International Journal of Central Banking | Macro Paper Warehouse

A Shadow Policy Rate to Calibrate U.S. Monetary Policy at the Zero Lower Bound

This 2018 International Journal of Central Banking paper by Marco J. Lombardi and Feng Zhu proposes a “shadow policy rate” for U.S. monetary policy that is purely statistical rather than derived from a term-structure model, addressing the problem that once the federal funds rate is stuck at the zero lower bound (ZLB) it stops reflecting the stance of policy. Using monthly U.S. data from January 1970 to June 2016 organized into four blocks – interest rates (the effective federal funds rate, Treasury bill rates at one, three, and six months, Treasury bond yields at one, two, five, ten, and twenty years, and the OIS-LIBOR spread), monetary aggregates (M0, M1, M2, MZM), Federal Reserve balance-sheet assets (total assets, securities held outright, and their maturity composition), and reserves (total, excess, required) – the authors estimate a dynamic factor model with an arbitrary pattern of missing data, using the EM/Kalman-filter algorithm of Bańbura and Modugno (2014). Eight factors, chosen by the Hallin-Liska (2007) information criterion, explain 90.5 percent of the total variance of the data set (the first three factors alone account for almost 70 percent, with the first factor – linked to the interest-rate block – explaining about 38 percent, the second – linked to the monetary base – about 20 percent, and the third – linked to the size of Fed securities holdings – about 11 percent); the lag order is set to two by the Schwarz information criterion. The shadow federal funds rate is then recovered by treating the FFR and other short rates as missing once they reach the ZLB (from December 2008 for the FFR and three- and six-month bills, November 2009 for one- and two-year yields) and letting the model’s Kalman smoother impute the latent rate from its historical co-movement with the rest of the still-observed monetary data, including the balance sheet. The shadow rate tracks the effective FFR closely before the crisis, turns negative in early 2009, and – because it is directly driven by Fed balance-sheet changes rather than only the Treasury yield curve – registers substantial stimulus from the first large-scale asset purchase program (LSAP1, November 2008) that term-structure shadow rates (Krippner 2013a; Wu and Xia 2016) largely miss, since LSAP1 targeted mortgage-backed securities rather than Treasuries. The authors report the shadow rate delivered its greatest stimulus over 2011, dropping below -5 percent in August before becoming less accommodative and then loosening again from October 2012; a formal stability test finds the historical relationship between the funds rate and macro variables (real GDP, inflation) is not disrupted at the ZLB when the shadow rate is used (LR = 1.94, p = 0.38) whereas it is rejected when the observed FFR is used (LR = 15.77, p = 0.00). Benchmarked against Taylor (1993) and Taylor (1999)/balanced-approach rules, unconventional measures are found to have filled a substantial part of the post-2009 policy gap, broadly in line with Taylor (1993) but not fully sufficient under Taylor (1999), especially using the CBO unemployment gap – bearing on Bullard’s (2012, 2013) claim, based on a term-structure shadow rate, that policy became excessively loose in 2012. Finally, substituting the shadow rate for the actual FFR in two standard recursive-Cholesky monetary VARs (Bernanke-Blinder 1992; Christiano-Eichenbaum-Evans 1996, quarterly data 1970-March 2016, four lags) produces monetary policy shocks that clearly show sizable post-2008 easing timed with LSAP2 and LSAP3 and even a tightening shock after the 2014 taper, whereas shocks identified from the actual FFR are small and only mildly negative and so understate the true extent of stimulus. The authors describe the Section 4 exercises throughout as purely illustrative and caution the results should not be taken as conclusive.

Do Actions Speak Louder Than Words? The Response of Asset Prices to Monetary Policy Actions and Statements

This 2005 International Journal of Central Banking paper by Refet Gürkaynak, Brian Sack, and Eric Swanson tests whether asset-price responses to FOMC announcements can be adequately characterized by a single factor – the surprise change in the current federal-funds-rate target – and rejects that hypothesis using intraday (high-frequency) data around every FOMC announcement from January 1990 through December 2004. Using tick-by-tick federal funds futures, Eurodollar futures, on-the-run Treasury yields, and S&P 500 quotes measured in a tight 30-minute window (10 minutes before to 20 minutes after the announcement) and a wide one-hour window, the authors first show that narrowing the event window from a full day to 30 minutes sharply improves precision: the R-squared of the funds-rate-surprise regression on the S&P 500 triples from .12 (daily) to .36 (tight window), standard errors roughly halve, and the high-frequency design neutralizes the simultaneity and omitted-variable problems (notably contemporaneous employment reports) that contaminate daily- or monthly-frequency identification. They then fit a latent-factor model to the funds-rate-futures and Eurodollar-futures responses (138 FOMC announcements) and to Treasury-plus-stock responses (120 announcements), and use a Cragg-Donald (1997) matrix-rank test to reject both the zero-factor and one-factor hypotheses while failing to reject two factors. Rotating the two estimated principal components so the second has no effect on the current-month funds futures rate produces a “target” factor – surprise changes in the current funds-rate target, essentially the standard Kuttner (2001) measure – and a “path” factor, capturing movements in year-ahead policy expectations that are orthogonal to the current-rate surprise. The path factor is strongly associated with FOMC statements (regressing the absolute path factor on a statement-release dummy gives a coefficient of 0.070, R-squared = .18, and nine of the ten largest path-factor moves, including the largest on January 28, 2004, fall on statement dates) and it dominates the long end of the yield curve: in a joint two-factor regression, a one-percentage-point target surprise moves 2-/5-/10-year Treasury yields by 49/28/13 basis points and the S&P 500 by about -4.3%, while a one-percentage-point path innovation moves 5-/10-year yields by 37/28 basis points – a larger long-end effect – alongside a much smaller (roughly -1%) stock-market response; comparing one- versus two-factor R-squareds, the path factor accounts for roughly two-thirds of the explainable variation in two-year yields, three-fourths in five-year yields, and nine-tenths in ten-year yields, i.e., 75 to 90 percent of the explainable variation in long-term yields traces to statements rather than to funds-rate actions. An out-of-sample check using the first FOMC minutes released on the accelerated 2005 schedule (January 4, 2005) finds Treasury-yield movements broadly in line with the path-factor-implied predictions from the main sample, though the S&P 500 and long-forward-rate responses diverge somewhat from predicted magnitudes. The authors read the results as showing that FOMC statements are not an independent policy instrument but work by shaping financial-market expectations of future funds-rate actions, with a secondary possibility that the path factor also reflects revisions to expected output and inflation; the policy implication they draw is that the FOMC retains substantial ability to move long-term rates through a state-contingent path for the funds rate, and so is “largely unhindered” even when the current funds rate is at or near zero, consistent with Reifschneider-Williams (2000) and Eggertsson-Woodford (2003).

Targeting Constant Money Growth at the Zero Lower Bound

This 2018 International Journal of Central Banking paper by Michael T. Belongia and Peter N. Ireland asks two linked questions: could the Federal Reserve have maintained a constant rate of broad (Divisia) money growth once the federal funds rate hit its zero lower bound in 2008-09, and would doing so have produced a stronger, more rapid recovery than the unconventional policies (quantitative easing, forward guidance) actually pursued? The authors build a six-variable structural VAR over 2000:Q1-2016:Q2 (66 quarterly observations, 2 lags) in the GDP deflator, real GDP, an interest rate (either the Wu-Xia (2016) shadow federal funds rate or the two-year Treasury yield), Divisia M1 or M2 (Center for Financial Stability measures), the Divisia user-cost index, and the Gilchrist-Zakrajsek excess bond premium, estimating the system four times (two interest-rate measures times two money measures). Rather than the standard lower-triangular (Cholesky) identification – whose money-demand equation produces an implausible negative income elasticity, a supply-side rather than demand-side pattern – they identify the model with a non-recursive scheme (extending Belongia and Ireland 2015, 2016b) that lets the policy rule respond to money alongside prices and output, ties money demand to real balances relative to income with the Divisia user cost (not the interest rate) as opportunity cost, and lets a monetary-system equation link user cost to both interest rates and real balances; this non-recursive model imposes three testable over-identifying restrictions that a likelihood-ratio test fails to reject in all four specifications (p-values 0.28-0.71). Using the non-recursive SVAR to simulate constant-money-growth counterfactuals from 2008:Q1 forward while holding all other historical shocks at their realized values, the authors find that, although the faster-money-growth counterfactual would have required interest rates to fall more quickly at the onset of the recession than they actually did, the counterfactual rate paths lie above the historical path from 2011 onward, and (in the milder constant-historical-rate-growth scenario) the shadow rate never falls as far below zero as the actual historical path eventually does. A faster-money-growth counterfactual (12% for M1, 8.5% for M2, versus average historical rates of about 9% and 6.75%) raises average real GDP growth from its historical 1.19% to 1.67% per year over 2008:Q1-2016:Q2 (from 2.04% to 2.59% during the 2010:Q1-2016:Q2 recovery period specifically, in the benchmark shadow-FFR/M1 specification) while leaving inflation essentially unchanged (GDP deflator growth of 1.63% under both the historical and counterfactual paths in the recovery period); a slower-money-growth counterfactual (6% M1 / 5% M2), by contrast, would have cut average real GDP growth to roughly 0.57% and would have required even lower nominal rates than actually observed, which the authors interpret – following Friedman and Schwartz (1963) on the Great Depression – as reflecting excessively tight monetary policy despite low rates. These conclusions are robust across all four VAR specifications, though a price puzzle (a short-run rise in the price level after a contractionary shock) persists throughout, and monetary policy shocks account for only about 3-4% of GDP-deflator forecast-error variance versus roughly 20% of real GDP variance at four-to-five-year horizons, leaving the model’s inflation channel comparatively weak.

Term Structure Modeling with Supply Factors and the Federal Reserve's Large-Scale Asset Purchase Programs

This 2013 International Journal of Central Banking paper by Canlin Li and Min Wei asks whether changes in the supply of Treasury securities and agency mortgage-backed securities (MBS) affect nominal Treasury yields, and uses the answer to evaluate the Federal Reserve’s large-scale asset purchase (LSAP) programs. The authors build a no-arbitrage affine Gaussian term-structure model, motivated by the Vayanos-Vila (2009) preferred-habitat framework, whose state vector consists of two observable yield factors (the level, proxied by the 5-year yield, and the slope, the 5-year-minus-1-month spread, which together capture over 99% of yield variation) plus three observable supply factors: the Treasury ten-year-equivalents-to-GDP ratio, the agency-MBS par-to-GDP ratio, and MBS average duration. The model is deliberately restricted so the short rate loads only on the yield factors and supply factors carry zero own risk premium, meaning supply shocks affect yields only through the term premium and not through interest-rate expectations (the signaling channel is shut down by construction); the model is estimated by a two-step Ang-Piazzesi (2003) procedure on monthly pre-crisis data from March 1994 to July 2007. In-sample, supply factors are significantly and positively related to the term premium (reduced-form R-squared up to 0.89), a one-percentage-point decline in the Treasury ten-year-equivalents-to-GDP or MBS par-to-GDP ratio lowers the 10-year Treasury yield by roughly 10 basis points, a one-year shortening of average MBS duration lowers it by roughly 7 basis points, and supply factors account for about 9% (5-year) and 20% (10-year) of conditional term-premium variance at a 60-month horizon. Applying the estimated model out-of-sample to evaluate the Fed’s 2008-2012 asset purchases, and using the authors’ preferred approach that treats each program as a gradually implemented supply shock that investors expect to be partly reversed by future asset sales, the paper finds LSAP1 lowered 2-/5-/10-year Treasury yields by about 16/52/60 basis points, LSAP2 by about 2/13/19 basis points, and the Maturity Extension Program (MEP) by about 2/13/19 basis points, for a combined 10-year effect of roughly 100 basis points — the paper’s headline number. The authors are explicit that the model captures only the term-premium channel of LSAPs by construction, that estimates are sensitive to assumptions about the pace and timing of expected future asset sales, and that the model is fit on a pre-crisis sample and then applied out-of-sample to the very different 2008-2012 period.

The Aggregate and Country-Specific Effectiveness of ECB Policy: Evidence from an External Instruments VAR Approach

This 2020 International Journal of Central Banking paper by Lucas Hafemann and Peter Tillmann studies how ECB monetary policy transmits to the euro area as a whole and, separately, across individual member countries, using monthly data from 2002:M1 to 2016:M10 – a period spanning both conventional policy and unconventional measures (the asset purchase programme, TLTROs) during which short rates sat at the effective lower bound. Because the policy stance in this period is “no longer appropriately summarized by the short-term policy rate” and Cholesky or sign-restriction schemes are hard to justify for fast-moving financial variables, the authors identify the shock with an external instrument in a proxy-SVAR framework (following Stock-Watson 2012, Mertens-Ravn 2013, and Gertler-Karadi 2015): the daily change in the German 10-year government bond yield on ECB Governing Council meeting days, augmented with three special-event days (the May 2010 and August 2011 SMP announcements and Draghi’s July 2012 “whatever it takes” speech). The instrument clears a weak-instrument check (first-stage F = 10.44, above the Stock-Wright-Yogo threshold of 10) and an event-study validation showing it moves the EURIBOR future (beta = 0.890) and corporate bond spreads (beta = 0.192) with the expected sign. In a baseline monthly four-variable VAR (log industrial production, log HICP, a corporate BBB-minus-AA bond spread proxying the external finance premium, and a Wu-Xia shadow short rate, with the oil price entered exogenously to avoid the price puzzle), an expansionary shock normalized to a 25-basis-point drop in the shadow rate significantly raises output and prices and narrows the corporate spread – evidence of a credit channel that disappears under a comparable Cholesky-identified VAR, where the spread does not react significantly. Extending the system one variable at a time shows the real exchange rate depreciates on impact, a house-price proxy (the HICP rent component) rises, and bank lending standards relax while credit demand rises, yet – a “credit puzzle” – total loan volume to nonfinancial corporations actually falls in the post-2008 sample, while unemployment and equity prices move with the expected sign but are statistically insignificant (cannot rule out zero) over the full horizon. Decomposing the instrument via a Jarocinski-Karadi (2018)-style principal-component analysis of announcement-day yield and equity changes (the first two components jointly explain 92% of the variance) into a pure policy shock and a central-bank information shock shows the baseline results are reproduced by the pure policy component, so the findings are robust to stripping out information effects. Feeding the identified aggregate shock into Jordà (2005) local projections for ten member countries (covering more than 95% of euro-area GDP) plus a synthetic euro area reveals substantial cross-country heterogeneity beneath the homogeneous aggregate response: industrial production and consumer prices respond similarly almost everywhere, but unemployment falls significantly only in core countries (Germany, France, the Netherlands) and not in the periphery (Italy, Spain, Greece), stock prices deviate negatively in several countries after about ten months, and loan volumes rise significantly only in Germany, Austria, and Greece. The authors read this as evidence that impaired transmission through bank lending and equity markets – concentrated in periphery countries with stressed banking systems – and labor-market frictions drive the uneven effectiveness of a “one-size-fits-all” ECB policy, while explicitly cautioning that their country-level results are “purely positive” and that “we should be careful not to overemphasize the normative implications.”

The Financial Market Effects of the Federal Reserve's Large-Scale Asset Purchases

This 2011 International Journal of Central Banking paper by Gagnon, Raskin, Remache, and Sack provides the founding empirical assessment of the Federal Reserve’s first large-scale asset purchase program (LSAP1, later known as QE1): between December 2008 and March 2010 the Fed bought more than $1.7 trillion of longer-term Treasury, agency debt, and agency mortgage-backed securities, roughly 22% of the $7.7 trillion stock of those securities outstanding (about $850 billion, or over 20% of the $3.7 trillion stock, measured in duration-equivalent “ten-year equivalents”). The authors argue the purchases worked mainly through a portfolio-balance channel — removing duration from the market forces the private sector to hold less of that duration risk, bidding up prices and compressing term premiums across asset classes, including on securities the Fed never bought — rather than through a signaling channel that would work by lowering expected future short-term rates; MBS purchases additionally reduced prepayment/negative-convexity risk, and an early market-functioning/liquidity channel narrowed unusually wide agency and MBS spreads. Two independent empirical strategies are used. An event study of cumulative one-day changes around an eight-announcement “baseline event set” (November 2008 through November 2009) finds the 10-year Treasury yield fell 91 basis points, the 10-year agency debt yield fell 156 bp, agency MBS yields fell 113 bp, the 10-year Kim-Wright term premium fell 71 bp, the 10-year swap rate fell 101 bp, and the Baa corporate index fell 67 bp, while the 2-year Treasury yield fell only 34 bp — a pattern the authors read as showing the effect worked mainly through the term premium rather than expected future policy rates, since the two announcements that also carried forward-guidance language moved the Kim-Wright one-year-ahead instantaneous rate by only about 4 bp each. A separate time-series regression of the 10-year Kim-Wright term premium (monthly, January 1985-June 2008) on cyclical, uncertainty, and net public debt-supply variables, estimated by OLS and dynamic OLS exploiting a cointegrating relationship, implies the full $1.725 trillion LSAP program (about 12% of 2009 GDP) lowered the 10-year term premium by roughly 38-82 basis points depending on specification — a range the authors emphasize “overlaps considerably” with the event-study estimates despite using entirely different data and methods. The net 10-year Treasury yield did not actually fall over the full program window (it rose over 100 bp on non-event days), which the authors attribute to a rising expected fiscal deficit and a strengthening outlook rather than to any reversal of the LSAP effect. International comparisons show the UK’s 2009-10 gilt purchases produced a “strikingly similar” roughly 100 bp decline in 5-25-year yields, while Japan’s smaller and shorter-duration 2001-06 purchases had little effect on longer-term yields.