Liquidity effects in the bond market.

Jovanovic, Boyan ; Rousseau, Peter L.

Introduction and summary

Is money neutral? Most economists would now say that it is not, at least not in the short run. This belief derives partly from the results of studies done decades ago. In their book on monetary history, Friedman and Schwartz (1963) argued that the Federal Reserve may have caused or prolonged the Great Depression by a policy of tight money. And in another study, Phillips (1958) found a negative relation between wage inflation and unemployment. In the two decades that followed, other studies confirmed the view that money growth raises output in the short run.

Since the 1970s, however, the Phillips-curve relation seems to have broken down, and money seems to have no clear effect on real interest rates either. Only if we assume that some part of money responds to real variables can we conclude that the exogenous part of money does move interest rates. Evans and Marshall (1998), for example, describe several scenarios--identifying assumptions--under which some part of the money supply can plausibly be said to move real interest rates. In other words, what we infer about a liquidity effect on interest rates depends on what we believe the Fed reacts to when it sets the money supply.

But, if we wish to estimate the liquidity effect on interest rates, or even if we wish to study the interest rate channel of monetary policy, is money the right measure of policy? The rate of interest is the return on bonds, which depends most directly not on the supply of money but on the supply of bonds. Using bonds, one can find a liquidity effect without introducing a host of other variables.

Whether we measure money by nonborrowed reserves or more broadly, injections of money are not the same as withdrawals of, say, Treasury bills (T-bills). This is because the Fed sometimes injects money by buying long-term bonds, and this will affect short-term rates less than would a purchase of T-bills. Indeed, table 1 shows that, since 1961, the correlation between the real per capita supply of outstanding Treasury securities (T-secs) and nonborrowed reserves (NBR), which one might expect to be negative, has been slightly positive at .048. (1) The table also shows that, at least since 1980, growth in nonborrowed reserves has reduced short-term rates, but not as strongly as a contraction of T-secs. Over the whole period, however, growth in both nonborrowed reserves and T-secs is positively correlated with short-term rates--which, for nonborrowed reserves, is the wrong sign.

These conclusions do not change if we look instead at surprises, as implied in models like Lucas (1990) and Christiano and Eichenbaum (1995). Table 2 presents the correlations of interest rates with surprises in the growth of NBR and T-secs. (2) For the 1980-99 period, surprises to nonborrowed reserves come in with the wrong sign, whereas T-sec surprises have the positive correlation that a liquidity effect implies. Both correlations have the wrong sign for the 1961-99 period, but the correlation between surprises to growth in the bond supply and real rates is tiny.

Tables 1 and 2 suggest that, at least in recent decades, bonds have been the better measure of policy. The remainder of our analysis uses this measure more systematically to estimate the degree of risk that unpredictability in their supply imposes on the investor. A nominal bond carries two kinds of risk. First, its real return erodes with inflation, which may be uncertain. Second, unexpected changes in the supply of bonds may cause the value of a bond to change. If a large bond issue causes bond prices to fall, then the return on existing bonds is reduced and the cost of purchase is lowered for investors who are about to buy bonds. The bond issue therefore transfers wealth from existing bondholders to future bondholders. If such issues are not foreseen, they give rise to what we call bond-supply risk.

Supply risk can lead to an uncertain price, or (when prices do not clear markets) an uncertain availability. The Fed creates both kinds of risk in the primary market, where it acts as the Treasury's agent in the regular Dutch (that is, single-price) auctions of bonds. The Fed's current actions affect not only the current auction-price results, but also the number of bonds that will become available in later auctions. The Fed probably also contributes to price variability in the secondary bond markets, where it conducts open market operations. In this article, we find that bond-supply risk remains as important as ever, even though Fed policy has rendered the price level more and more predictable.

The lessons from the data that we highlight are the following:

1. Surprise sales of T-bills raise real rates: Unanticipated (month-to-month) positive shocks in the supply of T-bills or total Treasury securities available to the public have always had a large positive effect on the ex post real returns earned by these instruments.

2. Interest rates and stock returns: Popular wisdom holds that cuts in the federal funds rate raise stock prices. This seems to derive from the view that bonds and stocks are close substitutes so that when the Fed, say, cuts interest rates, stock prices will rise in order to allow price--earnings ratios to rise and, therefore, stock returns to fall. Yet the opposite seems to be true. Overall, if anything, T-bill rates are negatively correlated with stock returns.

3. The decline of Treasury finance: The supply of T-bills has decreased steadily over time, but this has been neutral in its effect on asset prices, including bond prices.

4. Lessons for policy: Supply risk stems from unpredictability in the growth rate of T-secs in the hands of the public--that is, by the unpredictability of changes in this supply relative to the amount outstanding. But the amount of T-secs has been declining relative to the unpredictable rollover demands for them at auction by foreign monetary authorities and financial institutions. If the inclusion of a broader range of short-term securities in the Fed's portfolio were to reduce unpredictability in the growth rate of T-secs, supply risk would decline. This is because the risk would be spread across a wider range of assets, many with deep markets, so that an unexpected change in the Fed's overall securities holdings would impact any one of these markets minimally relative to the amount outstanding.

In the next section, we provide more detail on how T-bills are sold and how open market operations work. Then, we assess the effects that bond-supply risk has had over the past 80 years on the ex post real returns obtained by purchasing a new three-month T-bill and holding it until maturity and compare them to the effects of bond-supply risk on real stock returns. We then consider the role of supply risk under an investment strategy of purchasing a seasoned three-month T-bill with two months until maturity and selling it one month later. Next, we document the recent decline of Treasury finance in the context of the Fed's history and show that supply risk is unrelated to this decline.

What causes bond-supply risk?

Bond-supply risk arises when agents commit funds to the bond market before they know the price at which they will buy the bonds or the price at which they will be able to sell them afterwards. Such risk arises because asset markets are incomplete and, in the sense of Grossman and Weiss (1983), segmented. Some agents and some fraction of their resources are ready to trade in the bond market and this exposes them to the risk that comes from randomness in the supply of bonds. Buyers are in luck when a bond-supply shock is positive because bond prices are then lower than expected and the rate of return is higher than expected. These agents get a good deal, and any real consequences are distributional because the shock has favored some agents at the expense of others.

To take part in the bond market, institutions must commit liquid assets to the new-issue and secondary markets. Primary dealers, who make competitive bids in the course of their direct interactions with the New York Fed in the conduct of Treasury auctions, pay for their winning bids when the new bonds are issued on the Thursday following the Monday auctions. Certain depository institutions and other broker/dealers may also pay for their winning bids on the date of issue. Other competitive bidders pay at the time of submission and are either refunded excess balances or called upon to remit additional funds based upon the final auction price and security allocations. A majority of secondary dealers, however, acquire new issues from primary dealers, and presumably pay for them upon delivery, though the bonds trade actively prior to their issue in a "when-issued" market. Noncompetitive tenders, or offers to purchase bonds at the final auction price, whatever that may be, are paid upfront on the auction day. (3) Noncompetitive bids at T-bill auctions are currently limited to $1 million per account, and they have accounted for only 10.4 percent of total auction sales since July 1998. (4) Thus, even though many bidders can delay payment until issue, they must be ready to purchase their entire bid if won, and, in the event of an unsuccessful bid, must act quickly to reinvest liquid assets that had been set aside. A closer look at how these markets work shows how the winning bids can become quite uncertain.

By "supply risk," in some cases, we mean "residual supply risk." A large chunk of the demand for T-bills comes from the decisions of foreign financial institutions and international monetary authorities (FIMA) regarding whether to roll over their substantial and various holdings of bonds, and these rollover decisions affect the residual supply that will be available to the remaining traders because they count against the issue quantity stated in the auction announcement. Further, when FIMA make rollovers, they do so at the single auction price as noncompetitive bidders. (5) Many individuals also bid noncompetitively, but, as mentioned above, the quantities of such bids are restricted and thus more predictable. All of this means that supply risk can arise at the auction stage, even though the Treasury announces the face value of the T-bills that it intends to issue. Since the public knows only the maturing quantity and not the rollover plans, the randomness in these plans, from the perspective of the dealer, m akes the final auction price less predictable.

The Fed itself must also decide whether to roll over portions of its own portfolio of maturing bonds at the final noncompetitive price. The securities that the Fed rolls over do not count against the total offered to the public in that week's auction and, thus, have at best a minimal impact on the final auction price, but they will affect the size of subsequent auctions. For example, if the Fed rolls over only half of the bills that it could have in a given auction, to maintain a constant debt level the Treasury would need to arrange a larger issue for the next week. It seems, however, that the Fed's rollovers, at least in recent years, have been quite predictable--the Fed rolls over its entire holdings unless that would exceed its self-imposed limit on individual securities holdings, in which case it redeems enough to meet that limit.

The Treasury has changed its usual procedures twice recently with regard to foreign rollovers, and the nature of these changes suggests that it may be trying to reduce supply risk. In early 1999, auction announcements still specified that the Treasury could, at its discretion, issue additional securities for foreign accounts whenever the total of new bids from these sources exceeded their total holdings of maturing bills. Beginning with the T-bill auctions of March 29, 1999, however, the Treasury usually placed an explicit limit of $3 billion on the amount of foreign rollovers that would be counted against the public's total, agreeing to make additional issues automatically if rollover bids were to exceed this amount. This practice became more common as 1999 progressed. The change signaled a more accommodative stance by the Treasury that would have reduced residual supply risk by limiting the degree to which unexpected noncompetitive rollover decisions could affect the final auction price. As of February 1, 2001, however, the Treasury has allowed only $1 billion in total foreign noncompetitive tenders, and that limit cannot be exceeded. (6) Foreign institutions seeking to purchase large amounts of T-secs at auctions must now bid competitively. Even though this change might ameliorate disturbances that would impede the systematic paying down of the federal debt, it is also likely to raise residual supply risk.

Cammack (1991, p. 110) reports that the Fed and FIMA combined to buy 43 percent of all T-bills that were sold at auction between 1973 and 1984. By examining the press releases of auction results, we have found that this portion has risen to 44.8 percent since mid-1998. The risk associated with rollover decisions exceeds both the spread in the distribution of bids and the time-series variation of the winning bids, because the losing bidders (of which there are more either immediately or in future auctions when the Fed absorbs its limit) must end up holding cash or a lower-return substitute.

Bond-supply risk and interest rates

How much do bond supplies vary from month to month? Figure 1 shows the standard deviation of the monthly per capita real growth of the monetary base, T-bills and T-notes, and all marketable T-secs, including bills, notes, bonds, and certificates of indebtedness since 1920. (7) The Treasury quantities reflect securities that are outstanding and in the hands of the public (that is, excluding the Fed's holdings). (8)

The striking feature of figure 1 is the high month-to-month variability of total T-secs in the hands of the public. This variability was particularly high in the early 1940s due to large issues of securities of all maturities to finance the Second World War. We also observe large rolling standard deviations for the T-bills and T-notes subset in the midst of the Depression and again from 1942 to 1947. Interestingly, variability in the supply of T-secs is much larger than that of the monetary base itself, which suggests that a considerable portion of what we call supply risk may have served to stabilize money growth.

How strongly do bond-supply surprises affect the real rate of interest? We use the effects of inflation surprises as a standard of comparison and compare the two kinds of risk, first for the entire 1920-99 period and then for three subperiods. Here is how we proceed: The nominal return at date t on a one-period zero-coupon bond maturing at date t + 1 is

[R.sub.t, t+1] = (1/[P.sub.t]-1),

where [P.sub.t] is the price of the bond at date t. The ex post real return on this bond is

[r.sub.t, t+1] = (1/[P.sub.t][1/1+[[pi].sub.t, t+1]]-1),

where [[pi].sub.t,t+1] is the rate of inflation of goods prices between dates t and t+1. Rearranging and taking logs,

ln(1+[r.sub.t, t+1]) = -ln [P.sub.t]-ln(1+[[pi].sub.t, t+1]),

for any small number [epsilon], ln (1 + [epsilon]) [approximately equal to] [epsilon]. Using this, we approximate the above equation by

[r.sub.t, t+1] [approximately equal to] [i.sub.t, t+1] - [[pi].sub.t, t+1],

where [i.sub.t, t+1] [equivalent to] 1/[P.sub.t]-1.

Let the superscript e denote an expected value given information from the previous period, which we shall denote [I.sub.t-1], so that, for instance,

[r.sup.e.sub.t, t+1] = E{[r.sub.t, t+1]\[I.sub.t-1]}. (9)

Let the superscript u denote the surprise component of a random variable so that, for instance, [r.sub.t, t+1] = [r.sup.e.sub.t,t+1] + [r.sup.u.sub.t,t+1] and so on. Then to a first approximation,

1) [r.sup.u.sub.t, t+1] = [i.sup.u.sub.t, t+1] - [[pi].sup.u.sub.t, t+1].

The first term is the bond-supply risk and the second is inflation risk.

Now assume a liquidity effect of bond-supply surprises on the price of bonds as in, say, Lucas (1990). That is, assume that

2) [i.sup.u.sub.t,t+1] = [alpha][g.sup.u.sub.t-1,t],

where, once again, [g.sup.u.sub.t-1,t] is the surprise growth in the number of bonds at given [I.sub.t-1]. Substituting into equation 1 leads to

3) [r.sup.u.sub.t,t+1] = [alpha][g.sup.u.sub.t-1,t] + [[pi].sup.u.sub.t,t+1].

The notation may suggest that the surprises in the above three variables are formed at different dates and are based on different information sets, but this is not the case. The dependent variable and the regressors all derive from the information set [I.sub.t-1] that we describe in note 9 on page 33. To reiterate, at the start of date agents know the realization of [[pi].sub.t-1,t]. But the presence of bond-supply risk means that the agents do not know the date t supply of bonds when they form their expectations of [P.sub.t] and, hence, of [i.sub.t,t+1]. This means that they cannot yet know [g.sub.t-1,t], since its realization comes too late to be included in the date t information set. Therefore, in spite of the dating differences in the subscripts, [r.sup.u.sub.t,t+1], [g.sup.u.sub.t-1,t], and [[pi].sup.u.sub.t,t+1], are surprises based on the same information set, [I.sub.t-1].

We estimate equation 3 with the regression

4) [r.sup.u.sub.t,t+1] = [a.sub.0] + [a.sub.1] [g.sup.u.sub.t-1,t] + [a.sub.2] [[pi].sup.u.sub.t,t+1],

where [r.sup.u.sub.t,t+1], [g.sup.u.sub.t-1,t], and [[pi].sup.u.sub.t,t+1] are surprises of the three variables. In practice, we obtain these surprises using de-seasonalized monthly observations as the one-step ahead forecast errors from a set of vector autoregressions (VARs) with a rolling estimation window. To be more precise, the variables in the forecasting equations are:

1. g, the growth rate of real per capita T-secs in the hands of the public,

2. r, the ex post real return on T-bills, (10)

3. [pi], the rate of growth of the consumer price index, (11) and

4. the ex post real return on the S&P 500. (12)

Thus, all four variables in the system are dimensionless. We then pool the forecasts and errors from the VARs over the sample period and use them to estimate equation 4.

The monthly data represent the highest frequency that is available continuously for the past 80 years of Fed history. The T-bill return is the monthly average of daily rates for the current (that is, "on the run") three-month T-bill, from which we subtract realized inflation over the next three months. The returns that we consider first, and the only ones that can be constructed going back to 1920, correspond to an investment strategy of buying the current three-month T-bill and holding it until maturity. Later we consider one-month holding period returns on seasoned T-bills since 1961. Box 1 describes in detail the methods we used to prepare the data for analysis and to compute the surprises.

Supply risk 1920-99

Using monthly data from January 1920 through December 1999 and forecasting equations with a 36-month rolling window and three lags, figure 2 shows the effects of one-standard-deviation surprises to both the price level and the supply of marketable T-secs available to the public on the annualized ex post real return on T-bills. (13) Pooling the surprises across periods, we obtain the following estimates for equation 4 (with t-statistics in parentheses):

5) [FORMULA NOT REPRODUCIBLE IN ASCII]

The superscript u in equation 5 denotes a variable's deviation from its one-step-ahead forecast from the rolling VAR.

As limited participation models would suggest, [g.sup.u.sub.t-1,t] raises ex post real T-bill returns because a release of T-bills lowers T-bill prices. This in turn contributes to better-than-expected returns for those who have committed funds to the T-bill market. Unanticipated inflation enters with, essentially, a unit coefficient, which suggests that [[pi].sup.u.sub.t,t+1] is indeed a true surprise.

To obtain the series plotted in figure 2, we multiply the coefficients [g.sup.u.sub.t-1,t] and [[pi].sup.u.sub.t,t+1] by the centered values of their rolling 12-month standard deviations and compound the result over 12 months to annualize. This measures the effects of the surprises on annualized real T-bill returns. (14) The figure indicates that both sources of risk have always mattered, with inflation risk at times quite large, especially at the height of the Great Depression in 1933 and in the year immediately following the end of the Second World War. The relative importance of inflation risk has declined dramatically over the past two decades, however, as the price level has stabilized.

The effect of supply risk in three subperiods

The method used to construct figure 2 assumes that the seasonal adjustment coefficients applied to the raw data and the responses of the T-bill rate to unexpected inflation and T-sec growth are stable across the 1920-99 period. One way to examine the robustness of our results to these assumptions is to repeat the analysis over subperiods. We do this for 1920-46, 1947-79, and 1980-99, and display the results in figures 3-5. We split the postwar period into pre-1980 and post-1979 segments because of the shift in Fed targeting policy that occurred in 1979. To accommodate the shorter sample periods, we limit the underlying VAR models to two lags and shorten the length of the estimation periods to 30 months. Table 3 includes regression results for equation 5.

Figure 3 reaffirms the importance of inflation risk in the pre-1947 period, including the 1933 and 1946 episodes. The effects of supply risk on T-bill returns rise at these same times and average 0.36 percent over the 1920-46 period, but are always less important than the effects of inflation risk, which average 5.31 percent. In figure 4, the narrower scaling reflects the overall decline in inflation risk that occurred from 1947 to 1979, during which it averaged only 1.35 percent. Even though supply risk also fell to 0.12 percent over this same period, the decline is considerably less in percentage terms than that of inflation risk. Figure 5, on the other hand, shows that supply risk has if anything become more important over the past 20 years, averaging to 0.14 percent, while inflation risk has continued to decline, averaging 0.99 percent.

By 1980, the Treasury had completed a long-term shift in financing away from T-bonds and into shorter-term T-bills and T-notes (see figure 15 on page 30). It is therefore possible that fluctuations in the quantity of T-bills and T-notes are more precise measures of supply risk for the post-1980 period than the total of outstanding marketable T-secs. To see if this preference shift has influenced our results, we compute supply shocks to T-bills and T-notes only after 1980, and in figure 6 once again display their effects on real T-bill returns. The results are similar to those observed for all T-secs, with average real effects of 0.16 percent and 1.0 percent, respectively. Once again, supply risk grows in relative importance over time.

That bond-supply risk, which arises from committing funds to the T-bill market before supply is revealed, should even approach inflation risk in importance is quite striking. After all, if inflation surprises are measured over the entire term of the T-bill, they should affect ex post yields virtually point for point. (15)

To generate bond-supply risk, however, it is necessary for open market operations or variations in auction quantities to have large effects on interest rates, and this in turn suggests some degree of market segmentation. Otherwise, in the absence of segmentation, investors could offset T-sec supply shocks with transactions in the markets for substitute assets.

Bond-supply risk and real stock returns

Theory leads us to expect a positive relation between stock returns and real bond returns. If stocks and bonds were perfect substitutes and if they traded in the same market, their real rates of return would always be equal. In such a world, an open market operation of the Fed or, indeed, any other event that changed the return on bonds would change the return on stocks by the same amount. For example, a cut in the federal funds rate would cause bond prices and stock prices both to rise and the holding rate of return on each asset to fall. The presence of inflation risk on bonds and dividend risk on stocks would, perhaps, weaken the contemporaneous correlation between the ex post real returns on the two assets, but would not eliminate it entirely.

One implication of this logic is that if the Fed's actions can affect the stock market, we should expect to find a positive correlation between bond returns and stock returns. Surprisingly, we find no evidence of a positive correlation between the two ex post returns. We proceed as we did with T-bill returns, but now the dependent variable in equation 5 is the unanticipated component of the real return on the S&P 500, [S.sup.u]:

6) [S.sup.u.sub.t, t+1] = [a.sub.0] + [a.sub.1][g.sup.u.sub.t t-1,t] + [a.sub.2][[pi].sup.u.sub.t, t+1] + [e.sub.t].

Table 4 presents our findings using surprises from the same VAR models that we used to examine T-bill returns. Interestingly, T-sec surprises never affect real stock returns. Inflation surprises, on the other hand, enter with the expected negative and significant coefficients in the 1947-79 and 1980-99 subperiods, but with a positive and significant coefficient for 1920-46. The latter result may be driven by a few extraordinary events, such as the sharp deflation and decline of equity values associated with the Great Depression and the inflation and rising market values of the immediate postwar period. In all, the evidence suggests that the stock market has been relatively unaffected by Fed policy.

In table 5, we report contemporaneous correlations among the variables in our VARs (that is, the variables themselves and not their surprises) and for the monetary base over the 1920-99 period and the three subperiods. (16) Once again, links between stock returns and growth in bond supplies are weak and inconsistent across subperiods. For example, correlations between real growth in the T-sec supply and stock returns never exceed 0.05 and have the expected negative sign only for 1980-99. T-bill returns vary inversely with stock returns in all but the 1947-79 period, but in all cases the correlations are small. As it turns out, the most consistent correlations are positive ones between growth in T-sec quantities on the one hand and real T-bill returns on the other. This is true for the full 1920-99 sample period and for all of the subperiods. It is also as we might expect, since more T-secs in the hands of the public require higher interest rates to induce investors to hold them.

Since a rise in T-bills and T-notes in the hands of the public usually implies bond sales and, hence, a monetary tightening, it is surprising that growth in the real monetary base--a monetary loosening--seems to go hand in hand with bond sales (and the higher interest rates that they imply) in all but the 1980-99 period. To explore this further, we compute the correlations using growth in real per capita nonborrowed reserves, which is probably a closer indicator of policy stance than growth in the monetary base, for 1959-99--the period over which we have a series for nonborrowed reserves. We find in this case that a monetary loosening, as measured by growth in nonborrowed reserves, also has an unexpected positive correlation with T-bill returns and T-sec growth, and that this result obtains for both the 1959-79 and 1980-99 subperiods. (17) This may again reflect important differences between indicators of policy stance that are based on monetary aggregates and our bond supply measures.

An alternative measure of real T-bill returns

Until now, we have considered the effects of bond-supply risk on T-bill returns under a buy-and-hold strategy. This, of course, is only one strategy that a T-bill investor might follow, as it is easy for an investor to liquidate a T-bill, and in particular after a supply or price shock has been realized. To analyze such a holding strategy, we now estimate equation 5 using surprises to the ex post real one-month holding period return on a seasoned T-bill as the dependent variable.

The effects of supply risk should be different under this shorter-term strategy. This is because the investor now faces two sources of supply risk--one that occurs just before the bond is purchased and another that occurs over the holding period. A positive shock after commitment but before purchase will lower the bond price and raise the real return, yet a similar shock over the holding period will lower the resale value of the bond. Thus, it is deviations of resale values from investor expectations that were formed prior to purchase that impart risk to the strategy.

To derive the equivalent of equation 4 for multi-period bonds, we again define the cost of such a bond at date t as 1/[P.sub.1] units of real consumption. The bond's nominal return over the holding period is

[i.sup.*.sub.t,t+1] = [P.sub.t+1] - [P.sub.t]/[P.sub.1],

where we introduce asterisks to reflect the change from the buy-and-hold investment strategy discussed earlier to the seasoned one-month holding strategy considered here. The ex post real return is again [r.sup.*.sub.t,t+1] = [i.sup.*.sub.t,t+1] - [[pi].sup.*.sub.t,t+1], and as in equation 1,

[r.sup.[u.sup.*].sub.t,t+1] = [i.sup.[u.sup.*].sub.t,t+1] - [[pi].sup.[u.sup.*].sub.t,t+1].

Now we need to be quite precise about the dating of information. Let [Z.sup.u.sub.t-1] the surprise component of a random variable z given [I.sub.t-1], and suppose that

7) [FORMULA NOT REPRODUCIBLE IN ASCII]

The right-hand side of equation 7 is based on the logic behind equation 2. The first term deals with the denominator of the left-hand side; it is the one-step-ahead surprise and is the same as in equation 2. The second term deals with the numerator, [P.sub.t+1], and is a two-step-ahead surprise to growth in the bond supply. We compute this term as a VAR forecast using [I.sup.*.sub.t-1]. Isolating the return surprises on the left-hand side, we have the holding-period analog of equation 3:

[FORMULA NOT REPRODUCIBLE IN ASCII]

or, roughly, the linear relation that we estimate:

8) [FORMULA NOT REPRODUCIBLE IN ASCII]

The final term in equation 8 is inflation risk over the holding period.

Under the buy-and-hold strategy that we considered earlier, we subtracted realized inflation over the three-month term of the T-bill and, assuming monthly compounding, converted to a monthly return. The result there reflected an average of inflation over the next three months. Here we proceed slightly differently: For the one-month holding strategy, we subtract the one-month inflation rate that corresponds to the actual holding period.

Our analysis of one-month investments in seasoned three-month T-bills is limited to 1961 to 1999--the period for which daily secondary market prices on U.S. Treasury securities are available from the New York Fed and the Wall Street Journal. (18) Using the composite "quote sheets," we collected the annualized yield-to-maturity on the final trading day of the month for the T-bill with closest to 60 days until maturity and then recorded its yield on the final trading day of the next month. We then computed a synthetic annualized 30-day holding period yield as

[R.sub.2,1] = [1+([R.sub.2]60/365)/1+([R.sub.1]60/365)]-1,

where [R.sub.2] is the annualized yield-to-maturity on the reference T-bill with approximately 60 days until maturity, and [R.sub.1] is the annualized yield on the same T-bill a month later. Due to weekends, holidays, and the monthly calendar, we do not always observe prices 30 days apart, so our computation assumes that [R.sub.1] whenever observed also applies on the 30th and final day of the holding period. This ignores changes in secondary market yields that might arise for a seasoned T-bill over at most a two-day period, but does not generate any systematic bias. We convert to real terms by subtracting Consumer Price Index (CPI) inflation.

After again obtaining surprises to T-bill returns, inflation, and growth of the T-sec supply from a series of 30-month rolling VARs with two lags and the S&P 500 return as a control, we use the coefficient estimates from equation 8 to compute the overall effects of supply risk over the course of a month (that is, both pre-purchase and holding period risk) as the square root of

[FORMULA NOT REPRODUCIBLE IN ASCII]

where the Var(.)terms are variances and Cov(.) the covariance. The effects of inflation risk are the product of [a.sub.3] and the standard deviation of the forecast errors for inflation. We obtained the series of variance-covariance matrices from 12-month rolling samples of the forecast errors. Figure 7 presents our results for the 1961-79 period, which have been annualized by compounding over 12 months. We report the corresponding estimates for equation 8 in table 6.

In figure 7, an inflation surprise of one standard deviation lowers the holding period yield by 1.77 percent on average. Like the results in figures 2 and 5 for the buy-and-hold strategy, inflation risk rises to nearly 4.5 percent in the mid-1970s after fluctuating at about 1 percent to 2 percent throughout the 1960s. Supply risk, though not significant in equation 8, averages .10 percent, which is only slightly smaller than that observed under the buy-and-hold strategy for 1947-79.

Figure 8 and the two other columns of table 6 cover the 1980-99 period and offer a direct comparison with figures 5 and 6. Whether we use all T-secs in the hands of the public (figure 8) or only T-bills and T-notes (figure 9) in forming [g.sup.[u.sup.*]] the effects of supply risk on one-month yields are similar to those obtained under the three-month buy-and-hold strategy, averaging .16 percent and .21 percent in figures 8 and 9, respectively. The coefficients on the pre- and post-purchase surprises to growth in the T-sec supply variables also have the expected and opposite signs, but are statistically significant only when T-bills and T-notes are included in [g.sup.[u.sup.*].sub.t-1,t]. This differs from the results under the buy-and-hold strategy, where our analysis of pre-purchase risk in isolation showed significant effects of supply surprises for total T-secs as well. Inflation risk is larger on average with the one-month holding strategy than with the buy-and-hold. The closeness of the coefficients on th e inflation surprises to unity is also good news for our specification, as inflation should affect the real return point for point when the time periods for the inflation and return observations coincide.

Next, we again place the unanticipated component of the real S&P 500 return ([S.sup.[u.sup.*]])on the left-hand side of equation 8 to obtain

9) [FORMULA NOT REPRODUCIBLE IN ASCII]

The results, which we report in table 7, indicate that surprises to g do not generate substantive supply risk for investors who are about to buy the S&P portfolio, but that positive shocks after purchase raise one-month stock returns for the 1980-99 period. This runs counter to the standard view that stocks lose when the Fed tightens and gain when the Fed cuts rates.

The lack of significance on the coefficient for the pre-purchase surprise could simply suggest that the Fed cannot directly and consistently affect the stock market. The positive and significant coefficient on the holding period supply shock, on the other hand, is consistent with a policy of passive responses by the Fed to changing conditions in other asset markets. For example, when the stock market is surging, the Fed may try to slow it down a bit by injecting bonds and raising interest rates. Since any relationship between Fed policy and the stock market is probably loose, however, the bond sale often seems to have little effect, and the market continues to push ahead.

The effects of foreseen policy changes: The secular decline of Treasury finance

The relative importance of T-bills and other marketable T-secs in the aggregate portfolio has declined over the postwar period. This should not matter for real interest rates if it is only surprises to the growth of bond supplies that matter. Indeed, most rational expectations models with money and no nominal rigidities specify no real effects for expected changes in the money or bond supplies. One such change is the gradual decline in outstanding T-secs, since this is probably well understood by agents in the bond and money markets. But this change may not be neutral, or at least may begin to matter soon if the trend continues. This is because fluctuations in bond supplies stemming from rollover risk and other sources have become larger relative to the quantity of outstanding T-secs. Figures 10 and 11 suggest that such a trend may be emerging. Figure 10 shows that the amount of T-secs in the hands of the public has fallen since the mid-1990s. Figure 11, on the other hand, indicates that the standard deviatio n of the growth rate surprises (the cause of supply risk) has increased a little. (19) In this section, we document long-run trends in Treasury financing over the Fed's history and argue that their effects on supply risk up until now have probably been small.

The size of the bond market can be measured by the share of these securities in the aggregate portfolio. This share will decline if, because of a policy change, the quantity of Treasury securities made available to the public begins to shrink. The share will also decline as more individuals gain access to instruments other than bank deposits for lodging their surplus balances. Figures 12 and 13, which include the ratios of federal debt, commercial and corporate debt, and corporate equities to gross domestic product and the aggregate portfolio, respectively, indeed show substantial declines in the share of marketable federal debt from its postwar high in 1945. The growing importance of financial assets in the U.S. economy and the rapidly rising share of equity in total finance are also apparent. Figure 14 provides additional detail on the rising share of equity in total business finance, with both the corporate bond and bank lending components of business debt falling to their lowest levels in recent years. Th e market for commercial paper has also grown rapidly over the past three decades, but it remains a small part of total finance. (See boxes 2 and 3 for descriptions of how we constructed the series for outstanding corporate equities and the components of outstanding debt that are presented in these figures.)

Figure 15, which provides a breakdown of marketable Treasury securities by type, shows that long term bonds dominated government finance between 1915 and 1960, but that medium-term T-notes and short-term T-bills have risen to preeminence more recently. These shifts suggest that a broad measure of government bond activity, such as the sum of all marketable Treasury securities in the hands of the public, may be best for evaluating the effects of supply shocks related to the Fed's open market policies over the long term, but that the quantities of T-bills and T-notes might be more relevant in recent years. These considerations more precisely explain our choices of variables for quantifying supply risk earlier in this article. Interestingly, and in keeping with most rational expectations models, we found in most cases that the choice of supply variable did not matter.

Figures 12 and 13, when combined with the effects of changes in the supply of T-sees presented in figure 2, suggest that the decline in the share of these securities in the aggregate portfolio has had little effect on the distribution of [r.sub.t]--the real return on T-bills. This stands in sharp contrast to the implications that such a decline would have in the limited participation model of Alvarez et al. (2001), in which the interest rate effects of monetary injections depend inversely on the fraction of agents that take part in the bond market.

Conclusion

Bond-supply risk normally contributes between 10 basis points and 40 basis points to movements in the real rate of interest on T-bills. The effect has shown no tendency to decline over the past half century. The Fed will find it harder and harder to push this risk to zero because the gradual paying down of the federal debt has meant that it has become harder to expand T-bill issues to accommodate unexpectedly large rollover demands from foreign sources. Further, so long as the Fed uses the secondary market for Treasury securities as its chief means of conducting open market operations, shocks to the supply of these securities to the public will persist. If the supply of outstanding Treasury securities indeed does continue its decline, an increase in the use of other debt instruments for open market operations will reduce the supply-risk for the group as a whole.

We also find that despite the challenges to implementing monetary policy that are imposed by supply risk, the Fed has been managing this risk well. This is clear from observing that the variability of the monthly growth rate of the T-bill supply has not changed much in recent years.

The bond and stock markets also show a lack of comovement that is hard to explain unless one assumes that the markets are segmented. Characterizing the nature of such segmentation is an endeavor in which we are actively engaged.

Boyan Jovanovic is a professor of economics at the University of Chicago and New York University, a research associate of the National Bureau of Economic Research (NBER), and a consultant to the Federal Reserve Bank of Chicago. Peter L. Rousseau is an assistant professor of economics at Vanderbilt University and a faculty research fellow of the NBER. The authors thank the National Science Foundation (NSF) for financial help, Fernando Alvarez and Robert Lucas for useful comments, and Timothy Daniels for assistance in obtaining data. Special thanks go to David Marshall and Helen Koshy for many detailed comments on earlier drafts.

NOTES

(1.) Tables 1 and 2 both deal with ex post real returns of investors who purchase three-month U.S. Treasury bills in the secondary market with two months remaining until maturity and sell them a month later. We obtain monthly nonborrowed reserves from the FRED database of the Federal Reserve Bank of St. Louis, and describe other data sources in the text and note (8).

(2.) We compute surprises to T-secs and nonborrowed reserves as one-step ahead forecast errors from a series of rolling bivariate vector autoregressions (VARs) with four lags and a 30-month estimation window.

(3.) Noncompetitive bidders who specify a bank account for direct debit under the Treasury Direct investment plan also do not pay for their bills until the issue date.

(4.) We compute this figure as the average share of accepted noncompetitive bids in the total face value of T-bills sold at each weekly auction of 13-week and 26-week T-bills from July 30, 1998, through April 5,2000. Press releases of auction results are available at the Bureau of the Public Debt's website, www.publicdebt.treas.gov.

(5.) Before November 1998, marketable Treasury securities were auctioned in a discriminatory fashion, with the highest bidders receiving their requested quantities in full at the tendered price subject to a maximum of 35 percent of the total quantity auctioned (this "35 percent rule" is still in effect). Noncompetitive bidders received their requests in full at prices based on a weighted average of accepted competitive bids. Both auction systems, discriminatory and single-price, generate some degree of supply risk.

(6.) Foreign bids are now restricted to $200 million or less per account, and are filled from smallest to largest until the $1 billion total limit is reached, The size of foreign bids will be restricted to $100 million or less as of January 1, 2002.

(7.) We compute the standard deviations using a 12-month rolling window and then apply the Hodrick-Prescott filter to each series before plotting.

(8.) The quantities of outstanding marketable Treasury securities are end-of-month observations from individual issues of the Annual Report of the Secretary of the Treasury for 1920-31, the Board of Governors of the Federal Reserve System's Banking and Monetary Statistics (1976a, pp. 868-873; 1976b, pp. 509-511) for 1932-70, and individual issues of the U.S. Department of the Treasury's Monthly Statement of the Public Debt of the United States thereafter. To compute the quantity in the hands of the public, we subtract the Fed's holdings from Banking and Monetary Statistics (1976a, p. 343; 1976b, pp. 485-487) for 1932-70 and from individual issues of the Federal Reserve Bulletin for 1920-31 and 1971-99.

The monetary base is from the FRED database of the Federal Reserve Bank of St. Louis for 1936-99, with Ml from the Friedman and Schwartz (1970, table 1, pp. 4-58) ratio, spliced to the MO aggregate for 1920-35.

(9.) The information set [I.sub.t-1] consists of the realized inflation rate from t-I to t (that is, [[pi].sub.t-1,t]), the real T-bill return from t-1 to t (that is,[r.sub.t-1,t]), the real return on the S&P 500 portfolio from t-1 to t, and the growth in the bond supply from t-2 to t-l (that is, [g.sub.t-2,t-1]). In other words, thinking of date t as February and date t-l as January, and so on, when we commit funds to the bond market before any February auction, we know the return on the S&P 500 and the inflation rate for January, and the growth of the bond supply in December. We do not include the growth of bond supply in January, however, because that would imply knowledge of [P.sub.t], and an absence of bond-supply risk. Therefore, [I.sub.t-1] contains insufficient information to forecast [P.sub.t] perfectly.

(10.) Nominal secondary market interest rates on three-month T-bills are from the FRED database for 1934-99 and Board of Governors 1976a) for earlier years.

(11.) The Consumer Price Index, which we also use to deflate the T-sec quantities, is that for all urban consumers from the U.S. Bureau of Labor Statistics.

(12.) Nominal calendar-month returns on the S&P 500 assume the reinvestment of dividends and are from worksheets underlying Wilson and Jones (2001).

(13.) As we show in a later section, the government's maturity preferences have shifted considerably over time, but these shifts in themselves did not introduce risk in the total supply of securities available to the public. Thus, focusing on supply shocks to a single instrument such as T-bills over the long term would overemphasize variations in the maturity structure of government finance that were not "shocks" but rather just substitutions of one maturity for another. For this reason, we work primarily with the total of marketable Treasury securities in the hands of the public rather than a narrower quantity measure such as T-bills alone.

(14.) Figure 2 does not span the full 1920-99 period because observations are lost in accommodating the lag length of the VAR, in constructing the initial estimation window, and in computing the initial and final rolling standard deviations of the forecast errors. We also lose observations early in the sample when making similar computations for figures 3-9.

(15.) In this section, however, we measure inflation over only the first month of the T-bill term and then assess its effect on the three-month real yield. Even here we obtain coefficients on the inflation surprises that are close to unity for the 1920-99 period and the 1920-46 subperiod, though the coefficients are considerably below unity for 1947-79 and 1980-99.

(16.) Since an adequate breakdown of Treasury securities into its T-bill and T-note components is not available on a monthly basis prior to 1932, the correlations that include T-bills and T-notes in the two upper panels of table 5 begin in 1932 rather than in 1920.

(17.) The correlations of nonborrowed reserves for 1959-79 are .110 with the S&P 500, .216 with T-bill returns, .071 with T-bill and T-note quantities, and .091 with T-sec quantities. For 1980-99, the respective correlations are .104, .134, .068, and .087. Correlations of the real monetary base for 1959-79 are .096 with the S&P 500, .461 with T-bill returns, .010 with T-bill and T-note quantities, and .094 with T-sec quantities. The correlations of nouborrowed reserves with real T-bill returns differ from those reported in table 1 because contemporaneous rather than leading relationships are considered here. In addition, the return measure in table 1 reflects a one-month yield on a seasoned T-bill rather than the return to the "buy-and-hold" strategy considered here.

(18.) We obtained the secondary market quotes for 1961-86 from the master microfilm reels that are on deposit at the New York Fed's Department of Public Information. Quote sheets for 1987-96 are available at their website (www.ny.frb.org) We collected quotes for 1997-99 from individual issues of the Wall Street Journal.

(19.) We compute surprises to T-secs and the monetary base as one-step-ahead forecast errors from a series of rolling bivariate VARS with four lags and a 30-month estimation window. In this figure and all others in this section, we apply the Hodrick-Prescott filter to our data series before plotting them.

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Dow Jones and Company, 1997-99, The Wall Street Journal, New York, various issues.

Evans, Charles L., and David A. Marshall, 1998, "Monetary policy and the term structure of nominal interest rates: Evidence and theory," Carnegie-Rochester Series on Public Policy, Vol. 49, pp. 53-111.

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_____, 1970, Monetary Statistics of the United States, New York: Columbia University Press.

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Lucas, Robert E., Jr., 1990, "Liquidity and interest rates," Journal of Economic Theory, Vol. 50, No. 2, pp. 237-264.

New York Times Co., The, 1913-25, The Annalist: A Magazine of Finance, Commerce, and Economics, New York, various issues.

_____, 1897--1928, The New York Times, New York, various issues.

Phillips, A. W., 1958, "The relation between unemployment and the rate of change of money wage rates in the United Kingdom, 1861-1957," Economica, Vol. 25, No. 100, pp. 283-299.

Standard and Poor's Corporation, 2000, Compustat, database, New York.

U.S. Department of Commerce, Bureau of the Census, 1975, Historical Statistics of the United States, Colonial Times to 1970, Washington, DC: Government Printing Office.

U.S. Securities and Exchange Commission, 1935-49, Annual Report of the Securities and Exchange Commission. Washington, DC: Government Printing Office, various issues.

U.S. Department of the Treasury, 1917-31, Annual Report of the Secretary of the Treasury on the State of Finances, Washington, DC: Government Printing Office, various issues.

U.S. Department of the Treasury, Bureau of the Public Debt, 1975-2000, Monthly Statements of the Public Debt of the United States, Washington, DC: Government Printing Office, various issues.

University of Chicago, Center for Research on Securities Prices, 1999, CRSP, database, Chicago.

Wilson, Jack W., and Charles P. Jones, 2001, "An analysis of the S&P 500 index and Cowles' extensions: Price indexes and stock returns," Journal of Business, forthcoming.

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TABLE 1

Correlation among monthly growth rates

Variable 1961-99 1980-99

1-month real return on T-bills
 and previous month's real
 growth in NBR .046 -.063

1-month real retrn on T-bills
 and previous month's real
 growth in T-secs .137 .107

Real monthly growth in NBR
 and T-secs .048 -.007

Notes: NBR = real per capita value of nonborrowed reserves; and T-secs =
real per capita value of outstanding Treasury securities.

Sources: see note 1 on p. 33.
TABLE 2

Correlations among growth-rate surprises

Variable 1961-99 1980-99

Unexpected components of:

1-month real return on T-bills
 and previous month's real
 growth in NBR .056 .138

1-month real return on T-bills
 and previous month's real
 growth in T-secs -.008 .142

Real monthly growth in NBR
 and T-secs -.060 -.118

Sources: see note 1 on p. 33.
TABLE 3

Interest rate regressions for buy-and-hold strategy

 g = Marketable T-secs

 1920-99 1920-46 1947-79 1980-99

Constant .0001 .0002 .0000 -.0000
 (0.60) (1.04) (0.01) (-0.24)
[g.sup.u.sub.t-1,t] .0274 0.140 .0069 .0100
 (7.45) (1.97) (1.42) (2.37)
[[pi].sup.u.sub.t,t+1] -1.082 -.9963 -.3837 -.3446
 (-17.31) (-9.43) (-6.04) (-6.54)
[R.sup.2]/(DW) .361 .255 .092 .206
 (1.98) (1.19) (1.70) (1.81)
N 919 290 370 205

 g = T-bills
 and notes
 1980-99

Constant -.0000
 (-0.29)
[g.sup.u.sub.t-1,t] .0104
 (2.66)
[[pi].sup.u.sub.t,t+1] -.3537
 (-6.79)
[R.sup.2]/(DW) .216
 (1.77)
N 205

Notes: The dependent variable is the unanticipated real return on a
three-month T-bill, [r.sup.u.sub.t,t+1]. The table presents coefficient
estimates for equation 5 over the subperiods included in figures 2-6
with T-statistics in parentheses. The [R.sup.2] and Durbin-Watson (DW)
statistics and number of observations (N) for each regression appear in
the final two rows.
TABLE 4

Stock return regressions

 g = Marketable T-secs

 1920-99 1920-46 1947-79 1980-99

Constant -.0014 -.0033 .0014 -.0002
 (-0.55) (-0.50) (0.57) (-0.06)

[g.sup.u.sub.t-1,t] .1085 -.0851 -.0558 -.2390
 (1.20) (-0.42) (-0.36) (-0.76)

[[pi].sup.u.sub.t,t+1] 0.2446 5.753 -5.571 -6.013
 (0.16) (1.92) -(2.81) (-1.53)

[R.sup.2]/(DW) .002 .014 .022 .013
 (1.76) (1.96) (1.84) (1.78)

N 919 290 370 205

 g = T-bills
 and notes
 1980-99

Constant -.0008
 (-0.19)

[g.sup.u.sub.t-1,t] -.1476
 (-0.503)

[[pi].sup.u.sub.t,t+1] -6.296
 (-1.61)

[R.sup.2]/(DW) .014
 (1.77)

N 205

Notes: The dependent variable is the unanticipated real return on a
one-month investment in the S&P 500 portfolio, [S.sup.u.sub.t,t+1]. The
table presents coefficient estimates for equation 6, with T-statistics
in parentheses. The [R.sup.2] and Durbin-Watson (DW) statistics and
number of observations (N) for each regression appear in the final two
rows.
TABLE 5

Correlations of real asset returns and real per capita quantities

 T-bills
 S&P 500 T-bills and notes T-secs

1920-99

Real return on S&P 500 1.00
Real return on T-bills -0.034 1.00
Growth in real T-bills and notes 0.046 0.071 1.00
Growth in real T-secs 0.006 0.110 0.669 1.00
Growth in real monetary base 0.067 0.235 0.040 0.142

1920-46

Real return on S&P 500 1.00
Real return on T-bills -0.075 1.00
Growth in real T-bills & notes -0.022 0.108 1.00
Growth in real T-secs 0.040 0.048 0.680 1.00
Growth in real monetary base 0.064 0.161 0.067 0.145

1947-79

Real return on S&P 500 1.00
Real return on T-bills 0.028 1.00
Growth in real T-bills & notes 0.040 0.096 1.00
Growth in real T-secs 0.003 0.185 0.575 1.00
Growth in real monetary base 0.011 0.470 0.017 0.112

1980-99

Real return on S&P 500 1.00
Real return on T-bills -0.032 1.00
Growth in real T-bills & notes -0.061 0.188 1.00
Growth in real T-secs -0.050 0.208 0.962 1.00
Growth in real monetary base 0.102 0.064 -0.065 -0.003

 Monetary
 base

1920-99

Real return on S&P 500
Real return on T-bills
Growth in real T-bills and notes
Growth in real T-secs
Growth in real monetary base 1.00

1920-46

Real return on S&P 500
Real return on T-bills
Growth in real T-bills & notes
Growth in real T-secs
Growth in real monetary base 1.00

1947-79

Real return on S&P 500
Real return on T-bills
Growth in real T-bills & notes
Growth in real T-secs
Growth in real monetary base 1.00

1980-99

Real return on S&P 500
Real return on T-bills
Growth in real T-bills & notes
Growth in real T-secs
Growth in real monetary base
TABLE 6

Interest rate regressions for the one-month holding strategy

 g = Marketable T-secs g = T-bills
 and notes
 1961-99 1980-99 1980-99

Constant .0000 .0001 .0001
 (0.17) (1.12) (1.03)

[[blank].sub.t-1][g.sup. .0046 .0061 .0075
[u.sup.*].sub.t-1,t]
 (1.02) (1.28) (1.77)

[[blank].sub.t-1][g.sup. -.0041 -.0064 -.0076
[u.sup.*].sub.t-1,t]
 (-0.83) (-1.36) (-1.76)

[[blank].sub.t-1].[[pi].sup. -.9644 -.9370 -.9501
[u.sup.*].sub.t,t+1]
 (-27.10) (-20.54) (-21.32)

[R.sup.2]/(DW) .796 .683 .704
 (2.09) (1.50) (1.50)

N 196 205 205

Notes: The dependent variable is the unanticipated real return on a
T-bill [[blank].sub.t-1].r.sup.[u.sup.*].sub.t,t+1]. The table presents
coefficient estimates for equation 8, with T-statistics in parentheses.
The [R.sup.2] and Durbin-Watson (DW) statistics and number of
observations (N) for each regression appear in the final two rows.
TABLE 7

Stock return regressions for the one-month holding strategy

 g = Marketable T-secs

 1961-99 1980-99

Constant -.0070 .0042
 (-1.89) (1.12)

[[blank].sub.t-1].g.sup.[u.sup.*] .1020 .3533
.sub.t-1,t] (0.37) (1.17)

[[blank].sub.t-1].g.sup.[u.sup.*] .2447 .5797
.sub.t,t+1] (0.81) (1.93)

[[blank].sub.t-1].[[pi].sup. -4.153 .6752
[u.sup.*].sub.t,t+1] (-1.913) (0.24)

[R.sup.2]/(DW) .023 .019
 (1.93) (1.71)

N 196 205

 g = T-bills
 and notes
 1980-99

Constant .0040
 (1.07)

[[blank].sub.t-1].g.sup.[u.sup.*] .3089
.sub.t-1,t] (1.12)

[[blank].sub.t-1].g.sup.[u.sup.*] .5693
.sub.t,t+1] (2.03)

[[blank].sub.t-1].[[pi].sup. .1401
[u.sup.*].sub.t,t+1] (0.05)

[R.sup.2]/(DW) .020
 (1.73)

N 205

Notes: The dependent variable is the unanticipated real return on the
S&P 500, [[blank].sub.t-1] .S.sup.[u.sup.*].sub.t,t+1]. The table
presents coefficient estimates for equation 9, with T-statistics in
parentheses. The [R.sup.2] and Durbin-Watson (DW) statistics and number
of observations (N) for each regression appear in the final two rows.

RELATED ARTICLE: BOX 1

Estimating the impact of price and T-sec supply risk on real T-bill returns

The methodology underlying figures 2-9 begins with adjusting the raw data to make the timing of monthly observations consistent across variables. Since the nominal quantity of T-secs in the hands of the public ([X.sub.t]) is available at the end of each month, while the consumer price index ([CPI.sub.t]) and population ([pop.sub.t]) are computed as annualized monthly averages, we derive the real quantity of Treasury securities at the end of month t as:

[x.sub.t] = 4 x [X.sub.t]/([CPI.sub.t+1] + [CPI.sub.t]) x ([pop.sub.t+1] + [pop.sub.t]),

which amounts to averaging the consumption deflator and population across periods to center them with [X.sub.t].

To approximate the ex post real return on T-bills ([r.sub.t,t+1]) associated with the buy-and-hold strategy discussed in this article, we start with the annualized yields to maturity on three-month (91-day) T-bills that are computed by the Fed as averages of daily yields over the course of a calendar month ([R.sub.t]) and subtract the annualized inflation rate implied by the change in the CPI over the next three months. Since the CPL is a monthly average and [R.sub.t] is annualized, we have

[r.sub.t,t+1] [approximately equals to] [[1+([R.sub.t] - [[(1 + [CPI.sub.t+3] - [CPI.sub.t]/[CPI.sub.t]).sup.4] - 1])].sup.1/12] - 1.

This is the monthly real return that an investor would receive by buying a three-month T-bill and holding it until maturity, assuming that the inflation rate is steady across the three months.

The nominal return on the S&P 500 ([S.sub.t]) covers an actual calendar month, so we derive an ex post return by subtracting the growth rate of the consumer price index ([CPI.sub.t]),

[s.sub.t] = [S.sub.t] - [([CPI.sub.t+1] - [CPI.sub.t]/[CPI.sub.t] - [CPI.sub.t-1]) -1],

which amounts to computing inflation as the growth in the CPI after averaging across periods.

Before using the series derived above (as well as CPI inflation itself), we de-seasonalize by regressing each on monthly dummy variables and an adequately high-order polynomial in time. We include the time polynomial to reduce the degree to which the estimates of the monthly effects reflect cyclical and trend components. After subtracting the coefficients on the monthly dummy variables from the raw series, we add the mean of the detrended series back in to complete the seasonal adjustment. See Johnston (1984, pp. 23--49) for a clear exposition of this method along with its advantages and drawbacks.

The VAR equations used to compute the surprises to growth in the supply of T-secs (g) and inflation ([phi]) have the form

[g.sub.t] = [summation over (k/i=1)] [c.sub.1,k][g.sub.t-k] + [summation over (k/i=1)] [d.sub.1,k] [[pi].sub.t-k] + [summation over (k/i=1)] [f.sub.1,k][r.sub.t-k] + [summation over (k/i=1)] [h.sub.1,k][S.sub.t-k] + t + [e.sub.1,t]

[[pi].sub.t] = [summation over (k/i=1)] [c.sub.2,k][g.sub.t-k] + [summation over (k/i=1)] [d.sub.2,k][[pi].sub.t-k] + [summation over (k/i=1)] [f.sub.2,k][r.sub.t-k] + [summation over(k/i=1)] [h.sub.2,k][S.sub.t-k] + t + [e.sub.2,t],

where k is the lag length and t is a linear time trend. The time subscripts refer to the information sets [I.sub.t-k] from which the variables derive. To allow the forecasts to reflect recent economic conditions, we allow the VAR samples to roll with time, choosing estimation windows of 36 months (figure 2) or 30 months (figures 3-9). This implies that each successive one-step ahead forecast and forecast error is computed with an information set that overlaps the previous one in all but the latest and earliest periods. Using the coefficients from the time t regression, we compute the forecasts for time t + 1 as fitted values obtained with the information set from time t.

In estimating equation 4, we pool the monthly surprises across the sample period to obtain a single set of regression coefficients.

BOX 2

Estimating the market value of outstanding corporate equity

To estimate the market value of outstanding corporate equity, we extend the Federal Reserve Board's Flow of Funds series (table L.4) backwards, using the available data on capitalization for the New York Stock Exchange (NYSE), the regional exchanges, and over-the-counter (OTC) markets. We work backwards not from 1945 (which is when the Flow of Funds data series begins) but, rather, from 1949 because the closest over-lapping observations of OTC activity are for 1949.

The Flow of Funds reports $117 billion for outstanding corporate equities in 1949, which we divide into the value of NYSE-listed firms, the value of firms listed exclusively on The American Stock Exchange (AMEX) and the regional exchanges, and the value of firms traded exclusively in OTC markets. Friend (1958) estimates the sum of NYSE and regional capital in 1949 at $95 billion. We know from the Center for Research on Securities Prices (CRSP) database that NYSE capitalization was $68 billion. This implies a regional capitalization of $27 billion and OTC capital of $22 billion in 1949. Assuming that the capitalizations of NYSE listed and regionally listed firms are proportional to their transaction values, which are available from various issues of the Annual Report of the Securities and Exchange Commission for 1935-49, we multiply NYSE capital by the ratio of regional to NYSE transactions to approximate movements in capitalization on the regional exchanges. We then adjust the resulting regional series to mat ch the $27 billion that we estimate for 1949. To estimate regional capital for 1920-34, we observe that the ratio of regional to NYSE transaction value was steady at 0.18 for 1935-50 and again use NYSE capital to derive regional capital from 1920.

The OTC market presents a double-counting problem. Friend estimates that, in 1949, 25 percent of quoted OTC issues were also listed on a registered exchange. Our measure of OTC capital must exclude such firms. To derive estimates for 1920-49, we use Friend's counts of the number of OTC-quoted firms over a three-month window surrounding three benchmark dates in 1949, 1939, and 1929. There were 5,300 such OTC firms in 1949, of which 75 percent were not listed on registered exchanges. The median market value of these unlisted firms was $2.4 million. Therefore, we approximate exclusive OTC capital at $9.54 million (.75 x 5,300 x $2.4) in 1949. Assuming that the real median size of unlisted OTC firms did not change over 1920-49, we next use the gross domestic product (GDP) deflator to convert the median size into nominal terms at the other benchmark dates. Next, we observe that the $9.47 million for 1949 is too small by a factor of 2.3, given our comparable estimate from the Flow of Funds, and adjust the OTC bench mark estimates by this factor. Finally, we interpolate between the benchmarks to obtain an annual OTC series for 1929-49.

To obtain OTC capital for 1920-28, we continue to assume that capital on the exchanges is proportional to relative transaction values. Since we know NYSE capitalization and now have estimates for the regional and OTC markets in 1929, we can estimate the share of the OTC in total market value in 1929. Using Friend's (1958, p. 109) estimates of this share for 1926 and 1920, we can estimate OTC capital for these years given the values of NYSE capitalization from CRSP and our earlier estimates of regional capital. We interpolate between the benchmarks once again to obtain OTC capital for 1920-29.

By adding NYSE, regional and OTC capitalizations, we obtain a series for total market value for 1920-49 that is consistent with the Flow of Funds in the sense that the two segments coincide in 1949. Our final estimates of equity capital outstanding, displayed in figure 2A, are obtained by splicing our series with the Flow of Funds in 1945. The figure also includes the series for equity capital that would result from the use of CRSP (1925-99) and our NYSE listings (1900-24) data alone. The importance of equities that were not listed on the NYSE from the end of the First World War to the start of Nasdaq in 1971, as depicted by the vertical distance between the black and colored lines in the figure, is considerable. Since we wish to use market value from 1900 in figures 12 and 13, for the purpose of computing the share of equity in total finance, we ratio splice the value of NYSE capital for 1900-20 (obtained from individual issues of the New York Times Co.'s The Annalist, Dana & Company's Commercial and Financi al Chronicle, the New York Times, and Bradstreet's) to our result for 1920-99.

[Graph omitted]

BOX 3

Estimating the market value of business debt

We define U.S. business debt as the value of outstanding commercial and industrial bank loans, corporate bonds, and commercial paper. For 1945-99, book values for loans and corporate bonds are from the Flow of Funds (table L.4, lines 5 and 6, respectively). For 1900-44, the book value of outstanding corporate bonds is from Hickman (1952) and that of bank loans is from the Federal Reserve Board's All-Bank Statistics. Since bank loans are reported in the latter source as June 30 figures, we average across years for consistency with the calendar-year basis of the Flow of Funds.

For commercial paper, the outstanding amount for 1970-93 is available from the FRED database of the Federal Reserve Bank of St. Louis. We carry this series to the present using the quantity of open market paper from the Flow of Funds (table L.4, line 2). We extend the series backwards to 1959 using the Federal Reserve Board's Banking and Monetary Statistics (Board of Governors, 1976b, pp. 717-719). These quantities include paper placed both directly (that is, finance company) and by dealers. For 1919-58, we have a continuous series for dealer-placed paper only, again from Banking and Monetary Statistics (1976b, pp. 714-717; 1976a, pp. 465-467), which we ratio-splice to the later series. The splice leads to what is likely to be an overestimate of outstanding commercial paper by 1918 due to the rapid growth of directly placed paper between the mid-1920s and 1941. For example, Greef (1937, p. 118) presents a figure of $874 million for outstanding commercial paper in 1918, while the spliced series would imply a t otal of $4.2 billion. Since we do not have the data on finance paper that would be required to reconcile these series, we have chosen to simply use Greef's figures before 1931, the point at which the outstanding totals from both series differ the least in percentage terms. Prior to 1918, Greef (1937, pp. 57-59) provides estimates of the volume of commercial paper trading in 1907 and 1912-16. Assuming four- to six-month maturities, we then estimate the amount of commercial paper outstanding at 5/12 of the trading volume, and assume constant growth between the benchmarks of 1907 and 1912. We apply the same growth rate to 1900-06 to complete the series. From the above, it should be clear that the commercial paper series is not very reliable prior to 1931. Since we do not perform any econometric analysis with this series, however, and it turns out to be a small portion of total debt finance in any case during this period, we consider the inclusion of the totals in figures 12-14 to be useful.

To build a market value series, we include both commercial paper and bank loans, due to their short maturities, at their book values. We then convert outstanding corporate bonds from par values to market values using the average annual yields on Moody's AAA-rated corporate bonds (from Moody's Investors Service for 1919-98 and Hickman's "high grade" bond yields, which line up precisely with Moody's, for 1900-18). To determine market value, we let [r.sub.t] be the bond interest rate and compute the weighted average

[r.sup.*.sub.t] = 1/[[sigma].sup.t.sub.i=1885] [(1 - [delta]).sup.t-i] [simmuation over (t/i=1885)] [(1 - [delta]).sup.t-i][r.sub.t-i].

We choose [delta] = 10 percent to approximate the growth of new debt plus retirements of old debt and multiply the book value of outstanding corporate bonds by the ratio [r.sup.*.sub.t]/[r.sub.t] to obtain their market value.