A Granular Investigation on the Stability of Money Demand

The Instability of U.S. Money Demand After 1980 Is a Measurement Artifact

TL;DR: The post-1980 breakdown of U.S. money demand functions is not evidence that households changed their preferences for monetary assets — it is evidence that simple-sum aggregation stopped tracking monetary services once interest-bearing deposits mattered. Chen and Valcarcel (2024, Macroeconomic Dynamics) show that Divisia monetary aggregates paired with their own user costs deliver a stable cointegrating money demand function across both the 1980 DIDMCA deregulation break and the post-2008 zero-lower-bound period. The T-bill yield, by contrast, loses all information content after 2008. At the asset level, 29 of 40 granular tests show correct-sign cointegration between individual monetary components and their own user costs.

Key Concepts

Measurement-not-preference verdict

The paper’s bottom-line conclusion: post-1980 money demand instability comes from how money is measured, not from households’ changing preferences over monetary assets. Chen and Valcarcel (2024) .

User-cost sufficiency for money demand

The finding that Divisia real user costs, but not the T-bill yield, maintain cointegration with monetary aggregates through the 1980 deregulation and post-GFC zero-lower-bound periods. Chen and Valcarcel (2024) .

Granular money-demand cointegration

Bilateral cointegration between each disaggregated monetary asset (currency, demand deposits, savings, repos, CP, etc.) and its own CFS user cost. The paper is the first to run this exercise historically. Chen and Valcarcel (2024) .

Q1. Why is the U.S. money demand function unstable after 1980?

The instability is a measurement artifact of simple-sum aggregation, not a change in households’ preferences for monetary assets. Simple-sum M2 and M3 treat interest-bearing deposits as perfect substitutes for non-interest-bearing currency, which breaks down after the 1980 Depository Institutions Deregulation and Monetary Control Act legalized interest on checkable accounts.

The instability itself is well-documented. Friedman and Kuttner (1992) show that postwar time-series relationships between money and nominal income weaken sharply when the sample extends into the 1980s , and Ball (2001) rejects a stable long-run M1 demand once the sample extends to 1996 . Choi and Jung (2009) locate two structural breaks in 1959-2000 simple-sum data . The standard explanation has been financial innovation inducing preference change.

Chen and Valcarcel (2024) show the instability is instead about measurement . Using CFS Divisia M2 and M3 with Barnett (1980) aggregation — which weights monetary assets by their expenditure shares via user costs — the cointegrating relationship between money and output survives straddling 1980. Andrews-Ploberger and Bai-Perron structural break tests locate the break in Divisia balances around 1980:Q2, consistent with DIDMCA’s institutional timing, but the relationship itself reconstitutes in the post-1980 subsample when user costs are used as the opportunity cost.

This is the measurement-not-preference verdict: the 1980 break shows up because simple-sum aggregation stops tracking monetary services once interest-bearing deposits matter; it does not show up in properly aggregated money.

Four Measurement Combinations for U.S. Money Demand

Q2. Does Divisia money demand remain stable across the 1980 DIDMCA break?

Yes — the cointegration between Divisia M2 (or M3) and its own user cost holds in both the pre-1980:Q2 and post-1980:Q2 subsamples, across all four Johansen (1995) deterministic-trend specifications. Simple-sum aggregates do not pass this subsample test.

The pre-1980 result is not itself surprising. Belongia (1996) established that replacing simple-sum with Divisia indexes reverses the qualitative conclusions of several influential money studies , and Serletis and Gogas (2014) found cointegration between Divisia aggregates and the T-bill yield in a Johansen (1991) framework . Belongia and Ireland (2019) estimate a stable Divisia M2 and MZM demand over 1967-2019 .

Chen and Valcarcel (2024) extend this by explicitly straddling the 1980:Q2 DIDMCA break and testing across all four Johansen (1995) deterministic-trend specifications — restricted constant, unrestricted constant, restricted trend, unrestricted trend. Key results:

• Divisia M2 with user cost of M2: significant cointegration, correct-sign coefficient, all four specifications, both subsamples.
• Divisia M3 with user cost of M3: significant cointegration under three of four specifications post-1980.
• Simple-sum M2 with user cost of M2: loses cointegration in three of four specifications post-1980.
• Simple-sum M3 with user cost of M3: never cointegrates post-1980.

The sharper-than-usual contrast with simple-sum comes from testing multiple Johansen specifications rather than picking one. This is the user-cost sufficiency for money demand result, part one.

Q3. Does the T-bill yield cointegrate with monetary aggregates after the Great Financial Crisis?

No — the three-month T-bill yield loses cointegration with Divisia M3 and Divisia M4 in the post-2008:Q3 subsample, because the yield was pinned near zero for roughly seven years. Divisia user costs do not suffer this information loss because user costs, while compressed, remained well above zero throughout.

Anderson, Bordo, and Duca (2017) document the Great Recession as a major stress test for M2 velocity models , and Lucas and Nicolini (2015) argue that adding money-market deposit accounts to M1 restores stability of the money-interest-rate relationship through the zero-lower-bound period . Mattson and Valcarcel (2016) show Divisia M4 user costs compressed but stayed positive after 2008, while the federal funds rate collapsed .

Chen and Valcarcel (2024) split the sample at 2008:Q3 and test cointegration for Divisia M3 and Divisia M4 . Results:

• Pre-GFC sample (1967:Q1-2008:Q3): Divisia M3 and Divisia M4 cointegrate with the T-bill yield under all Johansen specifications, with correct sign.
• Post-GFC sample (2008:Q4-2020:Q1): neither Divisia M3 nor Divisia M4 cointegrates with the T-bill yield under any specification.
• Post-GFC sample, using the user cost of Divisia M3/M4 instead: cointegration holds under all specifications, with correct sign, and the magnitude of the elasticity is higher than pre-GFC.

The T-bill breakdown is not about the monetary aggregates — it is about the interest rate losing signal when pinned at the effective lower bound. This is the user-cost sufficiency for money demand result, part two.

Q4. Are Divisia user costs better than the T-bill yield as the opportunity cost of holding money?

Yes — on both theoretical and statistical grounds. The user cost is the spread between a benchmark asset’s yield and the asset’s own interest return, which is the textbook opportunity cost of holding a monetary asset. The T-bill yield is the price of a monetary substitute, not of money itself. Statistically, Divisia user costs maintain cointegration through the 1980 and 2008 breaks; the T-bill yield does not.

The theoretical case traces to Barnett (1978), who derived the user cost for each monetary asset under aggregation theory , and Barnett (1980) formalized Divisia monetary aggregation . The statistical case builds on Belongia and Ireland (2014), who argue the Barnett critique — that inconsistent aggregation distorts inference — remains as relevant as when first articulated , and on Belongia and Ireland (2019), who develop a money-in-the-utility model with interest-bearing deposits that predicts a stable Divisia demand function .

Chen and Valcarcel (2024) make the direct statistical comparison . Divisia M2 and Divisia M3 cointegrate with their own user costs under all Johansen (1995) specifications in the full sample and across subsamples straddling 1980 and 2008. The same aggregates cointegrate less reliably with the T-bill yield, and not at all in the post-2008 subsample. Simple-sum M2 and M3 fail both tests.

One more practical point: unit-root tests are consistent with Divisia user costs being level-stationary around a deterministic trend, while the T-bill yield is not level-stationary under any of the DF-GLS specifications. This is consistent with Belongia and Ireland’s (2019) observation of low-frequency stochastic trends in user costs that are swamped by transitory volatility in market rates .

Q5. Which individual monetary assets cointegrate with their own user costs?

Currency, demand deposits, savings deposits, small time deposits, large time deposits, overnight and term repos, institutional money market funds, and the aggregate of commercial paper plus T-bill balances all cointegrate with their own CFS user costs in at least two of four Johansen (1995) specifications, with the correct sign. Only the less-established innovations — other checkable deposits and retail money market funds — show weak or no cointegration. This is the granular money-demand cointegration finding.

CFS provides user costs for each monetary asset separately following Barnett, Liu, Mattson, and van den Noort (2013) . This makes it possible, in principle, to run cointegration tests on each (asset quantity, asset user cost) pair — but to the paper’s knowledge, this had not been done historically before Chen and Valcarcel (2024) .

Numbers from the paper (double-log specification, full sample):

• Of 40 estimates (10 asset pairs x 4 Johansen specifications), 29 show the expected negative user-cost elasticity of demand with the correct sign.
• Nine specifications fail to find cointegration.
• Only two show an inverted sign (both trend specifications for small time deposits).

By contrast, when the same asset quantities are paired with the T-bill yield (semi-log specification), most pairs fail to cointegrate, and those that do often show the wrong sign. For example, savings deposits and repos cointegrate with the T-bill yield but with positive coefficients — inconsistent with a money demand interpretation.

The asset-level result buttresses the aggregate finding: information content for money demand runs through the price duals, not through a generic short rate. Newer assets that emerged as a direct consequence of 1980s deregulation (OCDs, retail money-market funds) are the ones whose demand is hardest to pin down historically — consistent with the structural-break timing.

Q6. Should I use semi-log or double-log money demand specification for Divisia aggregates?

Use the semi-log form (interest rate in levels) for the full sample and the pre-GFC sample. Use the double-log form (log interest rate) when the sample includes the post-2008 zero-lower-bound period, because log transformations accommodate the nonlinearity induced by near-zero rates better than semi-log.

The two canonical functional forms are the Cagan (1956) semi-log form and the Meltzer (1963) double-log form . Bae, Kakkar, and Ogaki (2006) argue the double-log form better accommodates the liquidity-trap region , and Hendrickson (2014) re-evaluates money demand with Divisia across both forms .

Chen and Valcarcel (2024) use both forms . In the full sample, the semi-log form delivers strong cointegration between Divisia M2/M3 and their user costs across all Johansen specifications, with the elasticity estimates stable around 6.5-10 (semi-elasticities). The double-log form also works well and tends to be slightly more robust to the choice of Johansen deterministic-trend assumption.

For samples straddling the GFC, the double-log form is the better default. The paper estimates Divisia M3/M4 demand as a function of the log of their user costs from 2008:Q4 to 2020:Q1 and finds significant cointegration with correct sign for all Johansen specifications; the semi-log form with the T-bill yield fails in the same sample.

Q7. Is money demand instability evidence of a structural change in preferences?

No. The evidence is more consistent with the “measurement-not-preference” reading: once the proper aggregation (Divisia) and the proper opportunity cost (asset-specific user cost) are used, the long-run demand for money is stable across the 1980 DIDMCA deregulation and the post-2008 zero-lower-bound period.

The preference-change story dates to Friedman and Kuttner (1992) and Bernanke and Blinder (1992) , whose finding that simple-sum money aggregates lose their link to nominal income after 1980 drove much of macroeconomics toward pure interest-rate frameworks. Many subsequent papers interpreted the post-1980 breakdown as evidence that financial innovation had changed how households allocate monetary balances — an implied preference shift.

The measurement reading has accumulated support. Belongia (1996) reversed several prominent null results by substituting Divisia for simple-sum . Lucas and Nicolini (2015) restored stability by adding MMDAs to M1 , pointing to the 1982 Regulation Q weakening as the source of the apparent break. Barnett, Ghosh, and Adil (2022) find stable demand for broad Divisia money across multiple countries . Jadidzadeh and Serletis (2019) reject simple-sum aggregation assumptions using a disaggregated demand system .

Chen and Valcarcel (2024) make the cleanest version of this case by running the subsample test on both the aggregate index and its components, both before and after 1980, using both the T-bill yield and the Divisia user cost, across all Johansen (1995) specifications. The result: simple-sum breaks, Divisia does not; T-bill breaks after 2008, user costs do not. 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.” That is the measurement-not-preference verdict.

Q8. How do I run a Johansen cointegration test of Divisia money demand on my own data?

Six steps in any econometrics package (R, Stata, EViews, Python with statsmodels). Chen and Valcarcel (2024) follow the Johansen (1995) framework — the practical recipe:

1. Pull quarterly (or monthly) data on real money balances, real income, and the relevant opportunity cost. For Divisia, use the matching CFS aggregate and its own real user cost (not the T-bill yield).
2. Take logs of money and income. Try both the semi-log form (user cost in levels) and the double-log form (log user cost).
3. Run unit-root tests (ADF, DF-GLS) on each series. Most monetary aggregates and real income are I(1); user costs typically test as level-stationary, while T-bill yields fail unit-root tests post-2008.
4. Select VAR lag length via AIC/BIC/HQIC on the levels system.
5. Estimate the Johansen VECM under all four deterministic-trend specifications: restricted constant, unrestricted constant, restricted trend, unrestricted trend. A result holding across all four is robust; a result conditional on one is fragile.
6. Test cointegration rank with trace and maximum-eigenvalue tests. Confirm the sign on the user-cost coefficient is negative.

Subsample test for structural breaks: Re-run the entire procedure on pre-1980Q2 and post-1980Q2 samples for the DIDMCA break, and pre-2008Q3 vs. post-2008Q3 for the ELB break. Cointegration that survives both subsample splits is what supports the measurement-not-preference verdict .

Related questions: Should I use semi-log or double-log? · Where do I get the matching Divisia user costs?

Q9. Where do I download CFS Divisia aggregates, user costs, and component-level series?

All from the Center for Financial Stability’s AMFM page at centerforfinancialstability.org/amfm_data.php , updated monthly. CFS publishes Divisia M1, M2, M3, M4-, and M4 aggregates, each accompanied by its corresponding real user cost — the opportunity cost variable Chen and Valcarcel (2024) show is the correct partner for cointegration tests.

What to download:

• Divisia monetary services indexes (DMSI): monthly levels of DM1, DM2, DM3, DM4-, DM4. Use logs for cointegration work.
• Real user costs (DMSI_UC): the matching real user cost for each aggregate. Use levels for semi-log specifications, logs for double-log.
• Component-level data: 15 monetary asset series (currency, demand deposits, OCDs, savings, retail and institutional MMFs, small and large time deposits, repos, CP, T-bills) each with its own user cost. These are what the granular money-demand cointegration tests use.

Companion U.S. macro data — real personal income, PCE price index, three-month T-bill yield — are from FRED . CFS Divisia goes back to January 1967, matching the Belongia and Ireland (2019) sample . Barnett, Liu, Mattson, and van den Noort (2013) document the user-cost construction , and Mattson and Valcarcel (2016) show user costs stayed positive through 2008–2015 while the federal funds rate collapsed — exactly the reason user costs work where the T-bill fails.

Related questions: What user cost do I use for Divisia M4? · How are user costs constructed?

Q10. Do the Divisia money demand stability results hold for other countries?

Yes — Divisia demand stability has been documented for the UK, Eurozone, Japan, Canada, and several emerging markets, and the qualitative finding generalizes: simple-sum aggregates break with financial deregulation, Divisia aggregates do not. The portability of this result is strong support for the measurement-not-preference verdict in Chen and Valcarcel (2024) — if the U.S. instability were preference-driven, similar institutional features should not produce the same Divisia-versus-simple-sum gap elsewhere.

Cross-country evidence:

• U.K.: Belongia and Ireland’s (2014) New Keynesian formalization uses U.K. data alongside the U.S., and CFS-style Divisia for the U.K. shows stable demand patterns.
• Multi-country: Barnett, Ghosh, and Adil (2022) document stable demand for broad Divisia money across multiple countries , reinforcing the pattern.
• Mexico: Colunga-Ramos and Valcarcel (2024) construct Mexican Divisia M4 and show monetary identification works ; a follow-on money-demand cointegration paper is the natural extension.

For researchers in countries without an official Divisia series, the Barnett (1980) construction is well-documented. The required inputs — component quantities and a benchmark yield — are typically in national monetary statistics.

Related questions: How is Divisia constructed for countries without an official series? · Does the post-2008 user-cost-sufficiency result hold abroad?

Q11. What does a stable Divisia money demand imply for monetary policy frameworks like NGDP targeting or money-growth rules?

It removes the strongest empirical objection to money-quantity-based policy frameworks. The standard case against rules like Friedman’s k-percent rule or NGDP targeting has been that “money demand is unstable” — making any money-quantity target a moving target. Chen and Valcarcel (2024) show this objection rests on simple-sum aggregation and on using the T-bill yield as the opportunity cost ; with Divisia aggregates and matching user costs, the long-run demand relationship is stable across the 1980 DIDMCA break and the post-2008 ELB.

Implications for policy design:

1. Money-growth rules become operational again. Belongia and Ireland’s (2022) theoretical case for a money-growth rule responding gradually to inflation and output requires a stable demand function as a precondition; the stability is now empirically supported.
2. NGDP targeting becomes more credible. If real money demand is stable, then nominal NGDP can be controlled via a Divisia M4 instrument with predictable elasticity, even at the ELB.
3. Operational policy monitoring. For central banks not formally adopting a money-quantity rule, Divisia M4 growth alongside the policy rate provides a robust real-time measure of monetary stance, particularly through ELB periods where the rate alone loses content.

The point is not that money-growth rules are necessarily optimal — that depends on the loss function, transmission lags, and exogenous shocks — but that the empirical precondition for considering them is now met.

Related questions: What does a money-growth policy rule look like operationally? · How does Divisia M4 perform through the ELB?

Data and Code

The CFS Divisia monetary aggregates and their real user costs used in Chen and Valcarcel (2024) are from the Center for Financial Stability’s AMFM program . Other series — PCE price index, real personal income, three-month Treasury yield — are from FRED . Sample period: January 1967 - March 2020, monthly.

Replication files are available on request. Contact: zhengyang.chen@uni.edu .

Citation

Chen, Zhengyang, and Victor J. Valcarcel. 2024. “A Granular Investigation on the Stability of Money Demand.” Macroeconomic Dynamics. https://doi.org/10.1017/S1365100524000427

@article{chenvalcarcel2024granular,
  title={A Granular Investigation on the Stability of Money Demand},
  author={Chen, Zhengyang and Valcarcel, Victor J.},
  journal={Macroeconomic Dynamics},
  year={2024},
  publisher={Cambridge University Press},
  doi={10.1017/S1365100524000427}
}