Measurement Matters: Recent Results from Monetary Economics Reexamined
📄 Summarized from the full manuscript · Human-reviewed for faithfulness before publication
In brief
Does it matter whether economists measure money by adding up dollar balances or by weighting each type according to the monetary services it provides? Belongia re-runs five prominent published results both ways on United States data through 1992. In four of the five the conclusion changes: money looks acyclical one way and strongly procyclical the other; positive and negative money shocks look asymmetric one way and symmetric the other; and only the weighted measure helps predict output. He argues simple addition wrongly treats different monetary assets as perfect substitutes, especially after the 1980 deregulation. It matters because settled findings may rest on the yardstick rather than on economics.
What this paper finds — and why it matters
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.
Summary of a classic paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.
Questions & answers
Q1. What question is this paper asking, and why does it matter?
The paper asks whether the substantive, qualitative conclusions of recent monetary economics change depending on whether money is measured as a simple-sum aggregate or a Divisia aggregate — and answers that in most of the cases it examines, they do. Simple-sum aggregates (just adding face values of currency, checking deposits, savings deposits, etc.) implicitly treat all monetary assets as perfect substitutes, which Belongia argues violates the aggregation conditions Hicks (1946) established for when adding up quantities is valid: those conditions require that component prices (here, yields) move proportionally. Divisia aggregates instead weight each component by its expenditure share in the flow of monetary services, based on the user cost (the yield gap between that asset and a benchmark asset), following Barnett (1978, 1980) and Diewert (1976) index-number theory. Belongia’s contribution is not new theory but a direct test: replicate several well-known empirical results with both types of aggregate and see whether the story changes.
Q2. How does the paper structure its test — what is being replicated, and how?
Belongia re-estimates five previously published empirical exercises using U.S. data (quarterly for four cases, monthly for the fifth, mostly spanning 1960:2-1992:4), substituting Divisia measures for the simple-sum aggregates the original studies used, and compares the qualitative conclusions. The five cases are: (1) money innovations generated from the De Long-Summers (1988) equation as applied by Rotemberg (1993); (2) Cover’s (1992) test of whether positive and negative money shocks have symmetric effects; (3) the Kydland-Prescott (1990) test of whether money is pro- or countercyclical; (4) a stability check of that cyclicality result across subsamples; and (5) Stock-Watson and Friedman-Kuttner-style VAR tests of whether money predicts output (industrial production, with price changes and an interest rate as controls). This is explicitly framed as a comparative replication study, not a claim that these five cases are representative of the literature as a whole — the paper states the selection reflects the author’s judgment of prominent recent work.
Q3. In the money-innovations case (Case 1), how much does the choice of aggregate matter?
Extracting money innovations from the De Long-Summers (1988)/Rotemberg (1993) equation, simple-sum M1 innovations produce an R-squared of 0.36 versus 0.23 for Divisia M1 — broadly similar fits — but the residual plots show the two innovation series diverging: Belongia notes that “the residuals for 1989:3 and 1990:3 have opposite signs precisely at a time — a business cycle turning point — when inferences about the thrust of policy are most important” (p. 1072). This is the one case among the five where the paper’s own framing is more about economically meaningful divergence in extracted shocks than a flat reversal of a qualitative conclusion.
Q4. Does the money aggregate chosen change the answer to whether monetary shocks are symmetric (Case 2)?
Yes, sharply: Belongia replicates Cover’s two-equation system (a money-supply process plus an output equation) across three alternative money-supply processes used to generate the innovations — “Barro-Rush,” “Modified Mishkin,” and “Optimal” — using the specification that includes the Treasury-bill rate and four lags of money shocks (Cover’s table 4). For simple-sum M1, Cover’s own results reject the null hypothesis of symmetric effects of positive versus negative money shocks in 5 of 6 cases, with Wald chi-square statistics across the three processes of roughly 25.3 to 43.5; but replacing M1 with Divisia M1 or Divisia M1-plus, the symmetry null cannot be rejected for any of the three processes with either Divisia aggregate (chi-square roughly 1.01-1.03). As Belongia summarizes it: “Whereas Cover reports an asymmetric response for M1 in five of six cases, neither Divisia aggregate rejects the hypothesis of symmetric effects” (p. 1075). The qualitative conclusion — whether monetary policy has asymmetric real effects — depends entirely on which aggregate is used.
Q5. Is money procyclical or countercyclical, and does that depend on the aggregate (Cases 3 and 4)?
Table 3 shows simple-sum M1’s correlations with the cycle are small but uniformly positive across every lead and lag — never negative — peaking at about 0.35 when money leads real GNP by one quarter and about 0.31 contemporaneously, which leads Belongia to conclude only that “M1 does not appear to behave procyclically” (p. 1077), not that it is countercyclical. Divisia M2 and Divisia M1-plus, by contrast, are strongly procyclical, peaking at about 0.70 and 0.65 when leading the cycle by two quarters and roughly 0.48 and 0.47 contemporaneously; Divisia M1 itself, unlike the other two Divisia measures, is not strongly procyclical. In Case 4, splitting the sample into 1960-79 and 1970-89 subperiods does not weaken the money-output correlations for Divisia M2, Divisia M1-plus, or simple-sum M2, refuting Friedman and Kuttner’s (1992) conjecture that 1960s data were driving those correlations; the two M1 series behave differently — their results are “consistent with both the Friedman-Kuttner conjecture about the importance of data from the 1960s and the Kydland-Prescott assertion of a weak or nonexistent relationship between M1 and output” (p. 1080).
Q6. Does money still help predict output once Divisia aggregates are used (Case 5)?
Table 5 reports F-statistics for a single equation — money’s joint effect on industrial production (the paper’s monthly proxy for real income) — estimated over three different sample end-dates, not separate output and price equations. Using the Treasury-bill rate (panel A), Divisia M1-plus is the only aggregate with statistically significant F-statistics across every sample and lag length, e.g., F = 4.23 (six lags) over the sample through 1985:12 and F = 3.76 (six lags) over the longer sample through 1990:12; simple-sum M1 and Divisia M1 are not significant in any of these specifications. This case is the paper’s most qualified result: using the commercial paper rate instead (panel B), “none of the money measures demonstrates a significant effect on output over any of the sample periods” (p. 1082) — including Divisia M1-plus, whose significance in panel A does not survive the change in interest-rate control.
Q7. What mechanism does the paper offer for why measurement changes the answer?
Belongia’s explanation is that simple-sum aggregation is a flawed index-number procedure that becomes increasingly wrong as financial innovation proceeds, especially after the 1980 Depository Institutions Deregulation and Monetary Control Act (DIDMCA) introduced interest-bearing NOW accounts. Simple-sum aggregation, by adding components with equal weights, implies that “each good is a perfect substitute for every other good in the group” (p. 1067), so when households shift funds into a new, interest-bearing instrument, simple-sum M1 can rise even though the actual flow of monetary services households are consuming has not changed proportionally — introducing measurement error that distorts inference in exactly the kind of regressions the paper re-examines. This is a theoretical argument grounded in Hicksian aggregation theory and Divisia index theory (Barnett, Diewert), not something separately identified via a structural model in this paper.
Q8. What are the main limits on how far these results should be pushed?
The paper is explicit that it is a comparative replication exercise covering only five cases chosen for prominence, not a representative survey, that it establishes no structural identification of monetary policy shocks, and that its sample ends in 1992:4 — well before the near-zero interest-rate period after 2008, when Divisia and simple-sum measures would be expected to diverge most. Belongia also flags that the “Divisia M1-plus” aggregate used here is a 1996-vintage broad aggregate closer to what would later be called Divisia M2, so it should not be directly equated with the modern Divisia M1 series when comparing to current Center for Financial Stability data. The Case 5 result is also the paper’s most qualified: Divisia M1-plus’s significant effect on industrial production holds only under the Treasury-bill-rate specification — with the commercial paper rate, no monetary aggregate, including Divisia M1-plus, shows a significant effect on output.
Key terms in this paper
Definitions below follow the paper's own usage.
- Simple-sum monetary aggregate
- an index that adds the dollar face values of monetary components (currency, checking deposits, savings deposits, etc.) with equal weight, an approach the paper argues implicitly assumes all components are perfect substitutes for one another — an assumption violated once components pay different yields.
- Divisia monetary aggregate
- a weighted index of monetary components, following Barnett (1978, 1980) and Diewert (1976) index-number theory, in which each component's weight is its expenditure share in the flow of monetary services, computed from its user cost (the yield gap between that asset and a benchmark asset); constructed in this paper following the Barnett (1981, 1982) expenditure-share weighting formula.
- Divisia M1-plus
- the broadest Divisia measure used in the paper, defined at the 1996 vintage in a way the paper itself notes is closer to what became known as modern Divisia M2 rather than modern Divisia M1 — the aggregate that most consistently outperforms simple-sum measures across the paper's five cases.
- Hicksian aggregation conditions
- the requirement, from Hicks (1946), that for simple face-value addition of quantities to be a valid index number, the prices (here, yields) of the components being summed must move proportionally; the paper's central theoretical claim is that monetary components fail this condition once they pay differentiated interest rates.
- Measurement error from financial innovation
- the paper's proposed mechanism for why simple-sum and Divisia aggregates diverge in ways that matter empirically — following the 1980 DIDMCA introduction of interest-bearing NOW accounts, households' substitution into new instruments raises simple-sum M1 without a proportional change in the actual flow of monetary services consumed, distorting inference in models that use simple-sum money.