Victor J. Valcarcel | Macro Paper Warehouse

A granular investigation on the stability of money demand

This 2024 Macroeconomic Dynamics paper by Zhengyang Chen and Victor J. Valcarcel asks whether the long-documented instability of U.S. money demand reflects a genuine structural break in households’ and firms’ preferences for monetary assets, or is instead an artifact of measuring money with simple-sum aggregates (which just add up dollar balances) rather than Divisia aggregates (which weight each monetary asset by its real user cost, i.e., the foregone return from holding it instead of a benchmark asset). Using monthly U.S. data from January 1967 to March 2020 (the sample stops there because the Federal Reserve’s April 2020 redefinition of M1 and a simultaneous Center for Financial Stability accounting change make later observations non-comparable), the authors estimate bivariate Johansen (1991, 1995) cointegrating VECMs between real money balances scaled by nominal income and an opportunity-cost variable – either the 3-month T-bill yield or each aggregate’s own Divisia real user cost – in both semi-log (Cagan) and double-log (Meltzer) functional forms, checked across four Johansen trend specifications and corroborated with Andrews-Ploberger (1994) and Bai-Perron (2003) structural-break tests. They find that simple-sum M2 and M3 fail to cointegrate with the T-bill yield over the full sample, whereas Divisia M2 cointegrates robustly with its own user cost under every specification and functional form, and Divisia M3 cointegrates under most specifications; splitting the sample at the 1980 DIDMCA deregulation break (located via Andrews-Ploberger at 1979:M10 for Divisia M2 and 1980:M2 for Divisia M3) shows simple-sum M2’s relationship with the T-bill yield breaking down after 1980 (surviving only in trend specifications, and then with the wrong sign), while Divisia M2 continues to cointegrate correctly in both subperiods. After the Global Financial Crisis, the near-zero T-bill yield loses its cointegrating relationship with Divisia M3 and M4 entirely, yet both continue to cointegrate with their own real user costs, which never collapsed to zero. A granular decomposition of ten individual Divisia components against their own user costs finds that 29 of 40 estimated coefficients (10 components times 4 Johansen criteria) carry the theoretically correct sign, versus much weaker and more often wrong-signed cointegration between those same components and the T-bill yield. The authors conclude that the instability documented in the money-demand literature is a matter of measurement – the T-bill yield and simple-sum aggregation strip out information that Divisia aggregation and its user costs preserve – rather than a structural shift in money demand itself; scope is limited throughout to bivariate (two-variable) cointegrating relationships, with income elasticity imposed as unity rather than estimated.

A Model of Monetary Policy Shocks for Financial Crises and Normal Conditions

This 2019 Journal of Money, Credit and Banking paper by John Keating, Logan Kelly, A. Lee Smith, and Victor Valcarcel asks whether replacing the federal funds rate with Divisia M4 (DM4) – a user-cost-weighted monetary aggregate – as the policy indicator in a Christiano-Eichenbaum-Evans (1999)-style block-recursive structural VAR can identify monetary policy shocks that behave sensibly in both normal times and financial-crisis/near-zero-lower-bound conditions, when standard funds-rate-based shocks are prone to implausible (“puzzle”) responses. The empirical model partitions macro variables into three ordered blocks – a slow-moving block (real GDP, the GDP deflator, a commodity price index), the policy indicator (DM4), and a fast-responding money-market block (the monetary base and DM4’s user cost) – estimated by Bayesian Gibbs sampling (following Sims and Zha 1999) with a noninformative prior and 90% probability intervals, at 5 lags quarterly (13 lags in a monthly robustness check), across three overlapping samples: 1967:Q1-1995:Q2 (replicating the original CEE funds-rate sample), 1967:Q1-2007:Q4 (precrisis), and 1967:Q1-2015:Q4 (full sample including the 2008-09 crisis and the ZLB period). A complementary small-scale New Keynesian model with money shows that when the Fed’s estimated interest-rate rule displays high inertia (rho approximately 0.94, estimated by nonlinear GMM on 1967-2007 quarterly data), its policy dynamics can be closely replicated by a non-inertial money-growth rule reacting to output and inflation – providing theoretical grounding for using DM4 in a Cholesky-ordered VAR even though the Fed never formally targeted it – whereas a low-inertia Taylor (1993) rule is not well replicated by a money-growth rule. Empirically, the DM4-based VAR produces no output, price, or liquidity puzzles in any of the three samples: GDP falls in a significant, hump-shaped (U-shaped) pattern for three years after a contractionary shock, the price level declines with a lag (becoming significantly negative after about two years), DM4 itself falls on impact with a significant liquidity effect, and its user cost rises on impact – a pattern the authors describe as “remarkably stable” across samples and broadly similar to the CEE funds-rate benchmark in the precrisis sample. By contrast, VARs built on three shadow short rates (Lombardi-Zhu, Krippner, Wu-Xia) all generate persistent, statistically significant price puzzles, with two of the three also generating liquidity puzzles. The cumulative identified DM4 shocks crest around QE1-QE3 and register the 2013:Q2 taper tantrum as a large negative shock, and a historical decomposition finds monetary policy shocks after 2008 were mildly net expansionary (real GDP 0.48% and the GDP deflator 0.50% higher than they otherwise would have been), with monetary policy shocks accounting for 8.44% (90% interval 1.73%-18.78%) of real GDP forecast-error variance at 8 quarters and 6.47% (0.66%-17.04%) of GDP-deflator variance at 20 quarters. A Great Depression counterfactual – applying the 1929:Q3-1937:Q3 pace of M2 collapse to DM4 starting in 2007:Q4 – implies a hypothetical 12.65% peak-to-trough GDP decline and 4.1% deflation, versus the actual -4.35% GDP decline and +0.26% inflation, which the authors interpret as evidence that post-2008 Fed actions, while not large departures from its historical policy rule, prevented a much deeper contraction. Long-run policy-rule coefficients on inflation are negative and significant in all three samples (-1.83, -2.26, and -0.88 respectively across the three samples) while the output-growth coefficient stays small and insignificant throughout, which the authors read as the Fed behaving “as if” it stabilized inflation via broad money growth. Results are robust to a monthly-frequency VAR (only 1 of 102 responses falls outside the quarterly model’s 90% bands, though the monthly liquidity effect is not statistically significant) and largely, though not entirely, to substituting DM2 for DM4 (DM2 shows a small, statistically insignificant price puzzle and a rising monetary base in the full crisis-inclusive sample). The authors attribute DM4’s puzzle-free performance in the crisis period to two features: its Divisia expenditure-weighting, which (per a DSGE decomposition) avoids the aggregation bias that afflicts simple-sum aggregates like M1 and M2 when asset substitutability is time-varying, and its breadth, since DM4 includes institutional money-market funds, repos, commercial paper, and Treasury bills – assets specifically targeted by the Fed’s 2008-09 liquidity facilities (PDCF, TSLF, CPFF, ABCPMMMFLF).

Modeling inflation expectations in forward-looking interest rate and money growth rules

This 2025 Journal of Economic Dynamics and Control paper by Zhengyang Chen and Victor J. Valcarcel proposes a “rational expectations structural VAR” (RE-SVAR) — a way to embed rational expectations directly into a low-dimensional structural VAR without mapping the system to a fully specified DSGE model — and uses it to compare two candidate monetary-policy indicators, the Wu and Xia (2016) shadow federal funds rate and Divisia M4 money growth, on which produces a larger share of theoretically sensible (“non-puzzling”) impulse responses. The model starts from a three-equation consensus New Keynesian system (a forward-looking monetary policy rule written in either an interest-rate or a money-growth form, an IS equation, and a Phillips-curve AS equation, all estimated simultaneously) and identifies the monetary policy shock using a rational-expectations forecast-revision restriction that recovers it as a linear combination of reduced-form VAR residuals — not a Cholesky/recursive scheme, and without imposing any delayed-reaction exclusion restriction on the policy indicator. Rather than estimating the policy rule’s forward-looking parameters, the paper runs a “pseudo-calibration” grid search over the inflation- and output-response coefficients (φ_π, φ_y, each cycling over 61 values from 0 to 4) and the horizons over which expectations are formed (h_π = 0,…,12 months for inflation, h_y = 0,…,4 months for output), yielding 241,865 structural VAR specifications (8 lags, monthly U.S. data) and a resulting “cloud” of impulse responses; a response counts as a “puzzle” if output or inflation turns negative at any point within the first year following an expansionary shock to the policy indicator. In the main October 1988-February 2020 sample (377 monthly observations), the shadow federal funds rate produces output puzzles in 98.68% of the 241,865 specifications and inflation puzzles in 99.13%, with only 0.87% (2,109 specifications) surviving a no-joint-puzzle criterion; replacing it with Divisia M4 growth as the policy indicator cuts output puzzles to 4.02% and inflation puzzles to 4.13%, with 95.85% (231,825 specifications) surviving. This Divisia advantage holds up under a coarser 25,137-specification grid, a post-Global-Financial-Crisis effective-lower-bound sample (December 2008-February 2020, where even the shadow rate’s best-case output and inflation puzzle rates remain high at 72% and 93%), a long historical sample back to January 1967, a narrower Divisia M2 aggregate, and a PCE-based inflation measure — with one partial exception: in the long historical sample under PCE, the output-puzzle gap between indicators narrows substantially (53.3% for the shadow rate vs. 56.0% for DM4 vs. 47.9% for DM2). Longer inflation-expectation horizons help Divisia far more than the shadow rate (at a 12-month horizon, 18,430 of 241,865 DM4 specifications are non-puzzling versus only 5 for the shadow rate), and extending the model to four variables by adding the Gilchrist-Zakrajsek excess bond premium (July 1979-February 2020 sample) still yields an 81.45% no-joint-puzzle survival rate with DM4 as the indicator, alongside IS- and AS-shock responses that are broadly consistent with textbook signs. The authors read the results as evidence that the federal funds rate — especially its shadow-rate extension through the effective lower bound — is an inadequate standalone policy indicator in low-dimensional VARs, and that Divisia M4’s richer information content lets it capture forward-looking central bank behavior without added information variables, while cautioning that the RE-SVAR’s validity is conditional on the sensibility of its underlying three-equation theoretical structure and that, unlike a standard recursive VAR, it is not modular: adding any variable (as they do, only loosely, for the excess bond premium) requires specifying a full structural equation for it.

Monetary transmission in money markets: The not-so-elusive missing piece of the puzzle

This 2021 Journal of Economic Dynamics and Control paper by Zhengyang Chen and Victor Valcarcel shows that the Wu-Xia (2016) shadow federal funds rate — a standard modern-sample proxy for the stance of monetary policy that extends below the zero lower bound — produces a persistent, statistically significant price puzzle in a time-varying-parameter VAR estimated on 1988-2020 U.S. data, and that this puzzle survives the standard fixes (adding commodity prices, federal funds futures, or forward rates) that resolved the price puzzle in earlier, pre-1988 samples. In its place, the authors propose Divisia monetary aggregates — weighted monetary aggregates that account for the different liquidity services of component assets, rather than simply summing dollar balances — as an alternative policy indicator: using Divisia M4 (and, with more muted magnitudes, the narrower Divisia M2) in place of the shadow rate produces no puzzling price response in the first three months and the theoretically correct price-level increase at 18-, 30-, and 60-month horizons following an expansionary shock, a correction the authors show is not an artifact of their time-varying estimation approach since it also holds in a constant-parameter VAR. Extending the analysis to the transmission of monetary shocks into 14 disaggregated money-market components (spanning currency, deposits, retail and institutional money-market funds, time deposits, repurchase agreements, commercial paper, and Treasury bills), the paper documents that transmission strengthened substantially after the 2007 financial crisis, with patterns in the responses of savings deposits and less-liquid institutional instruments that the authors interpret as evidence of a “flight-to-safety” effect among both households and firms during and after the crisis. The authors attribute the shadow rate’s breakdown as a policy indicator to the Federal Reserve’s increased forward-looking transparency (making it harder to generate a true interest-rate “surprise”) and to the post-crisis shift from reserve scarcity to reserve abundance, concluding that reintroducing monetary aggregates — measured correctly via the Divisia index rather than simple summation — may be “the missing piece of the puzzle” in a low-rate environment where a key short-term policy rate is highly persistent.

The financial market effects of unwinding the Federal Reserve's balance sheet

This 2023 Journal of Economic Dynamics and Control paper by A. Lee Smith and Victor J. Valcarcel asks whether the financial-market effects of shrinking (“unwinding”) the Federal Reserve’s balance sheet are simply quantitative easing (QE) in reverse, studying the Fed’s 2014-2019 balance-sheet normalization episode with U.S. data only and no DSGE model. The paper combines three empirical strategies: a reduced-form regression of the federal-funds/IOR spread on log reserves, where the liquidity-effect coefficient rises in magnitude from -0.086 (s.e. 0.009) during the 2009Q1-2014Q3 expansion to -0.299 (s.e. 0.015) during the 2014Q4-2019Q3 normalization – an effect roughly three-and-a-half times larger in magnitude, attributed to the zero lower bound having put a floor under the spread during QE while no symmetric ceiling constrained it during QT; a two-day event study around 11 quantitative-tightening announcements (January 2008-December 2018, 4,016 daily observations) that splits 2 “taper” announcements from 9 “unwind” announcements, finding that while 9 QE announcements produced large, statistically significant cumulative declines (-1.49 percentage points on the 10-year Treasury yield, -3.70pp on MBS, -1.00pp on 8-quarter Eurodollar futures), the 11 QT announcements produced no significant cumulative effect on any of these series, and within QT only the 2 taper announcements – not the 9 unwind announcements – had statistically significant effects across the yield curve and other assets; and a block-triangular structural VAR that orders reserves first, identifying “reserve supply shocks” tied to the Fed’s own balance-sheet decisions rather than to Treasury-bill supply (which affects reserves only with a one-week settlement lag), estimated both as a Bayesian time-varying-parameter VAR (October 2015-October 2019, following Cogley and Sargent 2005 and Primiceri 2005) and, over the Asset Runoff sample alone (October 2017-August 2019), as a constant-parameter Bayesian SVAR for each of several individual asset prices. The TVP-VAR shows that negative reserve-supply shocks produced no significant response in the Goldman Sachs Financial Conditions Index during the September 2014-September 2017 Full Reinvestment phase but a significant financial-tightening response emerging in early 2018 during the October 2017-August 2019 Asset Runoff phase, with the FF-IOR spread’s response to reserve shocks increasing roughly threefold in magnitude between the two phases; the granular asset-level SVAR finds that a negative one-standard-deviation reserve-supply shock raises the 10-year Treasury yield by roughly 4 basis points within 2-4 weeks, with the VAR-implied term premium accounting for nearly all of that increase (suggesting a term-premium channel rather than revised short-rate expectations), raises BBB corporate and MBS yields by comparable amounts (BBB remaining elevated near 2bp at 28 weeks), raises the broad dollar index by about 0.3% around week 8, and produces only a small, imprecisely estimated, statistically insignificant decline in the S&P 500; and a counterfactual simulation against continued full reinvestment implies the balance-sheet unwind raised the 10-year Treasury yield by a peak of approximately 40 basis points around mid-2018 and by approximately 8 basis points on average over the full Asset Runoff period. The paper’s central conclusion is that unwinding tightened financial conditions even in the absence of significant announcement effects, but transmitted through liquidity and implementation channels rather than through the signaling and duration-driven announcement channels that dominated QE – an asymmetry the authors attribute to the FOMC’s deliberate post-taper-tantrum strategy of communicating balance-sheet normalization as separate from the policy-rate path (Yellen’s 2017 “watching paint dry” characterization) and to the absence of a zero-lower-bound-style ceiling on rates during reserve drawdowns. The sample deliberately stops short of the September 2019 repo-rate spike because of endogeneity concerns about aggregate reserve dynamics, so the authors note the results may understate the ultimate tightening effect as reserves approached scarcity.