A-30

EXPORTS OF GOODS AND SERVICES: BRIDGE EQUATION (balance of payments basis
to National Income Accounts basis}

XGSNIVS = - 0.003 + 1.000 (XGV + xSOV + xSyYV)
(0.2) (1578.4)

R? = 0.999 SEE = 0.051 DW = 3.08

Period 61:1 to 75:4


-28-

Table 7

Effects of a 10 percent Revaluation
of the Canadian Dollar

1967 1968 1969
1 | 2 | 3 | 4 1 | 2 | 3 | 4 1 | 2 | 3 | 4
one! -.009°  =.107=.205-..251 -.227 -.218 -.407 -.029 | -.613 ~ 495 -.689 _-.597
? -.006 = -.012,-.017_—-.021 ~ 1026 -.027 -.030 0 -.032 -.034 -.036 -.038 -.040
w? =.126 +056 +145 2273 338 +381 +401 418 +382 +409 +395 118
rs‘ -+103 +346 642 +949 +386 +494 1.33 1.69 1.82 2.26 2.12 2.09
vosurvs! 7-781 =.757=.743 =. 786 | -1.04 -1.09 “1.17 71.260 | -1.58 0 -1.61 “1.80 -1,97
z 092 +092 092 092 092 +092 +092 092 +092 +082 +092 +092
paral 71.08 9 =.781 1.03 =.971 | -1.34 = 2924 -.598 -.676 --796 = 412 ~.723 -.541
wc! +312 +520 512 +546 +516 +543 Ahh +597 407 459 -368 409
xc! 1035-481 =.679=.970 | -1.03-1,16 71.06 --1.15 | -1.05 1.13 “1.030 -1,17

1 billions ef Canadian dollars, annual rate.
2 1972 = 1.0.

3 Percentage points.

4 U.S. dollars per Canadian dollar, 1972 = 1.0.

5 In this experiment, the discount did not exceed the short-term rate until the
last quarter of 1975, so the switch of interest rate equations occurred here
vather than in the first quarter. Like the previous multiplier responses, the

drop in the interest rate response is the result of switching between interest

rate equations and no’ the number of periods after the introduction of the shack.


The ‘Canadian Sector of the Multi-Country Model*
by Howard Howe

Introduction
The quarterly econometric model of Canada described in this paper
is based on the prototype model of MCM presented in previous papers and in

/

1
the forthcoming book, The U.S. Economy in an Interdependent World.— Few

departures from the prototype specification were required to represent

the functioning of the Canadian economy. The most critical area for
adaptation of the prototype to Canada lay in the financial sector. The
Canadian financial system is characterized by close linkage to U.S.
finencial markets. Consequently, Canadian interest rates have traditionally
moved closely with U.S. interest rates. Because, of this linkage, the Bank
of Canada, in its RDX2 model, chose to model the process of interest rate
determination by postulating a central bank reaction function for the short-
term interest rate. Thus, the application of the MCM prototype to Canada
represents a departure from accepted procedure for an influential group of
Canadian modelers and merits further discussion. The first part of this
paper reviews the model's financial sector. The second and third parts
present dynamic simulation results and selected multiplier responses that
characterize the Canadian model.

The Canadian Financial Sector

Aside from the departure from the RDX2 interest-rate reaction
function, several features of the Canadian financial system required
adaptation in the prototype model:

(1) Canada has a secondary reserve requirement against time and

demand deposits that is to be filled by Treasury bill holdings,


A-39

SERVICE DEFLATOR, EXPORTS

LOG(PXS) = - 0.017 + 1.111 LOG(P)
(2.7) (41.9)

BR? = 0.9675 SEE = 0.041

Period 61:1 to 75:4

DW = 2.15


A-50,

REQUIRED RESERVES

RR = 0.083 + 0.908 (A * DD + B * TD)/100
(7.0) (158.6)

R2 = 0.998 SEE 0.035 DW = 1.41

Period 61:1 to 75:4


-18-

Multipliers of the Canadian Model

The multipliers presented in this section were calculated by comparing
a solution of the Canadian model that was aligned to history by adding the regression
residuals to the estimated equations with a solution using the same regression
residuals and a change in the policy instrument. These multipliers solutions
were made with the Canadian model in isolation from the rest of the MCM; that
is, all foreign variables remained exogenous.

The single-model multipliers presented here differ from those of the
MCM version of the model in one crucial aspect. The single model results were
obtained with an aggregate export equation used before the MCM bilateral trade
system was completed. This is a significant difference in the case-of the
Canadian model because the export price elasticities in the two trade systems
differed significantly. The aggregate’export equation had an export price
elasticity of -0.73, whereas the trade-weighted average of the bilateral price
‘elasticities was -1.08. ‘with the lower export price elasticity, these
multipliers using the aggregate export equation are larger than those of the
final MCM version using the bilateral trade equations.

In that the multipliers depend on the magnitudes of activity and prices
existing in the period for which the model is solved, it is useful to recall
the economic environment between 1973 and 1975. In late 1974 Canada aad the
rest of the world economy entered a recession. The general effect of this
environment on the multiplier paths studied here is a downward bias in the

initial real effects and an upward bias in the initial price effects of an

economic stimulus.


A-45

LABOR FORCE PARTICIPATION

LOG(LF/POPI5) = - 0.709 + 0.279 LOG(W.4/P_3) - 0.014 LOG(UN_,)
(8.8) (5.9) (1.4)

- 0.001 NW, / P.
-2 ol
(1.3)

= 0.4371 SEE = 0.004 DW= 1.68 p = 0.906

Period 62:1 to 75:4


PAGE
E. Labor Market
Wages A-42
Wage Bill A-43
Employment A-44
Labor force participation A-45
F. Domestic asset demand and interest rate determination
Temand deposits A-46
Savings deposits A-47
Notice deposits A-48
Currency A-49
Required reserves A-50
Short-term interest rate
When short-term rate exceeds the discount rate A-51
When the discount rate exceeds short-term rate A-52
Long-term interest rate A-53
G. Capital Movements, official reserves, forward and led
exchange rates
Errors and omissions A-54
Change in short-term liabilities A-55
Change in short-term claims A-56
Change in long-term liabilities A-57
Change in long-term claims A-58
Forward exchange rate A-59

Led exchange rate A-60


Gcu

GGNP

GNP
GNPV

GP
GPXGUV

Gv

GYDVNSA
IFG

IFGV
IFGVNSA

IFP

IFPV
IFPVNS.

Il
IIv
INTSHK

JCcU

JE

A-74

German capacity utilization rate
German spot exchange rate index, $/DM (FRB)

German gross national product

gross national product -(STATCAN)

German absorption deflator
German export unit value ‘index

government expenditure on goods and services, current

value (STATCAN)
German disposable income proxy.

government gross fixed capital formation (IFGV/P)

} government gross fixed capital formation (STATCAN)

private fixed investment, housing plus plant and equipment
(IFPV/P)

private fixed investment, housing plus plant and equipment.
(STATCAN) .

inventory investment (1Iv/P)

inventory investment, current value (STATCAN)

dummy variable for simulating changes in foreign exchange
intervention, normal value is zero.

Japanese capacity utilization index, ratio of industrial
Production index to production capacity index (BANK OF JAPAN)

spot exchange rate index, U.S.$/YEN, (FRB)


A-10

TPERV = - 4.489 + 0.604 Ql + 0.217 Q2 + 0.110 Q3 + 0.321 WBNSA
(15.2) (2.6) (0,9) (0.5) (52.6)

- 0.013 WBNSA * P * QTAXT
(3.9)

R? = 0.991 SEE = 0.627. DW = 1.61

Period 61:1 to 75:4


A=35

INVESINENT INCOME PAYMENTS

MSYV = 0.057 FL - 0.0002 Q2 * FL = 0.002 Q3 * FL + 0.011 Q4 * FL
(5.4) (0.2) (1.8) (11.0)

+ 0.026 (RS * (-STL_|) + RL * CLTPL_1)).- 0.032 RL * (-LIDL_,)
(7.0)

R’ = 0.9178 SEE = 0.155 DW+ 1.95 p = 0.415

. Period 61:1 to 75:4


A-6

CONSUMPTION

C = - 10.873 + 0.484 Cl) + 0.387 YOV/P + 0.119 NW.) /P?
(5.4) (6.6) (7.0) (6.2)

=2
R= 0.9987 SEE = 0.387 DW = 1.72
Period 61:1 to 75:4


A-38
IMPORT UNIT VALUE

LOG(PMGUV) + LOG(E) = - 0.027 + 0.370 LOG(FPXGUVD) + 0.369 LOG(FPXGUVD_})
(4.0) (4.3) (4.2)

=2
R = 0,951 SEE = 0.011 DW=1.77° p = 0.798

Period 61:1 to 75:4


JGNP
JP
JPXGUV
JYDVNSA

KFIX

KG

LIDL

LTPC

LIPL

MCEV
MCGV
MCJV
MCRV

MCTV

A-75

Japanese gross national product (BANK OF JAPAN)

Japanese deflator for aggregate expenditure

Japanese unit value of merchandise exports, Yen (IFS)

Japanese disposable income proxy

dummy to reflect a fixed exchange rate regime (1 in 6202
to 7002)

government gross fixed capital stock (cumulated value of
IFG, less scrappage)

private gross fixed capital stock (cumulated value of IFP
less scrappage)

labor force (STATCAN)

stock of long-term direct claims on foreigners (cumulated
value of DLTDC) ,
stock of long-term direct liabilities to foreigners
(cumulated value of DLTDL)

stock of long-term portfolio claims on foreigners
(cumulated value of DLTPC)

stock of long-term liabilities to foreigners (cumulated
value of DLTPL)

merchandise imports from the U.K., c.i.f. (DOT)
merchandise imports from Germany, c.f. (@or)
merchandise imports from Japan, c.i.f, (DoT)

merchandise imports from R.O.W., c.i.f. (DOT)

merchandise imports, c.i.f. customs clearance basis (DOT)


A-16

IMPORTS OF GOODS: BRIDGE EQUATION (Customs clearance to balance of
payments basis)

MGV * ER = 0,133 + 0.942 MCTV/1.1
(3.0) (366.8)

R2 = 0.999 SEE = 0.184 DW = 0.94

Period 61:1 to 75:4


A-58

CHANGE IN LONG-TERM CLAIMS

- DLTPC = 0.072 - 0.117 Q2 + 0.020 Q3 + 0.098 Q4 + 0.098 Q2 * KFIX
(0.7) (1.6) (0.3) (1.4) (1.1)

= 0.005 Q3 * KFIX - 0.106 Q4 * KFIX + 0.191 A(URL) - A(RL)
(0.1) (1.2) (2.3) .

+ 0.002 (1 - KFIX) * A(DEFLOAT) - 0.167 QFRID
(0.5) . q.1)

R = 0.082, SEE = 0.174 “DW= 1.84 p = 0.374

Period 61:1 to 75:4.


-11-

Emprical testing revealed that the Canadian short-term interest rate

behaved somewhat differently when the discount rate acted as a penalty rate
(RD > RS) than when short-term rates exceeded the discount rate. There
are two versions of equation (12) in the MCM, each is switched on during its
respective regime! In the penalty-rate regime, the U.S. short-term rate enters
the inverted free reserve equation (with a small negative coefficient). In
the regime where the discount rate was less that the short-term rate, the
U.S. interest rate does not enter the equation at all. The small direct presence
of the U.S. interest rate in the MCM equation contrasts sharply with the dominant
presence of the U.S. rate in the RDX2 equation. This has important structural
ramifications for the functioning of the model. In the MCM, changes in the
U.S. interest rate alter the differential between U:S. and Canadian interest
rates, cause a capital flow, a change ‘in the level of foreign exchange holdings,
thereby affecting the sources of the monetary base and free reserves (on
the uses side of the monetary base) and, in this way, cause a change in Canadian
interest rates. In the RDX2 approach, the U.S. effect occurs directly via the reduced
form equation, thus, circumventing these important channels of financial flow.
The three key differences in the two interest rate functions can be summarized
as:

(1) The MCM makes use of the discount rate as one of three policy

instruments whereas RDX2 does not. Canadian scholars argue that

borrowed reserves and PRAs are a very small share of. financial

flows and constitute an unreliable link to interest rates. We

argue that while smallness may cause estimation problems, the

link to the monetary base exists. We also argue that the market rate

functions as a signal mechanism much as the discount rate in the

United States.


-4-

Within the framework of the consolidated monetary authorities, the
sources and uses of the unborrowed monetary base are similar to those of the

German and Japanese cases.

(1) Sources: BU = NFA + NGP + OTH (met)

(2) Uses: BU = RR + RF + CUR
where:
BU = wumborrowed monetary base;

NFA = net foreign assets;
NGP = net government position;
OTH = other assets (net);

RR

required reserves; ,

RF = free reserves; and

CUR = currency.
Unlike the German and Japanese cases, vault cash is an eligible component
of reserves and is included there. There is no need for the variable curs® ,
included in the prototype.

Canadian reserve requirements are much simpler than in the German

and Japanese cases. There is no distinction by size of bank. Furthermore,
the reserve requirement changed only once over the sample period. Unlike
the U.S. monetary system, changes in reserve requirements are not used for
monetary control. Prior to 1967, the primary reserve requirement or. both
demand and time deposits was held at 8 percent. After a 3 quarter transition
period, the requirements were set to 12 percent for demand deposits and 4
percent for time deposits. This was a statutory change made for institu-

tional purposes rather than monetary control.


A-13

‘TAXES - INDIRECT
TINDV = 0.471 + 0.697 Ql - 0.371 Q2 - 0.866 Q3 + 0.134 GNPVNSA

(1.8) (2.9) (1.6) (3.6) (59.3)

W = 0.983 SEE = 0.653 DW = 1,16

Period 61:1 to 75:4


EMPLOYMENT,

LOG(1.- UN/100) + LOG(LF) = 0.675 + 0.005 TIME +
: (3.7) (11.4)

4
Dy a, LOG(GNPV_;/(W_;))

i=0
R? = 0.9826° SEE = 0.005 Dw = 1.62 ‘p= 0.768

Period 62:1 to 75:4

i oO 1 2 : 3 4 Sum
i 0.149 0.095 0.053 0.024 0.006 0.326
(3.6) (5.5) (2.9) (1.1) (0.3) (5.3)


LONG-TERM INTEREST RATE

15

RL= 1.735 + &

om

om

(3.3)

0:
0.079
(3.1)

8
0.050
(5.3)

C1)
13.076
(2.8)

i=0

1
0.077
G.7)

0.045
(4.7)

9.804
(2.3)

2
0.074
(4.5)

10 ©
0.040
(4.2)

6.970
(1.5)

A-53

a, RS_; +
i <i
i=0

Period 61:1 to 75:4

3
0.071
(5.4)

11
0.034
(3.7)

4.572
(0.8)

by

4
0.068
(6,2)

12
0.028
(3.4)

2.611
(0.5)

=)
0.064
(6.7)

13
0.021
(3.1)

1.087
(0.3)

A (Loc(P_,))

FR = 0.743 SEE = 0.289 Dw = 1.58 p = 0.667

6
0.597
(6.6)

4

0.015

(2.9)

7
0.055
(6.0)

15
0.007
(2.7)

3

SUM
0.789
(6.7)

8.120
(1.8)


International Finance Discussion Papers
Number 209

September 1982

THE CANADIAN SECTOR OF THE MULTI-COUNTRY MODEL

by

Howard Howe

NOTE: International Finance Discussion Papers: are preliminary materials
circulated to stimulate discussion and critical comment. References in
publications to International Finance Discussion Papers (other than an
acknowledgment by a writer that he has had access to unpublished material)
should be cleared with the author or authors.


x = QSCALE
x — QSMI'TH
x = QTAXI
x QUI
X ~— QZEUROE'
x MQ}.
93,4
x RD
* RED
x RES }
RESNSA,
x  RESV
RF
RL
* ~ROWPMG
* ROWPXG
RR
RS
RSLD

A-79

dummy to reflect economies of scale in Canadian auto
manufacture
dummy to reflect the Smithsonian agreement

dummy for indexation of tax structure to Canadian price

level
dummy for revision of the unemployment act

dummy to account for federal borrowing in Deutsche marks

seasonal dummies

discount rate (BOC)

three month Eurodollar deposit rate (FRB)

residual error of estimate - from GNP component.

residual error of estimate (STATCAN)

free reserves, excess reserves less borrowed reserves
long-term interest rate Government of Canada Bonds --
10 years and over (BOC)

ROW import price index

ROW export price index

required reserves (BOC)

short-term interest rate, 90 day finance company
paper (BOC)

short-term interest rate (when discount rate is lower than

short-term interest rate)


measure of net foreign assets in the monetary base equation, it is
necessary to work with a balance sheet for the consolidated monetary
authorities. (This was done for Japan also.) The consolidated account
is generated from the balance sheets of the Bank of Canada (BOC) and the

Exchange Fund Account (EFA). For our purposes the balance sheets can be

written:

Bank of Canada (BOC) Exchange Fund Account (EFA)
Assets Liabilities Assets Liabilities
Net Foreign Currency (CUR) Net Foreign Claims of the
Assets (NFABOC) Assets (NFAEFA) Government of
Net Government Total Reserves (RT) Canada on the EFA
Position (NGPBOC)
Borrowed

Reserves (RB)

Other Assets (OTH)

The assets of the EFA are combined with those of the BOC to yield
total foreign exchange reserves. The liabilities of the EFA are subtracted
from the net government position of the BOC (NGPBOC) to obtain NBP of the

consolidated monetary authorities (NGP = NGPBOC - NFAEFA).

Assets Liabilities
wat! CUR

NGP RT

RB


RU
SCRG
SCRP
sD
SDRVAL

stc

STL

TB

TCORPV

TD
TIME
TINDV
TNRESV
TPERV

TRANV

ucU

UGNP

A-80

short-term interest rate (when discount rate is higher than
short term interest rate)

unborrowed reserves, total reserves less borrowed reserves
discard rate for gross government fixed capital stock
discard rate for gross private fixed capital stock
savings deposits (BOC)

SDR allocations and valuation adjustment (NFAT - NFA)
stock of private short-term claims on foreigners
(cumulated value of DSTC)

Canadian stock private short-term liabilities on foreigners
(cumulated value of DSTL)

trade balance (XGV - MGV)

direct taxes on corporate and government business
enterprises (STATCAN)

time deposits held by residents (BOC)

linear time trend

indirect taxes (STATCAN)

direct taxes on non-residents (STATCAN)

direct taxes, personal (STATCAN)

government transfers (STATCAN)

government tax revenue (STATCAN)’

U.S. capacity utilization index

U.S. gross national product

unemployment .rate (STATCAN)


LIST OF BEHAVIORAL EQUATIONS

A. Domestic expenditure sector

Disposable income bridge
Consumption function
Private fixed investment
Inventory investment
Capital consumption allowance
B. Government sector
Tax functions:
Personal
Nonresidential
Corporate
Government transfers
C. Current account

Exports of goods: bridge equation (customs clearance
basis to balance of payments basis)

Imports of goods: bridge equation (customs clearance
basis to balance of payment basis)

Kilateral import demand functions:
Imports from Germany
Imports from Japan
Imports from the rest-of-the-world
Imports from the United Kingdom

Imports from the United States

PAGE

A-6
A-7

A-8

A-10
A-11
A-12

A-14

A-15

A-16

A-17
A-18
A-19

A-20


A-60

LED EXCHANGE RATE

2 2° .
ELEAD = 0.588 - 0.241 KFIX+ = ay B.yiy + EF by Eygiy
(4.6) (0.6) i-0 i=0
2 . 2
*KFIX+ EZ cy DNFA_, + dy DNFA_, * KFIX
4=0 1 460 .
1 , 1
+ Ee NGP,+ gf f NGP_, * KFIX
i=0 ; i=0

R = 0.923 SEE = 0.010 DW = 1.33

Period 61:1 to 75:4

i 0 1 2 .
a 1,133 = 0.226 - 0.511
(5.6) (0.8) (2.5)
b= :0.093 0.574 - 0.253
(0.1) (0.5) (0.4)
ce 0.016 0.005 = 0.007
(5.0) (1.0) (2.3)
€@ -=-0.013 ~ 0.005 0.006
(3.2) (0.9) (1.5)
e .0.055 = (0.056
(2.7) (2.6)
£ + 0.091 0.091

(3.1) (3.1)


A-55

CHANGE IN SHORT-TERM LIABILITIES

DSTL = - 0.387 - 0.943 Q2 - 0.324 Q3 - 0.466 Q4 + 0.091 A(MGV)
(0.2) (3.6) (1.9) (2.0) (1.7)

- 0.406 QCRISIS ~ 0.115 A(URS) + 0.265 A(MGV) * KFIX

(1.5) (1.5) (3.2)
5
- 0.446 QIET2 - 0.914 QRFID + 0.307 QEREG69 + © a; ACUNW_,)
(3.0) (1.9) > (1.6) i=0 : 7
3
+ = by L/ER_ + 0.850 QSMITH
i=0 (1.9),
R = 0.4256 SEE = 0.424 DW = 2.45
Period 61:1 to 75:4
i 0 1 2 3 4 5 SUM

a 0.014 0.011 0.009 0.007 0.004 0.002 0.048
(3.2) (3.2) (3.2) (3.2) (3.2) (3.2) (3.2)

b -2.138 0.140 -0.882 -0.929 . 0.468
(0.6) (0.2) (0.5) (0.5) (0.3)


-15-

In-sample tracking.--The Canadian model by itself was simulated dynamically
over the eleven-year period between the fourth quarter of 1964 and the fourth
quarter of 1975. This simulation period spans both fixed and floating exchange
rate regimes. The first column of Table 1 presents the mean percentage
errors and the root mean squared percentage errors for key variables in the
sample period; the second column presents the same statistics for the five-
quarter post-sample period available at the time the model was tested before
inclusion in the MCM.

In-sample errors are, by and large, within the range of acceptable
error for medium-sized macroeconomic models. The root mean square percentage
error (RMSE) for GNP is 2.4 percent over the 45 quarter sample period. This
error falls within the bounds for other MCM models wihc range from 2.4 percent
for the U.S. model to 4.4 percent for the German model. It compares favorably
with the 1.7 percent in-sample error of the RDX2 model of the Bank of canada .2/
The domestic absorption deflator tracks very well at a RMSE of 0.6 percent,
the lowest of the MCM models. Unemplcyment rates, being a residual number,
normally tracx with a RMSE in the double-digit range; the Canadian model's
RMSE for the unemployment rate is 14.1 percent, the lowest of the MCM models.

The interest rate performs worse than the other domestic variables.
While interest rate equations normally track on the high side of other variables,
the RMSE of 26 percent is the highest of the errors for MCM interest rates
This RMSE compares unfavorably with the 6.8 percent error observed for
the RDX2 mode1.2/ The tracking properties of the Canadian interest rate could
have been improved considerably by Linking the rate directly to the U.S.
short-term interest rate. But as explained in the previous section on the

financial sector, this approach was eschewed in favor of the specification


A-25

BILATERAL BRIDGE EQUATION: IMPORTS FROM THE U.K.

MCEV = - 0.003 + 0.941 XECV + 0.155 XECV_y
(0.1) (19.1) (3.1)

R? = 0.967 SEE = 0.047 pw = 1.94

Period 61:1 to 75:4



A-67

Short-term liabilities and claims, stocks

52. STL = STL.) - DSTL / 4

53. STC

STC. - DSTC / 4

Long-term direct liabilities and claims, stocks

54, LIDL = LTDL.y - DLIDL / 4
55. LIDC = LTDC_, ~ DLTDC / 4

Long-term protfolio liabilities and claims, stocks

56. LIPL = LYPL_y - DLTPL / 4
57. LIPC = LTPC_y - DLTPC / 4

Net_government capital account, stock .

58. NGK = NGK_, - NGKA / 4”

Stock of financial liabilities and claims by foreigners

59, FL = - (STL + LTPL + LTDL)
60. FC = STC + LIPC + LTDC + NFAEQQ + NGK

Foreign average short-term interest rate

61. FRSC = .268 * URS + .732 * RED

62. FRSL = .219 * URS + .781 * RED

"

Proxy for expected exchange rate

63. DEFLOAT (E / ELEAD - 1) * 400

4"

64. DEFIXED = MGV_, / (NFAEOQ_, + NFAEOQ_>) * 2 *
PXGUV_1 / PCOMP_y
65. DEFIXE2 = MGV_, / (NFAEOQ | + NFAEOQ_) * 2

Change in reserve requirement

66. “DRR = A(A) * (DD_y = 7.4) / 100


A-46

DEMAND DEPOSITS

DD/NWNSA = - 0.001 - 0.007 Q2 - 0.009 Q3 - 0.001 Q4 - 2.2E-04 TRE .
~ (0.3) = (6.0) (4.4) (0.8) (2.0)

+ 0.698 DD_,/NWNSA + 0,072 GNPVNSA/NWNSA ~ 0.001 RS
(8.0) (3.6) G.5)

B= 0.950 SEE = 0.002 DW = 1.21

Period 61:1 to 75:4


PRIVATE FIXED INVESTMENT

5 11
IFP = - 5.275 + 0.083 KP_, + 2, a, A(RL, .) +,2 b. A(GNP. . -G
(2.9) (11.3) -1 1=0 “i -i-1 : i=0 “1 i -i-1 -i-1
R? = 0.760 SEE = 0.375 DW=1.5 p = 0.919
4 0 1 2 3 4 5 sum
a, 0.349 «0.781 0.985 -0.984 0.803 0.467 -4.369
(2.2) (3.8) (4.2) (41) (35) (2,8) (4.1)
i 0 1 2 3 4 5
by 041050102, «0,119 0.148 = 0185 0,222
(2.1) (2.2) (2.0) (222) (25) (2,9)
6 7 8 9 10 rey SUM
0.255 0.276 «= 0.279 «0.260 0.2110. 126 2.288

(3.1) (3.3) (3.3) (3.3). (3.2) (3.1) (3.3)


A-19

BILATERAL IMPORT DEMAND FUNCTION: IMPORTS FROM THE REST-OF-THE-WORLD
LOG(MCRV/ROWPXG) = - 5.610 - 0.088 Ql + 0.026 Q2 ~ 0.134 Q3
(25.6) (2.9) (0.9) (4.4)
+ 1,529 LOG(GNEVNSA/PGNP) + 0.290 LOG(P./ (ROWPXG/E))
(30.8) (4.0)
R? = 0.949 SEE = 0.083 DW = 1.57

Period 61:1 to 75:4


A-24

BILATERAL BRIDGE EQUATION: IMPORTS FROM THE REST-OF-THE-WORLD

MCRV = 0.209 + 0.643 XRCV + 0.271 XRCV_)
(3.8) (10.5) (4.3)

® = 0.991 SEE = 0.263 Dw = 1.39

Period 61:1 to 75:4


BILATERAL IMPORT DEMAND FUNCTION: IMPORTS FROM THE U.K.

LOG(XECV/(EPXGUV * EE)) = - 0.734 - 0.128 Ql + 0.039 Q2 - 0.093 Q3
(1.3) (4.0) (1.2) (3.0)
+ 0.153 LOG(GNPVNSA/PGNP) - 0.141 EDV41 - 0.150 EDV50
(1.2) (1.5) (1.7)
. : 4
~ 0.043 EDV30 + 0.064 EDV49 - 0.125 EDVS + Za,
(0.7) (0.7) (1.4): i=0
LOG(P_; /(EPXGUV_; * EEL; / E_;))
—2 S
R= 0.604 SEE = 0.089 DW = 2.02 p= 0.329 iy
Period 61:1 to 75:4 ‘
i 0 1 2 3 4 SUM
ay -0.032 0.289 0.453 0.460 0.309 1.479

(0.1) (3.2) (3.4) (2.5) (2.2) (4.8)


A-49

CURRENCY

CUR/NWNSA = 0.004 - 0.002 Q2 - 0.004 Q3 ~ 0.002 Q4 - 1.5E-04 TIME
(4.0) (4.8) (7.7) (5.0) (4.4)

+ 0.047 GNPVNSA/NWNSA - 3.3E-04 RS
(9.4) (4.0)

B © 0.941 SEE = 7.5E-04 DW = 0.80

Period 61:1 to 75:4


FORWARD EXCHANGE RATE

EF = 10.022 + 8.142E-05 Q2 + 1.108E-04 Q3 = 3.4498-04 Q4 + 0.002 E * FRSL
(2.8) (0.3) (0.4) (1.1) (16.2)

= 0.002 E * RS + 0.977 E - 4.407E-04 KFIX * DEFIXED * E
(13.1) (118.5) (2.9)

+ 8,006E-05 (1 - KFIX) * DEFLOAT * E
(2.6)

BR = 0.9995 SEE = 8.18E-04 DW = 1.18

Period 61:1 to 75:4


A-14

GOVERNMENT SRANSFERS

TRANV = - 2.119 - 1.738 Q2 - 2.764 Q3 ~ 2.033 Q4 + 0.152 (GNFVNSA ~ XGV)
(1.7) (5.6) (7.3) (6.4) (7.5)

+ 0.283 XGV + 2.965 (UN * LF/100) - 46.473 A (LOG(P)) - 0.085 Timi:
(4.2) (YD) (2,0) (4.6)

RB? = 0.982 SEE = 0,732 DW = 1.57

Period 61:1 to 75:4


(2) The bulk of Canadian foreign exchange reserves are not
held by the Bank of Canada,
(3) The reserve requirement is lagged, and
(4) Borrowed reserves are a very small fraction of central bank
assets.2/
Secondary reserves.--Most Canadian financial modelers do not seem to
think that the secondary reserve requirement has been a binding condition.
If it were, however, the requirement would add another component in the
demand for Treasury bills. Suppose that the demand for Treasury bills
in the absence of a secondary reserve requirement followed a conventional
portfolio demand specification where the nonbank demand component isa
function of private wealth, income, and rates of return and the bank
demand component is a function of deposits (time plus demand), net of the
cash reserve requirement and rates of return. Now, if a secondary reserve
requirement is imposed, the banks' demand for Treasury bills is the
maximum of either the conventional demand for Treasury bills or the
secondary reserve ratio times total deposits.

Recall, however, that the MCM does not model the bond market .3/
Hence, secondary reserves are important only insofar as they might affect
the demand for money or other assets (foreign short- or long-term capital
inflows and outflows). This indirect effect on the banks' demand for
money is probably small. Early tests for this effect by including the
secondary reserve requirement in the inverted free reserves equation
and the capital flow equations showed no significant effect.

Exchange Fund Account.--The bulk of Canadian foreign exchang2? reserves

are held in the Exchange Fund Account (EFA). Therefore, to get a meaningful


A-77

NGK stock of government assets -- excluding foreign private
holding of government which are included in LTPL
(cumulated value of NGKA)

NGKA net government capital account (STATCAN)

NGP net government position of the consolidated monetary

authorities (BOC)

NW : +
Nunsa stock of private net worth (cumulated value of DNW)

OTH other assets of the Bank of Canada (BOC)

P implicit deflator for domestic absorption ((CV + IFGV
+ IFPV + IIV + GV)/(C + IFG + IFP + II + G))

PCHGNP percentage: change in gross national product

PCHP percentage change in domestic price level

PCHW percentage change in wages

PCOMP foreign weighted average of the price of exports!

PGNP implicit deflator for GNP (GNPV/GNP)

PMGSNI implicit deflator for imports of goods and services,
national income accounts basis (MGSNIV/MGSNI)

PMGUV unit value of merchandise imports (STATCAN)

PMS implicit deflator of import services ((MGSNIVS - MGV)/
(MGSNINS - MG))

POP15 Canadian population 15 years of age and older (STATCAN)

lpyade weighted average for Germany, Japan, the United Kingdom
and the United States.


A-37

EXPORT UNIT VALUE
PXGUV = 0.213 = 0.005 TIME + 0.002 CUSTCU 0.486 LOG(PCOMP) * (1-KFIX)
(2.4) (3.6) (2.0) (8.3)

+ 1,038 LOG(P) - 0.252 LOG(P) *-(1-KFIX)
(7.2) (4.6)

R = 0,967 SEE = 0.012 DW

1

‘1.76 p = 0.746
Period 61:1 to 75:4


A-23

BILATERAL BRIDGE EQUATION: IMPORTS FROM JAPAN

MCIV = 0.004 + 0.518 xscv + 0.564 XJCV_)
(0.4) (8.6) (9.2)

R? = 0.987 SEE = 0.057 pw = 3.27

Period 61:1 to 75:4


DITPL
DNFA

DNFAFL
DNFAFX

DNGP

DNGPFL
DNGPFX

. DNW
DNWNSA

DRR
DSTC

DSTL

EANDO .

ECU
EDV30
EDV41

EDV49

EDVS

EDV50

change in long-term portfolio liabilities to foreigners (STATCAN)
change in net foreign assets of the central bank (STATCAN)

DNFA * (1-KFIX)

DNFA * KFIX

change in net government position of the consolidated monetary
authorities ,

DNGP * (1-KFIX)

DNGP * KFIX

¢hange in private net worth (STATCAN)

change in required reserves

change in short-term claims on foreigners (STATCAN)
change in short-term liabilities to foreigners (STATCAN)
Canadian spot exchange rate index, US$/C$, (ER/1.009)
errors and omissions (STATCAN) ,

U.K. capacity utilization index (WHARTON)

U.K. dummy for shift in automobile imports, 7001 = 1
U.K. dock strike dummy, 7203 = 1

U.K. dummy for anticipation of floating of sterling,
7202 = 1

U.K. dock strike dummy, 1 from 6701 to 6704 (LONDON BUSINESS
SCHOOL)

U.K. dock strike dummy, 7002 = 1

spot ‘exchange rate index, U.S.$/£ (FRB)


-29-

The expected exchange rate function during a fixed exchange rate regime
in the Canadian model is an inverse function of the Canadian export price 22/
With an exogenous revaluation of the currency, the relative export price
increases and agents' expectations. of. a future devaluation increase. With
these expectations, capital inflows decrease and contribute to the decline

in exchange rate reserves.

In response to the contraction in the monetary base resulting from the

decline in the stock of-reserves, the interest rate increases by 94 basis points

- at the enc. of the first year. Since the effect on the monetary base is
cumulative, the three-year continuation of an increased trade deficit and
decreased capital inflows eventually lead to an increase in the short-term
interest rate on the order of 200 basis points.

The increases in both the trade deficit and the interest rate reinforce
each other in reducing the level of GNP. The effect is small initally and
increases to the order of $C 0.6 billion at the end of three years. The domestic
price level declines accordingly. Corresponding to the decline in activity,
the unemployment rate increases, eventually by 0.4 percentage points. The initial
decline in the unemployment rate is the result of an initial decline in the
real wage resulting from a larger decrease in nominal GNP than in the money

wage.


25-

eleven periods after the increase in the discount rate. In response to this
decline in activity, the domestic price level falls slowly at first, eventually
declining six tenths of one percent below its base level at the end of 11 quarters.
Unemployment increases by one-half percentage point four quarters afer the monetary
contraction begins and then fluctuates slightly about that change for the
remainder of the period.

The short-term interest rate increases 83 basis points initially, and
then by 90 basis points in the second quarter. As activity and loan demand
slow, the increase in the short-term interest rate drops back to the 80 basis
point range for the remainder of the period. In response to both the slowing
of imports and capital inflows responding to the widening of the Canadian-
foreign interest rate differential, the Canadian dollar appreciates by roughly
10 percent at the end of two years.

Foreign interest rates.--The final experiment presented for the floating
exchange rate period tests the effects:of a 100 basis point increase in the
U.S. short-term rate accompanied by a 70 basis point increase in the Eurodollar
rate. Table 6 presents the multiplier responses indicating that the narrowing
of the Canadian-foreign interest rate differential leads intially to a 0.7
percent depreciation of the Canadian dollar. As a result of the depreciation
the import price in local currency increases and real imports decrease. The
average import price elasticity is less than one, however, (the import
price elasticities for the United States and the rest of the world are 0.6
and 0.3, respectively) so the value of imports increases by 0.3 percent in the
initial period. As the size of the depreciation diminishes over time, so does

the increase in the value of imports.


MCUV

MGSNI

MGSNINS

MGSNIV

MGSNIVS

MGV

MSOV

MSYV

MIRANV

MUJEGV

NFAEOQ

NFAEOQR

NFAFED

A-76

merchandise imports from the U.S., c.i.f. (DOT)

import of goods (STATCAN)

import of goods and services, national income accounts
basis (STATCAN)

import of goods and services, national income accounts

basis, not seasonally adjusted (STATCAN)

_ import of goods and services, national income accounts

basis, current value (STATCAN)

import of goods and services, national income accounts
basis, not seasonally adjusted (STATCAN)

import of goods, current value (STATCAN)

service account payments, except investment income (STATCAN)
investment income payments, current value (STATCAN)

BOP transfer payments, current value (STATCAN)

Canadian imports from Japan, Germany, the United Kingdom and
the United States

notice deposits (BOC)

net demand deposits, (1-A) * DD

stock of net foreign assets of the monetary authorities,

end of quarter (cumulated value of DNFA)

non-dollar component of stock of net foreign assets of

the monetary authorities, end of quarter

net foreign assets, foreign exchange in U.S. dollars,

end of quarter


DISPOSABLE INCOME BRIDGE

YDVNSA = = 1,311:+ 2,655 Ql + 1.259 Q2 + 1/116 Q3'+ 0.955 YDPVNSA
(4.1) (8.8) (4.2) (3.7) (230.6)

R’ = 0.9989 SEE. = 0.818 - DW = 1.87

Period 61:1 to 75:4 &


A~29

IMPORTS OF OTHER SERVICES

LOG(MSOV/PMS) = - 1.471 + 0.132 Q2 + 0.083 Q3 - 0.081 Q4
(3.8) (8.5) (4.3) (4.0)

+ 0.617 LOG (MSOV_/PMS_,) + 0.450 LOG(GNP) + 0.388 LOG(P/PMS)
(6.6) (3.9) (1.3)

2 = 0.9794. SEE = 0.042 DW = 1.97

Period 61:1 to 75:4


A-83

YDPVNSA. proxy fox disposable income (GNPVNSA - TV + TRANV - CCAV)

YDV . TAT
yovesa} disposable income (STATCAN)


A-47

SAVING DEPOSITS

SD/NWNSA = ~ 0.014 - 0.007 Q2 - 0.002 Q3 - 0.016 Q4 + 0.320 CVNSA/NWNSA

(3.3) (5.2) (1.6) (10.3) (19.3)
7 .
- 0.002, KFIX * DEFIXED + EZ a; RS_,
(5.6) i=0

= 0.981 SEE = 0.004 DW = 0.65

Period 61:1 to 75:4

i 0 1 2 3 4 5
a, 7.0E-04 6.0E-04 5.0E-04 4.1E-04 3.2E-04  2.3E-04
(3.2) (4.3) (5.4) (4.9) | G.5) (2.5)

6 7 SUM
1,5E-04  0.7E-04 3.0E-03
(1.9) (1.5) .

(5.4)



-F2-

9/ "The Equations of RDX2 Revised and Estimated to 4Q72", Bank of Canada
Technical Report 5, 1967, pp.. 262, 263.

10/ The MCM models can be operated as both fixed and floating exchange
rate systems. When fixed, the exchange rate is declared exogenous and
the change in reserves is declared endogenous. When solved as a floating
rate system, the exchange rate is declared endogenous and the change in
reserve is declared exogenous or explained behaviorally with and
additional intervention function.

11/ See equation 3la and related discussion in IFDP No. 115, pp. 12, 68.


A-65 . : ~

Trade balance

33, TB = XGV - MGV

Total world exports, excluding Canada

34, WIV = XGIV + XJIV + XUIV + XETV + XRTV

Canajian exports to trading partners

35. XUJEGV = XCUV + XCJV + XCEV + XCGV

Canajian imports to trading partners

36, MUJEGV = XUCV + XJCV + XECV + XGCV

Weighted foreign averages of competitors price, capacity utilization
price of exports, gross national product, domestic deflator, and

disposable income 4
37. PCOMP = (GE * GPxcUV)XGTV/WIV » (jg * spxcuv)XJtV/WIV

* (EE * EPXGUV)*£2V/NIV * upxcuysULV/WIV

* ROWPXGRIV/WIV
38. CUSTCU = UCUXCUV/XUJEGV 4 yopXCJV/XUJEGV

ECUXCEV/XUJEGV  ggyXCGV/XUJEGY
39. FEXGUVD = UPXGUVMCUV/MCTV % (Jpxcuy * je) MCIV/MCTV

* (EPXGUV * EE)MCEV/MCTV % (cpxcuy * GE)MCGV/MCTV

* ROWPXCMCRV/MCTV

40. FGNP = UGNPXCUV /XUJEGV * JonpXCIV/XUJEGV

* EcppXCEV/XUJEGV

* conpXCGV/XUJEGV



-12-

(2) The U.S. interest rate appears with a (small) negative sign

in the MCM interest rate equation whereas it appears with a large

(0.5) positive sign in the RDX2 equation. While the linkages:

between the U.S. and Canadian financial markets are strong and

the total effect of U.S. rates on Canadian rates must be positive

(as shown in the multiplier experiments to tollow), the

MCM equation is a structural representation in that it

captures the substitution effect between U.S. and Canadian

assets. When U.S. rates increase, free reserves should decline

as indicated in equation (9). But for a ceteris paribus interpretation
of equation (12), holding free reserves constant would require an
expansion of the Canadian monetary base resulting in a decrease

in the Canadian short-term interest rate.

(3) Through their linkage to the monetary base equation, free

reserves in the MCM transmit the portfolio effects of changes in
foreign financial conditions, via capital flows ‘and changes in foreign
exchange holdings, to the Canadian short-term interest rate. As far

as responsiveness to Candian policy instruments, the RDX2 interest rate
equation responds only indirectly through portfolio holdings (bank loans
aud private holdings of government securities). Thus, while the MCM may
be vulnerable through the small size and volatility of free reserves,
the RDX2 structure depends crucially on the ability to model dependably
the domestic short- and long-term securities markets. Additionally,
while small size and volatility could cause some difficulties

in dynamic tracking performance, once the model is aligned on a
solution path, the dependability of multipliers depends

upon estimation accuracy and the fidelity of the model


A-48

NOTICE DEPOSITS

ND/NWNSA = - 0.044 - 0.004 Q2 - 0.011 Q3 - 0.006 Q4 + 0.129 GNPVNSA/NWNSA
(15.3) (3.1) (7.7) (4-1) (31.2)

+ 8.0E-04 (RS - URS) - 9.8E-04 KFIX * DEFIXE2
(1.3) (3.2)

BR? = 0.957 SEE = 0.004 DW = 0.52

Period 61:1 to 75:4


A-54 -

ERRORS AND OMISSIONS

EANDO = - 1,123 + 1.531 Q2 + 2.192 Q3 + 0.930, Q4— 0.338 A (NWNSA)
(4.0) (4.4) (4.6) (2.6) (3.6)

- 0.528 (A (XGV) - A(MGV)) - 0.229 (XGV + XSOV + XSYV + XTRANV
(3.1) " (2.4)

- MGV - MSOV - MSYV - MIRANV) - 1.662 QNEP + 1.235 QSMITH
(1.8) (1.3)

R = 0.3805 SEE = 0.898 DW = 2.48

Period 61:1 to 75:4


~8-

where a and b are the primary reserve requirements. The bridge equation is

given by:

(4) RR = a + BRRC +e
Substituting computed required reserves from (3) into the bridge equation (4)

and that result into the uses of the unborrowed base (3) yields

(5) BU = a + #aDD + BbTD +c + RF + CUR

Equation (5) can be expressed in terms of demand deposits.
(6) DD = [BU-a- BbTD - € - RF - CUR] /Ba

Equation (6) is a rearrangement of ‘the uses side of the monetary base equation.
Given BU (from the sources side of the base, eq. (1)), reserve requirements
a and b, and n-l uses of reserves (RF and CUR), the stock of demand deposits
that can be supported by the remaining reserves (RR) is determined.

The specifications of the equations determining the four components

of equation (6) are as follows:

(7) 22 = po(enpv/Nw, RS, URS, (EE-E)/E)
NW

Unlike the German case, there are no appreciable government holdings
of time deposits. TD is composed of savings deposits (82% in 1969LV) and
other notice deposits or "deposit receipts." Deposit receipts are sold in
denominations of $C 100,000 or more and are described as temporary repositories
of excess balances of corporations, governments and other organizations. These

corporate notice deposits seem essentially to be negotiable certificates of


XG
XGCV

XGSNI

XGSNINS

XGSNIV

XGSNIVS

XGIV
XGV
XJCV
XJIV
" xRev
XRIV

XSOV

XUCV
XUTV
XSYV
XTRANV

XUJEGV

A-82

export of goods (STATCAN)

Gennan exports to Canada, f£.0.b. (DOT)

exports of goods and services, national income account
basis (STATCAN)

export of goods and services, national income
accounts basis, not seasonally adjusted (STATCAN)
exports of goods ‘and services, national income
accounts basis, current value (S'TATCAN)

export of goods and services, national income
accounts basis, not seasonally adjusted (STATCAN)
total German merchandise exports

exports of goods (STATCAN)

Japanese exports to Canada, f.o.b, .(DOT)

total Japanese merchandise exports

R.O.W. exports to Canada, f.o.b. (DOT)

total R.O.W. merchandise exports

service account receipts, excluding investment income
(STATCAN)

U.S. exports to Canada, f.o.b. (DOT)

total U.S. merchandise exports

investment income receipts (STATCAN) .

transfer receipts (STATCAN)

Canadian exports from Germany, Japan, the United Kingdom

and the United States


A-52

SHORT TERM INTEREST RATE: WHEN. DISCOUNT RATE EXCEEDS SHORT-TERM RATE

RSHD = - 5.558 RF/NDD - 0.143 URS - 38.880 DRR/NDD + 1.034 RD
(0.5) (1.0) (1.1) (8.7) :

- 0.048 DEFLOAT * (1 - KFIX)
(7) ;
R? = 0.934 SEE = 0.383 DW = 1.70
Period: 62:2 to 62:4, 63:2, 68:1 to 68:2, 70:4 to 72:1,

75:1 to 75:3


A-78

PPC dollar export price index of cereals, 1972=100 (United Nations
Monthly Bulletin of Statistics)

PXGUV ; unit value of merchandise exports (STATCAN)

PXS implicit deflator of export services ((XGSNIVS - XGV)
/(XGSNIVS - XG)) :

QAUTO dummy to reflect Canadian-U.s. auto agreement

QAUIST dummy to reflect U.S. auto strike

QBACTS dummy for enactment of bank acts of 1967

QCNTRL dummy to reflect Canadian wage and price controls

QCRISIS dummy for exchange rate crises in 1962 and 1968

QEIETB dummy for deferral of new bond issues in the U.S.

QEREG69 dunmy for divergance of weighted foreign rate from true
foreign rate

QEXPO dumny to reflect effects of Expo 67

QFRID dummy to reflect end of quarter occurring on a Friday

QIET1 dummy to reflect interest equalization tax

QIET2 dummy to reflect interest equalization tax

QLOBO dummy for exchange rate uncertainty and federal policy
discouraging foreign borrowing

QMIDEA dummy for Suez Canel closing

QNEP dummy for new economic program in U.S.

QRD dummy for periods when the discount rate is greater than the

short term interest rate


A-63

LIS’ OF IDENTITIES

Ll. GNP = C + IFP + IFG + II + G + XGSNI - MGSNI + RES
2. GNPV = CV + IFPV + IFGV + ILIV + GV + XGSNIV - MGSNIV + RESV
3.  GNPVNSA = GNPV / SAFGNPV
4.  PCHGNP = A(LOG(GNP)) * 400
. Comporents of GNP
5. G=Gv/P

5. CV=C*P

7. %IFPV = IFP * P
8. IFGV = IFG * P

9. IIV=IL*P

u

10. NGSNIV = SAFMNIV * MGSNIVS
11. XGSNIV = SAFXNIV * XGSNIVS
12. CVNSA = CV / SAFCV
13, IFGVNSA = IFGV / SAFIFGV
14. IFPVNSA = IFPV / SAFIFPV

Disposable income proxy

15. YDPVNSA = GNPVNSA - TV + TRANV - CCAV
16, YDV = YDVNSA * SAFYDV

- Capital stock
17. KG = (1 - SCRG / 4) * KG_y + IFG / 4

18. KP = (1 - SCRP / 4) * KP_y + IFP / 4


A-31

IMPORTS OF GOODS AND SERVICES: BRIDCE EQUATION (balance of payments basis

to National Income Accounts basis)

MGSNIVS = ~ 0,002 + 1.000 (MGV + MSOV + MSYV)
(0.2) (2263.9)

: 2
R? = 0.999 SEE = 0.038 DW = 2.17

Period 61:1 to 75:4


EXPORT OF coops!/

LOG(XG) = -2.662 - 0.102 Ql + 0.002 Q2 - 0.036 Q3 + 0.930 LOG (WNGV/ROWPMG)

(5.5) (6.8) (0.1) (2.5) (10.1)

2 3

= ay LOG (PXGUV_ ; /UPXGUV_,;) + 2 i LOG(E_;_4) + 0,054 QSCALE
i=0 i=0 . (1.5)

+ 0.006 QAUTST
(1.0)

R? = 0.9661 SEE = 0.045 DW=1.77 p = 0.418

Period 61:1 to 75:4

i 0 1 2 3 Sum
a, 0.364 -0.243 -0.121 0.728

(1.3) (1.3) (1.3) (1.3)

by 0.430 -0.322, 0.215. -0.197. 1.075
(2.3) (2.3) (2.3) (2.3) (2.3)

L/ This equation is used only when the Canadian model is
simulated in isolation from the other models of the MCM.


-21-

Table 3

Historical Values for Key Variables
in Canadian Multiplier Experiments

1973 1974

2ts]se6iti{tsiteztsti|-.

fi. | 2} 3].

GaP 112.0 113.1 116.2 117.8 117.4 117.2 116.9

r 1.067 1.089 1.118) 1,152 1,200 1.249 1.284

w 5.45 5.38 5.57 5.30 5.23 5.20 5.53

as* 6.27 8.20 9.43 9.20 11.00 11.60 10.20

vosurvs? 3.6 29.3 34.8 35.4 41.6 40.9 46.0

i‘ 991 987 991 1.011 1.026 1.010 1.006
1

{1lions of Canadian dollars, annual rate.

2 1972 = 1.00

3 Percentage points.

4 U.S. dollars per Canadian dollar, 1972 = 1.0.

116.7 117.9 119.6 120.0
1.329 1.353 1.388 1.416
6.55 6.95 7.07 7.07
7.43 7.27 8.09 9.10

43.3 47.7 43.4 47.6
992 +969 961 2975,


A-18

BILATERAL IMPORT DEMAND FUNCTION: IMPORTS FROM JAPAN

LOG (XJCV/JPXGUV * JE)) = - 10.502 + 0.052 Ql + 0.043 Q2 - 0.130 Q3
(7.1) (1.4) (1.4) (3.5)

+ 2.199 LOG (CNPVNSA/PGNP) + 1.248 LOG (P/(JPXGUV * JE/E)
(6.8) (2.4) ;

1

wl

= 0.615 SEE = 0.111 DW= 1.86 p = 0.853

Period 61:1 to 75:4


A-22

BILATERAL BRIDGE EQUATION: IMPORTS FROM GERMANY

MCGV = - 0.004 + 0.974 xcCV + 0.172 xccv
(0.3) (14.1) (2.3) vi

R? = 0.971 SEE = 0.042 DW = 1.95

Period 61:1 to 75:4


A-51

SHORT-TERM INTEREST RATE: WHEN SHORT-TERM RATE EXCEEDS THE DISCOUNT RATE

RSLD = - 1.190 - 27.949 RF/NDD + 12.057 4 (RU)/NDD - 67.746 DRR/NDD
(2.4) (2.0) (1.2) (2.7)

+ 1,090 RD + 0.270 RS_, - 0.0217 DEFLOAT * (1 - KFIX)
(5.6) (2.4) (1.0)

~ 0.094 QBACTS * RD -.0,139 DEFIXED * KFIX
(1.6) (3.1)

—2

R® = ,9525 SEE = 0.469 DW ='1.00

Périod 61:1 to 62:1, 63:1, 63:3.to 67:4, 68:3 to 70:3,
72:2 to 74:4, 75:4


-16-

Table 1

Dynamic Simulation of the Canadian Model
in Isolation from the MCM

Variables In-Sample Errors Post-Samp:.e Errors
64:4-75:4 76:1--77:1
GNP - vel 0.087 0.3787
RMSE? 2.403 1.403
P ME 0.161 -0.324
RMSE 0.633 0.600
cu ME 0.428 -0.659
RMSE 3.980 1.067
UN. ME 2.705 ~8.896
RMSE 14.130 . 12.798
RS ME ~8.683 16.170
RMSE 26.064 17.494
MG ME 70.554 0.055
RMSE 6.660 3.630
MGV ME -0.490 9.521
RMSE 5.821 12.959
PMGUV ME 0.178 9.094
RMSE 2.557 10.612
XG ME -0.232 5.076
RMSE 1.208 . 7.393
PXGUV ME 0.214 9.775
RMSE 2.200 10.€16
E ME 1.044 -10.062
RMSE 2.512 10.765
NFAEOQ ME 39.732 22.402
RMSE 57.732 23.713

lvean percentage error.

2Root mean squared percentage error.


A-26

BILATERAL BRIDGE EQUATION: IMPORTS FROM THE U.S.

MCUV = - 0.411 + 1.182 XUCV + 0,018 XUCV_,
(4.7) (39.8) (0.6)

R = 0.997 SEE = 0.337 DW = 1.32

Period 61:1 to 75:4


-5-

Laggei_ reserve requirements.

Required reserves are actually based on

average deposits over the four consecutive Wednesdays ending with the second
last Wednesday of the previous month. The current averaging period for meet-
ing reserve requirements is 15 days. Because U.S. reserve requirements are
also lagged, this difference with respect to the prototype is one of degree.
The reserves computed from end-of-month deposit data do not correspond to

the "true" reserves based on deposits during the previous month. Required
reserves ere reported on a daily average basis for the month. All other

items in the monetary base equation are reported on an end-of-month basis.

On a monthly. basis, then, bank deposits are not at all tied to primary
reserves. On a quarterly basis, however, a large component (roughly two-

thirds) of required reseves are contemporaneous with bank deposits. The

procedure in the MCM databank constructs mid-quarter averages of bank
deposits and then computes required reserves from the statutory require-
ments. This computed reserve requirement is linked to the mid-quarter average
of the reported daily-average required reserves with a bridge equation. The
use of actual required reserves gives a better measure of free reserves than
would computed required reserves for use in the inverted reserve identity.
Chartered banks.--Reserves and time and demand deposits are obtained from
the balance sheet of the chartered banks. In the Canadian case, the balance
sheet wag constructed according to a slightly disaggregated version of the

balance sheet in the prototype model.


A-43,

WAGE BILL

WB = - 10.667 + 1.019 LF * (1 - UN/100) *W * 2+ 0.104 cu
(4.1) (168.7) (3.7)

R? = 0.998 SEE = 0.438 DW = 1.83 p = 0.586
Period 61:1 to 75:4


Footnotes

%/ The work described in this Paper was carried out while I was an
Economist in the International Finance Division. I am very grateful to
John Boschen and Joseph Formoso for their important contributiors to the
construction and testing of the Canadian model. The views expressed in
this paper are mine and do not necessarily represent the views cf the
Federal Reserve System.

1/ The book will be published by the Board of Governors of the Federal
Reserve System in late 1982. See also Richard Berner, et al., "Modeling
the Internationai Influences on the U.S. Economy: A Multi-Country Approach"
(IFDP No. 93) and Richard Berner, et. al. "A Multi-Country Model of the
International Influences on the U.S. Economy: Preliminary Results,"

(IFDP No. 115).

2/ For a useful presentation of Canadian central banking and the financial
system see D. E. Bond and R. A. Sherer The Economics of the Canadian
Financial System: Theory, Policy and Institutions Preatice Hall Canada
Scarborough: Ontario 1972, especially chaps. 16-18.

3/ Refer to the arguments in IFDP No. 98 (pp. 32-37) for the justificaticn
behind the substitution of the balance of Payments conditions for the bond
market.

4/ NFA (which excludes valuation adjustments and SDR allocations) is
constructed by accumulating CDNFA (D50712 - D50710) from 19731V benchmark.
The benchmark is B3800 (total reserves) converted to $C by CE x 1.00937.
The 1973IV benchmark is chosen for consistency with the stocks of
international claims and liabilities. The fourth quarter of 1973 was

the latest date for Canada's balance of international indebtedness (Cat.
67-202, Table 1, pp. 72-73) at the time of constructing the MCM databank.

5/ Borrowed reserves, RB, consist of advances to chartered and savings
banks plus bankers acceptance plus GOC securities held under repirchase
agreements (B209). This last item is netted out from the BOC holdings of
own advances to chartered banks, B658, appears as ADV.

6/ Currency held by banks (B252) counts as a reserve asset. Total reserves
are B608 = B252 + B255. Comparison of B603 for Jan. 75 end-of-month

(3370) with B819, actual reserves of chartered banks, for daily average

for second half of Jan. 75 (3571) verifies this. There is no need to handle
vault cash separately.

7/ The two versions have the effect of giving different elasticities over
different time periods. This problem shows up in the multiplier responses
of Tables 2 through 7.

8/ Purchase of foreign exchange reserves to resist an expected appreciation
of the Canadian dollar will be lower, as the stock of foreign exchange
reserves is higher. Note that this intervention function alse behaves

as if it were specified as a "target level of reserves" function.


CAPACITY UTILIZATION

LOG(GNE/LF) - 0.28 * Loc(KP/LF) = 1.286 + 0.003 TIME + 0.584 LOG(CU/100)
(110.6) (20.0) (10.4)

= 0.933 SEE = 0.008 DW= 2.03 p = 0.637

. Period 61:1 to 75:4


A-34

INVESTMENT INCOME RECEIPTS

XSYV = 0.003 FC + 0.003 Q2 * FC ~ 0.001 Q3 * FC
(0.9) (2.0) “ (0.8)

+ 0. 006 Q4 * FC + 0.004 (E -1/E) * NFAEOQ_ * FRSC
(4.2) (2.1) .

+ 0.008 (E 1 /E) * URL * LIDC_)
(3.9)

R2 = 0.7934 SEE = 0.091 DW=1.9 p = 0.315

Period 61:1 to 75:4


-23-

Table 4

Effects of a $C 1 billion Increase
in Personal Tax Revenues (current dollars)

1973 1974 1975

2 |,il., 1 ats 4 it. 3 4
-.207 =.347 ~.489 -.612 -.724 -.748 ~.825 ~.881 =.925 -.936 -.971
0.000 -.001 ~.001 -.002 =.004 ~.005 -.007 ~-.010 -.013 -.015 -.017
+028 +058 096 114 129 *, 133 129 116 114 «lll 092
1037-097 --.172 | -.262,=.381 =.482-.589 | -.2347  -.260° -.3527 -.853
=.085 9 =.170=.268 | -.398 = =:541 --.709 -.842 | -1.001 -1.140 -1.225 1.262
1001 003-004 |. 006 008 = 011.014 020.028.023.021

billions of Canadian dollars, annual rate.

1972 = 1.0.

Percentage points.

U.S. collars per Canadian dollar,.1972 = 1.0.

This drop.in the interest rate effect is spurious.

It occurs historically

at a point where the interest rate equation experiences a behavioral shift

between discount rate regimes.

See discussion of the two interest rate

equations above in the financial sector of this paper.

The 50-odd basis

point drop is related to the first quarter of 1975 and not to the eighth

period after the fiscal stimulus.


A-8

INVENTORY INVESTMENT

4
IL = - 1.719 + 0.493 E. (C_, + IFP_; + IFG_, + XxG_,) /4
(0.7) (3.8) tt 0 F t i i

4 ;
- 0.865 5. Qig_5) /4 + 0.551 MG - 0.404 (C + IFP + IFG + XG)
(2.9) 4°12 (4.8) (4.5)

R? = 0.258 SEE = 0.683 DW = 2.23 p = 0.491

Period 61:1 to 75:4

ts aged phick.


A-28

EXPORTS OF OTHER SERVICES

LOG(XSOV/PXS) = = 1.095 + 0.387 Q2 + 0.527 Q3 - 0.028 Q4 +
(2.1) (11.6) (17.5) - (0.5)

+ 0,500 LOG(XSOV_, /PXS p + 0.202 LOG(FGNP)- + 0.060 QEXPO
(3.6) - (2.3) (1.4)

+ 0.034 QAUTO + 0.197 LOG(FP/PXS)
(2.0) qa.)

BR = 0.9681 .SEE = 0.061 DW = 2.34

Period 61:1 to 75:4


-26-

Table 6

Effects of an Increase in Foreign Interest
Rates (100 basis points in the U.S. Short-term
rate and 70 basis points in the Eurodollar rate).

1973 1974 1975
| 1, i [1 |» | s/.]4{, [sf .

cur? +007 030.045 | .062 048 = 032.017 018 = 013,015,
? +001 = .001,—S 001 | .001 +001 = .001.001 002.002.002.001
w? +001 -.014=.025} -.024 = -.014--.006~—.001 010.014.011.006
rs‘ 1054 1669 | 45 1086 045.028 | -.1199 1299-120 -. 0099
vcsntvs! +127, 4122, 078 | .062 062.065 .053 | 052.049.038.026
z =-004 — -,006 — -.003 | ~.001 .  -.001  =.001 -.001 | =.002 -.001-.062 oo

1 billions of Canadian dollars, annual rate.

2 1972 = 1.0.
3

Percentage points.
4 U.S. dollars per Canadian dollar, 1972 = 1.0.

In this experiment, the discount did not exceed the short-term rate until
the last quarter of 1975, so the switch of interest rate equations occurred
here rather than in the first quarter. Like the previous multiplier responses,

the drop in the interest rate response is the result of switchine between

interest rate equations and not the number of periods after the introduction

of the shock.


A-61

NET FOREIGN ASSETS: FLOATING EXCHANGE RATE PERIOD

DNFAFIL = 1.219 (1 - KFIX) + 0.114 (E/E_1-1) * (1 - KFIX)
(0.7) (3.8)

- 0.228 (NFAEOQ,) + NFAEOQ_,) * 5 * (1 - KFIX)
(0.7) :

R? = 0.5011 SEE = 0.650 DW = 1.72

Period 70:3 to 75:4


A-15

EXPORTS OF GOODS: BRIDGE EQUATION (Customs clearance to balance of
payments basis)

XGV * ER = 0.679 - 0.205 Ql - 0.024 Q2 - 0.172 Q3 + 0.950 XCTV:
(6.9) (2.0) (0.2) (1.7) (244.5)

R? = 0.999 SEE = 0.282 DW = 1.27

Period 61:1 to 75:4


A-56

CHANGE _IN SHORT-TERM CLAIMS

- DSTC = - 0.534 - 0.160 Q2 + 0.952 Q3 + 0.423 Q4 - 0.483 A(RS)
(1.7) (0.4) (3.0) (1.1) (2.5)

+ 0.549 AFRSC + 0.757 QEREG69 + 0.035 .A (DEFLOAT) * (1-KFIX)
(3.4) (2.2) (1.5)

+ 0.157 A(XGV) + 0.129 DLTPL - 1,172 QFRID + 0.282 QIET1
(2.0) . (1.5) (1.4) (0.7)

+ 0.124 QIET2 - 1.493 QNEP
(0.5) (1.8) ©

R= 0.404 SEE = 0.771 DW = 2.18

Period 61:1 to 75:4


A-33

TRANSFER PAYMENTS

MIRANV = 0.183 + 0.007 YDVNSA
(8.2) (18.4)

2
R = 0.8515 SEE = 0.073 DW = 1.87

Period 61:1 to 75:4


A-57

CHANGE IN LONG-TERM LIABILITIES

DLTPL = - 8.439 - 0.327 Q2 - 0.203 Q3 + 0.304 Q& + 0.155 QMIDEA
Q.3) (0.9) (0.5) (0.8) (0.2)

+ 0.590 A(RL - URL) - 1.037 QIET1 - 1.261 QIET2
(1.0) q.7) (2.8)

+ 0.009 QZEUROF + 1.019 QEREG69 - 0.579 QLOBO + 0. 791 QEIETB
(1.5) (2.3) (0.8) (0.8)

5 5 .
+ £ a, AGN) + EF by TER, - 1. 369 QSMITH
{=0 i=0 x)
R? = 0.4442 SEE = 1.001 DW = 1.31
Period 61:1 to 75:4 °
r 1 2 3 4 5 6 sum

a 0,049. 0.041 0.033 «0.025 (0.016 = (0.008) (0. 171
G.4)  G.4) 3-4) (3.8) G4) G4) 3-4)

b 8,510 3.906 0.577 -1.479  -2.260 -1.767 7.486
q1.5) (1.9) (0.4) (0.5) (0.7) (0.8) q.3)


PAGE
Bilateral bridge equation:
Imports from Germany A~22
Imports from Japan A--23
Imports from the rest-of-the-world A--24
Imports from the United Kingdom A~25
Imports from the United States A-26
Exports of goods (volume) A-27
Exports of other services A~28
Imports of other services An29
Exports of goods and services: bridge equation
(balance of payments basis to national income
accounts basis) A-30
Imports of goods and services: bridge equation
(balance of payments basis to national income
accounts basis) A-31
Transfer receipts A--32
Transfer payments A~33
Investment income receipts A-34
Investment income payments A-35
D. Price determination and capacity utilization
Domestic price (absorption deflator) A-36
Export unit value A~37
Import unit value A-38
Service deflator, exports A--39
Service deflator, imports A-40

Capacity utilization A-41


-10-

«Public holdings of currency are a simple function of consumption (as

a proxy for transactions) and the short-term interest rate.
(10) CUR = CUR(CV, RS)
A term-structure equation explains the long-term interest rate.

(11) RL = RL(RS, RS_ RS__)

yore -n

Five behavioral equations (7) - (11) along with (1) and (6) are used

to determine BU, DD, TD, RF, CUR, and RL.

Reduced form interest rate equation.--In estimating the Canadian monetary

sector, equation (9) for free reserves was normalized on the short-term interest
rate. In this respect, the MCM monetary sector is similar to that of RDX2.
But because RF is tied to the monetary base equations, there is a difference
in the signs of arguments in the interest rate equation and, indeed, in the
roles the equations perform in their respective models. When inverted, equation
(9) takes the form

+ t+ -
(12) RS, = £(RS(-1), RD, URS, RF/NDD, ....)
The U.S. interest rate enters with a negative sign because the return on U.S.
securities represents an opportunity cost of excess reserves in the free
reserve equation. Using the same mnemonics, the key conceptual elements of
the RDX2 short-term interest rate equation can be written as

+ + + +

(13) RSoox2 = £(RS(-1), URS, chartered bank loans, private holdings of government
securities)


BILATERAL IMPORT DEMAND FUNCTION: IMPORTS FROM GERMANY

LOG (XGCV/(GPXGUV * GE)) = - 8.268 - 0.164 Ql - 0.046 Q2 - 0.273 Q3
; " (7.5) (4.0) (1.3) (6.6)

+ 1.652 LOG(GNPVNSA/PGNP) + 0.898 LOG(P) - 1.021 LOG(GPXGUV * GE)
(6.9) (1.9) (4.9)

+ 1,805 LOG(E)
(3.5)

R= 0.941 SEE = 0.100 DW = 2.04

Period 61:1 to 75:4


deposit. Since government deposits could not have been more than part of the
remaining 18 percent of time deposits in 1969, wealth (NW) is used as a
scale variable for the aggregate TD equations. Savings deposits are not,

handled separately in the Canadian financial sector.

(8) 42 = rp (GNPV/NW, RS, URS, (EE-E)/E)
Ny

The equation for free reserves is of the same form as the prototype.

RF 2 oo - + =

(9) —— = RF(RS, RS-RD, URS, ARU, ARR)
NOD

where:
NOD = (1 - Ba) DD, net demand deposits;
URS = U.S. short-term interest rate;.
RU = BU - CUR arid, unborrowed reserves; and
ARR =

4a(DD_,) + Ab(TD_}), change in required reserves.

ARR is zero except for a transition period of 3 quarters in 1967 when
reserve requirements were changed from a uniform 8 percent to 12 percent on
DD and 4 percent on TD. The sign pattern in equation (9) is important for
determining the eventual sign on the U.S. short-term interest rate in the
Canadian ‘interest rate equation. Borrowed reserves including purchase and
resale agreements (PRA) are a negative component of free reserves. Borrowed
reserves and PRAs will increase with an increase in the domestic or foreign
(U.S.) short-term interest rate, so both the domestic and U.S. short-term

rates carry a negative sign.


4-11

TAXES -- NONRESIDENT

TNRESV = 0.087 - 0.086 Ql = 0.043 Q2 + 0.163 Q3 + 0.003 GNPVNSA
(5.0) (5.3) (2.7) qo.) (18.0)

R =.0.878 SEE = 0.044 DW = 2.83

Period 61:1 to 75:4


Under the fiscal stimulus, the capital inflow resulting from portfolio
rebalancing in response to the widening of the Canadian interest rate differential
is not sufficient to offset the currency outflows resulting from the increase
in imports. Consequently, the Canadian dollar depreciates steadily over the
period, reaching a peak of 3.5 percentage points 10 quarters after introducing
the stimulus.

Taxes.--Table 4 presents the multipliers for a 1 billion (current
Canadian dollars) increase in personal income taxes. The multipliers are all
smaller (in absolute magnitude) than those for the increase in government
spending because the tax increase of $C 1 billion in current dollars is less
than $C 1 billion in constant dollars and because the increase in tax revenues
affects GNP indirectly by changing disposable income. The patterns on the
GNP and price paths are similar (with opposite sign) to those of the government
spending increase. The unemployment rate effect, however, peaks in the sixth
quarter after the stimulus rather than the third. This is most likely the
result of smaller productivity effects than in the case of the larger fiscal
stimulus.

Interest rates decline because of the slackening tn loan demand. The
narrowing interest differential and $C 1.2 billion decrease in imports lead
to an appreciation of the Canadian dollar. As the fiscal restraint is about
1/3 the magnitude of the fiscal stimulus (measured by the change in GNP), so
is the appreciation of the Canadian dollar about 2/3 the size of the depreciation
under the stimulus.

Monetary policy.--The contractionary effects of a tightening in Canadian
monetary policy are shown in Table 5 with a one percentage point increase in

the discount rate. GNP eventually declines by one half billion Canadian dollars


-17-

that linked interest rate determination more directly to the monetary base.
While Canadian exchange rate tracking was good over the sample period
with a RMSE of 2.5 percent, the error on the stock of foreign exchange
reserves (NFAEOQ) was the highest of all the MCM models at 58 percent. In
a simultaneous system it is difficult to establish cause and effect, but the
large error on foreign exchange reserves disrupts the monetary base and the
interest rate. Correspondingly, large errors in the interest rate cause
large errors in capital flows and the change in foreign exchange reserves.
Exports track more closely during the sample. period (1.2: percent) than
do imports (6.6 percent) largely because foreign activity is exogenous and only
the export price and exchange rate are subject to solution error. For imports,
the exchange rate and domestic activity are simultaneous. Because the GNP
tracking errors (2.4 percent) are larger than those for domestic prices
(0.6 percent:), imports tend to be thrown off track more than exports.
Post--sample tracking.--Except for the exchange rate and the trade flows
affected by it, tracking errors are smaller in the post-sample period than in
the sample period. The GNP and interest rate errors decrease. to 1.4 percent
and 12.8 percent, respectively. The exchange rate error increases to 10.7 percent;
and because it affects the relative competitiveness of exports, the errors on
exports increase to 7.4 percent. Evidently the individual errors on the exchange
rate and GNF are offsetting because the import error declines to 3.6 percent
in the post-sample period. Although the post-sample period is relatively short,
the goodness of the tracking errors outside the estimation period indicates
that the model is a reliable representation of the Canadian economy in the mid-

1970s.


Chartered Banks

Assets

Liabilities

Required Reserves (RR)
Excess Reserves (RX)

Total Reserves (RT)

less: Required Reserves (-RR)
Long-term Securities (LTS)
Short-term Securities (STS)

Foreign Assets (net) (FA)

Other Assets (OTHCH)

Demand Deposits (DD)
Time Deposits (TD)
Borrowed Reserves (RB)

(Includes purchase and resale
agreements)

Net Worth (NWCH)

In this scheme of generating the data, NFA, NGP, RB, CUR, and RT come

from the balance sheet of the Consolidated Monetary Authorities. RR, RX, DD,

TD, SD are generated from the Chartered Bank balance sheet. It is useful

to note that RR is obtained on a different basis from all the other data

(daily average for the month). In terms of the balance sheet, assets still

equal liabilities exactly because excess reserves are calculated as a

residual from total reserves. RT, as all other items in the balance sheet

except RR, is available on an end of month basis.


UNW

UP

UPXGUV
URL

uyov
W

WB’ }
WBNSA
WMcV
wiv
XCEV

.XCGV

XCIUNK

XCJV
XCRV.

XCTV

XCUV
XECV

XETV

A-81

U.S. private net worth proxy (cumulated value of private
savings)

U.S. deflator for aggregate expenditure

U.S. export unit value (Department of Commerce, Survey
of Current Business)

U.S. long-term interest rate

U.S. Treasury Bill rate (FRB)

U.S. disposable income proxy

wage rate in manufacturing (STATCAN) -

wage bill (STATCAN)

merchandise imports, balance of payments basis

total exports of world excluding Canada

merchandise exports to the U.K., c.i.f. (por)
merchandise exports to Germany, c.i.f, (DOT)

slack variable to insulate bilateral export variables when
Canadian model is shocked in isolation (normal value = 0)
merchandise exports to Japan, c.i.f. _(DOT)

merchandise exports to R.O.W., c.i.f. (DOT)

total Canadian merchandise exports, c.i.f., customs
clearence basis (DOT) ,

merchandise exports to the U.S.; c.i.f. (Dor)

U.K. exports to Canada, f.o.b. (DOT)

total U.K. merchandise exports


A-40

SERVICE DEFIATOR IMPQRTS

LESS eat

LOG(PMS) = 0.496 LOG(PMS.,) + 0.550 LOG(FP)
(5.2) (5.3)

RZ = 0.9856 SEE = 0.023 DW = 2.05

Period 61:1 to 75:4


-27-

Export volume increases as a result of the depreciation and acts as a
stimulus to GNP. The domestic price level increases slightly in response to
the increase in domestic activity.

The depreciation is caused by the narrowing of the Canadian-foreign
interest rate differential. The resulting portfolio readjustment results in
capital outflows from Canada. These outflows reduce the monetary base. The
intervention reaction function which resists the depreciation also results in
a reduction in the monetary base. The reduction in the base, in turn, results
in a small increase in the Canadian interest rate which peaks at 17 basis point.
three quarters after the increase in foreign interest rates.

Revaluation of the Canadian dollar.--The final experiment presented in

this section explores the effects of a 10 percent revaluation of the Canadian
dollar. The experiment was performed during the fixed exchange rate period to
illustrate the properties of the Canadian model operating as a fixed exchange
rate system.L0/ The exchange rate index had the value of .920 (1972 = 1.0) in
the first quarter of 1967, so the exchange rate was increased by .092 for the
duration of the experiment.

The contractionary effects are best traced through the trade response
first. By raising the relative price of Canadian exports and reducing the
relative price of imports, the trade balance in real terms is reduced. As
indicated in the last two rows of Table 7, the responses on exports and imports
are initially similar in magnitude. But by the fourth period after the shock,
the decline in exports is about twice the size of the increase in imports. The

resulting increase in the trade deficit is reinforced by a decrease in capital

inflows.


-13-

structure. On this count we had a decided preference for the
thonetary base approach over the reduced-form reaction function
approach taken in RDX2. In estimation, the discount rate

tends to dominate (and stabilize) the MCM short-term interest
rate equation while the U.S. rate performs the same function in
the RDX2 equation.

The. verdict clearly remains open on these two approaches to interest
rate determination in the Canadian economy. The MCM approach represents a
conscious risk on estimation and tracking performance (although these are not
decidedly inferior to other Canadian results as can be seen in the results of
the following section) in order to attempt a structural representation of the
danterdeperidence between domestic and international financial flows. It is
hoped that. this work will stimulate additional efforts on structural modeling
of the Cariadian financial system.

Reaction functions.--Because the model's sample period spanned both
fixed and floating rate regimes, different operating rules for the financial
authorities were invoked. During the fixed exchange rate period (19611 to 1970 II),
the model allows changes in foreign exchange reserves to be determined from
the balance of payments identity. Because uncompensated reserve chamges during
a fixed-rate regime would cause severe fluctuations in the monetary base, we
tested for central bank behavior attempting some degree of sterilization of
the foreign flows. Systematic partial offset (-.46) of foreign exchange
reserves was observed in the equation for changes in the open market position
of the monetary authorities.

During the floating exchange rate regime, a stabilizing reaction of

"leaning against the wind" to dampen exchange rate fluctuations was observed.


Il.

III.

Iv.

Appendix

The Equations of the Canadian Sector of the

Multi-Country Model

List of behavioral equations..............6. A-1
Behavioral equations........... oe cee ccc cete, A-5
Identities............6. eee e cece ee eeeenne A-63


A-69

DEFINITION AND SOURCES OF VARIABLES

All national product and income account variables are expressed
at annual rates and are seasonally adjusted (unless indicated by the
mremonic "NSA"). All balance of payments variables are expressed at
arnual rates and are not seasonally adjusted (unless indicated by the
mnemonic "SA"). The prefix "SAF" indicates a seasonal adjustment
factor used to translate variables from an "NSA" to an "SA" basis or

. yice-versa. All monetary stock items are measured as mid-quarter
ayerages and are not seasonally adjusted. Where monetary stocks are
measured at end of quarter, the suffix "E0Q" is employed.

The letter "V" appended to a variable name indicates measure-
ment in billions of Canadian dollars. When the "Vv" is absent, the

. variable is generally expressed in constant 1972 Canadian dollars.
Exceptions to this role are financial variables, such as capital
account items and components of the monetary sector, which are all
in nominal terms.

Interest rates are in per cent per annum; and price variables
are indexes based at 1.0 in 1972. Exchange rates and interest rates
are averages of daily rates. The symbol "x" indicates an exogenous
variable. The "*" indicates a variable endogenously determined within
the multi-country model, but exogenous (or not included in the isolated

Canadian model.



A-62

CHANGE IN NET GOVERNMENT POSITION: FIXED EXCHANGE RATE PERIOD

DNGPFX = - 0.139 KFIX - 0.457 DNFA * KFIX + 0.173 A(GNP) * KFIX
(0.9) (7.0) (1.5)

- 0.247 A(URS - RS) * KFIX
(1.4)

@ = 0.5671 SEE = 0.444 DW '= 1.60

Period 61:1 to 70:2


-14-

Expected exchange rate changes were resisted by foreign exchange market
intervention. The stock of foreign exchange reserves entered the equation with
a negative sign representing an "ability to intervene". 8/ Both these functions
were operating during the dynamic simulation of and shocks to the model
analyzed in the following sections.

Expected exchange rate.--Another significant difference from tke
specification of the prototype model occurs in the treatment of the expected
future spot exchange rate (equation 3la of the prototype, see IFDP No. 115,

p. 68). For the fixed exchange rate regime, the Canadian equation uses the
product of the relative Canadian export price and net foreign assets scaled by
the value of imports, just as specified in the prototype model.

For the floating exchange rate regime, however, the Canadian model
uses the specification origninally sought in the MCM. The expected future
spot rate is assumed to equal the actual spot rate observed one quarter ahead
plus a random error. Only for Canada did this specification provide good
estimation results. In simulation of the model, the value of the spot. rate
one period ahead is replaced by an estimated value obtained from a regression

using past exchange rates and changes in net foreign assets as explanatory

variables (see ELEAD in the equation list of the appendix to this paper).

Analysis of Errors

The equations of the prototype model, modified in the financial
sector and the expected exchange rate equation as described above, were
estimated with quarterly Canadian data from the first quarter of 1961 to the
fourth quarter of 1975. Ordinary least squares regressions were employed for
estimation. Thus, the equation estimates may be subject to simultaneous

equation bias.


A-68

Net demand deposit
67. NDD - (1 - .9078 * A / 100) * DD

Unborrowed monetary base, sources and uses

68. BU = (NFAEOQ.] + NFAEOQ) * 0.5 + SDRVAL + NGP + OTH
69. BU = RR + RF + CUR :
Unborrowed reserves
70.’ RU = BU - CUR
Time deposits
71. TD = SD + ND

Short-term interest rate

72, RS = RSHD * QRD + RSLD * (1 = QRD),

Spot exchange rate
73. ER = E * 1.00937

Official reserves changes and exchange rate

74. E = EFX * KFIX + EFL * (1 - KFIX)
75. DNFA = DNFAFX * KFIX + DNFAFL * (1 - KFIX)

76. O = EFL * KFIX + DNFAFX * (1 - KFIX)


EF

EFL
EFX
EGDP
ELEAD
EP
EPXGUV
ER
EYDVNSA

FC

FGNP

FL

-FP

FPXGUVD

FRSC }

FRSL

FYDVNSA

A-73

Canadian forward exchange rate index, U.S.$/C$, (EFR/1.008)
E * (1-KFIX)

E * KFIX

U.K. gross domestic product, output estimates

Canadian led spot exchange rate index (Ex)

U.K. absorption deflator (index, 1972=1.0)

U.K. export unit value index (1972=1.0) °

Canadian exchange rate, U.S.$/CS (FEDERAL RESERVE BULLETIN)
U.K. disposable income proxy

stock of financial claims on foreigners (cumulated value
of DFC)

foreign weighted average of gross national product?

stock of financial liabilities to foreigners (cumulated
value of DFL)

foreign weighted average of prices!

foreign weighted average of price of export s2

weighted average of U.S. rate and Eurodoliar short-term
rates. (Weights based on external claims and liabilities,
respectively

foreign weighted average of disposable income!

government expenditure on goods and services (GV/P)

Iprade weighted average for Japan, Germany, the United Kingdom,

and the United States.

Weights are percentages of Canadian imports from Germany,

Japan, R.O.W., the United Kingdom and the United States.



A-36

DOMESTIC PRICE
LOG(P) = - 0,185 + 0.732 LOG(P_,) + 0.122 LOG(W) + 0.096 LoG(PMGSNI)
; (4.5) (10.2) (3.9) (3.1)

+ 0.0004 CU + 0,017 LOG(PEC)
(2.6) (3.7)

R? = 0.999 SEE = 4.09 E-3. DW = 2.30

Period 61:1 to 75:4


A-42

WAGES

(WW 4) /Wiy = - 0.001 + 0.069 QUI + 0.0003 TIME - 0.008 QCNIRL

(0.2) (2.4) (1.4) (0.9)
-3
+ 0.210 (EZ (Py - Py_4)/P,_,)/4 = 0.0001 UN_, = 0.012 UN_y*QUI
(2.2) iso 2 PA a4 on - Gn

+ 0.737 (Wy - Wis) /WLs
(6.1)

R? = 0.9663 SEE = 0.007 DW= 2.19 .

Period 62:2 to 75:4


-19-

Government spending.--Table 2 presents key multipliers for a sustained

increase in real government purchases of $C 1 billion. The real GNP multiplier
starts from 1.013 and increases to 1.428 by the end of the two-year period.
The price level also increases steadily over the two-year period to a maximum
of 28 percentage points higher than its historical value.

The effect of the increase in government spending on the unemployment
rate peaks at a reduction of .192 percentage points three quarters after the
fiscal stimilus begins. Thereafter, the unemployment rate remains below that
of the control baseline, but the difference oscillates slightly before diminshing
in the eleventh period. The early peak is due to the productivity effects of
the increase in investment. In the early periods, the rise in investment affects
the capital stock only slightly, most of the increased output must come from
added labor. As the stimulus continues, the capital stock becomes ‘larger than
otherwise and productivity increases. Additionally, the increase in économic
activity draws new entrants into the labor force and puts upward pressure on
the unemployment rate. These countervailing effects turn back the path of
the decline in the unemployment rate and cause its oscillation.

The added activity creates increased loan demand. ‘Since monetary policy
remains unchanged with the fiscal stimulus, the added loan demand leads to a
steady increase in the short-term interest rate. By the end of 11 quarters,‘
the interest rate is 1.3 percentage points above that of the control path,

The stimulus to activity draws in a large and increasing flow of imports.
Table 3 presents the historical levels for the selected multiplier responses
reported in this section. With a base level of imports (in current dollar
terms) of $C 47.6 billion, the increase of $C 1.9 billion amounts to a 4 percent

increase in the value of imports after 11 periods.


A-70

The following abbreviations are used:

STATCAN Statistics Canada

BOC Bank of Canada

DOT Direction of Trade (IMF)

FRB Federal Reserve Board

WHARTON Wharton Econometric Forecasting Assoc:.ates

IFS : International Financial Statistics


Table 5

Effects of a One Percentage Point Increase
in the Canadian Discount Rate (Bank Rate)

1973 1974 1975
[2 bstetatetsatetitrat st.

one! | -.090 -.130 1163 | -.217 -.266 = -.319=.377 | 2413-2452 +681 =.507
e | -.001 00: + -.002 | -.002 ~—-.002--~.003 -.006 | -.005 -.006 007 -.008
w 010.031 .046 | .051 1068 049.049 1044 = 047.051 049
rs“ 635.907 840 | 80S .798 798.798 812.872.823.907
wontvs* 1048-072 -~.077 | ~.104 = =.171 6266-2360 | 2489 «= ~.509 559-588
zt | 006 007 005 | .003 003 = 005,006 1009 = «601001. 010
I billions of Canadian dollars, annual rate.

2

1972 = 1.6

Percentage points.
4 U.S. dollars per Canadian dollar, 1972 = 1.0.
5 In this experiment, the discount did not exceed the short-term rate until
the last quarter of 1975, so the switch of interest rate equations occurred
here rather than in the first quarter. Like the previous multiplier
responses, the drop in the interest rate response is the result of switching
between interest rate equations and not the number of periods after the

introduction of the shock.


A-21

BILATERAL IMPORT DEMAND FUNCTION: IMPORTS FROM THE U.S.

LOG(XUCV/UPXGUV) = - 4.237 + 0.024 Qu + 0.084 Q2 - 0.218 Q3
(16.1) (1.6) (5.5) (15.5)

2
+ 1,460 LOG(GNPYNSA/PGNP) + Ea, LOG(P_;/(UPXGUV_;/E_;))
(25.5) i=0_ :
+ 0.017 QAUTST
(2.9)

R? = 0,944 SEE = 0.047 DW = 2.35 6 = 0.568
Period 61:1 to 75:4
i 0 1 2 suM

ay 0.301 0.201 0.100 0.603
(2.7) (2.7) (2.7) _ (2.7)


A-66

XUCV/MUJEGV XJ€V/MUJEGV
41. FP = UP f * (JP * JE) !

XGCV/MUJEGV
* (EP * EE) ECV /MUSEGY * (GP * GE) / IE
42, FYDVNSA = vypyXCUV/XUJEGV % sypyygaXCJV/XUJEGV

* EYDVNSAXCEV/XUJEGY 4 GypyygaXCCV /XUJEGV.

Percentage change in domestic deflator

43. PCHP = A(LOG(P)) * 400

Percentage change in wages
44, PCHW = A(LOG(W)) * 400

GNP deflator .
45. PGNP = GNPV / GNP

Deflator for imports of goods and services

46. PMGSNI = MGSNIV / MGSNI

Net foreign assets
47. DNFA = XGV + XSYV + KSOV + XTRANV - MGV - MSYV - Msov -

MIRANV + DSTL + DLTPL + DSTC + DLTPC + DLTDL
+ DLTDC + EANDO + NGKA

48. NFAEOQ

"

NFAEOQ_, + DNFA / 4
49, NFAFED = (NFAEOQ - NFAEOQR) * ER

Net_government position of the monetary authority

50. DNGP = DNGPFX * KFIX + DNGPFL * (1 - KFIX).

51. NGP = NGP_; + DNGP / 4


PAGE
G. Capital Movements, official reserves, forward and led
exchange rates (continued)
Reaction function for change in net foreign assets A-61

Reaction function for change in net government position A-62


-20-

Table 2

Effects of a $C 1 billion Increase in
Real Government Purchases of Goods and Services
(1972 dollars)

1973 1974 1975
[2t>sts4.i/ijler2}siu4]if2] 5],
cre! 1.013 1.066 1.106 1.108 1.145 1.167 1.287 1.310 1,362 1.400 1.428
r .001 002 004 -006 007 +010 .013 017 021 025 +028
w? 7-136 -.192 ~.192 | +.170 -.159 -.150 -.113 | -.088 -.111 ~.129 -.090
rs? ls 258 +384 541 +740 895 +946 392° 418° .555> 1.309

wosnivs! +336 6483) 628 | ©.799 965 1.209 1.384] 1.621 1.824 1.945 1.986

001 -.005 -.009 | -.012 -.015 -.019 -.022] -.030 -.034 -.035 -.031

1 billions of Canadian dollars, annual rate.

2 1972 = 1.00

3 Percentage points.

4 U.S. dollars per Canadian dollar, 1972 = 1.0.
5 This drop in the interest rate effect is spurious. It occurs historically at a
point where the interest rate equation experiences a behavioral shift between
discount rate regimes. See discussion of the two interest rate equations above in

the financial sector of this paper. The 50-odd basis point drop is related to the

firat quarter of 1975 and not to the eighth period after the fiscal stimulus.


A-32

TRANSFER RECEIPTS

XTRANV = 0.009 + 0.137 Q2 + 0.099 Q3 0.131 Q4 + 0.001 FYDVNSA
(0.3) (5.9) (3.8) (5.6) (21.2)

R? = 0.9014 SEE = 0.077 DW = 2.08 p = 0.404

_ Period 61:1 to 75:4


The apparent time pattern of reserve assets over the 15-day averaging
period permits RR on a daily-average basis to exceed total reserves on an
end-of-month basis. Computation of RX from RT-RR thus leads to negative
excess reserves for most observations in the sample. Another difficulty
with this procedure for creating data on excess reserves is that all the
discrepancy between end-of-month and daily-average measurement of total
reserves is picked up in RX. This discrepancy is then passed on to free
reserves when RF is calculated as RX-RB. However, a discrepancy of some
kind will always be present in RF because RB is also measured on an end-
of-month basis.

The final difference between the prototype balance sheets and those
for Canada relates to the importance of government securities held by the
Chartered Banks under purchase and resale agreements (PRA). Holding
eligible securities in a PRA is a legitimate means for a chartered bank to
comply with its reserve requirement. In fact, borrowed reserves are very
small in Canadian banking, and PRAs exceed borrowed reserves. Thus, in the
MCM, FB is defined as borrowed reserves plus PRAs. This procedure requires
the assumption that the spread between the purchase and resale price of the
security is equivalent to the interest payment on borrowed reserves of the
same magnitude at the bank rate (discount rate).

Monetary Sector.--From this point on, the structure of the Canadian
monetary sector follows closely that laid out for the prototype model.

RRC is computed from statutory reserve requirements as

(3) RRC = a+ DD+b- TD


A-64

Private net worth proxy

19, DNWNSA = YDPVNSA - CVNSA + XTRANV - MIRANV - RESNSA
20. NWNSA = NWNSA_, + DNWNSA / 4

21. DNW = DNWNSA * SAFDNW

22. NW = NW, + DNW / 4

Exports of goods and services

23. XGSNINS = XG + (XSOV + XSYV) / PXS
24, XGSNI = SAFXNI * XGSNINS

Imports of goods and services

25. MGSNINS = NG -+ (MSOV + MSYV) / PMS.
26. MGSNI = SAFMNI * MGSNINS

Merchandise exports, balance of payments basis

27. XGV = XG * PXGUV

: 1
Merchandise exports, customs clearance basis (U.S.$)

28. XCTV = XCJV + XCGV + XCEV + XCUV + XCRV + XCJUNK

Merchandise imports, ‘balance of payments basis

29. MGV = GM * PMGUV

Merchandise imports, customs clearance basis (u.s.$)!

30. MCTV = MCJV + MCGV + MCEV + MCUV + MCRV

Total tax revenue

31. TV = TPERV + TNRESV + TCORPV + TINDV

Wage Bill
32. WBNSA = WB / SAFWB

lipplied only to linked version of the model.


CAPITAL CONSUMPTION ALLOWANCE

CCAV = - 8.570 + 0.073 Q2 - 0.270 Q3 + 0.229 Q4 + 0.016 KP)
(45.2) (0.9) (1.7) (2.7) (6.9)

+ 15.402 P_, + 0.038 (GNPVNSA - TV - CVNSA)
(22.8) (2.9)

R= 0.996 SEE = 0.226 DW = 0.54 ©

Period 61:1 to 75:4


BU

CCAV
cu
CUR
CUSTCU
cv
CVNSA
DD

DEF “XED

DEF (XE2

DEF LOAT

DLTDC

DLIDL

DLTPC

A-71

reserve requirements on demand deposits (STATCAN)

reserve requirements on time deposits (STATCAN)

unborrowed reserves (RR + RF + CUR)

consumption expenditure (cv/P)

total capital consumption allowance (STATCAN)

capacity utilization rate -- total manfactures (WHARTON)
currency held by nonbank public (STATCAN)

foreign weighted average of capacity utilization!
consumption expenditure (STATCAN)

consumption expenditure, not seasonally adjusted (STATCAN)
demand deposits held by residents (BOC)

proxy for expected exchange rate change during the fixed-
rate regime (before 70:2); the ratio of imports to foreign
exchange reserves times the ratio of Canadian export price to
competitors' export price index

proxy for expected exchange rate change during the fixed-
rate regime (before 70:2); the ratio of imports to foreign
exchange reserves

proxy for expected exchange rate change during the floating
rate period (after 70:2); percentage change between current
and led exchange rates

change in long-term direct claims on foreigners (STATCAN)
change in long-term direct liabilities to foreigners (STATCAN)

change in long-term protfolio claims on foreigners (STATCAN)

lfrade weighted average for Germany, Japan, the United Kingdom

and the United States.


A-12

TAXES - CORPORATE

TCORPV = - 0.320 + 0.480 Qu + 0.451 Q2 - 1.242 Q3
(1.4) (2.6) (2.6) (6.7)

+ 0.180 (GNPVNSA - WBNSA - CCAV) - 0.025 TIME
(12.7) ; (2.5)

R2 = 0.9368 SEE = 0.468 DW = 1.56

Period 61:1 to 75:4