The application of neural networks to the Divisia index debate: evidence from three countries

If monetary policy is to be effective in controlling the macroeconomy, accurate measurement of the money supply is essential. The conventional way of measuring the level of the money supply is to simply sum the constituent liquid liabilities of banks. However, a more sophisticated, weighted monetary index has been proposed to take account of the varying degrees of liquidity of the short-term instruments included in money. Inferences about the effects of money on economic activity may depend importantly on the choice of monetary index because simple sum aggregates cannot internalize pure substitution effects. This hypothesis is investigated in the current paper. A Divisia index measure of money is constructed for the USA, UK and Italian economies and its inflation forecasting potential is compared with that of its simple sum counterpart in each of the three countries. The powerful Artificial Intelligence technique of neural networks is used to allow a completely flexible mapping of the variables and a greater variety of functional form than is currently achievable using conventional econometric techniques. The application of neural network methodology to examine the money-inflation link is highly experimental in nature and, hence, the overriding feature of this research is one of simplicity. Superior inflation forecasting models are achieved when a Divisia M2 measure of money is used in the majority of cases. This support for Divisia is entirely consistent with findings based on standard econometric techniques reported from the respective central and Federal Reserve banks of each country. Divisia monetary aggregates appear to offer advantages over their simple sum counterparts as macroeconomic indicators. Further, the combination of Divisia measures of money with the artificial neural network offers a promising starting point for improved models of inflation.     

Financial Innovation and Divisia Money in Taiwan: Comparative Evidence from Neural Network and Vector Error-Correction Forecasting Models

In this article a Divisia monetary index is constructed for the Taiwan economy, and its inflation forecasting potential is compared with that of its traditional simple sum counterpart. The Divisia index is adjusted in two ways to allow for the financial liberalization that Taiwan has experienced since the 1970s. The powerful artificial intelligence technique of neural networks is used and is found to beat the conventional econometric techniques in a simple inflation forecasting experiment. The preferred inflation forecasting model is achieved using networks that employ a Divisia M2 measure of money that has been adjusted to incorporate a learning mechanism to allow individuals to gradually alter their perceptions of the increased productivity of money. The explanatory power of the two innovation-adjusted Divisia aggregates dominates that of the simple sum counterpart in the majority of cases. (JEL C4 , E4 , E5 )     

Monetary aggregates and core inflation: evidence from India

This study constructs a model-based core inflation for India using Divisia monetary aggregates instead of traditional money measures with the methodology proposed by Bagliano and Morana (2003) and evaluates its forecasting abilities. The core inflation derived from Divisia monetary aggregates is found to be a better leading indicator of measured inflation than the core inflation derived from traditional money measures. These results argue for a case in favour of using monetary aggregates in the construction of core inflation for policy purposes.     

MONEY AND INFLATION IN INDIA: EVIDENCE FROM P‐STAR MODEL

This study uses P‐star model to examine the role of money in explaining inflation in India. In particular, we compare the performance of traditional Phillips curve approach against P‐star model in forecasting inflation. Moreover, the study estimates P‐star model using the alternative measures of money such as simple sum and Divisia M3, to examine the relevance of aggregation theoretic monetary aggregates in explaining inflation. The empirical results indicate that P‐star model with real money gap has an edge over traditional Phillips curve approach in forecasting inflation. More importantly, we found that the P‐star model estimated with Divisia real money gap performs better than its simple sum counterpart. These empirical findings suggest that the changes in real money gap play a crucial role in explaining inflation in India.     

An alternative monetary policy target

For most of the period since the mid-1970s, the Federal Reserve has expressed its monetary policy intentions by announcing the target growth rates of three principal monetary aggregates: the simple-sum M1, M2 and M3. However, the sweeping changes and the deregulation in the financial industry have greatly affected the relevance of these traditional monetary aggregates. The unusual behaviour of the simple-sum monetary aggregates has forced the Federal Reserve to stop setting target range for M1. The measuring of monetary aggregates has become a controversial question. This paper constructs the new-benchmark Divisia monetary indexes which reflect ‘moneyness’ more accurately than the old Divisia indexes. I demonstrate that the historical trends of the Divisia monetary indexes are sensitive to the brenchmark rates chosen in constructing these indexes. In addition, I compare the forecasting performance of the new-benchmark Divisia monetary indexes with the simple-sum and the old Divisia monetary indexes in the estimated money demand functions. I find that the new-benchmark Divisia monetary indexes provide the best statis forecasting performance. The result indicate that the new-benchmark Divisia monetary indexes should be considered as alternative measures of money in studying the relationship between money and the economy.     

货币中介目标的国际比较*——基于DAG SVAR模型

学术界围绕最优货币中介目标的选择,在利率、简单加总货币量、迪维西亚货币量之间争论不休。本文基于DAG SVAR模型,分别对美国、欧元区、英国的银行间隔夜拆借利率R、简单加总货币量M2、迪维西亚货币量D2对物价P、产出Y影响的相对重要性进行实证比较。结果发现,在美国,M2对Y的影响最大,R对P的影响最大;在欧元区,D2对Y的影响最大,M2对P的影响最大;在英国,M2对Y和P的影响都最大。总的来说,若货币最终目标是经济增长,则美国、英国的最优中介目标是简单加总货币量,欧元区的最优中介目标是迪维西亚货币量;若货币最终目标是物价稳定,则美国的最优中介目标是利率,欧元区、英国的最优中介目标是简单加总货币量。由此可见,对于不同的经济体或者不同的货币最终目标,最优中介目标的选择可能有所不同。本文的研究结论在一定程度上是对“利率普遍优于货币量,迪维西亚货币量普遍优于简单加总货币量”学术共识的反向补充。     

A composite leading indicator of the inflation cycle for the Euro area

We evaluate the performance of composite leading indicators of turning points of inflation in the Euro area, constructed by combining the techniques of Fourier analysis and Kalman filters with the National Bureau of Economic Research methodology. In addition, the study compares the empirical performance of Euro Simple Sum and Divisia monetary aggregates and provides a tentative answer to the issue of whether or not the UK should join the Euro area. Our findings suggest that, first, the cyclical pattern of the different composite leading indicators very closely reflect that of the inflation cycle for the Euro area; second, the empirical performance of the Euro Divisia is better than its Simple Sum counterpart and third, the UK is better out of the Euro area.     

Business cycle,interest rate and money in the euro area: A common factor model

In this paper we model and analyze the contemporaneous correlation between interest rate, monetary aggregates, production and prices (of consumer goods, financial assets and real estate) of the euro area. To do this, firstly we estimate a common cyclical factor by means of an unobserved component model with the common factor located in variations in the underlying growth rates, that is, accelerations and decelerations of the variables. The variables mentioned share a significant cyclical factor being all procyclical except for narrow money. Finally we offer an explanation of this empirical finding based on the monetary policy strategy of interest rate pegging followed by the European Central Bank. In this regard, the shared cyclical information suggests (a) that inflation should be considered as a phenomenon that affects the whole economy, and therefore all prices, and (b) that monetary indicators such as monetary aggregates may contribute to the assessment of inflationary risks throughout the cycle.     

A two-pillar DSGE monetary policy model for the euro area

The current financial crisis has revived the interest for monitoring both monetary and credit developments. Over the past two decades, consistent with the adoption of inflation targeting strategies by a growing number of central banks and the development of New Keynesian models for which monetary aggregates are largely irrelevant, money and credit have been progressively neglected in the conduct of monetary policy. A striking exception has been the Eurosystem, which has implemented a strategy known as the “two-pillar monetary policy strategy” giving a prominent role for money. In this paper, we develop a small optimizing model based on Ireland (2004), estimated on euro area data and featuring this two-pillar strategy. We evaluate an ECB-style cross-checking policy rule in a DSGE model with real balance effects of money. We find some evidence that indeed money plays a non-trivial role in explaining the euro area business cycle. This provides a rationale for the central bank to factor in monetary developments but also raises some issues regarding the reliability of M3 as an appropriate monetary indicator. We find some evidence that the ECB has systematically reacted to a filtered measure of money growth but weak evidence it has reacted more aggressively during excess money growth periods.     

Recent monetary policy and the credit card-augmented Divisia monetary aggregates

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.     

A note of caution on the relation between money growth and inflation

We assess the bivariate relation between money growth and inflation in the euro area and the United States using hybrid time-varying parameter Bayesian VAR models. Model selection based on marginal likelihoods suggests that the relation is statistically unstable across time in both regions. The effect of money growth on inflation weakened notably after the 1980s before strengthening after 2020. There is evidence that this time variation is related to the pace of price changes, as we find that the maximum impact of money growth on inflation is increasing in the trend level of inflation. These results caution against asserting a simple, time-invariant relationship when modeling the joint dynamics of monetary aggregates and consumer prices.     

Endogeneity in European money demand

European wide monetary aggregates constructed from pre-unification data cannot be used as evidence that money demand in the euro area is stable. To overcome the Lucas critique, we apply the standard foreign exchange rate model. Since the uncoordinated country specific money supply system is abolished, the increased comovement between local monetary aggregates leaves little room for a free ride on the law of large numbers. Current monetary policy decisions must be based on untested relations, and given ‘the long and variable lags’, we conclude that the road towards monetary stability is a non-activist steady money supply policy.     

On the empirical relevance of the Lucas critique: the case of euro area money demand

This paper examines the relevance of the Lucas critique for euro area money demand. Based on the money in the utility function approach, a vector error correction model is specified to investigate the relationship between money and inflation in times of policy shifts. A well defined equation for money demand is obtained. The results indicate that the evolution of M3 is still in line with money demand. In the long run, inflation is affected by asset prices and detrended output. Our results show that the Lucas critique can be refuted in case of euro area money demand for the period of quantitative easing. Thus, the estimated money demand equation provides reliable information for the conduct of future monetary policy.     

Measures of underlying inflation in the euro area: assessment and role for informing monetary policy

The paper evaluates the 24-month-ahead inflation forecasting performance of various indicators of underlying inflation and structural models. Measures derived using the generalized dynamic factor model (GDFM) overperform other measures over the monetary policy horizon and are leading indicators of headline inflation. Trimmed means, although weaker than GDFM indicators, have good forecasting performance, while indicators by permanent exclusion underperform but provide useful information about short-term dynamics. The forecasting performance of theoretically-founded models that relate monetary aggregates, the output gap, and inflation improves with the time horizon but generally falls short of that of the GDFM. A composite measure of underlying inflation, derived by averaging the statistical indicators and the model-based estimates, improves forecast accuracy by eliminating bias and offers valuable insight about the distribution of risks.     

Data uncertainty and the role of money as an information variable for monetary policy

In this study, we perform a quantitative assessment of the role of money as an indicator variable for monetary policy in the euro area. We document the magnitude of revisions to euro area-wide data on output, prices, and money, and find that monetary aggregates have a potentially significant role in providing information about current real output. We then proceed to analyze the information content of money in a forward-looking model in which monetary policy is optimally determined subject to incomplete information about the true state of the economy. We show that monetary aggregates may have substantial information content in an environment with high variability of output measurement errors, low variability of money demand shocks, and a strong contemporaneous linkage between money demand and real output. As a practical matter, however, we conclude that money has fairly limited information content as an indicator of contemporaneous aggregate demand in the euro area.     

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

This 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.     

The (in)stability of money demand in the euro area: lessons from a cross-country analysis

The instability of standard money demand functions has undermined the role of monetary aggregates for monetary policy analysis in the euro area. This paper uses country-specific monetary aggregates to shed more light on the economics behind the instability of euro area money demand. Our results obtained from panel estimation indicate that the observed instability of standard money demand functions could be explained by omitted variables like e.g. technological progress that are important for money demand but constant across member countries.     

Some Thoughts on Monetary Targeting vs. Inflation Targeting

We offer some empirical evidence on the likely scale of control and indicator problems surrounding alternative monetary targets and a direct inflation target. The links between monetary policy actions and inflation are estimated in dynamic linear models using the Kalman filter. We compare alternative intermediate-target and final-target monetary strategies using German data from the end of the Bretton Woods system until 1997. The estimation results show that broad money dominates narrow money as an intermediate target, while control problems involved in targeting broad money are larger than for direct inflation targets.     

The information content of money in forecasting euro area inflation

This article contributes to the debate on the role of money in monetary policy by analysing the information content of money in forecasting euro-area inflation. We compare the predictive performance within and among various classes of structural and empirical models in a consistent framework using Bayesian and other estimation techniques. We find that money contains relevant information for inflation in some model classes. Money-based New Keynesian Dynamic Stochastic General Equilibrium (DSGE) models and Vector Autoregressions (VARs) incorporating money perform better than their cashless counterparts. But there are also indications that the contribution of money has its limits. The marginal contribution of money to forecasting accuracy is often small, money adds little to dynamic factor models, and it worsens forecasting accuracy of partial equilibrium models. Finally, nonmonetary models dominate monetary models in an all-out horserace.     

Assessing the predictive power of financial spreads in the euro area: does parameters instability matter?

In the empirical literature there is wide consensus that financial spreads cannot constitute a broadly based assessment on future output growth and inflation because the bivariate estimated regressions are not stable over time and lead to relatively poor out-of-sample forecasting performance (e.g. J Econ Liter 41:788–829, 2003). This conclusion arised for the USA, as well as for several European countries. In this paper we check whether the marginal predictive content of some financial spreads (the slope of the yield curve, the reverse yield gap and the credit spread) for macroeconomic forecasting in the euro area can be recovered using techniques taking into account potential parameters instability. We set up a quarterly Bayesian vector autoregression model with time-varying coefficients, comprising both target variables, as well as other monetary policy indicators, to serve as a benchmark. Then, the properties of the spreads as leading indicators are assessed by augmenting this benchmark BVAR with the spreads, one at a time. We find time variation of the coefficients to be a relevant issue in our model, especially for forecasting output growth, but financial spreads continue to have no or negligible marginal predictive content for both output growth and inflation. Overall, our results confirm that there is no ready-to-use financial spread that can replace an encompassing multivariate model for the prediction of target variables in the euro area.