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The empirical properties of a monetary aggregate that adds bond and stock funds to M2.

Over the past few years, the unexpected slowdown of M2 growth and strength in its velocity have coincided with a surge in outstanding balances in bond and stock mutual funds. Although this surge partly reflects capital gains from

rising prices in stock and bond markets, it also is due to record inflows of new balances. Indeed, anecdotal and statistical evidence suggests that a significant portion of these inflows have come from M2, contributing to the unexpected weakness in this aggregate. Consequently, augmenting M2 with bond and stock funds in order to internalize these flows offers the prospect of an aggregate that is more stably related to income and prices than M2 has been of late.

This article examines empirical issues associated with whether such an augmented aggregate, called M2+, would be useful in the conduct of monetary policy. The three main issues examined are the stability of its demand function, its information content as an indicator of spending, and its controllability. To assess these characteristics of M2+, demand functions and reduced-form relationships between M2+ and income have been estimated. The M2+ series used in this empirical work includes capital gains and losses on bond and stock funds. M2+ was defined in this manner on the presumption that meaningful behavioral distinctions cannot be made between balances generated in the past by capital gains and balances originally brought into stock and bond funds from outside sources.

Specifying a demand function for M2+ requires identifying its close substitutes. One broad class of substitutes includes real assets such as commodities and durable goods, while alternative financial assets may include direct holdings of short-term market instruments, bonds and stocks. The estimated demand functions posit direct holdings of Treasury bonds and bills as the sole substitutes for M2+ because of difficulties in finding plausible measures of expected ex ante returns on real assets and equities. Using rough proxies for ex ante financial returns, including those on stock and bond funds themselves, the estimated demand functions have reasonable behavioral properties. But perhaps because of the problems with measuring ex ante returns, as well as the difficulty in distinguishing between returns on direct and mutual-fund holdings of the same assets, the estimated demand functions are not very stable. Hence, the usefulness of these equations in interpreting and forecasting movements in M2+ may prove to be limited. Moreover, these relationships have been estimated over a period of major innovation and growth of the bond and stock fund industry, raising further questions about the stability of the specification.

In terms of information content, M2+ and M2 do not appear to have differed significantly. The velocity of M2+ may have been more "sensible" than that of M2 over the past three years, given the anomalous behavior of V2, which was rising while the opportunity cost of M2 was declining. As a consequence, in reduced-form relations, forecasts of nominal GDP growth for 1992 are somewhat stronger and more accurate when based on M2+ rather than M2. But leading into the past recession and continuing to the end of 1991, both aggregates yielded substantial overpredictions of nominal GDP growth. Within M2+, the volatile monthly swings in M2 are modestly offset by changes in net inflows to stock and bond funds, but capital gains and losses cause growth of M2+ to be more volatile than that of M2. Moreover, the capital gains and losses in M2+ may cause movements in the aggregate that neither reflect shifts in the stance of monetary policy nor provide appropriate signals for changes in policy.

The remainder of the paper addresses these issues in more detail. Section two explains why the inclusion of capital gains and losses in M2+ seems necessary and highlights some of the problems that result from their inclusion. The section also briefly describes the data used to create a bond and stock mutual fund series that is comparable to M2.(1) Section three provides a broad empirical overview of the growth of bond and stock mutual funds over the past decade. The section then goes on to describe the recent behavior of M2+ and compares its behavior with that of M2. In the final section, we conduct an econometric investigation of M2+ demand, noting several of the difficulties associated with specifying a demand function for M2+ and with the stability and controllability of the aggregate. Also in this section, the indicator properties of M2+ are formally examined and contrasted with those of M2.


Because stock and bond funds are revalued daily to reflect realized capital gains and losses (unlike the deposit components of the current monetary aggregates whose values are fixed at par), questions arise as to the proper treatment of these changes in value. One option is to exclude capital gains by selecting a value of outstanding balances on a specific historical date to which subsequent inflows (net of capital gains) are added. However, both the selection of this date and the assumption that net capital gains before this date, but not after, constitute money are arbitrary. Presumably after some period of time, mutual fund shareholders cease to distinguish between balances generated by capital gains and those that stem from new investments of funds.

A second problem with excluding net capital gains is that, at least conceptually, M2+ balances (or at least the mutual fund component) could become negative. For example, if an individual starts with no M2+ and then adds $100 to a bond fund, the M2+ holdings would then equal $100. If capital gains add $50 to the value of the bond fund account, M2+ will still equal $100 if capital gains are excluded from M2+. If the individual then withdraws all $150 from the bond fund, net inflows would equal minus $150, and M2+ would equal minus $50 for this individual. To avoid such problems, M2+ is defined to include capital gains.(2)

But the inclusion of capital gains and losses raises issues about the signals that M2+ can convey about the stance and proper course of monetary policy. For example, a decline in the stock market that reflected lower profit expectations and slower business activity would lower M2+, ceteris paribus, and may appropriately be calling for a more stimulative monetary policy. But, if capital losses and lower M2+ result from an increase in long-term interest rates in response to rising inflation, a monetary ease is not likely to be the appropriate response. With bond and stock funds currently amounting to about 15 percent of M2+, and likely to increase further, capital gains and losses can have noticeable short-run effects on the growth of the expanded aggregate.

Data used to measure bond and stock fund balances are provided to the Federal Reserve by the Investment Company Institute (ICI). As received from ICI, the bond and stock fund balances include IRA/Keogh and institutional holdings.(3) Because IRA/Keogh and institutional holdings of M2-type accounts are netted from M2, such holdings of bond and stock funds need to be netted out in constructing the bond and stock fund component of M2+. Such netted bond and stock fund series will be referred to as M2-type series. For M2-type bond and stock funds, it would be useful to have data on inflows excluding capital gains as a direct measure of portfolio shifts, but this series is not reported by ICI and cannot be constructed from available data.(4) To proxy for this missing series, we rely on total inflows excluding capital gains.(5)


Historical Trends of Bond and Stock Mutual Funds

Although bond and stock mutual funds have existed in the United States since 1924, most of their growth has been quite recent. In the early 1970s, there were about 400 such funds with total assets of about $40 billion. Today, there are more than 3,000 funds with total assets of about $1.4 trillion.(6) The bottom panel of Figure 1 shows that holdings of aggregate bond and stock mutual funds have grown roughly in parallel and are about equal.(7)

This growth may be attributed, in part, to declining transaction costs when investing in mutual funds. Between 1970 and 1992, load fees on mutual funds fell from an average of 8.5 percent to 4.5 percent. In addition, during the past decade, no-load mutual funds have become more widely available, further reducing the transaction costs involved in shifting in and out of mutual funds.(8)

In reducing transaction costs associated with moving into mutual funds, banks have also been playing a role. Large domestic banks sampled for the Federal Reserve System's March 1993 Senior Financial Officer Survey reported significant increases during the past few years in their overall sales staffs for mutual funds, as well as in the share of branch offices with sales representatives located at them.(9) These developments suggest that investment balances that previously had been held in M2 can now be moved more readily into bond and stock funds, and may be more likely to be switched back and forth between these two lodgings as relative yields shift.

Another innovation that may have contributed to the growth of the industry is that the balances held in such funds can be used more readily as a means of payment in the purchase of goods and services, in part because many funds now allow withdrawals to be made by checks. However, the writing of a check means that mutual fund shares must be sold, so there is a potential capital gain or loss associated with each check. Anecdotal evidence suggests that the inconvenience of tabulating capital gains and losses for the purpose of income taxes significantly limits the frequency of the writing of checks on stock and bond fund accounts.(10)

The transaction activity in bond and stock funds is presented in Figure 2, which plots gross outflows from total bond and stock funds measured as a share of outstanding balances.(11) Contrary to what would be expected if transaction activity had increased, there is no discernible secular trend in the ratio of gross outflows to the value of shares, and the most recent value of the ratio seems rather modest.(12)

Consequently, the rationale that we explore for adding such funds to M2 is based on the substitutability of bond and stock funds for small time deposits or other M2 balances as savings vehicles, and not on the transactability of bond and stock funds.

Recent Behavior of M2+

Figure 3 displays the levels of M2 and M2+, with M2+ defined to include capital gains and losses, but excluding IRA/Keogh accounts and institutional holdings. The upper panel of Figure 4 shows the GDP velocities of the two aggregates and the bottom panel shows the growth rates of M2 and M2+. Three distinct episodes are evident: (1) From 1984 through 1986, the gap between the two velocity measures increased as growth in M2+ outpaced that of M2 (lower panel); (2) From 1986 through 1990, the velocities moved roughly parallel to each other; (3) From 1990 to the present, the velocity of M2 rose sharply while that of M2+ is about unchanged.

Figure 5 shows the monthly growth rates of M2 and M2+. As shown in the top panel, much of the monthly variability of M2 growth shows through to M2+ growth. Monthly net inflows to stock and bond funds apparently are negatively correlated with changes in M2, but offset only a small portion of the change in M2, as shown in the middle panel.(13) However, as shown in the bottom panel, capital gains and losses can induce positive co-movements between the changes in the value of bond and stock funds and changes in M2 - such as from 1990:Q4-1991:Q3.

As a consequence, M2+ is slightly more variable than M2, including the most recent years. In terms of deviations from trend, and as shown in the top panel of Table 1, the mean absolute deviation of M2+ growth over the period from March 1984 through September 1993 is 3.07 percentage points - somewhat greater than that for M2 growth at 2.46 percentage points. However, during the recent sub-sample of January 1989 to September 1993, the difference in variability is much smaller. The middle panel of the table indicates that these differences persist using quarterly data. The bottom panel of the table examines the variability of velocity growth about its mean. The variability of V2+ has been close to that of V2 in recent years, but V2+ was considerably more variable in the mid-1980s.


Modeling the demand for any monetary asset requires identifying alternative uses for the balances held in the aggregate. Bond and stock funds compete with M2 for balances, and a potential advantage of considering M2+ is that this competition need not be addressed in modeling M2+. But bond and stock funds compete with many more assets than just M2 - such as commodities or other real assets. Because reasonable proxies for the expected rates of return on real assets are not available, these assets will not be included in the models developed below.

The only alternatives to M2+ that are included in the models below are direct holdings of Treasury bonds and bills. As a result, analyzing M2+ entails the measurement of own-rates that determine the flows among the following five assets: M2, bond funds, stock funds, and direct holdings both of bonds and bills. The own-rate for M2 can be calculated from posted rates on M2 deposits. Proxies for ex ante returns on bond and stock funds are examined immediately below.
Table 1

Variability of Money and Velocity About Trend(*) (percent annual

 Monthly money growth
 Mean absolute Standard
 deviation deviation

Sample period M2 M2+ M2 M2+

1984:M3 - 1993:M9 2.46 3.07 3.04 3.81
1984:M3 - 1988:M12 2.72 3.37 3.25 4.15
1989:M1 - 1993:M9 2.23 2.38 2.82 3.05

 Quarterly money growth
 Mean absolute Standard
 deviation deviation

Sample period M2 M2+ M2 M2+

1984:Q3 - 1993:Q3 1.80 2.43 2.10 2.91
1984:Q3 - 1988:Q4 1.99 2.46 2.33 3.09
1989:Q1 - 1993:Q3 1.56 1.80 1.88 2.15

 Quarterly velocity growth
 Mean absolute Standard
 deviation deviation

Sample period M2 M2+ M2 M2+

1984:Q3 - 1993:Q3 2.89 3.40 3.60 4.25
1984:Q3 - 1988:Q4 3.04 4.06 3.91 5.12
1989:Q1 - 1993:Q3 2.45 2.61 2.98 3.10

* For money growth rates, regressions were used to estimate
separate time trends for each sub-period. The time trends pick up
the general slowing of money growth since 1984. For velocity
growth, for each sub-period the summary statistics refer to the
growth of velocity about its mean for that sub-period. No trend in
the growth of velocity (that is, acceleration of velocity) was
removed before calculating the summary statistics.

Some of the additional variability in M2+ may be because the monthly
figures for mutual funds represent averages of end-of-month
figures, while M2 data represent averages of daily data.

Proxies for Ex Ante Returns and their Effects on Changes in M2-Type Bond and Stock Funds

This sub-section attempts to identify determinants of the demands for bond and stock mutual funds. In particular, proxies are needed for the ex ante returns on mutual funds.

For bond funds, two alternative proxies are available. One approach relies on contemporaneously observable market rates and the other employs lags of ex post realized returns.(14) The first approach uses the slope of the Treasury yield curve and recent changes in the Treasury bond rate. The yield curve captures the difference between quoted yields to maturity on long-term bonds and posted returns on short-term assets including small time deposits or money market mutual funds (MMMFs) in M2 as well as money market instruments. As such, increases in the spread will make bond mutual funds (as well as direct holdings) look more attractive. Recent bond rate changes may affect investors' expectations of prospective capital gains or losses if investors have extrapolative expectations.

The top panel of Figure 6 shows that both net aggregate inflows to bond funds and the change in market value of M2-type bond funds surged from 1984 through the first quarter of 1987. This surge may well have reflected the relatively steep yield curve going into that period (middle panel) and capital gains caused by falling bond rates throughout most of the period (lower panel).(15) But then with the upturn in bond rates in the second quarter of 1987, bond funds initially experienced modest average outflows during the last half of 1987, and then grew moderately over the next two years as long rates leveled off and the slope of the yield curve fell because of rising short-term rates. More recently, aggregate bond inflows surged as bond rates started to drift down again (although more slowly than during the 1984-1986 period) and as the slope of the yield curve rose to record heights.

A quarterly regression that examines the effects of the slope of the yield curve and recent capital gains and losses is given in equation 1. The change in market value of M2-type bond funds is scaled by the lagged value of M2+.(16)

[Mathematical Expression Omitted]

[R.sup.2] = .735

[Mathematical Expression Omitted]

D.W. statistic = 1.22

Estimation period: 1985:Q2 - 1993:Q3,

where: [Delta]BFUND is the change in the market value of M2-type bond funds;

RT30Y is the 30-year Treasury bond rate;

RT5Y is the five-year Treasury note rate;

RTBE is the three-month Treasury bill rate;

and the absolute values of t-statistics are in parentheses.

The positive coefficient on the spread variable indicates that a steep yield curve draws balances into bond mutual funds. The negative coefficients on the changes in the five-year Treasury note show that recent capital losses reduce bond fund inflows. The contemporaneous change in the note rate also captures the direct effect of changes in the market values.

While the top panel of Figure 7 repeats that of Figure 6, the lower panel of 7 uses the realized returns on bond funds to proxy for expected returns. Comparisons across the two panels show a rough relation between the changes in bond fund balances and the spread of realized returns over Treasury bill rates. A regression relating the change in market value of M2-type bond funds to the opportunity cost that uses the four-quarter moving average of the realized returns is given in equation 2.(17)

[Mathematical Expression Omitted]

[R.sup.2] = .758

[Mathematical Expression Omitted]

D.W. statistic = 1.33

Estimation period = 1985:Q2 - 1993:Q3,

where: [Delta]BFUND is the change in market value of M2-type bond funds;

RETBND4 is a four-quarter moving average of the ex post realized return on bond funds;

RTBE is the three-month Treasury rate;

and the absolute values of t-statistics are in parentheses.

These results are similar to those reported in equation 1, with both equations having [R.sup.2]s of about. 75.

For stock funds, the upper panel of Figure 8 shows two measures of changes in balances and the lower shows the spread of the realized returns over the Treasury bill rate. Comparing the two panels, the surge in balances prior to the stock market crash of 1987, the subsequent falloff, and then the resurgence in balances in 1989 are all tracked by the movements in realized returns minus the Treasury bill rate. The latest spurt in balances seems anomalous, but some of this rise is lessened when the changes in market values are scaled by M2+ as in the following regression, which explains the change in the market value of M2-type stock funds:

[Mathematical Expression Omitted]

[R.sup.2] = .661

[Mathematical Expression Omitted]

D.W. statistic = 2.15

Estimation period = 1985:Q2 - 1993:Q3,

where: [Delta]SFUND is the change in market value of M2-type stock funds;

RETEQ4 is a four-quarter moving average of the ex post realized return on stock funds;

NYSE is the New York Stock Exchange price index;

and the absolute values of t-statistics are in parentheses.

As with the bond inflow equations, the spread of the three-month Treasury bill rate over the realized return has a significant, negative impact. Moreover, the overall fit of the equation is quite high, as the capital gains reflected in the contemporaneous change of stock prices explain most of the variation in the market value of stock fund balances.

An unattractive aspect of equations 1-3 is the absence of a scale variable such as income or wealth and, consequently, the absence of well-defined, long-run equilibrium levels of bond and stock funds relative to income or wealth, or even to M2+. Specifications of such relations were unsuccessful, apparently because innovation and growth of the bond and stock fund industry have caused bond and stock fund balances to grow relative to other nominal quantities. As a result, in what follows we do not attempt to provide a model of the components of M2+ but only of M2+ as a whole, which can be modeled with such a scale variable.

Modeling the Demand for M2+

This section presents and evaluates simple models of the demand for M2+. The models are similar to earlier specifications for the demand for M2 that posit a long-run demand in which velocity is a linear function of opportunity costs. The regression models are of the general form:(18)

[Delta]log(M2+) = c0 + c1 Time + c2 log[(M2+/GDP).sub.-1] + c3 [(opportunity cost variables).sub.-1] + c4 [(RT30Y- RTBE).sub.-1] + error.

Opportunity costs are defined as the difference between the yield on the three-month Treasury bill and the own-rate of return on monetary assets. For own-rates we use the own-rate on M2 (RM2E), and as proxies for the own-rates of return on bond and stock mutual funds, we use the four-quarter moving averages of realized returns on bond and stock mutual funds (RETBND4 and RETEQ4), as in equations 2 and 3. Because we assume direct holdings of bonds and bills are the primary competing asset for M2+ balances, the opportunity cost variables all incorporate Treasury rates as the competing rate. For this, the three-month Treasury bill rate is used.

Because longer-maturity Treasury securities may also be competing assets for M2+, especially for the M2 balances in M2+, all specifications considered below include the slope of the term structure. This variable has been found to have a significant, negative impact on M2 in recent years and above we found that it had a positive impact on bond-fund inflows.(19) If the substitution away from M2 that this variable captures is towards bond and stock funds only, there would be no net impact on M2+.(20) Indeed, it is the internalization of just such substitutions that makes M2+ a potentially useful aggregate. However, if the slope of the term structure captures some substitution of M2 into direct holdings of stocks and bonds, then it would have a negative impact on M2+.


Within this general specification, we fit three alternative M2+ demand functions. In the first alternative, we used the slope of the yield curve and one opportunity cost that incorporates a weighted-average own-rate on M2+.(21) The regression in column one implicitly contains the restriction that the responses of M2+ to the opportunity costs of the three components (M2, bond funds and stock funds) after being weighted by dollar shares are equal. To allow for different responses to changes in the individual opportunity costs, column two of Table 2 shows a regression in which the unweighted opportunity cost for each of the three components of M2+ (OCM2, OCMB and OCMS) is entered separately.(22) As can be seen, the adjusted [R.sup.2] rises significantly when the constraint is relaxed. However, the opportunity costs of bond and stock funds are statistically insignificant.


As a final specification, an attempt is made to incorporate the effects of the increasing access of retail customers to bond and stock funds. In column three of Table 2, the bond and stock fund opportunity costs are weighted by the ratio of bond and stock fund balances to the value of M2+.(23) As can be seen, the fit of the equation improves modestly with the incorporation of these weights. In addition, the statistical significance of the opportunity cost of bond funds improves noticeably. The opportunity cost of stock funds remains insignificant, which may not be surprising because the highly volatile ex post returns on stock funds may be little used by investors in forming expectations of future movements in the market.

Stability of M2+ Demand and the Controllability of M2+

The stability of the above estimated demand functions for M2+ is generally suspect for a number of reasons. First, 10 years is a very short sample period. Second, within that period there was considerable innovation in the bond and stock fund industry. The weights used in the model of column three of Table 2 are likely at best to capture only broadly the effects on M2+ of such innovations. Third, there are the obvious limitations of the opportunity cost variables in terms of identifying competing rates of return when the aggregate is as broad as M2+ and in terms of proxying ex ante expected rates of return on bond and stock funds.

Indeed, all three equations in Table 2 fail Chow tests, strongly suggesting a lack of stability. Under these tests, the estimation period is split into two sub-periods, and the estimation results over the two sub-periods are compared statistically. In a less formal check, the model of column three in Table 2 was estimated over a sub-period that starts in 1986:Q3 and ends in 1991:Q2, allowing for an examination of the model's forecasting performance both before and after this period. The simulation shown in Figure 9 shows fairly substantial errors over the pre-estimation period, but reasonable accuracy starting by 1988 and carrying through nearly to the present.

Figure 10 provides some evidence on the historical contribution of capital gains and losses to the growth of M2+. These can be a guide to the size of the shocks to the growth of M2+ that might need to be offset if fairly close control of M2+ were taken seriously. Although these estimates likely are somewhat imprecise, they do show the effects of the stock market crash of 1987 and major market swings. However, since stock and bond funds are becoming a larger proportion of M2+, the aggregate is probably becoming increasingly vulnerable to swings in capital gains and losses.


As a final set of statistical comparisons of the behavior of M2 and M2+, the ability of these aggregates to predict changes in nominal GDP is examined. Each test regresses one-quarter nominal GDP growth on lagged nominal GDP growth, lagged growth in one of the monetary aggregates, and lagged changes in the three-month Treasury bill rate.(24) The regression models are of the general form:

[Mathematical Expression Omitted]


GDPN = nominal GDP, M = monetary aggregate, and RTBE = three-month Treasury bill.

The top panel of Figure 11 presents in-sample measures of the statistical significance of the lagged money measures for a rolling 15-year estimation window. The measure of significance at an indicated date is the significance level when the estimation period includes 15 years of data ending at that date. By this measure, the two aggregates performed equally well in predicting nominal GDP growth until the mid-1980s. In 1986, inflows to bond and stock funds were heavy in response to falling interest rates, and in 1987 there were modest net outflows when interest rates reversed course early in the year and the stock market crashed late in the year. The resulting swings in M2+ growth were not subsequently reflected in nominal GDP growth and, thus, the rise in significance levels. In the past couple of years, the significance levels of the two aggregates moved closer together.

The lower panel of the figure presents the statistical significance levels for the same specification using a shorter, seven-and-a-half-year, rolling estimation window. With a shorter estimation horizon, the ill behavior of M2 over the past few years becomes clear with the large significance level since 1991. This increase is not accompanied by the corresponding increase in the significance level of M2+.(25)

Figure 12 shows the results of out-of-sample experiments that compute one-period-ahead forecast errors based on the regressions used in the previous exercise. Again, the time horizons over which the forecasting equations are estimated are 15 and seven-and-a-half years prior to the forecast date. Figure 13 presents results for four-period-ahead forecasts. The forecast errors in both figures are calculated as actual minus forecasted growth - a positive error indicates an underprediction. Comparing the results for M2 and M2+, these figures indicate that the forecast errors for the two aggregates are about the same over the whole period shown, as would be expected given that both aggregates are marginally useful in explaining future nominal GDP growth in-sample. Both aggregates tended to overpredict GDP growth in late 1990. Reasonably strong money growth in the second half of 1989 was not consistent with the subsequent recession at the end of 1990. Both aggregates generally underpredicted nominal GDP growth in 1992, with M2+ forecast errors being smaller than those of M2.

1 For a more complete discussion of the issues associated with constructing the bond and stock fund component of M2+, see Collins and Edwards (1994).

2 Defining an aggregate by adding only bond funds to M2 would mitigate some of the problems associated with capital gains because such gains are more volatile for stock funds than for bond funds. However, such an aggregate suffers from the data limitation that a large number of mutual funds invest in both bonds and stocks, and therefore separating mutual funds into these two categories is problematic. An aggregate consisting of M2 plus bond funds has been examined by Duca (forthcoming).

3 See ICI (1994, Appendix A) for the type of funds classified as stock and bond funds.

4 Inflows to M2-type bond and stock funds can be estimated by starting with the change in the market value of M2-type bond and stock funds and subtracting estimated capital gains. These capital gains and losses can be estimated from capital gains and losses on total bond and stock funds, which are available. We have made these estimates by taking total capital gains and losses and multiplying them by the lagged ratio of M2-type outstandings to total outstandings of bond and stock funds.

Although we show such estimates of M2-type capital gains and losses in Figure 10, these estimates and the associated estimates of M2-type inflows do not seem reliable enough to use throughout the analysis.

5 Reinvested earnings are included in both the M2-type and total inflows. This treatment is conceptually similar to the interest crediting of M2 balances. According to ICI data, about 75 percent of shareholders automatically reinvest their earnings in the mutual fund.

6 For an overview of the growth of the mutual fund industry and how mutual funds operate and compete, see Sirri and Tufano (1993).

7 This growth of the bond and stock fund industry has been associated with increased diversity and specialization of the types of funds offered, and much of the growth has occurred in specialized funds. For example, municipal bond funds, which were introduced in 1976, had total assets of $50 billion by 1985, and had grown to $225 billion by 1993. Government income and Ginnie Mae funds, which had a total of about $2.5 billion under management at the start of 1984, had $175 billion by 1993.

8 See Mack (1993) for a more extended discussion of the decline in load fees.

9 The percentage of sampled banks with more than 50 representatives selling retail mutual funds increased from less than 10 percent three years ago to more than 40 percent currently; and nearly all sampled banks currently have some retail sales force. Also, banks have made mutual funds more accessible through their branches. Over half the sampled banks have personnel selling retail mutual funds on a part-time basis or by appointment at 90 percent or more of their branches, a significant increase from three years ago, when only 20 percent of the banks had sales representatives available part-time at 90 percent or more of their branches. The results of the March 1993 Senior Financial Officer Survey and the growth of bank-related mutual funds more generally is discussed by Reid and Small (1993).

10 Although mutual funds could compute the capital gains on the checks written by each shareholder, this does not seem to be a widespread practice as yet. See Clements (1993).

11 Gross outflows are the value of all balances withdrawn, whether or not the balances are reinvested in another fund.

12 As shown in the figure, recently this ratio has averaged about 2.5 percent, which at an annual rate yields a turnover rate of 0.3. In comparison, the turnover ratio for traditional savings accounts is 4.7. See Collins and Edwards (1994) for a further discussion.

13 The modest offset is only apparent because the inflows shown are aggregate inflows that include flows to IRA/Keogh and institutional balances.

14 Increases in these proxies would be expected to increase demands for the relevant type of mutual funds, but may also raise demands for direct holdings.

15 Decreases in aggregate bond and stock fund inflows in 1987 were related in part to changes in the tax exemption for IRA contributions; which were liberalized in 1981 and tightened in 1987. The latter change in the tax law does not seem to be the dominant reason for the dropoff in aggregate inflows in 1987. Net inflows went from $144 billion in 1986 to $49 billion in 1987, but data on IRAs indicate that a drop in their flows account for no more than $7 billion of this slowing.

16 Bond funds are scaled by M2+ to avoid placing undue weight on the early years of the regression. Such overemphasis could result if bond fund changes were scaled by lagged bond funds (that is, if we modeled the growth rate of bond funds) because during the early years when bond funds were modest, a small shift from M2 would represent a large percentage change in bond funds.

17 The four-quarter moving average is used for realized returns to save on the number of freely estimated parameters, in comparison to using four lags of realized returns. When the spread between the quarterly realized return and the Treasury bill rate is entered with four lags, the four individual coefficients are roughly of the same magnitude and the sum of the coefficients is statistically insignificantly different from the estimated coefficient on the four-quarter moving average reported in equation 2.

Also, the realized return is entered in the form of the spread of the Treasury bill rate over the realized return in keeping with standard usage of entering opportunity costs.

18 These are error-correction models. To derive the long-run properties of the model, let nominal GDP and all interest rates be constant. Then M2+ will also be constant and the left-hand side of the regression model can be set to zero. The logarithm of velocity can then be solved for as a linear function of the opportunity costs and the Treasury yield curve spread.

19 Recent models that estimate significant yield-curve effects on M2 demand were developed by Hess(1990). Subsequently, Feinman and Porter (1992) found the same effect, and Mehra (1992) obtained similar results.

20 Indeed, such substitution is consistent with the findings of equation 1, which showed a positive impact of the yield curve on bond fund balances.

21 In this setting, the M2+ own-rate, RM2+, is constructed as the weighted average of RM2E, RETBND4 and RETEQ4, weighted by the quantities of M2, bond funds and stock funds held in the previous quarter relative to M2+. The opportunity cost of M2+ is defined as OCM2+ = RTBE - RM2+, where RTBE is the yield on three-month Treasury bills.

22 There are several reasons to believe that separating the two opportunity costs will produce better estimates. First, given the likely error in measuring expected ex ante own-rates for bond and stock mutual funds, the aggregation of those two rates with the better-measured M2 own-rate will contaminate the estimated response to all three own-rates, in general lowering the estimated coefficient from its true value. Second, and equally important, since the relevant alternative assets for stock and bond mutual funds outside M2+ are likely to include assets other than three-month Treasury bills, the opportunity cost relative to the three-month Treasury bill may be more important for M2 than for stock and bond mutual funds.

23 As a proxy for the availability of mutual fund accounts, these weights suffer from being determined in part by the other factors driving demand for M2+. A better, but unavailable, proxy would be one based on transaction costs.

The weight grows from about 3 percent in 1984 to around 8 percent in 1988 and then to 15 percent currently.

24 The observation for 1980:Q2, during which credit controls were imposed, was omitted from the data.

25 The results are little changed when interest rates are omitted from the equations, although significance levels are lower (money is more important) since money picks up some of the variability of nominal GDP growth explained by interest rates in the broader model.


Clements, Jonathan. "Wait! Don't Write That Mutual Fund Check," Wall Street Journal (November 1993), p. C14.

Collins, Sean, and Cheryl Edwards. "An Alternative Monetary Aggregate: M2 Plus Household Holdings of Bond and Equity Funds," this Review (November/December 1994), pp. 7-29.

Duca, John V. "Should Bond Funds Be Included in M2?" Journal of Banking and Finance (forthcoming).

Feinman, Joshua, and Richard D. Porter. "The Continuing Weakness in M2," Board of Governors of the Federal Reserve System, Finance and Economics Discussion Series Paper #209 (September 1992).

Investment Company Institute. Trends in Mutual Fund Activity. October 1994.

Mack, Phillip R. "Recent Trends in the Mutual Fund Industry," Board of Governors of the Federal Reserve System, Federal Reserve Bulletin (November 1993), pp. 1001-12.

Mehra, Yash. "Has M2 Demand Become Unstable?" Federal Reserve Bank of Richmond Economic Review (September/October 1992), pp. 27-35.

Reid, Brian, and David H. Small. "Bank Involvement in the Mutual Fund Industry," Board of Governors of the Federal Reserve System, mimeo (September 1993).

Sirri, Eirk K., and Peter Tufano. "Competition and Change in the Mutual Funds Industry," in Samuel L. Hayes, ed., Financial Services: Perspectives and Challenges. Harvard Business School Press, 1993, pp. 181-214.

Athanasios Orphanides, Brian Reid and David H. Small are staff economists with the Board of Governors of the Federal Reserve System, Division of Monetary Affairs.
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Author:Orphanides, Athanasios; Reid, Brian; Small, David H.
Publication:Federal Reserve Bank of St. Louis Review
Date:Nov 1, 1994
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