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

Once the federal funds rate (FFR) is constrained at the zero lower bound (ZLB), it stops being informative about the stance of monetary policy, and existing “shadow rate” alternatives – built on term-structure models in the Black (1995) tradition, such as Krippner (2013a) and Wu and Xia (2016) – read the stance of policy off the Treasury yield curve alone. Lombardi and Zhu instead construct a shadow policy rate that is “essentially statistical”: it does not depend on any term-structure or other formal economic model, but is estimated from a dynamic factor model fit to a broad monetary data set – interest rates, monetary aggregates, Federal Reserve balance-sheet assets, and reserves – so that it directly incorporates the balance sheet rather than inferring stance only from bond yields. The resulting index maps onto the same scale as the FFR so it can be used, and interpreted, exactly like the funds rate before and after the ZLB binds.

The data set is monthly, January 1970 to June 2016, organized into four blocks. Block 1 (interest rates): the effective FFR, U.S. Treasury bill rates at one, three, and six months, Treasury bond yields at one, two, five, ten, and twenty years, and the overnight-indexed-swap (OIS)-three-month-LIBOR spread. Block 2 (monetary aggregates): the monetary base (M0), M1, M2, and MZM. Block 3 (Federal Reserve balance-sheet assets): total assets, total securities held outright, their average maturity, and the percentage of long-term Treasury holdings under five years, under ten years, and over ten years. Block 4 (balance-sheet liabilities): total, excess, and required reserves. Quantity variables in blocks 2-4 enter as year-on-year rates of change to ensure stationarity.

The model is a dynamic factor model with an arbitrary pattern of missing data (observable series load on r common factors via a measurement equation with idiosyncratic noise, and the factors follow a VAR(p) transition equation), estimated with the generalized EM algorithm and Kalman filter/smoother of Bańbura and Modugno (2014), building on Doz-Giannone-Reichlin (2011, 2012) and Dempster-Laird-Rubin (1977). The number of factors (eight) is chosen by the Hallin-Liska (2007) information criterion using only the pre-crisis sample (so the joint dynamics used for model selection are fully observed), and the lag order (two) is chosen by the Schwarz information criterion (the Akaike criterion agrees). To construct the shadow rate itself, the FFR and other short rates that hit the ZLB are treated as missing from the date each reaches its practical floor – the FFR, three-month, and six-month bill rates from December 2008 (when they stood at 0.16, 0.03, and 0.26 percent respectively), and one- and two-year Treasury yields from November 2009 (0.31 and 0.80 percent) – and the Kalman smoother imputes their values from the historical correlation structure with the remaining, still-observed monetary variables. The authors describe the resulting shadow FFR as a “weighted average” of all the monetary information in the data set, with weights set by historical correlations with the funds rate.

Eight factors explain 90.5 percent of the total variance of the data set, just above the conventional 90-percent rule of thumb. The first three factors alone account for almost 70 percent of total variance: the first factor (about 38 percent) is strongly associated with the interest-rate block and tracks the FFR closely until the ZLB binds; the second factor (about 20 percent) is mainly driven by the monetary base; and the third factor (about 11 percent) is more correlated with the growth of the Federal Reserve’s outright Treasury securities holdings, adding information on unconventional measures. A fourth factor is linked to M1/M2 and a fifth to the maturity structure of the Fed’s balance sheet, though the paper does not report their variance shares.

The shadow rate tracks the effective FFR closely before the crisis – with only modest deviations in 1974-75 and 1982, both preceding recessions when the authors suggest the actual rate may not have fully captured how loose policy was. After the FFR reaches the ZLB in late 2008, the shadow rate turns negative in early 2009 and, according to the paper’s concluding summary, provides its greatest stimulus over 2011, dropping to below -5 percent in August of that year, before becoming less accommodative and then loosening again starting in October 2012. Its movements track the phases of unconventional policy: it registers a large easing associated with LSAP1 (announced November 2008, reinforced with Treasury purchases in March 2009), edges back toward zero after LSAP1’s completion in March 2010, dips again with LSAP2 (November 2010), rises somewhat once LSAP2 ends in mid-2011 as the Maturity Extension Program (MEP, from September 2011) only partially offsets the halt in outright purchases, falls again with LSAP3 (from September 2012, $40 billion/month in agency MBS, later $45 billion/month in Treasuries), moderates as the “taper tantrum” begins (June 2013) and as tapering is announced (January 2014), reaches roughly zero shortly after purchases are halted (end-October 2014), and rises with the FFR after the December 2015 liftoff.

The Lombardi-Zhu rate, the Krippner (2013a) rate, and the Wu-Xia (2016) rate all indicate sizable ZLB-period stimulus, but their dynamics differ substantially, especially around LSAP1. The Lombardi-Zhu rate shows a large stimulus from LSAP1 starting in late 2008 that both term-structure rates miss: Wu-Xia’s estimate actually points to a tightening over this period, and Krippner’s shows only a slow, moderate decline. The authors attribute this to the fact that term-structure shadow rates are driven entirely by the Treasury yield curve, while LSAP1 purchased mortgage-backed securities and “toxic assets” rather than Treasuries, so it had limited direct impact on Treasury yields even though it plausibly provided real stimulus through portfolio rebalancing and bank balance-sheet relief. At the point purchases were halted altogether at end-October 2014, the Lombardi-Zhu rate had already returned to about 0 percent, while the Wu-Xia rate remained at -2.8 percent (having reached a low of -2.9 percent in August 2014) – a divergence the authors read as the term-structure rate signaling a much easier policy than was actually being withdrawn. A restricted version of their own model using only yield-curve data behaves similarly to the term-structure shadow rates and likewise underestimates the LSAP1 stimulus, which the authors take as evidence that it is the comprehensiveness of the underlying data set – not the factor-model methodology per se – that drives the difference.

Using a simple three-variable VAR (real GDP, inflation, and either the actual or shadow FFR, following the building block of Bernanke and Blinder 1992) and a likelihood-ratio test of whether the funds-rate coefficients differ between the pre- and post-ZLB periods, the authors reject stability when the observed FFR is used (LR = 15.77, p = 0.00) but cannot reject it when the shadow FFR is used (LR = 1.94, p = 0.38). They interpret this as showing that the observed FFR’s relationship with the macroeconomy genuinely broke down once it stopped reflecting policy actions at the ZLB, while the shadow rate’s historical relationship with output and inflation “appears unaltered” – supporting its use as a single, continuous indicator spanning both regimes.

Benchmarked against the Taylor (1993) rule (i = π + 0.5y + 0.5(π-2) + 2) and the Taylor (1999)/“balanced-approach” rule (i = π + y + 0.5(π-2) + 2), computed using CBO output-gap and unemployment-gap measures, the shadow rate’s post-2009 stimulus was broadly consistent with the Taylor (1993) prescription but not sufficient to match the more aggressive Taylor (1999) rule, particularly when the unemployment gap is used as the slack measure. The shadow rate rebounded above zero in May 2010 as LSAP1 wound down, consistent with the Taylor (1999)/output-gap benchmark but leaving a gap relative to the unemployment-gap version; it was pulled back down to align with that benchmark only once LSAP2 (November 2010) was implemented. This bears on Bullard’s (2012, 2013) claim – based on Krippner’s shadow rate – that policy had become “excessively loose” by 2012; the authors note their results “raise some questions” about that assessment, without asserting a definitive rebuttal. The authors are explicit that this exercise is “purely illustrative” and that assessing monetary policy stance and effectiveness is “a daunting task beyond the scope of this paper,” so the evidence “should not be taken as conclusive.”

In both the Bernanke-Blinder (1992) VAR (log real GDP, log GDP deflator, FFR) and the more elaborate Christiano-Eichenbaum-Evans (1996) VAR (adding commodity prices, non-borrowed reserves, and total reserves), estimated on quarterly data from 1970 to March 2016 with four lags under recursive Cholesky identification, monetary policy shocks extracted using the actual FFR are small and only mildly negative after 2008 – wrongly implying that little additional stimulus was provided. Shocks extracted using the shadow FFR instead “clearly indicate sizable easing,” timed with LSAP2 and LSAP3, and even reveal a positive (tightening) shock following the 2014 taper that the actual-FFR-based VAR cannot detect at all. The gap between the two narrows somewhat in the CEE model because it already includes reserve aggregates that partly capture unconventional measures, but the authors conclude that standard VAR-based shock measures using the observed FFR would “severely understate the true extent of monetary expansion” during the ZLB period. A comparison against monetary shocks built from the Krippner and Wu-Xia shadow rates finds the three approaches agree before the ZLB but diverge sharply afterward – the Krippner-based shocks are more volatile with a tightening spike at the end of 2013, and the Wu-Xia-based shocks appear “much more stable and neutral” and register a large stimulus only in mid-2014, which the authors call “rather surprising” given tapering had already been announced by then.

The shadow rate is robust to the choice of lag order – one- and twelve-lag versions both mostly fall within the baseline two-lag model’s 95 percent confidence band. It is more sensitive to the number of factors and to which data are included. A three-factor specification (chosen by the alternative Bai-Ng 2007 criterion, explaining about 70 percent of variance) somewhat underestimates the LSAP1 stimulus though it stays within the confidence band and still captures LSAP2; a one-factor model is “clearly inadequate,” failing to display enough variation to capture most easing programs. On the data side, a restricted data set using only the yield-curve block behaves like a term-structure shadow rate and misses the LSAP1 stimulus, while a restricted set adding monetary aggregates but excluding the Fed balance sheet stays closer to the baseline (especially after 2011) but still understates the extent of asset-purchase stimulus. The authors also report, without detailed tables, that excluding the 1970s and starting estimation in 1985 left results “virtually unchanged.”