Michael T. Belongia | Macro Paper Warehouse

A reconsideration of money growth rules

This 2022 Journal of Economic Dynamics & Control paper by Michael Belongia and Peter Ireland asks whether a policy rule that steers the growth rate of money, rather than the short-term nominal interest rate, could have delivered macroeconomic stabilization comparable to the Federal Reserve’s actual interest-rate policy — including through the 2009:1-2015:4 zero-lower-bound (ZLB) episode. They build a New Keynesian DSGE model with real Divisia M2 balances entered directly in household utility (with quadratic adjustment costs), habit formation in consumption, Rotemberg price-adjustment costs with backward-looking indexation, and five structural shocks (preference, productivity growth, money demand, cost-push, and monetary policy), and estimate it by Bayesian methods on quarterly U.S. data from 1983:1-2019:4, using the Kulish et al. (2017) piecewise-linear algorithm to handle the ZLB period (during which the funds rate is dropped from the observables and time-varying expected ZLB durations, informed by survey forecasts, are estimated as parameters). Comparing log marginal likelihoods, they find that augmenting the estimated Taylor rule with a contemporaneous money growth term raises the fit only slightly (2412.7 to 2413.3, with the money-growth response coefficient’s posterior mode a modest 0.0605), while adding lagged money growth actually lowers it — money growth adds a little information but not much on top of the interest-rate rule. Variance decompositions show monetary-policy shocks account for only 0.7% of output-growth variance and 5.6% of output-gap variance, with productivity, preference, and cost-push shocks dominating instead, and the model attributes the Great Recession’s declines in inflation and interest rates mainly to adverse preference and productivity shocks. The paper’s central counterfactual result is that a flexible money growth rule of the form mu-hat_t = mu-hat_{t-1} - 0.125 x-hat_{t-1} (found by grid search to minimize macroeconomic volatility and ZLB-equivalent duration) generates standard deviations of output growth (2.5511), inflation (1.1226), and the output gap (0.7095) that closely approximate those implied by the estimated Taylor rule (2.3762, 0.9774, and 0.5481 respectively), while producing a much shorter and milder episode of negative implied interest rates than the actual seven-year ZLB period. By contrast, a strictly constant money growth rule (all feedback coefficients set to zero) sharply amplifies volatility, raising the output-growth standard deviation to 3.6423 (more than 50% larger than under the Taylor rule) and the inflation standard deviation to 1.8871, confirming earlier findings by Ireland (2000), Collard and Dellas (2005), and Galí (2015) that fixed money growth performs poorly. The authors conclude that a flexible, output-gap-responsive money growth rule — not a rigid quantity-theoretic constant-growth rule — belongs on the list of policy alternatives capable of avoiding the ZLB while matching Taylor-rule-level stabilization performance.

Measurement Matters: Recent Results from Monetary Economics Reexamined

This 1996 Journal of Political Economy paper by Michael T. Belongia asks a narrow but consequential question: do the qualitative conclusions of recent monetary economics depend on whether money is measured as a conventional simple-sum aggregate (just adding up the dollar face values of currency, checking deposits, savings deposits, and so on) or as a Divisia aggregate (which weights each component by its expenditure share in the flow of monetary services, using the Barnett 1981 user-cost formula, so that a dollar of a low-yield, highly liquid asset counts differently from a dollar of a higher-yield, less liquid one)? Rather than proposing new theory, the paper is a comparative replication study: it takes five previously published, prominent empirical results in monetary economics and re-runs each one twice, once with the original simple-sum aggregate and once substituting a Divisia (or Divisia M1-plus) aggregate in its place, using U.S. quarterly data mostly spanning 1960:2-1992:4 (monthly for the fifth case). In four of the five cases the qualitative conclusion flips or is substantially altered by the choice of aggregate: extracted money innovations from the De Long-Summers (1988)/Rotemberg (1993) equation fit similarly well by R-squared (0.36 for simple-sum M1 versus 0.23 for Divisia M1) but diverge sharply at business-cycle turning points (1989:3 and 1990:3); Cover’s (1992) test of symmetric effects of positive versus negative money shocks rejects the symmetry null in 5 of 6 specifications for simple-sum M1 (Wald chi-square roughly 25.3-43.5) but cannot reject it in any specification for Divisia M1 or Divisia M1-plus (chi-square roughly 1.01-1.03); the Kydland-Prescott (1990) cyclicality exercise finds that simple-sum M1 does not behave procyclically (correlations with the cycle are small but uniformly positive, peaking around 0.35) while Divisia M2 and Divisia M1-plus are strongly procyclical (contemporaneous correlations of about 0.48 and 0.47 with real output, peaking near 0.70 and 0.65 when leading the cycle by two quarters), a divergence that Belongia shows is stable across the 1960-79 and 1970-89 subsamples for the procyclical measures; and in Stock-Watson/Friedman-Kuttner predictive-power VARs using the T-bill rate, Divisia M1-plus is the only aggregate with statistically significant F-statistics for predicting output (industrial production) at multiple sample end-dates (F = 4.23 for the sample through 1985:12 and F = 3.76 for the longer sample through 1990:12, both with six lags of money), with simple-sum aggregates performing poorly, though none of the money measures — including Divisia M1-plus — shows a significant effect when the commercial paper rate is used instead of the T-bill rate. Belongia argues the mechanism is that simple-sum aggregation implicitly assumes perfect substitutability among monetary assets, a condition that Hicks (1946) aggregation theory requires but that is violated once components pay different yields, and that this measurement error became especially acute after the 1980 Depository Institutions Deregulation and Monetary Control Act introduced interest-bearing NOW accounts. The paper is explicit that this is comparative replication of five results the author judged prominent, not a representative or exhaustive sample, that it identifies no structural monetary policy shock, and that its sample ends in 1992:4, well before the near-zero-rate period when simple-sum and Divisia measures would be expected to diverge most.

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.

The Barnett critique after three decades: A New Keynesian analysis

This 2014 Journal of Econometrics paper by Michael Belongia and Peter Ireland asks whether Barnett’s (1980) decades-old critique of simple-sum monetary aggregation – that adding up the nominal values of different liquid assets as if they were perfect substitutes is theoretically inconsistent with monetary aggregation theory – still applies inside a fully modern, dynamic, stochastic New Keynesian (DSGE) model. The authors build a calibrated (not estimated) NK model in which a representative household derives liquidity services from both currency and interest-bearing bank deposits through a CES aggregator (governed by a substitution elasticity omega and a steady-state currency-share parameter v), and in which a representative bank sets deposit rates through a zero-profit condition tied to a reserve ratio and a financial-sector cost shock. Using a standard quarterly Kydland-Prescott calibration (beta=0.99, a markup of 20%, benchmark omega=1.5, v matched to US M2-to-consumption and currency-to-M2 ratios over 1959-2009, and a benchmark Taylor rule with interest-smoothing 0.75 and an inflation-response coefficient of 0.30), the authors simulate impulse responses to six structural shocks – money demand, household preference, technology, bank reserve-ratio (“reserves demand”), deposit-servicing cost, and monetary policy – and compare three measures of money: the model’s true theoretical aggregate, a Divisia (Tornqvist-Theil) index built from time-varying expenditure shares, and a conventional simple-sum aggregate. The central finding is that the properly weighted Divisia quantity index tracks the true monetary aggregate’s impulse responses so closely that, plotted together, “the two lines would appear indistinguishable” (p. 11), and this holds across all six shocks and across a wide range of substitution elasticities (omega = 0.10 to 5.0) – a result the authors attribute to Diewert’s (1978) theorem that the Tornqvist-Theil Divisia index is a second-order approximation to any linear-homogeneous aggregator regardless of its true functional form or parameter values. By contrast, the simple-sum aggregate – which implicitly weights currency and deposits 1:1 as perfect substitutes – diverges substantially from the true aggregate, and can even differ in the sign of its response, especially following reserve-ratio shocks, deposit-cost shocks, and monetary policy shocks; an analogous Divisia-versus-simple-weighted-average contrast holds on the price (opportunity-cost) side of money as well. The simulations further show that under the benchmark backward-looking Taylor rule, financial-sector shocks generate persistent output declines that ordinary interest-rate policy cannot offset, because the underlying disturbance is a change in the money multiplier rather than in inflation; adding a very large output-gap response coefficient to a backward-looking Taylor rule can insulate output from all five non-technology shocks while still allowing an efficient output response to a technology shock, whereas pushing the same coefficient into a forward-looking rule specification instead produces indeterminacy. All reported results are calibration/simulation outcomes from a theoretical model – the paper contains no empirical estimation.