Changes in Wealth and the Velocity of Money

FEDERAL RESERVE BANK OF ST. LOUIS MARCH 1981

Changes in Wealth and the Velocityof MoneyG. J. Santoni

NE long-standing view among economists isthat the quantity of money in circulation and aggre-gate income are closely related in the long run.’ Thisrelationship, known as the income velocity of money,is particularly important because it makes it possibleto determine the effect ofchanges in money growth onincome over extended periods ,~

Unfortunately, this relationship has not behavedwell in recent years. Various investigators have at-tempted to identity the reasons for this unusual be-havior) focusing on institutional changes that allowedthe payment of interest on transaction deposits, therise in the trade deficit, and changes in tax rates.3 Ingeneral,however, their results havebeen inconclusive.

This article discusses how changes in wealth canaffect velocity and considers whether the atypical be-

G. J. Santoni is a senior economist at the Federal Reserve Bank of St.Louis. Thomas A. Pollmann provided research assistance.‘See, for example, Fisher (1963) who notes that: “This theory,though often crudely formulated, has been accepted by Locke,Hume, Adam Smith, Ricardo, Mill, Walker, Marshall, Hadley, Fetter,Kemmerer, and most writers on the subject.” (p. 14) See also pp.157—59 and 296—97. More recent examples are Friedman andSchwartz (1963 and 1982). Thornton (1983) presents a nontechni-cal discussion of the theory.

2Using monetary policy to hit short-run stabilization objectives isproblemmaticat if not impossible. See Thornton (1983) and Mankiwand Summers (1986), p.4l9, for discussions of this point.

3Rasche (1986), Mankiw and Summers (1988), Tatom (1983), Taylor(1986), Siegel and Strongin (1986) and Kopcke (1986) representsome of the recent attempts to resolve the issue,

havior that velocity has exhibited in recent years canbe attributed to changes in wealth.’

VELOCITY: A MEASURE OF THERELATIONSHIP BETWEEN MONEYAND SPENDING

The most commonly used measure of the relation-ship between income and the stock of money is theincome velocity of money. It is the ratio of GNP to Ml(the sum of currency in the hands of the public andcheckable deposits).

Chart I plots the income velocity of money from 1/1959 through 111/1986. As indicated, this measure hasrisen fairly steadily throughout most of the period.Before 1982, the growth rate of income velocity wasremarkably stable, averaging about 3 percent peryear.’Hence, the average annual growth rate of GNP ex-ceeded the average annual growth rate of the quantity

‘See Knight (1941), Friedman (1956) and Meltzer (1963) for exam-ples of this argument.

‘The average annualized growth rate was 3.13 percent with a stand-ard deviation of 4.03. The standard deviation is a measure of thevariation in velocity growth around its average. Short-run changes invelocity growth have been attributed to cyclical factors, changes inthe pattern of receipts and payments, financial innovations andchanges in the nominal interest rate. See, for example, Fisher(1963), pp. 58—73, Tatom (1983) and Thornton (1983), p. 10.

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FEDERAL RESERVE BANK OF St LOUIS MARCH 1987

Chart 1

Income Velocity

8.0

6.0

4.0

2.0

8.0

6.0

4.0

2.0

of money by about 3 percentage points.8 In recentyears, however, velocity growth has changed consid-erably. As chart I indicates, velocity generally hasdeclined at an annual average rate of about 3.0 percentsince the end of 19817

If monetary policymakers were certain that thelong-run average growth invelocity had changed per-

‘If V is the income velocity of money while Y and Mare GNP and thequantity of money, then V~Y/M.This equation can be written ingrowth rate form as below. The dots over the variables indicatecompounded annual growth rates.

‘c’- rA

Since “ averaged about 3 percent before 1982, t exceed M byabout 3 percentage points on average.‘The breakin velocity growth has been dated at the end of 1981. SeeRasche (1986), pp.2 and 8. The average annualized growth rate invelocity during 1/1982—111/1986 was —2.9 percent with a standarddeviation of 5.67.

manently from + 3 percent peryear to —3 percent peryear, they could, once again, determine the impact ofany given long-mn growth in Ml on GNP. There isconsiderable uncertainty, however, about whether thechange in velocity’s average growth is permanent oronly temporary. Identifying the reasons for the recentdeclines might help resolve this issue.

VELOCITY AND MONEY DEMAND

Velocity relates the equilibrium level of income tothe equilibrium quantity of money; the latter dependsimportantly on the quantity of money demanded.’Momentarily ignoring other things that may influencepeople’s choices, money demand theory states thatthe demand for money is proportionally related to

‘See Friedman (1956), p,4.

Y~Y/M Y~Y/M

I I I I I I I I I I I I I I I I I I I I I I I I I I I1960 62 64 66 68 70 72 74 76 78 80 82 84 1986

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some scale variable, either income or wealth. Thetransaction theory of money demand uses the flow ofcurrent income as the scale variable while the portfo-ho approach to money demand uses the stock ofwealth.’

The Transaction Approach toMoney Demand

The transaction approach presumes that money isheld to support current spending and that currentspending is closely related to current income. Thistheory relates the demand for money (M”) to currentincome (Y( by some proportion (k). In equilibrium,since the quantity of money demanded is equal to thequantity supplied (M” = M’ = kY), the ratio ofincome tothe quantity of money (incomevelocity) is equal to theinverse of this proportion (V = Yaw= Y/kY = 1/k). If cur-rent income rises, desired spending rises in propor-tion; consequently, people will want more money tofacifitate their increased spending.

The transaction approach has an important advan-tage from an empirical point of view. The data onincome are relatively good and readily available -

What’s more, numerous empirical tests of the theoryhave been conducted, and the empirical relationshipsbetween money and income have performed well dur-ing certaln time periods.” There have been occasions,however, when they have broken down. Various ana-lysts have pointed to breakdowns in the mid-1960s,when velocity fell unexpectedly, in the mid-l970s,when it rose unexpectedly, and, in recent years, whenit has fallen again unexpectedly.”

A Portfolio Approach to Money Demand

An alternative theory of money demand suggeststhat the quantity of money balances that people holdis related more closely to their wealth than their cur-rent income.’2 Money is simply one of many assets in

~Thetransaction approach includes other variables besides currentincome in the money demand function. These are mentioned below.See Laidler (1985), pp. 49—97, for a more complete discussion of thevarious approaches to money demand.

“See Laidler (1985), pp. 117—34.“Fewpeople dispute the importance of the recent breakdown. There

is some disagreement, however, regarding the significance of theearlier breaks. See Judd and Scadding (1982), Laidler (1985), pp.135—51, and Rasche (1986), p. 7, for a discussion of the earlierbreaks.

“See Knight (1941) and Friedman (1956), pp. 4—5. Knight, for exam-ple, argues that “The economic process in a pecuniary economyinvolves the holding or owning, by somebody, of wealth — all the

which wealth may be held. The desired mix of assetsthat make up wealth depends on both the net benefitsof holding wealth in the various forms and risk prefer-ences. The portfolio theory states that an increase inwealth is associated with an increase in the quantity ofmoney people want to hold and vice versa.

Again, ignoring other factors that may influencechoices, this theory says that the demand for money isa constant proportion (0) of wealth 1W).” In equilib-rium, the quantity of money demanded is equal to thequantity supplied; thus, the ratio of wealth to money(wealth velocity) is equal to the inverse of this propor-tion (W/M = W/OW = 1/0) -

The Djfference between the Two

Both theories of money demand agree that certainvariables, such as short-term interest rates, popula-tion, the pattern of receipts and payments, the tech-nology of the payment system and risk preferences,are important for money demand. They differ, how-ever, in regard to the scale variable,

If current income were always a constant propor-tion of wealth, there would be no substantive em-pirical difference between the two theories. In thiscase, 0 and k would differ by a constant factor thatreflects the ratio of income to wealth [V = 1/k = Y/M =

(W/M)(Y/W) = (1/0)(Y/W)]. If income is not a constantproportion of wealth, however, and if the portfoliotheory of money demand is correct, income velocitywill fluctuate whenever current income changes rela-tive to wealth. If current income rises relative towealth, for example, the income velocity of money willrise also, other things the same. The reverse move-ment in the income velocity of money would occur ifwealth rises relative to current income.

Two Important Conditions

The above discussion indicates that two conditionsmust hold if changes in wealth relative to income areimportant in explaining the decline in velocity since

wealth of the economy— and also the entire stock of money. Henceeven,’ property owner has the altemative either of holding money upto the amount of his fortune or of choosing the concrete kind ofwealth other than money he will hold.” (p. 210)

“The portfolio theory does not necessarily imply a constant propor-tional relationship between money and wealth. This is an empiricalquestion. See Laidler (1985), p. 58. There is evidence that therelationship is proportional for at least some wealth proxies. See, forexample, Mankiw and Summers (1986) and Meter (1963). It isassumed to be proportional above for illustrative purposes.

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the end of 1981: 1) the demand for money must bemore closely related to wealth than to current income(that is, wealth is the appropriate scale variable); 2(wealth must have risen relative to current incomesince 1981.

Although the choice of the appropriate scale vari-able is still an unresolved issue among economists, itis useful to determine whether the second conditionholds - If wealth has not risen relative to current in-come since 1981, whether the first condition holds ornot is irrelevant; we can conclude that changes inwealth do not help explain the recent decline inveloc-ity. On the other hand, if wealth has risen relative tocurrent income, resolving the first issue becomesmore important.

WHAT IS WEALTH?

To see why the ratio of current income to wealthmay vary, it is helpful to understand how they arerelated.

An individual’s wealth is the market value of his netassets; this market value is found by adding togetherthe present values of all his assets and subtracting thesum of the present values of all his liabilities - Thisdifference is equal to the present value ofthe expectedstream of net receipts (income minus expenses). In thesimplest case, it is the expected net income flowdivided by the long-term interest rate.” Thus, an indi-vidual’s wealth at any time depends on both the ex-pected future flow of net income and the relevanthong-term interest rate.

The Effect ofCurrent Income on Wealthand Vice Versa

Current income is the actual amount of incomereceived each period. Because unanticipated eventsinfluence the income actually received, current in-come generally differs from the income expected forany period. The difference between current and ex-pected income is called transitory income.

Since wealth is the present value of the expectedfuture income flow, transitory income has only a small

“See Fisher (1954), pp. 12—13, and Friedman (1956), pp. 4—5.Fisher, for example, defines wealth (or capital value) as “simplyfuture income discounted or, in other words, capitalized. The valueof any property, or rights to wealth, is its value as a source ofincomeand is found by discounting that expected income. - - The bridge orlink between income and capital is the rate ofinterest.” (emphasis inoriginal)

effect on wealth. For example, suppose a person re-ceives a surprise Christmas bonus of $2,000. If theperson’s annual income is $20,000, the bonus is 10percent of current income, a fairly large percentage - If,however, the person does not associate the bonuswith a change in his future income prospects, and hiswealth before the bonus was $200,000, the effect of thebonus on his wealth is relatively small (1 percent ofwealth) -

Another way to view this is to note that the individ-ual’s ‘permanent income” is not much affected by thebonus. Permanent income is the amount of consump-tion that can be sustained without changing wealth.Permanent income and wealth are closely related.” Inthe above example, if the person consumed $22,000 inthe year the bonus is received, he would necessarilyhave to reduce his consumption in the fohhowing yearor draw down his wealth, other things the same.

Suppose the person in this example is promised anincrease in his annual salary beginning some time inthe future. His wealth increases immediately uponlearning of the prospective raise, other things thesame, and his expected stream of future income isnow higher, even though his current income does notyet reflect the raise. A decline in the interest rateinduces a similar increase in wealth, other things thesame, because it increases the present value of theunchanged stream ofexpected future income; currentincome, again, is unchanged.

While these examples refer to individuals, the argu-ment applies to the whole community as well. Unex-pectedly good harvests, favorable relations betweenunions and management, or tranquil foreign relationscan produce positive transitory components of in-come for the whole community. A reduction in tradebarriers or changes in the tax laws that result in moreproductive use of resources can raise the expectedfuture flow of aggregate income and, thus, raise wealthrelative to current income. Finally, a decline in thelevel of interest rates can raise the present value of agiven expected future flow of aggregate income; thisincrease in wealth occurs without affecting the cur-rent or expected future levels of income.

“See Friedman (1956), p-5. For a perpetual stream of income that isexpected to increase at a constant rate (p), wealth is

w = y,(l±p)/(r.—p),

where y, is the initial income receipt and r is the real interest rate(r>p). Permanent income is y’ = rw. Wealth and permanent incomeare constant across time as long as rand pare constant and savingis zero. Expected income in period n, however, is y, = y, (1 + p)’.

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As the above discussion suggests, the ratio of cur-rent income to wealth generally is not a constant.Thus, if wealth is the appropriate scale variable formoney demand, velocity will vary as the ratio of cur-rent income to wealth varies.

MEASURING NATIONAL WEALTH

Since we are concerned with the relationship be-tween wealth and society’s demand for money, weneed to establish a concept of national wealth. Na-tional wealth is simply the aggregate wealth of thenation’s residents.” There ar-e two theoretically equiv-alent methods of measuring nationah wealth: the in-come and balance sheet methods.

The Income Approach

National wealth, in theory, can be measured bydiscounting the expected stream of net national in-come by the appropriate interest rate. Some practicalproblems must be dealt with, however, when applyingthis method of measuring national wealth. One obvi-ous problem is that the expected stream of income isnot directly observed. Only current and past incomesare known. Thus, practical applications of the incomemethod must depend on good estimates of the ex-pected stream of net national income.

Many studies have used univariate time-seriesmethods to estimate the expected stream of futureincome.” Roughly, time-series models account furpatterns in past movements of a particular variable(national income, in this case) and use the informationcontained in the pattern to predict future values of thevariable. In a sense, a time-series model is a sophisti-cated method of extrapolation.”

Whihe these models are a useful estimating tool,they have a serious drawback. When using them, theinvestigator must assume that the underlying eco-nomic structure that generated the observations willremain unchanged during the period of analysis. Forexample, a time-series model is not designed to fore-cast changes in the stream of future income that areproduced by significant technological changes, insti-tutional changes such as a major shift in the tax law, or

“See Goldsmith (1968), p. 51.

“See Laidler (1985), pp. 88—90.“See Pindyck and Rubinfeld (1981), p. 470.

significant changes in relative supplies such as pro-duced by OPEC production quotas.

Another problem concerns the interest rate that isappropriate for discounting expected national in-come. National income is the sum of wages, rents andprofits. Wage income, which accounts for about 75percent of national income, is produced by humancapital while nonhuman capital is the source of rentsand profits. Unfortunately, the interest rate that isrelevant in discounting the expected stream of wageincome (i0) is not observable; moreover, because hu-man capital is not as liquid as nonhuman capital, i~isprobably higher than the interest rate that applies toincome produced by nonhuman capital (ik).” hf ex-pected wages are discounted at the lower rate i,,national wealth will be overstated.” Of course, per-centage changes in the wealth estimate will not bedistorted as long as the ratio ofi11 to i, does not change.Empirical estimates that depend on a constant rela-tionship between these two interest rates, however,will produce misleading results whenever this ratiochanges substantially.

The Balance Sheet Approach toEstimating Wealth

Some investigators have estimated national wealthusing the balance sheet approach.” This measure isobtained by summing the present values of the assetsowned by U.S. residents and subtracting the sum ofthe present values of all the liabilities owed by U.S.citizens.

When these assets and liabilities are aggregated, allclaims of one U.S. citizen against another U.S. citizencancel out. Since most liabilities of U.S. citizens areowed to other U.S. citizens, these liabilities and theirasset counterparts disappear from the aggregation.What remains is national wealth. It includes nonre-producible and reproducible tangible assets such asland, buildings, structures, machinery, vehicles, con-sumer durables, inventories (of raw materials, work in

“See Friedman (1956).“The only interest rates that are directly observable are those that

apply to financial instruments. Consequently, neither i~or ~karedirectly observable. The capital asset pricing theory developed inthe finance literature, however, can be used to produce estimatesof i,

“See Goldsmith (1968). In theory, the balance sheet and incomeapproaches to measuring wealth are equivalent. But there arenumerous practical problems that arise. These are discussedbelow.

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process and finished goods), military assets, works ofart, human capital and net claims on foreigners.”Most investigators who estimate national wealth bythe balance sheet method agree that the above itemsbelong in national wealth. There is some disagree-ment, however, about which other things should alsobe included. These controversial items are discussedin the shaded box above.

“See Goldsmith (1968), p. 52.

The balance sheet method of estimating nationalwealth is costly because it requires an extensive inven-tory of the nation’s assets and liabilities. As a result,estimates of national wealth that employ this methodare available only on an annual basis.

There are several other problems with thismethod.” It requires that assets and liabilities be val-

“See Goldsmith (1968), pp. 52—54, for a further discussion of thepractical problems of applying this method.

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Chart 2

Log levels

10.0

8.0

6.0

4.01959 61

ued at their market prices. Many assets, however, aretraded infrequently, if at all. For example, the dis-counted value of people’s wages is never traded inmarkets, yet this makes up a substantial part of every-one’s wealth. There are many privately held busi-nesses, unique pieces of real estate and personalproperty that are infrequently traded; consequently, itis difficult to obtain accurate assessments of theirmarket values.

In practice, measurements ofnational wealth basedon the balance sheet method depend on estimates ofmarket values. Reproducible assets are valued at theirreplacement cost net of straight-line depreciation,land holdings are valued at assessed market pricesand no estlinates are made of the value of humancapitaL” The exclusion of human capital means thatestimates of national wealth seriously understate theactual wealth of the nation.

“See for example, “Balance Sheets for the U.S. Economy 1946-85,”p. i.

HAS WEALTH RISEN RELATIVE TOCURRENT INCOME?

Empirical studies that test the portfoliotheory haveused various empirical measures for national wealth.In most cases, the studies have based the wealthestimates on either the income or balance sheet ap-proach to measuring wealth.”

Various empirical estimates of money demand haveused three different scale variables as proxies for na-tional wealth: expected income, permanent income

“Some studieshave used “financial weafth” as an empirical measureof national wealth. Financial wealth is the sum of ‘household andbusiness deposits and credit market instruments.” This measurebears little theoretical relationship to the measures of nationalwealth discussed above. It is largely composed of claims by oneU.S. citizen on another, claims that cancel when national wealth iscalculated. As a result, it is difficult to interpret empirical estimatesthat employ this wealth proxy, so they are ignored in the followinganalysis. See, for example, Kopcke (1986), p. 19, and Friedman(1978), p. 625, note b.

Expected Income and Physical WealthS

4.063 65 67 69 71 73 75 77 79 81 83 1985

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FEDERAL RESERVE DANK OF ST LOUIS MARCH 1987

/

and physical nonhuman wealth taken from balancesheet data.” These proxies are examined to determinewhether they have risen relative to current incomesince 1981.

Chart 2 plots the logarithms of expected income (VI,permanent income (YP) and physical nonhumanwealth (W). The time-series model used to estimateexpected income is given in the appendix. Personalconsumption expenditures are used as a proxy forpermanent income.27 Finally, physical nonhumanwealth is estimated from balance sheet data and in-cludes an estimate of the market value of federalgovernment debt.”

Chart 2 indicates that all three wealth proxies be-have in much the same way over 1959—85. Each vari-able rises in a smooth fashion at about the samegrowth rate.

2OSee, for example, Meltzer (1963), Brunner and Meltzer (1963),Chow (1966), Laidler (1966), Laumas and Spencer (1980), Mankiwand Summers (1986) and Rasche (1986).

271t has been suggested recently that “consumption is an ideal proxy(for permanent income) since it is proportional to this unobservedvariable. Indeed, it has often been noted that the procyclical behav-ior of the velocity of money is evidence for a permanent income viewof money demand, since the ratio of GNP to consumption is alsoprocyclical.” Mankiw and Summers (1986), p. 416. See, in addition,Friedman and Schwartz (1982) who note that “income as measuredby statisticians may be a defective index of wealth because it issubject to erratic year-to-year fluctuations, and a longer-term con-cept, like the concept of permanent income developed in connectionwith the theory of consumption, may be more useful.” (p. 38)

“The data source for the wealth estimate is “Balance Sheets for theU.S. Economy 1946—85.” It is Total Consolidated Domestic NetAssets (line 10) minus U.S. Gold and SDR’s (line 8) pIus the marketvalue of federal debt. The market value of federal debt is calculatedby the method suggested by Butkiewicz (1983). See also Seater(1981).

The average annual growth rates of these variablesare presented in table 1 along with the average annualgrowth rate of current income. The growth ratesacross all four variables are virtually identical for the1959—85 period.”

Changes in wealth help explain a decline in velocityif wealth rises relative to current income. The datapresented in table 1 give no indication that this oc-curred during 1982—85, the period of declining veloc-ity. In fact, the growth rate of physical nonhumanwealth actually fell relative to the growth of currentincome from 1982—85. Thus, changes in this estimateof national wealth do not help explain the decline inthe income velocity of money that began in 1982. Otherinvestigators havefound similar results.”

The average growth rates of expected income (tIand permanent income (tn) are somewhat greaterthan the average growth rate of current income 12°)during 1982—85. The averages of the quarterly differ-ences between these growth rates and the growth rateof current income, however, are not significantly dif-ferent from zero in a statistical sense.3’ The smallpositive differences that are observed are likely theresult of chance variation in the data.

On net, then, table I indicates that none of the threewealth measures rose significantly relative to current

“This result is expected for the growth rates of ‘I’ and Y’ over longperiods. Recall that ye is generated from a time-seriesmodel of V°which is a sophisticated technique for estimating the trend of V°.

“See, for example, Rasche (1986), pp.50 and 94.

“Thet-ratio is .33 for the average of the differences between ~e andye for the 1982—85 period. The t-ratio is 1.12 for the average of thedifferences between Y’ and Y°for the 1982—85 period. Both are in-significant at the 5 percent level.

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Chart 3

Velocity and Stock Market Measures of Yc/Wy YC/W ~9.0 9.0

1.0

5.0

3.0

1.0

1959 61 63 65 61 69 11 13 15 11 19 81 83 1985

1.0

5.0

3.0

1.0

income during the 1982—85 period. Consequently,changes in these measures of wealth do not helpexplaln the decline in the income velocity of moneythat began in 1982.

A Stock Market Wealth Measure

The conclusion that wealth has not increased rela-tive to current income since 1981 appears to conflictwith the recent behavior of the values of commonstock. This narrow measure of wealth has received anincreasing amount of attention, especially as variousindexes of stock market values have risen to recordhigh levels.

Common stock values of publicly traded firms are aprecise measure of the capital values of the firms.Chart 3 examines the behavior of one measure of the

ratio of current income to the capital values ofpubliclytraded firms and compares this to the behavior ofincome velocity over 1959—as. The measure used inchart 3 is the ratio of current income to the marketvalue of stocks included in the Standard and Poor’s5130 composite stock index.”

Chart 3 indicates that both the ratio of currentincome to stock market wealth and velocity have de-clined from 1982—85. At first glance, it appears that therecent decline in velocity may be the result of anincrease in wealth relative to current income.

“Hamburger (1977 and 1983) uses the ratio of dividends paid (ameasure ofthe current income generated by the capital of the firms)to the market value of stocks in his estimates of money demand.Hamburger’s ratio behaves similarly to the ratio shown in chartS.

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Looking at the entire period shown in chart 3, how-ever, there does not appear to be a close relationshipbetween V and this income/wealth ratio. For example,the ratio did not change much from 1959 to 1969 orfrom 1978 to 1981, yet velocity rose. Except for theyears 1973—74 and 1977—78, the income to wealth ratioappears to move “sideways” while velocity continu-ously rises over the whole period until 1981. Althoughother things that influenced velocity over the periodshown in chart 3 were no doubt changing, perhapsmarkedly, it is stifi interesting to note that the simplecorrelation coefficient between changes in theincome-wealth ratio and changes in velocity is .17,which is not significantly different from zero.

SUMMARY

The income velocity of money — the ratio of GNP toMl — has behaved differently since 1981 than it hadover the previous 30 years. This paper discusses theportfolio approach to money demand, which suggeststhat money demand is more closely related to wealththan to current income. The portfolio theoiy impliesthat, when wealth increases relative to current in-come, income velocity falls, other things the same.Therefore, if the theory is valid, a substantial increasein wealth since 1981 would serve as a possible expla-nation of the recent fall in velocity.

The paper examines the behavior of current incomerelative to alternative measures of wealth. With oneexception, a stock market wealth measure, the wealthmeasures examined here did not increase signifi-cantly relative to current income during 1982—85.

Moreover, while the ratio of current income to thestock market measure of wealth declined after 1982,the behavior of this ratio over longer periods does notappear to be related to the behavior of velocity. Thus,the evidence suggests that the decline in the incomevelocity of money since 1981 cannot be attributedsolely to an increase in these measures of wealth.

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Appendix

Time Series Forecasts and B is a backward shift operator, that is, (1— B)x, =

A time series forecast of the GNP growth rate is used (1 — 24811) i~LnGNP= 5.93 + e,.

as a proxy for the expected percentage change in GNP. (2 63)The model, which uses quarterly data) was estimatedover the period I/1959—IV/1985. Chi-square (2, 24) = 23.53

GNP appears to be a first-order homogeneous pro’- This equation forecasts the growth in GM’. These

cess. The estimated time series model is reported forecasts were integrated to generate a forecast of thebelow. Calculated t-statistics appear in parentheses, level of GNP.

26

Changes in Wealth and the Velocity of Money

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