The future of monetary aggregates in monetary policy analysis

Nelson poses four questions about money’s role in New Keynesian (NK) monetary policy models – two about money and inflation, two about the transmission mechanism – and argues the answer to all four is “yes,” though only in a qualified sense. The questions are: (a) do NK models imply that inflation is, in the long run, governed by money growth as the quantity theory holds; (b) can inflation dynamics in these models be given a conventional quantity-theory interpretation; (c) is the basic transmission mechanism of monetary policy in these models the same as in pre-1990s models that gave money a more explicit role; and (d) are there aspects of the pre-1990s transmission mechanism that could usefully be added to NK models. Nelson contrasts his conclusion with two polar readings found elsewhere in the literature – that current models represent a decisive and justified rejection of quantity-theory analysis (answers all “no”), or that current models are secretly monetarist already (answers (a)-(c) “yes,” (d) “no”). His own reading is that current NK models are “partially monetarist” already, but that further insights from monetarist analysis – particularly a richer money demand specification – could still be fruitfully added.

Nelson argues AEMP survives as a steady-state, not a contemporaneous, proposition: even though the three-equation system (an IS curve, an expectations-augmented Phillips curve, and a Fisher equation) contains no explicit money term, its constant terms still imply that a sustained g-percentage-point change in inflation requires an equal change in the steady-state money growth rate. This follows McCallum’s (2001) demonstration that adding a conventional money demand function to the system does not change the solution for inflation, yet the model’s long-run behavior still pins inflation to money growth. Nelson adds to McCallum’s point that this long-run money-inflation link deserves special attention relative to other steady-state relations (such as the Fisher relation between nominal rates and inflation, which Galí, 2002, argues deserves no special status): unlike the Fisher relation, which has a direct counterpart in the dynamic equation (3), the money-growth/inflation link is “buried” in constant terms and has no counterpart at all in the equations describing inflation dynamics around the steady state – so central banks setting the steady-state inflation target cannot infer this link merely from the short-run model.

Nelson argues De Grauwe and Polan’s rejection of AEMP for low-inflation countries is undermined by three problems: their cross-country regressions implicitly assume a constant steady-state velocity trend across countries, which advocates of AEMP never claimed; their money data (IMF International Financial Statistics M1/M2 series) are subject to statistical breaks from reclassification and interest-payment changes that Friedman and Schwartz (1970) had already flagged as reasons to prefer currency in cross-country work; and their regressions of inflation on same-period or multi-year-averaged money growth do not properly allow for the lag between money growth and inflation that Friedman’s own writings emphasize. He also disputes their interpretation of a negative money-growth/velocity-growth correlation as ipso facto inconsistent with AEMP, noting that a protracted post-disinflation fall in nominal interest rates can generate exactly this pattern (higher money growth, slower velocity growth, unchanged inflation) while remaining, in Wicksell’s words, “in complete agreement with the Quantity Theory.”

Using Batini and Nelson’s (2001) US data for January 1970-August 2001, Nelson reports that annual CPI inflation regressed on contemporaneous M2 growth alone gives a small, marginally significant coefficient of 0.211 (Newey-West s.e. 0.118) with R²=0.052, while inflation regressed on M2 growth lagged two, three, and four years gives individual coefficients of 0.257, 0.376, and 0.182, summing to 0.814 (s.e. 0.190), with R²=0.555. He reads the weak contemporaneous relationship not as evidence against AEMP but as consistent with it once the “long and variable lags” from money growth to inflation (Friedman, 1961) are taken into account; the much higher explanatory power of the lagged specification is, in his view, “decidedly more favorable to the quantity theory.” A parallel exercise using UK base-money growth and consumer price (RPIX) inflation over the same sample shows a similar, though less pronounced, gain in explanatory power from allowing for lags.

No – Nelson argues that because the quantity theory does not require an explicit money term in the price-setting (Phillips curve) equation, evidence that money growth loses significance once output-gap terms are added to an inflation regression is not evidence against a structural role for money. He states explicitly that he would not expect the money-growth terms in his own lagged regression to remain significant once output-gap terms were added to the specification, and interprets Estrella and Mishkin’s (1997) finding that money has no explanatory power for inflation conditional on real-activity terms as confirming that flexible-price, direct-money-effect models are wrong – not as evidence against the monetary origins of inflation more generally. Conversely, he reads Gerlach and Svensson’s (2002) finding that money terms retain explanatory power for inflation even after conditioning on measured output gaps as suggestive of measurement error in the output-gap proxy.

Nelson draws four conclusions: (1) the AEMP proposition remains valid in present-day models and applies to both the dynamics and the steady-state determination of inflation; (2) it can be given a similar interpretation regardless of the monetary policy regime in place; (3) the quantity theory neither requires nor is undermined by the absence of an explicit money term in the price-setting relations, and money growth entering significantly in an empirical Phillips curve more likely reflects misspecification than a genuine structural channel; and (4) the long-run money-growth/inflation relation deserves separate policy attention precisely because, unlike other steady-state relations, it has no direct counterpart in the equations governing inflation dynamics. He characterizes the disagreement between this reading and much of the recent literature (Galí, 2002; McCallum, 2001; Svensson, 1999a, 2002) as “more with the letter than the spirit,” since he agrees that day-to-day control of inflation around its steady-state value need not involve an explicit policy response to money.

No – Nelson argues the real balance effect was never central to the monetarist transmission story, so evidence that it is quantitatively negligible (as found in studies of nonseparable-utility IS terms by Andrés et al., 2001, Ireland, 2001a, McCallum, 2000, and Woodford, 2003) does not refute monetarism. He cites Friedman’s own statement, “I never have believed that the real balance effect is of much empirical significance” (1972), and Brunner and Meltzer’s (1968) description of their transmission model as one that “does not depend on the real-balance effect” and in which “the money supply does not even occur as a variable in the system.” Instead, the monetarist claim was that monetary policy affects aggregate demand through a broad “spectrum of rates” – not only the short-term rate emphasized in textbook IS-LM and New Keynesian models – so the relevant test of monetarist transmission is not whether money enters the IS equation directly.

Nelson argues that if money demand follows Friedman’s (1956) specification – in which a spectrum of yields, not just the short-term nominal rate, enters as the opportunity cost of holding money – then money growth can carry information about aggregate-demand-relevant yields that is not contained in the short rate, giving money value as a policy indicator even though it appears in no structural IS or Phillips curve equation. He formalizes this with a money demand function in which real balances depend on expected future real balances (weight 0.47) and lagged real balances (weight 0.48), forward- and backward-looking terms he attributes to portfolio adjustment costs; because of these dynamics, expected future short rates, and so the long-term rate, become relevant to current money demand. This differs from optimizing-based specifications such as McCallum and Goodfriend (1987) and Lucas (1988), which reject any role for yields beyond the current short rate, but Nelson notes that Anderson and Rasche (2001) and Meltzer (1998) document a long-standing empirical relationship between US monetary base velocity and the long-term interest rate, and Gerlach and Svensson (2002) find a similar role for the long rate in euro-area money demand.

In a model combining the three-equation NK system with the Friedman-Meltzer money demand function, solved for the optimal commitment policy under Aoki’s (2002) fixed-point algorithm when the central bank observes only noisy real-time output and inflation data, the optimal policy coefficient on money-growth news rises from 0.170 (standard money demand, calibration coefficient μ₁=0) to 0.235 (Friedman-Meltzer specification, μ₁=0.47) – an increase of about a third – while the optimal coefficients on inflation news (0.262) and output news (3.631) are unchanged across the two specifications. The calibration sets the Phillips curve slope to 0.024, discount factor to 0.99, the welfare weight on the output gap to 0.047, the natural-rate and potential-output shocks to AR(1) processes with persistence 0.33 and 0.99 and innovation standard deviations of 1.1% and 0.7%, and the output/inflation measurement-error standard deviations to 0.89% and 0.35%. Nelson frames the result as illustrating that “the role of the money stock as an indicator is thus shown to be totally independent from its occurrence as a variable in the system” (quoting Brunner, 1971b). The exercise is explicitly a calibrated simulation, not an estimated model – parameter uncertainty is not quantified, and the paper as a whole contains no structural VAR or instrumental-variables identification; its supporting inflation-money evidence (Q4) is simple reduced-form OLS on a pre-2003 US sample that predates the zero lower bound, quantitative easing, and post-2020 disinflation episodes.