Detecting cointegration relationships under nonlinear models: Monte Carlo analysis and some applications

Testing for cointegration in the presence of nonlinear adjustments or structural breaks is important for examining the equilibrium relationship among economic variables. It is known that standard cointegration tests perform poorly when a cointegration relationship has nonlinear adjustments or structural breaks. However, it is not clear how some cointegration tests allowing for nonlinearity perform under other classes of nonlinear cointegration models. This paper investigates which cointegration tests help detect a cointegration relationship with nonlinear adjustments or structural breaks. Our Monte Carlo simulation results demonstrate that the cointegration test with threshold adjustment generally has better power performance under most cointegration relationships with nonlinearity. We also provide empirical applications to the money demand and term structure of the U.S. interest rates. The empirical results show that the test allowing for threshold adjustment provides strong evidence of the cointegration relationships of money demand and the term structure of interest rates.     

Long-run estimates of money demand: new evidence from East Asian countries and the presence of structural breaks

Conventionally, the money demand function is estimated using a linear regression of the logarithm of money demand on a number of variables. In this article, we aim to estimate the long-run properties of money demand specification for a number of East Asian economies and within a panel framework with the presence of structural breaks. Various country-specific coefficients are allowed to capture inter-country heterogeneities. Consistent with theoretical postulates, it is found that (a) the demand for money in the long-run positively responds to real income and inversely to the interest rate spread, inflation, the real effective exchange rate and the US real interest rate; (b) the long-run income elasticity is greater than unity; and (c) both the currency substitution and capital mobility hypotheses hold. The empirical findings in this article can provide useful policy guidelines to the East Asian countries’ central banks in their quest for price stability. If one of the primary objectives of these countries is to minimize price instability, they should avoid creating unnecessary disequilibrium in the money market, while the employment of cointegration with the presence of structural breaks clearly recommends to central banks to use the supply of money to attain price and macroeconomic stability.     

Estimation of a German money demand system – a long-run analysis

This study presents a multivariate analysis of the stability of long-run relationships between variables that influence the conduct and transmission process of the German monetary policy. The initial VAR comprises the variables real money M3, real GNP, the inflation rate, a long-term and a weighted short-term interest rate. A multivariate approach has been chosen, as this allows for more than one cointegration relationship and to test restrictions on the cointegration space. In contrast to most other studies on German monetary policy, three stable and economically plausible cointegration relationships are obtained simultaneously within the framework of the Johansen procedure: a money demand relationship, a long-run Fisher effect and a long-run relationship between the short- and the long-term interest rate. It is apparent that the structural break of German reunification can be modelled incorporating dummy variables in the model. First version received: October 1996/final version received: July 1997     

Demand for money in Bangladesh: a cointegration analysis

The aim of this study is to estimate the demand for real broad (M2) money in Bangladesh using the most recently developed autoregressive distributed lag approach to cointegration analyses. The empirical results show that there is a unique cointegrated and stable long-run relationship among real per capita broad money demand, real per capita income, domestic interest rates and unofficial exchange rate (UM) premiums which act as a surrogate for foreign interest rates. With money as the dependent variable, the results show that the income and interest elasticities are positive while the UM premium elasticity is negative. These results suggest that distortions in the financial and foreign exchange markets should be reduced in order to increase financial saving or monetary accumulation. Our results also reveal that the demand for money in Bangladesh is stable despite the changes in financial and exchange rate policies between 1975 and 1995.     

Long-run money demand in OECD countries: what role do common factors play?

This article examines the long-run money demand function for 11 OECD countries from 1983Q1 to 2006Q4 using panel data. The distinction between common factors and idiosyncratic components using principal component analysis allows for the detection of cross-member cointegration and the determination as to whether national or international sources are responsible for the non-stationarity of money and its determinants. Indeed, the finding that the common factors are I(1) while the idiosyncratic components are I(0) indicates that cross-member cointegration may exist and non-stationarity in the variables is primarily driven by common international trends. Furthermore, it is found that the impact of income on money demand is positive, whereas it is negative for the interest rate, exchange rate and stock prices. Except for the income elasticity of money demand, all estimated long-run coefficients are larger for the common factors of the variables than for the variables themselves. This article provides evidence that the exchange rate is an important determinant of money demand, whereas the results for the stock prices are ambiguous. Finally, the results of a panel-based error-correction model suggest that several domestic money stocks converge to a common international equilibrium relationship between the common factors.     

Stability of money demand function revisited in China

As China's economic reforms have undergone significant structural changes after 1979, it has been rather difficult to formulate a stable money demand function over the period following that year. While previous literature on the long-run relationship of money demand in China shows the existence of stable money demand, this article revisits the stability of the China money demand function over the period after 1979. To employ the unit root tests and the cointegration tests with structural break, the empirical evidence demonstrates that economic and financial deregulation did affect the stability of demand for money in China over the period 1977 to 2002. Moreover, the estimated long-run income and interest elasticity are respectively 1.01 (1.11) and ?0.14 (?0.08) using the real M1 (M2) equation. In addition, real income and the interest rate are found to be weakly exogenous. We overall do find structural breakpoints mainly in 1980 and 1993, and they look to match clearly with corresponding critical financial and economic incidents.     

Modelling of narrow money demand in Australia: an ARDL cointegration approach, 1970–2009

Using annual data for the period 1970?C2009, this paper deploys the ARDL cointegration approach to determine whether there exists an economically meaningful, stable narrow money demand relationship in Australia. The statistical results suggest the presence of a long-run equilibrium relationship between real narrow money balances, real income, a representative domestic interest rate (e.g., the yield on Australian government short-term bonds) and the nominal effective exchange rate of the Australian dollar. The statistical tests suggest no significant instability in the narrow money demand relationship despite financial deregulation and innovation in Australia since the early 1980s. In contrast, the paper reports statistical results which suggest no meaningful, stable broad money demand relationship in Australia over the sample period.     

The demand for money in korea: Evidence from the cointegration test

This paper shows that there exists a long-run equilibrium relationship between M2 and its determinants, real income and the long-term interest rate, in Korea by using Johansen and Juselius maximum likelihood cointegration method. However, M1 does not have any meaningful cointegration relationships with its determinants. The long-term interest rate is a better proxy than the short-term rate to measure the opportunity cost of holding money. Based on the results, a broad definition of money is a better measure than a narrow definition of money in considering the long-run economic impacts of changes in monetary policy in Korea.     

MODELLING DEMAND FOR BROAD MONEY IN AUSTRALIA*

The existence of a valid long‐run money demand function is still important for the conduct of monetary policy. It is argued that previous work on the demand for money in Australia has not been very satisfactory in a number of ways. This paper examines the long‐ and short‐run determinants of the demand for broad money employing the Johansen cointegration technique. Using quarterly data for the period 1976:3–2002:2, this paper finds, inter alia, that the demand for broad money is cointegrated with real income, the rate of return on 10‐year Treasury bonds, the cash rate and inflation. It appears that a disequilibrium in the demand for money can affect the efficacy of interest rate policy in the long run via its impact on future output growth and output gap.     

Money demand in China in the reform period: an error correction model

Based on integration and cointegration test findings, this paper constructs an error correction (ECM) model to evaluate the dynamic adjustment process of money demand in China in the reform period (1979 to 1990). The cointegration tests suggest that some long-run relationship exists among money demand, real income, price, and the real interest rate. The ECM model shows that the dynamic adjustment process of money demand maintains stable and significant relationships to most of its determinants.     

Monetary transmission in Germany: Lessons for the Euro area

This study analyses the transmission of monetary policy in Germany for the EMS period in the framework of a structural vector error correction model (S-VECM).Three stable cointegration relationships are found: a money demand relation, an interest rate spread and a stationary real interest rate. Based on both contemporaneous and long-run restrictions, five structural shocks to the economy are identified. In contrast to analyses for the euro area, we find that output and inflation are not independent in the long run for Germany. In accordance with results previously found for Europe, we do not find strong support for monetary targeting for Germany. Our analysis indicates that uncertainties remain concerning the controllability of money and its usefulness as a leading indicator with respect to inflation. Stability of the money demand relationship does not seem to be problematic.Jel classification:C32, C52, E41, E43, E52We would like to thank Jörg Breitung, Bertrand Candelon, Peter van Els, Carsten Folkertsma, Helmut Lütkepohl, Dieter Nautz, Hans-Eggert Reimers, Nikolaus Siegfried and Jürgen Wolters, two anonymous referees as well as participants of the 8th World Congress of the Econometric Society in Seattle and the Annual Meeting of the Verein für Sozialpolitik in Berlin for helpful comments. The views expressed in this paper do not necessarily reflect those of the European Central Bank or De Nederlandsche Bank.Both authors were working at the research department of De Nederlandsche Bank at the time of writing.First revision received: April 2002/Final revision received: January 2003     

An empirical investigation of monetary interaction in the Korean economy

This paper conducts an econometric investigation of monetary interaction in the Korean economy over the past two decades. The study pays close attention to a critical role played by broad money and an interest rate term spread in the economy. A vector autoregression reveals two cointegrating relationships, both of which are consistent with macroeconomic theory: the first relationship corresponds to a broad money demand function, while the second represents a monetary policy rule function. The cointegrated system is then reduced to a vector equilibrium correction system, which characterizes the interaction between money demand and monetary policy rule. It is also demonstrated that the preferred model is a reliable forecasting device, suggesting that the broad money contains information about the real economy in the future.     

Stock prices and long-run demand for money: evidence from Malaysia

This paper investigates the money demand function for Malaysia in the 1971-1996 period using the multivariate cointegration and error correction model methodology. The results suggest that a stable long-run relationship exist between real M2, the interest rate differential, income and stock prices. Stock prices have a significant negative substitute effect on long-run as well as short-run broad-money demand (M2) and its omission can lead to serious misspecification in the money demand function. The analysis from the vector error correction model (VECM) and the Toda & Yamamoto (1995) causality tests find that money is endogenous and that there is at least a unidirectional relationship between stock prices and real M2. Stock prices Granger cause real M2 indirectly through income between interest rates and stock prices and stock prices and money stock. This paper comes to the conclusion that due to the endogeneity of money, M2 cannot be completely controlled by Malaysia's central bank. Therefore, in formulating future monetary policy, the response of money demand to stock prices should be considered.     

Globalization,Financial Liberalization and the Behavior of the Long Run Money Demand in the Bangladesh Economy

ABSTRACT

The paper estimates the long run demand for money function in the Bangladesh economy using cointegration and the Vector Error Correction Modeling (VECM) technique. The cointegration results suggest that although the process of globalization has shown no significant impact on money demand by the fact that the foreign interest rate is seen as statistically not significant, the financial liberalization has an important impact, reflected in the statistically significant role of domestic interest rate, in influencing both M1 and M2 money demand. An estimate of VECMs also reveals the fact that the short run speed of adjustment is moderately influenced by the financial reform measures to establish the long run relation between money balances, income and domestic interest rates. The phenomenon of credit constraint in the context of a developing country has shown no significant role in influencing money demand, which may imply that the stage of financial development is getting higher level in the Bangladesh economy. The existence of exchange rate depreciation in the cointegration relation with the expected sign suggests that currency substitution is now effective in the monetary sector and, therefore, its impact should be considered in the Bangladesh monetary policy matrix.     

Does money have a role in the inflation process? Evidence from Australia

Inflation, defined as a sustained increase in the price level, is considered a monetary phenomenon, as it can be explained within the framework of money‐demand and money‐supply relationships. In the extant literature, money growth is shown to remain causally related to inflation across countries and over time, irrespective of the exchange rate regime and stability of the money‐demand function. Nevertheless, emerging literature suggests a diminishing role of money in the conduct of monetary policy for price stability, especially under inflation targeting. Monetary policy in Australia under inflation targeting since 1993 is an example of policy that denies a relationship between money growth and inflation. The proposition that money does not matter insofar as inflation is concerned seems odd in both theory and the best‐practice monetary policy for price stability. This paper uses annual data for the period 1970–2017 and quarterly data for the period 1970Q1–2015Q1. It deploys both the Johansen cointegration approach and the autoregressive distributed lag (ARDL) cointegration approach to investigate for Australia whether money, real output, prices and the exchange rate (non‐stationary variables) maintain the long‐run price‐level relationship that the classical monetary theory suggests in the presence of such stationary variables as the domestic and foreign interest rates. As expected, the empirical findings for Australia are consistent with the classical long‐run price‐level relationship between money, real output, prices and the exchange rate. The error‐correction model of inflation confirms the presence of a cointegral relationship among these variables; it also provides strong evidence of a short‐run causal relationship between money supply growth and inflation. On the basis of a priori theoretical predictions and empirical findings, the paper draws the conclusion that the monetary aggregate and its growth rate matter insofar as inflation is concerned, irrespective of the strategy of monetary policy for price stability.     

Money demand stability: Evidence from Spain

Using several tests for structural stability in regressions with I(1) variables and for the existence of cointegration in models with regime shifts, the empirical evidence on the existence of a structural break in the Spanish long-run demand for broad money (ALP2) is analysed.The results indicate that shifts affecting the demand for ALP2 in recent years have substantially altered its long-run properties. As to the cause of this structural break, emphasis is placed on the role played by the increasing openness of the Spanish financial system to international markets as obstacles to free capital movements have progressively disappeared.This paper represents the views of the author and should not be interpreted as reflecting those of any institution. I am grateful to J. Ayuso, J. J. Dolado, F. Restoy and two anonymous referees for helpful comments. The data may be obtained from the internet, http://wotan.wiwi.hu-berlin.de/oekonometric/engl/data.html. This paper was written while the author was working at the Banco de España.     

How stable is the demand for money in Greece?

Abstract

The cointegration technique is now a common method of estimating any money demand function. Numerous studies that applied this technique to estimate the money demand function in Greece, interpreted their finding of cointegration as a sign of stable money demand. In this paper, after incorporating CUSUM and CUSUMSQ tests into cointegration analysis, we show that even though M1 and M2 monetary aggregates are cointegrated with income and interest rate, the M2 money demand function is unstable while M1 is stable.     

Money Demand and Purchasing Power Parity (PPP), in the Republic of South Africa

We have examined empirically two important economic relationships, the Purchasing Power Parity (PPP) and the money demand relationship, among the consumer prices, money, output, interest rates, and the nominal rand/dollar exchange rate of the Republic of South Africa (RSA) for the sample period from 1993 second quarter to 2003 second quarter within the frameworks of co-integration and Error Correction Model (ECM). It is established that the strong version of the PPP including the proportionality and the symmetry hypothesis, is supported. The changes in the rand/dollar exchange rates are influenced by the long term trends in the consumer prices of the RSA and the USA. There also exists a well defined money demand function for this period. The broad money demand is influenced by the consumer prices, the GDP and the interest rates. The short-term interest rates are found to be the own rate of return for broad money and the long-term bond yield is the opportunity cost of holding money. The monetary policy works through the short term interest rates.

     

基本面因素与人民币汇率的协整和方差分析——基于行为均衡汇率理论

在行为均衡汇率理论的基础上,选择对美净出口额、国内生产总值、广义货币供给量和实际利率作为影响人民币汇率的基本面因素,进行协整和方差分析。协整回归结果表明:在长期,广义货币供给量和对美贸易是影响人民币汇率的两个重要因素,广义货币供给量的弹性大于对美贸易量的弹性。但方差分析结果显示:对美贸易量对人民币汇率的贡献程度却大于广义货币供给量对人民币汇率的贡献程度。     

Analysing money demand relation for OECD countries using common factors

This article investigates the existence of a long-run money demand relation for a panel data consisting of 13 OECD countries. The analysis is based on the most recent data. The existence of a long-run money demand relation is tested with two new meta-analytic panel cointegrating rank tests which are robust to cross-sectional dependence. Cross-sectional dependency in the data generating process is modelled by unobserved common factors. The observed data are decomposed into idiosyncratic and common components, and these two components are analysed separately to find out the driving forces of the long-run stationary relationship. The evidence shows that the long-run money demand relation is driven by the cross-unit cointegration. Finally, the long-run relation is estimated by taking the common factors into account.