advertisement

Demand for Money, Economic Policies and Stability Working Paper Amir Kia* Emory University, Department of Economics Atlanta, GA 30322-2240 U.S.A. E-mail: aki[email protected] Tel.: (404) 727-7536 Fax: (404) 727-4639 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. 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 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 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. 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-Dt) varies over time, where Dt 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 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 1981-1990 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 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: rmt = F(rindpt, cprt, rtset, DUMt), (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: Frindp>0, Fcpr<0 and Frtse =?, where Frindp, Fcpr and Frtse are the partial derivatives of rm with respect to rindp, cpr and rtse, respectively. 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 Frtse is an empirical issue. Let us assume Equation (1) has the following semi-log-linear form: lrmt =β0 + β1 lrindpt + β2 cprt + β3 lrtset + DUM’tδ+ ut, (2) where β’s are parameters to be estimated with the expected signs: β1 (income elasticity of money demand)>0, β2 (semi-interest elasticity of money demand)<0, β3 =?, and δ is a 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, DUMt = (Post75t, Post78t, Post81t (Jul81t, Aug81t,), Post97t (Nov 19 to Dec 5), INOV76t, INOV80t, Bat, GSTt, Revisiont, Inftart, Freet, Naftat, Ntart, Zerot, St) 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. 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 Ba81t, GSTt, Revisiont, Inftart, Freet, Naftat, Ntart, and Zerot 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 1981. The Bank Act of 1980 4 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). 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 1991. 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 10 and the Bank of Canada in February 1991. 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 1991. 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 10-15 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). 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 12 June 1992 and one after June 1994. Starting from June 1992 it increases by 0.20 every six months so that to get a value of one in July 1994. The variable S includes 11 centered seasonal dummies. The centered seasonal dummies are constructed such that they sum to zero for each t, i.e., 11 ∑S it = 0, where St is equal to (Dect - 1/12) and Dec is a dummy i =1 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. 2.2. 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 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 lrmt =α0 + α1 lrindpt + α2 cprt + α3 lrtset + α4 lrext + α5 ccprt + DUM’tδ+ ut, (3) where lrext is the log of real exchange rate, ccprt 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 α4 >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 α4 <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 α5 <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 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 2001. 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 2001. Table 1 reports sources and descriptions of the variables used in this paper. 6 Monthly total industrial production is only available up to June 2001. 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. 7 15 3.2 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 λmax 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 λmax 16 and Trace tests reject r=1 while we cannot reject r≤2, implying that r=2. However, as the results of both λmax 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 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 λmax 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. 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 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 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 1975-77 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 1975-87 period is reserved for the initial estimate and the impact of 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. 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, Li is Hansen’s (1992) stability test for the null 23 hypothesis that the estimated ith coefficient or variance of the error term is constant and Lc 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 1999. 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 (Lc=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 (Lc=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 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 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 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 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 (Lc=5.89>4.52 for 20 degrees of freedom) when the impact of policy dummy variables are ignored and are stable, otherwise (Lc=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 1980. 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 28 then the estimated coefficients of the model are not policy invariant. We will deal with this issue later in this section. The estimated coefficient of the covered U.S. interest rate was not statistically significant and was dropped. This result can be due to a high colinearity between Canadian rate and the covered U.S. rate as it was evidenced by Kia (1996a). In fact, I reestimated the equation without domestic rate, but kept the covered U.S. rate. The estimated coefficient of the covered U.S. rate had a correct sign (-0.002, SE= 0.001) and statistically significant. This result is consistent, among many, with the finding of Arango and Nadiri (1981), Handa (1988) and Hueng (1998, 1999). It should be mentioned that Hueng (1998, 1999) include the U.S. rate and not the covered rate.10 The estimated coefficient of the growth of real exchange rate is negative implying the existence of dolarization over the short term. However, this result should be interpreted cautiously. We can write: ∆lrex = log(ext*pft/pt) – log(ext-1*pft-1/pt-1) = ∆log(ext) + ∆log(pft/pt). Where ex is the nominal exchange rate, pf and p are U.S. and Canada price levels, respectively. Consequently, instead of the change of the log of real exchange rate I included the change of log of nominal exchange rate and U.S.-Canada inflation rates differential and reestimated the equation. The estimated coefficient of the change of log of exchange rate was positive and statistically significant (0.16 with SE = 0.07) and the estimated coefficient of U.S.-Canada inflation rates differential was also positive and statistically significant (0.57 with SE = 0.26). All other coefficients were the same or not materially different than what are reported in Table 12. 29 The estimated positive coefficient of the growth of the exchange rate, for a given U.S.-Canada inflation rates differential, indicates that a depreciation of the Canadian dollar increases domestic consumption and, therefore, demand for real cash balances in Canada will go up. Namely, there is no evidence of dollarizaton in Canada during the sample period. This result is consistent with the Bank of Canada current study, Murray and Powell (2002). The estimated positive coefficient of the inflation rates differential, for a given exchange rate, implies that as the U.S.-Canada inflation rates differential increases the Canadian demand for the U.S. goods (dollars) will fall. Hueng (1999) finds that the Canadian consumption of the U.S. goods has a positive impact on the Canadian demand for the real balances over, both, short and long-run, but the relationship is statistically significant only over the long run. This finding indirectly confirms our interpretation of the impact of Canada-U.S. inflation rates differential on the demand for money. Furthermore, our estimated negative coefficient for the growth of real exchange rate is consistent with Hueng (1998, 1999). The impact of the lag dependent variable is almost the same as in Model 1, except, with the correct specification, the impact before and after the introduction of Nafta and zero reserve requirements remain the same (Table 12). The error term associated with the real stock price determination was not statistically significant when all policy dummy variables were included and so was dropped, but, the error term associated to the covered interest parity was significant (Table 12). The reverse was true when the policy dummy variables were excluded (Table 11). Similar to Model 1 the error term generated from long-run demand for money has a linear effect on the demand for 10 The estimated coefficients of all other variables were not materially different than what are reported in 30 real money when the impact of economic policy changes is not incorporated (Table 11). However, with the correct specification, according to the estimation result reported in Table 12, the impact is nonlinear, i.e., the agents may ignore small deviations from the desired demand for real balances, but react drastically to a large deviation. This is also true for the impact of error associated with long-run covered interest parity term. To the best of my knowledge there is no study on the Canadian demand for money with non-linear ECM, but our result is consistent with, e.g., the findings of Ericsson, et al. (1998) and Teräsvirta and Eliasson (2001), although these studies use restricted non-linear ECM. The impact of all dummy variables on the real demand for money is the same as in Model 1. In sum, we conclude again that when the impact of fiscal and monetary policy regime changes which enhances/weaken the services of money is ignored the estimated demand for real balances will be biased and unstable. Furthermore, it was found in this section that a non-linear and stable ECM for M1 demand for money in Canada exists. Having established this fact, we need to verify whether the coefficients of this money demand equation specified according to Model 2 are invariant to the process of forcing variables. Namely, we need to verify whether the contemporaneous variable ∆ lrtset is superexogenous. This requires the establishment of the marginal model for our contemporaneous variable ∆lrtset. 4.2. Marginal Model There have also been several potential regime changes over the sample period as follows: (i) The introduction of SPRA (the Special Purchase and Resale Agreements) and Table 12. The full estimation result is available upon request. 31 SRA (Sales Repurchase Agreements) in June 1985.11 (ii) The change of the Bank of Canada’s policy management approach (tight monetary policy) under Governor Crow, February 1987-February 1994.12 (iii) The introduction of term deposit auction in April 1986.13 Dummy variables were created for step changes, i.e., (i) Spra = 1 for June 1985 and after, zero otherwise, (ii) Crow = 1 for February 1987-February 1994, zero otherwise and (iii) Term = 1 for April 1996 and after, zero otherwise. 14 To construct a marginal model for a variable one can use a data generating process of the variable or use a theoretical model, see, Engle et al. (1983), Engle and 11 With SPRA instrument, Bank of Canada is involved in the purchase of short-term Government of Canada securities under an agreement to sell them back on the following day. This temporary supply of funds can ease the market. SRA is the reverse of SPRA. 12 In this period Canada-U.S. overnight interest rate differential (overnight rate minus Fed Fund rate) went up from an average of 1.41% (standard deviation=2.39) during the 1975:01-1987:01 period to an average of 2.64% (standard deviation=1.33) during 1987:02 to 1994:02 period. 13 In Canada, the day-to-day operations of monetary policy seek to influence the overnight financing rate, primarily through the management of the supply of settlement balances provided to the direct clearers.13 The direct clearers use their accounts at the Bank of Canada only to settle transactions between themselves or with the government. Currently, Bank of Canada influences the daily level of these balances, retroactively, through the drawdown/redeposit (D/R) mechanism. Even though the bank’s actions as fiscal agent of the government are not directly linked to the implementation of monetary policy, the two functions are related. Interactions occur principally on two major fronts. The use of the Receiver General deposits in the D/R mechanism changes the overall level of government balances every day. Consequently, treasury management decisions must take into account actual and potential monetary operations. The net investment of government balances in the overnight market can then be an important net source or use of funds for the market, influencing the evolution of the overnight financing rate and should, therefore, be taken into account by the Bank when determining the supply of settlement balances (Montador, 1995). A portion of Receiver General deposits has been auctioned among direct clearers since April 1986, and has become the largest component of the government’s cash balances. Furthermore, the auction for term deposits is now an important daily event for the overnight money market in Canada. Indeed, the yields on these deposits are one of the key indicators for the evolution of overnight rates during the course of a daily overnight funds cycle. The one-day funds won at the term deposit auctions are part of the pool of one-day resources available to the financial institutions to lend or meet their financing needs (Kia 1996b). 14 Dummies for other potential regimes were also created and used as regressors in marginal equations. However, none of these dummies was found to be significant in any of the marginal equations. These potential regime changes include: the revision to the reserve requirement in Canada in August 1983 (Bank of Canada (1983)) and the introduction of zero reserve requirements and operating band in July 1994. In compliance with the Bank Act, the statutory requirement on chartered banks to hold reserves against certain of their deposit liabilities was phased out gradually over a two-year period in June 1992 and Reserve requirements were reduced to zero in July 1994 (Bank of Canada Review (1994), p. 80, Footnote 1). Reserve requirements were reduced every six months by three percents until June 1994, when the remainig requrement was entirely removed. 32 Hendry (1993), Psaradakis and Sola (1996). We will follow the latter approach. Kia (2002) developed a macro-determinants model of stock prices for a small open economy like Canada and tested the model on Canadian data. Given that a model is only an approximation to reality we will use Kia‘s (2002) Equation 4 and assume that the change of logarithm of real stock price has the following distributed lag model: l1 l1 k l1 k j=1 j=1 i =1 j=1 i =1 ∆lrtset = αj(1+ ∑ d j ) + α1ji(1+ ∑ d j ) ∑ ∆lrindpt - i + α2ji(1+ ∑ d j ) ∑ ∆lrspt - i + l1 k l1 k l1 k j=1 i =1 j=1 i =1 j=1 i =1 l1 k l1 k l1 k j=1 i =1 j=1 i =1 j=1 i =1 l1 k j=1 i =1 α3ji(1+ ∑ d j ) ∑ ∆lext - i + α4ji(1+ ∑ d j ) ∑ ∆lrcompt - i + α5ji(1+ ∑ d j ) ∑ ∆onrt - i + α6ji(1+ ∑ d j ) ∑ lindift - i + α7ji(1+ ∑ d j ) ∑ premt - i + α8ji(1+ ∑ d j ) ∑ ∆lrcpt - i + α9ji(1+ ∑ d j ) ∑ ∆l( indp ) t - i + λ1 OCT87t+ λ2 Asiat + vt, findp j = 1 to 11 and k = 1 to 12. (4) Where ∆lrindpt is, as before, the change of the logarithm of real industrial production, ∆lrspt is the change of the logarithm of the real S&P 500 index, where the real S&P 500 is defined as the nominal S&P 500 multiplied by the exchange rate divided by the Canadian Consumer Price Index, ∆lext is the change of the logarithm of Canada-U.S. exchange rate, ∆lrcompt is the change of the logarithm of real commodity price index, ∆onrt is the change in the Canadian overnight financing rate, intdift is Canadian overnight financing rate less Fed fund rate, premt is the difference between one-month Canadian corporate paper and Treasury Bill rates, ∆lrcpt is the change of the logarithm of the ratio of Canada-U.S. Consumer Price Indexes, ∆l(indpt/findpt) is the change in the logarithm of the ratio of Canada-U.S. industrial production and vt is the disturbance term which is assumed to be white noise with zero mean. Other dummy variables are defined before. 33 The coefficients of α’s and λ’s are assumed to be constant. Dummy variables d1 to d11 are respectively Bat, GSTt, Revisiont, Inftart, Freet, Naftat, Ntart, Zerot, Sprat, Crowt and Termt. Level and interactive combinations of dummy variables d’s were tried, as explained by Equation (4), for the impact of all potential shift events in the marginal model for ∆ lrtset and any first round significant effects were retained. In the first round of estimation normality test was significant due to large outliers in March 1980 and August 1998. To offset the impact of these outliers the dummy variables N803 (equal to one in March 1980 and zero, otherwise) and N988 (equal to one in August 1988 and zero, otherwise) were created. The resulting parsimonious marginal model took the form reported in Table 13. As the result in Table 13 indicates Equation (4) passes the diagnostic checks for residual autocorrelation, residual heteroskedasticity and the RESET as well as normality tests. Overall, equation (4) seems reasonable marginal model for the analogues of the first conditional moment of ∆lrtset, especially since the standard errors is very small, i.e., σ is 0.04. Clearly there is evidence of the structural break in the equation, i.e., possible break points are due to the introduction of overnight repoes (spra and sra), zero reserve requirements and change of Bank Act. Note that non-constancy of the marginal model is related to the concept of superexogeneity, which implies that the parameters of conditional model remain constant if agents are not forward looking. Furthermore, these policy changes did not change the nature of the equities in Canada as some could change, as explained before, the services of money. 34 In Equation (4) the ‘spra’, ‘zero’ ‘Ba’ and ‘Oct87’ dummy variables are significant. Dummy variables ‘spra’, ‘zero’ and ‘Ba’ affect the slope, while ‘Oct87’ affects the intercept. According to the estimated results before the introduction of spra the growth of real industrial production had a negative effect on the growth of real stock price, but after the introduction of spra the negative effect became weaker after a month and stronger after a 12-month lag length. One possible explanation is that the growth of real industrial production, along the aggregate supply function, influences the price level more than the nominal stock price. The real commodity price did not have any impact on the growth of real stock price before the introduction of spra while it influences, as one would expect theoretically, positively the growth of real stock price with a lag length of seven months. The real stock price, as it would be expected, is affected negatively by the change in the overnight rate, Canada-U.S. inflation and interest rates differential. However, the interest rate differential has a wrong sign after the revision in the Bank Act. The real S&P 500 stock price index has a correct sign before and after the change in the Bank Act and a wrong sign (negative) after the introduction of zero reserve requirements in Canada. However, the overall impact, as it would be expected, is positive. The growth of the nominal exchange rate does not have any impact on the growth of the real stock price before the introduction of the spra, but it has a negative impact (a correct sign) after the introduction of spra. For a complete and thorough explanation on the impact of these variables on stock price in Canada see Kia (2002). 35 4.3 Superexogeneity Test and Results In this section we need to verify if the contemporaneous variable ∆lrtset in the ECM of Model 2, when all policy dummy variables are included, fails to be superexogenous. Letting Zt= ∆lrtset and following Engle et al. (1983), Engle and Hendry (1993) and Psaradakis and Sola (1996), we can write the relationship between ∆lrmt and Zt as: ∆lrmt = α0 + ψ0 Zt + (δ0 - ψ0) (Zt - ηZt) + δ1 σtZZ (Zt - ηZt) + ψ1 (ηZt)2 + ψ2 (ηZ)3 + ψ3 σtZZ ηZt + ψ4 σtZZ (ηZt)2 + ψ5 (σtZZ)2ηZ + z’tγ + ut (5) where α0, ψ0, ψ1, ψ2, ψ3, ψ4, ψ5, δ0 and δ1 are regression coefficients of ∆lrmt on Zt conditional on z’tγ, and term ut is assumed to be white noise, normally, identically and independently distributed. Vector z includes past values of ∆lrmt, Zt, and other explanatory variables in the ECM as well as current and past values of other valid conditioning variables in the ECM. Furthermore, ηZt=E(Zt│It) and σtZZ=E[(Zt - ηZt )2│It] are the conditional moments of Zt, given information set It which includes the past values of ∆lrmt and Zt as well as the current and past values of other valid conditioning variables included in zt. Under the null of weak exogeneity, δ0-ψ0=0. Under the null of invariance, ψ1=ψ2=ψ3=ψ4=ψ5=0 in order to have ψ0=ψ. Finally, if we assume that σtZZ has distinct values over different, but clearly defined regimes, then under the null of constancy of δ, we need δ1=0. If all these hypotheses are accepted the contemporaneous variable in the ECM is superexogenous and coefficients of the money demand equation (ECM) for M1 are invariant to policy shocks. 36 From the marginal model, reported in Table 13, estimates of ηZ and σtZZ, for Z=∆lrtset were calculated. As for σtZZ, since the error for ∆lrtest variable, according to ARCH test, is not heteroskedastic, a five-period moving average of the variance of the error was tried. All of these constructed variables were then included in the ECM reported in Table 12. The model was re-estimated and the estimation results on these constructed variables are given in Table 14. None of the diagnostic checks reported in the table is significant. The individual F-test is on the null hypothesis that the coefficient of each variable is zero. The F-test on the null hypothesis that all constructed variables are jointly zero is given in the last row of the table. As the estimation result in Table 14 shows, both the individual F-test (on the null hypothesis that the coefficient of the constructed variable is zero) and the joint F-test (on the null hypothesis that coefficients of all constructed variables are jointly zero) is not significant, indicating that these variables, individually or together should not be included. This result immediately implies that the contemporaneous variable (∆lrtset) in the conditional model, reported in Table 12, is superexogenous, and the demand for real balances in Canada is invariant to policy shocks. It should be noted that even when superexogeneity holds, policy can and, in fact, does impact agents’ behavior by affecting the variables entering the conditional model, albeit not through the parameters of that model. In our models the policy might well affect the interest rate, income, exchange rate and stock price and so the demand for M1. More explicitly, as mentioned by Ericsson et al. (1998, p. 320), “...under super 37 exogeneity, the precise mechanism that the government adopts for such a policy does not affect agents’ behavior, except insofar as the mechanism affects actual outcomes.” It should be mention that one could argue that since the structural invariance implies that the determinant of parameter nonconstancy in the marginal process should not affect the conditional model and in our estimation result dummy variables ‘zero’ and ‘Ba’ enter both the conditional and marginal models (see tables 12 and 13) then Model 2 is not invariant to policy shocks. Here again, along with Ericsson et al. (1998), we re stress the fact that the precise mechanism that the Bank of Canada adopted these policy regime changes did not affect agents’ behavior as the superexogeneity test indicates, but, in fact, it affected the actual outcomes by changing the services of money. Consequently, one should distinguish between policy regime changes, which influence the behavior of agents and those changes that influence directly the demand for real balances. For example, in our model if the introduction of the overnight repo (spra dummy variable) in Canada would affect the demand for real balances in Canada we could argue that the demand is not invariant to policy shocks. Note that the dummy variable ‘spra’ affects the marginal model, but not directly the conditional model. The indirect affect of the policy on the demand for real balances is through the direct affect of the policy on the contemporaneous variable ∆lrtset. 4.4 Encompassing Tests Having established that the demand for real balances (M1) in Canada is stable and invariant to policy shocks it is natural to investigate which model between our two models performs better. The encompassing principle provides a formal basis for such practice. Several encompassing test results on these models are reported in Table 15. 38 According to ex-post RMS, and ex-ante (one-year) RMS tests result none of these models variance-dominate the other. It seems according to ex-post RMS percent error and Ex-ante (one-year) RMS percent error tests result Model 1 encompasses Model 2, but the stronger tests results indicate that Model 2 encompasses Model 1. Namely, Theil’s inequality coefficient (U)15 calculated for ex-post, one-year and five-year ex-ante U clearly indicates the superiority of Model 2 over Model 1. Furthermore, the estimated ex-ante (five-year) RMS percent error and Cox’s (1961 and 1962) F-test and Pesaran’s (1974) N-test results clearly evidence Model 2 can account for the salient features of Model 1. Consequently, we may conclude that Model 2 encompasses Model 1. 15 . See Theil (1965, pp. 31-37 and 1966, pp. 26-36). If Theil’s coefficient is zero then the fitted and actual values are equal for all observations, i.e., there is a perfect fit. If the coefficient is equal to one the predictive performance of the model is as bad as it possibly could be. 39 4.5 Identification of Money Demand The error correction models reported in tables 9, 10, 11 and 12, along with their associated cointegration relationships reported in tables 3, 4, 5 and 6, can be interpreted as money demand functions for two reasons. First, being conditional models, the parameterization of these functions is unique. Since the contemporaneous variable in Table 12 is superexogenous and all other variables in these error correction models, with or without policy dummy variables, are exogenous/predetermined, factorizing the joint distribution of real balances, income, interest rate and stock prices into a distribution for real balances conditional on income, interest rate and stock prices constitutes the demand for money. However, when the impact of policy regime changes, which influence the services of money, is ignored, the coefficients may be constant in a “raw” concept à la Ericsson, et al. (1998), but they vary if underlying parameters are evaluated. Second, in Canada the real supply of money shifted as some economic policy regimes changed over the sample period. These specific regime changes include the abolition of targeting M1 in October 1982, the revision to the reserves regulations on August 24, 1983 and the introduction of inflation targeting in February 1991. Namely, as the growth of real money supply was estimated on its twelve lagged values and the set of DUM variables, the dummy variables accounting for the abolition of targeting M1 in October 1982, the revision to the reserves regulations on August 24, 1983 and the introduction of inflation targeting in February 1991 were found to be statistically significant. Consequently, any combination of the shifting supply function with the demand equation would be nonconstant. In effect, these shifts in the supply function (over-) identify the demand function. Note that the dummy variables accounting for the 40 abolition of targeting M1 in October 1982 and the introduction of inflation targeting in February 1991 do not enter in the demand for money when all appropriate policy regime changes are taken into consideration (tables 10 and 12). 5. Concluding Remarks Some policy regime changes enhance or weaken the services of money. In the same way that a dollar, e.g., provides better services as a result of financial innovations and other financial developments some policy regime changes also create different environments for the money in circulation. This paper argues that if a proper allowance for such policy regime changes is not accounted for in estimating the M1 definition of the Canadian demand-for-money relationship the parameter instability is inevitable. Then using monthly data for the period 1975-2001 the paper provides evidence for such a claim. Furthermore, this paper shows that the long-run relationship of the demand for real balances is sensitive to the inclusion of policy dummy variables accounting for regime changes which influenced the services of money in Canada. It was found that the estimated coefficient of the scale variable is negative over the long run (a wrong sign) when the appropriate policy regime changes are not incorporated in the short-run dynamic of the system. Namely, this study evidenced that when the impact of economic policy regime changes is ignored the estimated long-run demand for money could be biased. The adjustment (reaction) to the disequilibrium will be also different when the appropriate policy regime changes are not incorporated in the estimation. Namely, the error term generated from the long-run demand for money has a linear effect on the 41 demand for real balances when the impact of economic policy regime changes is not incorporated while, with the correct specification, the impact is nonlinear. This is an important factor in the estimation of demand for money since non-linearity in ECM mechanism, as Teräsvirta and Eliasson (2001) evidenced, is a step towards a model with constant parameters. This study also shows that there has not been any evidence of dollarizaton in Canada during the sample period. 42 References Arango, Sebastian and Ishag Nadiri (1981) Demand For Money in Open Economics. Journal of Monetary Economics 7, 69-83. Arestis, Philip, George Hadjimatheou and George Zis (1992) The Impact of Financila Unnovations on the Demand for money in the UK and Canada. Applied Financial Economics 2, 115-123. Bank of Canada (1983) Overnight Financing in Canada: Special Call Loans, Bank of Canada Review, May, 4-13. Ottawa, Bank of Canada. _____________ (1994) Bank of Canada Review, Autumn. Boothe, Paul M. and Stephen S. Poloz (1988) Unstable Money Demand and the Monetary Model of the Exchange Rate. Canadian Journal of Economics XXI, No. 4, 785-798. Bordo, Michael D.and Ehsan U. Choudhri (1982) Currency Substitution and the Demand for Money: Some Evidence for Canada. Journal of Money, Credit and Banking 14, No. 1, February, 48-57. ______________, Lars Jonung and Pierre L. Siklos (1997) Institutional Change and the Velocity of Money: A Century of Evidence. Economic Inquiry XXXV, October, 710-724. Cameron, Norman (1979) The Stability of Canadian Demand for Money Functions 1954-75. Canadian Journal of Economics XXII, No. 2, 258-281. Cheung, Y. and K.S. Lai (1993) Finite-sample Sizes of Johansen’s Likelihood Ratio Tests for Cointegration. Oxford Bulletin of Economics and Statistics 55, 313-328. 43 Choudhry, Taufiq (1996) Real Stock Prices and the Long-run Money Demand Function: Evidence from Canada and the USA. Journal of International Money and Finance 15, No. 1, 1-17. Clark, Carolyn (1973) The Demand for Money and the Choice of a Permanent Income Estimate. Journal of Money Credit and Banking 5, Issue 3, August, 773-793. Clinton, Kevin (1997) Implementation of Monetary Policy in a Regime with Zero Reserve Requirements. Bank of Canada Working Paper 97-8. Cox, D.R. (1961) Tests of Separate Families of Hypotheses. Proceedings of the Fourth Berkeley Symposium 1. ________ (1962) Some Further Results on Separate Families of Hypothesis. Journal of the Royal Statistical Society B 38, 45-53. Deaves, Richard (1991) Canadian Weekly Money Supply Announcements and Financial Market Reactions in the First Year of Targeting: A View of Market perceptions of Bank of Canada. Canadian Journal of Economics, XXIV, No.2, 282-299. Elyasiani, Elyas and Ali H. M. Zadeh (1999) Econometric Tests of Alternative Scale Variables in Money demand in Open Economies International Evidence from Selected OECD Countries. The Quarterly Review of Economics and Finance 39, 193-211. Engle, Robert F., David F. Hendry and Jean-François Richard (1983) Exogeneity. Econometrica 51, No. 2, March, 277-304. _____________ and David F. Hendry (1993) Testing Superexogeneity and Invariance in Regression Models. Journal of Econometrics 56, 119-139. 44 ______________ (1982) Autoregressive Conditional Heteroskedasticity With Estimates of the Variance of United Kingdom Inflation. Econometrica, July, 987-1007. Ericsson, Neil R (1998) Empirical Modeling of Money Demand. Empirical Economics 23, 295-315. Ericsson, Neil R., David F. Hendry and Kevin M. Prestwich (1998) The Demand for Broad Money in the United Kingdom, 1878-1993. Scandinavian Journal of Economics 100(1), 289-324. Escribano, A. (1985) Nonlinear Error-Correction: The Case of Money Demand in the U.K. (1878-1970). Mimeo, University of California at San Diego, La Jolla, California, December. Favero, Carlo and David F. Hendry (1992) Testing the Lucas Critique: A Review. Econometric Reviews 11, No. 3, 265-306. Friedman, Milton (1988) Money and the Stock Market. Journal of Political Economy 96, No.2, 221-245. Ghosh, Madhusudan (2000) The Stability of Money Demand Function in Five Major Industrial Countries: Evidence from Cointegration Tests. Indian Economic Review XXXV, No. 2, 175-192. Godfrey, Les G. (1978) Testing Against General Autoregressive And Moving Average Error Models When the Regressors Include Lagged Dependent Variables. Econometrica November, 1293-1301. Granger, Clive W.J. (1986) Developments in the Study of Cointegrated Economic Variables. Oxford Bulletin of Economics and Statistics August, 213-218. 45 Gregory Allan W. and James G. Mackinnon (1980) Where’s My Cheque? A Note on Postal Strikes and the Demand for Money in Canada. Canadian Journal of Economics XIII, No. 4, 683-687. Gregory, Allan W., Gregor W. Smith and Tony Wirjanto (1992) Synthesis of Money-Demand and Indicator Models. Bank of Canada Monetary Seminar 90: A Seminar Sponsored by the Bank of Canada, May 7-9, 1990, Bank of Canada, Ottawa. Handa, Jagdish (1988) Substitution Among Currencies: A Preferred Habitat Hypothesis. International Economic Journal 2, No. 2, 41-61. Handa, Jagdish and I. M. Bana (1990) Currency Substitution and Transactions Costs. Empirical Economics 15, No. 3, 231-243. Hansen, H. and S. Johansen (1993) Recursive Estimation in Cointegrated VAR-models. Preprint 1993, No.1, Institute of Mathematical Statistics, University of Copenhagen. Hansen, H and Katarina Juselius (1995) CATS in RATS Cointegration Analysis of Time Series, Institute of Economics, University of Copenhagen. Hansen, Bruce E. (1992) Testing for Parameter Instability in Linear Models. Journal of Political Modeling 14, No. 4, 517-533. Harvey, A. C. (1993) The Econometric Analysis of Time Series, The MIT Press, Cambridge, 2nd edition. Hendry, David F. and N. R. Ericsson (1991) An Econometric Analysis of U.K. Money Demand in Monetary Trends in the United States and the United Kingdom by 46 Milton Friedman and Anna J. Schwartz. American Economic Review 81, No. 1, 8-38. Hendry, David F. and Grayham E. Mizon (1998) Exogeneity, Causality, and Co-breaking in Economic Policy Analysis of a Small Econometric Model of Money in the UK. Empirical Economics 23, No. 3, 267-294. Hendry, Scott (1995) Long-Run Demand forM1. Bank of Canada Working Paper 95-11. Hoffman, Dennis, Robert H. Rasche and Margie A. Tieslau (1995) The Stability of Long-Run Money Demand in Five Industrial Countries. Journal of Monetary Economics 35, 317-339. Hueng, James C. (1998) The Demand for Money in an Open economy: Some Evidence for Canada. North American Journal of Economics & Finance 9(1), 15-31. Hueng, James C. (1999) Money Demand in an Open-economy Shopping-Time Model: An Out-of-Sample-Prediction Application to Canada. Journal of Economics and Business 51, 489-503. Jarque, Carlos M. and Anil K. Bera (1987) A Test for Normality of Observations and Regression Residuals. International Statistical Review 55, No. 2, August, 163-172. Johansen, Soren (1995a) Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford: Oxford University Press. _____________ (1995b) Identifying Restrictions of Linear Equations With Applications to Simulations Equations and Cointegration, Journal of Econometrics, 69, 11132. 47 Johansen, Soren and Katarina Juselius (1991) Testing Structural Hypotheses in a Multivariate Cointegration Analysis of the PPP and the UIP for UK. Journal of Econometrics 53, 211-244. Kabir, M. and I. Mangla (1988) Effects of Financial Innovations on the Money Demand Function: Canadian Evidence. Applied Economics 20, 1263-1273. Kia, Amir (1996a) Overnight Covered Interest Parity: Theory and Practice, International Economic Journal, Vol. 10. No. 1, Spring, 59-82. Kia, Amir (1996b) Day-of-the-Week Effect and the Overnight Money Market Efficiency. Bank of Canada mimeograph. Paper presented at the annual meeting of the Canadian Economics Association, May 1996. ________ (2002) Forward-Looking Agents and Macroeconomic Determinants of the Equity Price in a Small Open Economy. Applied Financial Economics, forthcoming. Koutoulas, George and Lawrence Kryzanowski (1996) Microfactor conditional volatilities, time-varying risk premia and stock return behavior, The Financial Review, Vol. 31, No. 1, 169-227. McCornac, D. (1991) Money and the Level of Stock Market Prices: Evidence from Japan. Quarterly Journal of Business and Economics 30, 42-54. Montador, Bruce (1995) The Implementation of Monetary Policy in Canada. Canadian Public Policy, XXX:1, 107-20. Murray, John and James Powell (2002) Dollarization in Canada: The Buck Stops There. Bank of Canada Technical Report No. 90, August. 48 Osterwald-Lenum, Michael (1992) Practitioners, Corner: A Note With Quantiles of the Asymptotic Distribution of the Maximum Likelihood Cointegration Rank Test Statistics. Oxford Bulletin of Economics and Statistics 54, No. 3, 461-472. Pagan, Adrian (1984) Econometric Issues in the Analysis of Regressions with Generated Regressors. International Economic Review 25, 221-247. ____________ (1986) Two Stage and Related Estimators and Their Applications. Review of Economic Studies 53, 517-538. Pesaran, M. H. (1974) On the General Problem of Model Selection. Review of Economic Studies 4, 153-171. Psaradakis, Zacharias and Martin Sola (1996) On the Power of Tests for Superexogeneity and Structural Invariance. Journal of Econometrics 72, 151-175. Poloz, Stephen S. (1980) Simultaneity and the Demand for Money in Canada. Canadian Journal of Economics XIII, No. 3, 406-420. Ramsey, J.B. (1969) Tests for Specification Errors in Classical Linear Least-squares Regression Analysis. Journal of Royal Statistical Society, Series B 31, No. 2, 350-371. Sidrauski, Miguel (1967) Rational Choice and Patterns of Growth in a Monetary Economy. The American Economic Review, Vol. 57, Issue 2, 534-544. Sriram, Subramanian S. (2002) Determinants and Stability of Demand for M2 in Malaysia. Journal of Asian Economics 13, 337-356. Stock, James H. and Mark W. Watson (1993) A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems. Econometrica 61, No. 4, July, 783-820. 49 Teräsvirta, Timo and Ann-Charlotte Eliasson (2001) Non-linear Error Correction and the U.K. Demand for Broad Money, 1878-1993. Journal of Applied Econometrics, 16, 277-288. Theil, H. (1965) Economic Forecasts and Policy, North-Holland Publishing Company, Amsterdam, 2nd edition. _______ (1966) Applied Economic Forecasting, North-Holland Publishing Company, Amsterdam. Thornton, John (1998) Real Stock Prices and the Long-run Demand for Money in Germany. Applied Financial Economics, 8, 513-517. White, Halbert (1980) A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity. Econometrica May, 817-837. 50 Table 1* Description of Variables, Mnemonics and Sources (CANSIM Numbers) lrm = log of real M1, in millions of dollars (B2033), deflated at Consumer Price Index (P100000) lrindp = log of real total industrial production, in million of dollars, (I57001) cpr = 30-day corporate paper rate, annual percentage rate, (B14039) lrtse = log of the real TSE 300 Composite Index, closing quotations at monthend (B4237) deflated at Consumer Price Index (P100000) lrex = log of the real exchange rate = the nominal exchange rate ($Canadian of one unit $US), the last day of the month (B3414) multiplied by the U.S. Consumer Price Index (D139105) divided by the Canadian Consumer Price Index (P100000) ccpr = one-month U.S. covered corporate rate, annual percentage rate = 30-day U.S. corporate rate (B54416) plus the difference of one-month forward rate (B3419) and nominal exchange rate divided by nominal exchange rate onr = Canadian overnight financing rate**: B14044 lrcp = log of the ratio of Canadian-U.S. consumer price indexes: P100000 and D139105 lcomp = log of real commodity price index in Canadian dollars: B3300*** lrsp = log of real S&P 500 where real S&P 500 is the S&P 500 Index (quotations at month-end: B4291) multiplied by the exchange rate divided by the Canadian Consumer Price Index intdif = Canadian overnight rate less Fed Fund rate: B14044 and B54408 prem = Differences between monthly Canadian corporate paper and TB rates****: B14039 and B14059 * All of the data is as of the last day of the month. ** The overnight financing rate is the call loan rate. Call loans are money market instruments designed to finance the acquisition or holding of securities by investment dealers for short periods of time. These loans are callable and their suppliers accept a wide range of collateral. *** The commodity price index is a fixed-weight index of the spot or transaction prices of 23 commodities produced in Canada and sold in world markets. The weight of each commodity in the total index is based on the average value of the Canadian production over the 1982-90 period (Bank of Canada Review (1994)). Consequently, the data was converted to the Canadian dollar by multiplying it by the exchange rate and dividing it by the average of exchange rate for the period 1982-90 (i.e., 1.269193474994). **** Note that monthly TB rates are only available from 1989. I, consequently, followed Korkie (1990) and Koutoulas and Kryzanowski (1996) and calculated these rates for the 1975:1-1979:12 period as tbr1t=log(1+kt), where kt=1200[(1+(91/365)*tbr3t-1/100)30.4/91-1] and tbr3 is the three-month TB rate (B14060). 51 Table 2: Stationarity Tests: 1975 (Jan.) - 2001 (June)* Absolute Values Variables Augmented Dickey-Fuller τ-Stat. Phillips-Perron Z-Stat. 0.20 3.10b 4.75a 2.69 3.47a 4.96a 2.86 1.20 2.56 1.71 1.30 0.50 2.75 11.24a 2.85 6.36a 13.29a 3.20b 1.31 3.53a 1.86 1.45 8.30a 6.41a 14.30a 7.70a 8.40a 7.17a 8.85a 7.36a 6.94a 21.57a 16.69a 29.42a 16.70a 20.40a 18.62a 22.28a 19.21a 16.27a Levels:** lrm lrtse lrindp cpr intdif prem ccpr lrex onr lex lrcomp Changes of: lrm lrtse lrindp cpr ccpr lrex onr lex lrcomp * All tests include constant. The critical value for Augmented Dickey-Fuller τ test (lag-length = 5) and for Phillips-Perron non-parametric Z test (window size = 4) is 2.87 at 5% and 3.44 at 1%. The number of observations is 317. a=Significant at 1%. b=Significant at 5%. ** lrm is the log of the real M1, lrtse is the log of the real TSE 300 stock index, lrindp is the log of real industrial production, where all deflated at Consumer Price Index (CPI). cpr is one-month corporate paper rate. lrsp is the log of real S&P 500, lrcomp is the log of real commodity price index, onr is the Canadian overnight rate, intdif is the difference between the Canadian overnight and Fed Fund rates and prem is the monthly corporate rate less TB rate. Note that monthly TB rates are only available from 1989. I, consequently, followed Korkie (1990) and Koutoulas and Kryzanowski (1996) and calculated these rates for the 1975:1-1979:12 period as tbr1t=log(1+kt), where kt=1200[(1+(91/365)*tbr3t-1/100)30.4/91 -1] and tbr3 is the three-month TB rate 52 Table 3: Tests of the Cointegration Rank Model 1: Without Any Policy Dummy Variable* Period 1975:Jan.-2001:June H0=r λmax(1) λmax90 λmax95(2) Trace(3) Trace90 Trace95(4) 0 50.59 18.03 28.14 90.16 49.92 53.42 1 23.81 14.09 22.00 39.57 31.88 34.80 2 13.71 10.29 15.67 15.76 17.79 19.99 3 2.05 7.50 9.24 2.05 7.50 9.13 Diagnostic tests**: LM(1) p-value = 0.01 LM(4) p-value = 0.64 Normality p-value = 0.00 (1) λmax has been adjusted to correct a possible small sample biased error. Namely, λmax has been multiplied by the small sample correction factor ((N – kp)/N)=0.9361, where N (=313) is the number of observations, k (=5) is the number of lag length and p (=4) is the number of the endogenous variables, see Cheung and Lai (1993). Consequently, λmax =- (N-kp) ln(1- Dr). (2) The source is Osterwald-Lenum (1992), Table 1*, p. 467. (3) Trace has been multiplied by the small sample correction factor (N – kp)/N, see Cheung and Lai P (1993). Consequently, Trace test = -(N- kp) ln(1 - D i ). Both Trace and λmax tests were developed in ∑ i = r +1 Johansen and Juselius (1991). (4) The source is Johansen (1995a), Table 15.2, p. 215. * The model includes constant and a short-term exogenous vector of dummy variables DUM, where . DUMt = (Post75t, Post78t, Post81t, Post97t, INOV76t, INOV80t, Oct87t, Asiat, St). Post75 = 1 for the period October to December 1975, a value of negative one in January 1976, and zero otherwise. Post78 = 1 in October 1978, a value of negative one in November 1978, and zero otherwise. Post81 = 1 in July 1981, a value of negative one in August 1981, and zero otherwise. Post97 = 1 in November and December 1997, a value of negative one in January 1997, and zero otherwise. INOV76 = 1 after 1976(Jan.) and zero, otherwise. INOV80 = 0 until 1980-Jan. and then commences linearly upwards to a value of one for December 1982 and remains one after. Oct87 = 1 in October 1987 and zero otherwise. Asia = 1 in November and December 97 and zero otherwise. S includes 11 centered seasonal dummies. ** LM(1) and LM(4) are one and four-order Lagrangian Multiplier test for autocorrelation, respectively (Godfrey (1988)). 53 H0=r Table 4: Tests of the Cointegration RankModel 1: With All Policy Dummy Variables* Period 1975:Jan-2001:June (3) (1) Trace90 Trace95(4) λmax λmax90 λmax95(2) Trace 0 48.66 18.03 28.14 79.48 49.92 53.42 1 20.70 14.09 22.00 30.82 31.88 34.80 2 9.30 10.29 15.67 10.13 17.79 19.99 3 0.82 7.50 9.24 0.82 7.50 9.13 Diagnostic tests**: LM(1) p-value = 0.01 LM(4) p-value = 0.61 Normality p-value = 0.00 (1) λmax has been adjusted to correct a possible small sample bias error. Namely, λmax has been multiplied by the small sample correction factor ((N – kp)/N)=0.9361, where N (=313) is the number of observations, k (=5) is the number of lag length and p (=4)is the number of the endogenous variables, see Cheung and Lai (1993). Consequently, λmax =- (N-kp) ln(1- Dr). (2) The source is Osterwald-Lenum (1992), Table 1, p. 468. (3) Trace has been multiplied by the small sample correction factor (N – kp)/N, see Cheung and Lai P (1993). Consequently, Trace test = -(N- kp) ln(1 - D i ). Both Trace and λmax tests were developed in ∑ i = r +1 Johansen and Juselius (1991). (4) The source is Johansen (1995a), Table 15.2, p. 215. * The model includes constant and a vector of exogenous short-run dummy variables DUMt = (Post75t, Post78t, Post81t, Post97t, INOV76t, INOV80t, Oct87t, Asiat, Bat, GSTt, Revisiont, Inftart, Freet, Naftat, Ntart, Zerot, St). u is the disturbance term which is assumed to be white noise with zero mean. Ba = 1 in November 1981 and after, zero otherwise. GST = 1 in January 1991 and zero otherwise. Revision = 1 in August 1983 and after and zero otherwise. Inftar = 1 for February 1991 and after and zero, otherwise. Free = 1 for January 1991 and after, zero otherwise. Nafta = 1 for January 1994 and after, zero otherwise. Ntar = 1 for the October 1982 and after and zero, otherwise. Zero = 0 before June 1992 and one after June 1994. Starting June 1992 it increases by 0.20 every six months to get a value of one in July 1994. S includes 11 centered seasonal dummies. For the definition of other dummy variables see Footnote to Table 3. ** LM(1) and LM(4) are one and four-order Lagrangian Multiplier test for autocorrelation, respectively (Godfrey (1988)). 54 H0=r Table 5: Tests of the Cointegration RankModel 2: Without Any Policy Dummy Variable* Period 1975:Jan-2001:June (3) (1) Trace90 Trace95(4) λmax λmax90 λmax95(2) Trace 0 52.96 25.51 40.30 151.79 97.17 101.84 1 37.89 21.74 34.40 98.83 71.66 75.74 2 29.61 18.03 28.14 60.94 49.92 53.42 3 22.82 14.09 22.00 31.32 31.88 34.80 4 5.28 10.29 15.67 8.51 17.79 19.99 5 3.49 7.50 9.24 3.49 7.50 9.13 Diagnostic tests**: LM(1) p-value = 0.10 LM(4) p-value = 0.76 Normality p-value = 0.00 (1) λmax has been adjusted to correct a possible small sample bias error. Namely, λmax has been multiplied by the small sample correction factor ((N – kp)/N)=0.88, where N (=312) is the number of observations, k (=6) is the number of lag length and p (=6)is the number of the endogenous variables, see Cheung and Lai (1993). Consequently, λmax =- (N-kp) ln(1- Dr). (2) The source is Osterwald-Lenum (1992), Table 1, p. 467. (3) Trace has been multiplied by the small sample correction factor (N – kp)/N, see Cheung and Lai P (1993). Consequently, Trace test = -(N- kp) ln(1 - D i ). Both Trace and λmax tests were developed in ∑ i = r +1 Johansen and Juselius (1991). (4) The source is Johansen (1995a), Table 15.2, p. 215. * The model includes constant and a vector of exogenous short-run dummy variables DUMt = (Post75t, Post78t, Post81t, Post97t, INOV76t, INOV80t, Oct87t, Asiat, St). u is the disturbance term which is assumed to be white noise with zero mean. For the definition of dummy variables see Footnote to Table 3. ** LM(1) and LM(4) are one and four-order Lagrangian Multiplier test for autocorrelation, respectively (Godfrey (1988)). 55 H0=r Table 6: Tests of the Cointegration RankModel 2: With All Policy Dummy Variables* Period 1975:Jan-2001:June (3) (1) Trace90 Trace95(4) λmax λmax90 λmax95(2) Trace 0 51.56 25.51 40.30 155.14 97.17 101.84 1 39.68 21.74 34.40 108.59 71.66 75.74 2 36.56 18.03 28.14 63.91 49.92 53.42 3 23.15 14.09 22.00 27.35 31.88 34.80 4 2.71 10.29 15.67 4.20 17.79 19.99 5 1.50 7.50 9.24 1.50 7.50 9.13 Diagnostic tests**: LM(1) p-value = 0.48 LM(4) p-value = 0.75 Normality p-value = 0.00 (1) λmax has been adjusted to correct a possible small sample bias error. Namely, λmax has been multiplied by the small sample correction factor ((N – kp)/N)=0.88, where N (=312) is the number of observations, k (=6) is the number of lag length and p (=6)is the number of the endogenous variables, see Cheung and Lai (1993). Consequently, λmax =- (N-kp) ln(1- Dr). (2) The source is Osterwald-Lenum (1992), Table 1, p. 467. (3) Trace has been multiplied by the small sample correction factor (N – kp)/N, see Cheung and Lai P (1993). Consequently, Trace test = -(N- kp) ln(1 - D i ). Both Trace and λmax tests were developed in ∑ i = r +1 Johansen and Juselius (1991). (4) The source is Johansen (1995a), Table 15.2, p. 215. * The model includes constant and a vector of exogenous short-run dummy variables DUMt = (Post75t, Post78t, Post81t, Post97t, INOV76t, INOV80t, Oct87t, Asiat, Bat, GSTt, Revisiont, Inftart, Freet, Naftat, Ntart, Zerot, St). u is the disturbance term which is assumed to be white noise with zero mean. For the definition of dummy variables see Footnote to tables 3 and 4. ** LM(1) and LM(4) are one and four-order Lagrangian Multiplier test for autocorrelation, respectively (Godfrey (1988)). 56 Table 7*: Long-Run Relationships Maximum Likelihood Estimation Results Dependent Variable: Log of Real M1 Description C lrindp cpr lrtse lrex ccpr Model 1- Standard errors are in brackets No Policy Dummy Variable: r=2, Unrestricted** 16.91 -1.29 -0.12 1.21 No Policy Dummy Variable: r=2, Unrestricted** 39.59 4.66 -0.03 -1.02 No Policy Dummy Variable: 29.26 -1.39 -0.98 r=2, Restricted Equation*** (4.44) (0.45) (0.16) All Policy Dummy Variables: r=1 ** 2.75 0.21 -0.09 0.63 Model 2- Standard errors are in brackets No Policy Dummy Variable: r=3, Unrestricted** 8.78 -0.42 0.37 0.91 -0.57 -0.47 No Policy Dummy Variable: r=3, Unrestricted** -32.70 3.85 0.12 -0.60 0.10 -0.13 No Policy Dummy Variable: r=3, Unrestricted** -29.11 2.88 4.14 2.27 -10.40 -4.10 No Policy Dummy Variable: 0.49 -0.04 0.61 -0.56 -0.05 r=3, Restricted Equation**** (0.04) (0.09) (0.13) (0.33) (0.10) All Policy Dummy Variable: r=3, Unrestricted** 23.12 -1.80 1.27 1.03 -0.77 -1.42 All Policy Dummy Variable: r=3, Unrestricted** -8.95 1.42 -0.21 0.31 -0.16 0.13 All Policy Dummy Variable: r=3, Unrestricted** -78.22 8.49 1.56 1.17 -4.97 -1.54 All Policy Dummy Variables: 0.53 -0.04 0.54 -0.44 -0.06 r=3, Restricted Equation ***** (0.03) (0.08) (0.12) (0.41) (0.08) * lrm is the log of the real M1, lrtse is the log of the real TSE 300 stock index, lrindp is the log of real industrial production, where all deflated at Consumer Price Index (CPI). cpr is one-month corporate paper rate, lrex is the log real exchange rate, ccpr is the covered one-month U.S. corporate paper rate and r is the cointegration rank. ** Since the equation is an unrestricted no standard error can be estimated for any coefficient. *** The other restricted equation is: lrtset = 0.70 (0.10) lrindpt – 0.49 (0.09) cprt. With these two restrictions the system is identified, and according to Chi-squared = 2.79, with p-value = 0.09, we can not reject the restrictions. ****. The other two restricted equations are: The one-month Canada-U.S. cover interest parity, cprt = 0.22 (0.14) + ccprt, and lrtset = - 29.12 (3.81) + 2.99 (0.35) lrindpt + 0.07 (0.02) cprt. With these three restrictions the system is identified, and according to Chi-squared = 9.40, with p-value = 0.05, we can not reject the restrictions. *****. The other two restricted equations are: The one-month Canada-U.S. cover interest parity, cprt = 0.437 (0.07) + ccprt, and lrtset = 38.04 (5.94) + 3.83 (0.57) lrindpt – 0.08 (0.03) cprt. With these three restrictions the system is identified, and according to Chi-squared = 3.85, with p-value = 0.43, we cannot reject the restrictions. 57 Table 8*: Long-Run Relationships Stock and Watson’s (1993) Dynamic OLS Results Dependent Variable: Log of Real M1(lrm) Description C lrindp cpr lrtse lrex ccpr Model 1 (Standard error-adjusted for long-run variance in brackets)** No Policy Dummy Variable: 1.76 0.61 -0.02 0.52 Wald statistic = 88.95 (p-value=0.00) (4.30) (0.46) (0.01) (0.20) All Policy Dummy Variables: -2.57 0.73 -0.02 0.39 Wald statistic = 69.10 (p-value=0.00) (2.90) (0.31) (0.01) (0.11) Model 2 (Standard error-adjusted for long-run variance in brackets)*** No Policy Dummy Variable: -1.12 0.56 0.01 0.41 0.41 -0.03 Wald statistic = 239 (p-value=0.00) (4.20) (0.45) (0.10) (0.19) (0.34) (0.11) All Policy Dummy Variables: -3.02 0.77 -0.5 0.37 0.10 0.03 Wald statistic = 86.49 (p-value=0.00) (3.12) (0.32) (0.07) (0.11) (0.31) (0.07) * lrm is the log of the real M1, lrtse is the log of the real TSE 300 stock index, lrindp is the log of real industrial production, where all deflated at Consumer Price Index (CPI). cpr is one-month corporate paper rate. lrex is the log of real exchange rate and ccpr is the covered one-month U.S. corporate paper rate. ** Stock and Watson’s (1993) test (DOLS) is based on the following regression: lrmt = β0 + β1 lrindpt + β2 cprt + β3 lrtset + δ1(L) ∆lrindpt + δ2(L) ∆cprt + δ3(L) ∆lrtset + constant + DUMt’ α + ut,, where δi(L), for i=1 to 3, has three leads and lags as suggested by Stock and Watson for the number of observations of 300 or more. DUM is a vector of dummy variables and α is a vector of coefficients. In the absence of policy dummies DUMt = (Post75t, Post78t, Post81t, Post97t, INOV76t, INOV80t, Oct87t, Asiat, St) and with policy dummies DUM also includes Bat, GSTt, Revisiont, Inftart, Freet, Naftat, Ntart, Zerot. u is the disturbance term which is assumed to be white noise with zero mean. For the definition of dummy variables see Footnote to tables 3 and 4. *** DOLS for Model 2 is based on the following regression: lrmt = β0 + β1 lrindpt + β2 cprt + β3 lrtset + β4 lrext + β5 ccprt + δ1(L) ∆lrindpt + δ2(L) ∆cprt + δ3(L) ∆lrtset + δ4(L) ∆lrext + δ5(L) ∆ccprt + constant + DUMt’ α + ut,, where δi(L), for i= 1 to 5, has three leads and lags as suggested by Stock and Watson for the number of observations of 300 or more. DUM is a vector of dummy variables and α is a vector of coefficients. In the absence of policy dummies DUMt = (Post75t, Post78t, Post81t, Post97t, INOV76t, INOV80t, Oct87t, Asiat, St) and with policy dummies DUM also includes Bat, GSTt, Revisiont, Inftart, Freet, Naftat, Ntart, Zerot. u is the disturbance term which is assumed to be white noise with zero mean. 58 Table 9*: Error Correction: Model 1-No Policy Dummy Variable Dependent Variable = ∆lrm Variable Coefficient Standard Error Hansen’s (1992) stability Li test (5% critical value=0.47) ∆lrindp t-4 0.0001 0.00002 0.22 ∆cpr t-1 -0.0002 0.0001 0.03 ∆lrtse t-2 0.07 0.02 0.05 ∆lrmt-1 -0.18 0.05 0.25 ∆lrmt-2 -0.17 0.05 0.04 ∆lrmt-3 -0.11 0.04 0.10 ∆lrmt-5 -0.11 0.04 0.12 ECt-1 -0.0002 0.00003 0.01 Asiat 0.03 0.01 0.002 Post81t 0.04 0.01 0.002 Post97t -0.03 0.01 0.003 Trendt 0.000001 0.0000001 0.07 Septt -0.02 0.0004 0.17 Octt -0.02 0.001 0.37 Novt -0.05 0.001 0.64 Dect 0.03 0.0004 0.77 N8112t 0.08 0.02 ∆lrm was adjusted for theses dummy variables to avoid N9904t -0.06 0.02 non-invertible matrix Hansen’s (1992) stability Li test on variance of the ECM = 0.23 Joint (coefficients and the error variance) Hansen’s (1992) stability Lc test = 4.21 > 3.95 = 5% critical value(df=17) *. Period=1975(Jan)-2001(June) while the first 12 observations were reserved for the lagged values, ∆ means the first difference, Mean of dependent variable=0.002. ∆lrm is the change of log of the real M1, ∆lrtse is the change of log of the real TSE 300 stock index, ∆lrindp is the change of log of real industrial production, where all deflated at Consumer Price Index (CPI). ∆cpr is the change of one-month corporate paper rate and EC is the error correction term. Trend is a linear time trend. Sept, Oct, Nov and Dec, are dummy variables for the month of September, October, November and December, respectively. For example, Dec = 1 in December and zero, otherwise. N8112t and N9904t are dummy variables to capture the outliers observed in December 1981 and April 1999. These dummy variables have a value of one in December 1981 and April 1999, respectively, and zero, otherwise. The estimation method is Instrumental variable OLS. The instrument is one lagged error term. R 2=0.67, σ=0.015, DW=2.14, Godfrey(6)=1.08 (significance level=0.37), White=125 (significance level=0.99), ARCH(5)=9.37 (significance level=0.10), RESET(3)=0.33 (significance level=0.80) and Normality(χ2=2)=1.11 (significance level=0.57). 59 Table 10*: Error Correction: Model 1 -All Policy Dummy Variables: Dependent Variable = ∆lrm Variable Coefficient Standard Error Hansen’s (1992) stability Li test (5% critical value=0.47) ∆lrindp t-4 0.0001 0.00002 0.34 ∆cpr t-1 -0.003 0.001 0.02 (∆cpr)(Free) t-5 0.006 0.002 0.03 ∆lrtset-1 0.04 0.02 0.11 (∆lrtse)(Nafta) t-5 0.51 0.21 0.05 (∆lrtse)(Zero) t-5 -0.51 0.21 0.05 ∆lrmt-1 -0.32 0.05 0.03 ∆lrmt-2 -0.22 0.04 0.16 ∆lrmt-3 -0.11 0.04 0.12 ∆lrmt-4 -0.22 0.04 0.07 ∆lrmt-5 -0.11 0.04 0.49 ∆lrmt-8 -0.08 0.03 0.25 (∆lrm)(Free) t-4 0.21 0.03 0.13 (∆lrm)(Nafta) t-6 -0.69 0.30 0.06 (∆lrm)(Zero) t-6 0.77 0.31 0.06 ECt-1 -0.05 0.007 0.03 t-6 0.07 0.02 0.08 (EC)3t-6 0.11 0.04 0.06 -0.15 0.04 0.04 -0.05 0.02 0.04 -0.19 0.08 0.03 Asiat 0.02 0.01 0.002 Post75t 0.03 0.01 ∆lrm was adjusted for this dummy to avoid non-invertible matrix Post81t 0.03 0.01 0.002 Post97t -0.03 0.01 0.003 Revisiont -0.01 0.003 0.08 Mayt 0.01 0.003 0.14 Septt -0.02 0.004 0.34 Octt -0.02 0.01 0.50 Novt -0.05 0.01 0.43 (EC) (EC) 2 4 t-6 (EC)(EC)4t-1 (EC)(EC) 4 t-6 60 Table 10*: Continues Variable Coefficient Standard Error Hansen’s (1992) stability Li test (5% critical value=0.47) Dect 0.03 0.004 0.52 N8112t 0.06 0.02 ∆lrm was adjusted for this dummy to avoid non-invertible matrix N9904t -0.06 0.01 ∆lrm was adjusted for this dummy to avoid non-invertible matrix Hansen’s (1992) stability Li test on variance of the ECM = 0.89 Joint (coefficients and the error variance) Hansen’s (1992) stability Lc test = 5.25 < 6.61** = 5% critical value(df=31) * Period=1975(Jan)-2001(June) while the first 12 observations were reserved for the lagged values, ∆ means the first difference, Mean of dependent variable=0.002. ∆lrm is the change of log of the real M1, ∆lrtse is the change of log of the real TSE 300 stock index, ∆lrindp is the change of log of real industrial production, where all deflated at Consumer Price Index (CPI). ∆cpr is the change of one-month corporate paper rate and EC is the error correction term. May = 1 in May and zero, otherwise. For the definition of other dummy variables see tables 3 and 4. The estimation method is OLS instrumental technique. The instrument is one lagged error term. R 2=0.74, σ=0.014, DW=2.11, Godfrey(6)=1.45 (significance level=0.19), White=310 (significance level=1.00), ARCH(5)=3.32 (significance level=0.65), RESET(3)=0.48 (significance level=0.70) and Normality(χ2=2)=0.04 (significance level=0.98). ** This number was interpolated from Hansen’s (1992) critical values which are available for df=20. 61 Table 11*: Error Correction: Model 2-No Policy Dummy Variable Dependent Variable = ∆lrm Variable Coefficient Standard Error Hansen’s (1992) stability Li test (5% critical value=0.47) Constant 0.005 0.001 0.14 ∆lrindp t-4 0.0001 0.00002 0.31 ∆cpr t-1 -0.003 0.001 0.02 ∆lrmt-1 -0.14 0.05 0.15 ∆lrmt-3 -0.10 0.04 0.24 ∆lrmt-4 -0.09 0.04 0.35 ∆lrmt-5 -0.09 0.04 0.05 ∆lrext-2 -0.20 0.06 0.08 ECt-1 -0.02 0.003 0.15 EClrtset-1 0.01 0.004 0.13 EClrtset-5 0.03 0.01 0.06 -0.04 0.01 0.08 -0.02 0.01 0.19 Asiat 0.03 0.01 0.002 Post81t 0.04 0.01 0.002 Post97t -0.03 0.01 0.003 Octt -0.02 0.001 0.67 Novt -0.05 0.001 0.43 Dect 0.03 0.0004 0.67 N8112t 0.08 0.02 ∆lrm was adjusted for theses dummy variables to avoid N9904t -0.06 0.02 non-invertible matrix EClrtset-6 (EClrtset-8) 2 Hansen’s (1992) stability Li test on variance of the ECM = 0.85 Joint (coefficients and the error variance) Hansen’s (1992) stability Lc test = 5.89 > 4.52 = 5% critical value(df=20) Period=1975(Jan)-2001(June) while the first 12 observations were reserved for the lagged values. ∆lrex is the change of log real exchange rate and ∆ccpr is the change of covered one-month U.S. corporate paper rate. EClrtset (=lrtset - 0.70 lrindpt + 0.49 cprt) is the error correction term generated from the long-run log of real TSE relationship and EC is the error correction term. For definitions of the dummy and other variables see Footnote to tables 3 and 10. The estimation method is Instrumental variable OLS. The instrument for each of the error term is its one-lagged value. R 2=0.75, σ=0.013, DW=1.98, Godfrey(6)=0.99 (significance level=0.43), White=272 (significance level=1.00), ARCH(5)=3.30 (significance level=0.65), RESET(3)=0.35 (significance level=0.79) and Normality(χ2=2)=2.04 (significance level=0.36). 62 Table 12*: Error Correction: Model 2 -All Policy Dummy Variable: Dependent Variable = ∆lrm Variable Coefficient Standard Hansen’s (1992) stability Li test (5% critical value=0.47) Error ∆lrindp t-4 0.0001 0.00002 0.22 ( ∆lrindp)(Revision)t-2 0.0002 0.0001 0.13 ( ∆lrindp)(Ba)t-2 -0.0002 0.0001 0.12 ∆cpr t-1 -0.003 0.001 0.03 ∆lrtset 0.04 0.02 0.06 ∆lrtset-1 0.05 0.02 0.21 ∆lrtset-2 0.04 0.02 0.03 (∆lrtse)(Nafta) t-5 0.50 0.20 0.06 (∆lrtse)(Zero) t-5 -0.48 0.20 0.06 ∆lrext-1 -0.18 0.06 0.27 ∆lrmt-1 -0.33 0.05 0.06 ∆lrmt-2 -0.23 0.04 0.08 ∆lrmt-3 -0.14 0.04 0.18 ∆lrmt-4 -0.20 0.04 0.05 ∆lrmt-5 -0.12 0.04 0.41 ∆lrmt-8 -0.07 0.03 0.20 (∆lrm)(Free) t-4 0.17 0.06 0.08 ECt-1 -0.05 0.005 0.03 (EC)2t-6 0.05 0.01 0.04 (EC)3t-6 0.09 0.03 0.03 (EC)4t-6 -0.06 0.02 0.02 (EC)(EC)4t-6 -0.11 0.04 0.02 (ECcover)2t-1 -0.03 0.01 0.03 (ECcover)(ECcover)3t-1 0.07 0.03 0.04 Asiat 0.02 0.01 0.002 Post81t 0.03 0.01 0.002 Post97t -0.03 0.01 0.002 Revisiont -0.01 0.003 0.05 Mayt 0.01 0.003 0.28 Septt -0.02 0.004 0.25 63 Table 12*: Continues Variable Coefficient Standard Error Hansen’s (1992) stability Li test (5% critical value=0.47) Octt -0.02 0.005 0.51 Novt -0.05 0.004 0.57 Dect 0.03 0.004 0.57 N8112t 0.06 0.02 ∆lrm was adjusted for this dummy to avoid non-invertible matrix N9904t -0.06 0.01 ∆lrm was adjusted for this dummy to avoid non-invertible matrix Hansen’s (1992) stability Li test on variance of the ECM = 1.20 Joint (coefficients and the error variance) Hansen’s (1992) stability Lc test = 5.80 < 6.99** = 5% critical value(df=34) * Period=1975(Jan)-2001(June) the first 12 observations were reserved for the lagged values. EC is the error correction term and ECcovert (=cprt - 0.22 - ccprt) is the one-month Canada-U.S. long-run covered corporate paper rate error correction term. May = 1 in May and zero, otherwise. For the definition of other dummy variables as well as other variables see tables 3, 4 and 11. The estimation method is OLS instrumental technique. The instrument is one lagged value of the each error term. R 2=0.74, σ=0.014, DW=2.11, Godfrey(5)=1.45 (significance level=0.19), White=310 (significance level=1.00), ARCH(5)=3.32 (significance level=0.65), RESET=0.48 (significance level=0.70) and Normality(χ2=2)=0.04 (significance level=0.98). ** This number was interpolated from Hansen’s (1992) critical values which are available for df=20. 64 Table 13*: Marginal Model: Dependent Variable = ∆lrtse Variable Coefficient Standard Error constant 0.01 0.003 ∆lrindp t-1 -0.0003 0.0003 ∆lrindpt-2 -0.0001 0.00003 ( ∆lrindp)(spra)t-1 0.0002 0.0001 ( ∆lrindp)(spra)t-12 -0.0001 0.00005 ( ∆lrcomp)(spra)t-7 0.25 0.12 ∆onr t-8 -0.008 0.002 ∆onr t-9 -0.007 0.002 ∆lrcp t-3 -2.04 0.69 ∆lrsp t-12 0.19 0.07 (∆lrsp)(Zero) t-1 -0.25 0.11 (∆lrsp)(Ba) t-3 0.12 0.06 ∆lrtset-12 -0.28 0.06 intdift-9 -0.006 0.002 (intdif)(Ba) t-9 0.01 0.003 (intdif)(Ba) t-10 -0.009 0.003 (∆lex)(spra) t-1 -0.62 0.20 (∆lex)(spra) t-7 -0.51 0.23 Oct87t -0.31 0.01 N803t -0.21 0.01 N988t -0.19 0.01 * Period=1975(Jan)-2001(June) while the first 12 observations were reserved for the lagged values, ∆ means the first difference, Mean of dependent variable=0.003. ∆lrtse is the change of log of the real TSE 300 stock index, ∆lrindp is the change of log of real industrial production and ∆lrcomp is the change of log of real commodity price index where all deflated at Consumer Price Index (CPI). ∆onr is the change of overnight interest rate, ∆lrcp is the change of the log of Canada-U.S. Consumer Price Index ratio, intdif is the difference between the Canadian overnight and Fed Fund rates and ∆lex is the change in the log of exchange rate. ∆lrsp is the change of the log of the real S&P 500 index. The index was multiplied by the exchange rate and then deflated by CPI. spra = 1 in June 1985 and after and zero, otherwise. N803 and N988 are dummy variables to capture the outliers observed in March 1980 and August 1998. These dummy variables have a value of one in March 1980 and August 1998, respectively, and zero, otherwise. For the definition of other dummy variables see tables 3 and 4. The estimation method is the robusterror OLS estimation technique. The instrument is one lagged value of the each error term. R 2=0.38, σ=0.04, DW=1.95, Godfrey(6)=0.68 (significance level=0.66), White=154 (significance level=1.00), ARCH(5)=27.91 (significance level=0.00), RESET=0.11 (significance level=0.96) and Normality(χ2=2)=3.35 (significance level=0.19). 65 Table 14*: Superexogeneity Tests Variable (Z = ∆lrtse) Z – ηZ σZZ (Z – ηZ) ( η Z) 2 ( η Z) 3 σZZ ηZ σZZ (ηZ)2 F(1, 301=Usable observations) (P-Value) Model 2 All Policy Variables 0.17 (0.68) 0.07 (0.78) 0.28 (0.60) 0.50 (0.48) 0.32 (0.57) 0.09 (0.77) 0.45 (0.50) DevZ 1.26 (0.21) F-Statistics (8, 301) on coefficients of all above variables 0.32 (0.96) * ∆lrtse is the change of log of the real TSE 300 stock index. ηZ is the conditional mean of Z and σZZ is the conditional variance of Z. ∆lrm t = α0 + ψ0 Zt + (δ0 – ψ0) (Zt – ηZt) + δ1 σtZZ (Zt – ηZt) + ψ1 (ηZ)2 + ψ2 (ηZ)3 + ψ3 σtZZ ηZ + ψ4 σtZZ (ηZ)2 + ψ5 (σtZZ)2ηZ + z’tγ + ut, where the vector z includes past values of ∆lrm t, Zt, and current and past values of other valid conditioning variables. The estimation method is OLS estimation technique: R 2=0.74, σ=0.01, DW=2.01, Godfrey(6)=0.71 (significance level=0.64), White=115 (significance level=0.99), ARCH(5)=3.81 (significance level=0.58), RESET=0.40 (significance level=0.75) and Normality(χ2=2)=2.34 (significance level=0.31). (σZZ )2ηZ 66 Table 15: Encompassing Tests Models with policy dummy variables Model 1 Model 2 0.014 0.014 11.21E 16.28 0.26 0.25 E 0.015 0.015 21.99E 22.34 0.40 0.38E 0.024 0.022 E 43.79 35.70 E 0.54 0.51 E Descriptions of the tests Ex-post RMS* Ex-post RMS percent error Ex-post Theil’s inequality coefficient (U) ** Ex-ante (one-year) RMS*** Ex-ante (one-year) RMS percent error*** Ex-ante (one-year) Theil’s inequality coefficient (U)*** Ex-ante (five-year) RMS**** Ex-ante (five -year) RMS percent error**** Ex-ante (five -year) Theil’s inequality coefficient (U)**** Minimal Nesting Model: Cox ‘s (1961, 1962) F-squared (P-value) The Null: Model 1 encompasses Model 2 Model 2 encompasses Model 1 Pesaran’s (1974) N test***** 2001:6 * RMS is the root-mean-square prediction error, RMS= 1 / 306 ∑ (∆lrm 7.95 (0.00) -1553 f − ∆lrma ) 2 2.21 (0.02) E -1801 E , where ∆lrmf is the t =1976:1 a fitted value and ∆lrm is the actual value of ∆lrm. Note that the first 12 observations were reserved for the lagged values. ** If Theil’s inequality coefficient U=0 there is a perfect fit, and if U=1 there is worse possible fit, see Theil (1965, pp. 31-37 and 1966, pp. 26-36). *** The model estimated on 1975:Jan-2000:May period (while the first 12 observations were reserved for the lagged values) and the estimated model was used to forecast the real growth of money demand for 2000:June-2001:May period. **** The model estimated on 1975:Jan-1995:May period (while the first 12 observations were reserved for the lagged values) and the estimated model was used to forecast 1995:June-2001:May period. ***** A significant negative value of N means a rejection of the alternative model in favor of the current model. E means the model in this column encompasses the other model. 67 Figure 1 Long-Run Stability Test: Model 1-No Policy T esto fkn o w nb etaeq . tob eta(t) 2.25 B E T A _Z B E T A _R 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 0.00 1985 1987 1989 1991 1993 1isth e5 % s ig n ific a n c ele v e l 1995 1997 1999 2001 68 Figure 2 Long-Run Stability Test: Model 1 All Policy Testofknownbetaeq. tobeta(t) 3.0 BETA_Z BETA_R 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 1985 1987 1989 1991 1993 1isthe5%significancelevel 1995 1997 1999 2001 69 Figure 3 Long-Run Stability Test: Model 2-No Policy T esto fkn o w nb etaeq . tob eta(t) 3.5 B E T A _Z B E T A _R 3.0 2.5 2.0 1.5 1.0 0.5 0.0 1985 1987 1989 1991 1993 1isth e5 % s ig n ific a n c ele v e l 1995 1997 1999 2001 70 Figure 4 Long-Run Stability Test: Model 2 All Policy T esto fkn o w nb etaeq . tob eta(t) 4.0 B E T A _Z B E T A _R 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 1985 1987 1989 1991 1993 1isth e5 % s ig n ific a n c ele v e l 1995 1997 1999 2001