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

Questions & answers

Q1. What is the paper’s central research question?

The paper asks whether the Wu and Xia (2016) shadow federal funds rate — the standard way researchers extend federal-funds-rate-based monetary policy analysis through the effective lower bound (ELB) period — produces reliable impulse responses in a modern sample (1988-2020), or instead generates persistent price puzzles, and whether Divisia monetary aggregates can serve as an alternative policy indicator that both resolves any such puzzle and usefully tracks transmission into individual, disaggregated money-market instruments.

Q2. What empirical methodology does the paper use, and why?

The primary specification is a time-varying-parameter VAR (TVP-VAR, following Primiceri 2005), in which both the autoregressive coefficients and the shock covariance matrix evolve over time via a random walk, identified with a zero restriction that binds only on impact (a short-run timing restriction, not a full recursive ordering); the authors also estimate a TVP-FAVAR (following Koop and Korobilis 2014) that extracts a common factor from the monetary variables, which has the advantage of not requiring a lengthy pre-sample “training” period, allowing the analysis to begin directly in October 1988 (when Divisia data first become available). As a check that their results are not an artifact of allowing time variation, the authors also estimate constant-parameter VAR counterparts, and find their central conclusions “qualitatively robust” across all three approaches.

Q3. What does the paper find about the shadow federal funds rate and the price puzzle in the modern sample?

Using the Wu-Xia shadow federal funds rate as the policy indicator, the paper finds a persistent price puzzle: the price level responds in a puzzling contractionary direction to an expansionary shadow-rate shock, a pattern that “seems to emanate quickly,” is “already statistically apparent by the third month post shock,” and is “quite persistent,” with the magnitude of the puzzling response diminishing only slowly. Critically, the standard remedies that resolved the classic 1965-1995-era price puzzle documented by Christiano, Eichenbaum, and Evans (1999) — adding commodity price indexes (either the CRB spot index or the IMF global price index), federal funds futures rates, or forward-rate data — all fail to resolve the puzzle in this modern sample, and the puzzle appears at both monthly and quarterly frequencies and across 23 different three-to-five-variable model specifications the authors test.

Q4. How does using Divisia M4 as the policy indicator change the results?

Replacing the shadow rate with Divisia M4 — a broad monetary aggregate that weights each component asset by its user cost (reflecting its liquidity/monetary service value) rather than simply summing dollar balances — produces no statistically significant price response in the first three months after a shock and the theoretically expected rise in the price level at 18-, 30-, and 60-month horizons; the authors describe Divisia as doing “the heavy lifting in the resolution of the puzzle(s).” A narrower aggregate, Divisia M2, produces qualitatively similar, puzzle-free dynamics but with more muted response magnitudes, which the authors attribute to the broader DM4 aggregate capturing a wider array of monetary shocks across more asset classes; visual comparison of many specifications (23 iterations for the shadow-rate model versus the Divisia M4 counterpart) shows the price puzzle is “generally pervasive” under the shadow rate but shows “little evidence” of a puzzle under Divisia M4.

Q5. Does the price-puzzle resolution hold specifically during and after the effective lower bound period?

Examining impulse responses estimated at three points corresponding roughly to the start of each round of quantitative easing (December 2008, November 2010, and September 2012), the shadow rate continues to generate a price puzzle at all three dates, while both Divisia M4 and Divisia M2 continue to produce the theoretically correct qualitative price response — with the magnitude of the Divisia-based price-level response notably larger around the QE1 and QE2 episodes than at the very onset of the ELB period — while output responses are “quite similar” across the three specifications regardless of which policy indicator is used.

Q6. What does the paper find about how monetary transmission into individual money-market instruments changed after the 2007 financial crisis?

Decomposing the transmission of an expansionary shadow-rate shock into 14 individual money-market components (organized into M1, M2, and M4 tiers — currency, deposits, retail and institutional money-market funds, time deposits, repurchase agreements, commercial paper, and Treasury bills), the paper finds that all components respond in the expected direction but that the magnitude of these responses “increases following the 2007 Financial Crisis,” indicating a marked strengthening of monetary transmission into money markets in the post-crisis decade. Following an expansionary shock, savings deposits show a response that “outstrips those of currency or demand deposits” — which the authors read as suggestive of a household “flight-to-safety” effect — while post-2008, responses of less-liquid instruments held mainly by firms (institutional money-market funds, large time deposits, repurchase agreements, commercial paper, and Treasury bills) become larger than those of currency and ordinary deposits, which the authors interpret as a parallel firm-level flight-to-safety effect accompanying the large-scale asset purchases and reserve expansion of the QE era.

Q7. Why do the authors argue the federal funds rate (and its shadow-rate extension) has lost effectiveness as a policy indicator?

The paper attributes the breakdown to two structural changes: first, “the Federal Reserve is more forward-looking than it once was,” and its increased transparency about how it manages short-term lending rates in reserve markets “has made it more difficult to ‘shock’ financial markets” in the way a surprise-based identification requires; second, the interbank system has structurally “transitioned from scarcity to an overabundance of reserves” following the crisis-era asset purchases, changing how a given policy action maps into observable short-term rate movements. Divisia aggregates, by contrast, are argued (following Friedman 1956 and Meltzer 1963) to capture a comprehensive information set about monetary conditions — the yields and liquidity services of a whole spectrum of monetary and near-monetary assets — that a single short-term nominal interbank rate cannot convey, and the paper attributes the historical poor performance of simple-sum monetary aggregates (which do not weight by liquidity/user cost) to measurement error rather than a genuine structural breakdown of the money-output relationship, citing Belongia (1996) and Hendrickson (2014).

Q8. What limitations and puzzling results do the authors themselves acknowledge?

The authors explicitly flag two specific anomalies within their own results: the response of small time deposits at thrifts is “puzzling and somewhat inconsistent,” and Treasury bills show “a glaring and implausible contractionary effect” in the shadow-rate specification. They also note the sample ends in February 2020, just before the COVID-19 pandemic, so the analysis does not speak to pandemic-era transmission; that identification relies on a short-run zero restriction on impact only, without sign restrictions or external instruments to bolster it; and that the lag length is fixed at 3 across all specifications for comparability, even in cases where standard lag-selection criteria (AIC) would have chosen a different lag length for a specific model.