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.     

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.     

The information content of the divisia monetary aggregates in forecasting inflation in the euro area

The paper investigates the performance of a set of monetary indicators, based on the Divisia money constructed for the euro area, on forecasting euro area inflation. The paper first briefly discusses on the relative information contents of the Divisia aggregates and the simple sum aggregates. The forecasting performance of the former is then examined by means of simulated out-of-sample forecasting. In addition to examining the information contents of the Divisia aggregate constructed for M3 money, the study also examines the performance of the Divisia M1 money to gain evidence on the relative performance between the broad and narrow Divisia monetary aggregates. According to the results, only some of the monetary indicators considered can significantly improve the univariate inflation forecasts. The Divisia M3 money based monetary indicators turned out to perform better than their Divisia M1 based counterparts. The result contradicts some previous evidence on the optimal level on monetary aggregation in the context of broad versus narrow money.      

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.     

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.     

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.     

Compression in monetary user costs in the aftermath of the financial crisis: implications for the Divisia M4 monetary aggregate

Differences in Divisia and simple-sum money arise from appropriate weighing mechanisms in Divisia, which rely on information on the user cost of monetary assets. We show convergence in the growth rate of Divisia M4 and its simple-sum counterpart beginning in early 2009, shortly after the collapse in the Federal Funds rate. This phenomenon results from compression in user costs.     

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.     

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.     

Rational expectations and the demand for money: A nonparametric approach

This paper tests the U.S. demand for money for evidence of the effect of rational expectations of the income and interest rate variables that enter as arguments into that function. The data employed are simple-sum and Divisia aggregates, and the nonparametric tests are of the identification and information orthogonality of the various monetary measures. The Akaike Criterion is used to distinguish among the alternative specifications. While non-rationality is the typical result, Divisia aggregates appear to be more “rational” than simple sum. There is evidence of mean-reversion in interest rates as well.     

On the demand for money in the United States

One of the current issues in the literature on the demand for money is whether the adjustment of actual to desired money holdings is in real or nominal terms. This paper tests the real against the nominal adjustment hypothesis using United States data. Comparisons are made among simple sum and Divisia aggregates (of M1, M2, M3, and L) and with Spindt's monetary velocity (MQ) aggregate. The results strongly support the nominal adjustment hypothesis, but they do not reveal a single uniformly best monetary aggregate.     

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。     

货币增长不确定性与通货膨胀不确定性——“波动溢出”假说与实证检验

文章基于通货膨胀——通货膨胀不确定性关系的理论研究,提出货币增长不确定性向通货膨胀不确定性波动溢出的计量检验假说,并利用中国数据,运用多元GARCH模型进行实证检验。结果发现,存在货币增长不确定性显著向通货膨胀不确定性波动溢出的效应。这意味着,货币增长不确定性具有提供有关预测通货膨胀不确定性信息的能力。同时也表明,货币增长不确定性是通货膨胀不确定性的重要解释变量,其重要性不应被忽视。实证结论的政策含义是:减少货币增长不确定性是降低通货膨胀不确定性的重要途径,我国20世纪90年代中后期稳健的货币政策所带来的通货膨胀不确定性显著降低的现实支持了这个观点。     

Monetary policy arithmetic: reconciling theory with evidence

Abstract.  Empirical evidence indicates that, in countries with low inflation rates, a permanent decrease in inflation rate either has no impact on capital stock and output (superneutrality) or causes them to fall moderately. Existing budget arithmetic models of monetary policy cannot deliver superneutrality. In this paper, we conduct a budget arithmetic analysis of monetary policy using a money demand specification – money in the utility function – that is new to this literature. We find that one simple assumption about utility from money delivers superneutrality, while a more general assumption delivers departures from superneutrality in the direction consistent with the evidence. JEL classification: E60, E13     

Divisia monetary aggregates and US GDP nowcasting

ABSTRACT

This article nowcasts US quarterly real GDP growth rate with dynamic factor model (DFM) using Divisia Monetary Aggregate Index, Divisia M1, M2, M3, and exploits information from a large, unbalanced panel data. GDP nowcasting is evaluating the current quarter GDP given the available economic data up to the point when the nowcasting is conducted. GDP data is published quarterly with a substantial lag, while many monetary and financial decisions are made at a higher frequency. Therefore, nowcasting GDP has become an increasingly important task for central banks. This article uses DFM to nowcast GDP, compares the nowcasting results from DFM with the simple sum monetary aggregate M1, M2, M3, to the Model with weighted corresponding Divisia Index, then calculates the contributions of the Divisia Monetary index to US GDP nowcasting.     

Monetary Disequilibrium, Endogenous Money, Stability and the Determinacy of Inflation

This paper examines the stability of the disequilibrium money model, with endogenous money and transitory interest rate control by the Central Bank. In the tradition of the post-Keynesian literature, the money supply is determined by bank lending and disequilibrium between money demand and supply determines the business cycle. The rate of interest is assumed to react to an inflation target and inflation responds to the business cycle. The paper examines the stability of the model under three inflation response systems: the accelerationist model, adaptive expectations and rational expectations.
(J.E.L.: E3, E4, E5).     

Money Demand in an EU Accession Country: A VECM Study of Croatia

The paper estimates the money demand in Croatia using monthly data from 1994 to 2002. A failure of the Fisher equation is found, and adjustment to the standard money‐demand function is made to include the inflation rate as well as the nominal interest rate. In a two‐equation cointegrated system, a stable money demand shows rapid convergence back to equilibrium after shocks. This function performs better than an alternative using the exchange rate instead of the inflation rate as in the ‘pass‐through’ literature on exchange rates. The results provide a basis for inflation rate forecasting and suggest the ability to use inflation targeting goals in transition countries during the EU accession process. Finding a stable money demand also limits the scope for central bank ‘inflation bias’.     

THE SUITABILITY OF THE DIVISIA INDEX FOR THE MEASUREMENT OF ECONOMIC AGGREGATES

This paper considers the properties of the Divisia, or chain-link, index, as they relate to the argument that this is the most appropriate index for use in studying the sources of economic growth. The great advantage of the Divisia index is alleged to be its "accuracy", that is, its capacity to combine time series of prices and quantities to give a true reflection of the height of a utility or production function over time. The paper shows that there are circumstances where the confidence in the accuracy of the Divisia index is justified, but that the conditions required are very restrictive and typically do not obtain in the contexts where the Divisia index is used. Misplaced confidence in the Divisia index has led to errors of interpretation that might otherwise have been avoided, and has given rise to a distorted view of the process of economic growth.     

A classroom experiment in monetary policy

The authors propose a classroom experiment implementing a simple version of a New Keynesian model suitable for courses in intermediate macroeconomics and money and banking. Students play as either the central bank or members of the private sector. The central banker sets interest rates to meet twin objectives for inflation and the output gap or to meet only an inflation target. In both settings, private sector agents are concerned with correctly forecasting the inflation rate. The authors show that an experiment implementing this setup is feasible and yields results that enhance understanding of the New Keynesian model of monetary policy. They propose alternative versions where the central bank is replaced by a policy rule and provide suggestions for discussing the experimental results with students.     

DSGE model-based forecasting of modelled and nonmodelled inflation variables in South Africa

Inflation forecasts are a key ingredient for monetary policy-making – especially in an inflation targeting country such as South Africa. Generally, a typical Dynamic Stochastic General Equilibrium (DSGE) only includes a core set of variables. As such, other variables, for example alternative measures of inflation that might be of interest to policy-makers, do not feature in the model. Given this, we implement a closed-economy New Keynesian DSGE model-based procedure which includes variables that do not explicitly appear in the model. We estimate such a model using an in-sample covering 1971Q2 to 1999Q4 and generate recursive forecasts over 2000Q1 to 2011Q4. The hybrid DSGE performs extremely well in forecasting inflation variables (both core and nonmodelled) in comparison with forecasts reported by other models such as AR(1). In addition, based on ex-ante forecasts over the period 2012Q1–2013Q4, we find that the DSGE model performs better than the AR(1) counterpart in forecasting actual GDP deflator inflation.