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: akia@emory.edu
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
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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