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

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)

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:

1. A gradual (and correctly-signed) price level response consistent with New Keynesian sticky-price predictions.
2. Theory-consistent real output responses across PCE, CPI, core price measures, and three alternative output indicators.
3. 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.
4. 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:

1. 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.
2. 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.
3. 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.
4. 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:

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

Related Work

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}
}