Abstract
This paper empirically investigates stability of money demand function in China using autoregressive distributed lag (ARDL) approach to co-integration. CUSUM and CUSUMSQ are employed to test the stability of the relationship between monetary aggregates (M1 and M2) and their determinants. The results indicate that while there exists cointegration between money aggregates (M1 and M2) and their determinants, only M1 has a stable long run relationship with its determinants. The sign of estimated exchange rate coefficient supports currency substitution phenomenon in China. This could be due to the mix of both currency substitution and wealth effects in the long run. Furthermore, it determines the asymmetric effects of monetary policy on output.
Keywords: Money demand stability, ARDL, CUSUM, CUSUMSQ, China
INTRODUCTION
Sound monetary policy is crucial for any economy and therefore the formulation of such a policy and its conduct should be done as precise as possible. The central issue on monetary policy is money demand. The existence of stable and predictable relationship between money demand and its determinants is very important for the formulation of monetary policy. It is therefore necessary to test the stability of money demand as it has serious implications on monetary policy. This can be achieved by using co-integration techniques to examine long run relationship between money demand and its determinants. Moreover, monetary aggregate (M1 or M2) that can be found to be stable over time can be regarded as a better aggregate for monetary policy hence the research on stability of money demand can be used to prescribe a better monetary policy.
In fact, the instability of the relationship between monetary aggregates and goals variables such as inflation (or income) leads to the failure of the monetary policy. Mishkin F.S (1997) states that it is because of the instability of the relationship between monetary aggregates and goals variables such as inflation and nominal income that U.S, U.K and Canada abandoned the strategy of monetary targeting and instead adopted inflation targeting. However it is the very inflation targeting that partly contributed to the decline of the U.S GDP. This is because, Mishkin argues, the weak relationship between money and nominal income imply that as a country pursues monetary targeting policy by increasing or decreasing money supply, the goal variable will remain unchanged.
Due to the implications that stability of money demand has on monetary policy, there has been a lot of research on this subject. One of the key implications that stable money demand has on monetary policy is that stable money demand ensures that money supply would have predictable and desired impact on other economic variables such as inflation rate, interest rate and national income. As Caporale and Gil-alana (2005) put it, stability of money demand is a prerequisite for effective formulation of monetary targeting policy. Many studies on money demand stability used Johansen (1988) and Johansen and Juselius (1990) co-integrating technique in examining the long run relationship between money demand and its determinants. Examples of such studies include Hafer and Jansen (1991) for United States, Adam (1991) and Johansen (1992) for United Kingdom, Hansen and Kim (1995) and Bahmani-Oskooee and Bohl (2000) for Germany. Most of these studies concluded that M2 money aggregate is co-integrated with income and interest rate.
China has not been an exception to this massive research on money demand function stability. The literature on money demand in China includes Chow (1987), Chen (1989), Chan et al (1991), Ma (1993), Huang (1994), Xu (1998) and Huang (2000). These studies used regular estimation techniques or recent co-integration technique. These papers focused on different aspects of monetary policy in China such as; the right explanatory variables to be included in the money demand function in China, definition of monetary aggregate, the effects of economic reform on money demand and the causal relationship between monetary aggregate and other macroeconomic variables. There were however many limitations for these studies. For instance, the data was only available up to mid 1990s and no paper used stability tests such as the one suggested by Brown et al (1975). Also most of these studies did not take into account the impact of currency substitution on money demand as China continued to open up. However Wang, Y. (1999) included the currency substitution although there was no strong evidence that supports the impact of currency substitution.
Motivation
Given the importance of a stability of money demand function on monetary policy, it is very important to test whether monetary demand function is stable for China. This is because after determining which money aggregate has a stable long run relationship with its determinants, then it will be recommended as a better tool in conducting monetary policy. Also it is important to ensure the money demand function is stable as this will mean changes in monetary policy will have the desired impact. This paper will adopt a relatively new co-integration technique called autoregressive distributed lag (ARDL). Moreover the asymmetric effects will be taken into account.
LITERATURE REVIEW
Quantity Theory of Money
The Classical economists, led by Irving Fisher, proposed the quantity theory of money. They argued that movements in the price level result solely from changes in the quantity of money. To illustrate their conclusion, the following equation was used;
……………………………….(1)
Where Quantity of money
Velocity of money
Price level
output
From equation (1), both and are believed to be constant hence any change in will have to be accompanied by equivalent change of . Fisher reasoned that velocity is determined by institutions in an economy that affect the way consumers conduct transactions and therefore it is constant especially in the short run. He further argued that produced in the economy during normal times would remain at full employment level, hence can also be treated as constant in the short run.
Contrary to the Classical school of thought, Keynes argued that demand for money depends on the motives of individuals for holding money. He classified motives for holding money into three categories namely; transaction motive, precautionary motive and speculative motive. Another variation was that Keynes emphasized the importance of interest rate as a determinant of money demand. Keynes claim of inverse relationship between interest rate and money demand was supported by many researchers including James Tobin (1947). Tobin studied the link between interest rate and money demand in the United State using data from 1922 to 1941. Tobin separated transaction balances from other money balances, which he called "idle balances", under the assumption that transaction balances were proportional to income only while idle balances are related to interest rate only. The average level of idle balances was then plotted against average interest rate on commercial paper for that year. The finding was that there is strong evidence that there is inverse relationship between interest rate and idle balances and he concluded that indeed money demand is responsive to interest rate as Keynes claimed.
However, Driscoll and Ford (1980) used IS-LM approach to show that stability of money demand may not be a significant issue as monetarist-Keynesian debate has made it to be. This is because, they reason, the money income multiplier would be stable only if the demand for money were a stable function of income only. If money demand function were a function of other variables such as interest rate and wealth then it may be necessary to have instability in demand for money function in order to have a stable money-income multiplier.
Generally, it is believed that money demand has long run stable function with its determinants; Stock and Watson (1993) argue that for this relationship to be predicted accurately, an important prerequisite is long span of data. To reach this conclusion, they applied different methods of estimating co-integrating vectors to U.S money demand function from1900 to 1988 and tested parameter stability. A semi logarithm M1 money aggregate was taken as dependent variable while real GDP while various long run and short run term interest rate were used as scale and opportunity cost variables respectively.
EMPERICAL EVIDENCE ON MONEY DEMAND STABILITY
Due to the importance of stability of money demand function on monetary policy, there has been a lot of research on this area using Johansen (1988) and Johansen and Juselius (1990) co-integrating technique in examining the long run relationship between demand for money and its determinants. However after Bahmani-Oske and Bohl (2000) suggested ARDL as a better co-integration approach, there has been a renewed interest in the research on stability of money demand using this relatively new co-integration approach. For instance, McCandless and Weber (1995) examined data from 110 countries and concluded that correlation between growth rate of money supply and inflation rate was almost 1. This strong positive relationship between money supply growth and inflation rate is consistent with quantity theory of money as proposed by Keynes. This correlation however should not be interpreted as causality between the two variables. McCandless and Weber however found no evidence that supports the existence of correlation between inflation or money supply and real output growth.
Although money supply has no effects whatsoever on income in the long run, there is evidence that suggest correlation between money and income in the short run. Friedman and Schwartz (1963b) concluded that faster money growth is usually followed by increase in output. Their evidence was based on the study 100 years U.S data. Like in the long run case, this correlation should not be understood to be the causality between the two variables.
Friedman and Meiselman (1963) conducted a study with the objective of testing whether monetary or fiscal policy was more important in determining nominal income in the short run. They reported that there was more stable and statistically significant relationship between output and money than there is between output and expenditures. This study received much criticism from Modigian and Ando (1976) and De Prano and Mayer (1965) who argued that the model used by Friedman and Meiselman was mispecified.
In as much as the money demand function stability has been widely researched, a significant research was done on developed economies. It is therefore important to look at some research done for developing countries. Sharifi-Renani (2007) studied the stability of money demand function in Iran with two main objectives namely; 1) to shed light on co-integrating properties of M1 and M2 money aggregates, income, inflation and exchange rate using ARDL co-integrating technique and 2) to determine the stability of M1 and M2 money demand function. Some of the main findings were that co-integration does not imply stability between the variables and that M1 and not M2 has stable relationship with money demand determinants hence M1 can be taken as a better monetary aggregate for formulation of monetary policy.
A similar study to the one conducted in Iran was carried out in Nigeria by Akinlo A.E (2005). Unlike the study in Iran, the findings were that it is M2 and not M1 that is co-integrated with income, interest rate and exchange rate.
OBJECTIVES
To estimate demand for money in China using autoregressive distributed lag (ARDL) approach to co-integration
To test the stability of money demand over time in China (using M1 and M2 to represent money demand)
To test the asymmetric effects of monetary policy on output
METHODOLOGY
Money demand stability has been researched extensively using the conventional co-integration method. However, some authors such as Bahmani-Oske and Bohl (2000) have proved that when two or more variables are co-integrated, it does not necessarily mean there exist long run relationship between them. As a result some authors proposed that CUSUM and CUSUMQ test should be incorporated into co-integration and error correction model (ECM). As a result, this paper will adopt error correction version of autoregressive distributed lag (ARDL) approach to co-integration. Unlike regular co-integration method, ARDL does not require prior knowledge of the order of integration of all the variables.
BASIC MODEL
The conventional approach to money demand function is to assume that money demand depends on scale variable and the opportunity cost variable. The scale variable is usually represented by real income or the real consumption expenditure, whereas opportunity cost variable is represented by interest rate on alternative assets. The general specification of money demand function is assumed to take the following functional form;
……………………………………………….(1)
Where = demand for money balances
Price level
Real income
Opportunity cost variable
Inflation is used as a proxy for interest rate when dealing with less developed countries which normally have less developed financial markets. Examples of such cases include Bahmani-Oskooee and Tanku (2006) and Budina et al (2006). Exchange rate variable is included in equation (1) when dealing with developing countries due to currency substitution. The inclusion of exchange rates in a standard money demand function was first suggested by Mundell (1963). Evidence of currency substitution in developing countries was provided by Zamaroczy and Sa (2002), Kang (2005) and Samreth (2008) who conducted a study on Cambodia. Thus money demand function becomes;
………………………………………….(2)
Where inflation rate
Exchange rate
In this context, exchange rate is defined as the amount of domestic currency per unit of foreign currency. This implies that an increase (decrease) of can be understood as depreciation (appreciation) of domestic currency against the foreign currency. In more explicit form, equation (2) can be rewritten as follows;
…………………………….(3)
Where = real monetary aggregate (M1 or M2)
= real income
= nominal effective exchange rate
= inflation rate
My Contribution
While most researchers use equation (3) with income, interest rate (or exchange rate) and inflation rate to represent money demand equation, Friedman (1988) emphasized the importance of stock market activity in money demand function using U.S data. There are two main ways through which through which stock market activity can influence money demand. First this can be through substitution effect; an increase in asset prices means investors would rather hold more assets than money. Secondly, an increase in wealth (as asset prices increase) may mean that part of the additional gains may be stored as cash. Other authors such as Chowdhry (1996), Thornton (1998) and Kia (2006) also showed that stock prices form an important part of money demand for developed economies. Also Baharumshah (2004) studied the demand for money function in Malaysia using multivariate co-integration and error correction model and found that stock prices have a significant negative substitution effect on long run as well as short run broad money demand (M2).
As mentioned before there has been a lot of research on money demand in China, but most of the studies used conventional stability tests and a few that used ARDL co-integration approach such as a recent study by Bahmani-Oskooee, M and Wang, Y. (2007) ignored the effect of stock prices on money demand. This paper will attempt to include this important variable.
Morten, O. R. and Martin, S. tested the asymmetric effects of monetary policy in the U.S using post war data. The importance of testing for asymmetric effects is that it helps to determine if the coefficients of explanatory variables are the same before and after a regime. Moreover, it can also be tested whether positive or negative monetary policy shocks have different effects on output, whether big or small shocks have different effects and whether low variance negative shocks have asymmetric effects on output. This paper will adopt Markov Switching Vector Autoregressive (VAR) model as it was used by Krolzig (2006) to test for asymmetric effects.
EXPECTED RESULTS
According to Arango and Nadiri (1981) the sign of is expected to be positive while that of is expected to be negative. Estimation of can either be negative or positive. If is defined as the number of domestic currency per U.S dollar, then if increases then it means that the foreign assets in terms of domestic currency become more expensive. If this increase is caused by increase in wealth, then demand for domestic currency will increase hence the sign of will be positive. But if consumers expect the domestic currency to depreciation further in future, then they will hold more of foreign currency and less of domestic currency which implies that in this case the sign of will be negative.
ARDL
Perasan et al (2001) introduced a new improved method of testing co-integration known as autoregressive distributed lag (ARDL). Bahmani and Oskooee (2000) conducted a study on Germany money demand function and concluded that although variables in the money demand function were co-integrated, the parameters in the model were unstable, thus further nullifying the conventional interpretation that co-integration between money aggregate and its determinants imply existence of stable long run relationship. Unlike traditional co-integration where order of co-integration of all variable has to be known, ARDL does not need to classify variables as I(1) or I(0) or conduct pre-testing unit root test. Under standard co-integration approach, not only should the order of integration be known, but the variables should be integrated of the same order. This requirement causes problems where variables integration order is different. Hence autoregressive distributed lag (ARDL), proposed by Pesaran et al (1996,2001), becomes an alternative. The error correction version of ARDL model related to variables in equation (1) can be specified as follows;
………………………..(4)
The null hypothesis of no co-integration is defined by and is tested against the alternative of and is tested by F-test. The decision to either accept or reject the null hypothesis is based on the set of critical values suggested by Pesaran et al (2001). Persaran et al suggested two sets of critical values in which one set is computed with the assumption that all the variables in equation (4) are I(1) and another set of critical values is computed with the assumption that the variables are I(0). The decision rule is that if the computed F statistic is higher than the appropriate upper bound of the critical value, then the null hypothesis is rejected. If it lies within both the lower and upper bounds then the test is inconclusive. If the F test supports the existence of co-integration, then the second step of ARDL can be conducted. In this step, Akaike Information Criteria (AIC) or Schwarz Bayesian Criteria (SBC) is used to choose the lag length. The main difference between this F-test and the conventional way of conducting F-test is that here there is no need to classify variables as I(0) or I(1).
Expected Conclusion
The coefficients of the explanatory variables are expected to have the same signs as the theory dictates. Furthermore, conclusions should include findings about which of the monetary aggregates (M1 or M2) has a long run stable with the determinants of money demand. This money aggregate will then be recommended as a better monetary aggregate for conduct of monetary policy in China. Given the literature on this subject, the monetary demand function is expected to be stable.
