Targeting Constant Money Growth at the Zero Lower Bound

Belongia and Ireland ask whether the Federal Reserve could have maintained a constant rate of broad (Divisia) money growth once the federal funds rate hit the zero lower bound in 2008-09, and whether doing so would have produced a stronger and more rapid recovery than the unconventional policies (QE, forward guidance) actually used – and they answer “yes” to both. The motivation is a documented tension: while the Fed’s balance sheet expanded enormously during QE (the adjusted monetary base rose from $872 billion in August 2008 to $4,097 billion in August 2014, with roughly 84% of that increase accounted for by excess reserves), Divisia M1 and M2 growth was “consistently inconsistent” over the same period – averaging a moderate 9% and 6.75%, respectively, over 2008:Q1-2016:Q2, but falling after QE1 ended and after brief suspensions of QE2, rather than tracking the base expansion. The paper’s own explanation, following Ireland (2014), is that paying interest on reserves shifted banks’ demand for reserves rightward, letting the base expand without generating proportional broad money growth – so QE’s effect on broad money was largely “sterilized.” This sets up the paper’s test: would a simpler policy of targeting steady money growth, implemented with the same tools, have worked better?

The model is a six-variable structural VAR in the log GDP deflator, log real GDP, an interest rate, log Divisia money, the Divisia user-cost index, and the Gilchrist-Zakrajsek excess bond premium, estimated quarterly over 2000:Q1-2016:Q2 (66 observations) with 2 lags. The interest rate is measured two ways – the Wu and Xia (2016) shadow federal funds rate, which remains informative below zero, or the two-year Treasury yield as an alternative ZLB-robust measure – and money is measured two ways – Divisia M1 or Divisia M2 (Center for Financial Stability data, following Barnett et al. 2013) – so the model is estimated four times in total. The two-lag choice is explicitly a function of the short sample: with only 66 quarterly observations and six variables, the VAR already has 99 autoregressive parameters to estimate before the contemporaneous (A) matrix, and the paper notes this implies large standard errors for some parameters. All variables enter in logarithms except the interest rate, user cost, and excess bond premium, which enter as decimals (e.g., a shadow rate of +5% is 0.05).

Under the standard lower-triangular (Cholesky-style) ordering – prices, then output, then the interest rate, then money, then user cost, then the excess bond premium – the estimated money-demand equation implies a statistically significant negative coefficient on real GDP, meaning nominal money and real output move inversely. That is the signature of a money-supply relationship, not a demand relationship, and it arises because the triangular scheme forces an assumption of infinite money-supply elasticity that confounds supply and demand. This flaw in the workhorse identification is the direct motivation for the paper’s alternative, non-recursive scheme.

The non-recursive model (extending Belongia and Ireland 2015, 2016b) replaces the triangular ordering with three economically motivated cross-equation restrictions: a monetary policy rule in which the Fed responds to money alongside prices and output (generalizing a Taylor 1993 rule), a money-demand equation for real balances relative to income in which the opportunity cost is the Divisia user-cost index rather than the interest rate, and a monetary-system equation in which the user cost depends on both the interest rate and real balances. This imposes 18 restrictions against the 15 needed for identification, yielding three over-identifying restrictions that are testable against the triangular model by a likelihood-ratio test; across the four specifications the test p-values are 0.65 (shadow FFR/M1), 0.71 (shadow FFR/M2), 0.28 (two-year/M1), and 0.58 (two-year/M2) – in every case failing to reject the non-recursive restrictions, so the added structure “provides no sacrifice in statistical fit relative to the triangular model.” Global identification of the non-recursive system is separately verified in the appendix using the rank conditions of Rubio-Ramirez, Waggoner, and Zha (2010).

In the benchmark shadow-FFR/Divisia-M1 specification, a one-standard-deviation contractionary monetary policy shock raises the shadow rate by about 25 basis points over the first four quarters, stays elevated for more than two years, real GDP falls with a lag over three to four years, and the money stock falls with large, persistent effects – while the GDP deflator initially rises (a “price puzzle”) before falling more persistently later. The price puzzle is smaller under the shadow-rate specification than under the two-year-Treasury specification, and it does not disappear even when commodity prices are added to the system. In variance-decomposition terms, monetary policy shocks explain roughly 20% of real GDP’s forecast-error variance at four-to-five-year horizons (23.4% at 16 quarters and 17.0% at 20 quarters for shadow FFR/M1; 21.4% at 16 quarters for shadow FFR/M2) but only about 3-4% of the GDP deflator’s variance across specifications and horizons – so the model identifies a real-activity channel much more sharply than an inflation channel.

The non-recursive SVAR’s estimated monetary policy shocks are mostly positive (i.e., contractionary) during 2009 and 2010, which the authors interpret as the estimated policy path having been unexpectedly tight relative to what the model would have prescribed; only from 2011-2012 onward does the model suggest the Fed’s actions began lending “full support to the economic recovery.” This historical-shock pattern is what motivates asking whether a steadier, rules-based money-growth path over the same period would have done better.

Simulating three constant-money-growth counterfactuals from 2008:Q1 forward with all other historical shocks held at their realized values, the paper finds that a faster-money-growth path (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, and from 2.04% to 2.59% per year over the 2010:Q1-2016:Q2 recovery window specifically, in the benchmark shadow-FFR/M1 case. Crucially, this faster growth in output comes with essentially unchanged inflation: the GDP deflator averages 1.63% under both the historical path and the faster-money-growth counterfactual during the recovery period. A more conservative counterfactual that simply holds money growth at its actual historical average rate (9% M1 / 6.75% M2) but smooths out its fluctuations produces GDP-deflator and real-GDP paths similar to the historical ones. In both of these counterfactuals, the implied interest-rate paths lie above the historical path from 2011 onward, though achieving the faster-growth scenario would still have required interest rates to fall more quickly than they actually did at the onset of the recession; the paper notes only for the milder constant-historical-rate scenario that the shadow rate never falls as far below zero as the actual historical path eventually does.

A slower-money-growth counterfactual (6% for M1, 5% for M2) would have cut average real GDP growth to roughly 0.57% per year over 2008-2016 in the shadow-FFR/M1 case (versus the historical 1.19%), and it would have required lower nominal interest rates than were actually observed. The authors read this as a case in which persistently low observed rates would have reflected excessively tight monetary policy rather than easy policy – explicitly invoking the Friedman and Schwartz (1963) reading of the Great Depression, in which low nominal rates coexisted with a contractionary stance. The contrast between this scenario and the faster-growth scenario is the paper’s central argument for feasibility: money growth, not the level of the policy rate itself, is what determines whether policy is actually tight or easy at the zero lower bound.

The authors flag four main caveats: the short 66-observation sample forces a constrained 2-lag specification with large standard errors on some parameters; a price puzzle persists across every specification, including when the excess bond premium or commodity prices are added to the system; the model does not attempt to separate shocks originating in the non-bank financial sector from other non-policy disturbances, since the excess bond premium enters only as a composite “information sector” variable; and the counterfactual exercise relies on a constant-coefficient SVAR, which is exposed to the Lucas critique in the event of a large regime change (though the authors note, following Leeper and Zha 2003, that policy paths remaining small relative to historically realized shocks – as their counterfactuals do – are less likely to trigger such instability). They also note that monetary policy shocks’ weak explanatory power for the GDP deflator (3-4% of forecast-error variance) is consistent with Reynard (2007)’s argument that the lag between money and inflation is too long to show up cleanly at conventional VAR horizons.