Demand for Money, Economic Policies and Stability. Working Paper. Amir Kia*

Transcription

1 Demand for Money, Economic Policies and Stability Working Paper Amir Kia* Emory University, Department of Economics Atlanta, GA U.S.A. Tel.: (404) Fax: (404) November 2002 * The author would like to thank Deliana Kostova for the excellent technical support she provided in calculating the critical values of Hansen s (1992) stability test.

2 Demand for Money, Economic Policies and Stability Abstract: This study identifies Canadian fiscal and monetary policy regime changes that could influence the services of money. It is argued that if these policy regime changes are not incorporated in the estimation of demand for real balances the result would be biased and unstable. Using Canadian monthly data for the 1975:Jan-2001:June period, the paper estimates two demand-for-money (M1) functions. It was found the demand for money in Canada is stable over the short- and long-run periods when these policy regime changes are incorporated and the estimated coefficients have correct signs. Key words: Demand for money, policy regime changes, services of money, constancy JEL classification = E41, E52

3 Demand for Money, Economic Policies and Stability 1. Introduction A model instability may be caused simply by the omission of an important variable or by a regime shift. A stable demand for money is especially important for policy makers since the policy may become ineffective or dangerously unproductive if the implementation of a policy change results in an unpredictable change in the parameters of the model. However, a policy regime change when successful may also influence the parameters of the relevant model. These parameters, as a result of a policy regime change, will not be constant if their changes are unpredictable and/or have a direction opposite to what the policy makers had predicted. There are, of course, policy changes, which can enhance/weaken services of money. For example, if banks have to pay three-day interest on checks that are deposited on Fridays, but checks are only cleared on the following Mondays then banks may refuse to accept checks, or at least large-amount checks, on Fridays. This may lower the number of transactions done with checks on Fridays, i.e., a part of M1 may lose its services on Fridays. Now suppose the central bank keeps its books open until the following Monday when checks are cleared and backdates its books to the previous Friday. Obviously, after this regime change there will not be any reason for banks not to accept checks on Fridays and the services of money will be enhanced. If in the estimation of the demand for money one does not incorporate, e.g., this policy regime change, the estimation result will be unstable and may be biased and inconsistent. Note that it is generally assumed that the distribution of parameters in the model is identical for all observations in the sample. However, it is possible a policy regime change results in a change in the distribution of

4 2 the parameters in the sample period. Failing to recognize this possibility may lead to biased estimation results as well as inconsistent test inferences. There are, of course, policy regime changes, which do not affect the services of money, but may influence the behavior of forward-looking economic agents in demanding money. In this case the demand for money is not policy invariant and is unstable. To elaborate on the above discussion, following Sidrauski (1967), assume the flow of services of money per unit of time is a determinant of the utility function. Furthermore, the flow of services derived from the holding of real cash balances is proportional to the stock of real cash balances, but contrary to Sidrauski, assume the factor of proportionality is a function of policy changes that influence the services of money. In the absence of any financial innovation, postal strike, wars, etc. the coefficients of the demand for real cash balances in this economy - derived from the households utility maximization subject to budget constraints and other restrictions - can vary because of the changes in policies that affect the services of money and/or by changes in tastes/behavior and technology. The variations due to changes in policy which affect the services of money are predictable, but other variations in coefficients, e.g., due to structural breaks, a lack of policy invariance coefficients and/or other irregularities should be regarded as instability in the demand for money. These variations are not predictable and are not the goals of the monetary authorities. The predictable variations similar to financial innovations, postal strikes, wars, etc. should be dummied out in the estimation of the demand for real cash balances. In general, changing environments may require the economic adaptation of a model.

5 3 In a recent work Ericsson, et al. (1998) and Ericsson (1998) discuss how the change in the measurement of money, the changes in policy, e.g., deregulation, the allowance of interest-bearing sight deposits, and a 1986 Act of Parliament should be modeled by using dummy variables in order to avoid inconstancy. These studies argue that the constancy of a model depends upon how the model is formulated and how its variables are updated for the extended samples. In their expanded and translated versions of a model, to ensure the constancy of their demand-for-money model, Ericsson, et al. (1998) and Ericsson (1998) suggest adding to the model new variables with zero values for the first part of the sample (the initial sample) and non-zero values for the second part of the sample. As also noted by Ericsson, et al. (1998), constant models can have time-varying coefficients if a deeper set of constant parameters characterizes the data generation process. Examples include, when the coefficients of a model are adjusted due to a change in the characteristic of the dependent variable (the services of the same money supply are enhanced/weakened for a part of the sample) or when the introduction of financial innovation results in a more efficient use of the money in circulation. Thus, the existence of constancy, as mentioned by Ericsson, et al. (1998), may depend on whether raw coefficients or underlying parameters are evaluated. For example, β, a coefficient of a variable in the model, can be constant, but β(1-d t ) varies over time, where D t is a dummy variable that accounts for, e.g., a policy regime change. This study concentrates on demand for money for a small resource-dependent country like Canada, which has internationally integrated stock markets. Studies on Canadian demand for money either completely ignored the impact of economic policy

6 4 changes that influence the services of money or incorporated only some of these changes. Consequently, most studies on demand for narrow definition of real balances (M1) in Canada concluded that demand for real balances is unstable. For example, Clark (1973) finds some evidence of structural break in the demand for M1 money. Boothe and Poloz (1988) find an unstable demand for M1 money due to financial innovation. Hoffman, et al. (1995) incorporate an intercept dummy for the period to avoid instability in demand for money in Canada. To the best knowledge of the author, only few studies incorporated one or two policy regime changes in their analysis of demand for real balances. These studies include Cameron (1979) who incorporates the impact of the 1967 Bank Act revision, Kabir and Mangla (1988) who incorporate the impact of the 1980 Bank Act revision and Arestis, et al. (1992) who suggest that if proper allowance for financial innovations and other financial developments is not accounted for in estimating the M1 definition of the demand-for-money relationship the parameter instability is inevitable. Finally, Hendry (1995) incorporates the impact of the1980 Bank Act change and the introduction of Goods and Services Tax, but finds an unstable M1 demand for money, when monthly data is used. In this study we identify Canadian fiscal and monetary policies that could influence the services of money. Then we will test the standard demand for money in Canada for parameter constancy using different measures for constancy. The structure of the paper is as follows. Section 2 focuses on the models and describes the policy regime changes during the sample period (1975: January-2001: June) in Canada, which influence the services of money. Section 3 discusses the data, the long-run methodology and the results. It also discusses the long-run stability of the demand for

7 5 money and shows the long-run demand for real cash balances in Canada is stable if we allow the appropriate policy regime changes to affect the short-run dynamic of the system. Section 4 is devoted to short-run demand for money, its stability as well as its identification. Finally, Section 5 concludes. The overall result of this paper is that when the proper allowance for the impact of monetary/fiscal policies on the services of money is taken into account the demand for narrowed money is stable both over the short- and long-run periods. 2. The Models 2.1. Model 1 The standard demand for money assumes demand for real balances is a function of real income and nominal interest rate. We will follow Friedman (1988) and Choudhry (1996), among others, and assume the real equity price is also a determinant of the demand for real cash balances. Furthermore, we will also let the demand for real cash balances reflect the impact of policy and other environmental changes so that we will have the following function: rm t = F(rindp t, cpr t, rtse t, DUM t ), (1) where rm is the real money (M1), rindp is the real income (industrial production), cpr is the opportunity cost of holding cash balances (one-month corporate paper rate), rtse is the real stock price (the TSE 300 Stock Index which is currently known as S&P/TSE Composite Index) and DUM is a vector of all other exogenous variables that account for policy and other environmental changes. According to the behavioral assumptions and Friedman (1988), the expected signs are: F rindp >0, F cpr <0 and F rtse =?, where F rindp, F cpr and F rtse are the partial derivatives of rm with respect to rindp, cpr and rtse, respectively.

8 6 Equation (1) states that demand for real balances will go up with an increase in the real income (the scale variable) and will fall with the rate of interest (the opportunity cost of holding cash balances). The real demand for money, depending on the net effect of the wealth, risk-spreading and substitution effects, will increase or decrease with the real stock price (Friedman (1988)). According to Friedman (1988), stock prices can influence the quantity of money demanded through four effects: wealth, risk-spreading, transaction and substitution effects: (i) A rise in stock prices results in a higher wealth which can be expected to increase demand for money. (ii) For a given risk aversion/preference, a rise in stock prices reflects an increase in the expected return from risky assets relative to safe assets, implying a higher relative risk. The higher risk can be offset by lowering the weight of long-term bonds in the portfolio and/or by increasing the weight of highly liquid fixed-income assets as well as money in the portfolio. (iii) An increase in stock prices may be taken to imply a rise in the dollar volume of financial transactions, resulting in an increase in the demand for money to facilitate transactions. (iv) An offsetting effect of these factors is a substitution effect of a change in stock prices. The higher the real value of stocks is, the more attractive stocks are as a component of the portfolio. Consequently, the sign of F rtse is an empirical issue. Let us assume Equation (1) has the following semi-log-linear form: lrm t =β 0 + β 1 lrindp t + β 2 cpr t + β 3 lrtse t + DUM t δ+ u t, (2) where β s are parameters to be estimated with the expected signs: β 1 (income elasticity of money demand)>0, β 2 (semi-interest elasticity of money demand)<0, β 3 =?, and δ is a

9 7 vector of constant parameters. 1 Furthermore, lrm is the logarithm of real money, lrindp is the logarithm of real income, lrtse is the logarithm of real stock price, DUM t = (Post75 t, Post78 t, Post81 t (Jul81 t, Aug81 t,), Post97 t (Nov 19 to Dec 5), INOV76 t, INOV80 t, Ba t, GST t, Revision t, Inftar t, Free t, Nafta t, Ntar t, Zero t, S t ) and u is the disturbance term which is assumed to be white noise with zero mean. Dummy variables Post75, Post78, Post81 and Post97 are postal strike dummies. Post75 has a value of one for the period of October to December 1975, a value of negative one in January 1976, and zero otherwise. Post78 has a value of one in October 1978, a value of negative one in November 1978, and zero otherwise. Post81 has a value of one in July 1981, a value of negative one in August 1981, and zero otherwise, see Hendry (1995). 2 Post97 has a value of one in November and December 1997, a value of negative one in January 1997, and zero otherwise. 3 Note that one effect of a postal strike is an increase in the money supply. Customers payments were delayed while firms obligations such as payrolls could not be postponed. Consequently, firms borrowed from the banking system. Bank of Canada s policy has been to accommodate this additional and temporary demand for cash balances. At the same time agents who had bills to pay had higher cash balances than desired balances. Since they mentally debited their accounts they thought they were holding their desired levels. Consequently, this phenomenon causes standard demand for money to underestimate demand for real cash balances (Gregory and MacKinnon (1980)). 1 Note that the vector DUM is chosen in such a way that the parameter-vector δ contains only short-run coefficients. 2 The effect of these postal strikes is believed to be a one-month accumulation of the level of money. This would mean a positive spike in the money growth in the first month followed by a negative offsetting spike in the money growth in the following month. So in a growth rate model, it makes more sense to have a dummy [..., 0, 1, -1, 0,...]. 3 In our sample period the important postal strikes include: October 21 to December 2 of 1975, October 16 to 25 of 1978, July 1981 and November 19 to December 5 of 1997.

10 8 To account for the financial innovation in the sample period the dummy variables INOV76 and INOV80 are included. Following Boothe and Poloz (1988), the dummy variable INOV76 has a value of zero before January 1976, when banks first began offering cash management services to large firms, and one, otherwise. 4 Furthermore, in the early 1980 s when interest rates were high money demand shifted due to the spread of corporate cash management services to smaller firms and also the introduction of daily interest checkable savings accounts. Since this shift was not abrupt but rather continued into at least 1983, following Hendry (1995), the dummy variable INOV80, which has a value of zero until January 1980 and then commences linearly upwards to a value of one for December 1982 and remains one after, is included. The impact of financial innovations on M1 demand for money also incorporated in other studies for Canada, e.g., Kabir and Mangla (1988), and Arestis, et. al. (1992). Dummy variables Ba81 t, GST t, Revision t, Inftar t, Free t, Nafta t, Ntar t, and Zero t are policy variables, which account for the change of monetary or fiscal policies that enhance (e.g., by reducing imperfection in the market) or reduce (e.g., an imposition of reserve requirements) the services of money. Ignoring the impact of these policy dummy variables in the estimation of the demand-for-money function may result in a biased and unstable estimate of the function. The dummy variable Ba81 is equal to one in November 1981 and after, zero otherwise. This dummy is included to account for the 1980 Bank Act, which resulted in an unusually large change in M1 in Canada since November The Bank Act of This new cash management technique included centralized accounting, which allowed for integrated book keeping for several accounts. Smaller firms and households later on adopted similar arrangements, Kabir and Mangla (1988).

11 9 fundamentally changed conditions for entry into chartered banking (Kabir and Mangla (1988)). The impact of this change was also incorporated by Hendry (1995). Following Hendry (1995), the dummy variable GST(=1 in January 1991 and zero otherwise) was included to capture the introduction of the Goods and Services Tax in January The dummy variable Revision (=1 in August 1983 and after and zero otherwise) accounts for the revision to the reserves regulations on August 24, 1983 in order to reduce a number of money-market imperfections. Prior to August 24, 1983, a Canadian bank that invested funds in the money market on Friday would earn three days interest and, because of the lag in settlement, experienced a drain on its reserves on the following Monday. If the bank had to borrow a corresponding amount on Monday to reconstitute its reserve position, it would pay just one day s interest on the borrowing, and hence profited from two days interest in the case of a regular weekend. Similarly, banks used to reject individuals large or even small-denominated checks to be deposited in their accounts on Fridays. This money market imperfection could lower the services of money (demand deposits). By giving larger weight on any day after a holiday (three for a Monday after a regular weekend) Bank of Canada reduced any incentive for banks to be aggressive in lending overnight funds in the money market or rejecting checks to be deposited - on any day before a holiday (Bank of Canada (1983)). This policy could reduce irregularity in the demand for money and so contribute to the stability of M1 in Canada. To the best of the author s knowledge no study on the Canadian demand for money so far has taken into account the impact of this policy change. The dummy variable Inftar (=1 for February 1991 and after and zero, otherwise) accounts for the introduction of inflation rate target band by the Department of Finance

12 10 and the Bank of Canada in February Clearly, the reduction of inflation uncertainty increases services of money. Missing to include this variable in the demand for money function may wrongly result in the estimation of an unstable money demand equation. Again, no study on the Canadian demand for money, to the best of the author s knowledge, incorporated the impact of this policy. The dummy variables Free accounts for the implementation of the free trade agreement between Canada and the United States in January Furthermore, the dummy variable Nafta accounts for the implementation of NAFTA (North American Free Trade Agreement between Canada, the United States and Mexico in January 1994). These two agreements could improve the services of money by allowing the holder of Canadian dollars to purchase goods and services produced outside Canada at the same price, excluding transportation cost, charged at the production site. Free = 1 for January 1991 and after, zero otherwise, and Nafta = 1 for January 1994 and after, zero otherwise. To the best of the author s knowledge, none of these policy regime changes has been incorporated in the existing Canadian money demand literature. In November 1975 Bank of Canada formally adopted M1 targeting. 5 The intention was to lower permanently the rate of inflation. The conventional wisdom was that such a policy will lead to lower adjustment costs if the monetary authority s stated intention is deemed credible by the public (Deaves, 1991). Consequently, if such a policy had an adjustment cost impact its abolition should have an impact on the demand for money. The dummy variable Ntar (= 1 for the October 1982 and after and zero, 5 Using a base of a three-month average of the seasonally adjusted level of M1, beginning April 1975, the Bank specified a target range of per cent. The following changes were announced: 8-12 per cent in September 1976, 7-11 per cent in October 1977, 6-10 per cent in October 1978, 5-9 per cent in January 1980, and 4-8 per cent in March 81 (Deaves, 1991).

13 11 otherwise) is created to account for the impact (the abolition) of this policy regime change. To the best of the author s knowledge no study has incorporated the impact of this policy regime change. It is known that reserve requirements act as a tax on banks and lead to a higher spread between borrowing and lending rates. Since large depositors and borrowers have the power to bargain for a better rate, the banks transfer the tax mostly to their small depositors or borrowers. Consequently, customers with small deposits, or borrowers of small loans will probably shoulder more the burden of reserve requirements tax. In Canada prior to 1992, only chartered banks were subject to reserve requirements while other deposit-taking institutions were exempted. This created a discrimination against chartered banks in favor of non-bank financial institutions that were competing with them. This policy created an inequality in competition. To avoid such imperfection deposits were booked at non-bank subsidiaries within bank conglomerates or were moved off-shore. Since the supply of deposits (money) is not possible if it is not demanded the reserve requirements in general, and in the Canadian situation in particular, could result in a reduction of services of money. Consequently, reserve requirements were reduced every six months by three per cent from June 1992 until June 1994, when the remaining requirements were entirely removed; see, e.g., Clinton (1997). Ignoring the elimination of reserve requirements in the estimation of the demand for money could contribute to a false estimate of an unstable demand function. To the best of the author s knowledge no study has incorporated the impact of this policy. The dummy variable Zero was created to account for this monetary policy regime change. The value of this dummy variable is zero before

14 12 June 1992 and one after June Starting from June 1992 it increases by 0.20 every six months so that to get a value of one in July The variable S includes 11 centered seasonal dummies. The centered seasonal dummies are constructed such that they sum to 11 S it zero for each t, i.e., i= 1 = 0, where S t is equal to (Dec t - 1/12) and Dec is a dummy variable which has a value of one in December and zero otherwise. The advantage of centered dummies is that they do not change the limit distribution of the rank tests Model 2 Equation 1 does not allow for the impact of foreign variables, which can influence the demand for the real cash balances. For example, changes in foreign interest rates affect desired stock of real cash balances, and the exchange rate expectation plays an important role in portfolio decisions concerning the degree of substitution between money and foreign assets. Since Canadian and U.S. assets are highly substitutes (see Kia (1996a)) the covered U.S. interest rate should influence the desired demand for money in Canada. Because of globalization, there has been a dramatic growth in world trade and investment in recent years that has led to a sharp increase in the number of transactions that Canadian business and households have with foreigners, especially Americans. Besides diversification and globalization there is a possibility of dollarization in the sense that domestic economic activity being conducted increasingly in U.S. dollars. Such a possibility further emphasizes the role of the exchange rate in the demand for the real cash balances. As Arango and Nadiri (1981) also mentioned when the impact of international factors are omitted the empirical results point to significant misspecification

15 13 biases in the traditional demand functions for real cash balances. Furthermore, Hueng (1998 and 1999) evidence, both theoretically and empirically, that the Canadian demand for money is also a function of the U.S. interest rate, Canadian real exchange rate and Canadian consumption of the U.S. commodity. Other studies (e.g., Bordo and Choudhri (1982), Handa (1988) and Handa and Bana (1990)), testing for currency substitution, included the U.S. interest rate and the Canadian exchange rate in terms of U.S. dollars in their estimation of the Canadian demand for money. To capture the impact of globalization, diversification and perhaps dollarization we will include the real exchange rate as well as one-month covered U.S. interest rate in Equation 2. We will, therefore, define Model 2 as lrm t =α 0 + α 1 lrindp t + α 2 cpr t + α 3 lrtse t + α 4 lrex t + α 5 ccpr t + DUM t δ+ u t, (3) where lrex t is the log of real exchange rate, ccpr t is the covered one-month U.S. corporate paper rate. Noting that the exchange rate is defined in this paper as Canadian dollars per unit U.S. dollar, as the real exchange rate increases the Canadian demand for the foreign (U.S.) goods (dollars) will fall and, therefore, demand for Canadian real balances will go up, indicating α 4 >0. Note that, for a given Canadian-U.S. price ratio, a higher real exchange rate can result in a reduction in the demand for the real cash balances if there is an evidence of dollarization. In this case one would expect α 4 <0. A higher covered U.S. rate may result in a substitution of U.S. issued assets for domestically issued assets in Canadian investors portfolios and a reduction in the demand for the real cash balances, i.e., one would expect α 5 <0. It should be emphasized again that ignoring the policy dummy variables in models 1 and 2 results in a significant biased estimate of the

16 14 coefficients and unstable demand for the real cash balances. Next section is devoted to the testing of these two facts. 3. Data, Long-Run Empirical Methodology and Results 3.1 Data The demand for money (M1) will be estimated on monthly Canadian data from January 1975 to June The choice of sample period is according to the availability of the data. 6 All observations are for the last day of the month. All data are obtained from Statistics Canada CANSIM database. On March 22, 2002 the monetary aggregates were adjusted historically to take into account Canadian Imperial Bank of Commerce (CIBC)'s recent acquisition of the retail client business of Merrill Lynch Canada. M1 used in this paper is March 22, 2002 adjusted data. Following, e.g., Poloz (1980), Gregory et. al (1990) and Choudhry (1996) seasonally unadjusted data was used. 7 Total industrial productions are used as the scale variable. The opportunity of holding money is one-month corporate paper rate. The TSE 300 Composite Index represents domestic stock price. Note that on May 1, 2002 the name of this index was changed to the S&P/TSE composite index. The changes associated with the name change do not have any impact on the result in this paper as our sample ends June Table 1 reports sources and descriptions of the variables used in this paper. 6 Monthly total industrial production is only available up to June Choudhry (1996), Footnote 4, provides a good explanation, with relevant literature, that the use of seasonally unadjusted data is preferable to the seasonally adjusted data.

17 Long-Run Methodology and Result According to the stationarity test results (Table 2) all variables are integrated of degree one (non-stationary). 8 They are, however, first-difference stationary. Consequently, we will first verify if long-run relationships exist between the level of M1 and their determinants, as specified by models 1 and 2. Tables 3, 4, 5 and 6 report the cointegration test results on models 1 and 2 with and without policy dummy variables. First equations 2 and 3 are estimated without allowing the estimate of short-run dynamic of the equation be affected by policies represented by dummy variables Ba81, GST, Revision, Inftar, Free, Nafta, Ntar and Zero. Namely, dummy variables Post75, Post78, Post81, Post97, INOV76, INOV80, as well as Seasons were included in the short-run dynamic of the equation (tables 3 and 5). Then all dummy variables were included (tables 4 and 6). In determining the lag length one should verify if the lag length is sufficient to get white noise residuals. LM(1) and LM(4) will be employed to confirm the choice of lag length. The order of cointegration (r) will be determined by using Trace and λ max tests developed in Johansen and Juselius (1991). Following Cheung and Lai (1993), both tests were adjusted in order to correct a potential bias possibly generated by small sample error, see footnote to tables 3 to 6 for the formulas. A lag length of five and six months (k=5 and 6) for models 1 and 2 respectively is required to ensure the residuals are white noise. The only non-congruency is non-normality. However, as it was mentioned by Johansen (1995a), a departure from normality is not very serious in cointegration tests, see also, e.g., Hendry and Mizon (1998). According to the result of Table 3, both, the λ max

18 16 and Trace tests reject r=1 while we cannot reject r 2, implying that r=2. However, as the results of both λ max and Trace tests reported in Table 4 indicate, when we allow policy dummy variables influence the short-run dynamics, we can not reject r=1 while we can reject r 2 indicating r=1. This implies that the long-run relationship of Model 1 (a closed-economy model) is sensitive to the inclusion of policy dummy variables. According to the Maximum Likelihood estimation (MLS) result of the long-run relationship of Model 1, reported in Table 7, the estimated sign of the scale (income) variable is incorrect in one of unrestricted relationships. However, since the coefficients of unrestricted equations are not identified we cannot rely on these coefficients. Assuming a zero restriction for the coefficient of the real stock price in the demand for real balances and the determinants of real stock price in Model 1 are real income and interest rate we could estimate an identified relationship. As the result reported in the footnotes of Table 7 indicates the restrictions are accepted (Chi-squared=2.79, with p-value=0.09), i.e., the system is empirically identified. According to the rank condition, for the sake of brevity not reported but available upon request, the system is generically identified. The estimated coefficients of the determinants of the real stock price in the cointegrating space are, as one would expect theoretically, positive for the real income and negative for the interest rate and both statistically significant. Furthermore, the fact that the real stock variable is already excluded from the other cointegrating space (demand for money) the economic identification is guaranteed. For these conditions see Johansen (1995b, Theorem 3) and for a similar case, r=2, see Kia (2002). The restricted and identified relationship is 8 Note that variable ccpr according to Phillips-Perron s test result is stationary at 90% level, but it is not

19 17 reported in Table 7. We can see that both estimated coefficients are statistically significant, but the estimated coefficient of income variable is negative (a wrong sign). However, when we allow the policy dummy variables influence the short-run dynamic the estimated coefficients have correct signs. The dynamic OLS (DOLS) test of Stock and Watson s (1993) also was used to estimate the above long-run demand-for-money relationships. Table 8 reports the estimation results. See the footnote of the table for the formula. The DOLS Wald test result indicates a long-run relationship for the model with or without inclusion of policy dummy variables. According to the estimation results we can see that when the policy dummy variables are not included in the short-run dynamic of the system, the estimated sign of the scale variable (income) has a correct sign, but it is statistically insignificant. However, the estimated coefficient of the scale variable has a correct sign and statistically significant when all policy dummy variables are allowed to influence the short-run dynamic of the system. In sum, so far in this section, using a standard model for the demand for money, we evidenced that when the impacts of economic policy are ignored the estimated long-run demand for money can be biased. According to the result of both λ max and Trace tests, tables 5 and 6, we cannot reject the null hypothesis of r 3 at 5% level while we can reject the null hypothesis of r 2 implying that there are three cointegration relationships in the system when Model 2 (an open-economy model) is estimated. Both unrestricted and restricted (identified) long-run relationships of Model 2 are reported in Table 7. Since the estimated stationary according to Augmented Dickey-Fuller s test.

20 18 coefficients of unrestricted equations are not identified we will concentrate on the identified restricted equation. As for the estimation of Model 2 when the policy dummy variables are not included the three restrictions for the identification include a zero restriction on the constant of the demand for money, the covered interest parity (CIP) equation and, as before, a relationship for real stock price determination. Footnote **** of Table 7 reports the estimated CIP and stock price equations. We can see that the long-run CIP relationship in the cointegration space exists, as the estimated constant is not statistically significant. This result confirms an earlier finding of Kia (1996a) for Canada. The estimated coefficient of the interest rate in the stock price determination has a wrong sign, i.e., the system is not identified economically. However, the Chi-squared = 9.40 with p-value = 0.05 accepts the restriction, i.e., the system is empirically identified. According to the rank condition, for the sake of brevity not reported, but available upon request, the system is generically identified. According to the estimated long-run demand for money, Model 2 (when the impact economic policy is not incorporated), the coefficient of income has the correct sign and is statistically significant and the coefficient of the domestic interest rate has a correct sign, but it is not statistically significant. The coefficient of the real stock price is statistically significant and positive implying that over the long-run the combination of wealth, risk-spreading, and transaction effects has a stronger impact on the demand for real cash balances than the effect of substitution effect. The coefficient of real exchange rate is negative, but not statistically significant implying that there is no statistically significant evidence for dollarization over the long run. The coefficient of foreign interest

21 19 rate is negative, but statistically insignificant implying that there is no significant substitution of U.S. assets for Canadian assets over the long run. As for the estimation of Model 2 when the policy dummy variables are included the three restrictions for the identification are the same as the previous case. However, the coefficient of the interest rate in the stock price determination equation has the correct sign. Consequently, the system is also economically identified. See Footnote***** of Table 7 for the estimated CIP and stock price equations. The result of the identified estimated Model 2 when the impact of policy dummy variables are included is the same as when the impact of these dummy variables were not included. In sum we can conclude that when the impact of changes in economic policy is incorporated, in contrast to the case when this impact is ignored, the system is also economically identified. Table 8 also reports the DOLS estimation results of Model 2. The DOLS Wald test result indicates a long-run relationship for the model with or without inclusion of policy dummy variables. According to the estimation results we can see that when the policy dummy variables are not included in the short-run dynamic of the system, the estimated sign of the income, similar to Model 1, has a correct sign (positive), but it is statistically insignificant. However, when all policy dummy variables are allowed to influence the short-run dynamic of the system the estimated coefficient of the income variable is positive and statistically significant. Furthermore, the estimated coefficient of domestic interest rate has a wrong sign when the policy dummy variables are not included and has a correct (negative) sign when these dummy variables are included. The estimated coefficient of the real exchange rate and foreign interest rate as in the case of MLS is statistically insignificant. We can conclude again that ignoring the impact of

22 20 economic policy changes in the estimation of demand for money results in a misspecified estimation. 3.3 Long-Run Stability Having established that when the impact of appropriate economic policy is incorporated the system is economically identified and have the correct sign we need to investigate the long-run stability of the models. Figures 1, 2, 3 and 4 show Hansen and Johansen s (1993) LR test for the stability of cointegration space for models 1 and 2 without and with inclusion of policy dummy variables in the short-run dynamic of the system. The upper graph (BETA_Z) in each plot pictures the actual disequilibrium as a function of all short-run dynamics including policy dummy variables, seasonal and other dummy variables. At the same time the lower graph (BETA_R) is corrected for the short-run effects, including the policy effects and pictures the clean disequilibrium. In fact, it is the series in the lower graph that is tested for stationarity and determination of the number of cointegration space in the maximum likelihood procedure, Hansen and Juselius (1995). In these figures the first ten years reserve for the initial estimate. As we can see from LR test results both models are stable over the long run when series are corrected for the short-run effects. However, as figures 1 and 2 show estimated β s in Model 1 are not stable over the long run before 1987 and when period is reserved for the initial estimation these parameters are barely stable between 1987 and 1993 for the case that the impact of economic policy regime changes were ignored (Figure 1). Alternatively, the long run relationship of Model 1 is always stable, according to Figure 2, when the period is reserved for the initial estimate and the impact of

23 21 economic policy regime changes are taken into consideration. As for Model 2, when the impact of policy regime changes are ignored the estimated β s are stable only after 1996 (Figure 3) while the estimated β s are stable since 1992 when the impact of policy changes are incorporated. Note that Model 2 has more variables and we need a longer initial period to conduct our LR recursive test. Since again, to the best of author s knowledge, there is no study so far in the literature that investigated the stability of long-run demand-for-money function while incorporating the impact of all policy changes in Canada, no comparison is possible. However, this result confirms Sriram s (2002) study for M2 in Malaysia. In sum, we can conclude in this section that the long-run demand for real balances in Canada may also be stable if the appropriate economic policy changes are taken into consideration. 4. Short-Run Demand for Money and Economic Policy. The existence of cointegrating relationships between the levels of variables in models 1 and 2 indicates that valid error correction models (ECM) exist. To be consistence with literature (e.g., Favero and Hendry (1992), Engle and Hendry (1993)) the ECM term generated from the long-run relationships estimated with the Maximum Likelihood Estimation technique will be used. 4.1 Error-Correction Results Let us assume, in determining the lag length, agents incorporate current available information as well as past information up to a year. Consequently, the lag length of 12 was chosen. 9 Given the lag length of 12, the parsimonious ECM was obtained by 9 It should be noted that in ECM we allow agents to be backward looking (reacting to previous deviations from equilibrium) while they may also be forward looking if at least one of the variables in the system has a statistically significant and instantaneous relationship with the demand for real balances.

24 22 engaging in general-to-specific modeling procedure (a specification test, see, e.g., Harvey (1993)). Following Granger (1986), we should note that: (a) the inclusion of a constant in ECM makes the mean of error zero, and (b) if small equilibrium errors can be ignored, while reacting substantially to large ones, the error correcting equation is nonlinear. In fact, a non-linear error-correction model for money demand function, in a restricted form, was originally developed by Escribano (1985). This model was used, among others, by Hendry and Ericsson (1991) and recently Teräsvirta and Eliasson (2001) developed two unrestricted versions of the model. This paper, however, uses data-determined unrestricted non-linear error-correction models. It should be noted that the error terms are generated regressors and their t-statistics should be interpreted with caution (Pagan (1984) and (1986)). To cope with this problem, following Pagan (1984 and 1986), we implement the instrumental variable estimation technique, where the instruments are lagged values of the error terms. Tables 9 and 10 report the parsimonious estimation results on ECM model of Model 1 without and with policy dummy variables, respectively. Tables 11 and 12 report the parsimonious estimation results on ECM model of Model 2 without and with policy dummy variables, respectively. In these tables, denotes a first difference operator, EC, R 2, σ and DW, respectively, denote the error correction term from the identified long-run equation; the adjusted squared multiple correlation coefficient, the residual standard deviation and the Durbin-Watson statistic. White is the White s (1980) general test for heteroskedasticity, ARCH is five-order Engle s (1982) test, Godfrey is five-order Godfrey s (1978) test, REST is the Ramsey (1969) misspecification test, Normality is Jarque and Bera (1987) normality statistic, L i is Hansen s (1992) stability test for the null

25 23 hypothesis that the estimated ith coefficient or variance of the error term is constant and L c is Hansen s (1992) stability test for the null hypothesis that the estimated coefficients as well as the error variance are jointly constant. None of these diagnostic checks is significant. However, in the first round regression the normality test was significant for both models. The significant non-normality statistic was due to two large outliers in December 1981 and April Dummy variables N8112 and N9904, which are respectively equal to one in December 1981 and April 1999 and zero otherwise, were used to capture the outliers in the data. According to the Hansen s joint stability test reported in Table 9 (L c =4.21>3.95 for 17 degrees of freedom) the coefficients as well as the error variance of the Model 1, when the impact of economic policy is ignored, are not jointly stable. However, when the impact of the appropriate economic policy is incorporated, as the parsimonious estimation results reported in Table 10 indicates (L c =5.25<6.61 for 31 degrees of freedom), the overall estimate is stable, even though the coefficient of the fifth-lagged dependent variable and the intercept in October and December is not stable. The immediate implication of this result is that ignoring the impact of policy regime changes, which influence the services of money, in the estimation of demand for money results in an unstable estimate of the demand. The growth of real income, as it would be expected, has a positive impact, after a four-month lag length, on the growth of the demand for real balances. The change of interest rate influences negatively, as it would be expected theoretically, the growth of the demand for real money with a month lag length. However, after the introduction of free trade agreement the rise in the interest rate reduces the growth of demand for money

26 24 after a month lag, but after five months demand for real balances will increase. A positive/negative estimated coefficient for income/interest rate is consistent with many studies in literature, e.g., for the Canadian case see Ghosh (2000). The net (wealth, risk-sharing, transaction and substitution) effect of the growth of real stock price on the growth of demand for money is positive after a month. This impact becomes stronger after five months since North American Free Trade agreement went into effect. However, after the implementation of zero reserve requirements in Canada, while the net effect of the stocks on the demand for real money is positive after a month, the negative substitution effect offsets the sum of positive impact of wealth, risk-sharing and transaction effects after five month, see Table 10. This decomposition of positive wealth, risk-sharing and transaction effect and negative substitution effect was not possible when the correct specification was not used; see Table 9. However, Friedman (1988), states that it is plausible that the substitution effect operates more rapidly than the wealth effect. Consequently, in his study on the U.S. data he included the real stock prices variable with zero and three-quarter lags and found while the instantaneous effect is negative (positive) on the money demand (income velocity), as the substitution effect would imply, the coefficient of the variable with lag length of three quarters is positive (negative) implying the existence of the wealth effect of the real stock price on demand for money (income velocity), though he found the latter effect to be stronger than the former effect. Note that a rise in the quantity of money demanded means a decline in velocity. However, when Friedman (1988) uses annual data he cannot separate substitution from other effects and he finds only a weak net effect (a negative coefficient) and

27 25 concludes that substitution effect dominates wealth effect. Consequently, the apparent dominance of the wealth effect, when quarterly data was used, is the exception, not the rule and he concludes the results are suggestive and not conclusive. McCornac (1991), using Japanese data, finds similar result. Choudhry (1996), using Canadian and U.S data, investigates long-run stationary relationship between stock prices and M1 and M2 and finds the direction and the size of the effect of stock prices on money demand depends upon the definition of money and suggests that the real money demand function in Canada and the U.S. in the post WWII period requires the inclusion of real stock prices. Thornton (1988), using German data, finds real stock prices play a significant and positive role in the long-run demand function for M1 balances. Namely, like previous work a net effect could be estimated. The lag dependent variable also influences the demand for real balances differently after the introduction of Free Trade, Nafta and zero reserve requirements (Table 10). All possible kinds of non-linear specifications, i.e., squared, cubed and fourth powered of the equilibrium errors (with statistically significant coefficients) as well as the products of those significant equilibrium errors were included. The error term associated with the real stock price determination was not statistically significant and so was dropped (Table 9). The error term generated from long-run demand for money has a linear effect on the demand for real money when the impact of economic policy is not incorporated (Table 9). However, with the correct specification, according to the estimation result reported in Table 10, the impact is nonlinear. Note that a non linearity in ECM is extremely important as Teräsvirta and Eliasson (2001) find that nonlinear ECM mechanism is a step towards a model with constant parameters. Here, of course, we

28 26 allowed both versions of the model, with or without policy variables, to incorporate nonlinear error term. Namely, the individuals reaction to equilibrium errors (departure from the desired level for M1) varies for different error sizes. For a small equilibrium error the non-linear part may not be as important, but for a very large error individuals reaction will be drastic. To the best knowledge of the author there is no study so far on a non-linear error correction model for Canadian demand for money (M1) in the literature. However, this result is consistent with e.g. Hendry and Ericsson (1991) and Ericsson, et al. (1998) for U.K. It is also consistent with, e.g., Bahmani-Oskooee and Bohl (2000) for Germany even though they used a linear EC model. According to the estimation result during the Asian Crisis, as it would be expected, the growth of the demand for money went up, as the coefficient of the dummy variable Asia is positive and statistically significant (tables 9 and 10). Since no study so far has incorporated the impact of the Asian crisis in the demand for money no comparison is possible. According to the estimated coefficients of postal strike dummy variables during the postal strikes, except the postal strike of 1997, demand for real money, as it would be expected, went up (tables 9 and 10). This result is consistent with, e.g., Hendry (1995). Among the coefficients of dummy variables representing policy regime changes that influence the intercept, only the coefficient of dummy variable Revision was found to be statistically significant. The estimated coefficient, as it would be expected, is negative (Table 10). To the best knowledge of the author no study so far has incorporated the implication of Revision in the demand for money. When the policy dummy variables

29 27 are not include in the Model 1 the coefficient of the linear trend variable is positive and statistically significant, indicating the demand for real cash balances went up through time (Table 9). However, we cannot observe the same evidence when the Model 1 is properly specified (Table 10). According to the estimation result during the month of May and December demand for money does go up and the reverse is true during October to November, inclusive (Table 10). Similar to Model 1 the estimated coefficients of Model 2 are not jointly stable (L c =5.89>4.52 for 20 degrees of freedom) when the impact of policy dummy variables are ignored and are stable, otherwise (L c =5.80<7.17 for 34 degrees of freedom), see tables 11 and 12, respectively. The growth of the real income has the same estimated sign as in Model 1, but with the correct specification (Table 12) the impact of the real income on the demand for real cash balances is more after the revision to the reserves regulations on August 24, 1983 and it is less after the change of Bank Act. Since the impact of the revision to the reserves regulations on August 24, 1983 was ignored in this literature no comparison is possible. Kabir and Mangla (1988) and Hendry (1995) included the impact of the Bank Act change in the estimation of the demand for money. They found, in contrast to this study, no statistically significant impact of the Bank Act change of The estimated sign of the change of interest rate and the growth of the real stock price is the same as in Model 1. However, now the growth of real stock price, when correct specification is used (Table 12), has contemporaneous effect on the demand for the real balances implying that the agents may be forward looking if this variable is not superexogenous. Furthermore, if the growth of real stock price is not superexogenous