This paper offers a framework for measuring global growth and inflation, built on standard index number theory, national accounts principles, and the concepts and methods for international macro-economic comparisons. Our approach provides a sound basis for purchasing power parity (PPP)- and exchange rate (XR)-based global growth and inflation measures. The Sato–Vartia index number system advocated here offers very similar results to a Fisher system but has the added advantage of allowing a complete decomposition with PPP or XR effects. For illustrative purposes, we present estimates of global growth and inflation for 141 countries over the years 2005 and 2011. The contribution of movements in XRs and PPPs to global inflation are presented. The aggregation properties of the method are also discussed.

While credit cards provide transactions services, as do currency and demand deposits, credit cards have never been included in measures of the money supply. The reason is accounting conventions, which do not permit adding liabilities, such as credit card balances, to assets, such as money. However, economic aggregation theory and index number theory measure service flows and are based on microeconomic theory, not accounting. Barnett et al. derived the aggregation and index number theory needed to measure the joint services of credit cards and money. They derived and applied the theory under the assumption of risk neutrality. But since credit card interest rates are high and volatile, risk aversion may not be negligible. We extend the theory by removing the assumption of risk neutrality to permit risk aversion in the decision of the representative consumer.

This paper is the introduction to the Macroeconomic Dynamics Special Issue on Measurement with Theory. The Guest Editors of the special issue are William A. Barnett, W. Erwin Diewert, Shigeru Iwata, and Arnold Zellner. The papers included are part of a larger initiative to promote measurement with theory in economics.

This paper compares the different dynamics of the simple-sum monetary aggregates and the Divisia monetary aggregate indices over time, over the business cycle, and across high and low inflation and interest-rate phases. Although traditional comparisons of the series sometimes suggest that simple-sum and Divisia monetary aggregates share similar dynamics, there are important differences around turning points that cannot be evaluated by their average behavior. We use a factor model with a regime-switching model that separates the common movements underlying the monetary aggregate indices from idiosyncratic variations in each series. We find that the major differences between the simple-sum aggregates and Divisia indices occur around the beginnings and ends of recessions and during some high-interest-rate phases. We note the inferences' policy relevance, which is particularly dramatic at the broadest (M3) level of aggregation. Indeed, as Belongia [Journal of Political Economy, 104 (5) (1996), 1065–1083] has observed in this regard, “measurement matters.”

Barnett originated the Divisia monetary aggregates, which in continuous time exactly track any monetary aggregator function under perfect certainty. With user costs measuring the prices of the services of components, Barnett's aggregates are based on Francois Divisia's derivation of the Divisia line integral from the first-order conditions for optimizing behavior by economic agents under perfect certainty. We derive an extended Divisia index from the first-order conditions (Euler equations) that apply under risk. Our extended Divisia index is the first extension of index number theory into the domain of decision making under risk and thereby produces a route for the extension of all index number theory to permit non-risk-neutrality. We generate simulated data from a modeled rational consumer and investigate the tracking accuracy of the extended Divisia index to the consumer's exact aggregator function.

New U.S. evidence from NIPA contradicts some of the well-known Kaldor stylized facts, and call for a reformulation of the modern theory of economic growth. Among these new facts, two must be stressed: A permanent decline in the relative price of durable goods, and a permanent increase in the real equipment to real GDP ratio. To be consistent with these new facts, growth models must include at least two sectors and address the problem of defining aggregate output. In this paper, the economic theory of index numbers is used to define the growth rate of real output in a growth model with embodied technical change. The main findings are: (i) NIPA’s methodology measures growth in accordance with the economic theory on index numbers, and (ii) when the growth rate is measured as in NIPA, the contribution of embodied technical change to per capital GDP growth in the U.S. is 69%, which reinforce the claim that embodied technical change is important for growth.

In aggregation theory, index numbers are judged relative to their ability to track the exact aggregator functions nested within the economy's structure. We compare two statistical index numbers—the Divisia monetary aggregate and the simple-sum monetary aggregate—with the exact rational expectations monetary aggregate, using actual data. Because we are not using simulated data, we estimate the parameters of the Euler equations, and thereby of the nested monetary aggregator function, using the generalized method of moments. We explore the tracking errors of the two index numbers relative to the estimated exact aggregate. We investigate the circumstances under which risk aversion increases tracking error. We also use polyspectral methods to test for the existence of remaining nonlinear structure in the residual tracking errors.