Barnett Critique | Robin Chen

Q: Does Divisia money demand remain stable across the 1980 DIDMCA break?

Yes. Chen and Valcarcel (2024) show 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 M2 loses cointegration with the user cost in three of four Johansen specifications post-1980; simple-sum M3 never cointegrates post-1980. This aligns with Belongia and Ireland (2019), who estimate a stable Divisia M2 and MZM demand over 1967-2019.

Q: Does the T-bill yield cointegrate with monetary aggregates after the Great Financial Crisis?

No. Chen and Valcarcel (2024) show the three-month T-bill yield loses cointegration with Divisia M3 and Divisia M4 in the post-2008:Q3 subsample under all Johansen specifications. The yield was pinned near zero for roughly seven years. The user costs of Divisia M3 and M4, which compressed but stayed well above zero (Mattson and Valcarcel 2016), continue to cointegrate with their respective aggregates post-GFC under all specifications, with the correct sign and larger elasticity estimates than in the pre-GFC subsample.

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

Yes. On theoretical grounds, the user cost derived by Barnett (1978) is the textbook opportunity cost of each monetary asset; the T-bill yield is the price of a substitute. On statistical grounds, Chen and Valcarcel (2024) show Divisia user costs maintain cointegration with Divisia M2 and M3 across the 1980 and 2008 structural breaks, while the T-bill yield does not. DF-GLS unit-root tests also indicate Divisia user costs are level-stationary around a deterministic trend while the T-bill yield is not. This is the user-cost sufficiency for money demand result.

Q: Which individual monetary assets cointegrate with their own user costs?

Currency, demand deposits, savings deposits, small and large time deposits, repurchase agreements, institutional money-market funds, and the aggregate of commercial paper plus T-bills all cointegrate with their own CFS user costs in at least two of four Johansen specifications, with the correct sign. Chen and Valcarcel (2024) report that of 40 estimates (10 asset pairs x 4 Johansen specifications) using the double-log form, 29 show the expected negative user-cost elasticity with the correct sign. The CFS user-cost data for individual components comes from Barnett, Liu, Mattson, and van den Noort (2013). This is the granular money-demand cointegration result.

Q: Should I use semi-log or double-log money demand specification for Divisia aggregates?

Use the Cagan (1956) semi-log form for the full sample and the pre-GFC sample. Use the Meltzer (1963) double-log form when the sample includes the post-2008 zero-lower-bound period, since Bae, Kakkar, and Ogaki (2006) show it better accommodates the liquidity-trap region. Chen and Valcarcel (2024) find Divisia M2/M3 demand cointegrates under both forms in the full sample; the double-log form is preferred for samples that include the ZLB.

Q: Is money demand instability evidence of a structural change in preferences?

No. Chen and Valcarcel (2024) 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 preference-change reading, implicit in Friedman and Kuttner (1992), is undermined once proper aggregation and proper opportunity costs are used. This reading is reinforced by Belongia (1996), Lucas and Nicolini (2015), Barnett, Ghosh, and Adil (2022), and Jadidzadeh and Serletis (2019).

A Granular Investigation on the Stability of Money Demand

Mon, 30 Sep 2024 00:00:00 +0000

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

Dimension	Simple-sum + T-bill	Simple-sum + user cost	Divisia + T-bill	Divisia + user cost
Theoretical coherence	Weak. Equal weights on heterogeneous assets; T-bill is the price of a substitute, not of money.	Weak on quantities; coherent on price.	Coherent on quantities; weak on price.	Fully coherent. Barnett (1980) aggregation paired with Barnett (1978) user cost.
Full-sample cointegration (M2)	Fails in both functional forms.	Intermittent — cointegrates under some Johansen specs, not others.	Robust. Cointegrates under all four Johansen (1995) specifications.	Robust. Cointegrates under all four specifications, correct sign, both semi-log and double-log.
Post-1980 subsample (M2)	Fails in semi-log form. Wrong sign in some trend specs.	Fails in 3 of 4 Johansen specifications.	Cointegrates under constant specs only; wrong sign under trend specs.	Robust across all specs, correct sign.
Post-GFC subsample (M3, M4)	Not applicable — simple-sum abandoned for this era.	Not applicable.	Fails under all specs (T-bill stuck near zero).	Robust across all specs, with higher elasticity estimates than pre-GFC.
Asset-level (granular) cointegration	Most components fail or show wrong sign with T-bill.	Not the paper’s focus.	Most components fail or show wrong sign.	29 of 40 specifications show correct sign (Chen & Valcarcel 2024 ).
What it takes as the break event	Money demand itself breaks in 1980.	Break arises from quantity side.	Break arises from price side (T-bill loses information post-1980 and post-2008).	No break — measurement-not-preference verdict. Apparent instability is an aggregation/measurement artifact.
Named concept	—	—	—	User-cost sufficiency for money demand · Granular money-demand cointegration (Chen & Valcarcel 2024 )

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.

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}
}

Monetary Transmission in Money Markets: The Not-So-Elusive Missing Piece of the Puzzle

Wed, 11 Aug 2021 00:00:00 +0000

In a Modern U.S. Sample, the Federal Funds Rate Is No Longer a Reliable Monetary Policy Indicator — but a Broad Divisia Monetary Aggregate Is

TL;DR: The price puzzle — contractionary monetary policy raising prices in VAR models — has resisted every standard fix in post-1988 U.S. data. Chen and Valcarcel (2021, Journal of Economic Dynamics and Control) show that swapping the Wu-Xia shadow rate for Divisia M4 resolves the puzzle without any ad hoc fixes, and reveals a post-2008 flight-to-safety pattern in which less-liquid money markets respond more strongly than currency and demand deposits. The problem was never the omitted information — it was the indicator itself.

Key Concepts

Modern-sample price puzzle: The post-1988 incarnation of the price puzzle that, unlike the historical version, is not resolved by the Christiano-Eichenbaum-Evans remedies (commodity prices, fed funds futures, forward rates). Coined by Chen and Valcarcel (2021) .
Divisia-sufficiency: The result that, in a modern-sample VAR, replacing the short-term rate with a Divisia monetary aggregate is by itself sufficient to restore theory-consistent responses of prices and output, even without commodity prices or futures data. Chen and Valcarcel (2021) .
Post-crisis flight-to-safety transmission: The finding that post-2008, less-liquid assets (IMMFs, large time deposits, repos, commercial paper, T-bills) respond with larger magnitudes than currency and demand deposits to an expansionary Divisia M4 shock — the opposite of the contractionary, liquidity-preserving pattern produced by shadow-rate shocks. Chen and Valcarcel (2021) .

Q1. Why does the U.S. price puzzle persist in modern-sample VARs even with commodity prices and futures data?

The price puzzle persists in post-1988 U.S. data because the federal funds rate — conventionally augmented with commodity prices, fed funds futures, or forward rates — has lost much of its identifying power for monetary policy shocks in an environment of heightened Fed transparency, forward guidance, and a near-zero neutral rate. The problem is not the omitted information; it is the indicator itself.

Christiano, Eichenbaum and Evans established that including commodity prices in a recursive VAR eliminates the price puzzle in a sample spanning 1965-1995 , and Kuttner introduced the use of fed funds futures data to separate anticipated from unanticipated target changes . Brissimis and Magginas argued that augmenting VARs with forward-looking variables such as futures and forward rates resolves the puzzle . Bernanke, Boivin and Eliasz proposed factor-augmented VARs as a more comprehensive information-set fix .

Chen and Valcarcel (2021) show that every one of these fixes fails in a 1988-2020 sample . Across 23 iterations of the federal funds rate specification — combining real output measures (IP, CFNAI, monthly RGDP), price levels (PCE, CPI, core variants), commodity prices (CRB, IMF), and federal funds futures or forward rates — price puzzles remain pervasive, both in time-varying-parameter VARs and in constant-parameter counterparts. This is the modern-sample price puzzle.

Consistent with this, Barakchian and Crowe find that monetary policy post-1988 became more forward-looking, invalidating the identifying assumptions in conventional methods , and Ramey’s Handbook synthesis confirms the preponderance of puzzles across post-1983 identification schemes .

Why the standard fixes fail: A neutral federal funds rate with enough room for material movement is a prerequisite for the short-rate indicator to work. The post-2008 effective-lower-bound period, combined with decades of increasingly transparent Fed communication and forward guidance, has squeezed the unanticipated component of federal funds rate movements toward zero — the thing SVARs need to identify a shock.

Three Approaches to Monetary Policy Indicator in a Modern U.S. Sample (1988-2020)

Dimension	Short Rate + Commodity Prices (CEE 1999)	Short Rate + Futures/Forward Rates (Brissimis-Magginas 2006)	Divisia M4 (Chen-Valcarcel 2021)
Core claim	Commodity prices proxy the Fed’s forward-looking information set and resolve the price puzzle.	Forward-looking variables (fed funds futures, forward rates) reflect market expectations of policy and resolve the price puzzle.	The short rate has lost identifying power in the modern sample; a Divisia monetary aggregate is the correct policy indicator.
Key references	Christiano, Eichenbaum & Evans (1999) , Bernanke, Boivin & Eliasz (2005)	Kuttner (2001) , Cochrane & Piazzesi (2002) , Brissimis & Magginas (2006) , Gertler & Karadi (2015)	Belongia (1996) , Belongia & Ireland (2014) , Keating, Kelly, Smith & Valcarcel (2019) , Chen & Valcarcel (2021)
Testable prediction	Including commodity prices eliminates the price puzzle across samples.	Including futures or forward rates eliminates the price puzzle.	Divisia M4 as the indicator eliminates the price puzzle without commodity prices or futures.
Empirical verdict in modern sample (1988-2020)	Fails. Price puzzle persists across 23 iterations of the federal funds rate specification with commodity prices .	Fails. Price puzzle remains even with 30-day fed funds futures, CRB or IMF commodity indices, or forward rates constructed from overnight repo spreads .	Succeeds. Divisia M4 resolves the puzzle across 23 specifications, including three-variable VARs with no commodity prices and no futures .
Policy transmission to money markets	Puzzlingly contractionary responses for currency, deposits, repos, CP, T-bills post-2008.	Same contractionary puzzles as commodity-prices specification; futures/forward rates do not rescue transmission.	Sensible expansionary responses; less-liquid assets respond more strongly than currency/DDs post-2008 (flight-to-safety).
Sample-period applicability	Works for historical samples (1960s-1990s); breaks down after 1988.	Works to varying degrees in historical samples; breaks down after 1988.	Designed for the modern sample; also works historically (Keating, Kelly, Smith & Valcarcel 2019 ).
Named concept	CEE identification / commodity-prices fix	Forward-looking-variables identification	Divisia-sufficiency · Modern-sample price puzzle · Post-crisis flight-to-safety transmission (Chen & Valcarcel 2021 )

Q2. Does replacing the federal funds rate with a Divisia monetary aggregate resolve the price puzzle in a modern sample?

Yes. Replacing the Wu-Xia shadow federal funds rate with Divisia M4 (or the narrower Divisia M2) produces sensible, theory-consistent price responses in every specification Chen and Valcarcel examine — including three-variable VARs that contain no commodity prices and no futures data. This is Divisia-sufficiency: the Divisia aggregate does the heavy lifting by itself.

The foundation for this result rests on the Barnett critique. Belongia demonstrated that replacing simple-sum aggregates with Divisia indexes reverses the qualitative inference of four out of five influential studies on the effects of money , and Belongia and Ireland formalized within a New Keynesian model that “measurement matters” — a Divisia quantity tracks the true monetary aggregate almost perfectly while simple-sum does not . Keating, Kelly, Smith and Valcarcel extended this to a VAR framework, showing Divisia M4 identification delivers plausible responses free of price, output, and liquidity puzzles in a historical sample .

Chen and Valcarcel (2021) extend the Divisia result to the post-1988 modern sample . Across three-variable TVP-VARs and larger TVP-FAVARs, specifications with DM4 or DM2 as the indicator yield:

A gradual (and correctly-signed) price level response consistent with New Keynesian sticky-price predictions.
Theory-consistent real output responses across PCE, CPI, core price measures, and three alternative output indicators.
Resolution that holds even when commodity prices and federal funds futures are excluded from the VAR — unlike the Christiano-Eichenbaum-Evans recipe, Divisia does not require these crutches.
Quantitatively larger post-2008 price responses for DM4 than for DM2, consistent with DM4 capturing a wider array of the monetary shocks that eventually pass through to prices.

This aligns with Belongia and Ireland’s finding of a stable Divisia money demand relationship in the modern sample , which is the microfounded underpinning for why a Divisia aggregate can serve as a policy indicator.

Q3. How does the transmission of monetary policy to money markets differ between the federal funds rate and Divisia M4 after 2008?

After 2008, expansionary federal funds rate shocks generate puzzlingly contractionary money-market responses — balances in currency, demand deposits, savings, repos, commercial paper, and T-bills all fall. Expansionary Divisia M4 shocks, by contrast, produce sensible expansionary responses, and the less-liquid assets (IMMFs, large time deposits, repos, CP, T-bills) respond with larger magnitudes than the highly liquid ones. Chen and Valcarcel call this post-crisis flight-to-safety transmission.

The standard VAR approach places money below interest rates and output. Bernanke, Boivin and Eliasz’s FAVAR treatment orders the rate indicator last and restricts monetary assets not to respond within the period , while Keating, Kelly, Smith and Valcarcel instead order the indicator before the monetary block, allowing money markets to respond freely to policy . Chen and Valcarcel adopt the latter block-recursive approach, letting 14 different deposits and money-market instruments respond unrestricted.

The results are stark . Under the Wu-Xia shadow federal funds rate:

Currency, demand deposits, and OCDs respond negatively to an expansionary shock, particularly after 2008.
Savings at banks and thrifts — counterintuitively — also contract.
IMMFs, repos, and T-bills show large negative responses post-crisis, which is the opposite sign from theory.

Under Divisia M4, the same specifications yield:

Sensible positive responses for currency and demand deposits.
Larger positive responses for savings at banks and thrifts (consistent with higher household personal saving after 2008).
Even larger positive responses for less-liquid assets — IMMFs, LTDs, repos, CP, T-bills — commensurate with savings rather than with currency.

The post-2008 magnitude pattern across asset classes is consistent with a flight-to-safety channel: households moved into savings, firms moved into less-liquid but safer instruments (time deposits, repos against Treasury collateral), and the Fed’s large-scale asset purchases mechanically expanded Treasury holdings in the monetary aggregate.

Q4. Can commodity prices or federal funds futures rescue the short-rate specification in a modern sample?

No. Commodity prices (both CRB and IMF indices), the 30-day federal funds futures rate, and the Brissimis-Magginas overnight-repo-spread forward rate all fail to resolve the modern-sample price puzzle when the Wu-Xia shadow federal funds rate is the indicator. The puzzle-fix-fails-in-modern-data pattern holds across 23 specifications.

Christiano, Eichenbaum and Evans concluded that including commodity prices was needed to resolve the puzzle in a 1965-1995 sample , and Cochrane and Piazzesi argued that high-frequency identification from daily target-change surprises avoids the omitted-variable problem of monthly VARs . Brissimis and Magginas advocated specifically for federal funds futures or forward rates in a recursive VAR , while Gertler and Karadi popularized the use of high-frequency surprises as external instruments in proxy SVARs .

Chen and Valcarcel test all of these within a common TVP-FAVAR framework and find the price puzzle remains . The envelope of impulse responses across 23 different federal funds rate specifications — crossing three output measures, four price indices, two commodity indices, and futures/forward rate variants — shows a generally pervasive price puzzle throughout the 1988-2020 sample, with no specification consistently escaping it. This matches the Barakchian-Crowe finding that a forward-looking Fed invalidates post-1988 identifying assumptions and Ramey’s broader synthesis .

The takeaway for practitioners: If your sample begins in the late 1980s or later and you must use a short-term rate, expect puzzles. If you use Divisia M4 instead, the puzzles disappear even without commodity prices or futures.

Q5. Should I use the Wu-Xia shadow federal funds rate to identify monetary policy shocks in a post-2008 sample?

Use it with caution. The Wu-Xia shadow rate extends the federal funds series through the effective-lower-bound period, but it generates persistent price puzzles in modern-sample VARs and the resulting shocks transmit implausibly through money markets. Its sensitivity to minor modeling choices adds further reason for caution.

Wu and Xia proposed the shadow rate to summarize the macroeconomic stance of policy during the effective-lower-bound period , and it has been widely adopted. Krippner, however, demonstrates that shadow short-rate estimates are sensitive to minor estimation choices, and those sensitivities propagate into wide variations in inferred UMP effects . Keating, Kelly, Smith and Valcarcel earlier showed that incidences of the price puzzle are exacerbated in SVARs that include various shadow interest rates for a modern sample .

Chen and Valcarcel (2021) find the shadow rate produces puzzling price responses across 23 specifications spanning 1988-2020, with the puzzle emerging as early as three months post-shock and persisting at 60-month horizons . The responses for slices at December 2008, November 2010, and September 2012 — the starts of QE1, QE2, and QE3 — all show price puzzles for the Wu-Xia specification while the DM4 and DM2 specifications at the same dates show theory-consistent, quantitatively large price responses.

Practical guidance for a modern-sample VAR:

If you need a rate indicator, document the puzzle and treat the effective lower bound period as a structural break rather than a continuous series.
Consider Divisia M4 as the policy indicator. The “post-1984” Great Moderation break in macro dynamics and the Monetary Control Act of 1980 are good reasons to begin samples in the late 1980s, where Divisia performs well.
If you need an external instrument, Arias, Caldara and Rubio-Ramírez’s agnostic sign-restriction identification of the systematic component offers an alternative to high-frequency surprise methods.
For event studies around quantitative tightening or balance-sheet normalization, Smith and Valcarcel demonstrate that short-rate indicators miss first-order financial-market effects that become visible through careful daily-frequency analysis .

Q6. What is the Divisia monetary aggregate and why does it matter for monetary policy identification?

Divisia monetary aggregates, developed by William Barnett, weight each component of the money stock by its user cost — recognizing that currency, demand deposits, savings, money-market funds, and T-bills provide different flows of liquidity services and have different opportunity costs. Simple-sum aggregates (M1, M2) treat all components as perfect substitutes, which is both theoretically wrong and empirically disabling.

The theoretical case is the Barnett critique: simple-sum aggregates violate aggregation theory by adding assets that are not perfect substitutes. Belongia showed empirically that replacing simple-sum with Divisia reverses the qualitative inference of four of five influential monetary studies . Belongia and Ireland formalized the Barnett critique inside a New Keynesian model, demonstrating that a Divisia quantity tracks the theoretically correct monetary services aggregate almost perfectly while simple-sum does not . They later showed that interest rates and Divisia money jointly provide the best measurement of monetary policy stance .

Belongia and Ireland also document a stable cointegrating money demand function for Divisia M2 and MZM over 1967-2019 — including the financial innovations of the 1980s and the post-2008 period — which undermines the long-standing claim that money demand is inherently unstable .

Chen and Valcarcel (2021) operationalize these insights for modern-sample monetary policy identification. They use the Center for Financial Stability’s Divisia series at three levels of aggregation : Divisia M1 (currency, demand deposits, OCDs at banks and thrifts); Divisia M2 (DM1 + savings deposits, retail money-market funds, small time deposits); and Divisia M4 (DM2 + institutional money-market funds, large time deposits, repurchase agreements, commercial paper, and 3-month T-bills — 15 components total, the broadest U.S. monetary aggregate currently available).

Why Divisia M4 is the right choice for modern-sample VARs:

Its 15-component breadth captures the post-1980 financial ecosystem — repos, institutional money funds, commercial paper — that narrow aggregates miss.
It properly weights each component by user cost, respecting the Barnett critique.
In Chen-Valcarcel’s block-recursive identification, it generates theory-consistent responses without commodity prices or futures data.
It exhibits a stable cointegrating money demand relationship over the full modern period.

This paper connects to Chen’s broader research program on monetary policy identification. Chen (2026, Journal of Macroeconomics) extends the identification question to high-frequency monetary policy surprises, showing that the Fed responds primarily to financial conditions while adopting a “wait-and-see” stance on recent economic data. Chen (2025, Journal of Economic Dynamics and Control) examines forward-looking monetary policy rules and their implications for inflation expectations.

Data and Replication

All data and code for Chen and Valcarcel (2021) are available at robinchen.org . The paper uses:

Center for Financial Stability Divisia Monetary Aggregates (monthly, M1/M2/M4)
Wu-Xia shadow federal funds rate
14 money-market component series (currency, demand deposits, OCDs, savings, IMMFs, LTDs, repos, CP, T-bills, and more)
CRB and IMF commodity price indices
30-day federal funds futures rate

Citation

Chen, Zhengyang, and Victor J. Valcarcel. 2021. “Monetary Transmission in Money Markets: The Not-So-Elusive Missing Piece of the Puzzle.” Journal of Economic Dynamics and Control 131: 104214. https://doi.org/10.1016/j.jedc.2021.104214

@article{chenvalcarcel2021,
 title={Monetary Transmission in Money Markets: The Not-So-Elusive Missing Piece of the Puzzle},
 author={Chen, Zhengyang and Valcarcel, Victor J.},
 journal={Journal of Economic Dynamics and Control},
 volume={131},
 pages={104214},
 year={2021},
 publisher={Elsevier},
 doi={10.1016/j.jedc.2021.104214}
}

Barnett Critique | Robin Chen

A Granular Investigation on the Stability of Money Demand

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

Key Concepts

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

Four Measurement Combinations for U.S. Money Demand

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

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

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

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

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

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

Data and Code

Citation

Monetary Transmission in Money Markets: The Not-So-Elusive Missing Piece of the Puzzle

In a Modern U.S. Sample, the Federal Funds Rate Is No Longer a Reliable Monetary Policy Indicator — but a Broad Divisia Monetary Aggregate Is

Key Concepts

Q1. Why does the U.S. price puzzle persist in modern-sample VARs even with commodity prices and futures data?

Three Approaches to Monetary Policy Indicator in a Modern U.S. Sample (1988-2020)

Q2. Does replacing the federal funds rate with a Divisia monetary aggregate resolve the price puzzle in a modern sample?

Q3. How does the transmission of monetary policy to money markets differ between the federal funds rate and Divisia M4 after 2008?

Q4. Can commodity prices or federal funds futures rescue the short-rate specification in a modern sample?

Q5. Should I use the Wu-Xia shadow federal funds rate to identify monetary policy shocks in a post-2008 sample?

Q6. What is the Divisia monetary aggregate and why does it matter for monetary policy identification?

Related Work

Data and Replication

Citation