A reconsideration of money growth rules

The paper asks whether a money growth rule — one that adjusts the growth rate of the money supply in response to the output gap — could have delivered macroeconomic stabilization comparable to the Federal Reserve’s actual interest-rate (Taylor rule) policy, including through the 2009:1-2015:4 episode when the federal funds rate was pinned near zero. The authors frame this as testing whether abandoning interest-rate management in favor of targeting money growth “should be added to the list of viable policy alternatives,” motivated partly by the fact that a money growth rule need not run into the zero lower bound the way an interest-rate rule does.

The model is a New Keynesian DSGE model in which real money balances (Divisia M2, deflated by the GDP deflator and detrended by productivity) enter the representative household’s utility function directly, alongside consumption habit formation and disutility of labor. Real balances are subject to quadratic portfolio-adjustment costs (following Nelson 2002 and Andrés et al. 2004, 2009), and the implied money-demand curve relates real balances to a satiation level, the interest semi-elasticity, and the (inverse) opportunity cost of holding money, 1/r_t. On the firm side, intermediate-goods producers face Rotemberg (1982) quadratic price-adjustment costs with a backward-looking indexation parameter, and a cost-push shock behaves as an AR(1) markup shock. In the purely forward-looking special case (no habits, no indexation), the model collapses to a standard IS curve and Phillips curve in which monetary policy affects the economy solely through the current and expected future path of the short-term nominal interest rate.

The model is estimated by Bayesian methods (randomized-block Metropolis-Hastings, following Chib and Ramamurthy 2010) on quarterly U.S. data from 1983:1 to 2019:4, using the Kulish et al. (2017) algorithm to splice in a separate ZLB regime for 2009:1-2015:4, during which the federal funds rate is dropped from the observables and replaced by the constraint that the policy rate equals its lower bound. Expected durations of the ZLB episode are treated as time-varying parameters, estimated using an 80%/20% weighted blend of survey-based forecasts (Blue Chip Financial Forecasts for 2009-2010, the New York Fed Primary Dealers Survey for 2011-2015) and a uniform prior over 1-23 quarters; the model is solved by standard log-linearization away from the ZLB and by a time-varying backward-recursion solution during it, both nested inside a single Kalman filter.

The Bayesian posteriors move away from prior means toward higher habit formation (mode 0.655), lower price indexation (mode 0.185), more elastic labor supply (mode 0.628), and a much flatter Phillips curve (slope mode 0.0153) than the priors implied, alongside high interest-rate smoothing (mode 0.862) and roughly balanced policy responses to inflation (mode 0.245) and the output gap (mode 0.275). Money-demand shocks and preference shocks are both estimated to be highly persistent (modes of 0.9815 and 0.9308, respectively), a feature that matters for how much volatility a policy rule can or cannot absorb.

Only marginally: the log marginal likelihood of the benchmark Taylor rule is 2412.7, and augmenting it with a contemporaneous money-growth term raises this only to 2413.3, with the estimated money-growth response coefficient’s posterior mode a modest 0.0605 (16-84 percentile interval [0.0433, 0.0939]). Adding lagged rather than contemporaneous money growth actually lowers the marginal likelihood (to 2397.7 or 2394.9 depending on specification), leading the authors to conclude that “the contemporaneous money growth rate adds information” to the interest-rate rule, but only in modest amounts, while lagged money growth adds none.

Very little: variance decompositions show monetary-policy shocks account for just 0.7% of output-growth variance and 5.6% of output-gap variance away from the ZLB, with output growth instead dominated by technology shocks (75.4%) and preferences (23.6%), inflation dominated by cost-push shocks (75.9%) and preferences (23.6%), and the nominal interest rate dominated by preference shocks (95.0%). Money growth variance itself is split across preference (43.7%), technology (17.3%), and money-demand (35.9%) shocks. Consistent with this, the model attributes the Great Recession’s declines in inflation and interest rates mainly to a sequence of large adverse preference shocks, with unfavorable productivity shocks also present throughout the post-2008 period — a reading the authors note is consistent with Aruoba et al. (2018), Campbell et al. (2016), and Gust et al. (2017).

Forward-guidance effects are largest during 2011-2013, when expected ZLB durations were longest; for 2013:Q4 specifically, the model implies that a further one-quarter increase in the expected duration of the zero-rate episode would have lifted inflation by almost 50 basis points and the output gap by more than 25 basis points. The authors note these effects do not become implausibly large, consistent with related findings in Carlstrom et al. (2015), Del Negro et al. (2015a), Campbell et al. (2016), and Harrison (2015).

A flexible money growth rule of the form mu-hat_t = mu-hat_{t-1} - 0.125 x-hat_{t-1} — identified by a grid search over rule coefficients as minimizing macroeconomic volatility while limiting the duration of negative implied interest rates — produces standard deviations of output growth (2.5511 median), inflation (1.1226 median), and the output gap (0.7095 median) that closely approximate those under the estimated Taylor rule (2.3762, 0.9774, and 0.5481, respectively). The output gap becomes somewhat, but “not dramatically,” more volatile under the money rule. Critically, the money growth rule also generates a much shorter and more moderate episode of implied negative interest rates than the seven-year span over which the actual federal funds rate sat near zero, because raising money growth when output is weak allows the model’s notional interest rate to fall below zero within a well-defined equilibrium rather than being constrained at the bound.

Holding Divisia M2 growth exactly constant (all three money-rule feedback coefficients set to zero) sharply amplifies volatility: the standard deviation of output growth rises to a median of 3.6423 — more than 50% larger than under the estimated Taylor rule — and the standard deviation of inflation rises from 0.9774 to 1.8871. The authors read this as confirming earlier results in Ireland (2000), Collard and Dellas (2005), and Galí (2015) that fixed money growth performs poorly, and argue it shows the flexible rule’s gains come specifically from its modest, persistent response to the output gap — which behaves similarly to Taylor-rule interest-rate smoothing and partially offsets the large, persistent money-demand shocks (posterior AR(1) coefficient mode near 0.98) that would otherwise pass straight through into output and inflation volatility under a rigid constant-growth regime.