1. 3. Disaggregation. While “proper” aggregation is one approach to modeling the demands for heterogeneous monetary assets, an equally time-honored tactic is to use a disaggregated approach.

For example, even in a world in which the definition of checkable deposits is relatively unambiguous, it is not clear that currency and checkable deposits should be regarded as perfect substitutes, a view that is implicit in simply adding them together to produce a measure of money. Currency and checkable deposits may differ in transactions costs, risk of loss, and ease of concealment of illegal or tax-evading activities. It may thus be preferable to estimate separate demand functions for currency and checkable deposits.

Once we recognize that checkable deposits may consist of heterogeneous subcomponents we have further grounds for disaggregation. An additional basis for disaggregation, alluded to above, is that a given monetary asset may be held by behaviorally diverse groups. What this suggests is that disaggregation offers a way to sidestep the definitional issues at the same time that it permits the use of econometric techniques that take account of the interrelated nature of demand functions. Disaggregation has yielded some promising empirical results but, as with proper aggregation, disaggregation hardly resolves the key empirical difficulties. . 2. 2. Scale variables Until relatively recently scale variables typically came from among GNP, permanent income, or wealth, all measured in real terms. GNP was used in transactions-oriented models, while permanent income, most frequently measured as an exponentially weighted average of current and past values of GNP, was used by modern quantity theorists. Since permanent income is often viewed as a proxy for wealth; direct measures of wealth (invariably only nonhuman wealth) have also been used. Given that financial transactions can generate a demand for money, the use of wealth is also consistent with a transactions view.

As an empirical matter, given the high correlation of GNP and permanent income, both tended to “work” reasonably well prior to the missing money 16Should it turn out that such measures yielded sensible and stable m o n e y d e m a n d functions, considerable thought would still be needed as to how these measures would best be incorporated into the monetary policy process. Ch. 8: The Demand for Money 319 episode, while the role of wealth was somewhat more ambiguous, especially if included with an income variable.

At a formal level, many early studies viewed the matter as a contest between these three variables, the winner often depending on the sample period, the definition of M, and the econometric details. When the transactions-oriented models began misbehaving, it was natural to examine whether permanent income or wealth might improve matters. There is a hint that wealth may be part of the story in B. Friedman (1978) but, on balance, as Judd and Scadding (1982a, p. 1008) have noted, “the solution probably does not reside in this area”.

In more recent years, research on scale variables has focused on the following two aspects of the transactions measure: (i) the construction of more comprehensive measures of transactions; and (ii) the disaggregation of transactions into various components, reflecting the notion that not all transactions are equally “money intensive”. We discuss each of these in turn. The construction of more comprehensive measures of transactions is motivated by the the fact that despite the appearance of “gross” in GNP it is much less inclusive than a general measure of transactions.

In particular, it excludes all sales of intermediate goods, transfers, purchases of existing goods, and financial transactions, all of which may contribute to the demand for money. At the same time, focus on the product side ignores the fact that the income side also generates payments needs. Finally, in one sense GNP may overstate transactions because it includes imputed items. While these shortcomings of GNP have long been recognized, thorny data problems have discouraged the construction of more general transactions measures.

As a proxy for such a measure, some researchers have used data on gross debits to demand deposit accounts. While in some instances substituting debits for GNP improves things, the effect is small and not terribly robust [see Judd and Scadding (1982a)]. Part of the problem may be that the behavior of debits is rather dramatically affected by financial transactions. Also of importance is the fact that increasing sophistication in cash management that reduces average holdings of money given the level of transactions, may be brought about by an increase in debits.

In recent years, however, there have been some noticeable advances in constructing general measures of transactions, particularly by Cramer (1986) and Corrado and Spindt (1986). Since only limited data are presently available, it is too early to tell if these new data will improve the performance of money demand functions. 17 ~7Corrado and Spindt (1986) make a major attempt to adjust the flow of payments for timing differentials stemming from purchases made on credit.

Like Cramer, however, they generally ignore transactions associated with exchanges of real or financial assets. A bit of evidence in Wenninger and Radecki (1986) suggests the latter omission may not be serious. Of course, if a general transactions measure proved useful, we would need to develop an adequate theory for its behavior. 320 S. M. Goldfeld and D. E. Sichel Whatever measure of transactions is chosen, there remains the question of whether it might usefully be disaggregated into several scale variables.

Thus, for instance, if real GNP is the basic scale variable, one might separately enter various compents of GNP on the grounds that these components are likely to generate different payments needs. For example, one might posit that consumption is more money intensive than other components of GNP, a hypothesis that is supported by some evidence. 18 In a similar vein, aggregate GNP is unlikely to capture the role of inventory investment since inventory liquidation is reflected negatively in GNP but sales from stocks do generate monetary transactions.

As a final illustration, it is likely that domestically produceddomestically consumed goods (DP), exports (X), and imports (IM) are sufficiently different in the nature of their production and distribution processes so as to generate different needs for dollar-denominated transactions balances. The disaggregation of a scale variable to reflect appropriately the nature of international transactions is likely to be particularly important for an economy with a substantial degree of openness, but there is evidence that the distinction is of relevance for the United States as well [Radecki and Wenninger (1985)].

On the whole, while there are some promising indications, there is no firm evidence that disaggregation of GNP yields a dramatic improvement in the behavior of aggregate money demand. The case for disaggregation, however, appears a bit stronger when coupled with the disaggregation of money into type of holder (e. g. consumer vs. business) and type of deposit) 9 3. 2. 3. Opportunity costs Measuring the opportunity cost of money, relative to a given definition of money, involves two ingredients: the own rate on money and the rate of return on assets alternative to money.

To keep matters simple we focus on the narrow definition of money: currency plus checkable deposits. When checkable deposits consisted solely of demand deposits with an explicit yield of zero, most empirical researchers treated the own rate as zero. Strictly speaking, this is not correct since deposit holders may earn an implicit rate of return, either because they receive gifts or services or because transactions fees may be forgone as the level of deposits rises. However, measuring lSSee Mankiw and S u m m e r s (1986).

A somewhat different a r g u m e n t in favor of consumption is that it serves as a good proxy for p e r m a n e n t income. 19For some early evidence on this see Goldfeld (1973, 1976). It should also be noted that formal testing of differential effects of s u b c o m p o n e n t s of G N P is a bit awkward in a logarithmic specification since the components of G N P are linearly related. Mankiw and S u m m e r s get around this by introducing a variable a[A log Y + (1 – A) log C] and examining A with A = 1 the conventional model.

Swamy, KennickeU and von zur Muehlen (1986) handle the international variables by noting that G N P = DP(1 + X / D P ) ( 1 – I M / ( D P + X)) and then include each term separately. If the coefficients are the same one can aggregate to log GNP. Ch. 8: The Demand for Money 321 this implicit return is no easy matter and it is, perhaps, not surprising that this issue was largely ignored. 2° This luxury is not available when even narrow money pays an explicit return, a situation that began in a small way in the United States in the early 1970s and become increasingly widespread in the 1980 deregulation.

Matters are somewhat complicated when only some components of money bear explicit interest and when several components may bear different nonzero rates of return. Both of these situations pertain to the United States at present. The aggregate own rate of return is then a complex function of the interest rates, shares, and elasticities of each of the components. These complexities have generally been ignored. For example, Roley (1985), following Cagan (1984), defines the own rate as the then-prevailing ceiling rate adjusted by the fraction of interest-bearing deposits in M1 and reports only limited success with this variable.

More promising, perhaps, is the use of such a variable in a disaggregated analysis that separates out other checkable deposits (OCDs) and demand deposits [see Porter, Spindt and Lindsey (1987)]. Unfortunately, the sample period available for estimating the OCD equation is quite short. As to the rate of return on assets alternative to money, those researchers adopting a transactions view typically use one or more short-term rates such as the yield on government securities, the yield on commercial paper, or the yield on savings deposits. 1 Those researchers adopting a less narrow view of the demand for money have used a correspondingly broader set of alternatives including proxies for the return on equities and long-term bond rates, either government or corporate. Hamburger (1977) has been one of the most ardent advocates of using long-term bond and equity returns, going so far as to suggest that the use of such variables solved the puzzle of the missing money. However, as a number of writers have observed, Hamburger’s model contains a number of constraints (e. g. unitary income elasticity) that are not warranted by the data [Roley (1985)]. A few studies have used proxies for the entire term structure of interest rates [Heller and Khan (1979)] and while it has been claimed that this specification also repaired the missing money episode, this also has not stood up to closer scrutiny [see Judd and Scadding (1982a)]. Finally, some have emphasized the importance of foreign interest rates and/or exchange rates. While this has been of particular importance outside the United States, there is some vidence that these might be of use for the United States as well. Nevertheless, these do not seem to cure the missing money period [Arango and Nadiri (1981)]. 2°For exceptions, see Klein (1974) and Startz (1979). 2~Even here, there are potential problems. For example, it matters whether interest earned on savings deposits is paid quarterly, monthly, or daily. For the United States, at least, at various points of time all three modes have existed. One might well see a “shift” in a simple money demand function as institutional practice changed. 322 S. M.

Goldfeld and D. E. Sichel As noted earlier, some writers have also emphasized the role of expected inflation. This has been variously measured by a distributed lag of actual inflation, by expectational proxies from surveys, and by using predictions of expected inflation generated from some sort of autoregressive process• While no clear-cut consensus appears to have emerged on the use of expected inflation, it should be noted that the nominal partial adjustment model with inflation excluded still embodies a permanent effect of inflation on the demand for real balances. 2 Those who use a rich variety of interest rates sometimes appeal to the portfolio approach, although, as noted above, there are some problems with this rationale. The portfolio approach also emphasizes the role of variances and covariances of the underlying expected returns. While these are not directly observable, a number of studies have used ex post measures of volatility in interest rates or inflation rates as proxies. While some have found support for such variables, others have concluded that there is little evidence that interest rate volatility affects the demand for M1. 3 One major source of this discrepancy is that there is an embarrassing number of ways in which volatility can be measured and the results appear sensitive to these and, of course, to the remaining aspects of the specification. A final issue concerning interest rates is the effect of deregulation on the interest elasticity of the demand for money. Deregulation has meant the availability of money substitutes paying competitive rates of return and the availability of increasingly competitive rates of return on transactions balances.

Some have argued that these events will lower the elasticity of M1 with respect to market interest rates while others have argued that the elasticity could increase. 24 Not surprisingly, the empirical results are inconclusive with Keeley and Zimmerman (1986) offering evidence of increased elasticities, while Roley (1985) suggests unchanged elasticities. At the very least, however, the possibility of a changed interest elasticity in response to deregulation suggests that a double logarithmic specification, which constrains the elasticity to be constant 25 over the sample period, may be inappropriate. • 22See Goldfeld and Sichel (1987a) and Section 4 below. 23Baba, Hendry and Start (1985) offer evidence in favor of volatility measures, while Garner (1986) provides negative evidence. Garner also contains a substantial number of references to earlier work. Walsh (1984) provides a formal model in which the interest elasticity of the demand for money is explicitly related to interest rate volatility. 24Keeley and Zimmerman (1986) consider the latter case while the former view is given in Judd and Scadding (1982b) and Santomero and Siegel (1986).

At issue is the extent to which depository institutions had formerly circumvented interest rate ceilings through nonprice competition. Also relevant, at least from a portfolio perspective, is what happens to the variability of interest rates in a deregulated environment. See Roley (1985)