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Divisia Monetary Data for the United States:
rigorously founded in economic aggregation and index-number theory. 

Federal Reserve Official Monetary Aggregates

Extensive published results demonstrate that the best monetary aggregate for almost all uses was the Federal Reserve’s former broadest aggregate, L, but only if computed as a properly weighted index number, such as the Divisia or Fisher-ideal index. The second-best monetary aggregate was the former next-broadest aggregate, M3, properly constructed as an index number. In contrast, when computed as simple-sum accounting numbers, disconnected from economic aggregation theory, M3 and L were among the worst monetary aggregates and were inconsistent with elementary principles of economic measurement. Narrow aggregates, such as M1 and M2, give no weight to many highly-liquid substitutes for money. That truncation is hard to justify. More...

Figures Provided on This Page

We are displaying on this page three, new, Divisia, monetary-quantity aggregates, and their corresponding, aggregation-theoretic interest-rate aggregates.

  • The primary one is what we are calling Divisia M4. It is a broad aggregate, including negotiable money-market securities, such as commercial paper, negotiable CDs, and T-bills. M4's components are similar to those of the monetary aggregate once called L, but modernized to be consistent with current market realities.a
  • The aggregate M4- (to be called "M4 minus") is M4 minus Treasury bills.
  • Divisia M3 excludes those money-market securities not issued by financial intermediaries, such as commercial paper and Treasury bills, but does include negotiable CDs and repurchase agreements.
  • We are providing narrower aggregates, such as Divisia M1 and M2, only on a spreadsheet and through a link to the St. Louis Fed’s source. We do not include those narrower aggregates among these featured charts. More...

More Information Below

CFS Money Supply for August
(Released September 17, 2014)

Featured Charts

Hover over chart to see a larger version, or click on the title for an even larger full-page version.

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Divisia Data Table

Levels normalized to equal 100 in Jan. 1967
Select a different start year for the table below:

Divisia M4
Including Treasuries (M4)
Divisia M4
Excluding Treasuries (M4-)
Divisia M3 (M3)
Date Divisia M4
Including
Treasuries1
Y/Y Pct.
Change2
Divisia M4
Excluding
Treasuries1
Y/Y Pct.
Change2
Divisia M31 Y/Y Pct.
Change2
Jan 2010 1,210.6 -6.34% 1,114.7 -6.43% 1,089.8 -4.19%
Feb 2010 1,201.6 -6.52% 1,112.8 -5.87% 1,087.9 -4.16%
Mar 2010 1,192.2 -7.32% 1,097.8 -7.13% 1,073.5 -5.17%
Apr 2010 1,197.5 -5.72% 1,099.0 -5.44% 1,075.7 -4.20%
May 2010 1,200.4 -6.17% 1,101.6 -5.60% 1,079.8 -4.64%
Jun 2010 1,185.8 -7.26% 1,087.8 -6.61% 1,066.5 -5.92%
Jul 2010 1,200.9 -4.95% 1,103.2 -4.09% 1,081.0 -4.24%
Aug 2010 1,208.7 -4.16% 1,112.2 -3.20% 1,090.5 -2.83%
Sep 2010 1,209.0 -3.67% 1,112.4 -2.83% 1,087.9 -1.85%
Oct 2010 1,220.8 -1.29% 1,123.9 -0.76% 1,101.8 -0.01%
Nov 2010 1,216.3 -0.72% 1,121.4 -0.35% 1,100.9 0.58%
Dec 2010 1,210.5 -0.67% 1,114.1 -0.52% 1,094.6 0.19%
Jan 2011 1,207.3 -0.27% 1,107.7 -0.63% 1,092.0 0.21%
Feb 2011 1,204.1 0.21% 1,115.2 0.22% 1,096.2 0.76%
Mar 2011 1,209.0 1.41% 1,126.2 2.59% 1,104.5 2.89%
Apr 2011 1,225.3 2.32% 1,143.2 4.03% 1,115.7 3.71%
May 2011 1,234.5 2.84% 1,155.9 4.94% 1,128.4 4.50%
Jun 2011 1,225.0 3.30% 1,147.1 5.45% 1,119.4 4.97%
Jul 2011 1,227.6 2.23% 1,152.1 4.43% 1,127.2 4.27%
Aug 2011 1,225.1 1.36% 1,152.8 3.65% 1,131.4 3.75%
Sep 2011 1,223.1 1.17% 1,148.9 3.28% 1,131.8 4.04%
Oct 2011 1,222.5 0.14% 1,147.3 2.08% 1,130.8 2.63%
Nov 2011 1,223.6 0.60% 1,149.0 2.46% 1,134.4 3.04%
Dec 2011 1,219.1 0.71% 1,142.6 2.56% 1,131.8 3.40%
Jan 2012 1,233.3 2.15% 1,153.5 4.14% 1,140.5 4.43%
Feb 2012 1,235.7 2.62% 1,157.9 3.83% 1,146.0 4.54%
Mar 2012 1,236.1 2.24% 1,157.2 2.75% 1,147.1 3.86%
Apr 2012 1,241.4 1.31% 1,161.7 1.61% 1,150.8 3.15%
May 2012 1,241.3 0.55% 1,159.7 0.32% 1,147.3 1.67%
Jun 2012 1,251.7 2.18% 1,168.7 1.88% 1,157.1 3.36%
Jul 2012 1,262.2 2.82% 1,179.9 2.41% 1,166.4 3.48%
Aug 2012 1,265.9 3.33% 1,182.0 2.53% 1,168.9 3.31%
Sep 2012 1,274.7 4.22% 1,190.2 3.59% 1,179.0 4.17%
Oct 2012 1,275.4 4.33% 1,190.9 3.80% 1,180.3 4.38%
Nov 2012 1,285.7 5.08% 1,200.7 4.50% 1,189.5 4.85%
Dec 2012 1,301.4 6.75% 1,219.8 6.75% 1,207.7 6.70%
Jan 2013 1,308.9 6.13% 1,225.6 6.24% 1,208.5 5.97%
Feb 2013 1,301.9 5.36% 1,217.8 5.17% 1,203.0 4.98%
Mar 2013 1,297.2 4.95% 1,213.3 4.85% 1,201.7 4.76%
Apr 2013 1,304.9 5.12% 1,220.8 5.09% 1,210.0 5.14%
May 2013 1,304.0 5.05% 1,223.3 5.49% 1,210.6 5.52%
Jun 2013 1,305.8 4.32% 1,225.3 4.85% 1,214.4 4.95%
Jul 2013 1,308.5 3.67% 1,229.1 4.17% 1,219.4 4.55%
Aug 2013 1,309.8 3.46% 1,229.2 4.00% 1,219.7 4.35%
Sep 2013 1,315.1 3.17% 1,237.6 3.99% 1,226.4 4.02%
Oct 2013 1,322.0 3.65% 1,244.6 4.51% 1,230.5 4.25%
Nov 2013 1,320.7 2.72% 1,243.1 3.53% 1,228.7 3.30%
Dec 2013 1,326.0 1.89% 1,248.6 2.36% 1,235.8 2.33%
Jan 2014 1,320.0 0.85% 1,246.3 1.69% 1,235.8 2.26%
Feb 2014 1,329.3 2.10% 1,255.8 3.12% 1,246.0 3.57%
Mar 2014 1,332.3 2.71% 1,259.8 3.83% 1,250.4 4.05%
Apr 2014 1,326.8 1.68% 1,260.2 3.23% 1,250.1 3.32%
May 2014 1,336.3 2.47% 1,268.3 3.67% 1,258.4 3.94%
Jun 2014 1,338.3 2.49% 1,272.0 3.81% 1,261.6 3.88%
Jul 2014 1,341.9 2.55% 1,274.9 3.72% 1,265.0 3.74%
Aug 2014 1,342.6 2.51% 1,276.9 3.88% 1,266.1 3.80%

1Level, normalized to equal 100 in Jan. 1967
2Year-over-year percentage growth rate. We are displaying year-over-year growth rates rather than monthly growth rates, since the volatility of the monthly growth rates masks information that is more evident from the smoother year-over-year growth rates. But users who prefer monthly growth rates can compute those month-over-month growth rates directly from the levels that we are providing. All component quantities that are not seasonally adjusted by the data source are being seasonally adjusted by the CFS using the Census X-12 program. As a result, any volatility in the monthly growth rates is not a consequence of seasonality.
3Interest-rate aggregate, percent per year. The formula and theory relevant to interest rate aggregation can be found in the AMFM’s data sources document.

Federal Reserve Official Monetary Aggregates

Extensive published results demonstrate that the best monetary aggregate for almost all uses was the Federal Reserve’s former broadest aggregate, L, but only if computed as a properly weighted index number, such as the Divisia or Fisher-ideal index. 

The second-best monetary aggregate was the former next-broadest aggregate, M3, properly constructed as an index number.  See, e.g., Barnett (1982), “The Optimal Level of Monetary Aggregation,” in the AMFM Library. In contrast, when computed as simple-sum accounting numbers, disconnected from economic aggregation theory, M3 and L were among the worst monetary aggregates and were inconsistent with elementary principles of economic measurement.

Narrow aggregates, such as M1 and M2, give no weight to many highly-liquid substitutes for money.  That truncation is hard to justify.  At the other extreme, the broad, simple-sum aggregates give equal weight to distant substitutes for money as to currency.  That far worse weighting cannot be justified at all.  Recognizing the distortions produced by improper weighting within the broad, simple-sum, monetary aggregates, the Federal Reserve has rightfully discontinued publication of both simple-sum M3 and L.

Figures Provided on This Page

We are displaying on this page three broad Divisia monetary aggregates. The primary one is what we are calling Divisia M4. It is a broad aggregate, including negotiable money-market securities, such as commercial paper, negotiable CDs, and T-bills. M4's components are similar to those of the monetary aggregate once called L, but modernized to be consistent with current market realities.a

The aggregate M4- (to be called "M4 minus") is M4 minus Treasury bills. In aggregation theory, M4 should always be preferred to M4-, since there is no good reason to give a weight of zero to T-bills in M4. Nevertheless, for some research purposes, it might be useful to separate the effects of monetary from fiscal policy. Including T-bills in M4 produces an overlap. The supply of T-bills can change either from monetary-policy open-market operations or from fiscal-policy changes in debt financing.

Divisia M3 excludes those money-market securities not issued by financial intermediaries, such as commercial paper and Treasury bills, but does include negotiable CDs and repurchase agreements. Divisia M3 may be closer than Divisia M4 to Federal Reserve actions in the policy transmission mechanism, so could be useful under some circumstances.  But aggregation theory provides no reason to impute weight of zero to the highly liquid money-market securities included in M4, but not in M3.

Simple-sum or arithmetic-average monetary-quantity aggregates are inconsistent with best practice economic measurement. For the same reasons, linear approaches to price aggregation are also unacceptable. The price of a monetary asset is its user-cost price, measuring the opportunity cost of holding the asset in terms of foregone interest. In continuous time, the real user-cost price of a Divisia monetary asset is the difference between the real rate of return on pure capital investment, R, called the “benchmark rate,” and the asset’s interest rate. We are providing as figures on this page the interest-rate aggregates, but not the aggregation-theoretic user-cost price aggregates, since there can be differences of opinion on how to compute the real rate of return on pure capital. However, we are providing our user-cost price aggregates on a spreadsheet for the benefit of experts. In our work, we are using the benchmark rate measure recently proposed by Akiva Offenbacher at the Bank of Israel.b

Interest rate aggregates, unlike quantity and price aggregates, are based on accounting conventions, rather than on deep aggregation and index number theory. The formulas and theory relevant to economic user-cost price aggregation and to accounting interest-rate aggregation are provided in the AMFM data sources document.

The Methodology

We are not supplying simple-sum M3 and L, since we agree with the Fed that those aggregates were severely defective by grossly overweighting distant substitutes for money.  In addition, constructing broad simple-sum aggregates, even as accounting numbers, cannot be based directly upon available data, since the Fed is no longer providing the former consolidated components.  Those consolidated components netted out overlaps, such as the overlaps among negotiable CDs and money market funds.  Adding up non-consolidated components produces double counting and other violations of accounting conventions.  But the need remains for the very best monetary aggregates --- M3 and L, produced as competently weighted index numbers.

We do so, using the highly-regarded Divisia monetary-index formula, as first derived and produced by Barnett (1980), “Economic Monetary Aggregates: An Application of Aggregation and Index Number Theory.” Consolidated components are not needed for that purpose.  Index number theory, being based on microeconomic theory, rather than on accounting conventions, uses market data.  Economic index numbers aggregate over assets and over economic agents in terms of demand for the imperfectly-substitutable services of the market assets and do not just add up the components.  No mathematical-economics training is needed to understand that “you can add apples and apples, but not apples and oranges.” For extensive background on how we are “getting it right,” see Barnett’s (2012) book, Getting It Wrong.

Download Data in Excel and Documentation in Word

Download:

  • All of the Divisia M3, M4-, and M4 aggregate data in an Excel sheet here.
  • The narrower Divisia monetary aggregates in an Excel sheet here.
  • The document describing data sources here.

See more information about the supporting data below.

Data Provided on a Spreadsheet, but Not Displayed on This Page

Data and analysis that cannot be replicated are not consistent with the normal standards of science, regardless of any claims of proprietary interest.  We use only component quantity and interest-rate data available to the public. The component data are provided at no cost only to established researchers, who need the data for use in their research for publication in major peer-reviewed journals, such as Macroeconomic Dynamics, edited by CFS Director, Professor William A. Barnett. For such academic research purposes, requests for the component data or the dual user-cost price aggregates should be sent to Professor Barnett.

We do not provide the Federal Reserve’s official simple-sum monetary aggregates.  We consider the Federal Reserve’s simple-sum monetary aggregates to be entirely without merit. The simple-sum aggregates are based on archaic economic-measurement methodology, incompetent since the appearance of Irving Fisher’s (1922) landmark book, The Making of Index Numbers, nearly a century ago. The simple-sum aggregates have been obsolete, since monetary assets began yielding interest. If you nevertheless should wish to see the Federal Reserve’s, official, simple-sum monetary aggregates, you can find them in the St. Louis Federal Reserve’s database, FRED.

While the broadest Divisia monetary aggregates are best for most purposes, some applications exist for which narrower Divisia monetary aggregates are of use.c  The St. Louis Federal Reserve is supplying narrower Divisia monetary aggregates, which the St. Louis Fed calls MSI (monetary services index). At present, the St. Louis Fed is providing most but not all the component data, included now with the MSI data in the St. Louis Fed’s excellent FRED database. Eventually all components are planned to be available within FRED. At that time, the FRED Divisia data will be easy to replicate and use, since FRED contains outstanding software for display and analysis. Although the component quantity and interest rate data are not yet all available on FRED, we are indebted to Richard Anderson at the St. Louis Fed for providing that data to us. As opposed to the Federal Reserve Board’s simple-sum monetary aggregates, which we consider to be entirely without merit, we consider the St. Louis Fed’s MSI (Divisia) narrow monetary aggregates to be an admirable and important contribution to public information.

We also compute and provide narrow Divisia monetary aggregates, such as M1 and M2.  Our series differ from the St. Louis Fed’s only in our use of the Bank of Israel’s benchmark-rate procedure, described above.  But the Divisia monetary-quantity index is highly robust to the choice of benchmark rate, so our narrow Divisia monetary aggregates can be expected usually to track the St. Louis Fed’s MSI aggregates relatively closely.d  Because of the anticipated inclusion of the MSI data in the excellent FRED database, the difference in benchmark rate alone would not have been adequate reason for the CFS to produce those aggregates in a manner nearly redundant with MSI.  But the St. Louis Fed froze its MSI data for over five years, from the start of the housing crises through the financial crisis and Great Recession.  To protect the public from any such future freezes in that data, we are providing our own parallel computations as a backup source — in response to popular demand.

There is one entirely nontrivial difference between our narrow aggregates and MSI:  the dual user-cost aggregate, which is not robust to changes in the benchmark rate.  If you only need the quantity aggregates, there is little reason to prefer our CFS narrow Divisia monetary aggregates over the St. Louis Fed’s, especially when the MSI Divisia monetary aggregates become conveniently available within FRED.  But if you need the dual user-cost aggregates in your research, you may find that you will have good reason to prefer ours.

Key Takeaway Points

  • The broadest monetary aggregates are almost always the best monetary aggregates, when their components are properly weighted.
  • When computed as unweighted simple sums, the broadest monetary aggregates are among the worst monetary aggregates ever provided by the Federal Reserve.
  • The Federal Reserve was right to discontinue publication of the broad, simple-sum, monetary aggregates.
  • The Fed has hampered computation of simple-sum, broad, monetary aggregates as accounting numbers, by discontinuing publication of their consolidated components.  But there is no good reason to compute simple-sum broad monetary aggregates at all.
  • Aggregation-theoretic monetary aggregates, such as our Divisia monetary aggregates, use available market data and do not need consolidated components, since those aggregates are based on microeconomic theory, not accounting.
  • Imperfect substitutes are never given equal weights in economic aggregation theory or in economic index-number theory.  Valid aggregation over imperfect substitutes is the primary focus of the field of economic measurement.
  • While economic aggregation and index number theory provide the relevant principles for quantity aggregation over monetary assets and for price aggregation over user costs, accounting principles are relevant to aggregation over interest rates. We use accounting principles where relevant and economic theory where relevant, as is consistent with best practice economic measurement. Details are provided in the AMFM data sources document.

2014 CFS Divisia Release Schedule

CFS Divisia Aggregates are released at 9:00 AM Eastern time on the following dates in 2014: January 22, February 19, March 19, April 16, May 21, June 18, July 16, August 20, September 17, October 22, November 19, December 17.

a The Federal Reserve discontinued publication of its broadest aggregate, L, in 1998.  There have been substantial changes in money markets since then.  M4’s components take into considerations those changes.  Similarly the component data for M3, which was discontinued by the Fed in 2006, have been modified to take into consideration market data availability and market structural changes.  For example, the repurchase agreements in our Divisia M3 and M4 are from the New York Federal Reserve Bank and include the total market values, rather than from the narrower definition previously adopted by the Federal Reserve Board in its aggregates, and provided by the St. Louis Fed.

b In discrete time, the foregone interest is discounted to present value from the end of the period to the start of the period, by division by 1 + R.  The real user cost is multiplied by the cost-of-living index to convert to the nominal user cost. If p is the cost-of-living index and ri is the interest rate on monetary asset i, then the asset’s nominal user cost in discrete time is p(R – ri)/(1 + R). For the formal derivation, see Barnett (1980).  The Bank of Israel’s measure of the rate of return on pure investment is the short-term, bank, loan rate.  To protect against the highly improbable risk that a monetary component’s interest rate might occasionally exceeding that loan rate, we incorporate the short-term bank-loan rate into the upper envelope over all of M4’s monetary-asset component yields.

c For the relevant criterion, since Barnett and de Peretti (2009).

d The Divisia monetary-quantity index computes the growth rate of the aggregate as a weighted average of the growth rates of the component quantities.  The weights are the expenditure shares of the components with user-cost prices in the share computations.  Since the benchmark rate appears symmetrically in all terms in the numerator and denominator of the share weights, those weights are not highly sensitive to variations in the benchmark rate.