Divisia Aggregates Research Articles

A granular investigation on the stability of money demand

Abstract A large literature has shown money demand functions constructed from simple-sum aggregates are unstable. We revisit the controversy surrounding the instability of money demand by examining cointegrating income-money relationships with the Divisia monetary aggregates for the U.S., and compare them with their simple-sum counterparts. We innovate by conducting a more granular analysis of various monetary assets and their associated user costs. We find characterizing money demand with simple-sum measures only works well in a period preceding 1980. Divisia aggregates, their components, and their user costs provide a more reliable interpretation of money demand. Subsample analysis across 1980 and 2008 suggests the instability of money demand is a matter of measurement rather than a consequence of a structural change in agents’ preference for monetary assets.

Money growth and inflation in the Euro Area, UK, and USA: measurement issues and recent results

Abstract This paper identifies several ways in which “measurement matters” in detecting quantity-theoretic linkages between money growth and inflation in recent data from the Euro Area, United Kingdom, and USA. Elaborating on the “Barnett critique,” it uses Divisia aggregates in place of their simple-sum counterparts to gauge the effects that monetary expansion or contraction is having on inflationary pressures. It also uses one-sided time series filtering techniques to track, in real time, slowly shifting trends in velocity and real economic growth that would otherwise weaken the statistical money growth-inflation relationship. Finally, it documents how measures of inflation based on GDP were distorted severely, especially in the EA and UK, during the 2020 economic closures. Using measures based on consumption instead, estimates from the P-star model confirm that changes in money growth have strong predictive power for subsequent movements in inflation.

The credit-augmented Divisia aggregates and the monetary business cycle

Abstract We follow Belongia and Ireland (2021) and investigate the role that the Center for Financial Stability credit card-augmented Divisia monetary aggregates could play in monetary policy and business cycle analysis. We use Bayesian methods to estimate a structural VAR under priors that reflect Keynesian channels of monetary transmission, but produce posterior distributions for the structural parameters consistent with classical channels. We also find that valuable information is contained in the credit-augmented Divisia monetary aggregates and that they perform even better than the conventional Divisia aggregates, in terms of highlighting the role of the money supply in aggregate demand.

The transmission of monetary policy shocks through the markets for reserves and money

This paper identifies supply and demand curves for bank reserves and a Divisia aggregate of monetary services within a structural vector autoregressive time-series model. Estimated over four sample periods spanning 1967 through 2020, the model illustrates how monetary policy actions can be interpreted with reference to their initial impact on bank reserves and the federal funds rate and their subsequent effects on Divisia money, nominal consumption spending, the aggregate nominal price level, and the unemployment rate. Model estimates attribute strong inflationary effects to monetary policy in the late 1960s and 1970s and also show that changes in the supply of reserves associated with the Fed's large-scale asset purchases since 2008 worked, as intended, to offset deflationary pressures and reduce unemployment. The model describes a much richer monetary policy process than one focused on interest rates alone.

The impact of uncertainty on money demand in the UK, US and Euro area

We estimate money demand functions for the UK, the Euro area and the US using Divisia monetary aggregates and investigate the extent to which the uncertainty caused by Brexit and Covid have affected these relationships. Our cointegrated VAR analysis shows that for all three economies Brexit and/or Covid have had some impact on the stability of money demand functions. We find that including a measure of stock market volatility in the money demand specifications helps re-establish stability of the models, particularly for the UK and the Euro area. We also explore the uncertainty and money demand relationship in the context of a Markov-switching model. We find that the effect of uncertainty on the demand for money is more pronounced during periods of heightened uncertainty. The findings of this study lend support to studies calling for Divisia aggregates to be given a more prominent role in policymaking, especially when interest rates are in the zero lower bound environment and are less informative about the stance of monetary policy.

Nonlinear dynamics in Divisia monetary aggregates: an application of recurrence quantification analysis

We construct recurrence plots (RPs) and conduct recurrence quantification analysis (RQA) to investigate the dynamic properties of the new Center for Financial Stability (CFS) Divisia monetary aggregates for the United States. In this study, we use the latest vintage of Divisia aggregates, maintained within CFS. We use monthly data, from January 1967 to December 2020, which is a sample period that includes the extreme economic events of the 2007–2009 global financial crisis. We then make comparisons between narrow and broad Divisia money measures and find evidence of a nonlinear but reserved possible chaotic explanation of their origin. The application of RPs to broad Divisia monetary aggregates encompasses an additional drift structure around the global financial crisis in 2008. Applying the moving window RQA to the growth rates of narrow and broad Divisia monetary aggregates, we identify periods of changes in data-generating processes and associate such changes to monetary policy regimes and financial innovations that occurred during those times.

The Credit-Augmented Divisia Aggregates and the Monetary Business Cycle

The Credit-Augmented Divisia Aggregates and the Monetary Business Cycle

The Demand for Simple-sum and Divisia Monetary Aggregates for Pakistan: A Cointegration Approach

Financial liberalisation and the advance of financial innovation in a number of developed economies has been blamed for the break-down in the demand for money based on simple sum measures. This break-down has prompted research into Divisia measures of the demand for money. Like many developing countries, Pakistan is going through a period of financial deregulation which goes hand in hand with financial innovation due to increased competition in the banking industry. This paper employs the methodology of cointegration to compare simple-sum and Divisia level estimates of the demand for money for Pakistan for the period 1974Q4 to 1992Q4. Simple sum measures of M1 and M2 were compared with Divisia versions. The paper reports little evidence in support of the superiority of the Divisia monetary aggregates. Both types of measure produce a stable demand for money and perform satisfactorily in post-sample stability tests, although the Divisia measure appears to perform marginally better on conventional statistical criteria. However, our conclusions have to be qualified by the limitations of the data and the knowledge that the period of financial innovation and deregulation has been relatively recent. The policy significance of the results suggests that currently there is no advantage from switching from simple-sum to Divisia aggregates at the existing level of official aggregation as the proper indicator of monetary policy. However, if financial deregulation and innovation continues at the current pace, the Divisia aggregates may in future prove to be the better indicator.

The stability of UK households Divisia money balances

This paper examines the stability of holdings of Divisia money balances by UK households using step and impulse indicators. An error feedback equation for money demand is estimated that includes 5 step dummies and 6 impulse dummies. For comparison an error correction model for the traditional M4 aggregate is also estimated that includes 9 steps and 5 impulse dummies. Steps in 1983 and 1990 are common to both aggregates. Steps in 1992, 2012 and 2015 only affect the Divisia aggregate. The step in 2012 corresponds to the Bank of England’s second round of quantitative easing. The Divisia aggregate appears to be a useful guide for policy, especially when the policy rate is close to the zero lower bound.

Constructing Divisia Monetary Aggregates for Nigeria

This study computes Divisia monetary aggregates DM1, DM2, and DM3 for Nigeria using the Tornqvist-Theil quantity index for the period 2007M12 to 2020M12 and evaluates the performance of the higher-order aggregate (DM3) with a corresponding higher aggregate of the simple sum broad money supply (M3). Applying the indicators to money demand function the results showed that DM3 performed better than the matching simple sum measure M3 due to its faster convergence rate. This is because the Divisia aggregates contain additional information in the form of user-costs and spending shares that are not considered in the compilation of the traditional measure, information that may be important for the proper execution of monetary policy. It is therefore, recommended that the Divisia broad money index be used as complement to the simple sum broad money supply for policy decisions.

Forecasting inflation and output growth with credit‐card‐augmented Divisia monetary aggregates

AbstractThis paper investigates the performance of the credit‐card‐augmented Divisia monetary aggregates in forecasting US inflation and output growth at the 12‐month horizon. We compute recursive and rolling out‐of‐sample forecasts using an autoregressive distributed lag model based on Divisia monetary aggregates. We use the three available versions of those monetary aggregate indices, including the original Divisia aggregates, the credit card‐augmented Divisia, and the credit‐card‐augmented Divisia inside money aggregates. The source of each is the Center for Financial Stability. We find that the smallest root mean square forecast errors are attained with the credit‐card‐augmented Divisia indices used as the forecast indicators. We also consider Bayesian vector autoregression for forecasting annual inflation and output growth.

Euro area monetary asset demand and Divisia aggregates**

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. .

INTEREST RATES, MONEY, AND ECONOMIC ACTIVITY

In this paper, we are motivated by the fact that little is known about the relative performance of broad and narrow Divisia monetary aggregates, and by recent work that tests and rejects the appropriateness of the aggregation assumptions that underlie the various monetary aggregates published by the Federal Reserve as well as a large number of monetary asset groupings suggested by earlier studies. We present a comprehensive comparison of narrow versus broad Divisia monetary aggregates within three classes of empirical models. We compute correlations between the cyclical components of Divisia monetary aggregates at different levels of aggregation and the cyclical component of industrial production. We test for Granger causality running from the Divisia aggregates to industrial production and various other measures of real economic activity. We also reestimate a structural vector autoregression based on earlier work by Leeper and Roush [(2003) Journal of Money, Credit, and Banking 35, 1217–1256] and Belongia and Ireland [(2015) Journal of Business and Economic Statistics 33, 255–269; (2016) Journal of Money, Credit and Banking 48, 1223–1266], modifying that earlier work using monthly rather than quarterly data and extending it, both using broad as well as narrower Divisia monetary aggregates and by allowing for Generalized autoregressive conditional heteroskedasticity (GARCH) behavior in the structural shocks.

Structural changes and the role of monetary aggregates in the UK

We investigate whether or not monetary aggregates are important in determining output. In addition to the official Simple Sum measure of money, we employ the sophisticated weighted Divisia aggregate. We also investigate whether or not the influence of money on output is time varying using data-driven procedures to identify breaks in the data and conduct estimations for the different segments defined by these breaks. We find that structural breaks do exist in some of the variables under investigation and these do influence the relationship between monetary aggregates and output. However, the official Simple Sum aggregate appears to be more affected by the breaks than the theoretically superior Divisia aggregate. In particular, our results show that in some segments of our data, the Simple Sum aggregate does not influence output significantly whereas the Divisia aggregate maintains a significant relationship with output in all segments. We conclude that Divisia money is still influencing output in spite of the diminished role played in monetary policy. Our investigation also suggests that the recovery from the financial crisis using quantitative easing would have been faster if money was not being hoarded.

Divisia monetary aggregate and monetary transmission mechanism in the Democratic Republic of Congo (DRC)

ABSTRACTWhile the majority on the effectiveness of monetary policies focus on either interest or money channels, we analyze the effectiveness of a composite monetary instrument: The Divisia Aggregate Index (DMAI). Dynamic effects of the DMAI on other economic factors is analyzed through the Factor Augmented Vector Autoregressive model (FAVAR). The latter address the potential arbitrary selection of variables to incorporate in a standard VAR model, and is built from the ability of factor analysis to summarize a very high number of variables into few factors. The FAVAR is applied to monthly data over the period 01:1996-12:2017 from the Democratic Republic of the Congo. Our empirical results reveal that the DMAI outperforms other monetary policy instruments that use separately interest or money channels, in boosting output and triggering price stability.

The demand for Divisia money in the United States: evidence from the CFS Divisia M3 aggregate

ABSTRACTIn this paper, we analyse the demand for real money balances in the United States for the period 1990Q1–2017Q2 using a novel Divisia monetary aggregate developed by Barnett et al. (2013). Unlike simple-sum aggregates, Divisia aggregates take into account the different degrees of ‘moneyness’ of each monetary asset. In addition, Divisia aggregates have shown to be empirically superior to simple-sum aggregates, providing stable money demand functions for different periods and countries. In a first stage, we test for cointegration and estimate a long-run equilibrium model. In a second stage, we estimate an error correction model to study the short-run dynamics. Consistent with previous research, our findings show the existence of a stable money demand function, which suggests that monetary aggregates, when properly measured, can be useful tools in the conduct of monetary policy.

Divisia and Simple Sum Monetary Aggregates: Any Empirical Relevance for Turkey?

Abstract In consideration of channels through which monetary policy affects economic activity, the monetary aggregates have been mostly ignored by the monetary authorities instead of which shortrun interest rates have been given a priori role. These monetary aggregates are largely argued to fail in measuring the effectiveness of different monetary policy regimes in forecasting the macroeconomic fundamentals. Grounded on the “Barnett critique”, the formation of traditional simple-sum monetary aggregates assuming for perfect substitution among the components of the money supply is blamed for such a failure of money in explaining the real activity. Given increasing varieties of financial assets which have completely different “moneyness”, it is important to provide an alternative measure of the money supply. Hereby, the Divisia monetary aggregates which give different weights to different assets have arisen as an alternative approach. 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.

Modern and Traditional Methods for Measuring Money Supply: The Case of Saudi Arabia

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.

The Barnett critique after three decades: A New Keynesian analysis

This paper extends a New Keynesian model to include roles for currency and deposits as competing sources of liquidity services demanded by households. It shows that, both qualitatively and quantitatively, the Barnett critique applies: while a Divisia aggregate of monetary services tracks the true monetary aggregate almost perfectly, a simple-sum measure often behaves quite differently. The model also shows that movements in both quantity and price indexes for monetary services correlate strongly with movements in output following a variety of shocks. Finally, the analysis characterizes the optimal monetary policy response to disturbances that originate in the financial sector.

FORECASTING THE UK/US EXCHANGE RATE WITH DIVISIA MONETARY MODELS AND NEURAL NETWORKS

ABSTRACTThis paper compares the UK/US exchange rate forecasting performance of linear and nonlinear models based on monetary fundamentals, to a random walk (RW) model. Structural breaks are identified and taken into account. The exchange rate forecasting framework is also used for assessing the relative merits of the official Simple Sum and the weighted Divisia measures of money. Overall, there are four main findings. First, the majority of the models with fundamentals are able to beat the RW model in forecasting the UK/US exchange rate. Second, the most accurate forecasts of the UK/US exchange rate are obtained with a nonlinear model. Third, taking into account structural breaks reveals that the Divisia aggregate performs better than its Simple Sum counterpart. Finally, Divisia‐based models provide more accurate forecasts than Simple Sum‐based models provided they are constructed within a nonlinear framework.