Forward-Looking Agents and Macroeconomic Determinants of
the Equity Price in a Small Open Economy
Amir Kia*
Department of Economics, Emory University
Atlanta, GA 30322-2240
U.S.A.
E-mail: akia@emory.edu
Tel.: (404) 727-7536
Fax: (404) 727-4639
April 2001
* I would like to thank seminar participants at Emory University for their helpful
comments.
Forward-Looking Agents and Macroeconomic Determinants of
the Equity Price in a Small Open Economy
Abstract:
A macro-determinant model of stock price using monthly data on Canadian and
U.S. markets is estimated. It is found that the commodity price is also an important
component of stock prices. The economic agents in the stock markets are forward looking
and their reactions to equilibrium errors are asymmetric. It is also found that deviations
from fundamental price are short-lived. Furthermore, among long-run macrodeterminants of stock price, at least two long-run stationary relationships exist:
Uncovered Interest Parity and a long-run Canadian Monetary Policy Reaction function.
Key words: stock price, macro-variables, forward-looking agents, superexogeneity, weak
exogeneity, invariance, variation-free, bubbles
JEL classification = G120, G140 and G190
Forward-Looking Agents and Macroeconomic Determinants of
the Equity Price in a Small Open Economy
I.
Introduction
Numerous studies have analyzed the macro-determinants of stock returns and
volatilities. Macro-variables used in these studies include money supply, Consumer Price
Index, industrial production, news, the slope of the yield curve, as well as exchange,
inflation and interest rates. The impact of these variables on stock prices was found to be
often significant. For instance, see Hamao (1988), Schwert (1989), Mukherjee and Naka
(1995), Koutoulas and Kryzanowski (1996), Ely and Robinson (1997), Cheung and Lai
(1999) and Binswanger (2000). Further extension of the literature includes studies that
also incorporate foreign macro-variables as well as stock prices, e.g., Koutmos and Booth
(1995), Ammer and Mei (1996), Kearney (1998), Gjerde and Sttem (1999), and Cheung
and Lai (1999).
To the best of our knowledge, not much attention was given to resourcedependent internationally integrated stock markets. For example, in none of the existing
studies, the impact of commodity prices is incorporated. Moreover, macro-determinant
models of stock price reflect the fact that agents use macro-variables to forecast the future
stream of dividend payments. However, none of the existing studies in this literature
verified whether the model that is used reflects the behavior of forward-looking agents.
In fact, three decades ago, Elton and Gruber (1970), studying the ex-dividend
behavior of common stock, found that market participants incorporate future earnings
information and recently Francis and Leachman (1998) show market participants in U.S.,
U.K., Germany and Japan stock markets are forward looking in their international
portfolio diversification. However, this important investigation was ignored in the
macro-determinant stock price literature. This investigation specially becomes essential
when ad hoc models are used to explain the behavior of market participants in evaluating
asset prices in terms of expected future payments.
Finally, if speculators ignore a small deviation from the equilibrium price while
reacting drastically to large deviations, their behaviors are asymmetric. There is indeed a
strong possibility in a small and highly integrated country, like Canada, that speculators
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
2
react differently to different forms and sizes of equilibrium errors. Kia (1996a) evidences
such events in the Canadian money market. The existing literature completely overlooks
this aspect of the financial markets.
The purpose of this paper is to extend the literature, taking into consideration the
above facts, in the following way:
The monthly data on Canadian and U.S. stock markets for the period 1975-1999
are used. A macro-determinant stock price model for a small and open-resource-oriented
country is developed and estimated. The superexogeneity tests are used to examine
whether the model reflects the fact that agents are forward looking.
It is found that the commodity price index, along with other macro-determinants,
is in fact an important component of the stock price determination. The agents in the
stock markets are forward looking and their reactions to equilibrium errors are
asymmetric. Namely, they may react differently to small deviations from the equilibrium
price than large ones. It is also found that deviations from fundamental price (i.e.,
bubbles) are short-lived. Some long-run hypotheses are also tested. It is found that among
macro-determinants of stock price, at least two long-run stationary relationships exist.
These relationships include Uncovered Interest Parity and a long-run Canadian Monetary
Policy Reaction function.
The following section deals with the development of the theoretical model as well
as superexogeneity and invariance hypothesis for stock prices. Section III describes the
data and the long-run empirical methodology and results. Section IV is devoted to
conditional and marginal models as well as superexogeneity results. The final section
provides some concluding remarks.
II.
The Theoretical Model
In an exchange-economy asset-pricing model, Lucas (1978) finds the equilibrium
price of an asset is the expected, discounted, present value of its real dividend stream,
conditional on current information. A close approximation of the model is
Pt = Et [(1+rt)-1(Pt+1 + Dt+1)]
(1)
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
3
where Pt is the stock price at time t, Dt+1 is the dividend paid to the shareholders between t
and t+1, 0<(1+rt)-1<1 is the discount factor and E denotes the mathematical expectation
operator for information at time t. If the transversality condition, i.e.,
limn→∞ Et[(1+rt-n)-n (Pt+n)]=0, holds then the unique solution to Equation (1) is
∞
Pt = Et [ ∑ (1 + rt+i-1 ) -i (Dt+i) ]
i=1
(2)
Future dividends as well as discount rates are not observable. Consequently, we assume
that in a small, open and financially integrated economy, the discounted expected value of
future payments has the following function:
∞
Et [ ∑ (1 + rt+i-1 ) -i (Dt+i) ] = F(SPt, IPt, EXt, COMPt, PLt, Rt, PREMt, Rt-FRt,
i=1
PLt/FPLt, IPt/FIPt, zt)
(3)
where SPt is the foreign country stock price, IPt is the level of total industrial production,
EXt is the level of exchange rate (domestic currency value of a unit of foreign currency),
COMPt is the commodity price index (commodities produced in the domestic country
and sold abroad), PLt is the domestic price level, Rt is the domestic overnight interest
rate, PREMt is a measure for the risk premium (corporate paper minus Treasury Bill
rates), Rt-FRt is the domestic and foreign interest rates differential, PLt/FPLt is the ratio of
domestic to foreign price levels, IPt/FIPt is the ratio of domestic to foreign levels of total
industrial production, and zt includes past values of Pt and above-mentioned
macroeconomic variables as well as current and past values of other valid conditioning
variables.1
Substituting (3) in (2) yields
Pt = F(SPt, IPt, EXt, COMPt, PLt, Rt, PREMt, Rt-FRt, PLt/FPLt, IPt/FIPt, zt) (4)
Equation (4) is a modified version of Kearney’s (1998) model, which was tested
on Irish data. However, here we also included in the model the commodity price index,
the domestic price level relative to the foreign price level as well as a measure for the risk
premium, which reflects, among other things, attitudes of investors toward risk. In a
small, open and financially integrated economy one would expect stock markets to rally
as stock markets in the rest of the world or its largest trading partner. For example,
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
4
Canadian equity prices may move with U.S. equity prices as economic news in the U.S.
may also affect Canadian equity markets. 2
Furthermore, market psychology and speculative activities could lead stock
markets in Canada to move with the stock markets in the U.S. For example, a rally in the
U.S. stock markets and so higher equity prices will increase expectations of a higher
demand for Canadian exports through the wealth effect in the U.S. At the same time,
expectations of higher demand for Canadian exports lead to expectations of higher
corporate profits in Canada. This will increase demand for equity in Canada and result in
higher equity prices. Consequently, one would expect theoretically the sign of SPt in
Equation (4) to be positive. It should be noted that it is more appropriate for the foreign
stock price to be adjusted for the exchange rate. However, to avoid the introduction of an
extra stochastic variable in the system, we follow Kearney (1998) and Koutoulas and
Kryzanowski (1996) and allow the exchange rate to appear as a separate variable in the
equation.3
Moreover, in a small open economy with high capital mobility, cash flows (Dt+i),
as mentioned and shown by Kearney (1998) and others (see reference list given in
Kearney), are influenced by developments in the domestic macroeconomic variables like
the total level of industrial production, the price level, the exchange rate and interest
rates. For instance, a higher level of industrial production is associated with higher
corporate profits and cash flows. Consequently, it is expected theoretically for the
industrial production to have a positive relationship with the price of equity.
Furthermore, a higher exchange rate, which is associated with a lower foreign
currency price of the exports, results in an appreciation of the balance of trade, which
leads to higher corporate profits and cash flows. Consequently, a higher exchange rate is
expected to lead to a higher equity price. It should, of course, be mentioned that an
exchange rate appreciation could result in an improvement of the balance of trade if
Marshall-Lerner condition, a long-run condition, is satisfied. However, in the short term,
investors associate the deterioration of the domestic currency with a higher likelihood that
the central bank would raise the interest rate to defend the currency. Hence, the short-run
impact of the exchange rate appreciation on the equity price may be negative.
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
5
The weakness in the commodity price does hurt stock markets of a highly open
economy like Canada.4 Such a weakness can reduce corporate profits and lower
expectations of future cash flows. Consequently, one would expect a positive relationship
between the commodity and the stock prices. To the best of our knowledge, no study so
far incorporated the commodity price index in the determination of stock price or return.
Moreover, while a higher price level increases expectations of a future hike in
interest rates, it may also lead to higher offsetting cash flows. However, cash flows may
not rise at the same rate as the inflation rate, see Mukherjee and Naka (1995) and
references therein. Consequently, one would expect a negative relationship between the
level of price and the stock price. Furthermore, if stocks hedge against inflation, at least
in the long run, as it was shown by Kaul (1986), Ely and Robinson (1997), and Kia
(1997a, 1997b), then a positive relationship between stock price and the level of domestic
price may be expected. The overall impact of the price level on the stock price, therefore,
depends on the prevailing force. Following Ely and Robinson (1997), Kaul (1986) and
Kia (1997a, 1997b), we hypothesize the overall impact of the price is positive.
A higher domestic interest rate as well as the level of interest rate relative to
foreign interest rate is expected to have a positive impact on the investors’ subjective
discount rate. Furthermore, a higher interest rate is associated with expectations of lower
corporate profits. Both a higher subjective discount rate and expectations of lower
corporate profits result in a fall of the equity price. Furthermore, the more risk averse
investors are, the higher risk premium they will require and, therefore, the higher their
subjective discount rate will be. Consequently, we would expect the domestic level of
interest rate, and the domestic rate relative to foreign rate (interest rate differential) as
well as risk premium to have negative relationships with the stock price.
Cash flows are also influenced by the above macro-variables relative to their
foreign counterparts. For example, a higher domestic price relative to its international
level in a small open economy results in a deterioration of balance of trade and
expectations of a lower cash flow and, therefore, a lower stock price. Finally, if the
industrial production in the domestic country continuously outgrows its foreign
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
6
counterpart, rational investors expect a higher cash flow relative to the cash flow of
foreign stocks and a higher stock price.
Putting the above economic intuition and relationships together and following,
e.g., Darrat (1990), Mukherjee and Naka (1995), Ely and Robinson (1997) and Kearney
(1998) we will assume Equation (4) has the following explicit form:
∆log(Pt) = α0 + α1∆log(SPt) + α2 ∆log(IPt) + α3 ∆log(EXt) + α4 ∆log(COMPt)
+ α5 ∆log(PLt) + α6 ∆Rt + α7 (Rt - FRt) + α8 PREMt + α9 ∆log(PLt/FPLt)
+ α10 ∆log(IPt/FIPt) + z’tγ+ ut
(5)
where α’s and γ are constant coefficients, α1>0, α2>0, α3<0, α4>0, α5>0, α6<0, α7<0,
α8<0, α9<0, α10>0 and ∆ is the first difference notation. The vector z includes past values
of ∆log(Pt) and explanatory variables in Equation (5) as well as current and past values of
other valid conditioning variables. The error term ut is assumed to be white noise,
normally, identically and independently distributed.5
It is extremely important to mention that Equation (5) reflects the theoretical
behavioral Equation (2) if and only if it is a forward-looking relationship. Equation (5)
represents agents’ expectations on future dividend payments. Consequently, its
parameters are no longer invariant to the process of forcing variables as was mentioned
by Lucas (1976). Namely, at least one of the parameters varies with changes in the
expectation process. This requires that at least one of the variables in Equation (5) fails to
be superexogeneous in the sense of Engle et al. (1983) and Engle and Hendry (1993).
This important fact, to the best of our knowledge, was ignored in the literature of
macro-determinants of equity price.
To formulate superexogeneity and invariance hypothesis associated with
conditional model (5), let the set of variables Zt include all contemporaneous
macroeconomic variables in the conditional model and assume the information set It
includes the past values of ∆log (Pt) and Zt as well as the current and past values of other
valid conditioning variables included in zt. Define, respectively, the conditional moments
of ∆log (Pt) and Zt as ηPt=E(∆log(Pt)│It), ηZt=E(Zt│It), σtPP=E[(∆log(Pt) – ηPt)2│It] and
σtZZ=E[(Zt – ηZt )2│It], and let σtPZ=E[(∆log(Pt) – ηPt)(Z t – ηZt)│It]. Consider the joint
distribution of ∆log(Pt) and Zt conditional on information set It to be normally distributed
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
with mean
ηt=[ηPt,
ηZt]
7
 PP PZ 
σ σ .
and a non-constant error covariance matrix ∑ = 
 ZP ZZ 
σ σ

Then, following Engle et al. (1983), Engle and Hendry (1993) and Psaradakis and Sola
(1996), we can write the relationship between ∆log(Pt) and Zt as:
∆log(Pt) = α0 + ψ0 Zt + (δ0 - ψ0) (Zt - ηZt) + δ1 σtZZ (Zt - ηZt) + ψ1 (ηZt)2 +
ψ2 σtZZ + ψ3 σtZZ ηZt + ψ4 σtZZ (ηZt)2 + z’tγ + ut
(6)
where α0, ψ0, ψ1, ψ2, ψ3, ψ4, δ0 and δ1 are regression coefficients of ∆log(Pt) on Zt
conditional on z’tγ, and term ut is assumed to be, as before, white noise, normally,
identically and independently distributed.
Note that Zt includes some control/target variables (i.e., interest, exchange and
inflation rates) that are subject to policy interventions. Under the null of weak exogeneity,
δ0-ψ0=0. Under the null of invariance, ψ1=ψ2=ψ3=ψ4=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 these entire hypotheses are accepted the
equation will be reduced to Equation (5). However, in such a case Equation (5) will no
longer be an appropriate approximation for Equation (2). It should also be mentioned
“superexogeneity is sufficient but not a necessary condition for valid inference under
intervention” (Engle et al. (1983), p. 284). This is due to the fact that estimable models
with invariant parameters, but with no weakly exogenous variables are easily formulated.
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
III.
8
Data, Long-Run Empirical Methodology and Results
III.1 Data
We will test the model on monthly Canadian and U.S. data. All observations are
for the last day of the month. The sample period is January 1975-December 1999. All
data are obtained from Statistics Canada CANSIM database. Domestic stock markets are
represented by all stocks traded on the Toronto Stock Exchange, and so the TSE 300
Composite Index is considered to be the price of domestic stock markets. The Standard
and Poor 500 Index is a representative of the price of foreign stock markets. Table 1
reports descriptions of the variables and their summary statistics.
Table 1 about here
As stationary test results reported in Table 2 indicate, all variables, except ‘prem’
and the interest rate differential ‘ronff’, are integrated of degree one (non-stationary).
They are, however, first-difference stationary. Consequently, we will first verify if a longrun relationship exists between the level of stock price in Canada and levels of its
determinants, as specified in Equation (5).6 If cointegrating relations, conditional on stock
markets in the U.S., exist between the Canadian stock market and the macroeconomic
variables influencing the market, then short-term departures from equilibrium relationship
between these variables (including stock prices) are eliminated over the long run by
market forces and monetary or fiscal policies. 7
Table 2 about here
Note that the existence of cointegrating relationships between the levels of
variables in Equation (5) indicates that valid error correction models (ECM) exist.
However, the existence of an ECM in stock price determinants does not only indicate
economic variables adjust to past equilibrium errors, but as explained in the previous
section, it may also be due to changes of economic agents’ forecasts of future dividend
payments. To test this fact we need to test the superexogeneity of these variables. The
rejection of the superexogeneity test implies ECMs are also forward looking.
III.2 Long-Run Empirical Methodology
We analyze a p-dimensional vector autoregressive model with Gaussian errors of
the form
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
9
X t = A1 X t-1+… + Ak X t-k+ µ + φ DUMt + ut, ut ~niid(0, Σ), t = 1, …, N
(7)
where X t = [ltset, lindpt, lext, lcompt , lcpict, onrt, ronfft, premt, lrcpt, lrindpcust], µ is p×1
constant vector representing a linear trend in the system. ltse is the logarithm of the
TSE 300 index, lindp is the logarithm of total industrial production, lex is the logarithm
of exchange rate, lcomp is the logarithm of the commodity price index, lcpic is the
logarithm of the Consumer Price Index in Canada, onr is the overnight rate, ronff is the
overnight and Fed Fund rates differentials, and prem is the monthly corporate and
TB rates differentials, lrcp is the logarithm of ratio of Canada to U.S. consumer price
indexes and lrindpcus is the logarithm of ratio of industrial production in Canada and
U.S.
The
p-dimensional
Gaussian
Xt
is
modeled
conditionally
on
DUMt = (M1t, …, M11t, Oct87t, AS97t, lspt), where M’s are centered monthly seasonal
dummy variables and Oct87 is a dummy variable used to capture the impact of the
October 87 stock market crisis. It is equal to one in October 87 and zero otherwise.
AS97 is a dummy variable, which is equal to one for October and November 1997
observations, and is zero, otherwise.8 lsp is the logarithm of S&P 500 Index. The
parameters A1,…, Ak, φ, and Σ are assumed to vary without restriction. The error
correction form of the model is
∆X t = Γ1 ∆X t-1+… + Γk-1 ∆X t-k+1+ ΠX t-k + µ + φ DUMt + ut, t = 1, …, N (8)
where ∆ as before is the first difference notation, the first k data points X t-1,…, X 0 are
considered fixed and the likelihood function is calculated for given values of these data
points. The parameters Γ1,...,Γk-1 and Π are also assumed to vary without restriction.
However, the hypotheses of interest are formulated as restriction on Π.
In determining a long-run relation between stock markets in Canada and
macroeconomic variables, conditional on stock markets in the U.S., we need to test
whether stock prices contribute to the cointegrating relation. If Π has a reduced rank we
want to test whether some combinations of Xt have stationary distributions for a suitable
choice of initial distribution, while others are non-stationary. Consequently, we need to
find the rank of Π, i.e., r.
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
10
In our analysis throughout the paper, we will employ CATS in RATS. In
determining the lag length one should verify if the lag length is sufficient to get white
noise residuals. As it was recommended by Hansen and Juselius (1995, p. 26), set p=r in
Equation (8) and test for autocorrelation. 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). Both tests were adjusted in
order to correct a potential bias possibly generated by small sample error, see footnote to
Table 3 for the formulas. Table 3 reports the result of λmax and Trace tests for lag length of
four months (k=4). According to diagnostic tests reported in the table there is no
autocorrelation. 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). The λmax test rejects r ≤2 at
5% level while we can not reject r ≤3, implying that r=3. According to Trace test,
however, we reject the null hypothesis of r ≤5 at 5% level while we can not reject the null
hypothesis of r ≤6, implying that r=6.
Table 3 about here
Furthermore, we estimated eigenvalues of A’s in Equation (7). We found that all
roots were either equal to unity or inside the unit disc. Moreover, the two largest roots
were 0.9852 ≈ 1 and followed by a complex pair of roots with modulus 0.9623 ≠ 1. The
next largest root was 0.9558 implying two unit roots. Since the number of common
stochastic trends in the model should correspond to the number of unit roots equal or
close to unity in the companion matrix we conclude that r=2. It should, however, be noted
that, as we will further explain in this paper, the result reported in this paper is robust in
respect to the choice of the number of cointegrating vectors.
III.3 Cointegration Results and Identification
As it was mentioned earlier in this paper the existence of cointegrating
relationships between the levels of the variables in Equation (5) indicates that valid error
correction models (ECM) exist. However, since we found more than one cointegrating
relationship we need to identify the estimated cointegrating vectors. Namely, in order for
the estimated coefficients of cointegrating equations to be, in fact, economically
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
11
meaningful, identifying restrictions must be imposed to ensure uniqueness of both ß and
α. Following, e.g., Johansen and Juselius (1991) and Johansen (1995b), among many
others, we can test for the existence of possible economic hypothesis among the
cointegrating vectors in the system. We will, consequently, test for the Canadian
Monetary Policy Reaction function.
(i) Long-Run Canadian Monetary Policy Reaction Function
Since the introduction of the operating band in July 1994, Bank of Canada has
been changing the overnight financing rate, by changing the upper and lower bounds of
the band in order to control inflation and stabilize the Canadian currency. Then by using
the drawdown/redeposit mechanism it has been imposing its target overnight interest rate
within the operating band (Montador, (1995)). It was also shown (Kia (1990)) that while
Bank of Canada followed a successful “leaning against the wind” policy during the
1984-87 period it has changed its policy to a more active policy approach to overnight
rate to control inflation and stabilize Canadian dollar since 1987.
It should also be mentioned that the Bank of Canada exists to regulate credit and
currency as well as conduct monetary policy in a way that fosters confidence in the value
of money in the best interests of the economic life of the nation (Bank of Canada (1998)).
This implies that while the central bank pays a special attention to the inflation rate it
accommodates the market when there is a need for liquidity, enhances the confidence in
financial markets and stabilizes Canadian currency when the need arises. Consequently, it
may be appropriate to assume the following long-run monetary policy reaction function:
onrt = β1 lcpict + β2 lext + β3 lindpt + β4 premt + γ trend
(9)
where β1, β2, β3, β4, as well as γ are constant coefficients and one would expect β1>0,
β2>0, β3<0 and β4<0. Namely, everything else being constant, as Canadian prices grow
the overnight rate will increase in order to depress the growth of the Canadian prices.
Furthermore, whenever the exchange rate appreciates (the Canadian currency
depreciates), everything else being constant, the overnight rate tends to go up in order to
defend the dollar. Given inflation and exchange rates if industrial production increases,
over the long run, the central bank will accommodate the growth by lowering the
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
12
overnight rate. Finally, given inflation and exchange rates, if market participants’ attitude
toward risk changes the overnight rate will fall to restore the confidence in the economy.
Using this restriction the system is just identified, but clearly the rank condition is
not satisfied. Since prem as well as ronff are both trend stationary we impose a zero
restriction on the coefficient of the trend variable in the second equation. This restriction
guarantees generic, empirical and economic identifications. Note that a generic
identification is related to the estimability of a statistical model, while empirical
identification relates to the estimated parameter values and economic identification is
related to the economic interpretability of the estimated coefficients of an empirically
identified structure (see Johansen and Juselius (1994)).
Equation (10) reports the estimated long-run monetary policy reaction function,
where the figures in the brackets are standard errors.
onrt = 50.89 (12.78) lcpict + 10.52 (5.86) lext – 44.00 (9.82) lindpt
- 13.40 (2.20) premt + 0.06 (0.01) trend, χ2(5) = 6.17, p-value = 0.29 (10)
All coefficients are statistically significant and have correct signs. According to the
chi-squared test result we can not reject our hypothesized long-run monetary policy
reaction function. However, since all variables in (10), except prem, are non-stationary,
the standard errors are not very reliable. This is due to the fact that as the number of
observations becomes infinity large, the mean of the variables approaches to its true
value, and the distribution of, say, ((E(xt) - xt) /
n ), for x=onr, lcpic, lex or lindp
approaches quickly to the normal, but the variance of the estimator may explode quite fast
as n→∞. Thus, no matter how large the sample is the standard central limit theorem may
not apply.
(ii) Rank Condition
According to Theorem 3 of Johansen (1995b), the generic identification, for r = 2,
requires:
rank (R’2 H1, R’1H2) ≥ 1
where Ri (for i = 1 and 2) is a p × ki matrix of restrictions and Hi is a
p × si (ki + si = p = 12) matrix which satisfies R’i Hi = 0. Namely, there are ki restrictions
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
13
for the ith cointegrating relation, and, consequently, si parameters to be freely estimated,
where
0

0
0
H’1 = 
0
0

0
0
0
0
0
0
0
1 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0
 , R’1 = [1 1 0 0 1 0 0 1 0 1 1 0] ,
0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0

H’2 = 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 1
0
0
0

0
0

0 , R’2 = [0 0 0 0 0 0 0 0 0 0 1 ] ,
0

0
0

0

0
Rank(R’1 H2) = rank [1 1 0 0 1 0 0 1 0 1 1 ] = 1
Rank (R’2 H1) = rank [0 0 0 0 0 1] = 1
Consequently, rank condition for generic identification is satisfied. Furthermore,
according to the likelihood ratio test, χ2(5) = 6.17, (p-value = 0.29), the system is
empirically identified. Restriction (10), i.e., the long-run Monetary Policy Reaction
function, and the fact that the trend variable is already in the first cointegrating space
guarantee the economic identification. It should be emphasized again that the existence of
identified cointegrating vectors guarantees valid error-correction models which are
needed for the purpose of this paper. Furthermore, an investigation on whether economic
agents, using macro-variables specified in Equation (3), are forward-looking is valid only
when a short-run model (i.e., ECM) is used, as over the long-run expectations are
realized. We consequently concentrate on the short-run model. 9
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
IV.
14
Conditional and Marginal Models: Superexogeneity Test Result
Having established in the previous section that a long-run and identified
relationship to describe stock price with macro-variables exists, we need to verify if our
model is also forward looking. This requires a superexogeneity test of the variables. For
this test it is necessary to specify the ECM that is implied by our cointegrating vectors.
IV.1 Error-Correction Results: Conditional Models
In determining the lag length, following Mukherjee and Naka (1995), we assume
that, in evaluating stock prices, market participants incorporate the current available
information as well as past information up to one year. Consequently, the lag length of
twelve was chosen.10 Given the lag length of twelve, the parsimonious ECM was
obtained by engaging in general-to-specific-modeling procedure. 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 non-linear. To the best of our knowledge, no
study of this sort has investigated this possibility.
Table 4 reports the estimation results on ECM model. Columns headed by A
indicate the OLS result while those headed by B report the instrumental variable
(explained later in this section) result. In Table 4, ∆ denotes a first difference operator,
Ecg, Ecre, R 2, σ and DW, respectively, denote the error correction term from restricted
(the trend variable being zero) cointegrating equation, the error correction term from
monetary authority reaction function, the adjusted squared multiple correlation
coefficient, the residual standard deviation and the Durbin-Watson statistic. Hansen’s
(1992) stability L test for the null hypothesis that the estimated coefficient is stable (5%
critical value=0.47, Table 1, Hansen (1992)) denotes all of the coefficients, except the
coefficient of ∆lcompt-4, are stable.
Table 4 about here
However, the joint Hansen’s (1992) stability Lc test result for the null hypothesis
that the estimated coefficients as well as the error variance are jointly constant is
3.16 (<4.33 for 19 degrees of freedom), which indicates that we can not reject the null of
joint stability of the coefficients together with the estimated variance. We also estimated
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
15
recursively computed ‘break point’ Chow test (not reported, but available upon request)
which also indicated all coefficients are stable. Consequently, the error correction
equation appears to be constant over the sample period.
In Table 4 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-Bera (1987) normality statistic,
Li is Hansen’s (1992) stability test for the null 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.
Except the coefficient of premium and interest differential variables which was
statistically insignificant and dropped from the model, all coefficients are statistically
significant and have the correct sign. The sign of foreign stock price (S&P 500) is
positive as it was expected theoretically. This result is consistent with the findings of
Ammer and Mei (1996), Koutmos and Booth (1995), Kearney (1998), Francis and
Leachman (1998) and Ramchand and Susmel (1998). It appears that, according to the
estimation result, the S&P 500 Index grows at a stronger rate than the TSE 300
Composite Index. The estimated coefficient of the growth of the total industrial
production, as it was hypothesized, is positive. The positive impact of industrial
production on equity price is consistent with the finding of Kaul (1986), Cozier and
Rahman (1988), Fama (1965), Mukherjee and Naka (1995), Koutoulas and Kryzanowski
(1996) and Kearney (1998).
The estimated coefficient of the growth of the exchange rate as it was expected is
negative. As it was explained before in this paper, while a rise in the exchange rate
improves the balance of trade in the long run and so has a positive effect on the equity
price, a rise in the growth of the exchange rate, due to ‘J-curve’ effect, i.e., a short-run
deterioration of the balance of trade as the local currency deteriorates, has a negative
effect on the growth of the equity price in the short run.
The estimated coefficient of the growth of the commodity price, as it was
hypothesized, is positive. As it was mentioned earlier in this paper no study of this sort, to
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
16
our knowledge, has incorporated the commodity price in the determination of stock price.
The estimated coefficient of the inflation rate, as it was hypothesized, is positive. This
result confirms the earlier findings by Ely and Robinson (1997), Kaul (1986) and Kia
(1997a, 1997b). The estimated coefficient of the changes of interest rate, as expected, is
negative. The result confirms earlier findings of Darrat (1990), Balduzzi (1995) and
Groenewold et al. (1997). The estimated coefficient of interest rate differential was
statistically insignificant and so was dropped. One possible explanation for this result is
that in a small open economy like Canada, where capital is highly mobile, the interest rate
differential, as it was evidenced by Kia (1996a), is, on average, equal to the foreign
exchange swap rate. However, there is no reason to believe the foreign exchange swap
rate has any impact on the stock return (excluding dividends). The estimated coefficient
of the risk premium had also a correct sign, but was statistically insignificant. However,
as we will see later in this paper this variable has a statistically significant coefficient
when instrumental variable technique is used.
The estimated coefficient of Canada-U.S. price differential as it was hypothesized
is negative. To the best of our knowledge, no study has incorporated the price differential
in the determination of stock price.11 The estimated coefficient of the ratio of domestic to
foreign industrial production, as it was hypothesized theoretically, is positive.
Finally, 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. According to
our estimation results, the impact of equilibrium error on stock return (excluding
dividends) is non-linear. Deviations from equilibrium price result in more deviations, but
after five lags markets return to equilibrium. The even more interesting result is that,
because of the non-linear part, investors’ reaction to equilibrium errors created in the
stock markets varies for different error sizes.
Namely, assume our long-run restricted stock price is an estimate of the
fundamental price. Then we can conclude that, for a small equilibrium error (bubble) the
non-linear part may not be as important, but for a large bubble investors’ reaction will be
drastic, even though, the coefficient of the non-linear part is small relative to the
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
17
coefficient of the linear part. This result also implies that large bubbles in the equity price
in Canadian markets can not last for a long time. Consequently, bubbles do not distort
real investment decisions, which are made over longer period. This finding is consistent
with the finding of Chirinko and Schaller (1996) who show that, for the United States,
bubbles exist in stock prices, but do not influence investment spending.
The estimated coefficient of the error term generated from the central bank
reaction function is negative and statistically significant. This result might indicate that if
interest rate is above the level associated with the central bank reaction function (a
positive Ecre) the growth of the stock price would fall indicating lower dividend
payments. Clearly, the impact of the interest rate on the profitability, and so dividend
payments, is felt after more than a few months. This reflects the lag length of eight for the
error term Ecre to have a statistically significant effect on the stock price.
It should be noted that error terms Ecg and Ecre are generated regressors and their
t-statistics should be interpreted with caution (Pagan (1984)). To cope with this problem,
we also implemented, following Pagan (1984), the instrumental variable estimation
technique, where the instruments were sixth and seventh lagged values of the error terms
for the general price level and first, second and sixth error terms for the central bank
reaction function. The estimation result is reported in columns B of Table 4. As this result
indicates, the estimated coefficient of the risk premium variable as it was hypothesized is
negative, but now it is statistically significant. Furthermore, the estimated coefficient of
the error generated by the central bank reaction function is still negative, but not
statistically significant. This implies that market participants may consider the changes of
overnight rate to be sufficient to evaluate future profitability and dividend payments.
None of the other estimated coefficients is materially different than what is reported in
columns headed by A.
In sum, our findings so far add to the existing literature by showing that
commodity price and inflation differentials are also important factors in the determination
of stock price in a small, open and financially integrated economy. Bubbles exist in stock
markets in Canada, but can not last for a long run and they burst drastically if they are
large.
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
18
Assuming r=3 and imposing one more restriction (Uncovered Interest Parity (UIP)
Hypothesis) we found the system to be generically, empirically and economically
identified. According to likelihood ratio tests, χ2(4) = 2.66, p-value = 0.62 for the reaction
function and χ2(8) = 20.75, p-value = 0.01 for UIP Hypothesis, we could not reject these
two hypotheses. Note that, we followed Juselius (1995) and assumed Et[lext+1] = lrcpt.
Furthermore, we found, in the error-correction model, only error correcting terms related
to UIP and the overall stock price cointegrating vectors were statistically significant. The
error-correction term related to the central bank reaction function, similar to the case r=2,
when instrumental variable technique was used, was not statistically significant. All other
estimated coefficients were not materially different than those reported. For the sake of
brevity, these as well as rank condition results were not reported, but are available upon
request.
It should be noted that it would be very unrealistic to assume r=7. This is because
the fourth to seventh roots of eigenvalues of A’s in Equation (7) were found to be with
modulus 0.9623, 0.9558, 0.9558, and 0.9133, respectively. It may, therefore, be too
artificial to assume these values are close to one. However, for the sake of curiosity, we
also assumed r=7 and imposed four extra restrictions: premium and interest rate
differential being stationary, Purchasing Power Parity Hypothesis and Friedman Rule (a
long-run relationship between price and interest rate). According to the likelihood ratio
test result (not reported, but available upon request), we could not reject any of these
hypotheses. Namely, the system was economically identified.
However, the rank
condition was not satisfied, i.e., a generic identification failed, and according to the
likelihood ratio test result (χ2(21)=44.21, p-value=0.00), we rejected the null hypothesis
that this structure (i.e., our seven over identifying restrictions) is empirically identified.
Furthermore, we found again, in the error-correction model, only error correcting terms
related to UIP and the overall stock price were statistically significant. Namely, the
overall result would be the same for two, three, or seven cointegrating vectors. For the
sake of brevity, these results were not reported, but are available upon request.
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
19
IV.2 Weak Exogeneity of Contemporaneous Variables
It should be noted that, by including lsp in the short-run conditioning set DUM in
Equation (8), both weak exogeneity for the long-run coefficients and long-run exclusion
are assumed to hold for this variable. It is also interesting to verify whether other
contemporaneous variables in the system are weakly exogenous for the long-run
parameters. If a variable in Xt of Equation (8) is weakly exogenous for ß, then the loading
parameters (i.e., a row of α) associated with the variable will be zero. This implies that
the first differences of the variable do not contain information about the long-run
parameters ß.
If, for example, αi associated with xt (a variable in Equation (8)) is zero, then ∆xt
is weakly exogenous for α and ß in the sense that the conditional distribution of ∆Xt
given ∆xt as well as the lagged values of Xt contains the parameters α and ß, whereas the
distribution of ∆xt given the lagged Xt does not contain the parameters α and ß. This also
implies that the parameters in the conditional and marginal distributions are variation-free
(Johansen and Juselius (1991)). Namely, these parameters are constant over time when
there is no intervention. However, here again, weak exogeneity for long-run parameters
does not guarantee that the agents would not change their behavior in relation to
interventions. That is in a given regime the parameters are constant, but their variation
between regimes is interrelated. It should also be emphasized that the difficulty with the
single-equation estimation like Equation (8) is the estimation of the long-run parameter ß.
Unless there is weakly exogeneity, the asymptotic distribution of the estimator of ß does
not permit the use of usual χ2 distribution, even though the estimator of ß is consistent
(Johansen (1992)).
Table 5 reports the weak exogeneity tests. According to the result,
contemporaneous variables lex and lcomp, besides lsp, are weakly exogenous for ß in
Equation (8), as are lrcp and lindp in our model. This implies that the marginal model of
these variables does not react to equilibrium errors. Note that since the probability of the
rejection of the null, if it is true, for the overnight interest rate is only 2%, this variable
may not be weakly exogenous for ß in Equation (8). Moreover, according to the
likelihood ratio test result in Table 5, variables lindp, lcomp, lex and lrcp are jointly
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
20
weakly exogenous. However, unless these variables are strongly exogenous, they may
react to the lagged values of the variables in the system (Engle, et al. (1983)).
In fact, we tested for strong exogeneity of our contemporaneous variables. The
test result is reported in the bottom panel of Table 5. As the test result indicates, all
contemporaneous variables, except the overnight rate, are strongly exogenous at the
conventional level. Having established that the contemporaneous variables, except onr,
are weakly exogenous for the long-run parameters, we need to specify the stochastic
mechanism, which generates these variables, i.e., marginal models.
Table 5 about here
IV.3 Marginal Models
There have been several potential regime changes over the sample period as
follows:
(i)
The introduction of SPRA (the Special Purchase and Resale Agreements)
and SRA (Sales Repurchase Agreements) in June 1985.12
(ii)
The change of the Bank of Canada’s policy management approach (tight
monetary policy) under Governor Crow, February 1987-February 1994.13
(iii)
The implementation of a free trade agreement between Canada and the
United States in January 1991.
(iv)
The implementation of NAFTA (North American Free Trade Agreement
between Canada, the United States and Mexico in January 1994).
(v)
The introduction of inflation rate target band by the Department of
Finance and the Bank of Canada in February 1991.14
(vi)
The introduction of term deposit auction in April 1986.15
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,
(iii) free = 1 for January 1991 and after, zero otherwise, (iv) nafta = 1 for January 1994
and after, zero otherwise, (v) inftar = 1 for February 1991 and after, zero otherwise, and
(vi) term = 1 for April 1996 and after, zero otherwise. 16
Level and interactive combinations of these dummy variables were tried for the
impact of these potential shift events in the marginal models for lspt, lext, lcompt and onrt
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
21
and any first round significant effects were retained. The resulting marginal models took
the form:
∆lspt = 0.01 + 0.11 ∆lspt-5 - 0.01 (∆fft) - 0.02 (∆fft-1)(freet) + 0.03 (∆fft-1)(freet)
[SE]
[0.002] [0.05]
[0.002]
[0.01]
[0.001]
– 0.04 (∆fft-1)(naftat-1) + 0.20 (∆fft-1)( Oct87t-1) - 0.26 Oct87t
[SE]→ [0.02]
[0.07]
(11)
[0.04]
2
∆fft is the change of Fed Fund rate. R =0.20, σ=0.04, DW=2.15, Godfrey(5)=0.41
(significance
(significance
level=0.87),
White=9.85
level=0.98),
(significance
RESET=0.02
level=1.00),
ARCH(5)=0.73
(significance
level=1.00),
Normality(χ2(2))=25.91 (significance level=0.00),
∆lext = 0.002 - 0.09 ∆lext-1 + 0.004 ∆fft - 0.001 ∆onrt-2
[SE]→ [0.001] [0.05]
[0.001]
[0.0005]
- 0.003 (∆onrt-4 )(sprat-4) - 1.11 (∆lrcpt-1)( sprat-1)
[SE]→ [0.002]
[0.31]
- 0.09 (∆lindpt)(naftat) -0.07 (∆lindpt-1)(sprat-1)
[SE]→ [0.03]
[0.02]
- 0.34 (∆lrindpcust)(sprat) + 0.35 (∆lrindpcust)(crowt)
[SE]→ [0.15]
- 0.007 termt + 0.01 freet
[0.21]
(12)
SE→ [0.002]
[0.002]
R =0.20, σ=0.01, DW=2.06, Godfrey(5)=0.29 (significance level=0.94), White=26.22
(significance level=1.00), ARCH(5)=2.16 (significance level=0.83), RESET=0.08
(significance level=0.97), Normality(χ2(2))=8.40 (significance level=0.01),
2
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
22
∆lcompt = 0.002 + 0.35 ∆lcompt-1-0.18 (∆lcompt-2)(freet-2 )
[SE]
[0.001] [0.06]
[0.08]
- 0.17 (∆lcompt-4)(freet-4 ) - 0.65 ∆lext-1
[SE]→ [0.08]
[0.11]
- 2.14 (∆lrcpt-3 )(inftart-3)
(13)
[SE]→ [0.96]
2
R =0.13, σ=0.02, DW=2.02, Godfrey(5)=0.25 (significance level=0.96), White=20.66
(significance level=0.80), ARCH(5)=3.24 (significance level=0.66), RESET=1.78
(significance level=0.15), Normality(χ2(2))=26.21 (significance level=0.00),
and
∆onrt = - 0.50 inftart + 0.39 naftat - 0.50 ∆onrt-1- 0.21 ∆onrt-2 + 23.41 ∆lext-1
[SE]
[0.12]
[0.13]
[0.07]
[0.11]
[5.58]
+ 14.58 ∆lext-2 + 0.35 ∆ffrt-1 + 0.51 ∆ffrt-2 + 0.49 ∆ffrt-3
[SE]→
[4.03]
[0.15]
[0.08]
[0.13]
+ 0.56 (∆ffrt)(naftat ) + 2.80 (∆lindpt-2) – 3.45 (∆lindpt-1)(freet-1)
[SE]→ [0.26]
[1.50]
[1.90]
+ 22.79 (∆lindpt-2)(crowt-2) – 5.48 ∆lbondindpt-1
SE→
[9.92]
[1.81]
+ 24.29 (∆lbondindpt-2) (crowt-2)
SE→
(14)
[9.24]
Note that ∆lbondindp is the first difference of the log of the ratio of the Government of
Canada bond outstanding to industrial production and it is stationary, see Table 2.
2
R =0.41, σ=1.02, DW=2.08, Godfrey(5)=0.88 (significance level=0.51), White=241
(significance level=0.00), ARCH(5)=43.05 (significance level=0.00), RESET=8.73
(significance level=0.00), Normality(χ2(2))=50.87 (significance level=0.00).
Equations (11) to (13) pass the diagnostic checks for residual autocorrelation,
residual heteroskedasticity and the RESET test. However, the equations fail for the
normality of the residuals. The failure of the residuals normality is common in the
estimation of marginal equations; see, e.g., Hurn and Muscatelli (1992) and Metin (1998).
Equation (14) passes all diagnostic tests, except normality and heteroskedasticity.
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
23
However, here we used the robust-error regression estimation technique (White (1980)
and Hansen (1982)).
Overall, equations (11) to (14) seem reasonable marginal models for the
analogues of ηz, especially since the standard errors are very small, i.e., σ respectively is
0.04, 0.01, 0.02 and 1.02. Clearly, there is evidence of the structural break in all these
equations, i.e., possible break points are due to the introduction of Free Trade, NAFTA,
overnight repos (spra and sra), Bank of Canada’s auctions of the Government of Canada
funds (term) and the inflation target (inftar) as well as the appointment of Governor Crow
(crow), and the October 1987 stock crash. Note that non-constancy of the marginal
models is related to the concept of superexogeneity, which implies that the parameters of
conditional model remain constant if agents are not forward looking.
In Equation (11) the ‘Oct87’ dummy is significant. This dummy variable affects
the intercept and the slope while ‘free’ and ‘nafta’ dummy variables influence only the
slope. According to the estimated results, the U.S. overnight interest rate, as it is
expected, has a negative impact on the growth of the stock (S&P 500). This result is
stronger after the introduction of NAFTA.
In Equation (12), as it would be expected, the ‘spra’, ‘nafta’ ‘term, and ‘free’
dummies are significant. Dummy variables ‘free’ and ‘term’ affect the intercept and other
dummies influence the slope. The equation suggests that while a higher Fed Fund rate
leads to an outflow of capital and depresses the Canadian currency the reverse is true for a
higher Canadian overnight financing rate. The Canada-U.S inflation rate differential
(∆lrcp) has a wrong sign, i.e., it has an improving effect on the Canadian currency (recall
lex is the log of Canadian dollars per U.S. dollar) after the introduction of SPRA. The
other variables all have a correct estimated sign.
In Equation (13) dummy variables influence the slope. A higher ∆lex at time t-1
(lower value of Canadian dollar) results in a higher demand for Canadian exports which
leads to a higher value for the Canadian dollar at time t (see Equation (12)). A higher
value for the Canadian dollar makes Canadian goods more expensive and, therefore,
results in a lower demand for Canadian commodities and so a downward pressure on the
commodity price. This is also true for Canada-U.S. inflation rate differentials (∆lrcpt).
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
24
In Equation (14) dummy variables influence the slope and the intercept. As one
would expect, a lower value for Canadian dollar tends to let the central bank increase the
overnight financing rate. This is also true when Fed Fund rate (∆fft) increases. This result
became stronger after the introduction of NAFTA. As industrial production growth rate
(∆lindpt) rises, the overnight rate will go up to preempt potential inflation. During
John Crow’s tight monetary policy period, as suggested by the estimated coefficient of
((∆lindp)(crow)), a rise in the growth of industrial production resulted in an even higher
tightening in Canada.
Note that the sign of the growth of the industrial production over the long run is
negative in the long-run reaction function of the central bank (Equation 10). This is due to
the fact that the central bank, everything else being constant, accommodates the economy
over the long run to keep the economy in a steady state. As the growth of the government
bond relative to the growth of the industrial production increases, the price of bonds falls
and the rate goes up. Therefore, the estimated coefficient of (∆lbondindp) has a correct
estimated sign only during Crow’s tight monetary policy period.
IV.4 Superexogeneity Test Results
From marginal models 11 to 14, estimates of ηZ, and σtZZ, for Z = ∆lsp, ∆lex,
∆lcomp and ∆onr, were calculated. As for σtZZ, since the error for ∆lsp, ∆lex and ∆lcomp
variables is not heteroskedastic, according to ARCH test, a five-period moving average of
the variance of the error was tried. For ∆onr, however, the error is heteroskedastic,
according to ARCH test, a five-period ARCH error, therefore, was estimated. We also
constructed DevZ (Z = ∆onr) as differences between the variance of the error term in (14)
and the variance constructed by ARCH estimation. All of these constructed variables
were then included in the ECM reported in Table 4. The estimation results on these
constructed variables, for only the instrumental variable technique, are given in Table 6.
The result for OLS is not materially different and, therefore, for the sake of brevity, is not
reported, but is available upon request.
Table 6 about here
The individual F-test is on the null hypothesis that each variable is zero. The
F-test on the null hypothesis that all constructed variables are jointly zero is given in the
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
25
last row of the table. The F-test, given in the third to last row in Table 6, is on the
hypothesis that only the constructed variables related to each contemporaneous variable
while all other constructed variables are included, are jointly zero. We also included only
the constructed variables related to each contemporaneous variable and tested whether
these constructed variables are jointly zero. The F-test result is given in the second to last
row in Table 6.
As the estimation result in Table 6 shows the joint F-test on the null hypothesis
that coefficients of these constructed variables are jointly zero is rejected at the
conventional level, indicating that these variables together should be included. This result
immediately implies that the contemporaneous variables in the conditional model,
reported in Table 4, failed to be jointly superexogenous, i.e., agents are forward looking
and Equation (5) is an appropriate approximation of Equation (2). However, none of the
individual coefficients of ∆lcomp and ∆lex nor the joint F-tests on these coefficients are
statistically significant, implying the variables ∆lcomp and ∆lex are superexogenous (see
columns with the heading of ∆lcomp and ∆lex in Table 6).
Since the coefficient of (Z-ηZ) of both contemporaneous ∆lsp and ∆onr are
statistically insignificant, both of these variables, as it would be expected, are weakly
exogenous.17 However, the coefficient of σZZ (Z-ηZ) of both variables is significant at the
conventional level, implying that the null of constancy is rejected for both of these
variables. Furthermore, since the coefficient of (ηZ)2 of ∆lsp and the coefficient of σZZ of
∆onr is statistically significant, none of the coefficients of these variables is invariant with
respect to policy changes. Consequently, we reject the null of constancy and invariance,
while accepting weak exogeneity conditions for both ∆lsp and ∆onr variables.18 Note that
constancy and invariance are different concepts. Parameters could vary over time, but be
invariant with respect to policy changes.
However, as it was mentioned by Engle and Hendry (1993), we need all three
conditions to be satisfied in order to ensure superexogeneity. The failure of the constancy
condition, therefore, justifies the result of the joint F-test on the null hypothesis that all
coefficients of the constructed variables are jointly zero. Namely, in general, we reject the
null hypothesis that ∆lsp and ∆onr are superexogenous. That is, although the coefficient
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
26
of ∆lsp and ∆onr in the stock price (Table 4) is constant over the sample period, any
change in the regime affecting stock markets in the U.S. and/or in monetary policy makes
economic agents in Canadian stock markets change their investment behavior. The joint
F-test results given in the second and third to last row in Table 6 also confirm that ∆lsp
and ∆onr are not superexogenous.
In fact, since most policy rules relate to past information about the economy, the
possibility of a policy variable, like the overnight financing rate in Canada, being
superexogenous seems unlikely. Consequently, a change in the monetary policy, which
alters the process that the control variable ∆onr is formed, will affect investment
decisions made by economic agents in Canadian stock markets. Namely, the agents in
equity markets are forward looking. Furthermore, since all our contemporaneous
variables in the ECM reported in Table 4 are weakly exogenous, they can be treated as
though they are fixed in repeated samples, even though they may be generated by a
stochastic mechanism in the same way as the stock return (excluding dividends).
However, since the overnight rate is not strongly exogenous the ECM can not be used for
prediction.
It should be noted that, instead of marginal models 11 to 14, one could simply
estimate the DGP (data generating process) of each contemporaneous variable in the
ECM, while allowing level and interactive combinations of the above dummy variables to
reflect potential shifts events. The estimated equations, of course, would not have any
economic interpretation, but would be valid marginal equations for the superexogeneity
test, see Engle and Hendry (1993). In fact, we also tried this approach and found no
materially different result with what is reported. For the sake of brevity, this result is not
reported, but is available upon request.
V.
Concluding Remarks
This paper extends the model introduced by Kearney (1998) by incorporating the
commodity price, domestic-foreign price differential and risk premium and shows that
these variables are also significant components of the stock price determination. Using
superexogeneity test, we also find that agents in the stock markets are forward looking.
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
27
Furthermore, agents’ reactions to equilibrium errors are asymmetric. Namely, they may
react differently to small deviations from the equilibrium (or the fundamental) price than
large ones. It was also found that deviations from fundamental price (i.e., bubbles) are
short-lived. An important implication for these results is that agents form rational
expectations and macro-variables can be used in evaluating stock price indexes. However,
when agents are forward looking, the model can not be used for forecasting.
This paper also shows that among macro-determinants of stock price, at least two
long-run stationary relationships exist. These relationships include: Uncovered Interest
Parity as well as a long-run Canadian Monetary Policy Reaction function. Finally, since
the approach of this paper in testing for forward-looking agents in stock markets, using
macro-variables, is relatively new, it would be interesting to extend this study by
investigating the behavior of agents in large-country stock markets.
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
28
Table 1
Description of Variables: CANSIM Number
(1975:Jan. – 1999:Dec.)
∆ltse=Percentage change of the log of the TSE 300
Composite Index, closing quotations at month-end : B4237
∆lsp=Percentage change of the log of the S&P 500 Index,
quotations at month-end: B4291
∆lindp=Percentage change of the log of nominal
(unadjusted) total industrial production=log of real total
industrial production: I57001 plus log of Consumer Price
(unadjusted) Index: P100000
∆lcomp=Percentage change of the log of commodity price
index in Canadian dollars: B3300*
∆lrindpcus=Percentage change of the log of the ratio of
Canadian (SA) and U.S. (SA) industrial production**
∆lex=Percentage change of the log of the exchange rate
($Canadian of one unit $US), the last day of the month:
B3414
∆onr=Change of the Canadian overnight financing rate***:
B14044
ronff=Canadian overnight rate less Fed Fund rate: B14044
and B54408
∆lcpic=Percentage change of the log of Consumer Price
Index: P100000
∆lrcp=Percentage change of the log of the ratio of
Canadian-U.S. consumer price indexes: P100000 and
D139105
prem=Differences between monthly Canadian corporate
paper and TB rates****: B14039 and B14059
∆lbond=Percentage change of the log of the Government of
Canada bond outstanding: B2501
Mean
%
Standard
Deviation
0.77
4.82
1.02
4.26
0.63
5.42
0.30
2.43
-0.03
1.07
0.13
1.36
-0.006
1.30
1.34
2.13
0.40
0.40
0.02
0.35
0.34
0.30
0.89
1.58
* 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).
** Since corresponding data was not available the ratio was constructed by using the ratio of the log of real
indexes plus the log of the ratio of Canadian and U.S. consumer price indexes: D360048 converted to
1992=100, D360061, I56010, P100000 and D139105.
*** 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.
**** Note that monthly TB rates are only available from 1989. We, 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).
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
29
Table 2*
Stationary Tests: 1975 (Jan.) - 1999 (Dec.)
Absolute Values
Variables
Augmented Dickey-Fuller
τ-Stat.
Phillips-Perron
Z-Stat.
2.47
1.62
2.05
2.00
0.90
1.71
2.66
10.84a
0.94
0.94
7.52a
1.23
2.67
1.73
3.38
2.04
1.08
1.83
3.00
21.67a
0.86
0.82
7.26a
3.87b
Levels:**
ltse
lsp
lindp
lcomp
lrindpcus
lex
onr
ronff
lcpic
lrcp
prem
lbondindp
Changes of:
ltse
lsp
lindp
lcomp
lrindpcus
lex
onr
lcpic
lrcp
lbondindp
7.37a
16.55a
a
8.17
17.49a
a
13.94
28.80a
a
7.74
15.51a
a
8.61
23.03a
a
7.65
19.06a
a
10.84
21.67a
a
5.37
16.89a
a
6.39
16.55a
a
11.56
22.90a
* All tests include constant and trend. The critical value for Augmented Dickey-Fuller τ test (lag-length = 4)
and for Phillips-Perron non-parametric Z test (window size = 4) is 3.42 at 5% and 3.98 at 1%. The number
of observations is 288.
a=Significant at 1%.
b=Significant at 5%.
** ltse is the log of TSE 300, lsp is the log of S&P 500, lindp is the log of total industrial production,
lcomp is the log of commodity price index, lrindpcus is the log of ratio of industrial production in Canada
and U.S., lex is the log of exchange rate, onr is the Canadian overnight rate, ronff is the difference between
the Canadian overnight and Fed Fund rates, lcpic is the log of Consumer Price Index in Canada, lrcp is the
log of ratio of Canada to U.S. consumer price indexes and prem is the monthly corporate rate less TB rate.
Note that monthly TB rates are only available from 1989. We, 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.
lbondindp is the log of the ratio of the Government of Canada bond outstanding over industrial production.
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
H0=r
Eigenv.=D
D
Table 3*
Tests of the Cointegration Rank
Trace(3)
λmax(1)
λmax 95(2)
Trace 95(4)
0 0.2529
74.62
66.23
353.87
264.23
1 0.2201
63.65
61.29
279.32
221.56
2 0.1974
56.30
55.50
215.59
182.45
3 0.1487
41.21
49.42
159.28
146.75
4 0.1109
30.09
43.97
118.07
114.96
5 0.1079
30.09
37.52
87.99
86.96
6 0.0939
29.23
31.46
58.75
62.61
7 0.0630
25.24
25.54
33.51
42.20
8 0.0384
10.02
18.96
16.86
25.47
9 0.0264
6.83
12.25
6.83
12.39
Diagnostic tests**:
LM(1)
p-value = 0.31
LM(4)
p-value = 0.28
Normality
p-value = 0.00
(1) λmax is adjusted to correct a possible small sample bias error. Namely, N is replaced by (N – kp).
λmax =- (N-kp) ln(1- Dr), where N is the number of observations, k is the number of lag length and p is the
number of the endogenous variables.
(2) The source is Osterwald-Lenum (1992), Table 2, p. 469.
(3) Trace test is adjusted to correct a possible small sample bias error. Namely, N is replaced by (N – kp).
P
ln(1 - D i ). Both Trace and λmax tests were developed in Johansen and
Trace test = -(N- kp)
∑
i = r +1
Juselius (1991).
(4) The source is Johansen (1995a), Table 15.4, p. 216.
* The model includes constant, trend and seasonal dummies. Lag length is 4.
** LM(1) and LM(4) are one and four-order Lagrangian Multiplier test for autocorrelation, respectively
(Godfrey (1988)).
30
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
31
Table 4*
Error Correction Model: Dependent Variable = ∆ltset
Variable**
Coefficient
Standard Error
Hansen’s (1992) stability Li test
(5% critical value = 0.47)
A
B
A
B
A
B
Constant
-4.95
-
2.53
-
0.22
-
∆lspt
0.78
0.79
0.04
0.04
0.19
0.23
∆lspt-1
0.18
0.20
0.05
0.06
0.08
0.09
∆lindpt-3
0.09
0.08
0.03
0.03
0.15
0.13
∆lext
-0.78
-0.80
0.14
0.13
0.13
0.16
∆lcompt
0.26
0.28
0.08
0.08
0.24
0.31
∆lcompt -4
0.20
0.19
0.07
0.07
0.75
0.88
∆onrt
-0.004
-0.004
0.001
0.001
0.04
0.05
∆premt-1
-
-0.01
-
0.006
-
0.07
∆lrcpt-1
-0.93
-0.88
0.50
0.51
0.09
0.08
∆lrindpcust-1
0.31
0.34
0.16
0.17
0.07
0.06
∆lrindpcust-2
0.35
0.36
0.15
0.16
0.16
0.17
∆lcpict-9
2.00
1.88
0.45
0.46
0.09
0.07
∆ltset-1
-0.13
-0.14
0.05
0.05
0.12
0.12
∆ltset-3
0.11
0.12
0.03
0.03
0.03
0.02
Oct87t
-0.08
-0.07
0.03
0.03
**
0.001
0.001
0.0002
0.0004
0.22
0.19
(Ecg)t-5
-0.02
-0.002
0.01
0.0006
0.22
0.20
-7
0.22
0.20
0.23
0.19
0.15
0.20
3.16
3.39
Ecgt-1
(Ecg)
2
t-5
Ecret-8
**
-1*10
-5
-0.0007
-2*10
-6
-0.0002
7*10
-6
0.0003
5*10
0.0006
Hansen’s (1992) stability Li test on variance of the ECM
∆ltset was adjusted for Oct87 before the stability test.
in
Joint (coefficients and the error variance) Hansen’s (1992)
stability Lc test (5% critical value(df=19)=4.33
* Period=1975(Jan.)-1999(Dec.), ∆ means the first difference, Mean of Dep. Variable=0.007.
** Ecg and Ecre are the error correction term from restricted cointegrated equation (Endnote 9) and
Equation (10), respectively. For the description of the remaining mnemonics see footnote of Table 2.
A = The estimation method is OLS: R 2=0.69, σ=0.03, DW=2.1, Godfrey(5)=0.57 (significance
level=0.75), White=197 (significance level=0.71), ARCH(5)=6.78 (significance level=0.24), RESET=0.74
(significance level=0.53), and Normality(χ2(2))=0.09 (significance level=0.95).
B = The estimation method is the instrumental variables technique: R 2=0.69, σ=0.03, DW=2.1,
Godfrey(5)=0.52 (significance level=0.79), White=213 (significance level=0.41), ARCH(5)=7.67
(significance level=0.17), RESET=1.12 (significance level=0.34), and Normality(χ2(2))=1.07 (significance
level=0.59).
in = Statistically insignificant.
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
32
Table 5*
Test For Weak Exogeneity of the Variables of the Long-Run
Parameters
Variables
Null: The variable is weakly exogenous for the
long-run coefficients:
lindp
lcomp
lrindpcus
lex
onr
ronff
lcpic
lrcp
lprem
Null: Variables jointly are weakly exogenous:
lindp&lcomp&lex&lrcp
Null: The variable is strongly exogenous for ∆ltse:
∆lcomp
∆lex
∆onr
* See footnote of Table 2 for the description of the mnemonics.
** Can not reject the null.
p-value
0.45**
0.75**
0.01
0.57**
0.02
0.02
0.02
0.67 **
0.01
0.88
0.09**
0.51**
0.00
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
33
Table 6*
Superexogeneity Tests
Variable (Z)**
Z- ηZ
σZZ (Z - ηZ)
(ηZ)2
σZZ
σZZ ηZ
σZZ (ηZ)2
DevZ
F-Statistics on null hypothesis that coefficients of all constructed
variables in this column are jointly zero. The equation includes the
constructed variables related to other contemporaneous variables.
F-Statistics on null hypothesis that coefficients of all constructed
variables in this column are jointly zero. The equation excludes the
constructed variables related to other contemporaneous variables.
F-Statistics (25, 235) on coefficients of all variables in rows and
columns
0.05
(0.83)
3.97
(0.04)
6.07
(0.01)
1.00
(0.31)
0.81
(0.37)
1.26
(0.26)
2.26
(0.03)
F-Statistics (1, 235)
(p-values)
∆lex
∆lcomp
∆onr
0.72
0.12
0.17
(0.39)
(0.73)
(0.68)
3.44
2.72
5.41
(0.06)
(0.10)
(0.02)
0.01
0.08
0.01
(0.91)
(0.77)
(0.92)
1.76
0.31
5.40
(0.19)
(0.58)
(0.02)
0.002
0.80
2.36
(0.97)
(0.37)
(0.13)
0.41
0.001
4.80
(0.52)
(0.97)
(0.03)
0.47
(0.49)
0.77
1.18
2.09
(0.60)
(0.31)
(0.05)
2.16
(0.05)
1.16
(0.33)
∆lsp
1.82
(0.10)
2.81
(0.01)
1.79
(0.01)
* ∆lsp is the change of the log of S&P 500, ∆lex is the change of the log of exchange rate, ∆lcomp is the
change of the log of commodity price index, ∆onr is the change of overnight rate, ηZ is the conditional mean
of Z, σZZ is the conditional variance of Z, and DevZ is the deviation of variance of the error term from a
five-period ARCH error of Z.
** ∆ltset = α0 + ψ0 Zt + z’tγ + (δ0 - ψ0) (Zt - ηZt) + δ1 σtZZ (Zt - ηZt) + ψ1 (ηZt)2 + ψ2 σtZZ + ψ3 σtZZ ηZt +
ψ4 σtZZ (ηZt)2 + ut.
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
34
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Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
39
White, Halbert (1980) A Heteroskedasticity-Consistent Covariance Matrix Estimator and
a Direct Test for Heteroskedasticity, Econometrica, May, 817-37.
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
1
40
Note that, as Koutoulas and Kryzanowski (1996) also mention, there is no generally
accepted theory for linking stock returns to the economy. Consequently, general
economic theory and intuition have been the main input in the selection of macrovariables.
2
Note that the U.S. is Canada’s major trading partner. For example, in 1998, about 82%
of Canadian exports were sent to the U.S. while about 78% of Canadian imports
originated from the U.S. The value of goods and services that cross the Canada-U.S.
border every year amounts to about U.S.$370 billion, or 40% of the Canadian GDP.
Canada accounts for nearly one—fifth of U.S. international trade in goods and services,
while the U.S. accounts for close to four-fifths of Canadian international trade in goods
and services, Bank of Canada Review (2000).
3
This argument is also applicable for variables Rt-FRt, PLt/FPLt and IPt/FIPt.
4
About one-fifth of the Toronto Stock Exchange 300 Composite Index is made up of
commodity related companies and as much as 35% of Canada’s exports are raw
materials.
5
Note that the error term in Equation (5) does not have any relation with the variables on
the right hand side of the equation since we do not include in the equation actual values
of price and dividend at time t+1. Consequently, Equation (5) does not suffer from
errors-in-variables problems as well as forward autocorrelation; see, e.g., Cumby et al.
(1983).
6
Note that in a multivariate cointegrating relationship we need at least two variables to be
non-stationary.
7
Since Canada is a small open economy relative to the U.S. we can assume that the
S&P 500 index (SPt) is weakly exogenous to Canadian stock markets. As it was also
mentioned earlier in this paper it is more appropriate for the S&P 500 variable to enter in
the model in terms of the Canadian dollar, i.e., to be adjusted for the exchange rate.
However, we follow Kearney (1998) and Koutoulas and Kryzanowski (1996) and allow
the exchange rate to appear as a separate variable to avoid the introduction of an extra
stochastic trend in the cointegrating relation.
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
8
41
The TSE 300 Composite Index hit a record high on October 7, 1997, just 10 days before
the crisis. Up to January 12, 1998 the index fell 13.45%. However, the index hit a record
high on March 9, 1998 and by the end of March 1998 it hit 10 record highs.
Consequently, if the Asian crisis had any impact on Canadian stock markets, the impact
would have been completely dissipated by the end of February 1998. However, from the
end of September 1997 until the end of November 1997 the TSE 300 Composite Index
fell by 7.79% and rebounded after. This implies that for our monthly observations the
appropriate dummy variable, which may reflect the Asian Crisis, is a variable that is one
for the October-November period and zero, otherwise.
9
The estimated restricted cointegration equation for the stock price is:
ltset = 0.78 (0.93) lspt + 41.49 (15.62) lindpt - 15.30 (10.41) lext - 11.66 (2.16) lcompt
+ 49.77 (22.86) lcpict - 0.99 (0.12) ronfft + 2.54 (0.10) onrt + 22.24 (3.89)
premt - 33.38 (11.09) lrcpt + 32.64 (4.56) lrindpcust
where the figures in brackets are standard errors.
10
Using Akaike’s final prediction error criteria and a maximum lag length of 12, the same
optimum lag length was obtained. It should be noted that in using an ECM, we allow
agents to be backward looking (reacting to previous deviations from equilibrium) while
they may also be forward looking.
11
However, it should be noted that Kearney (1998) in the theoretical part of his paper
incorporates price differential in the determination of price.
12
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
(Bank of Canada (1989)).
13
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.
14
“… from 1982 to 1991, monetary policy in Canada was carried out with price stability
as the longer-term goal and inflation containment as the shorter-term goal, but without
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
42
intermediate targets or a specified path to the longer-term objective. In February 1991,
explicit targets for reducing inflation were introduced through joint announcements by the
Bank and the federal government. These announcements confirmed price stability as the
appropriate long-term objective for monetary policy in Canada and specified a target path
to low inflation….” (Thiessen (1998-1999, p. 91)).
15
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. 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).
Forward-Looking Agents and Macroeconomic Determinants of the Equity Price
16
43
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 reduced to zero in July 1994 (Bank of Canada
(1994), p. 80, Footnote 1).
17
Note that Canadian stock markets are small relative to the U.S. stock markets and the
overnight rate is a monetary authority control variable.
18
It should also be noted that since ∆lcomp as well as ∆lex are superexogenous and ∆lsp
as well as ∆onr are weakly exogenous the inference on the parameters in the agents’
model (ECM) is efficient.