A granular investigation on the stability of money demand
📄 Summarized from the full manuscript · Human-reviewed for faithfulness before publication
In brief
Is the famously unstable relationship between money and interest rates a real change in behavior, or a measurement problem? Using monthly United States data from 1967 to early 2020, this paper compares simply adding up dollar balances with an index that weights each kind of money by what holding it costs. The simple sums lose their stable long-run link to Treasury bill rates after the 1980 deregulation, while the weighted measures keep a correctly signed relationship with their own holding costs throughout, including after 2008 when bill rates hit zero. It matters because decades of evidence for unstable money demand may reflect how money was measured.
What this paper finds — and why it matters
This 2024 Macroeconomic Dynamics paper by Zhengyang Chen and Victor J. Valcarcel asks whether the long-documented instability of U.S. money demand reflects a genuine structural break in households’ and firms’ preferences for monetary assets, or is instead an artifact of measuring money with simple-sum aggregates (which just add up dollar balances) rather than Divisia aggregates (which weight each monetary asset by its real user cost, i.e., the foregone return from holding it instead of a benchmark asset). Using monthly U.S. data from January 1967 to March 2020 (the sample stops there because the Federal Reserve’s April 2020 redefinition of M1 and a simultaneous Center for Financial Stability accounting change make later observations non-comparable), the authors estimate bivariate Johansen (1991, 1995) cointegrating VECMs between real money balances scaled by nominal income and an opportunity-cost variable – either the 3-month T-bill yield or each aggregate’s own Divisia real user cost – in both semi-log (Cagan) and double-log (Meltzer) functional forms, checked across four Johansen trend specifications and corroborated with Andrews-Ploberger (1994) and Bai-Perron (2003) structural-break tests. They find that simple-sum M2 and M3 fail to cointegrate with the T-bill yield over the full sample, whereas Divisia M2 cointegrates robustly with its own user cost under every specification and functional form, and Divisia M3 cointegrates under most specifications; splitting the sample at the 1980 DIDMCA deregulation break (located via Andrews-Ploberger at 1979:M10 for Divisia M2 and 1980:M2 for Divisia M3) shows simple-sum M2’s relationship with the T-bill yield breaking down after 1980 (surviving only in trend specifications, and then with the wrong sign), while Divisia M2 continues to cointegrate correctly in both subperiods. After the Global Financial Crisis, the near-zero T-bill yield loses its cointegrating relationship with Divisia M3 and M4 entirely, yet both continue to cointegrate with their own real user costs, which never collapsed to zero. A granular decomposition of ten individual Divisia components against their own user costs finds that 29 of 40 estimated coefficients (10 components times 4 Johansen criteria) carry the theoretically correct sign, versus much weaker and more often wrong-signed cointegration between those same components and the T-bill yield. The authors conclude that the instability documented in the money-demand literature is a matter of measurement – the T-bill yield and simple-sum aggregation strip out information that Divisia aggregation and its user costs preserve – rather than a structural shift in money demand itself; scope is limited throughout to bivariate (two-variable) cointegrating relationships, with income elasticity imposed as unity rather than estimated.
Summary of a classic paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.
Questions & answers
Q1. What is the paper’s central research question and why does it matter?
The paper asks whether the well-documented instability of U.S. money demand reflects a genuine structural change in the public’s preference for monetary assets, or is instead a measurement artifact stemming from the use of simple-sum monetary aggregates rather than Divisia aggregates. This matters because money-demand stability is a precondition for using monetary aggregates as policy indicators or intermediate targets; if instability is really a measurement problem, then abandoning simple-sum aggregates for Divisia aggregates – rather than concluding that money demand itself is unmoored from its fundamentals – would be the appropriate response.
Q2. What data and sample period does the paper use, and why does the sample end in March 2020?
The analysis uses monthly U.S. data from January 1967 through March 2020, plus four subsamples (pre-1980: 1967:Q1-1980:Q2; post-1980: 1980:Q2-2020:Q1; pre-GFC: 1967:Q1-2008:Q3; post-GFC: 2008:Q4-2020:Q1), stopping in March 2020 because the Federal Reserve’s April 2020 redefinition of M1 (adding savings deposits) coincided with a Center for Financial Stability (CFS) accounting change for savings and OCD under “Other Liquid Deposits,” making it impossible to disentangle a post-2020 break from the pandemic itself. Money is measured as log real balances scaled by nominal income for Divisia DM2, DM3, and DM4 and for simple-sum M2 and M3 (simple-sum M3, no longer published by the Federal Reserve, is reconstructed by the authors from CFS component data). The granular analysis in Section 8 further decomposes the Divisia aggregates into ten individual component assets: currency, demand deposits, other checkable deposits, savings deposits, retail money-market funds, small time deposits, large time deposits, institutional money markets, repurchase agreements, and commercial paper plus T-bills.
Q3. What is the paper’s empirical method?
Each money-demand relationship is estimated as a bivariate Johansen (1991, 1995) cointegrating VECM between real money balances scaled by nominal income and an opportunity-cost variable – either the 3-month T-bill yield or the aggregate’s own Divisia real user cost – specified in both semi-log (Cagan 1956) and double-log (Meltzer 1963) functional forms, with unitary income elasticity imposed. Results are checked across four of Johansen’s five trend specifications (the no-constant specification (i) is excluded), lag length for the VECM is chosen by the Akaike (1974) information criterion (and confirmed with Schwarz and Hannan-Quinn criteria), unit roots are tested with DF-GLS (Elliott et al. 1996), and structural breaks are located with the Andrews-Ploberger (1994) single-break test and the Bai-Perron (2003) multiple-break test, applied to the money/income ratios, the real user costs, and the VECM residuals.
Q4. What does the full-sample (1967-2020) analysis find for simple-sum versus Divisia aggregates?
Over the full 1967-2020 sample, simple-sum M2 and M3 fail to cointegrate with the T-bill yield under any of the four Johansen trend specifications or either functional form, while Divisia M2 cointegrates robustly with its own real user cost under all specifications and forms, with user-cost coefficient estimates that are insensitive to which trend specification is used. Divisia M3 cointegrates with its user cost with the theoretically correct sign under semi-log specifications (ii)-(iv) and double-log constant specifications (ii)-(iii), whereas simple-sum M3 cointegrates only weakly with its own user cost and occasionally shows the wrong sign.
Q5. What happens at the 1980 structural break, and how do the pre- and post-1980 subsamples differ?
Both the Andrews-Ploberger and Bai-Perron tests locate a structural break around the 1980 Depository Institutions Deregulation and Monetary Control Act (DIDMCA): Andrews-Ploberger dates the break in Divisia M2’s log(M/PY) at 1979:M10 (95% CI 1979:M8-1980:M2) and in Divisia M3’s at 1980:M2 (95% CI 1980:M1-1980:M3), and Bai-Perron confirms breaks around 1980-1981 in both the quantities and the VECM residuals. In the pre-1980 subsample (1967:Q1-1980:Q2), both simple-sum M2 and Divisia M2 cointegrate with the T-bill yield with the correct sign under most Johansen criteria, with the user-cost coefficient “close in magnitude and statistically significant with t-statistics of 6.9 or greater.” After 1980, simple-sum M2’s cointegration with the T-bill yield largely breaks down – surviving only in the trend specifications, and there with a wrong (negative) sign – while Divisia M2 continues to cointegrate correctly with its own user cost under every criterion in both functional forms; simple-sum M3 never cointegrates with Divisia M3’s user cost in the post-1980 sample, even as Divisia M3 continues to cointegrate correctly in both subperiods.
Q6. What happens after the Global Financial Crisis, when the T-bill yield approaches zero?
After the Global Financial Crisis (2008:Q4-2020:Q1), Divisia M3 and M4 both lose their cointegrating relationship with the T-bill yield, which the authors attribute to the yield’s approach to and persistence at the effective lower bound “destroying the information content the T-bill yield carries for money demand determination”; both aggregates nonetheless continue to cointegrate with their own real user costs under all four Johansen criteria, with every user-cost coefficient statistically significant and correctly signed. This asymmetry is attributed to the fact that Divisia real user costs, unlike the T-bill yield, did not collapse to zero during the near-zero-rate period.
Q7. What does the granular, component-level analysis in Section 8 show?
Decomposing Divisia aggregates into ten individual component assets, only currency balances cointegrate with the T-bill yield under all Johansen criteria with the correct sign, and the paper describes “generally weak evidence of cointegration between most monetary assets and the T-bill yield”; against their own user costs, by contrast, currency, demand deposits, savings deposits, and repurchase agreements cointegrate correctly under every criterion, and all other components except institutional money markets (which cointegrates under only one criterion) find a correctly signed cointegrating relationship under at least two of the four criteria. Across all 40 estimated coefficients on the own-user-cost specification (10 components times 4 Johansen criteria), 29 carry the correct sign, 9 find no cointegrating relationship, and 2 (both trend specifications for small time deposits) show an inverted sign.
Q8. What do the authors conclude, and what mechanism do they propose?
The authors conclude that “the instability of money demand is a matter of measurement rather than a consequence of a structural change in agents’ preference for monetary assets.” The proposed mechanism is that DIDMCA-era financial deregulation eroded the institutional distinctions (such as Regulation D’s ban on interest-bearing demand deposits) that had made simple-sum aggregation a tolerable approximation, while later the near-zero T-bill environment after the GFC made the T-bill yield a poor proxy for the opportunity cost of money because it prices monetary substitutes (bonds) rather than monetary services. Divisia aggregates, which weight each component by its real user cost, correctly capture substitution across asset types and so preserve stable long-run money-demand relationships throughout the full sample and every subsample examined.
Q9. What are the paper’s main scope conditions and limitations?
The analysis is confined to bivariate cointegrating relationships (one money measure against one opportunity-cost variable at a time); no multivariate cointegration is explored, and income elasticity is imposed as unity rather than estimated. Other noted limitations: double-log user-cost coefficients are more sensitive to the choice of Johansen trend specification than the corresponding semi-log coefficients; Divisia M4 is not examined in the pre-/post-1980 split because its broadest components’ user costs are partly driven by the T-bill yield itself, complicating interpretation; and the institutional-money-market component’s cointegration with its own user cost is comparatively weak, holding under only one of the four Johansen criteria. Results are reported as qualitatively robust to using CPI instead of the PCE price index and real GDP instead of real personal income as the scale variable.
Key terms in this paper
Definitions below follow the paper's own usage.
- Divisia monetary aggregate
- a monetary aggregate that weights each component asset by its real user cost -- its expenditure share in providing monetary services -- rather than simply summing dollar amounts as simple-sum aggregates do; constructed by the Center for Financial Stability from January 1967 onward at multiple levels of coverage (DM2, DM3, DM4), and the paper's central object for demonstrating stable money demand.
- Real user cost (RUC)
- the opportunity cost of holding a specific monetary asset, reflecting its foregone yield relative to a benchmark rate of return; paired with each Divisia aggregate's own quantity in the paper's "own user cost" cointegration specifications, and the variable the authors argue retains informational content that the T-bill yield lost after 1980 and again after the GFC.
- Simple-sum aggregate
- a monetary aggregate (e.g., M2, M3) that sums the dollar value of its component assets with equal weight, treating a dollar of currency and a dollar of a large time deposit as perfectly substitutable units of money; the paper's simple-sum M3 series is reconstructed by the authors from CFS component data since the Federal Reserve no longer publishes it.
- Johansen cointegration / VECM
- the maximum-likelihood test (Johansen 1991, 1995) for a stationary long-run equilibrium relationship between two nonstationary series, estimated here as a bivariate vector error-correction model relating log real money balances scaled by nominal income to an opportunity-cost variable, under semi-log and double-log functional forms and across four alternative deterministic-trend specifications.
- Structural break (Andrews-Ploberger / Bai-Perron)
- tests for whether the parameters of a money-demand relationship -- its quantity, its user cost, or the VECM residuals -- shift at an unknown date; used in this paper to date the 1980 break associated with DIDMCA deregulation (found at 1979:M10 for Divisia M2 and 1980:M2 for Divisia M3).