Does the conclusion that Divisia M4 outperforms the federal funds rate depend on sample, price index, or aggregate choice?

No. Chen and Valcarcel (2025) verify the result across three samples (1967–2020, 1988–2020, 2008–2020), two price indexes (CPI and PCE), and two Divisia aggregates (M2 and M4). The Wu-Xia shadow rate produces 72–99% output puzzles and 93–99% price puzzles across all 12 combinations; Divisia M4 produces 2–24% output puzzles and 2–7% price puzzles (with one ambiguous cell in the historical PCE sample where both indicators struggle). The pattern is consistent with Keating et al. (2019) on pre/post-GFC stability and with Chen and Valcarcel (2024) on the stability of Divisia money demand.

From Disruption to Integration: Cryptocurrency Prices, Financial Fluctuations, and Macroeconomy

Q: What drives cryptocurrency price shocks — sentiment, technology, or regulation?

Sentiment and technology — not regulation or monetary policy. Chen (2025) classifies 67 major crypto-market events 2014–2023 into six categories and finds only sentiment (coefficient 1.36, t = 3.15) and technology (coefficient 1.02, t = 2.06) significantly explain the identified structural crypto shocks. Regulatory, monetary, infrastructure, and network-effect shocks are statistically insignificant. The narrative identification follows Romer and Romer (2004) . Sentiment dominance validates Baker and Wurgler (2007) , while the significant technology coefficient shows crypto is not pure speculation. This partially contradicts regulation-focused studies including Borri and Shakhnov (2020) and Chokor and Alfieri (2021) .

Q: How does cryptocurrency transmit to the real economy?

Cryptocurrency shocks now transmit through a dual-channel: sentiment drives financial-market integration and technology drives real-economy effects. Chen (2025) documents that a one-standard-deviation positive Bitcoin price shock produces a sustained 1.2% rise in the S&P 500, a 2% rise in the CRB commodity index, a delayed 0.15% rise in industrial production, a persistent 0.02% decline in unemployment, and a 0.15% rise in the PCE price index over a 30-month horizon. The real-economy effects are quantitatively modest but theoretically grounded in investment-channel mechanics from Jermann and Quadrini (2012) and uncertainty-channel mechanics from Bloom (2009) .

Q: Why use Bayesian SVAR with Pandemic Priors for this question?

Use Pandemic Priors. Cascaldi-Garcia (2022) proposes extending the Minnesota prior with time dummies for the pandemic period, controlled by a hyperparameter φ. As φ → 0 pandemic observations are treated as exceptional; as φ → ∞ the setup reverts to conventional Minnesota priors. Chen (2025) selects φ = 0.1 by marginal-likelihood maximization over a grid from 0.001 to 500, using the dummy-observation implementation of Bańbura, Giannone, and Reichlin (2010) . Setting φ = 500 (Minnesota limit) materially changes real-economy impulse responses — less persistent unemployment declines, more contractionary DM4 — confirming Pandemic Priors are necessary for this sample.

Q: What does cryptocurrency's macro role mean for monetary policy?

Central banks should incorporate cryptocurrency developments in inflation forecasting. Chen (2025) shows crypto shocks explain 18% of long-horizon PCE price-level forecast-error variance and produce a persistent 0.15% rise in the price level — a signature of demand-driven inflation rather than transitory financial noise. The contribution rises from 3.6% at 6 months to 17.6% at 30 months, while S&P 500, CRB, and FSI shocks combined contribute 10.1% at 30 months. Divisia M4 shows a contractionary response but insufficient to offset the price effect, suggesting monetary policy has been accommodative to crypto-driven inflation.

Q: Does the integration result hold beyond Bitcoin?

The current paper covers Bitcoin only, motivated by its dominant market capitalization during 2015–2024 and the need for a sufficiently long monthly time series for structural VAR identification. Bitcoin's market dominance averaged 40–65% of total cryptocurrency market cap over the sample, making the results descriptive of the overall market as well. Whether smaller cryptocurrencies, stablecoins, or DeFi tokens exhibit similar transmission mechanisms is an open empirical question. Main findings are robust to alternative variable orderings, price-level measures (CPI vs. PCE), and financial-stress indicators, suggesting the core result is not a Bitcoin-specific artifact.

Q: Does the cryptocurrency-macro spillover result extend to altcoins, DeFi protocols, or stablecoins?

Likely yes for altcoins (top-10 by market cap), more nuanced for DeFi, and structurally different for stablecoins — but the empirical evidence is sparse and a natural extension of Chen (2025) . Altcoins typically comove strongly with Bitcoin in return space, so the spillover pattern should replicate at smaller magnitudes; a natural extension applies the BSVAR with Bitcoin replaced by Ethereum or a market-cap-weighted top-10 index. DeFi protocols introduce additional channels — total value locked, governance token dynamics, liquidation cascades — that a price-only SVAR misses; the right extension would add aggregate DeFi TVL and a measure of leverage in lending protocols. Stablecoins are structurally different: their price shocks are small (depegging events are large but rare), and the relevant shock is the supply of stablecoins — a large stablecoin issuance amounts to mechanical T-bill demand, making the right framework closer to a money-supply shock in traditional monetary economics than a risk-asset price shock. Cross-country adoption rates vary enormously, so the U.S. results in Chen (2025) likely overstate the macro effect in low-adoption economies and understate it in high-adoption ones.

Q: What does cryptocurrency's 18% inflation variance contribution imply for monetary policy and CBDC design?

For monetary policy: the result implies that cryptocurrency markets have moved to a quantitatively significant input into the inflation process, and central banks should monitor crypto-driven financial conditions alongside traditional credit and equity measures. Chen (2025) documents that positive Bitcoin price shocks generate persistent inflationary pressure (a 0.15% rise in PCE), operating through wealth and investment channels familiar from the Bernanke-Blinder (1992) monetary transmission framework. The 18% long-horizon inflation variance contribution grows from 3.6% at 6 months to 17.6% at 30 months, making it the largest single non-own driver of price-level variance in this sample. Concrete implications: include crypto-driven financial conditions in monetary policy dashboards; recognize crypto wealth effects in consumption forecasting; distinguish sentiment-driven from technology-driven crypto shocks, since Chen (2025) finds sentiment shocks dominate and produce the inflation spillover. For financial regulators: prudential rules for bank crypto exposure and stablecoin reserve requirements need to account for the documented spillover magnitudes. The design implications for CBDC, if explored, would require a separate empirical framework beyond the scope of this paper.

Tue, 01 Jul 2025 00:00:00 +0000

How Cryptocurrency Markets Now Drive Macroeconomic Outcomes

TL;DR: Cryptocurrency has crossed the threshold from isolated digital experiment to systemically important financial asset. Chen (2025, Journal of Risk and Financial Management) uses a Bayesian SVAR with Pandemic Priors to show that cryptocurrency price shocks explain 18% of equity, 27% of commodity, and 18% of long-horizon inflation variance over 2015–2024, with sentiment-driven shocks dominant and regulatory effects negligible. Real economic effects on industrial production and unemployment exist but are modest.

Key Concepts

Cryptocurrency-as-systematic-risk-factor: The empirical result that cryptocurrency now functions as a systematic source of variance in equity (17.7%) and commodity (27.2%) markets over 2015–2024, rather than a portfolio diversifier — evidence that cryptocurrency has crossed from isolated asset to systemically integrated risk factor. Chen (2025) .
Sentiment-dominant transmission: The finding that, across narrative-identified shock categories from 67 major crypto-market events (2014–2023), sentiment shocks (coefficient 1.36, t = 3.15) are the strongest driver of cryptocurrency price movements, with technology shocks second and regulatory shocks statistically insignificant. Chen (2025) .
Pandemic-prior cryptocurrency identification: The methodological adaptation of Cascaldi-Garcia (2022) Pandemic Priors — which extend the Minnesota prior with time dummies controlled by hyperparameter φ — to handle COVID-era extreme observations in a Bayesian SVAR identifying cryptocurrency macroeconomic transmission. Chen (2025) .

Three Views of Cryptocurrency’s Macroeconomic Role

Dimension	Diversifier view	Speculative-only view	Systematic-risk-factor view (Chen 2025)
Core claim	Crypto provides portfolio diversification due to low correlation with traditional assets.	Crypto is a speculative asset with no fundamental macroeconomic role.	Crypto has crossed into systemic importance with measurable spillovers to equity, commodity, and inflation variance.
Key references	Bouri et al. (2017) ; Charfeddine et al. (2020)	Early speculative-bubble literature	Chen (2025) , grounded in Baker & Wurgler (2007)
Empirical verdict	Diversification benefits weaken sharply during stress; crypto-equity comovements are positive, not negative, in 2015–2024.	Cannot explain the 17.7–27.2% equity/commodity variance contributions in modern data.	Supported. Variance decompositions show systemic transmission; narrative validation confirms sentiment and technology as drivers.
Policy implication	No special monetary or regulatory framework needed.	Monitor for fraud only; macroeconomic role irrelevant.	Central banks should monitor crypto for inflation pressure; financial regulators should treat it as a source of systemic risk.

Note: Diversifier view reflects pre-2018 literature. Chen (2025) covers January 2015 – November 2024.

Q1. Has cryptocurrency become a systematically important financial asset?

Yes. Chen (2025) finds that cryptocurrency price shocks explain 17.7% of S&P 500 forecast-error variance at 6 months and 27.2% of CRB commodity variance at 30 months — placing crypto alongside traditional macro shocks as a first-order driver of financial-market fluctuations.

This finding overturns the early-literature claim that cryptocurrency offers diversification benefits. Bouri et al. (2017) originally characterized Bitcoin as a hedge against global uncertainty, and Charfeddine, Benlagha, and Maouchi (2020) found weak, time-varying cross-correlations with conventional assets consistent with diversification. The 2015–2024 sample in Chen (2025) spans the institutional-adoption era — spot Bitcoin ETFs, corporate treasury holdings, derivatives integration — and yields the opposite conclusion: cryptocurrencies have become systematic risk amplifiers, aligned with the contagion-vs-interdependence distinction formalized by Forbes and Rigobon (2002) .

The empirical fingerprint is a drop in the Financial Stress Index on impact followed by recovery. This pattern — stress alleviates, not intensifies, with a positive crypto shock — is consistent with a risk-on channel operating through intermediary balance sheets, as described in Adrian and Shin (2010) and Brunnermeier and Pedersen (2009) . Crypto shocks also explain 5.7% rising to 8.2% of the Financial Stress Index variance, a modest but statistically meaningful share.

The scale of equity and commodity variance contributions (17.7% and 27.2%) is quantitatively comparable to the contributions of monetary policy and aggregate demand shocks in standard macro VARs, marking a structural break from the pre-2015 period when cryptocurrency had negligible macro spillovers.

Q2. What drives cryptocurrency price shocks — sentiment, technology, or regulation?

Sentiment dominates. Chen (2025) classifies 67 major crypto-market events from 2014–2023 into six categories and finds only sentiment shocks (coefficient 1.36, t = 3.15) and technology shocks (coefficient 1.02, t = 2.06) significantly explain the identified structural crypto-shock series. Regulatory, monetary, infrastructure, and network-effect shocks are all statistically insignificant.

The narrative identification follows Romer and Romer’s (2004) approach to monetary policy shocks, coding each event as +1 (favorable), −1 (unfavorable), or 0 (absent) in a given month. The six categories are: technology (protocol upgrades, hard forks, outages), sentiment (institutional adoption announcements, mainstream coverage, exchange collapses), regulatory (legal recognition, bans, enforcement), monetary (central bank moves affecting alternative-asset demand), infrastructure (exchange launches, custody solutions), and network effects (adoption milestones, integrations).

Sentiment dominance validates Baker and Wurgler’s (2007) investor-sentiment framework — retail-dominated asset markets exhibit amplified price movements beyond fundamentals. It partially contradicts papers like Borri and Shakhnov (2020) and Chokor and Alfieri (2021) that emphasize regulation as a primary driver: Chen (2025) finds regulatory event dummies are statistically insignificant after controlling for the full SVAR system.

The significant technology coefficient establishes that cryptocurrency is not a pure speculative bubble — protocol upgrades and technical improvements generate measurable economic value, consistent with Caporale, Gil-Alana, and Plastun (2018) , who documented persistence in the cryptocurrency market consistent with technology-based fundamentals.

Q3. How does cryptocurrency transmit to the real economy?

Through a dual channel: sentiment drives financial-market integration and technology drives real-economy effects. Chen (2025) documents that a one-standard-deviation positive Bitcoin price shock produces a sustained 1.2% rise in the S&P 500, a 2% rise in the CRB commodity index, a delayed 0.15% rise in industrial production, a persistent 0.02% decline in unemployment, and a 0.15% rise in the PCE price index over a 30-month horizon.

Two theoretical frames ground the financial-market response. Markowitz’s portfolio theory and Sharpe’s CAPM predict that assets with similar systematic risk exposures comove, which reframes cryptocurrency as an integrated risk asset rather than an isolated instrument. Behavioral extensions come from Baker and Wurgler’s (2007) investor-sentiment framework, where mood-driven trading creates systematic factors affecting all risky assets.

The real-economy transmission is quantitatively modest but theoretically well-grounded in investment-channel mechanics from Jermann and Quadrini (2012) and uncertainty-channel mechanics from Bloom (2009) , where asset-price volatility creates real-options effects on investment timing. The asymmetry between the large financial-market response (17.7–27.2% variance shares) and the modest real-economy response (6.2% industrial production, 3.8% unemployment at 30 months) reflects how each channel works: the financial-market response operates within days through correlated asset repricing and intermediary balance-sheet adjustments, while the real-economy response requires investment and hiring decisions with inherent multi-month lags.

Three empirical signatures distinguish the transmission mechanism:

Immediate: equity (+1.2%), commodities (+2%), financial stress drops on impact, then recovers.
Delayed but persistent: industrial production rises ~0.15% with a multi-month lag; unemployment falls ~0.02% persistently.
Cumulative inflation: the contribution of crypto shocks to price-level forecast-error variance grows from 3.6% at 6 months to 17.6% at 30 months — a signature of demand-side transmission, not transitory financial noise.

Q4. Why use Bayesian SVAR with Pandemic Priors for this question?

Standard VARs fail when the sample includes COVID-era extreme observations. Cascaldi-Garcia (2022) proposes extending the Minnesota prior with time dummies for the pandemic period, controlled by a hyperparameter φ that governs how much signal the model extracts from pandemic observations — as φ → 0 the pandemic period is treated as exceptional and its variance is absorbed by the dummies; as φ → ∞ the setup reverts to a conventional Minnesota prior.

Chen (2025) selects φ = 0.1 via marginal-likelihood maximization over a grid from 0.001 to 500, and shows that setting φ = 500 (the Minnesota-prior limit) produces materially different real-economy impulse responses — less persistent declines in unemployment and industrial production, more contractionary Divisia M4 movement. The data strongly favor the Pandemic Priors specification, confirming that how one handles COVID-19 observations affects the estimated transmission of cryptocurrency shocks to macroeconomic variables.

The monthly SVAR includes eight variables ordered recursively: PCE price index, unemployment rate, industrial production, Divisia M4, cryptocurrency price, S&P 500, CRB commodity index, and the St. Louis Fed Financial Stress Index. The prior follows the dummy-observation implementation from Bańbura, Giannone, and Reichlin (2010) , extended with Cascaldi-Garcia’s time-dummy block for the pandemic period. Overall tightness λ = 0.2; optimal φ selected by maximum marginal likelihood; impulse responses at 30-month horizon with 68% posterior probability bands.

Robustness checks confirm the main findings are stable under: alternative variable orderings (crypto ordered last produces virtually indistinguishable impulse responses); CPI instead of PCE for the price level; excess bond premium (Gilchrist and Zakrajšek 2012 ) or Cleveland Fed FSI instead of St. Louis FSI; and narrative validation via Romer-Romer-style event regression on six categories of crypto-market events.

Q5. What does cryptocurrency’s macro role mean for monetary policy?

Central banks should monitor cryptocurrency markets for demand-driven inflation pressure. With cryptocurrency shocks explaining 18% of long-horizon inflation variance, the asset class has crossed the threshold of monetary-policy relevance. Chen (2025) finds the contribution to PCE price-level forecast-error variance rises from 3.6% at 6 months to 17.6% at 30 months, while S&P 500, CRB, and Financial Stress Index shocks combined contribute 10.1% at 30 months — making cryptocurrency the largest single non-own driver of price-level variance in this sample.

The inflation mechanism matches New Keynesian demand-side transmission: positive crypto shocks raise equity and commodity prices, ease financial stress, stimulate investment and consumption, and pass through to aggregate-demand-driven inflation via the wealth channel (Case, Quigley, and Shiller 2005 ) and the financial-accelerator channel (Bernanke, Gertler, and Gilchrist 1999 ).

Divisia M4 shows initial expansion followed by contraction after a positive crypto shock — evidence of endogenous monetary tightening, but not aggressive enough to offset the price effect. Chen and Valcarcel (2021) argue Divisia aggregates are the correct monetary indicator when short rates are uninformative, and Chen and Valcarcel (2025) document their superior information content relative to simple-sum measures. The implication is that the Fed’s accommodative response leaves meaningful crypto-driven inflation in the system.

The demand-driven nature of the inflationary impulse distinguishes it from a transitory financial-market disturbance and makes it policy-actionable. Monetary authorities should incorporate cryptocurrency developments into their inflation forecasting models, and financial regulators should monitor the cryptocurrency market as a source of systematic risk given its substantial contribution to financial-market volatility.

Q6. Does the integration result hold beyond Bitcoin?

The current paper covers Bitcoin only. Bitcoin’s dominant market capitalization during 2015–2024 — averaging 40–65% of total cryptocurrency market cap over the sample — and the need for a sufficiently long monthly time series for structural VAR identification motivated this scope. Bitcoin’s market dominance makes the results broadly descriptive of the overall cryptocurrency market for this period.

Whether the results generalize to the full cryptocurrency ecosystem involves two open questions. First, altcoins, stablecoins, and DeFi tokens have different fundamental characteristics and may transmit to macro variables through different channels or with different magnitudes. Second, the cryptocurrency market structure changed substantially over the 2015–2024 window — from Bitcoin-dominated speculation to institutionally integrated infrastructure — and continuation samples will likely show evolving transmission dynamics as institutional adoption deepens further.

The paper’s main findings are robust to alternative variable orderings, price-level measures (CPI vs. PCE), and financial-stress indicators (excess bond premium vs. St. Louis FSI vs. Cleveland FSI), suggesting the Bitcoin-specific result is not an artifact of particular specification choices. Extending the framework to other cryptocurrency assets as data availability improves remains an important direction for future empirical work.

Q7. How do I estimate a Bayesian SVAR with Pandemic Priors for cryptocurrency shock analysis?

The setup combines a standard BVAR with Cascaldi-Garcia (2022) Pandemic Priors , which down-weight COVID-period observations to prevent them from contaminating impulse-response estimates while preserving the information they carry about volatility.

Chen (2025) implements this in five steps:

Construct a monthly panel of cryptocurrency price (Bitcoin), traditional financial market variables (equity, commodity prices, financial stress index), and macro variables (industrial production, unemployment, PCE).
Specify the BVAR with Minnesota-style shrinkage on the coefficients, plus Pandemic Priors that introduce additional shrinkage on COVID-period error variances (March 2020 through approximately mid-2021), using the dummy-observation implementation of Bańbura, Giannone, and Reichlin (2010) .
Identify cryptocurrency shocks via recursive ordering — crypto last among financial market variables but before macro real activity — and validate with Romer and Romer (2004) narrative identification matched against 67 documented crypto-market events.
Estimate via Gibbs sampling with overall tightness λ = 0.2; select the Pandemic Prior hyperparameter φ = 0.1 by marginal-likelihood maximization.
Report impulse responses with 16/84 credible bands and forecast error variance decompositions at 12-, 24-, 36-month horizons.

Why Pandemic Priors matter here: cryptocurrency markets experienced extreme volatility in March 2020 that would dominate a standard BVAR’s estimated dynamics. Setting φ = 500 (conventional Minnesota limit) materially changes real-economy impulse responses — less persistent unemployment declines, more contractionary Divisia M4 — confirming the priors are necessary for this sample.

Related questions: What cryptocurrency price series is appropriate for an SVAR? · How does narrative identification validate the recursive ordering?

Q8. Which cryptocurrency price and macro variables are appropriate for systemic-risk SVAR analysis?

For the cryptocurrency variable, Bitcoin’s log price is the standard choice given its dominant 40–65% market capitalization share during 2015–2024. Chen (2025) uses an eight-variable monthly SVAR ordered recursively: PCE price index, unemployment rate, industrial production, Divisia M4, Bitcoin price, S&P 500, CRB commodity index, and the St. Louis Fed Financial Stress Index.

Data sources:

Cryptocurrency prices: CoinMarketCap (daily, aggregated to monthly).
Traditional financial markets: S&P 500 and CRB commodity index from FRED ; OFR Financial Stress Index .
Macro variables: industrial production (INDPRO), unemployment (UNRATE), PCE (PCEPI) from FRED.
Monetary aggregate: Divisia M4 from CFS AMFM .
Sample period: January 2015 onward — earlier data has too little institutional adoption to identify the integrated regime.

Variable selection cautions: do not include trading volume in the SVAR (it breaks identification); do include a financial stress measure in addition to equity prices, as they capture distinct channels; for research on monetary-policy effects on crypto, add a policy indicator using Divisia M4 following Chen and Valcarcel (2021) .

Related questions: How are Pandemic Priors implemented? · Does the result hold if Bitcoin is replaced by Ethereum?

Q9. Does the cryptocurrency-macro spillover result extend to altcoins, DeFi protocols, or stablecoins?

Likely yes for altcoins, more nuanced for DeFi, and structurally different for stablecoins — but the empirical evidence is sparse and a natural extension of Chen (2025) .

Altcoins typically comove strongly with Bitcoin in return space, so the spillover pattern should replicate at smaller magnitudes. A natural extension applies the BSVAR with Bitcoin replaced by Ethereum or a market-cap-weighted top-10 index. Ethereum, with its DeFi infrastructure role, may show distinct dynamics that warrant separate identification.

DeFi protocols introduce additional channels — total value locked, governance token dynamics, liquidation cascades during stress — that a price-only SVAR misses. The right extension would add aggregate DeFi TVL and a measure of leverage in lending protocols.

Stablecoins are structurally different: their price shocks are small (depegging events are large but rare), and the relevant shock is the supply of stablecoins. A large stablecoin issuance amounts to mechanical T-bill demand — making the right framework closer to a money-supply shock in traditional monetary economics than a risk-asset price shock.

Cross-country considerations: cryptocurrency adoption rates vary enormously. The U.S. results in Chen (2025) likely overstate the macro effect in low-adoption economies and understate it in high-adoption ones.

Related questions: How does DeFi affect monetary transmission? · What are stablecoins’ systemic risk implications?

Q10. What does cryptocurrency’s 18% inflation variance contribution imply for monetary policy and financial regulators?

For monetary policy: the result implies that cryptocurrency markets have moved to a quantitatively significant input into the inflation process, and central banks should monitor crypto-driven financial conditions alongside traditional credit and equity measures. Chen (2025) documents that positive Bitcoin price shocks generate persistent inflationary pressure — a 0.15% rise in the PCE price level over a 30-month horizon — operating through wealth and investment channels. The 18% long-horizon inflation variance contribution grows from 3.6% at 6 months to 17.6% at 30 months, making cryptocurrency the largest single non-own driver of price-level variance in this sample.

Concrete implications for central-bank monitoring:

Include crypto-driven financial conditions in the dashboard. The OFR Financial Stress Index does not currently include crypto-specific volatility; an extension would improve real-time signal.
Recognize crypto wealth effects in consumption forecasting. With large retail crypto holdings, even modest wealth elasticities translate to first-order consumption effects.
Distinguish sentiment-driven from technology-driven crypto shocks. Chen (2025) finds sentiment shocks dominate and produce the inflation spillover; technology shocks are smaller in magnitude.

For financial regulators: prudential rules for bank crypto exposure, stablecoin reserve requirements, and stress-test scenarios all need to account for the documented spillover magnitudes. The demand-driven nature of the inflationary impulse — as opposed to a transitory financial-market disturbance — makes it policy-actionable rather than a noise term.

Related questions: What is the wealth-effect channel for cryptocurrency? · How does Divisia M4 respond to crypto shocks?

This paper situates cryptocurrency within Chen’s broader research program on monetary transmission and financial market integration. Chen (2026, Journal of Macroeconomics) examines how the Federal Reserve responds to financial conditions in setting policy — a transmission channel through which cryptocurrency-driven volatility could affect monetary decisions. Chen and Valcarcel (2021, JEDC) and Chen and Valcarcel (2025, JEDC) develop the structural VAR identification methods that this paper extends to cryptocurrency markets.

Data and Replication

Bitcoin price data: CoinMarketCap (daily, aggregated to monthly)
Macroeconomic series: FRED — PCE price index, CPI, unemployment, industrial production, S&P 500, CRB commodity index, St. Louis Fed FSI, Cleveland Fed FSI, excess bond premium
Divisia monetary aggregates: Center for Financial Stability — AMFM dataset , Divisia M4
Pandemic Priors implementation: Cascaldi-Garcia (2022) , φ = 0.1, λ = 0.2, 30-month impulse horizons, 68% posterior bands
Sample: Monthly, January 2015 – November 2024
Open access: UNI ScholarWorks · Journal of Risk and Financial Management

Citation

Chen, Zhengyang. 2025. “From Disruption to Integration: Cryptocurrency Prices, Financial Fluctuations, and Macroeconomy.” Journal of Risk and Financial Management 18(7): 360. https://doi.org/10.3390/jrfm18070360

@article{chen2025crypto,
 author = {Chen, Zhengyang},
 title = {From Disruption to Integration: Cryptocurrency Prices, Financial Fluctuations, and Macroeconomy},
 journal = {Journal of Risk and Financial Management},
 volume = {18},
 number = {7},
 pages = {360},
 year = {2025},
 publisher = {MDPI},
 doi = {10.3390/jrfm18070360},
 url = {https://doi.org/10.3390/jrfm18070360},
 license = {CC BY 4.0}
}

Modeling Inflation Expectations in Forward-Looking Interest Rate and Money Growth Rules

Wed, 15 Jan 2025 00:00:00 +0000

A low-dimensional SVAR can directly embed rational expectations — and once it does, a forward-looking money growth rule with Divisia M4 delivers puzzle-free monetary transmission where the federal funds rate fails across 99% of specifications

Chen and Valcarcel (2025) propose the RE-SVAR: an internal instrumental-variable procedure that directly embeds forward-looking rational expectations into a three-variable consensus AS–IS–MP system. Searching over 241,865 forward-horizon and policy-coefficient combinations, the Wu-Xia shadow federal funds rate generates price puzzles in 99.13% of specifications; Divisia M4 as the policy indicator delivers puzzle-free responses in 95.85%.

Five named concepts anchored in this paper

RE-SVAR: Rational expectations-augmented structural vector autoregression. A low-dimensional SVAR that directly embeds forward-looking rational expectations via an internal instrumental-variable procedure, without mapping from a DSGE.
Response clouds (cloud of structural IRFs): The set of 241,865 impulse responses generated by grid-searching forward-looking horizons and policy-rule coefficients, with each combination producing a separate realization of the SVAR.
No-joint-puzzle response: The survival criterion: an IRF that avoids both the output puzzle and the price puzzle within the first year post-shock.
Low-dimensional forward-lookingness: The paper's methodological claim: forward-looking behavior can be modeled inside a three-variable AS–IS–MP consensus system without appending factors or unobservables.
Non-modularity of RE-SVAR: The property that each added variable requires a fully specified structural equation; you cannot simply append commodity prices, Greenbook forecasts, or factors without a theoretical construct.

How can rational expectations be embedded directly into a low-dimensional SVAR without mapping from a DSGE?

Through an instrumental-variable procedure internal to the SVAR that exploits the forecast-revision identity implied by rational expectations, applied to a fully specified consensus AS–IS–MP system.

The standard options have been unsatisfactory. Backward-looking recursive SVARs, in the tradition of Christiano, Eichenbaum and Evans's Handbook of Macroeconomics chapter, impose a delayed-reaction assumption through Cholesky ordering but struggle to accommodate forward-lookingness. The mapping approach — finding conditions under which a DSGE can be represented as a VAR or VARMA — requires lag truncation or dimension reduction that defeats the point. DSGEs themselves are RE-consistent but come with laws of motion for unobservables that constrain the parameter space in ways the textbook consensus model does not require.

Chen and Valcarcel (2025) propose a third path — the RE-SVAR — that stays within a three-variable consensus model and derives the structural monetary policy shock as a linear combination of reduced-form residuals using the forecast-revision identity. Taking a stand on the policy-rule coefficients and horizons (rather than estimating them) produces a unique structural shock for each parameter combination — a pseudo-calibration that yields response clouds rather than a single IRF.

Why this matters operationally:

No Cholesky ordering and no delayed-reaction assumption.
No unobserved state variables or moving-average components.
The three-variable system remains directly comparable to the textbook AS–IS–MP model, with each equation having a structural interpretation.
Forward-looking horizons (h_π, h_y) are parameters you iterate over, not constants you estimate.

The trade-off: the method is not modular. Adding a variable requires a fully specified structural equation for it — which the paper demonstrates for the Gilchrist-Zakrajšek excess bond premium in Section 7 but which rules out ad hoc inclusion of commodity prices or Greenbook forecasts.

RE-SVAR vs. Standard SVAR Approaches to Monetary Policy Identification
Dimension	Recursive SVAR (delayed reaction)	FAVAR / Factor-augmented	Proxy SVAR (external instruments)	RE-SVAR (Chen & Valcarcel 2025)
Core identification	Cholesky ordering with policy indicator ordered after economic activity; imposes delayed reaction.	Large information set spanned by principal-component factors; recursive identification within the factor VAR.	High-frequency monetary surprises used as external instruments for structural policy shock.	Forecast-revision identity applied to a fully specified AS–IS–MP system; shock is a linear combination of reduced-form residuals.
Key references	Christiano, Eichenbaum & Evans (1999), Hanson (2004)	Bernanke, Boivin & Eliasz (2005), Boivin, Kiley & Mishkin (2010)	Gertler & Karadi (2015), Kuttner (2001)	Chen & Valcarcel (2025); foundations in Blanchard & Perotti (2002)
Handles forward-looking expectations	No — inherently backward-looking; requires appending forward-looking variables.	Partially — factors can proxy for forward-looking information but lack structural interpretation.	Implicitly — high-frequency surprises embed forward-looking market expectations.	Yes — forward horizons h_π, h_y are parameters of the policy rule; RE restriction is internal.
Dimensionality	Small-to-medium (typically 6–8 variables); grows with information-set fixes.	High (100+ variables summarized by 3–5 factors).	Small-to-medium, augmented by external instrument.	Low (3–4 variables); strictly bounded by the number of structural equations available.
Modularity	High — append variables as needed.	High — scale factors up or down.	Medium — add instruments; adding endogenous variables remains standard.	None — each added variable requires its own structural equation.
Identification validity rests on	Restriction scheme (Cholesky ordering).	Approximating the true information set with a factor structure.	Validity and relevance of the external instrument.	Theoretical credibility of the consensus AS–IS–MP model itself.
Price puzzle incidence in low-dimensional form	Pervasive without commodity-price augmentation; still present even with it in many samples.	Generally resolved, but Boivin, Kiley & Mishkin (2010) show sensitivity to specification.	Generally resolved at short horizons; longer-horizon responses vary.	Resolved with Divisia M4 (<4%); unresolved with Wu-Xia shadow rate (>98%).
Works through the effective lower bound	Only with shadow-rate construction (e.g., Wu & Xia 2016).	Yes, via shadow rate or factors.	Yes, via high-frequency surprises.	Yes — Divisia growth rate is unbounded; Keating et al. (2019) document pre/post-GFC stability.
Named concept	Block-recursive identification	Information-sufficient factor identification	High-frequency external-instrument identification	RE-SVAR · Response clouds · Non-modularity (Chen & Valcarcel 2025)

Why does the federal funds rate fail as a monetary policy indicator in low-dimensional SVARs?

It generates the price puzzle and the output puzzle across virtually the entire parameter space once forward-looking rational expectations are enforced. In Chen and Valcarcel's modern sample, 99.13% of 241,865 parameter combinations produce at least one puzzling response within the first year after a federal funds rate shock.

The price puzzle — first documented by Eichenbaum (1992), who noted that the price level rises rather than falls after a contractionary interest rate shock — has been treated for three decades as a problem of information insufficiency. The standard fix, from Christiano, Eichenbaum and Evans (1999), is to augment the VAR with commodity prices. Hanson (2004) showed this fix is unreliable: many alternative indicators with strong inflation-forecasting power fail to resolve the puzzle, and the puzzle is particularly resistant in pre-1979 samples.

Chen and Valcarcel (2025) reveal that once rational expectations are embedded directly and the researcher searches over the full space of forward-looking policy-rule parameters, the price puzzle is not an incidental feature of particular specifications — it is the dominant outcome. Using the Wu and Xia (2016) shadow federal funds rate to span the effective lower bound period, the paper finds 98.68% output puzzles and 99.13% price puzzles across 241,865 realizations in the 1988–2020 sample. Only 2,109 combinations — less than 1% — produce non-puzzling responses in both industrial production and inflation. Chen and Valcarcel (2021) reached a similar conclusion with an entirely different methodology (TVP-FAVAR), suggesting the federal funds rate's weakness as a low-dimensional policy indicator is methodology-independent.

The interpretation: absent an augmented information set — factors à la Bernanke, Boivin and Eliasz's FAVAR, futures data, or Greenbook forecasts — the federal funds rate cannot carry the forward-looking information content required to identify monetary policy shocks in a consensus three-variable system.

Why does a forward-looking money growth rule with Divisia M4 produce sensible responses where the federal funds rate fails?

Because broad Divisia monetary aggregates internalize substitution effects across monetary assets that simple-sum measures and short-rate indicators discard — and because the growth rate of Divisia M4 is not bound to zero, it carries information through the effective lower bound period that the federal funds rate cannot.

The theoretical case for Divisia over simple-sum M2, established by Barnett (1980) with the derivation of the monetary services index from Diewert's index theory and reinforced by Belongia and Ireland (2014) in their New Keynesian formalization of the Barnett critique, is that a CES aggregate of interest-bearing and non-interest-bearing assets tracks the true monetary aggregate almost perfectly to second order. Keating, Kelly, Smith and Valcarcel (2019) show in a block-recursive SVAR that Divisia M4 resolves the price puzzle for both pre- and post-GFC samples, while Belongia and Ireland (2022) argue theoretically that a money growth rule responding to inflation and output gradually delivers stabilization comparable to an estimated Taylor rule.

Chen and Valcarcel (2025) extend this evidence into a fully forward-looking rational-expectations framework. In the same 1988–2020 sample where the shadow federal funds rate generates 99% puzzles, Divisia M4 as the policy indicator produces 95.85% no-joint-puzzle responses — 231,825 surviving IRFs out of 241,865. The output-puzzle rate drops to 4.02% and the price-puzzle rate to 4.13%. The pattern holds across CPI and PCE price indexes and across historical (1967–2020), modern (1988–2020), and post-ELB (2008–2020) samples, with narrower Divisia M2 performing comparably to the broader Divisia M4. Notably, at the longest expectation horizon considered (h_π = 12 months), fewer than 1% of Divisia specifications exhibit puzzles while 99.9% of shadow-rate specifications do.

Why the asymmetry is structural and not merely empirical:

Divisia M4 reflects substitution across a broader set of monetary assets than the segmented federal funds market, giving it richer information content per unit of variation.
The money growth rule remains operational through the ELB period — where even the Wu-Xia shadow rate is a constructed object — which matters for samples that straddle 2008–2015.
The long-run relationship between Divisia aggregates and economic activity is stable (Chen and Valcarcel 2024), consistent with its role as a forward-looking policy indicator.

How should researchers handle forward-looking horizons in the policy reaction function?

Iterate over them rather than estimate them — and report response clouds for different horizon choices rather than a single median IRF. Chen and Valcarcel's grid of h_π ∈ {0, 1, …, 12} months for inflation and h_y ∈ {0, 1, …, 5} months for output, combined with φ_π, φ_y ∈ [0, 4] in increments of 1/15, generates 241,865 distinct SVAR specifications from a single underlying model.

The theoretical motivation comes from Batini and Haldane (1999), who argued that forward-looking rules with flexibility over both the forecast horizon and the feedback parameter are the right analog to Svensson's flexible inflation-forecast-targeting rule. Estimating h_π and h_y requires either Fed-internal data (Greenbook forecasts, as in Orphanides (2001) on real-time monetary policy rules) or heavy structural assumptions.

Chen and Valcarcel (2025) exploit this flexibility to show that the qualitative conclusion — Divisia dominates the shadow federal funds rate in producing sensible responses — is invariant to which horizon assumption you make. More specifically, for the money growth specification the number of no-joint-puzzle responses increases with the horizon (from 88.4% at h_π = 1 to 99.1% at h_π = 12), while for the federal funds rate specification it decreases (from 2.1% at h_π = 1 to 0.03% at h_π = 12). The two indicators thus differ not only in level but in how they behave as forward-lookingness intensifies.

Practical implication: any paper reporting a single IRF from a forward-looking policy rule is reporting one realization from a response cloud. The distributional features matter because Inoue and Kilian (2022) argue against reporting median responses when the joint distribution of IRFs contains the policy-relevant information.

What is the non-modularity of the RE-SVAR approach, and why does it matter for applied work?

Non-modularity means that every variable added to the system requires its own fully specified structural equation — you cannot simply append variables to improve fit, as is routine in standard empirical VARs. This is the principal cost of the RE-SVAR framework, and the main reason it constrains itself to low-dimensional consensus models.

The contrast with standard practice is sharp. Standard VAR specifications treat the information set as expandable: Christiano, Eichenbaum and Evans (1999) add commodity prices, Bernanke, Boivin and Eliasz (2005) add 120+ factors in their FAVAR, Hanson (2004) surveys numerous alternative predictors, and Gertler and Karadi (2015) augment with high-frequency monetary surprises as external instruments. Each addition is defensible statistically — more information should improve identification — but often lacks a theoretical construct within the consensus macroeconomic model.

Chen and Valcarcel (2025) argue the non-modularity is a feature, not a bug: the identification validity depends on the suitability of the underlying theoretical structure, not on the restriction scheme. Section 7 of the paper demonstrates how to add the Gilchrist-Zakrajšek (2012) excess bond premium as a fourth variable — but this requires writing out a fourth structural equation, establishing a sequential IV procedure for each additional parameter, and verifying that the Rubio-Ramírez, Waggoner and Zha (2010) rank condition for global identification is satisfied.

Implication for applied researchers:

If your question requires adding commodity prices, Greenbook forecasts, or a factor for forward-looking expectations, the RE-SVAR is not the tool; a standard VAR with external instruments or a FAVAR is.
If your question is about whether the consensus AS–IS–MP model can carry forward-looking dynamics on its own, the RE-SVAR is specifically designed for that test, and the non-modularity guarantees you cannot cheat by adding variables with no structural role.

How should one interpret response clouds from 241,865 SVARs rather than a single impulse response function?

As a joint distribution over structural IRFs, where each point in the parameter grid is a distinct identification of the same underlying model. The cloud is the object of inference; any single IRF is a point in it.

The approach parallels the Bayesian posterior-over-impulse-responses literature but uses a frequentist grid rather than posterior draws. Inoue and Kilian (2022) argue that summarizing Bayesian VAR inference with median responses is misleading when the joint distribution contains features — such as multi-modality or sign reversals across plausible parameter regions — that a median collapses.

Chen and Valcarcel (2025) handle this in three ways:

Report the no-joint-puzzle share directly. The survival rate — 95.85% for Divisia M4, 0.87% for the shadow federal funds rate in the modern sample — is itself a summary statistic that preserves the joint distribution's information without collapsing to a point estimate.
Slice the cloud by horizon. Fixing h_π at different values (1, 3, 6, 12 months) and reporting median responses within each slice reveals how forward-lookingness interacts with indicator choice.
Slice by policy coefficient. Fixing φ_π = 1.5 (the Taylor (1993) classic value) and reporting median responses reveals which subsets of the cloud correspond to empirically relevant parameter choices.

This treatment provides a natural connection to set-identified SVAR literature (Rubio-Ramírez, Waggoner and Zha 2010) and to sign-restriction approaches such as Uhlig (2005): the response cloud is the identified set under the rational-expectations restriction combined with the parameter grid, and the no-joint-puzzle responses are the subset satisfying textbook sign restrictions as well.

Does the conclusion that Divisia M4 outperforms the federal funds rate depend on the specific sample, price index, or Divisia aggregate?

No — the dominance of Divisia money over the shadow federal funds rate is robust across three samples (1967–2020, 1988–2020, 2008–2020), two price indexes (CPI and PCE), and two Divisia aggregates (M2 and M4).

Chen and Valcarcel (2025) report Table 1 across all 12 combinations. A condensed summary:

Sample	Price	Wu-Xia FFR output puzzle	Wu-Xia FFR price puzzle	DM4 output puzzle	DM4 price puzzle
1988–2020	CPI	99.5%	99.4%	3.7%	3.8%
1988–2020	PCE	99.6%	99.4%	23.7%	4.2%
2008–2020	CPI	72.0%	93.0%	2.4%	1.6%
2008–2020	PCE	90.8%	96.1%	9.1%	5.1%
1967–2020	CPI	98.9%	98.8%	3.9%	4.1%
1967–2020	PCE	53.3%	94.7%	56.0%	7.4%

The single ambiguous cell is the 1967–2020 sample with PCE inflation, where both indicators show elevated output-puzzle rates — but even there, Divisia's price-puzzle rate (7.4%) is an order of magnitude below the shadow rate's (94.7%). The robustness is consistent with Keating et al. (2019), who find similar pre/post-GFC stability of money growth rules in a block-recursive setting. The narrower Divisia M2 performs comparably to Divisia M4 across all cells, consistent with Kelly, Barnett and Keating (2011) on the liquidity effects of broader Divisia aggregates. Chen and Valcarcel (2024) separately establish that the underlying money-demand relationships for Divisia aggregates are cointegrated and stable in modern samples, reinforcing that the SVAR results are not driven by spurious regression dynamics.

How do I implement the RE-SVAR procedure on my own data?

The implementation has five steps once you have a balanced panel of inflation, output, and a policy indicator: write down the AS–IS–MP consensus model with the forward-looking horizons you want to test, derive the forecast-revision identity for each equation, set up the IV procedure that yields the structural policy shock as a linear combination of reduced-form residuals, grid-search over the policy-rule parameters (φ_π, φ_y) and horizons (h_π, h_y), and compute impulse responses for each grid point. Chen and Valcarcel (2025) provide the full derivation in Sections 3–4.

The non-trivial step is the IV procedure itself. The forward-looking AS–IS–MP system implies a contemporaneous restriction between the structural policy shock and the reduced-form residuals through the rational-expectations forecast-revision identity. The structural shock for each grid point is a known linear combination of residuals — no estimation needed for the contemporaneous identification; only the lag dynamics need a reduced-form VAR.

Compute budget: With (h_π ∈ {0…12}) × (h_y ∈ {0…5}) × (φ_π ∈ [0,4] at 1/15) × (φ_y ∈ [0,4] at 1/15) = 241,865 specifications. Each grid point requires only matrix algebra applied to one reduced-form VAR — total runtime is minutes on a laptop. Adding a fourth variable multiplies cost: each new variable requires its own structural equation, its own IV step, and verification that the Rubio-Ramírez, Waggoner and Zha (2010) rank condition for global identification holds. The paper demonstrates the four-variable extension for the Gilchrist-Zakrajšek excess bond premium in Section 7.

Related questions: What is non-modularity? · How should horizons be handled?

What minimum data set is required to estimate an RE-SVAR with a forward-looking policy rule?

Three variables: a price index, a real activity measure, and a policy indicator — all monthly, ideally over a sample of at least 20 years. The RE-SVAR is deliberately low-dimensional and does not require commodity prices, factors, Greenbook forecasts, or futures data — the non-modularity property means each additional variable must come with a structural equation, so the minimum data set is the minimum model.

Recommended series for U.S. work, matching Chen and Valcarcel (2025):

Price: CPI or PCE deflator (the paper uses both and shows results are robust).
Activity: Industrial production index (monthly availability is the binding constraint).
Policy indicator (rate specification): Wu and Xia (2016) shadow federal funds rate.
Policy indicator (money specification): Divisia M4 (or M2) from CFS AMFM, in growth rates.
Sample length: The paper estimates over 1967–2020, 1988–2020, and 2008–2020 — the three-sample comparison gives the cleanest robustness test across structural breaks.

For non-U.S. work, the procedure does not require Greenbook-style internal forecasts, which sidesteps the Orphanides (2001) real-time-data problem — the rational-expectations restriction is inside the model, not imposed via external forecasts.

Can the RE-SVAR framework be extended to open-economy or international policy rules?

Yes, with two caveats: each open-economy variable (real exchange rate, foreign output, foreign rate) needs its own structural equation, and the rank condition for global identification must be re-verified for the larger system. This is the same non-modularity constraint that limits the framework's flexibility — but it is precisely what makes the open-economy extension principled rather than ad hoc.

The standard open-economy SVAR template comes from Cushman and Zha (1997) for Canada and Kim and Roubini (2000) for the G7, both using block-recursive identification with external variables ordered first. The RE-SVAR analog would write a forward-looking IS equation augmented by a real-exchange-rate term, derive the forecast-revision identity for each equation, and add a monetary block for the foreign central bank.

Practical entry points for researchers wanting to attempt this: for Eurozone monetary policy identification, Belongia and Ireland's (2022) money-growth-rule framework provides the theoretical anchor; for Mexico, Colunga-Ramos and Valcarcel (2024) construct a Mexican Divisia M4 that could serve as the policy indicator in an RE-SVAR adapted for a small open economy. The framework is, in principle, portable to these settings, though each extension requires verifying the identification conditions for the expanded system.

Related questions: What is non-modularity? · How is the RE-SVAR implemented?

What does the RE-SVAR evidence imply for central banks considering money-growth rules?

It implies that money-growth rules are more robust to forward-looking dynamics than interest-rate rules in low-dimensional consensus models — the opposite of the standard view that interest-rate rules are modern best practice and money-growth rules are historical curiosities. Chen and Valcarcel (2025) document that as the policy-rule's forward-looking horizon h_π increases from 1 to 12 months, the no-joint-puzzle share for Divisia M4 rises from 88.4% to 99.1%, while for the Wu-Xia shadow rate it falls from 2.1% to 0.03%. The asymmetry is structural and survives across price indices, sample periods, and aggregation tiers.

For applied central-bank work, three concrete implications:

Operational monitoring should include Divisia M4 growth alongside the policy rate, since the rate loses identifying content as the policy regime becomes more forward-looking.
Communication strategy: forward guidance and transparency are part of the reason the short-rate indicator fails — they are facts about the modern monetary regime that the monetary aggregate accommodates, not problems to walk back.
Post-QE normalization: Divisia M4's sensitivity to Treasury and repo holdings makes it a better real-time indicator of policy stance than the policy rate alone as central banks unwind balance sheets.

This complements Belongia and Ireland's (2022) theoretical case for money-growth rules, who argue that a rule responding gradually to inflation and output can deliver stabilization comparable to an estimated Taylor rule.

Data and reproducibility

Monetary policy indicator (shadow rate): Wu and Xia (2016) shadow federal funds rate, monthly.
Divisia monetary aggregates: Center for Financial Stability — AMFM dataset, Divisia M2 and M4.
Macroeconomic data: FRED (CPI, PCE, industrial production, unemployment).
Sample: Three samples — 1967–2020, 1988–2020, 2008–2020, monthly frequency.
Software: Custom RE-SVAR procedure; grid of 241,865 specifications from h_π ∈ {0,…,12}, h_y ∈ {0,…,5}, φ_π, φ_y ∈ [0,4] at increments of 1/15.
Open access: UNI ScholarWorks · SSRN preprint · Journal of Economic Dynamics and Control

Related publications

Chen and Valcarcel (2021), JEDC — methodology-independent evidence that the federal funds rate fails in low-dimensional settings (TVP-FAVAR approach).
Chen and Valcarcel (2024), Macroeconomic Dynamics — cointegration and stability of Divisia money demand; establishes the long-run foundation for the policy indicator results here.

Cite as: Chen, Z., & Valcarcel, V. J. (2025). Modeling inflation expectations in forward-looking interest rate and money growth rules. Journal of Economic Dynamics and Control, 170, 104999. https://doi.org/10.1016/j.jedc.2024.104999

@article{chenvalcarcel2025resvar,
 author = {Chen, Zhengyang and Valcarcel, Victor J.},
 title = {Modeling inflation expectations in forward-looking
 interest rate and money growth rules},
 journal = {Journal of Economic Dynamics and Control},
 volume = {170},
 pages = {104999},
 year = {2025},
 doi = {10.1016/j.jedc.2024.104999},
 url = {https://doi.org/10.1016/j.jedc.2024.104999}
}

Bayesian SVAR | Robin Chen