Advances in Monetary and Financial Measurement Library - The Center for Financial Stability

Advances in Monetary and
Financial Measurement (AMFM)

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Key articles and books surrounding the development of advances in monetary and financial measurement. This Library does not include data archives. International and US data archives, along with regular monthly updates, can be found within other sections of the AMFM site.

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Important Books
2012	Getting It Wrong: How Faulty Monetary Statistics Undermine the Fed, the Financial System, and the Economy William A. Barnett This book appeared from MIT Press in January 2012 in both hardcover and paperback editions. The hardcover edition is a library edition, missing the cover design and back cover information.
2011	Financial Aggregation and Index Number Theory William A. Barnett and Marcelle Chauvet This book contains a collection of Barnett's most important, recent, journal publications in monetary and financial measurement. The collection is subsequent to the year 2000, during which the prior collection, Barnett and Serletis (2000), leaves off. The two books together contain fundamental background relevant to AMFM, and are up to date to the year 2011, when this book appeared.
2007	The Demand for Money: Theoretical and Empirical Approaches, Second Edition Apostolos Serletis This book was published by Springer. The book is a textbook presentation, using valid aggregation and index number theory.
2007	Inside the Economist's Mind: Conversations with Eminent Economists William A. Barnett and Paul A. Samuelson This book is a collection of interviews with many of the world's most eminent economists, including eight Nobel Laureates, two central bank governors, and a chairman of the Council of Economic Advisors. The book has been translated into seven languages and has its own web site, linked to this entry in the AMFM library. The book also has its own Blog for discussion of issues raised by the book.
2006	Money and the Economy Apostolos Serletis This textbook, using valid index number theory and aggregation theory in monetary economics, is published by World Scientific, Singapore
2006	Money, Measurement, and Computation Michael T. Belongia and Jane M. Binner This book is a collection of papers, including some important international studies with Divisia monetary aggregation.
2004	Functional Structure and Approximation in Econometrics William A. Barnett and Jane Binner This book is a collection of Barnett's most important journal articles in econometric modeling.
2000	The Theory of Monetary Aggregation William A. Barnett and Apostolos Serletis This book is the best source of the fundamental background in monetary and financial measurement. The book contains a collection of Barnett's most important journal articles in monetary aggregation and index number theory up to the year of publication of this book. The newer book, Barnett and Chauvet (2011), takes over where this book leaves off.
2000	Divisia Monetary Aggregates: Right in Theory, Useful in Practice? Michael T. Belongia and Jane M. Binner This book is a collection of international studies of applications of Divisia monetary aggregates in policy.
1991	A Theory of Production for the Financial Firm Diana Hancock This book was published by Kluwer Academic Publishers, Norwell, Massachusetts.
1989	Money Demand and Monetary Policy Douglas Fisher This textbook, published by University of Michigan Press, uses valid aggregation theory and index number theory in a more elementary manner than the Serletis and Rahman (2007) book, which is more appropriate for a graduate course. The Fisher book is suitable for an undergraduate course.
1981	Consumer Demand and Labor Supply William A. Barnett W. A. Barnett's 1981 book, Consumer Demand and Labor Supply is out of print but has been scanned and put online. Chapter 7 is highly relevant to AMFM. That chapter provides systematic presentation of the relevant, fundamental theory and empirical applications, following publication of Barnett's seminal 1980 Journal of Econometrics paper, which marked the beginning of the modern literature on monetary aggregation and index number theory.
Important Papers Highly Relevant to AMFM
2022	Consumer Preferences, the Demand for Divisia Money, and the Welfare Costs of Inflation Apostolos Serletis and Libo Xu This paper uses neoclassical demand theory to calculate the welfare costs of inflation. It considers the demand interactions between money, consumption goods, and leisure, relaxes the assumption of fixed consumer preferences, and addresses the inter-related problems of estimation of money demand functions, instability of money demand relations, and monetary aggregation. It makes full use of the relevant economic theory and econometrics and generates inference in terms of long-run welfare costs of inflation that is internally consistent with the data and models used. Forthcoming in: Journal of Macroeconomics
2022	Shilnikov chaos, low interest rates, and New Keynesian macroeconomics William A.Barnett, Giovanni Bella, Taniya Ghosh, Paolo Mattana, Beatrice Venturi The paper shows that in a New Keynesian (NK) model, an active interest rate feedback monetary policy, when combined with a Ricardian passive fiscal policy, à la Leeper-Woodford, may induce the onset of a Shilnikov chaotic attractor in the region of the parameter space where uniqueness of the equilibrium prevails locally. Implications, ranging from long-term unpredictability to global indeterminacy, are discussed in the paper. We find that throughout the attractor, the economy lingers in particular regions, within which the emerging aperiodic dynamics tend to evolve for a long time around lower-than-targeted inflation and nominal interest rates. This can be interpreted as a liquidity trap phenomenon, produced by the existence of a chaotic attractor, and not by the influence of an unintended steady state or the Central Bank's intentional choice of a steady state nominal interest rate at its lower bound. In addition, our finding of Shilnikov chaos can provide an alternative explanation for the controversial "loanable funds" over-saving theory, which seeks to explain why interest rates and, to a lesser extent, inflation rates have declined to current low levels, such that the real rate of interest may be below the marginal product of capital. Paradoxically, an active interest rate feedback policy can cause nominal interest rates, inflation rates, and real interest rates unintentionally to drift downwards within a Shilnikov attractor set. Our results are robust to whether money is in the production function, in the utility function, or not in the model at all. But our results do depend upon the existence of sticky prices.
2022	Controlling chaos in New Keynesian macroeconomics William A. Barnett, Giovanni Bella, Taniya Ghosh, Paolo Mattana and Beatrice Venturi In a New Keynesian model, it is believed that combining active monetary policy using a Taylor rule with a passive fiscal rule can achieve local equilibrium determinacy. However, even with such policies, indeterminacy can occur from the emergence of a Shilnikov chaotic attractor in the region of the feasible parameter space. That result, shown by Barnett et al. (2022a), “Shilnikov Chaos, Low Interest Rates, and New Keynesian Macroeconomics,” Journal of Economic Dynamics and Control 134, and again by Barnett et al. (2022b), “Is Policy Causing Chaos in the United Kingdom,” Economic Modeling 108, implies that the presence of the Shilnikov chaotic attractor can cause the economy to drift towards and finally become stuck in the vicinity of lower-than-targeted inflation and nominal interest rates. The result can become the source of a liquidity trap phenomenon. We propose policy options for eliminating or controlling Shilnikov chaotic dynamics to help the economy escape from the liquidity trap or avoid drifting into it in the first place. We consider ways to eliminate or control the chaos by replacing the usual Taylor rule by an alternative policy design without interest rate feedback, such as a Taylor rule with monetary quantity feedback, an active fiscal policy rule with passive monetary rule, or an open loop policy without feedback. We also consider approaches that retain the Taylor rule with interest rate feedback and the associated Shilnikov chaos, while controlling the chaos through a well-known engineering algorithm using a second policy instrument. We find that a second instrument is needed to incorporate a long-run terminal condition missing from the usual myopic Taylor rule.
2021	Targeting Nominal Income under the Zero Lower Bound: The Case of the Bank of England Michael T. Belongia, Peter N. Ireland The Bank of England, like other central banks that use an interest rate as their policy variable, faces practical problems for implementation of monetary policy when interest rates are constrained by their zero lower bound. The quantity of money, however, faces no such constraint and, for that reason, policies that emphasize control of the money supply may offer an alternative path toward achievement of a central bank's nominal objectives. A simple model rooted in Quantity Theory principles suggests this is possible if the quantity of money is measured properly and slow-moving trends in velocity can be accommodated in the policy's implementation.
2021	Disentangling the Effects of Uncertainty, Monetary Policy, and Leverage Shocks on the Economy Cosmas Dery and Apostolos Serletis In this paper, we assess the information content and predictive ability of various risk and uncertainty measures in predicting various measures of real economic activity as well as undertake a comparative analysis of the relative importance of uncertainty, monetary policy, and leverage shocks in the macroeconomic business cycle. We find that the Jurado et al. (2015) macroeconomic uncertainty index and the Chicago Fed national financial conditions risk index have the strongest predictive relationship with economic activities. Also, in the context of a Bayesian monetary structural VAR, we use the penalty function approach to a sequential identification of uncertainty, monetary policy, and leverage shocks, and find that uncertainty shocks are a relatively more important source of variations in the economy than traditional monetary policy shocks. However, monetary policy shocks still outperform uncertainty shocks in explaining inflation dynamics.
2021	Is Broader Better? A Monetary Approach to Forecasting Economic Activity Michael Ellington & Marcin Michalski This paper investigates whether the use of broader Divisia monetary aggregates improves money's performance in forecasting economic activity within a time-varying parameter vector autoregressive (TVP-VAR) framework. We evaluate entire predictive densities from several alternative models of US output growth and inflation, each using eight different Divisia monetary aggregates. Using the broadest, M4 aggregate produces out-of-sample forecasts which consistently outperform those based on narrower measures of money, pooling of forecasts from several models, and a large-scale, 143-variable model. Our results show that TVP-VARs with Divisia M4 forecast economic activity more accurately than constant-parameter models with alternative or no measures of money.
2021	Credit Cards, the Demand for Money, and Monetary Aggregation Jinan Liu and Apostolos Serletis We use nonparametric and parametric demand analysis to empirically estimate a credit card-augmented monetary asset demand system, based on the Minflex Laurent flexible functional form, and a sample period that includes the 2007-2009 global financial crisis and the Covid-19 pandemic. We also use multivariate copulae in an attempt to capture various patterns of dependence structures. In doing so, we relax the joint normality assumption of the errors of the demand system and estimate the model without having to delete one equation as is usually the practice. We show that the Minflex Laurent copula-based demand system produces a higher income elasticity for credit card transaction services and higher Morishima elasticities between credit card transaction services and monetary assets compared to the traditional estimation of the Minflex Laurent demand system. We also show that credit cards are substitutes for monetary assets and that there is lower tail dependence between the demand for credit card transaction services and transaction balances.
2021	The Welfare Cost of Inflation Apostolos Serletis and Libo Xu This paper uses neoclassical demand theory and applied consumption analysis to calculate the welfare cost of inflation, in the context of the Bailey (1956) approach. We integrate the demand for money with the demands for consumption and leisure, estimate flexible demand functions in a systems context, and show that raising the inflation rate from 2% to 4% in the United States, would impose (on average) a welfare cost equivalent to a loss of 0.30 percent of output when money is measured by our preferred (broad) Divisia M4 monetary aggregate. We also show that the welfare cost of inflation is countercyclical and trends upward over time.
2021	The Demand for Assets: Evidence from the Markov Switching Normalized Quadratic Model Libo Xu and Apostolos Serletis Forthcoming in: Journal of Money, Credit and Banking. In this paper we provide and illustrate a solution to the inter-related problems of estimation of asset demand functions, instability of money demand relations, and monetary aggregation. We use an econometric framework that very flexibly allows for changes in the coefficients of the asset demand functions and then quantifying the implications that this asset demand instability has for monetary policy and monetary aggregation. Our approach allows the estimation of asset demand functions in a systems context, using a flexible functional form for the aggregator function, based on the dual approach to demand system generation. However, instead of assuming that consumer preferences are fixed as in the neoclassical demand theory, we assume Markov regime switching, thus allowing for complicated nonlinear dynamics and sudden changes in the parameters of the asset demand functions and the underlying aggregator function. We use the monthly time series data on monetary asset quantities and their user costs, recently produced for the United States and maintained within the Center of Financial Stability (CFS), and the Normalized Quadratic (NQ) flexible functional form with Markov regime switching, to generate inference in terms of a full set of elasticities, simultaneously achieving consistency with the data generating process and economic and econometric regularity. We find evidence that our five-regime NQ model provides a better fit of the actual data than a single regime model, that the asset demand specifications exhibit instability between regimes, but are rather stable within regimes, and that the assets are in general Morishima substitutes with the Morishima elasticities of substitution always being below unity.
2021	The Barnett Critique William A. Barnett, Hyun Park, and Sohee Park The Barnett critique states that there is an internal inconsistency between the theory that is implied by simple sum monetary aggregation (perfect substitutability among components) and the economic theory that produces the models within which those aggregates are used. That inconsistency causes the appearance of unstable demand and supply for money. The incorrect inference of unstable money demand has caused serious harm to the field of monetary economics.
2020	A Reconsideration of Money Growth Rules Michael T. Belongia and Peter N. Ireland A New Keynesian model, estimated using Bayesian methods over a sample period that includes the 2009-15 episode of zero nominal interest rates, illustrates the effects of replacing the Federal Reserve's historical policy of interest rate management with one targeting money growth instead. Counterfactual simulations show that a rule for adjusting the money growth rate, modestly and gradually, in response to changes in the output gap delivers performance comparable to the estimated interest rate rule in stabilizing output and inflation. The simulations also reveal that, under the same money growth rule, the US economy would have recovered more quickly from the 2007- 09 recession, with a much shorter period of exceptionally low interest rates. These results suggest that money growth rules can serve as simple but useful guides for monetary policy and eliminate concerns about monetary policy effectiveness when the zero lower bound constraint is binding.
2020	Recent Monetary Policy and the Credit Card-Augmented Divisia Monetary Aggregates Jinan Liu, Cosmas Dery, and Apostolos Serletis The main objective of this paper is to examine the information content of the credit card-augmented Divisia monetary aggregates and credit card-augmented Divisia inside monetary aggregates, recently produced by the Center for Financial Stability. We compare the inference ability of the credit card-augmented Divisia monetary aggregates and credit card augmented Divisia inside monetary aggregates to the conventional Divisia monetary aggregates, at all levels of monetary aggregation. Using cyclical correlations analysis and Granger causality tests, we find that both the conventional Divisia monetary aggregates and the credit card-augmented Divisia monetary aggregates are informative in predicting output. Moreover, during, and in the aftermath of the 2007-2009 financial crisis, the credit card-augmented Divisia measures of money are more informative when predicting real economic activity than the conventional Divisia monetary aggregates. We also find that broad Divisia monetary aggregates provide better measures of the flow of monetary services generated in the economy.
2019	Divisia Monetary Aggregates for Developing Economies: Some Theory John Nana Francois and Ryan S Mattson Asset market development is characterized by reducing market imperfections that generate costs incurred from participating in the financial system. In developing economies where financial markets are nascent, these costs are likely to be binding. This limits the typical economic agent's ability to fully access asset market, inducing partial access. In this note, we embed financial market imperfections into the Divisia aggregate-theoretic literature and illustrate their relevance in the derivation of user cost of money and consequently, Divisia monetary aggregates. Asset market imperfections are introduced through endogenous portfolio adjustment costs that proxy for, among other things, informational, transactional, liquidity, and portfolio management costs. The presence of adjustment costs induce additional costs that alter the standard user cost of money. We show that the user cost that arises from our model can be practically implemented in the construction of Divisia aggregates as in the standard Barnett (1978) user cost.
2019	Money Growth Variability and Output: Evidence with Credit Card-Augmented Divisia Monetary Aggregates Jinan Liu and Apostolos Serletis We reexamine the effects of the variability of money growth on output, raised by Mascaro and Meltzer (1983), in the era of the increasing use of alternative payments, such as credit cards. Using a bivariate VARMA, GARCH-in-Mean, asymmetric BEKK model, we find that the volatility of the credit card-augmented Divisia M4 monetary aggregate has a statistically significant negative impact on output from 2006:7 to 2019:3. However, there is no effect of the traditional Divisia M4 growth volatility on real economic activity. We conclude that the balance sheet targeting monetary policies after the financial crisis in 2007-2009 should pay more attention on the broad credit card-augmented Divisia M4 aggregate to address economic and financial stability. This paper will appear in the journal, "Studies in Nonlinear Dynamics and Econometrics".
2018	The case for Divisia monetary statistics: A Bayesian time-varying approach Michael Ellington The zero lower bound and quantitative easing policies have rekindled interest in the link between monetary aggregates and the business cycle. This paper argues, on the basis of Bayesian time-varying coefficient VAR models that use Divisia indexes, that money is more closely linked to the business cycle, as well as forecasting economic activity more accurately, than existing literature claims. Moreover, the relationship between money and economic activity is considerably more pronounced during periods of economic distress, such as in the Great Recession.
2018	Financial Firm Production of Inside Monetary and Credit Card Services: An Aggregation Theoretic Approach William A. Barnett and Liting Su A monetary production model of financial firms is employed to investigate supply-side inside money aggregation, augmented to include credit card transaction services. Inside money is a supply side concept. Financial firms are conceived to produce monetary and credit card transaction services as outputs through financial intermediation. While credit cards provide transactions services, credit cards have never been included into measures of the money supply. The reason is accounting conventions, which do not permit adding liabilities to assets. However, index number theory measures service flows and is based on microeconomic aggregation theory, not accounting. We derive theory needed to measure the supply of the joint services of credit cards and inside money, needed to estimate the output supply function and to compute value added. The resulting model could be used to investigate the transmission mechanism of monetary policy. The data needed for empirical implementation of our theory are available online from the Center for Financial Stability (CFS) in New York City. We show that the now discredited conventional accounting-based measures of privately produced inside money can be replaced by our measures, based on microeconomic aggregation theory, to provide the information originally contemplated in the literature on monetary theory.
2018	The Demand for Assets and Optimal Monetary Aggregation Ali Jadidzadeh and Apostolos Serletis This paper uses a highly disaggregated demand system to estimate the degree of substitutability among monetary assets and to address the issue of optimal monetary aggregation in the United States. We address the problems of dimensionality and nonlinearity, estimating a very detailed monetary asset demand system encompassing the full range of assets based on the locally flexible normalized quadratic (NQ) expenditure function. We treat the concavity property as a maintained hypothesis and provide evidence consistent with neoclassical microeconomic theory. Statistical tests reject the appropriateness of the aggregation assumptions for all the money measures published by the Federal Reserve as well as for a large number of groupings suggested by earlier studies. This supports and reinforces Barnett's (2016) assertion that we should employ the broadest M4 monetary aggregate published by the Center for Financial Stability.
2018	A Model of Monetary Policy Shocks for Financial Crises and Normal Conditions John W. Keating, Logan J. Kelly, A. Lee Smith and Victor J. Valcarcel Deteriorating economic conditions in late 2008 led the Federal Reserve to lower the target federal funds rate to near zero, inject liquidity through novel facilities, and engage in large-scale asset purchases. The combination of conventional and unconventional policy measures prevents using the effective federal funds rate to assess the effects of monetary policy beyond 2008. We employ a broad monetary aggregate to elicit the effects of monetary policy shocks both before and after 2008. Our estimates align well with major changes in the Fed's asset purchase programs and yield responses that are free from price, output, and liquidity puzzles that plague other approaches.
2017	The Demand for Liquid Assets: Evidence from the Minex Laurent Demand System with Conditionally Heteroscedastic Errors Dongfeng Chang and Apostolos Serletis We investigate the demand for money and the degree of substitutability among monetary assets in the United States using the generalized Leontief and the Minflex Laurent models as suggested by Serletis and Shahmoradi (2007). In doing so, we merge the demand systems literature with the recent financial econometrics literature, relaxing the homoscedasticity assumption and instead assuming that the covariance matrix of the errors of flexible demand systems is time-varying. We also pay explicit attention to theoretical regularity, treating the curvature property as a maintained hypothesis. Our findings indicate that only the curvature constrained Minflex Laurent model with a BEKK specification for the conditional covariance matrix is able to generate inference consistent with theoretical regularity.
2016	Data Sources for the Credit-Card Augmented Divisia Monetary Aggregates William A. Barnett and Liting Su In 2013, the Center for Financial Stability (CFS) initiated its Divisia monetary aggregates database, maintained within the CFS program called Advances in Monetaryand Financial Measurement (AMFM), in accordance with Barnett (1980, 2012). The CFS is now making available Divisia monetary aggregates extended to include the transactions services of credit cards. The theory on which the new aggregates is based is provided in Barnett and Su (2014). In this paper, we provide detailed information on the data sources used in producing the new augmented Divisia monetary aggregates.
2016	Money, Velocity, and the Stock Market Karl Pinno and Apostolos Serletis This paper provides a study of the relationship between money growth variability, velocity, and the stock market, using recent advances in financial econometrics. We estimate a trivariate VARMA, GARCH-in-Mean, BEKK model to quantify the effects of financial market and money supply instability. We investigate the robustness of the results to different definitions of money using monthly Divisia indices for the United States from the Center for Financial Stability (CFS). Empirical evidence supports significance of financial market and money supply volatility, and we conclude that Friedman's money supply volatility hypothesis is alive and well.
2016	Nowcasting Nominal GDP with the Credit-Card Augmented Divisia Monetary William A. Barnett, Marcelle Chauvet, Danilo Leiva-Leon and Liting Su 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. We derive theory needed to measure the joint services of credit cards and money.
2014	The Treatment of Financial Transactions in the SNA: A User Cost Approach W. Erwin Diewert The paper considers how to integrate financial transactions into the balance sheet and production accounts of a nonfinancial firm. The paper argues that the choice of a reference interest rate is just as important for nonfinancial firms as it is for financial firms and that the choice of the reference rate is tied to the firm's financing decisions. This paper is included in Eurostat Review on National Accounts and Macroeconomic Indicators in 2014, published by the Publications Office of the European Union.
2014	Shifting Perspectives on the Dual Mandate Peter Ireland The Federal Reserve's statutory dual mandate requires US monetary policymakers to focus on inflation and unemployment when managing interest rates and the money supply. Both economic theory and economic history strongly suggest, however, that the best way for the Fed to provide for maximum employment is by stabilizing prices first. This position paper, prepared for the March 2014 meeting of the Shadow Open Market Committee, argues that by adhering to an inflation targeting strategy and by monitoring more closely the behavior of the money supply, the Federal Reserve can continue to provide support for a strengthening economy without rekindling inflation.
2014	The Joint Services of Money and Credit William A. Barnett and Liting Su While credit cards provide transaction 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. But economic aggregation theory and index number theory are based on microeconomic theory, not accounting, and measure service flows. In this seminal paper, Barnett and Su derive the theory needed to measure the joint services of credit cards and money. William A. Barnett and Liting Su presented this paper via video at the International Conference on Economic Recovery in the Post-Crisis Period in Skopje, Republic of Macedonia (May 29-30, 2015). Click here to see a video of this presentation, or Download a high res .m4v (350 Meg).
2014	Interest Rates and Money in the Measurement of Monetary Policy Michael T. Belongia and Peter N. Ireland Over the last twenty-five years, a set of influential studies has placed interest rates at the heart of analyses that interpret and evaluate monetary policies. In light of this work, the Federal Reserve's recent policy of "quantitative easing," with its goal of affecting the supply of liquid assets, appears to be a radical break from standard practice. Alternatively, one could posit that the monetary aggregates, when measured properly, never lost their ability to explain aggregate fluctuations and, for this reason, represent an important omission from standard models and policy discussions. In this context, the new policy initiatives can be characterized simply as conventional attempts to increase money growth. This view is supported by evidence that superlative (Divisia) measures of money often help in forecasting movements in key macroeconomic variables. Moreover, the statistical fit of a structural vector autoregression deteriorates significantly if such measures of money are excluded when identifying monetary policy shocks. These results cast doubt on the adequacy of conventional models that focus on interest rates alone. They also highlight that all monetary disturbances have an important "quantitative" component, which is captured by movements in a properly measured monetary aggregate.
2014	Instability: Monetary and Real Michael T. Belongia and Peter N. Ireland Fifty years ago, Friedman and Schwartz presented evidence of pro-cyclical movements in the money stock, exhibiting a lead over corresponding movements in output, found in historical statistics for the United States. We find similar relationships in more recent data that span three distinct episodes in monetary policy and economic activity. To see them clearly, however, one must use Divisia monetary aggregates in place of the Federal Reserve’s official, simple-sum measures. A structural VAR draws tight links between Divisia money and output during each of these three periods.
2014	Real-Time Nowcasting Nominal GDP Under Structural Break William Barnett, Marcelle Chauvet and Danilo Leiva-Leon This paper provides early assessments of current U.S. Nominal GDP growth, which has been considered as a potential new monetary policy target. The nowcasts are computed using the exact amount of information that policy makers have available at the time predictions are made. However, real time information arrives at different frequencies and asynchronously, which poses the challenge of mixed frequencies, missing data, and ragged edges. This paper proposes a multivariate state space model that not only takes into account asynchronous information inflow it also allows for potential parameter instability. We use small scale confirmatory factor analysis in which the candidate variables are selected based on their ability to forecast GDP nominal. The model is fully estimated in one step using a nonlinear Kalman filter, which is applied to obtain simultaneously both optimal inferences on the dynamic factor and parameters. Differently from principal component analysis, the proposed factor model captures the comovement rather than the variance underlying the variables. We compare the predictive ability of the model with other univariate and multivariate specifications. The results indicate that the proposed model containing information on real economic activity, inflation, interest rates, and Divisia monetary aggregates produces the most accurate real time nowcasts of nominal GDP growth.
2013	The Treatment of Financial Transactions in the SNA: A User Cost Approach W. Erwin Diewert This working paper considers some of the problems associated with the indirectly measured components of financial service outputs in the System of National Accounts (SNA), termed FISIM (Financial Intermediation Services Indirectly Measured). The paper considers how to integrate financial transactions into the balance sheet and production accounts of a firm; i.e., the paper looks at FISIM more broadly. In order to minimize the role of imputations, the paper considers a firm that raises capital at the beginning of the accounting period, engages in some form of productive activity during the period and then distributes the initial capital and any profits back to the capitalists who financed the firm.
2013	The New CFS Divisia Monetary Aggregates: Design, Construction, and Data Sources William A. Barnett, Jia Liu, Ryan S. Mattson, Jeff van den Noort The Center for Financial Stability (CFS) has initiated a new Divisia monetary aggregates database, maintained within the CFS program called Advances in Monetary and Financial Measurement (AMFM). This paper documents the decisions of the CFS regarding United States data sources at the present time, with particular emphasis on Divisia M3 and M4. A revised version of this paper appeared in Open Economies Review, Volume 24, Issue 1, February 2013, pp 101-124.
2012	The Macroeconomic Effects of Interest on Reserves Peter N. Ireland This paper uses a New Keynesian model with banks and deposits to study the macroeconomic effects of policies that pay interest on reserves. While their effects on output and inflation are small, these policies require major adjustments in the way that the monetary authority manages the supply of reserves, as liquidity effects vanish in the short run. In the long run, however, the additional degree of freedom the monetary authority acquires by paying interest on reserves is best described as affecting the real quantity of reserves: policy actions that change prices must still change the nominal quantity of reserves proportionally.
2012	Interest Rates, Leverage, and Money Apostolos Serletis Professor Apostolos Serletis of the University of Calgary argues that properly measured monetary aggregates can and should play an important role for the conduct of monetary policy. This study is forthcoming in Open Economies Review.
2012	The Barnett Critique After Three Decades: A New Keynesian Analysis Michael T. Belongia and Peter N. Ireland This paper has been submitted to a Journal of Econometrics special issue being produced in honor of the paper, Barnett (1980). The editors of the special issue are James Heckman and Apostolos Serletis.
2012	Quantitative Easing: Interest Rates and Money in the Measurement of Monetary Policy Michael T. Belongia and Peter N. Ireland Over the last twenty-five years, a set of influential studies has placed interest rates at the heart of analyses that interpret and evaluate monetary policies. In light of this work, the Federal Reserve's recent policy of "quantitative easing," with its goal of affecting the supply of liquid assets, appears as a radical break from standard practice. Superlative (Divisia) measures of money, however, often help in forecasting movements in key macroeconomic variables, and the statistical fit of a structural vector autoregression deteriorates significantly if such measures of money are excluded when identifying monetary policy shocks. These results cast doubt on the adequacy of conventional models that focus on interest rates alone. They also highlight that all monetary disturbances have an important "quantitative" component, which is captured by movements in a properly measured monetary aggregate.
2012	A “Working” Solution to the Question of Nominal GDP Targeting Michael T. Belongia and Peter N. Ireland This paper provides a method of using Divisia monetary aggregates in policy to target nominal GDP.
2012	Divisia Monetary Aggregates, the Great Ratios, and Classical Money Demand Functions Apostolos Serletis and Periklis Gogas King, Plosser, Stock, and Watson (1991) evaluate the empirical relevance of a class of real business cycle models with permanent productivity shocks by analyzing the stochastic trend properties of postwar U.S. macroeconomic data. They find a common stochastic trend in a three variable system that includes output, consumption, and investment, but the explanatory power of the common trend drops significantly when they add money balances and the nominal interest rate. In this paper Serletis and Gogas revisit the cointegration tests in the spirit of King et al. (1991), using improved monetary aggregates whose construction has been stimulated by the Barnett critique. They show that previous rejections of the balanced-growth hypothesis and classical money demand functions can be attributed to mis-measurement of the monetary aggregate. This study is forthcoming in Journal of Money, Credit and Banking.
2012	Problems with the Measurement of Banking Services in a National Accounting Framework Erwin Diewert, Dennis Flxler and Kimberly Zieschang The paper considers some of the problems associated with the indirectly measured components of financial service outputs in the System of National Accounts (SNA), termed FISIM ( Financial Intermediation Services Indirectly Measured). This paper is published in "National Accounting and Economic Growth" published by Elgar Research Collection in 2016.
2011	A Comprehensive Revision of the U.S. Monetary Services (Divisia) Indexes Richard G. Anderson and Barry E. Jones This paper about the St. Louis Federal Reserve Bank's Divisia monetary aggregates has appeared in the Federal Reserve Bank of St. Louis Review, Sept/Oct, vol. 93, no. 4, 2011, pp. 325-359.
2011	How Better Monetary Statistics Could Have Signaled the Financial Crisis William A. Barnett and Marcelle Chauvet This important paper explores the disconnect of Federal Reserve data from index number theory and contains some of the motivation for Barnett's forthcoming MIT Press book, Getting It Wrong. We find that most recessions in the past 50 years were preceded by more contractionary monetary policy than indicated by simple-sum monetary data. Divisia monetary aggregate growth rates were generally lower than simple-sum aggregate growth rates in the period preceding the Great Moderation, and higher since the mid 1980s. Monetary policy was more contractionary than likely intended before the 2001 recession and more expansionary than likely intended during the subsequent recovery. A revised draft of this paper appeared in the Journal of Econometrics, vol. 161, no. 1, March 2011, pp. 6-23.
2011	The Case for Divisia Money Targeting Apostolos Serletis and Sajjadur Rahman This important paper is forthcoming in the journal, Macroeconomic Dynamics.
2007	Multilateral Aggregation-Theoretic Monetary Aggregation over Heterogeneous Countries William A. Barnett This paper appeared in revised form in the Journal of Econometrics, vol. 136, no. 2, February 2007, pp 457-482. It derives fundamental new theory for measuring monetary service flows aggregated over countries within a multicountry economic union and for monitoring distribution effects across countries within the union. The longer form ECB working paper, also included within the AMFM library, incorporates more specialized theory relevant to application of the general theory to the European Monetary Union. This paper is reprinted in the book, Barnett and Chauvet (2011), as chapter 6, and a revised version appears as appendix 3 to the new book, Barnett (2011).
2005	On the User Costs of Risky Monetary Assets William A. Barnett and Shu Wu A revised draft of this working paper appered in the Annals of Finance," vol. 1, no. 1, January 2005, pp. 35-50, and has been reprinted in the book, Barnett and Chauvet (2011), as chapter 3. We extend the monetary-asset user-cost risk adjustment of Barnett, Liu, Xu, and Jensen (1997) and their risk-adjusted Divisia monetary aggregates to the case of multiple non-monetary assets and intertemporal non-separability. Our model generates larger and more accurate CCAPM user-cost risk adjustments than those in Barnett, Liu, Xu, and Jensen.
1997a	Fellow's Opinion: Econometrics, Data, and the World Wide Web William A. Barnett This paper advocated an increased role for independent centers in providing economic data on the web and can be viewed as anticipating this Center for Financial Stability over a decade in advance. A revised draft of this working paper appeared in the Journal of Econometrics, vol. 77, 1997, pp. 297-302.
1997b	Which Road Leads to Stable Money Demand William A. Barnett This important working paper was subsequently published in a special issue of the Economic Journal, vol. 107, no. 443, July 1997, pp. 1171-1185, and has been reprinted in the book, Barnett and Serletis (2000), as chapter 24.
1997	The CAPM Risk Adjustment Needed for Exact Aggregation over Financial Assets William A. Barnett, Yi Liu, Haiyang Xu, and Mark Jensen This fundamentally important paper extended the field of index number theory to the case of contemporaneous risk. Much of this working paper subsequently appeared as "The CAPM Risk Adjustment for Exact Aggregation over Financial Assets," by W. A. Barnett, Yi Liu, and Mark Jensen, in Macroeconomic Dynamics, vol. 1, no. 2, 1997, pp. 485-512, and has been reprinted in the book, Barnett and Serletis (2000), as chapter 12. Much of this theory is included in appendix 4 of the new book, Barnett (2011).
1996	Measurement Matters: Recent Results from Monetary Economics Reexamined Michael T. Belongia This paper appeared in the Journal of Political Economy, vol. 104, no. 5, October, pp. 1065-1083.
1995	Money, Output, and Prices: Evidence from a New Monetary Aggregate Julio J. Rotemberg, John C. Driscoll, and James M. Poterba This NBER Working Paper No. 3824 appeared in revised form in the Journal of Business and Economic Statistics, vol. 13, no. 1, January, pp. 67-83. The paper originated the CE index as a measure of monetary service flow. Barnett (1991) proved that the CE index is inferior to the Divisia index as a flow measure. But Barnett (1991) also proved that the CE index can measure the economic capital stock of money as the discounted, expected Divisia flow under martingale expectations. This result has motivated the subsequent research on measuring the economic capital stock of money under weaker assumptions on expectations, such as Barnett, Chae, and Keating (2006) and Barnett, Keating, and Kelly (2008).
1994	A Perspective on the Current State of Macroeconomic Theory William A. Barnett This original working paper has appeared in a revised form in the International Journal of Systems Science, vol. 25, no. 5, 1994, pp. 839-848, and has been reprinted in the book, Barnett and Serletis (2000), as chapter 25. That special edition consisted of opinion papers regarding the state of the field of macroeconomics. This paper contains my views on that subject.
1994	Empirical Evidence on the Recent Behavior and Usefulness of Simple-Sum and Weighted Measures of the Money Stock K. Alec Chrystal and Ronald MacDonald This paper coined the term "Barnett critique." The paper appeared in the St. Louis Federal Reserve Bank Review, March/April, vol. 76, no. 2, pp. 73 - 109.
1989	The Changing Empirical Definition of Money: Some Estimates from a Model of the Demand for Money Substitutes Michael T. Belongia and James A. Chalfant This paper appeared in the Journal of Political Economy, vol. 97, pp. 387-97.
1987	The Microeconomic Theory of Monetary Aggregation William A. Barnett This paper provides a systematic derivation of the theory of monetary aggregation under perfect certainty for consumers, firms, and financial intermediaries. The paper first appeared in W. A. Barnett and K. Singleton (eds.), New Approaches to Monetary Economics, and was reprinted as chapter 3 of the book, Barnett and Serletis (2000). A revised version of that paper appears as appendix 1 to the new book, Barnett (2011).
1987	Money in the Utility Function: An Empirical Implementation James M. Poterba and Julio J. Rotemberg This NBER Working Paper No. 1796 appeared in the book, Barnett and Singleton (eds.), New Approaches to Monetary Economics, Cambridge U. Press, pp. 219-240. This paper was the first to point out that index number theory had not been extended to the case risk in prices and interest rates. This important insight motivated the subsequent, successful extension of the field of index number theory to include risk by Barnett and Liu (1997) and Barnett, Liu, and Jensen (1997).
1984	The New Divisia Monetary Aggregates William A. Barnett, Edward K. Offenbacher, and Paul A. Spindt This paper, based upon Barnett (1980), contains the first empirical comparisons of Divisia monetary aggregates with simple-sum monetary aggregates in policy applications. That paper, published in the Journal of Political Economy, vol. 92, 1984, pp. 1049-1085, has been reprinted as chapter 17 of the book, Barnett and Serletis (2000).
1981	Aggregation of Monetary Assets William A. Barnett The landmark paper that began the modern literature on monetary aggregation and index number theory is Barnett's "Economic Monetary Aggregates: An Application of Index Number and Aggregation Theory," Journal of Econometrics, September 1980, pp. 11-48, and has been reprinted in the book, Barnett and Serletis (2000), as chapter 2. The published paper cannot be put online, since the copyright is owned by the publisher. But the original, longer working paper, which contains more than appears in the published journal article, appeared as chapter 7 of Barnett's book, Consumer Demand and Labor Supply. Since that book now is out of print, we can put that chapter online and have done so here.
1980	Economic Monetary Aggregates: An Application of Aggregation and Index Number Theory William A. Barnett This paper contains the first derivation of the Divisia money formula and the first computation and use of Divisia monetary aggregates. The paper also contains the derivation and use of the Fisher idea monetary-aggregation formula. The paper appeared in the Journal of Econometrics, vol. 14, pp. 11-48, and was reprinted in the book, Barnett and Serletis (2000), as chapter 1.
1978	The User Cost of Money William A. Barnett This paper, which contains the first mathematical derivation of the user-cost price of money, was published in Economic Letters, vol. 1, no. 2, pp. 145-149. The paper is reprinted as chapter 1 of the book, Barnett and Serletis (2000). This proof ended the long debate about the "price of money" and provided the initial result needed in Barnett's (1980) derivation of the Divisia and Fisher ideal monetary aggregates.
Secondary Papers Highly Relevant to AMFM
2018	Monetary Services Aggregation under Uncertainty: A Behavioral Economics Extension Using Choquet Expectation William A. Barnett, Qing Han, Jianbo Zhang A central tenet of behavioral economics is that the axioms producing expected utility maximization by consumers are too strong to be descriptive of rational behavior. The existing theory of monetary services aggregation under risk assume expected utility maximization. We extend those results to uncertainty under weaker axiomatic assumptions by using Choquet expectations. Choquet integration reduces to Riemann integration as a special case under the stronger assumption of additive probability measure, not accepted in the literature on behavioral economics. Our theoretical results on monetary services aggregation are generalizations of prior results, nested as special cases of our results under stronger behavioral assumptions.
2014	Asymmetric Fiscal Policy Shocks Ioannis Praggidis, Periklis Gogas, Vasilios Plakandaras, and Theophilos Papadimitriou This paper, which is forthcoming in The Journal of Economic Asymmetries, empirically tests the effects of unanticipated fiscal policy shocks on the growth rate and the cyclical component of real private output and reveal different types of asymmetries in fiscal policy implementation. The data used are quarterly U.S. observations over the period 1967 to 2011.
2013	Federal Reserve Transparency: Should We Want It? William A. Barnett This op ed cites serious defects in Fed data and identifies adverse effects on the economy. Barnett discusses possible solutions, including creation of independent alternative data sources, such as the Center for Financial Stability.
2013	Comparison of Simple Sum and Divisia Monetary Aggregates in GDP Forecasting: a Support Vector Machines Approach Periklis Gogas, Theophilos Papadimitriou, and Elvira Takli This study compares the forecasting ability of the simple sum and Divisia monetary aggregates with respect to U.S. GDP. The study uses machine learning techniques and concludes that Divisia monetary aggregates are superior to the simple sum monetary aggregates in terms of standard forecast evaluation statistics. This study is forthcoming in Economics Bulletin.
2012	Monetary Policy: Why Money Matters, and Interest Rates Don't Daniel L. Thornton Since the late 1980s the Fed has implemented monetary policy by adjusting its target for the overnight federal funds rate. Money’s role in monetary policy has been tertiary, at best. Indeed, several influential economists suggest that money is irrelevant for monetary policy: Central banks effect economic activity and inflation by a) controlling a very short-term nominal interest rate and b) by influencing financial market participants’ expectation of the future policy rate. Dr. Thornton offers an alternative perspective: namely, that money is essential for the central bank’s control over the price level and that the monetary authority’s ability to control interest rates is greatly exaggerated.
2011	Redundancy or Mismeasurement? A Reappraisal of Money Joshua R. Hendrickson A revised version of this paper is forthcoming in Macroeconomic Dynamics.
2011	Rethinking the Liquidity Puzzle: Application of a New Measure of the Economic Money Stock Logan J. Kelly, William A. Barnett, and John W. Keating A revised draft appeared in the Journal of Banking and Finance, vol. 35, no. 4, April 2011, pp. 765-1026.
2010	Audit the Federal Reserve? William A. Barnett A revised draft appeared in the Central Banking Journal, vol. 20, no. 3, February 2010, pp. 45-50.
2009a	Who's Looking at the Fed's Books? William A. Barnett This op ed appeared in the New York Times, October 22, 2009, p. A35.
2009b	This is No Way to Fix the Fed William A. Barnett This op ed appeared in the Kansas City Star, December 15, 2009, pp. C7 and C16.
2009a	International Financial Aggregation and Index Number Theory: A Chronological Half-Century Empirical Overview William A. Barnett and Marcelle Chauvet A revised draft of this working paper appeared in the Open Economies Review, vol. 20, no 1, February 2009, pp. 1 - 37, and has been reprinted in the book, Barnett and Chauvet (2011), as chapter 1.
2009b	The End of the Great Moderation William A. Barnett and Marcelle Chauvet This paper appeared in the 2009 JSM Proceedings, American Statistical Association, 2009.
2009	Admissible Clustering of Aggregator Components: A Necessary and Sufficient Stochastic Semi-Nonparametric Test for Weak Separability William A. Barnett and Philippe de Peretti Blockwise weak separability is the fundamental, necessary condition for clustering of goods or assets into an admissible group for aggregation. This paper provides a state-of-the-art procedure for testing that admissibility condition. A revised draft of this working paper appeared in Macroeconomic Dynamics, vol. 13, Supplement 2, 2009, September, pp. 317-334. A related paper by de Peretti, "Testing the Significance of the Departures from Weak Separability," appeared as chapter 1 in the book, W. A. Barnett and A. Serletis (2007), Functional Structure Inference, Elsevier, 2007, pp. 3-22.
2009	Measurement Error in Monetary Aggregates: A Markov Switching Factor Approach William A. Barnett, Marcelle Chauvet, and Heather Tierney A revised draft of this working paper appeared in Macroeconomic Dynamics, vol. 13, Supplement 2, 2009, September, pp. 381-412, and has been reprinted in the book, Barnett and Chauvet (2011), as chapter 7.
2008a	Divisia Monetary Index William A. Barnett A revised draft of this encyclopedia entry appeared in William A. Darity (ed.), International Encyclopedia of the Social Sciences, 2nd Edition, vol. 2, Macmillan Reference, Detroit, 2008, pp. 422-423.
2008b	Supply of Money William A. Barnett A revised version of this encyclopedia entry appeared in William A. Darity (ed.), International Encyclopedia of the Social Sciences, 2nd Edition, vol. 5, Macmillan Reference, Detroit, 2008, pp. 260-261.
2008c	What Broke the Bubble? William A. Barnett A shorter version of the paper, without the charts, appeared as a Guest Commentary in the Kansas City Star Business Weekly on Tuesday, November 11, 2008, Section D, pp. D8-D9.
2008	Operational Identification of the Complete Class of Superlative Index Numbers: an Application of Galois Theory William A. Barnett and Ki-Hong Choi A revised draft of this working paper appeared in the Journal of Mathematical Economics, vol. 44, no. 7, July 2008, pp. 603-612.
2008	Divisia Second Moments: An Application of Stochastic Index Number Theory William A. Barnett, Barry E. Jones, and Travis D. Nesmith This paper appeared in the International Review of Comparative Public Policy, vol. 8, pp. 115-138.
2008	Toward a Bias Corrected Currency Equivalent Index William A. Barnett, John W. Keating, and Logan J. Kelly A revised draft of this working paper appeared in Economics Letters, vol. 100, issue 3, Sept 2008, pp. 448-451.
2007	Aggregation-Theoretic Monetary Aggregation over the Euro Area, when Countries are Heterogeneous William A. Barnett This paper also is available as ECB Working Paper No. 260 on the web site of the European Central Bank. A revised, shorter version of this working paper was published as "Multilateral Aggregation-Theoretic Monetary Aggregation over Heterogeneous Countries," in the Journal of Econometrics, vol. 136, no. 2, February 2007, pp. 457-482. A draft of the shorter, published version also is in the AMFM library.
2007	The Role of U.S. Risky Monetary Aggregate Young Jin Ro This PhD dissertation at the State University of New York at Binghamton produces broad Divisia monetary aggregates including bond mutual funds for the US. The dissertation incorporates CCAPM adjustment for risk.
2007	Flexible Functional Forms, Curvature Conditions, and the Demand for Assets Apostolos Serletis and Asghar Shahmoradi This paper appeared in Macroeconomic Dynamics, vol. 11, pp. 455-486.
2006	Is Macroeconomics a Science? William A. Barnett A revised draft of this paper appeared as the foreword to the book, Apostolos Serletis (2006).
2006	Exchange Rate Determination from Monetary Fundamentals: an Aggregation Theoretic Approach William A. Barnett and Chang Ho Kwag This paper finds that the monetary model of exchange rate determination, which has usually been found not to work with simple-sum monetary aggregates, succeeds when Divisia monetary aggregates are used. A slightly revised draft appeared in Frontiers in Finance and Economics, vol. 3, no. 1, 2006, pp. 29-48, and has been reprinted in the book, Barnett and Chauvet (2011), as chapter 5.
2006	The Own-Price of Money and the Channels of Monetary Transmission Michael T. Belongia and Peter N. Ireland This paper appeared in the Journal of Money, Credit, and Banking, vol 38, 429-445.
2006	The Discounted Economic Stock of Money with VAR Forecasting William A. Barnett, Unja Chae, and John Keating A revised draft appeared in the Annals of Finance, vol. 2, no. 2, July 2006, pp. 229-258. This paper measures the economic stock of money as the discounted present value of the Divisia service flow under various assumptions about expectations. The results have important implications for measurement of the wealth effects of monetary policy.
2005	Revisions to User Costs for the Federal Reserve Bank of St. Louis Monetary Services Indices Richard G. Anderson and Jason Buol This paper appeared in the Federal Reserve Bank of St. Louis Review, November/December, vol. 87, no. 6, pp. 735-749.
2005	Sweep Programs and Optimal Monetary Aggregation Barry Jones, Donald Dutkowsky, and Thomas Elger This paper appeared in the Journal of Banking and Finance, vol. 29, pp. 483-508.
2005	The Nonlinear Skeletons in the Closet William A. Barnett, Barry E. Jones, Milka Kirova, Travis Nesmith, and Meenakshi Pasupathy A revised draft of this paper appeared in the book, Belongia and Binner (2005), pp. 9-42.
2004	Searching for Divisia / Inflation Relationships with the Aggregate Feedforward Network V. Schmidt and J. M. Binner This paper appeared in Advances in Econometrics, vol. 19, pp. 225-241.
2004	Co-Evolving Neural Networks with Evolutionary Strategies: a New Application to Divisia Money J. M. Binner, G. Kendall, and A. M. Gazely This paper appeared in Advances in Econometrics, vol. 19, pp. 127-144.
2003	Divisia Index, Inflation, and Welfare Rubens Penha Cysne This working paper subsequently appeared in the Journal of Money, Credit, and Banking, 2003, vol. 35, no. 2, April, pp. 221-238. The paper extends Lucas's research on the welfare cost of inflation to the case of interest bearing money.
2003	The Differential Approach to Superlative Index Number Theory William A. Barnett, Ki-Hong Choi, and Tara M. Sinclair A revised version of this working paper appeared in a special issue of Agricultural and Applied Economics, vol. 35, supplement, 2003, pp. 59-64.
2001	The Relative Forecasting Performance of the Divisia and Simple Sum Monetary Aggregates Donald L. Schunk This paper appeared in the Journal of Money, Credit and Banking, vol. 33, pp. 272-283.
2000	Divisia Indexes, Money and Welfare Rubens Penha Cysne This paper suggests the use of a particular Divisia index for measuring welfare losses due to interest rate wedges and inflation.
2000	Microeconomic Foundations of an Optimal Currency Area James L. Swofford This paper appeared in the Review of Financial Economics, vol. 9, pp. 121-128.
2000	Beyond the Risk Neutral Utility Function William A. Barnett and Yi Liu This working paper appeared in revised form in the book, Belongia and Binner (2000), pp. 11-27.
2000	The Exact Theoretical Rational Expectations Monetary Aggregate William A. Barnett, Melvin J. Hinich, and Piyu Yue This working paper subsequently appeared in revised form in Macroeconomic Dynamics, June 2000, vol. 4, no. 2, pp. 197-221, and has been reprinted in the book, Barnett and Chauvet (2011), as chapter 2.
1999	Divisia Money in a Composite Leading Indicator of Inflation. J. M. Binner, A. Fielding, and A. W. Mullineux A revised version of this paper appeared in Applied Economics, vol. 31, pp. 1021-1031.
1998	Money Velocity with Interest Rate Stochastic Volatility and Exact Aggregation William A. Barnett and Haiyang Xu This paper appeared in revised form as "Stochastic Volatility in Interest Rates and Nonlinearity" in the International Journal of Systems Science, 1998, vol. 29, no. 11, pp. 1189-1201, and has been reprinted in the book, Barnett and Serletis (2000), as chapter 13.
1997	The CAPM-Extended Divisia Monetary Aggregate with Exact Tracking under Risk William A. Barnett and Yi Liu Much of this working paper subsequently appeared as "The CAPM Risk Adjustment for Exact Aggregation over Financial Assets," by W. A. Barnett, Yi Liu, and Mark Jensen, in Macroeconomic Dynamics, vol 1, no 2, 1997, pp. 485-512. This research extended the field of index number theory to the case of risk.
1997a	Building New Monetary Services Indexes: Concepts, Data, and Methods Richard G. Anderson, Barry E. Jones, and Travis D. Nesmith This paper appeared in the Federal Reserve Bank of St. Louis Review, vol. 79, 1997, pp. 53-82.
1997b	Monetary Aggregation Theory and Statistical Index Numbers Richard G. Anderson, Barry E. Jones, and Travis D. Nesmith This paper appeared in the Federal Reserve Bank of St. Louis Review, vol. 79, 1997, pp. 31-51.
1997c	Introduction to the St. Louis Monetary Services Index Project Richard G. Anderson, Barry E. Jones, and Travis D. Nesmith This paper appeared in the Federal Reserve Bank of St. Louis Review, vol. 79, 1997, pp. 25-29, and has been reprinted in the book, Barnett and Serletis (2000), as appendix A. The paper documents the work done there to produce its Divisia monetary aggregates, which the St. Louis Fed calls the Monetary Services Indexes (MSI). A newer paper is expected to appear in that Review documenting the updated vintage of MSI, following the five year freeze of the data.
1996	Statistics under the Spotlight: Improving the Consumer Price Index William A. Barnett, Katharine G. Abraham, Robert J. Gordon, Jack E. Triplett, David W. Wilcox, and Kirk M. Wolter This document includes the transcript of a tape-recorded statement by W. A. Barnett and the panel discussion that followed on the subject of the Consumer Price Index and of federal data quality. The tape recording was from an invited session, organized by the Bureau of Labor Statistics, at the annual meetings of the American Statistical Association in Chicago in 1996. Plots are provided of a newly merged long term data base produced by splicing Commerce Department data with Kuznet's earlier historical data base. The result is consumption quantity and price data at various levels of aggregation linked directly to federal data updates, but extending back over a century of economic history. This unique data base was produced by Barry Jones and Travis Nesmith, while working as Visiting Scholars at the St. Louis Federal Reserve Bank. The full transcript appeared in the American Statistical Association's 1996 Proceedings of the Section on Government Statistics.
1995	Estimating Policy-Invariant Technology and Taste Parameters in the Financial Sector, When Risk and Growth Matter William A. Barnett, Milka Kirova, Meenakshi Pasupathy, and Piyu Yue This working paper appeared in revised form in the Journal of Money, Credit, and Banking, November 1995, vol. 27, part 2, pp. 1402-1430, and has been reprinted in the book, Barnett and Serletis (2000), chapter 22.
1992	An Extended Series of Divisia Monetary Aggregates Daniel L. Thornton and Piyu Yue This paper appeared in the Federal Reserve Bank of St. Louis Review, November/December, pp. 35-52.
1992	Consumer Theory and the Demand for Money William A. Barnett, Douglas Fisher, and Apostolos Serletis This paper surveys the literature on the demand for money and on monetary measurement in a manner intended to be accessible to nonspecialists. The paper appeared in the Journal of Economic Literature, vol. 30, pp. 2086-2119 and has been reprinted in the book, Barnett and Serletis (2000), as chapter 18, pp. 167-194.
1991	A Reply to Julio J. Rotemberg William A. Barnett This paper appeared in the book, M. T. Belongia (ed.), Monetary Policy on the 75th Anniversary of the Federal Reserve System, Kluwer Academic, Boston, pp. 232-244, and has been reprinted in the book, Barnett and Serletis (2000), as chapter 14. The theory developed in this paper is the foundation for appendix 2 in the new book, Barnett (2011). The paper derives the economic stock of money as the discounted present value of the service flow and shows that the CE index can measure that stock under martingale expectations.
1991	The Demand for Divisia Money in the United States: A Dynamic Flexible Demand System Apostolos Serletis This paper appeared in the Journal of Money, Credit and Banking, vol. 23, pp. 35-52.
1985	The Financial Firm: Production with Monetary and Non-Monetary Goods Diana Hancock This paper appeared in the Journal of Political Economy, vol. 93, pp. 859-880.
1985	Currency Substitution and the New Divisia Monetary Aggregates: The U. S. Case Jaime Marquez This paper is Federal Reserve Board International Finance Discussion Paper 257. A revised draft appeared as "Money Demand in Open Economies: A Divisia Application to the U. S. Case," in W. A. Barnett and K. J. Singleton (eds.), New Approaches to Monetary Economics, Cambridge University Press, 1987.
1985	Revisions to the Monetary Services (Divisia) Indexes of the Monetary Aggregates Helen T. Farr and Deborah Johnson This paper appeared as Federal Reserve Board Staff Study 147.
1984	Recent Monetary Policy and the Divisia Monetary Aggregates William A. Barnett This paper demonstrated that Paul Volcker's policy during the period of the "monetarist experiment" produced a recession, because the policy was tighter than reflected by the official simple-sum monetary aggregates. Those simple-sum aggregates were on the intended target path, but the Divisia monetary aggregates were growing half as fast as the simple-sum aggregates and hence produced a greater shock to the economy than intended. The paper appeared in the American Statistical Association journal, the American Statistician, vol. 38, pp. 162-172, and is reprinted in the book, Barnett and Serletis (2000), as chapter 23.
1983a	New Indices of Money Supply and the Flexible Laurent Demand System William A. Barnett The "Barnett critique" is about internal inconsistency among data construction formulas and the models within which the formulas are used in applications. That internal inconsistency can produce the appearance of structural change, when none has occurred. The paper specifies and estimates a new demand-for-money system of equations, with Divisia monetary aggregates nested within them, in an entirely coherent manner. The paper appeared in the Journal of Business and Economic Statistics, vol. 1, pp. 7-23 and has been reprinted in the book, Barnett and Serletis (2000), as chapter 16. A more recent, similar paper by Apostolos Serletis and Asghar Shahmoradi, "Bayesian Estimation of Flexible Functional Forms, Curvature Conditions and the Demand for Assets," appears as chapter 4 in the book, W. A. Barnett and A. Serletis (2007), Functional Structure Inference, Elsevier, 2007, pp. 59 - 84.
1983b	Understanding the New Divisia Monetary Aggregate William A. Barnett This paper was produced to make the Divisia-monetary-aggregates formula understandable to users not fully familiar with the relevant index-number and aggregation theories. The paper also explains the source of various occasional misunderstandings about the formula and theory. The paper appeared in the Review of Public Data Use, vol. 11, pp. 349-355 and has been reprinted in the book, Barnett and Serletis (2000), as chapter 4. A revised version also appears as appendix 5 in the new book, Barnett (2011).
1982	The Optimal Level of Monetary Aggregation William A. Barnett This paper explores the theory and empirical evidence relevant to choosing the optimal level of monetary aggregation. When components are properly weighted in accordance with index number theory, the broadest level of aggregation captures the most information. Sadly the Federal Reserve, in correctly recognizing that improperly-weighted monetary aggregates deteriorate as the level of aggregation increases, terminated its two broad aggregates, M3 and L, rather than correcting the improperly-weighted simple-sum formula. The paper originally appeared in the Journal of Money, Credit, and Banking, vol 1, pp. 687-710 and has been reprinted in the book, Barnett and Serletis (2000), as chapter 7.
1976	Exact and Superlative Index Numbers W. Erwin Diewert This paper appeared in the Journal of Econometrics, vol. 4, pp. 115-45. The paper unified the fields of index number theory and aggregation theory over goods.
1963	Capital Theory and Investment Behavior Dale W. Jorgenson This paper appeared in the American Economic Review, vol. 53, pp. 247-259.
Technical Papers Relevant to Use within Econometric Models
2009a	Measuring Consumer Preferences and Estimating Demand Systems William A. Barnett and Apostolos Serletis A revised draft of this working paper appeared in Daniel Slottje (ed.), Quantifying Consumer Preferences, Contributions to Economic Analysis, Emerald Press, Bingley, UK, 2009, pp. 1-35.
2009b	The Differential Approach to Demand Analysis and the Rotterdam Model William A. Barnett and Apostolos Serletis A revised draft appeared in Daniel Slottje (ed.), Quantifying Consumer Preferences, Contributions to Economic Analysis, Emerald Press, Bingley, UK, 2009, pp. 61-81.
2008	Rotterdam Model versus Almost Ideal Demand System: Will the Best Specification Please Stand Up? William A. Barnett and Ousmane Seck A revised draft of this working paper appeared in the Journal of Applied Econometrics, vol. 23, no. 23, 2008, pp. 798-824.
2008	Consumer Preferences and Demand Systems William A. Barnett and Apostolos Serletis A revised draft of this working paper appeared in the Journal of Econometrics, vol. 147, 2008, pp. 210-224.
2007	The Theoretical Regularity Properties of the Normalized Quadratic Consumer Demand Model William A. Barnett and Ikuyasu Usui A revised draft of this working paper appeared in the book, W. A. Barnett and A. Serletis (2007), Functional Structure Inference, Elsevier, 2007, pp. 107 - 127.
2003	Regularity of the Generalized Quadratic Production Model: A Counterexample William A. Barnett and Meenakshi Pasupathy A revised version of this working paper appeared on pp. 135 - 154 of Econometric Reviews, vol. 22, no. 2, 2003.
2002	Tastes and Technology: Curvature is not Sufficient for Regularity William A. Barnett A revised version of this working paper appeared in the Journal of Econometrics, vol. 108, no. 1, May 2002, pp. 199-202, and has been reprinted in the book, Barnett and Binner (2004), as chapter 17.
2002	Technology Modeling: Curvature is not Sufficient for Regularity William A. Barnett, Milka Kirova, and Meenakshi Pasupathy A revised draft of this working paper appeared in the Journal of Econometrics, vol. 108, no. 1, May 2002, pp. 199-202.
1994	Financial Firms' Production and Supply-Side Monetary Aggregation Under Dynamic Uncertainty William A. Barnett and Ge Zhou This paper appeared in the Federal Reserve Bank of St. Louis Review, March/April, pp. 133-165, and has been reprinted in the book, Barnett and Serletis (2000), as chapter 21.
1990	A Dispersion-Dependency Diagnostic Test for Aggregation Error: with Applications to Monetary Economics and Income Distribution William A. Barnett and Apostolos Serletis A revised draft of this paper appeared in the Journal of Econometrics, vol. 43, pp. 5-34, and has been reprinted in the book, Barnett and Serletis (2000), as chapter 9.
Technical Papers Relevant to Nonlinear Dynamic Modeling
2015	Bifurcation of Macroeconometric Models and Robustness of Dynamical Inferences William A. Barnett and Guo Chen Bifurcation has long been a topic of interest in dynamical macroeconomic systems. Bifurcation analysis is important in understanding dynamic properties of macroeconomic models as well as in selection of stabilization policies. The goal of this survey is to summarize work by William A. Barnett and his coauthors on bifurcation analyses in macroeconomic models to facility and motivate work by others on further models. This paper appeared in Studies in Applied Economics No.32/ April 2015 from the Johns Hopkins Institute for Applied Economics, Global Health and Study for Business Enterprise.
2011	Bifurcation Analysis of Zellner's Marshallian Macroeconomic Model Sanjibani Banerjee, William A. Barnett, Evgeniya Duzhak, and Ramu Gopalan A revised draft of the paper appeared in the Journal of Economic Dynamics and Control, vol 35, no. 9, September 2011, pp. 1577-1585.
2010	Empirical Assessment of Bifurcation Regions within New Keynesian Models William A. Barnett and Evgeniya Aleksandrovna Duzhak A revised draft appeared in the journal, Economic Theory, vol. 45, nos. 1-2, 2010, pp. 99-128.
2010	Existence of Singularity Bifurcation in an Euler-Equations Model of the United States Economy: Grandmont was Right William A. Barnett and Susan He A revised draft appeared in a special issue of the journal, Economic Modelling, vol. 27, no. 6, November 2010, pp. 1345-1354.
2008	Non-Robust Dynamic Inferences from Macroeconometric Models: Bifurcation Stratification of Confidence Regions William A. Barnett and Evgeniya Aleksandrovna Duzhak A revised draft of this working paper appeared in Physica A, vol. 387, pp. 3817-3825.
2007	Gains from Synchronization William A. Barnett and Mehmet Dalkir This paper investigates the transmission mechanisms of noise and volatility among countries through trade links and the effects of synchronization on business cycles. A revised version of this working paper appeared in Studies in Nonlinear Dynamics and Econometrics, vol. 11, no. 1, March 2007, article 2, pp. 1 - 28.
2006	Singularity Bifurcation Yijun He and William A. Barnett A revised version of this working paper appeared in the Journal of Macroeconomics, vol. 28, 2006, pp. 5-22.
2004	Center Manifold, Stability, and Bifurcations in Continuous Time Macroeconometric Systems William A. Barnett and Yijun He A revised version of this working paper subsequently was included as "Bifurcations in Macroeconomic Models," in the book, Steve Dowrick, Rohan Pitchford, and Steven Turnovsky (eds), Economic Growth and Macroeconomic Dynamics: Recent Developments in Economic Theory, Cambridge University Press, 2004, pp. 95-112.
2002	Stabilization Policy as Bifurcation Selection: Would Keynesian Policy Work if the World Really were Keynesian William A. Barnett and Yijun He A revised version of this working paper appeared in Macroeconomic Dynamics, vol. 6, no. 5, November 2002, pp. 713-747.
2001	Unsolved Econometric Problems in Nonlinearity, Chaos, and Bifurcation William A. Barnett and Yijun He A revised version of this working appear appeared in the Central European Journal of Operations Research, vol. 9, July 2001, pp. 147-182.
2000	Martingales, Nonlinearity, and Chaos William A. Barnett and Apostolos Serletis This working paper was subsequently published in revised form in the Journal of Economic Dynamics and Control, June 2000, vol. 24, pp. 703-724. The subject of the paper is the relationship between the efficient markets hypothesis and chaotic dynamics. We explore the question of whether or not dynamical systems theory is relevant to finance, and we report on empirical evidence.
1999	Bifurcation in Continuous-Time Macroeconomic Systems William A. Barnett and Yijun He A revised version of this original working paper was subsequently published as "Stability Analysis of Continuous-Time Macroeconometric Systems," in Studies in Nonlinear Dynamics and Econometrics, January 1999, vol. 3, no. 4, pp. 169-188.
1997	Nonlinear and Complex Dynamics in Economics William A. Barnett, Alfredo Medio, and Apostolos Serletis This paper consists of a survey of the economics literatures on nonlinearity, complex dynamics, and chaos. The paper surveys both the theoretical and empirical research in these areas and emphasizes unsolved problems and unresolved issues. A revised draft will be published in Macroeconomic Dynamics.
1997	A Single-Blind Controlled Competition Among Tests for Nonlinearity and Chaos William A. Barnett, A. Ronald Gallant, Melvin J. Hinich, Jochen A. Jungeilges, Daniel T. Kaplan, and Mark J. Jensen This working paper contains the results of a large scale competition. The tests entered into the competition include White's neural net test, the BDS test, Kaplan's test, the NEGM Lyapunov exponent test, and the Hinich bispectrum test. The paper has been published in slightly revised form in the Journal of Econometrics, vol. 77, 1997, pp. 297-302, and has been reprinted in the book, Barnett and Binner (2004), as chapter 26.

Studies Using or Producing International Divisia Monetary Aggregates

	Australia
2000	Weighted Monetary Aggregates: Empirical Evidence for Australia G. C. Lim and Vance L. Martin This paper appeared in the book, Belongia and Binner (2000), pp. 249-262.
1985	A Divisia System Approach to Modeling Monetary Aggregates T. V. Hoa This paper appeared in Economics Letters, vol. 17, pp. 365-368.
	Austria
1996	Aggregating Money Demand in Europe with a Divisia Index Katrin Wesche This paper, using pre-euro data, is University of Bonn Institute für Internationale Wirtschaftspolitik Projektbereich B Discussion Paper No. B-392, November.
1985	Monetary Aggregates, Their Information Content and Their Aggregation Error: Some Preliminary Findings for Austria, 1965-1980 M. J. Driscoll, J. L. Ford, A. W. Mullineux, and W. Kohler This paper about pre-euro Austria appeared in Empirical Economics, vol. 10, pp. 13-25.
	Bahrain
2012	Divisia Monetary Aggregates for the GCC Countries Ryadh M. Alkhareif and William A. Barnett This paper is forthcoming in the book, W. A. Barnett and F. Jawadi (eds.), Recent Developments in Alternative Finance: Empirical Assessments and Economic Implications, Emerald Press.
	Barbados
1989	Money: Its Measure and its Influence on the Economy of Barbados Kurt Lambert This research is a Master's thesis at the University of Texas at Austin.
	Belgium
1996	Aggregating Money Demand in Europe with a Divisia Index Katrin Wesche This paper using pre-euro data is University of Bonn Institute für Internationale Wirtschaftspolitik Projektbereich B Discussion Paper No. B-392, November.
	Brazil
2002	Indicadores Derivados de Agregados Monetários F. A. F. Neto and J. Albuquerque This central bank working paper is in Trabalhos para Discussão 47, Banco Central do Brasil, Setembro.
2000	Weighted Monetary Aggregation: an Analysis of Causality J. A. Devino This paper appeared in "Economia Aplicada," São Paulo, vol. 4, pp. 723-742.
1997	An Analysis of the Money Demand Using Divisia Monetary Aggregates and Box-Cox Transformation J. A. Devino This paper appeared in Revista Nova Economia, Belo Horizonte, FACE/UFMG, December, pp. 181-246.
	Bulgaria
1997	Money Aggregates in a Transition Economy: the Case of Bulgaria, 1991-1995 Georgy Ganev This research is a Ph.D. thesis at Washington University in St. Louis.
	Canada
2000	The Canadian Experience with Weighted Monetary Aggregates David Longworth and Joseph Atta-Mensah This paper appeared in the book, Belongia and Binner (2000), pp. 265-291.
2000	Monetary Aggregation and Monetary Policy A. Serletis and T. E. Molik This paper appeared in Money, Monetary Policy and Transmission Mechanisms, Bank of Canada, pp. 103-135.
1998	The Demand for Money in an Open Economy: Some Evidence for Canada C. J. Hueng This paper appeared in the North American Journal of Economics and Finance, vol. 9, pp. 15-31.
1994	The Canadian Experience with Weighted Monetary Aggregates David Longworth and Joseph Atta-Mensah This paper is a Bank of Canada Working Paper.
1981	A Comparison of Alternative Methods for Monetary Aggregation: Some Preliminary Evidence J. Cockerline and J. Murray This paper is Technical Report #28, Bank of Canada, Ottawa, Canada.
1978	Modeling the Demand for Liquid Assets: An Application to Canada Donal J. Donovan This is IMF Staff Paper #25, pp. 676-704.
	Chile
1990	Divisia Monetary Aggregates: Could They Have Made a Difference in Chilean Monetary Policy, 1970-1987? Katerina Taiganides This research is a Master's thesis at the University of Texas at Austin.
	China
2016	Chinese Divisia Monetary Index and GDP Nowcasting William A. Barnett and Biyan Tang Abstract Since China's enactment of the Reform and Opening-Up policy in 1978, China has become one of the world's fastest growing economies, with an annual GDP growth rate exceeding 10% between 1978 and 2008. But in 2015, Chinese GDP grew at 7%, the lowest rate in 5 years. Many corporations complain that the borrowing cost of capital is too high. This paper constructs Chinese Divisia monetary aggregates M1 and M2, and, for the first time, constructs the broader Chinese monetary aggregates, M3 and M4. Those broader aggregates have never before been constructed for China, either as simple-sum or Divisia. The results shed light on the current Chinese monetary situation and the increased borrowing cost of money. GDP data are published only quarterly and with a substantial lag, while many monetary and financial decisions are made at a higher frequency. GDP nowcasting can evaluate the current month's GDP growth rate, given the available economic data up to the point at which the nowcasting is conducted. Therefore, nowcasting GDP has become an increasingly important task for central banks. This paper nowcasts Chinese monthly GDP growth rate using a dynamic factor model, incorporating as indicators the Divisia monetary aggregate indexes, Divisia M1 and M2 along with additional information from a large panel of other relevant time series data. The results show that Divisia monetary aggregates contain more indicator information than the simple sum aggregates, and thereby help the factor model produce the best available nowcasting results. In addition, our results demonstrate that China's economy experienced a regime switch or structure break in 2012, which a Chow test confirmed the regime switch. Before and after the regime switch, the factor models performed differently. We conclude that different nowcasting models should be used during the two regimes.
2007	Divisia Monetary Indexes of Aggregate Money: Measurement Method and Case Study Guo Hong-Xia This research is based on the author's Master's thesis at Hunan University in 2007.
2000	Monetary Services and Money Demand in China Q. Yu and A. K. Tsui This paper appeared in the China Economic Review, vol. 11, pp. 134-148.
	Denmark
2006	The Problem of Measuring Money: Results from an Analysis of Divisia Monetary Aggregates for Denmark Lisbeth la Cour This paper appeared in the book, Belongia and Binner (2006), pp. 185-210.
	European Monetary Union
2022	Euro area monetary asset demand and Divisia aggregates Adrian R. Fleissig, Barry E. Jones Zsolt Darvas Monetary asset user costs are functions of spreads between a benchmark rate of return and the own rates of return on the monetary assets. We analyze the impact of the benchmark rate on a Euro area Divisia M2 aggregate, on estimated elasticities of substitution, and on estimated impulse response functions. Substitution in response to changes in the user cost of M1 is generally elastic, but we find evidence of inelastic substitution along other dimensions. When a loan rate is used as the benchmark, substitution in response to changes in the user costs of the two components of M2-M1 is inelastic throughout the sample and the corresponding elasticity estimates are near their lowest levels during the pandemic. This is strong evidence that Divisia monetary aggregates are preferable to conventional monetary aggregates. Annual growth rates of simple sum and Divisia M2 monetary aggregates differ significantly in some periods, but not during the pandemic. Estimated impulse response functions using both Divisia and simple sum money measures indicate that money shocks have positive and statistically significant effects on real output. The response of the price level to a money shock tends to be more persistent when the models are estimated using Divisia aggregates.
2021	Multilateral Divisia Monetary Aggregates for the Euro Area William A Barnett and Neepa Gaekwad In light of the "two-pillar strategy" of the European Central Bank, good measures of aggregated moneyacross countries in the Euro area are policy relevant. The objective of this paper is to focus on the multilateral Divisia monetary aggregates for the Euro area to produce a theoretically consistent measure of monetary services for the Euro area monetary union. Based on theory developed in Barnett (2007), the multilateral Divisia monetary aggregates for 17 Euro area countries are found to provide a better signal of recession, when compared to the corresponding simple sum monetary aggregates.
2020	Strengthening the Second Pillar: A Greater Role for Money in Achieving the ECB's Nominal Objectives Michael T. Belongia and Peter N. Ireland Like most central banks, the European Central Bank makes and implements its monetary policy decisions by adjusting its targets for short-term interest rates in response to information gleaned from a wide range of macroeconomic indicators and projections. Unlike many other central banks, however, the ECB also monitors money growth as a "cross check" against the macroeconomic analysis that guides its policies of interest rate management. This paper argues that making further use of this "second pillar" would help the ECB to better achieve its nominal objectives in the present environment of exceptionally low inflation. By modifying the "P-star" framework — a small-scale model with Quantity Theory foundations — the paper shows how the ECB could use its influence over Divisia money growth to stabilize nominal spending around a target path, even while its traditional interest rate policies are constrained by the zero lower bound.
2019	Divisia Monetary Aggregates for a Heterogeneous Euro Area Maximilian Brill, Dieter Nautz, and Lea Sieckman We introduce a Divisia monetary aggregate for the euro area that accounts for the heterogeneity across member countries both, in terms of interest rates and the decomposition of monetary assets. In most of the euro area countries, the difference between the growth rates of the country-speci?c Divisia aggregate and its simple sum counterpart is particularly pronounced before recessions. The results obtained from a panel probit model con?rm that the divergence between the Divisia and the simple sum aggregate has a signi?cant predictive content for recessions in euro area countries.
2019	Money Neutrality, Monetary Aggregates and Machine Learning Periklis Gogas, Theophilos Papadimitriou and Emmanouil Sofianos The issue of whether or not money affects real economic activity (money neutrality) has attracted significant empirical attention over the last five decades. If money is neutral even in the short-run, then monetary policy is ineffective and its role limited. If money matters, it will be able to forecast real economic activity. In this study, we test the traditional simple sum monetary aggregates that are commonly used by central banks all over the world and also the theoretically correct Divisia monetary aggregates proposed by the Barnett Critique (Chrystal and MacDonald, 1994; Belongia and Ireland, 2014), both in three levels of aggregation: M1, M2, and M3. We use them to directionally forecast the Eurocoin index: A monthly index that measures the growth rate of the euro area GDP. The data span from January 2001 to June 2018. The forecasting methodology we employ is support vector machines (SVM) from the area of machine learning. The empirical results show that: (a) The Divisia monetary aggregates outperform the simple sum ones and (b) both monetary aggregates can directionally forecast the Eurocoin index reaching the highest accuracy of 82.05% providing evidence against money neutrality even in the short term.
2014	Does Money Matter in the Euro Area? Evidence from a New Divisia Index Zsolt Darvas The author has created a euro-area Divisia-money dataset and estimate theoretically correct responses to money, user cost and interest rate shocks using structural vector-autoregressions. His findings suggest that money matters for output, prices and interest rates, while the European Central Bank can influence monetary developments. Since no Divisia monetary aggregates are available for the euro area, the author has first created and made available a database on euro-area Divisia monetary aggregates. Plans are in place to update the dataset in the future and keep it publicly available.
2009	Comparison of Simple Sum and Divisia Monetary Aggregates Using Panel Data Analysis S. Celik and S. Uzun This paper appeared in the International Journal of Social Sciences and Humanity Studies, vol. 1, pp. 1-13.
2009	Admissable Monetary Aggregates for the Euro Area J. M. Binner, R. K. Bissoondeeal, C. T. Elger, B. E. Jones, and A. W. Mullineux This paper appeared in the Journal of International Money and Finance, vol. 28, pp. 99-114.
2008	Evaluating the Performance of a EuroDivisia Index Using Artificial Intelligence Techniques. J. M. Binner, A. M. Gazely, and G. Kendall A revised version of this paper appeared in International Journal of Automation and Computing, vol. 5, pp. 58-62.
2005	A Comparison of Linear Forecasting Models and Neural Networks; An Application to Euroinflation and EuroDivisia J. M. Binner, R. Bissoondeeal, T. Elger, A. M. Gazely, and A. W. Mullineux A revised version of this paper appeared in Applied Economics, vol. 37, pp. 665-680.
2003	Aggregation-Theoretic Monetary Aggregation over the Euro Area, When Countries Are Heterogeneous W. A. Barnett This paper is European Central Bank Working Paper No. 260, available on the ECB's web site. A shorter form appeared as Barnett (2007) in the Journal of Econometrics. For the reference to that published paper, see the Important Papers Highly Relevant to AMFM Section of the AMFM library.
2002	Analysing Divisia Aggregates for the Euro Area H. E. Reimers This paper, using pre-euro data, is Discussion Paper 13/02, Economic Research Centre of the Deutsche Bundesbank, Frankfurt.
2001	Does Liquidity Matter: Properties of a Synthetic Divisia Monetary Aggregate in the Euro Area L. Stracca The paper is European Central Bank Working Paper no. 79, Frankfurt.
2001	Constructing Historical Euro-Zone Data A. Beyer, J. A. Doornick, and D. F. Hendry This paper appeared in the Economic Journal, vol. 111, pp. 308-327.
2000	Divisia Aggregates and the Demand for Money in Core EMU M. M. G. Fase This paper appeared in the book, Belongia and Binner (2000), pp. 138-172.
1997	Monetary Integration and Currency Substitution in the EMS: The Case of a European Monetary Aggregate P. Spencer This article appeared in the European Economic Review, vol. 41, pp. 1403-1419.
1997	The Demand for Divisia Money in a Core Monetary Union K. Wesche This paper appeared in the Federal Reserve Bank of St. Louis Review, vol. 7, pp. 51-60.
1996	Aggregating Money Demand in Europe with a Divisia Index Katrin Wesche This paper, using pre-euro data, is University of Bonn Institute für Internationale Wirtschaftspolitik Projektbereich B Discussion Paper No. B-392, November.
1994	Money Demand within the EMU: an Analysis with the Divisia Measure M. M. G. Fase and C. C. A. Winder This paper appeared in De Nederlandsche BankNV, Amsterdam, pp. 25-55.
	Finland
2002	Analysing Divisia Aggregates for the Euro Area H. E. Reimers This paper, using pre-euro data, is Discussion Paper 13/02, Economic Research Centre of the Deutsche Bundesbank, Frankfurt.
	France
2002	Analysing Divisia Aggregates for the Euro Area H. E. Reimers This paper, using pre-euro data, is Discussion Paper 13/02, Economic Research Centre of the Deutsche Bundesbank, Frankfurt.
1996	Divisia Monetary Aggregates: A Survey in the Case of France S. Lecarpentier This paper about pre-euro France appeared in the book, A. Mullineux (ed.), Financial Innovation, Banking, and Monetary Aggregates, Edward Elgar, Cheltenham.
1996	Aggregating Money Demand in Europe with a Divisia Index Katrin Wesche This paper, using pre-euro data, is University of Bonn Institute für Internationale Wirtschaftspolitik Projektbereich B Discussion Paper No. B-392, November.
	GCC (Gulf States) Area
2014	Modern and Traditional Methods of Measuring Money Supply: the Case of Saudi Arabia Ryadh M. Alkhareif and William A. Barnett Saudi Arabian Monetary Authority (SAMA) Working Paper #1 was released in December 2014.
2013	Advances in Monetary Policy Design: Applications to the Gulf Monetary Union Ryadh M. Alkhareif and William A. Barnett This book, published by Cambridge Scholars Publishing, is the first to publish Divisia-based money supply indexes and core inflation indicators for the GCC.
2012	Divisia Monetary Aggregates for the GCC Countries Ryadh M. Alkhareif and William A. Barnett In William A. Barnett and Fredj Jawadi (eds.), Recent Developments in Alternative Finance: Empirical Assessments and Economic Implications, Emerald Press, 2012, pp. 1 - 37.
	Germany
2015	The Information Content of Monetary Statistics for the Great Recession: Evidence from Germany Wenjuan Chen and Dieter Nautz This paper introduces a Divisia monetary aggregate for Germany and explores its information content for the Great Recession. This paper appeared in SFB 649 Economics Risk Berlin, Humboldt Universitat Zu Berlin, Germany.
2006	Estimating a Regular Continuous-Time System of Demand for World Monies with Divisia Data K. P. Donaghy and D. M. Richard This paper appeared in the book, Belongia and Binner (2006), pp. 76-103.
2002	Analysing Divisia Aggregates for the Euro Area H. E. Reimers This paper, using pre-euro data, is Discussion Paper 13/02, Economic Research Centre of the Deutsche Bundesbank, Frankfurt.
2000	Consequences of Money Stock Mismeasurement: Evidence from Three Countries Michael T. Belongia This paper about pre-euro Germany appeared in Belongia and Binner (2000), pp. 292-312.
2000	Neural Networks with Divisia Money: Better Forecasts of Future Inflation Robert E. Dorsey This paper about pre-euro Germany appeared in Belongia and Binner (2000), pp. 28-46.
2000	Weighted Dutch and German Monetary Aggregates: How Do They Perform as Monetary Indicators for the Netherlands? Norbert G. J. Janssen and Clemens J. M. Kool This paper about pre-euro Germany appeared in Belongia and Binner (2000), pp. 120-137.
2000	Weighted Monetary Aggregates for Germany Heinz Herrman, Hans-Eggert Reimers, and Karl-Heinz Toedter This paper about pre-euro Germany appeared in Belongia and Binner (2000), pp. 79-101.
1996	Divisia in Germany W. Gaab This paper about pre-euro Germany appeared in the book, A. Mullineux (ed.), Financial Innovation, Banking, and Monetary Aggregates, Edward Elgar, Cheltenham.
1996	Aggregating Money Demand in Europe with a Divisia Index Katrin Wesche This paper, using pre-euro data, is University of Bonn Institute für Internationale Wirtschaftspolitik Projektbereich B Discussion Paper No. B-392, November.
	Hungary
1997	Divisia Indices and Estimated Money Demand Functions for Hungary Zsoldos István This working paper is from the Central Bank of Hungary and is written in Hungarian.
	India
2015	An SVAR Approach to Evaluation of Monetary Policy in India: Solution to the Exchange Rate Puzzles in an Open Economy William Barnett, Soumya Bhadbury and Taniya Ghosh This paper appeared in the journal, Open Economies Review.
2010	The Divisia Monetary Indices as Leading Indicators of Inflation M. Ramachandran, Rajib Das, and Binod B. Bhoi This paper is Reserve Bank of India Development Research Group Study No. 36, Mumbai
2001	Simple Sum vs. Divisia Monetary Aggregates: An Empirical Evaluation D. Acharya and B. Kamaiah This paper appeared in the Economic and Political Weekly, vol. 36, pp. 317-326.
1999	Will the Right Monetary Aggregate for India Please Stand Up? R. Jha and I. S. Longjam This paper appeared in the Economic and Political Weekly, vol. 34, pp. 631-630.
1995	Fiscal and Monetary Actions: A Test of Relative Importance of the Economic Monetary Aggregates and their Simple Sum Counterparts M. Ramachanran This paper appeared in Prajnan, vol. 24, pp. 125-137.
1991	Simple Sum vs. Superlative Monetary Aggregates for India Ganti Subrahmanyam and S. B. Swami This paper appeared in the Journal of Quantitative Economics, vol. 17, pp. 79-92.
1989	Weighted Monetary Aggregates: Rationale and Relevance for India N. Jadhav This paper is Reserve Bank of India Occasional Papers, 10, pp. 39-56.
1989	Weighted Monetary Aggregates for India: 1970-1986. R. Kannan This paper appeared in Prajnan, vol. 18, pp. 453-460.
	Indonesia
2017	Financial Liberalization and Divisia Money Demand in Indonesia Sianturi, Ronald Hasudungan; Tanjung, Ahmad Feri1; Leong, Choi-Meng; Puah, Chin-Hong; Brahmana, Rayenda Khresna Money demand function that turns out to be unstable due to the financial liberalization has affected the effectiveness of monetary policy that utilizes monetary targeting as policy target. Thus, Divisia monetary aggregate that is consistent with the economic theory has been used to examine the money demand function in Indonesia. Monetization is also included as a determinant of money demand to measure the financial deepening. A stable M2 money demand has been identified via the use of Divisia M2 money and the inclusion of monetization variable. Monetary targeting can serve as alternative policy target for Indonesia and there is a possibility for a return to monetary targeting in Indonesia.
2010	Financial Liberalization and Money Demand in Indonesia: Implications for Weighted Monetary Aggregates Hiew Lee Chea This study investigates Indonesia monetary regime changes and the significance of Divisia monetary aggregates in formulating the monetary policy in Indonesia from the period of 1981Q1 to 2005Q4.
2010	Financial Liberalization, Weighted Monetary Aggregates, and Money Demand in Indonesia Puah Chin-Hong and Heiw Lee-Chea This paper appeared in the Labuan Bulletin of International Business & Finance, vol. 8, December, pp. 76-93.
1999	Rationale for Divisia Monetary Aggregates in Deregulated Asian Developing Economies M.S. Habibullah This paper appeared in the book, M.S. Habibullah (Ed.), Divisia Monetary Aggregates and Economic Activities in Asian Developing Economics, Aldershot, Ashgate Publishing.
	Iran
2007	The Role of Definition of Money in the Stability of the Iranian Demand for Money P. Davoudi and Z. Zarepour This paper appeared in Iranian Economic Research, vol. 29, pp. 47-74.
	Israel
2016	Money and monetary policy in Israel during the last decade Jonathan Benchimol This study examines how money and monetary policy have influenced output and inflation during the past decade in Israel by comparing two New Keynesian DSGE models. One is a baseline separable model (Galí, 2008) and the other assumes non-separable household preferences between consumption and money (Benchimol and Fourçans, 2012). We test both models by using rolling window Bayesian estimations over the last decade (2001-2013). The results of the presented dynamic analysis show that the sensitivity of output with respect to money shocks increased during the Dot-com, Intifada, and Subprime crises. The role of monetary policy increased during these crises, especially with regard to inflation, even though the effectiveness of conventional monetary policy decreased during the Subprime crisis. In addition, the non-separable model including money provides lower forecast errors than the baseline separable model without money, while the influence of money on output fluctuations can be seen as a good predictive indicator of bank and debt risks. By impacting and monitoring households’ money holdings, policy makers could improve their forecasts and crisis management through models considering monetary aggregates. The link provided is for the original working paper version. The paper was later published in the Journal of Policy Modeling, volume 38, 2016, pp. 103-024.
2013	Divisia Monetary Aggregates for Israel: Background Note and Metadata Edward (Akiva) Offenbacher and Maayan Kellerman This Bank of Israel working paper provides background information relevant to the Bank of Israel Divisia monetary aggregates.
2011	Send requests for information about the Israeli Divisia monetary aggregates data to the Bank of Israel Information and Statistics Department or to Edward Akiva Offenbacher Bank of Israel Information & Statistics Department Email: statistics@boi.org.il or edward.offenbacher@boi.org.il
2011	Divisia Monetary Aggregates for Israel: Background Note and Metadata Edward (Akiva) Offenbacher and Shachar Shemesh This Bank of Israel working paper provides background information relevant to the Bank of Israel Divisia monetary aggregates.
	Italy
1999	A Neural Network Approach to Inflation Forecasting: the Case of Italy J. M. Binner and A. M. Gazely This paper on pre-euro Italy appeared in Global Business and Economics Review, vol. 1, pp. 76-92.
1996	Measuring Money with a Divisia Index: An Application to Italy E. Gaiotti This paper about pre-euro Italy appeared in the book, A. Mullineux (ed.), Financial Innovation, Banking, and Monetary Aggregates, Edward Elgar, Cheltenham.
	Japan
2009	Comparison of Simple Sum and Divisia Monetary Aggregates Using Panel Data Analysis S. Celik and S. Uzun This paper appeared in the International Journal of Social Sciences and Humanity Studies, vol. 1, pp. 1-13.
2006	Estimating a Regular Continuous-Time System of Demand for World Monies with Divisia Data K. P. Donaghy and D. M. Richard This paper appeared in the book, Belongia and Binner (2006), pp. 76-103.
2000	Consequences of Money Stock Mismeasurement: Evidence from Three Countries Michael T. Belongia This paper appeared in the book, Belongia and Binner (2000), pp. 292-312.
2000	Broad and Narrow Divisia Monetary Aggregates for Japan Kazuhiko Ishida and Koji Nakamura This paper appeared in the book, Belongia and Binner (2000), pp. 173-199.
1996	Financial Deregulation and Divisia Monetary Aggregates in Japan K. Hirayama and M. Kasuya This paper appeared in the book, A. Mullineux (ed.), Financial Innovation, Banking, and Monetary Aggregates, Edward Elgar, Cheltenham.
1984	Divisia Monetary Aggregates and the Demand for Money: A Japanese Case Kazuhiko Ishida This paper appeared in the Bank of Japan Monetary and Economic Studies, vol. 2, pp. 49-80.
	Kenya
2018	The Divisia monetary aggregates, demand for money stability, income, and inflation fluctuations in selected sub-Saharan Africa Shehu El-Rasheed The financial sector reforms adopted in the 4 selected Sub-Saharan Africa (SSA) countries, namely Kenya, Malawi, Nigeria, and South Africa have resulted to a remarkable change in the composition of monetary aggregates making the simple sum measure of money questionable. The reforms affect the stability of money demand function and create uncertainty in the macroeconomic environment leading to a slow growth and high inflation rates. This study constructs a new Divisia monetary aggregates for 4 selected SSA countries and investigate the role of monetary aggregates in the money demand stability, income and price fluctuations. Two variables; monetary uncertainty (MOU) and output uncertainty (OUU) were incorporated into the model. The study employed quarterly time series data covering 2000Q1 to 2015Q3. The ARDL and Toda Yamamoto causality methods were utilized in the analysis. The main objective of the study is to investigate the role of monetary aggregates in monetary policy decisions. The results indicate that Divisia monetary aggregates perform well in explaining the stability of money demand functions. Both MOU and OUU are quite significant in the money demand stability. The study added to the existing literature on money demand by empirically exploring the impact of the MOU and OUU on money demand stability using an alternative monetary aggregate. The results also shows a significant two-way causality between money and income, however, money and prices signifying an endogeneity in money supply. The Divisia monetary aggregates perform relatively well in explaining income and prices fluctuations. The important policy implication of this finding is that monetary targeting could be more appropriate for the 4 selected SSA countries monetary policy decisions and therefore that monetary aggregates can be used to influence the growth in income and to minimize price fluctuations.
	Kuwait
2012	Divisia Monetary Aggregates for the GCC Countries Ryadh M. Alkhareif and William A. Barnett This paper is forthcoming in the book, W. A. Barnett and F. Jawadi (eds.), Recent Developments in Alternative Finance: Empirical Assessments and Economic Implications, Emerald Press.
	Malawi
2018	The Divisia monetary aggregates, demand for money stability, income, and inflation fluctuations in selected sub-Saharan Africa Shehu El-Rasheed The financial sector reforms adopted in the 4 selected Sub-Saharan Africa (SSA) countries, namely Kenya, Malawi, Nigeria, and South Africa have resulted to a remarkable change in the composition of monetary aggregates making the simple sum measure of money questionable. The reforms affect the stability of money demand function and create uncertainty in the macroeconomic environment leading to a slow growth and high inflation rates. This study constructs a new Divisia monetary aggregates for 4 selected SSA countries and investigate the role of monetary aggregates in the money demand stability, income and price fluctuations. Two variables; monetary uncertainty (MOU) and output uncertainty (OUU) were incorporated into the model. The study employed quarterly time series data covering 2000Q1 to 2015Q3. The ARDL and Toda Yamamoto causality methods were utilized in the analysis. The main objective of the study is to investigate the role of monetary aggregates in monetary policy decisions. The results indicate that Divisia monetary aggregates perform well in explaining the stability of money demand functions. Both MOU and OUU are quite significant in the money demand stability. The study added to the existing literature on money demand by empirically exploring the impact of the MOU and OUU on money demand stability using an alternative monetary aggregate. The results also shows a significant two-way causality between money and income, however, money and prices signifying an endogeneity in money supply. The Divisia monetary aggregates perform relatively well in explaining income and prices fluctuations. The important policy implication of this finding is that monetary targeting could be more appropriate for the 4 selected SSA countries monetary policy decisions and therefore that monetary aggregates can be used to influence the growth in income and to minimize price fluctuations.
	Malaysia
2018	Revisiting Money Demand in Malaysia: Simple-Sum versus Divisia Monetary Aggregates Chin-Hong Puah, Choi-Meng Leong, Abu Mansor Shazali and Evan Lau BNM has discarded the use of monetary targeting due to the speeding up of financial reforms as the relationship between money and important macroeconomic indicators in Malaysia has weakened. However, the implementation of the interest rate targeting requires the authorities to alter the policy rate recurrently. Alternatively, the authorities may consider monetary targeting, which provides the ease of control of monetary aggregates, provided that a stable demand for money function can be derived. Nevertheless, financial liberalization has greatly affected the stability of money demand. Thus, this study estimated the demand for money function in Malaysia by considering the effect of the financial development in which a Divisia monetary aggregate has been constructed as an alternative measure of money and a monetization variable has been included in the function. The Johansen and Juselius cointegration test and error correction model are utilized to estimate the demand for money function. The empirical findings indicate that a plausible demand for money function is derived using Divisia M2. Furthermore, monetization appears as an important variable that contributes to a stable money demand. The presence of a stable Divisia M2 money demand has reassured the usefulness of monetary aggregate as the indicator for monetary policy purposes. Monetary targeting provides alternative policy target choice for the conduct of monetary policy. Divisia monetary aggregates can also serve as the alternative money measurement apart from the conventional money supply.
2016	Symmetric and Asymmetric Approaches in Estimating the Money Demand Function for Malaysia: A Comparison between Simple Sum and Divisia Indexes Amirul Afiq Kamaruddin and Norlin Khalid This study aims to estimate the money demand function by using simple sum monetary aggregates M1 and M2 monetary aggregate with weighted monetary aggregate Divisia DM1 and DM2. Both Divisia monetary aggregate for narrow money DM1 and Divisia for broad money DM2 are built using following discrete time estimation by Tornquist (1936) and Theil (1967). Divisia index is said to be better than the simple summation index as differences in liquidity levels and the cost of each asset in the monetary aggregates are taking into account by putting a different weight according to the liquidity level. Unlike previous studies, this study estimates the money demand function in asymmetric term by using the Non-Linear Autoregressive Distributed Lag (NARDL). The results proved the existence of a long-term relationship between money demand for both types of monetary aggregates with income levels, interest rates, and the inflation rates. This study also supports the existence of the effect of asymmetry in money demand for Malaysia. The implications of the study show that it is important for policy makers to take into account the effect of the asymmetry in income levels in determining the demand for money and its determinants in Malaysia.
2007	Scale Variable Specification in a Money Demand Function for Malaysia J. Dahalan, S. C. Sharma, and K. Sylwester This paper appeared in the Journal of Asian Economics, vol 18 pp. 867-882.
2005	Divisia Monetary Aggregates and Money Demand for Malaysia J. Dahalan, S. C. Sharma, and K. Sylwester This paper appeared in the Journal of Asian Economics, vol. 15, pp. 1137-1153.
2002	Determinants and Stability of Demand for M2 in Malaysia S. S. Sriram This paper appeared in the Journal of Asian Economics, vol. 13, pp. 337-356.
1999	Rationale for Divisia Monetary Aggregates in Deregulated Asian Developing Economies M. S. Habibullah This paper appeared in the book, M.S. Habibullah (Ed.), Divisia Monetary Aggregates and Economic Activities in Asian Developing Economics, Aldershot, Ashgate Publishing
	Mexico
1989	Construction of New Monetary Aggregates: the Case of Mexico Alfredo M. Sandoval This research is a Ph.D. thesis at the University of Texas at Austin.
	Myanmar
1999	Rationale for Divisia Monetary Aggregates in Deregulated Asian Developing Economies M. S. Habibullah This paper appeared in the book, M.S. Habibullah (Ed.), Divisia Monetary Aggregates and Economic Activities in Asian Developing Economics, Aldershot, Ashgate Publishing.
	Nepal
1999	Rationale for Divisia Monetary Aggregates in Deregulated Asian Developing Economies M. S. Habibullah This paper appeared in the book, M.S. Habibullah (Ed.), Divisia Monetary Aggregates and Economic Activities in Asian Developing Economics, Aldershot, Ashgate Publishing.
	Netherlands
2000	Weighted Dutch and German Monetary Aggregates: How Do They Perform as Monetary Indicators for the Netherlands? Norbert G. J. Janssen and Clemens J. M. Kool This paper about pre-euro Netherlands appeared in the book, Belongia and Binner (2000), pp. 120-137.
1996	Aggregating Money Demand in Europe with a Divisia Index Katrin Wesche This paper, using pre-euro data, is University of Bonn Institute für Internationale Wirtschaftspolitik Projektbereich B Discussion Paper No. B-392, November.
1985	Monetary Control, The Dutch Experience: Some Reflections on the Liquidity Ratio M. M. G. Fase This paper about pre-euro Netherlands appeared in the book, C. van Ewijk and J. J. Klant (eds.), Monetary Conditions for Economic Recovery, Martinus Nijhoff, Dordrecht, pp. 95-125.
	Nigeria
2019	Financial Sector Reforms, Monetary And Output Uncertainties and the Behavior of Money Demand in Kenya: the Divisia Index Approach Hussin Abdullah and Shehu El-Rasheed The financial sector reforms implemented by the Central Bank of Kenya (CBK) resulted in rapid financial innovation (such as the popular M-Pesa mobile money services) growth, and expansion of several interest earning financial instruments. These developments affect the definition and composition of monetary aggregates, posing a question on the correctness of the current money measures used by CBK. The simple sum aggregates were identified with several theoretical and empirical shortcomings. The rapid financial sector development might affect the stability of money demand function. This study constructs Divisia monetary aggregates for Kenya over the period of 2000’s first quarter to 2015’s third quarter and applies the ARDL method in investigating the stability of money demand function. For the first time, monetary uncertainty and output uncertainty variables are introduced to the Kenyan money demand model. The results reveal that both monetary and output uncertainty has significant influence on money demand in Kenya. This implies that omitting the two variables in the Kenya money demand function might lead to a wrong specification. The money demand function is stable over the period. It means that monetary aggregates targeting is the right framework for monetary policy formulation by the CBK.
2018	The Divisia monetary aggregates, demand for money stability, income, and inflation fluctuations in selected sub-Saharan Africa Shehu El-Rasheed The financial sector reforms adopted in the 4 selected Sub-Saharan Africa (SSA) countries, namely Kenya, Malawi, Nigeria, and South Africa have resulted to a remarkable change in the composition of monetary aggregates making the simple sum measure of money questionable. The reforms affect the stability of money demand function and create uncertainty in the macroeconomic environment leading to a slow growth and high inflation rates. This study constructs a new Divisia monetary aggregates for 4 selected SSA countries and investigate the role of monetary aggregates in the money demand stability, income and price fluctuations. Two variables; monetary uncertainty (MOU) and output uncertainty (OUU) were incorporated into the model. The study employed quarterly time series data covering 2000Q1 to 2015Q3. The ARDL and Toda Yamamoto causality methods were utilized in the analysis. The main objective of the study is to investigate the role of monetary aggregates in monetary policy decisions. The results indicate that Divisia monetary aggregates perform well in explaining the stability of money demand functions. Both MOU and OUU are quite significant in the money demand stability. The study added to the existing literature on money demand by empirically exploring the impact of the MOU and OUU on money demand stability using an alternative monetary aggregate. The results also shows a significant two-way causality between money and income, however, money and prices signifying an endogeneity in money supply. The Divisia monetary aggregates perform relatively well in explaining income and prices fluctuations. The important policy implication of this finding is that monetary targeting could be more appropriate for the 4 selected SSA countries monetary policy decisions and therefore that monetary aggregates can be used to influence the growth in income and to minimize price fluctuations.
2017	Divisia Monetary Aggregates and Demand for Money in Nigeria Shehu El-Rasheed and Hussin Abdullah The Nigerian financial system has undergone several transformations over the past few decades leading to financial innovations. These innovations have altered the definition and use of monetary aggregates as a monetary policy tool. The conventional simple sum aggregates were identified with an aggregation bias. The economy has experienced series of monetary and financial problems which requires further investigation into the causes and remedies. This paper construct the Divisia monetary aggregates (DM1 and DM2) for Nigeria using the Barnett 1980 Divisia index. Descriptive statistics were used to compare the simple sum and Divisia monetary aggregates. Using a data for 2000: 1 to 2015: 4 obtained from the International financial statistics (IFS) of the IMF, the study employs the ARDL approach to cointegration and estimated the demand for money function using the newly constructed Divisia aggregates...
	Oman
2012	Divisia Monetary Aggregates for the GCC Countries Ryadh M. Alkhareif and William A. Barnett This paper is forthcoming in the book, W. A. Barnett and F. Jawadi (eds.), Recent Developments in Alternative Finance: Empirical Assessments and Economic Implications, Emerald Press.
	Pakistan
2011	Money Demand Function for Pakistan (Divisia Approach) Haroon Sarwar, Zakir Hussain, and Masood Sarwar Awan This working paper is online in the Munich Personal RePEc Archive. The paper’s conclusion is that the “State Bank of Pakistan should abandon the simple sum aggregation technique and switch over to the Divisia aggregates, which have more aggregation theoretic foundations.”
2011	A Semi-Nonparametric Approach to the Demand for Money in Pakistan Haroon Sarwar, Zakir Hussain, and Masood Sarwar The degree of substitutability of different monetary assets serves as a valuable source of information for Pakistan’s monetary authorities in the context of money demand analysis. Barnett’s (1980) concept of the micro-foundations of money demand has paved the way for a more comprehensive demand system analysis. Locally flexible functional forms are unable to estimate substitution elasticities at all data points, and thus, we use the asymptotically ideal model, which is a semi-nonparametric globally flexible functional form. Our data on income, price, and substitution elasticities show that there is less-than-perfect substitution among monetary assets. The results of Allan and Morishima elasticities show that the former are inherently biased toward showing monetary assets as complements, making Morishima a better choice. The study recommends that it is high time Pakistan’s monetary authorities abandoned the simple-sum aggregation method, which assumes perfect substitution among monetary assets.
1997	The Demand for Simple-Sum and Divisia Monetary Aggregates for Pakistan: A Cointegration Approach S. M. Tariq and K. Matthews This paper appeared in the Pakistan Development Review, vol. 3, pp. 275-291.
1988	Substitutability of Pakistan’s Monetary Assets under Alternative Monetary Aggregates M Aynul Hasan, S. Ghulam Kadir, and S. Fakhre Mahmud The paper appeared in the journal, The Pakistan Development Review, vol. 27, pp. 317-326.
	Peru
1991	Seigniorage, Inflation and Monetary Policy: the Case of Peru, 1985-1989 Veronica Ruiz de Castilla This research is a Master's thesis at the University of Texas at Austin.
	Philippines
1999	Rationale for Divisia Monetary Aggregates in Deregulated Asian Developing Economies M. S. Habibullah This paper appeared in the book, M.S. Habibullah (Ed.), Divisia Monetary Aggregates and Economic Activities in Asian Developing Economics, Aldershot, Ashgate Publishing.
	Poland
2003	Monetary Assets Expenditures and Economic Growth Krysztof Kluza and Stanislaw Kluza This paper was presented at the 23rd Conference on Monetary Policy, National Bank of Poland, November 27-28, 2003.
2001	Zastosowanie Indeksów Divisia w Polsce S. Kluza This research appeared in rozprawa doctorska, Kolegium Analiz Ekonomicznych, Szkola Glówna Handlowa, Warszawa.
1999	Konstrukcja Pieniężnych Agregatów Divisia w Warunkac Polskich N. Cieśla This paper appeared in Materialy i Studia nr 89, NBP, Warszawa.
	Qatar
2012	Divisia Monetary Aggregates for the GCC Countries Ryadh M. Alkhareif and William A. Barnett This paper is forthcoming in the book, W. A. Barnett and F. Jawadi (eds.), Recent Developments in Alternative Finance: Empirical Assessments and Economic Implications, Emerald Press.
	Saudi Arabia
2020	Macroeconomic Policies and Econometric Models for the Kingdom of Saudi Arabia Ryadh M. Alkhareif Book titled "Macroeconomic Policies and Econometric Models for the Kingdom of Saudi Arabia" containing a number of chapters about Divisia (in Arabic).
2020	Estimating the Money Demand Function for Saudi Arabia Using Divisia Monetary Aggregate Ryadh M. Alkhareif and Moayad Al Rasasi This paper constructs the broader Divisia monetary aggregate (D2) for the Kingdom of Saudi Arabia over the period from 1999 to 2018. Unlike the traditional money supply aggregate (M2), movements of the Divisia monetary aggregate seems to reflect the domestic economic developments and hence can be very useful when setting macroeconomic policies in the Kingdom. In addition, the paper applies the Keynesian Money Demand Theory to estimate the demand for money using the Divisia monetary aggregate. The findings confirm the stability of the money demand function for Saudi Arabia.
2018	Nowcasting Real GDP for Saudi Arabia Ryadh M. Alkhareif Saudi Arabia has embarked on a bold socioeconomic reform program under Vision 2030 to diversify the economy and further improve living standards for citizens. The Saudi government had indeed made significant strides towards implementing wide-ranging structural reforms as set out in the Vision Realization Programs. Given the rapid pace of the reforms and their significant impact on macroeconomic conditions, it is becoming increasingly important to monitor economic activity in real time to ensure sound policy and investment decision-making. Like in many other countries, GDP data in Saudi Arabia are published with lags and subject to substantial revisions. Traditionally, policymakers and investors in Saudi Arabia have relied on a number of economic indicators to assess economic activity such as Purchasing Managers' Index, point of sale transactions, cash withdrawals from ATMs, letters of credit, automobile sales, cement production, electricity consumption, real estate developments, and the performance of the stock market. While these indicators are to some extent useful, they often tend to provide mixed inferences about the state of the economy. To overcome this issue, the paper constructs monthly GDP nowcasts for Saudi Arabia by estimating a Generalized Dynamic Factor Model (GDFM) on a panel of 272 variables over the period from January 2010 to June 2018. The GDP nowcasts produced in this paper can accurately mimic GDP growth rates for Saudi Arabia, including for the non-oil sector. Our GDFM has outperformed other traditional models in tracking the business cycle in Saudi Arabia. In our view, the non-oil private sector GDP nowcasts provided in this paper can substitute the traditional set of indicators used to monitor monthly private sector activity.
2015	Core Inflation Indicators for Saudi Arabia Ryadh M. Alkhareif and William A. Barnett This paper constructs and analyzes core inflation indicators for Saudi Arabia for the period of March 2012 to May 2014 using two alternative approaches: the exclusion method (ex food and housing/rent) and the statistical method. The findings of the analysis suggest that the ex food and housing/rent inflation is more volatile than the overall CPI inflation over the sample period. In contrast, the statistical core inflation is relatively more stable and less volatile. Moreover, the ex food and housing/rent inflation is only weakly correlated with headline inflation, whereas the statistical core inflation exhibits a stronger correlation. This combination of lower volatility and higher correlation with headline inflation makes the statistical method a much better choice for policymakers. From a monetary policy standpoint, using a bundle of core inflation measures, including both properly constructed exclusion and statistical methods, is more desirable, especially when variation across measures is widespread, as is the case in Saudi Arabia.
2015	Modern and Traditional Methods for Measuring Money Supply: The Case of Saudi Arabia William A. Barnett and Ryadh M. Alkhareif This paper compares the "simple-sum" monetary aggregates (M1 and M2) published by the Saudi Arabian Monetary Agency (SAMA) with the new monetary aggregates (D1 and D2)—known as the Divisia monetary indexes. The former aggregates are constructed from a simple accounting identity, whereas the Divisia aggregates are constructed using statistical index number theory and aggregation theory. The findings suggest that both D1 and M1 are identical, given the perfect substitutability of the monetary components within those aggregates. For the broader monetary aggregates where perfect substitutability assumption is not realistic, the two monetary indexes differ substantially. SAMA could benefit by using both monetary indexes simultaneously to better monitor liquidity in the market.
2012	Divisia Monetary Aggregates for the GCC Countries Ryadh M. Alkhareif and William A. Barnett This paper is forthcoming in the book, W. A. Barnett and F. Jawadi (eds.), Recent Developments in Alternative Finance: Empirical Assessments and Economic Implications, Emerald Press.
2009	Linear and Nonlineaer Techniques for Estimating the Money Demand Function for Saudi Arabia Mamdooh Saad Alsahafi This research is a Ph.D. thesis at the University of Kansas
	Singapore
2021	Constructing Divisia Monetary Aggregates for Singapore William A. Barnett and Van H. Nguyen Since Barnett derived the user cost price of money, the economic theory of monetary services aggregation has been developed and extended into a field of its own with solid foundations in microeconomic theory. Divisia monetary aggregates have repeatedly been shown to be strictly preferable to their simple sum counterparts, which have no competent foundations in microeconomic aggregation or index number theory. However, most central banks in the world, including that of Singapore, the Monetary Authority of Singapore (MAS), still report their monetary aggregates as simple summations. Recent macroeconomic research about Singapore tends to focus on exchange rates as a monetary policy target but ignores the aggregate quantity of money. Is that because quantities of money are irrelevant to economic activity? To examine the role of monetary quantities as potential monetary instruments, indicators, or targets and their relevance to predicting real economic activity in Singapore, this paper applies the user cost of money formula and the recently developed credit-card-augmented Divisia monetary aggregates formula to construct monetary services indexes for Singapore. We produce those state-of-the-art monetary services indexes from Jan 1991 to Mar 2021. We see that Divisia measures behave differently from simple sum measures in the period before the year 2000, while interest rates were high. Credit-card-augmented Divisia monetary services move closely with the conventional Divisia monetary aggregates, since the volume of credit card transactions in Singapore is relatively small compared with other monetary service assets. In future work, we plan to use our data to explore central bank policy in Singapore and to propose improvements in that policy. By making our data available to the public, we encourage others to do the same.
1999	Rationale for Divisia Monetary Aggregates in Deregulated Asian Developing Economies M. S. Habibullah This paper appeared in the book, M.S. Habibullah (Ed.), Divisia Monetary Aggregates and Economic Activities in Asian Developing Economics, Aldershot, Ashgate Publishing.
	South Africa
2018	The Divisia monetary aggregates, demand for money stability, income, and inflation fluctuations in selected sub-Saharan Africa Shehu El-Rasheed The financial sector reforms adopted in the 4 selected Sub-Saharan Africa (SSA) countries, namely Kenya, Malawi, Nigeria, and South Africa have resulted to a remarkable change in the composition of monetary aggregates making the simple sum measure of money questionable. The reforms affect the stability of money demand function and create uncertainty in the macroeconomic environment leading to a slow growth and high inflation rates. This study constructs a new Divisia monetary aggregates for 4 selected SSA countries and investigate the role of monetary aggregates in the money demand stability, income and price fluctuations. Two variables; monetary uncertainty (MOU) and output uncertainty (OUU) were incorporated into the model. The study employed quarterly time series data covering 2000Q1 to 2015Q3. The ARDL and Toda Yamamoto causality methods were utilized in the analysis. The main objective of the study is to investigate the role of monetary aggregates in monetary policy decisions. The results indicate that Divisia monetary aggregates perform well in explaining the stability of money demand functions. Both MOU and OUU are quite significant in the money demand stability. The study added to the existing literature on money demand by empirically exploring the impact of the MOU and OUU on money demand stability using an alternative monetary aggregate. The results also shows a significant two-way causality between money and income, however, money and prices signifying an endogeneity in money supply. The Divisia monetary aggregates perform relatively well in explaining income and prices fluctuations. The important policy implication of this finding is that monetary targeting could be more appropriate for the 4 selected SSA countries monetary policy decisions and therefore that monetary aggregates can be used to influence the growth in income and to minimize price fluctuations.
	South Korea
2000	The Signals from Divisia Money in a Rapidly Growing Economy Jeong Ho Hahm and Jun Tae Kim This paper appeared in the book, Belongia and Binner (2000), pp. 200-226.
1999	Rationale for Divisia Monetary Aggregates in 'Deregulated' Asian Developing Economies M. S. Habibullah This paper appeared in the book, M.S. Habibullah (Ed.), Divisia Monetary Aggregates and Economic Activities in Asian Developing Economics, Aldershot, Ashgate Publishing Limited, pp. 67-111.
	Spain
2002	Analysing Divisia Aggregates for the Euro Area H. E. Reimers This paper, using pre-euro data, is Discussion Paper 13/02, Economic Research Centre of the Deutsche Bundesbank, Frankfurt.
	Sri Lanka
1999	Rationale for Divisia Monetary Aggregates in Deregulated Asian Developing Economies M. S. Habibullah This paper appeared in the book, M.S. Habibullah (Ed.), Divisia Monetary Aggregates and Economic Activities in Asian Developing Economics, Aldershot, Ashgate Publishing.
	Switzerland
2000	Simple-sum versus Divisia Money in Switzerland: Some Empirical Results Robert Fluri and Erich Spoerndli This paper appeared in the book, Belongia and Binner (2000), pp. 102-119.
1996	Monetary Aggregates in Switzerland H. Genberg and S. Neftci This paper appeared in the book, A. Mullineux (ed.), Financial Innovation, Banking, and Monetary Aggregates, Edward Elgar, Cheltenham.
1991	Divisia Monetary Services Indexes for Switzerland: Are They Useful for Monetary Targeting? P. Yue and R. Fluri This paper appeared in the Federal Reserve Bank of St. Louis Review, vol. 73, pp. 19-33.
	Taiwan
2017	Modelling Money Shocks in a Small Open Economy: The Case of Taiwan Jane M. Binner and Logan J. Kelly This paper (which appeared in the British journal, The Manchester School) explores the relevance of the Divisia monetary aggregate in Taiwan over the period January, 1985 through to June, 2016.
2004	Financial Innovation and Divisia Money in Taiwan: Comparative Evidence from Neural Network and Vector Error-Correction Forecasting Models J. M. Binner, A. M. Gazely, S. H. Chen, and B. T. Chie This paper appeared in Contemporary Economic Policy, vol. 22, pp. 213-224.
2002	Financial Innovation in Taiwan; An Application of Neural Networks to the Broad Monetary Aggregates. J. M. Binner, A. M. Gazely, and S. H. Chen A revised version of this paper appeared in European Journal of Finance, vol. 8, pp. 238-247.
2000	Divisia Monetary Aggregates for Taiwan Y. C. Shih This paper appeared in the book, Belongia and Binner (2000), pp. 227-248.
1999	Rationale for Divisia Monetary Aggregates in Deregulated Asian Developing Economies M. S. Habibullah This paper appeared in the book, M.S. Habibullah (Ed.), Divisia Monetary Aggregates and Economic Activities in Asian Developing Economics, Aldershot, Ashgate Publishing
	Thailand
1999	Rationale for Divisia Monetary Aggregates in Deregulated Asian Developing Economies M. S. Habibullah This paper appeared in the book, M.S. Habibullah (Ed.), Divisia Monetary Aggregates and Economic Activities in Asian Developing Economics, Aldershot, Ashgate Publishing.
	Turkey
2017	Divisia and Simple Sum Monetary Aggregates: Any Empirical Relevance for Turkey? Umurcan Polat In this study, a Divisia index is constructed to test its predictive power on quantities and prices compared to its simple sum counterpart. Accordingly, a Divisia index is built-up for Turkish economy for the period 2006-2016 to see whether the utilization of the Divisia monetary aggregates in the conduct of monetary policy makes any difference compared to that of traditional simple sum money supply. Under different specifications, though the relative power of the Divisia aggregates in predicting quantity and price variables is found, still, it can be argued that theoretically well-rounded formation of the Divisia index is not that much empirically justified for the case of Turkey.
2009	An Empirical Study of Simple Sum and Divisia Monetary Aggregation: A Comparison of Their Predictive Power Regarding Prices and Output in Turkey Dogan Karaman This research is a PhD thesis at the University of Kansas.
2009	Comparison of Simple Sum and Divisia Monetary Aggregates Using Panel Data Analysis S. Celik and S. Uzun This paper appeared in the International Journal of Social Sciences and Humanity Studies, vol. 1, pp. 1-13.
2008	Divisia Measure of Currency and Asset Substitution for Turkey Ayse Ozden Birkan This paper is in Essays on Turkish Monetary Policy, PhD thesis, University of Utah
2006	Alternative Measures of Currency and Asset Substitution: The Case of Turkey Ayse Ozden Birkan This pape is a Policy Innovations working paper.
1999	Divisia Monetary Aggregates: An Empirical Investigation of Their Usefulness for Turkey S. Celik and S. Uzun This research is a PhD thesis at the University of Nebraska.
1993	Türkiye’deki Parasal Büyüklükler İçin İndeks ve Bilesim Teorisinin Bir Uygulamasi: Divisia ve Fisher İndeksi Kursat Kunter This paper is written in Turkish.
	United Arab Emirates
2012	Divisia Monetary Aggregates for the GCC Countries Ryadh M. Alkhareif and William A. Barnett This paper is forthcoming in the book, W. A. Barnett and F. Jawadi (eds.), Recent Developments in Alternative Finance: Empirical Assessments and Economic Implications, Emerald Press.
	United Kingdom
2022	Is Policy Causing Chaos in the United Kingdom? William A. Barnett, Giovanni Bella, Taniya Ghosh, Paolo Mattana, Beatrice Venturi In the journal, Economic Modelling. We study the stability properties and conditions for the onset of Shilnikov chaos in the UK New Keynesian macroeconomy, as well as the shifts in equilibrium dynamics under various policy regimes. Shilnikov chaos emerges for a restricted part of the free parameter space in the baseline rational expectations UK model with no regime switching. Chaos did not occur, when the UK's central bank showed a weak response to inflation in the high-inflation regime, while it appears easily in the low-inflation regime associated with the central bank’s use of aggressive monetary policy in recent years. As a policy alternative for restoring uniqueness, the local analysis proposes tightening the monetary policy rule via the Taylor coefficient. But we find that doing so could hasten the emergence of Shilnikov's chaotic dynamics. The magnitude of the Taylor coefficient thus becomes central in attaining the desired long run steady-state.
2021	Targeting Nominal Income under the Zero Lower Bound: The Case of the Bank of England Michael T. Belongia, Peter N. Ireland The Bank of England, like other central banks that use an interest rate as their policy variable, faces practical problems for implementation of monetary policy when interest rates are constrained by their zero lower bound. The quantity of money, however, faces no such constraint and, for that reason, policies that emphasize control of the money supply may offer an alternative path toward achievement of a central bank's nominal objectives. A simple model rooted in Quantity Theory principles suggests this is possible if the quantity of money is measured properly and slow-moving trends in velocity can be accommodated in the policy's implementation.
2018	"Risky" Monetary Aggregates for the UK and US Jane M. Binner, Sajid Chaudhry, Logan Kelly, and James L. Swofford We extend the scope of monetary aggregation beyond capital certain assets that make up central bank data sets and identify groups of assets that form monetary aggregates composed of both capital certain and risky, capital uncertain, assets. We construct monetary aggregates for the US and UK using a superlative index and relax a key assumption of the Consumption Capital Asset Pricing Model (CCAPM), a one year planning horizon, by using forecasted returns on risky assets. Our new risky monetary aggregates perform well in VAR tests. We recommended exploring risky assets as providers of liquidity services in future research on this topic.
2015	Evidence that Risk Adjustment is Unnecessary in Estimates of the User Cost of Money Diego A. Restrepo-Tobón Investors value the special attributes of monetary assets (e.g., exchangeability, liquidity, and safety) and pay a premium for holding them in the form of a lower return rate. The user cost of holding monetary assets can be measured approximately by the difference between the returns on illiquid risky assets and those of safer liquid assets. A more appropriate measure should adjust this difference by the differential risk of the assets in question. We investigate the impact that time non-separable preferences has on the estimation of the risk-adjusted user cost of money. Using U.K. data from 1965Q1 to 2011Q1, we estimate a habit-based asset pricing model with money in the utility function and find that the risk adjustment for risky monetary assets is negligible. Thus, researchers can dispense with risk adjusting the user cost of money in constructing monetary aggregate indexes.
2013	Amendments to Divisia Money Series R. Berar and J. Owladi This article describes improvements to be implemented to the Bank of England's Divisia money series and its components, effective the next edition of Bankstats to be published on 1st March 2013.
2010	Household-Sector Money Demand for the UK R. Bissoondeeal, B. Jones, J. M. Binner, and A. W. Mullineux This paper appeared in the journal, Manchester School (Economic and Social Studies), vol. 78, pp. 90-113.
2009	Financial Innovation in the UK: New Tier-Adjusted Household Sector Monetary Services Indexes J. M. Binner A revised version of this paper appeared in Global Business and Economics Review, vol. 11, pp. 44-64.
2009	Comparison of Simple Sum and Divisia Monetary Aggregates Using Panel Data Analysis S. Celik and S. Uzun This paper appeared in the International Journal of Social Sciences and Humanity Studies, vol. 1, pp. 1-13.
2009	An Evaluation of UK Risky Money: an Artificial Intelligence Approach. J. M. Binner, A. M. Gazely, and G. Kendall A revised version of this paper appeared in Global Business and Economics Review, vol 11, issue 1, pp. 1-18.
2008	A Note on the Optimal Level of Monetary Aggregation in the U.K. T. Elger, B. E. Jones, D. Edgerton, and J. M. Binner A revised version of this paper appeared in Macroeconomic Dynamics, vol. 12, pp. 117-131.
2006	Estimating a Regular Continuous-Time System of Demand for World Monies with Divisia Data K. P. Donaghy and D. M. Richard This paper appeared in the book, Belongia and Binner (2006), pp. 76-103.
2005	Divisia Money Matthew Hancock This paper appeared in the Bank of England Quarterly Bulletin, Spring, pp. 39-46.
2004	The UK Household Sector Demand for Risky Money T. Elger and J. M. Binner This paper appeared in Berkeley Electronic Press, Topics in Macroeconomics Series, vol. 4, no. 1, article 3.
2000	A Neural Network Approach to the Divisia Index Debate: Evidence from Three Countries A. M. Gazely and J. M. Binner A revised version of this paper appeared in Applied Economics, vol. 32, pp. 1607-1615.
2000	Weighted Monetary Aggregates for the UK Leigh Drake, K. Alec Chrystal, and Jane M. Binner This paper appeared in the book, Belongia and Binner (2000), pp. 47-78.
1996	On the Demand for Divisia and Simple-Sum M3 in German E. Gaiotti This paper appeared in the book, A. Mullineux (ed.), Financial Innovation, Banking, and Monetary Aggregates, Edward Elgar, Cheltenham.
1996	The Demand for Divisia Money by the Personal Sector and by Industrial and Commercial Companies N. Janssen This paper appeared in the Bank of England Quarterly Bulletin, November, pp. 405-409.
1996	Financial Innovation and Monetary Aggregates in the UK J. L. Ford and A. Mullineux This paper appeared in the book, A. Mullineux (ed.), Financial Innovation, Banking, and Monetary Aggregates, Edward Elgar, Cheltenham.
1993	Divisia Measures of Money P. G. Fisher, S. Hudson, and M. Pradhan This paper appeared in the Bank of England Quarterly Bulletin, vol. 33, no. 2. pp. 240-252.
1992	The Substitutability of Financial Assets in the U. K. and the Implication for Monetary Aggregation Leigh Drake This paper appeared in Manchester School of Economics and Social Studies, vol. 60, pp. 221-248.
1991	An Admissible Monetary Aggregate for the United Kingdom Michael T. Belongia and Alec K. Chrystal This paper appeared in the Review of Economics and Statistics, vol. 73, pp. 497-503.
1988	A Monetary Services Index R. Batchelor This paper appeared in Economic Affairs, vol. 8, pp. 17-20.
	United States
2011	Advances in Monetary and Financial Measurement Center for Financial Stability AMFM will be a central source for Divisia monetary aggregates data for the US and the rest of the world. While much of the data will be contributed, some US data will be produced by, and proprietary to, the CFS.
2011	A Comprehensive Revision of the U.S. Monetary Services (Divisia) Indexes Richard G. Anderson and Barry E. Jones This paper about the St. Louis Federal Reserve Bank's Divisia monetary aggregates is forthcoming in the Federal Reserve Bank of St. Louis Review, Sept/Oct, vol. 93, no. 4, 2011.
1984	The New Divisia Monetary Aggregates William A. Barnett, Edward K. Offenbacher, and Paul A. Spindt This paper, based upon Barnett (1980), contains the first empirical comparisons of Divisia monetary aggregates with simple-sum monetary aggregates in policy applications. That paper, published in the Journal of Political Economy, vol. 92, 1984, pp. 1049-1085, has been reprinted as chapter 17 of the book, Barnett and Serletis (2000).
1981	Aggregation of Monetary Assets William A. Barnett The landmark paper that began the modern literature on monetary aggregation and index number theory is Barnett's "Economic Monetary Aggregates: An Application of Index Number and Aggregation Theory," Journal of Econometrics, September 1980, pp. 11-48, and has been reprinted in the book, Barnett and Serletis (2000), as chapter 2. The published paper cannot be put online, since the copyright is owned by the publisher. But the original, longer working paper, which contains more than appears in the published journal article, appeared as chapter 7 of Barnett's book, Consumer Demand and Labor Supply. Since that book now is out of print, we can put that chapter online and have done so here.
1980	Economic Monetary Aggregates: An Application of Aggregation and Index Number Theory William A. Barnett This paper contains the first derivation of the Divisia money formula and the first computation and use of Divisia monetary aggregates. The paper also contains the derivation and use of the Fisher idea monetary-aggregation formula. The paper appeared in the Journal of Econometrics, vol. 14, pp. 11-48, and was reprinted in the book, Barnett and Serletis (2000), as chapter 1.
	Uruguay
2016	Divisia Monetary Aggregates and Demand for Money in Uruguay Jose Ignacio Gonzalez In this paper Divisia monetary aggregates were built for Uruguay in the period 1998.Q4- 2015Q2 and compared with traditional monetary aggregates. The difference increases in broader aggregates, being very small for M1 but significant for the case of M2 + bonds. Then these measures were incorporated into a money demand function and using error correction models short-run dynamics was examined, finding a quick adjustment towards long run equilibrium and with Divisia models a higher semi-elasticity for the opportunity cost of money. Over the six candidates, Divisia M2 model perform better and is the appropriate measure to track money demand and complement monetary policy analysis.
	World
2006	Estimating a Regular Continuous-Time System of Demand for World Monies with Divisia Data K. P. Donaghy and D. M. Richard This unique paper contains the only currently-available construction of a World Divisia monetary aggregate. The analytically sophisticated approach to that aggregation over world monies used numerical integration in continuous time. The paper appeared in the book, Belongia and Binner (2006), pp. 76-103.