ifdp · August 31, 1982

The Canadian Sector of the Multi-Country Model

International Finance Discussion Papers Number 209

September 1982

THE CANADIAN SECTOR OF THE MULTI-COUNTRY MODEL

Howard Howe

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acknowledgment by a writer that he has had access to unpublished material) should be cleared with the author or authors.

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 the forthcoming book, The U.S. Economy in an Interdependent wor1d.2/ 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. financial markets. Consequently, Canadian interest rates have traditionally moved closely with U.S. interest rates. necause, 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,

(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!

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 benk 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:.2/ 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 exchange reserves

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

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

NFA- CUR

NGP RT

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 (net)

(2) Uses: BU = RR + RF + CUR where:

BU = unborrowed 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 curse! , 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.

Lagged reserve reguirements.--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 requirements. 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 sneet in the prototype model.

Chartered Banks

Assets Liabilities Required Reserves (RR) Demand Deposits (DD) Excess Reserves (RX) Time Deposits (TD) Total Reserves (RT) less: Required Reserves (-RR) Borrowed Reserves (RB) (Includes purchase and resale Long-term Securities (LTS) agreements)

Short-term Securities (STS) Foreign Assets (net) (FA)

Other Assets (OTHCH) 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.

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 endof-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 y Ye! P

monetary sector follows closely that laid out for the prototype model.

RRC is computed from statutory reserve requirements as

(3) RRC = as: DD+b-: TD

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

given by:

(4) RR = a + BRRC + € 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+ BaDD + BbTD + € + RF + CUR

Equation (5) can be expressed in terms of demand deposits. (6) DD = [BU -a- BbID - € - 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 demanc 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:

: D (7) DD DD(GNPV/NW, RS, URS, (EE-E)/E) Unlike the German case, there are no appreciable government holdings of time deposits. TD is composed of savings deposits (82% in 1969IV) 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

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) 22 = TD (GNPV/NW, RS, URS, (EE-E)/E)

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

- - + <=

RF ~ — RF(RS, RS-RD, URS, ARU, ARR) |

(9) -—— NOD

where:

NDD = (1 - Ba) DD, net demand deposits; URS = U.S. short-term interest rate; .

BU - CUR and, unborrowed reserves; and

ARR

Aa(DD_,) + Ab(TD_1), 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.

~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_)

1’

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

+ + - -

(12) RS cM = £(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) RS pox? = £(RS(-1), URS, chartered bank loans, private holdings of government securities)

-1l1]-

Empr ical 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.

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(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

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structure. On this count we had a decided preference for the monetary 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 dnterdeperidence 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 changes 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.

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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 the 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.

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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 fivequarter 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. Unemployment rates, being a residual number, normally track 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 model. 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

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Table 1

Dynamic Simulation of the Canadtan Model in Isolation from the MCM

Variables In-Sample Errors Post-Samp-.e Errors 64:4-75:4 76:1--77:1 GNP si *s MEE 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 0.554 0.055 RMSE 6.660 3.630 MGV ME -0.490 9.321 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 10.616 E ME 1.044 -10.C62 RMSE 2.512 10.765 NFAEOQ ME 39.732 ~22.402 RMSE 57.732 23.713

Iyean percentage error.

2Root mean squared percentage error.

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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 (NIAEOQ) 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 ratte. 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.

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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 and the rest of the world economy entered a recession. The general effect of this environment on the multiplier paths studied here is a downward dias in the

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

economic stimulus.

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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 stimulus 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 increas2 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 economic 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.

Table 2 Effects of a $C 1 billion Increase in

Real Government Purchases of Goods and Services (1972 dollars)

1973 1974 1975

GNP 1,108 1.145 1.167 1.287 | 1.310 1.362 1.400 1.428 Pp? 006 .007 .010 .013| .017 021 .025 .028 w 7.170.159 -.150 -.113 | -.088 -.111 -.129 -.090 Rs? 541.740.895.946 | 3927 1418" 555° 1.309 Mesnivs! .799 1.209 1.384 | 1.621 1.824 1.945 1.986 e* -.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

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

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Table 3

Historical Values for Key Variables in Canadian Multiplier Experiments

1973 1974 . 1975

Gp 112.0 113.1 116.1 117.8 117.4 117.2 116.9 116.7 117.9 119.6 120.0 p 1.067 1.089 1.118 1.152 1.200 1.249 1.284 1.329 1.353 1.388 1.416 we? 5.45 5.38 5.57 5.30 5.23 5.20 5.53 6.55 6.95 7.07 7.07 as‘ 6.27 8.20 9.43 9.20 11.00 11.60 10.20 7.43 7.27 8.09 9.10 vesurvs! 31.6 29.3 34.8 35.4 41.6 40.9 46.0 43.3 47.7 43.4 47.6 x‘ 991 987 991 1.011 1.026 1.010 1.004 «992 969 -961 -975

1 billions of Canadian dollars, annual rate.

1972 = 1.00

3 Percentage points.

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

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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

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Table 4

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

1973 1974 . 1975 —3i__.

cup? =.347 -.724 =.748 ~.825 | =.881 -.925 -.936 -.971 p? -.001 -.004 -.005 -.007 | -.010 -.013 -.015 -.017 uN? -.058 129°. 41336129 1160S AACA «iw 092 Rs‘ .-.097 ~.381 =.482 -.589 | -.234> -.2607 -.3527 -.853 uesnivs! -.170 “i541 =.709 -.842 | -1,001 -1.140 1.225 -1.262 ES .003 008 ~=—«.011.—S««w014 |= .020-S 02802302

billions of Canadian dollars, annual rate.

2 1972 = 1.0.

Percentage points.

U.S. dollars 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.

Table 5

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

1974

| sup) | -.090 -.319 * | -.001 ~.00i -.002 ~.003 wn? 010 ~=—-.031._—Ss«. 046 .049 rs“ -835 907, s«. 840 |. 805 .798 798 wentvs? -.068 -.072 -.077 | -.104 -.171 7.266 ES .006 = .007 005 | .003 .003 ——-.005 billions of Canadian dollars, annual rate. 2

1972 = 1,6 Percentage points.

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

-.377

~.004

2049 -798

-.360 . 006

1975

-.006 ~.007 -047 031 871 - 823

~.509 7.559 -010 011

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.

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 Canadianforeign 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.

~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

GNP 007 030.045 .017 018 = 013,015,

p* 001 .001 ~—-.001 .001 002.002, .002,—S—=—0001

UN? 001 =.014 = =.025 .001 010.014. S01, 006

Rs‘ 054 9.114, 169 028 | -,1197 -.1299 ~-.1207 ~~, 0099 vesnrvs! 127.122, 0078 | .062 062 065.053 052.049.035.026

ES ~:004 -.006 = -.003 | ~.001 - -.001 = -.001--.001 | -.002=.001-.062

billions of Canadian dollars, annual rate. 2 1972 = 1.0. 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 switching between

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

of the shock.

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 points 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 20/

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.

-28-

Table 7

Effects of a 10 percent Revaluation of the Canadian Dollar

1969 | 3 | 4 cnp} -.495 =.689 =. 597 2 P -.034 ~.036 -.038 -.040 3 UN 382 409 395 -118 4 RS 1.82 2.26 2.12 2.09 vesnrvs! “1.58 1.6) “1.80 -1.97 4 z .092 202 .092 .092 pnFA} “1.08 -.781 -1.03 -.971 -.598 -.796 =.472,=.723 =. 54 1 MG 312, «6520-4512 546 hd .597 .407 .459 .368 .409 1 XG .035 --.481 = -=.679 Ss -.970 “1.0600 -=1.15) | -1.05) 0-12.13 -1.03,=1.17

billions cf Canadian dollars, annual rate. 2 1972 = 1.0.

Percentage points. 7 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 switching between interest

rate equations and no the number of periods after the introduction of the shock.

-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 At/ 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.

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 Appreach" (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 Prentice 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 19731V 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,

-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.

II.

ITl.

IV.

Appendix

The Equations of the Canadian Sector of the

Multi-Country Model

List of behavioral equations....... weeeeee And Behavioral equationS..........ceeeeeee eee AWS Identities.............. bocce cece eee eee ees eA-63

. 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)

Bilateral 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-10 A-11 A-12

A-14

A-15

A-16

A-17 A-18 A-19 A-20

A-21

A-2

Bilateral bridge equation: Imports from Germany Imports from Japan Imports from the rest-of-the-world Imports from the United Kingdom Imports from the United States

Exports of goods (volume)

Exports of other services

Imports of other services

Exports of goods and services: bridge equation (balance of payments basis to national income accounts basis)

Imports of goods and services: bridge equation (balance of payments basis to national income accounts basis)

Transfer receipts

Transfer payments

Investment income receipts

Investment income payments

Price determination and capacity utilization

Domestic price (absorption deflator) Export unit value

Import unit value

Service deflator, exports

Service deflator, imports

Capacity utilization

PAGE

A--22 A--23 A--24 A--25 A--26 A--27 A~28

A--29

A--30

A-31 A--32 A--33 A~34

A-35

A--36 A-37 A~38 A~39 A-40

A-41

E. Labor Market Wages Wage Bill Employment

Labor force participation

F. Domestic asset demand and interest rate determination

[Temand deposits

Savings deposits

Notice deposits

Currency

Required reserves

Short-term interest rate When short-term rate exceeds the discount rate When the discount rate exceeds short-term rate

Long-term interest rate

G. Capital Movements, official reserves, forward and led

exchange rates

Errors and omissions

Change in short-term liabilities Change in short-term claims Change in long-term liabilities Change in long-term claims Forward exchange rate

Led exchange rate

PAGE

A-46

A-47

A-48

A-49

A-50

A-51

A-52

A-53

A-54

A-55

A-56

A-57

A-58

A-59

A-60

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

DISPOSABLE INCOME BRIDGE

YDVNSA = = 1.311.-+ 2,655 Ql -(4.1) = (8.8)

BR. = 0.9989 SEE

Period 61:1 to 75:

ee ee ee

ASS.

+ 1.259 Q2 + 15116 Q3'+ 0.955 YDPVNSA ~ "(4.2) (3.7) (230.6) °°)

0.818 - DW = 1.87

4 oe

A-6

CONSUMPT ION

C= ~ 10.873 + 0.484 C_) + 0.387 YDV/P + 0.119 NW.) / P . 4) (6.6) (7.0) (6.2)

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

IFP = - 5.275 + 0.083 Kp (2.9) (11.3)

PRIVATE FIXED INVESTMENT

R* = 0.760

0 4 -0.349 -0.781 (2.2) (3.8)

0 1 0.105 0.102 (2.1) (2.1)

6 7 0.255 0.276 (3.1) (3.3)

5 -1 * 42

SEE = 0.375

2 -0.985 (4.2)

~ 0.119

(2.0)

0.279 (3.3)

11° r a, A(RL_,_)) + sty by ACGNP_

DW= 1.5 » = 0.919

3 & 5 -0.984 -0.803 -0.467 (4.1) (3.5) (2.8)

3 4 5 0.148 0.185 0.222 (2.2) (2.5) (2.9)

9 10 11 0.260° 0.211 0.126 (3.3) (3.2). (3.1)

i-1

-G

-1i-1

SUM (4.1)

SUM

2,288

(3.3)

A-8

INVENTORY INVESTMENT 4 IL = = 1.719 + 0.493 5 (C_; + IFP_, + IFG_, + XG_,) /4 (0.7) (3.8) * Pi - 0.865 z (MG_,) /4 + 0.551 MG - 0.404 (C + IFP + IFG + XG) (2.9) i= (4.8) (4.5) R « 0.258 SEE = 0.683 DW = 2.23 p = 0.491 Period 61:1 to 75:4

Cpa maggeat hier te

A-9

CAPITAL CONSUMPTION ALLOWANCE

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

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

Fz = 0.996 SEE = 0.226 DW = 0.54

Period 61:1 to 75:4

. A-10

TAXES -~ PERSONAL

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 * QTAXI (3.9)

R? = 0.991 SEE = 0.627. DW = 1.61

Period 61:1 to 75:4

A-11

TAXES -- NONRESIDENT

TNRESV = 0.087 = 0.086 Ql = 0.043 Q2 + 0.163 Q3 + 0.003 GNPVNSA (5.0) (5.3) (2.7) (10.1) (18.0)

R° = 0.878 SEE = 0.044 DW = 2.83

Period 61:1 to 75:4

. A-12

TAXES - CORPORATE

TCORPV = - 0.320 + 0.480 Ql + 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

A-13

TAXES - INDIRECT

Cee ames renee

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)

® = 0.983 SEE = 0.653 DW = 1.16

Period 61:1 to 75:4

A-14

GOVERNMENT SRANSFERS

TRANV = - 1.119 ~ 1.738 Q2 - 2.764 Q3 ~- 2.033 Q4 + 0.152 (GNEVNSA ~ 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 TIM: (4.2) (2,1) (2,0) (4.6)

. R? = 0.982 SEE = 0.732 DW = 1.57

Period 61:1 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-16

IMPORT. TS OF GOODS: BRIDGE EQUATION (customs clearance to balance of

payments basis)

MGV * ER = 0.133 + 0.942 MCIV/1.1 (3.0) (366.8)

= 0.999 SEE = 0.184 DW = 0.94

Period 61:1 to 75:4

A-17

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

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 (GNPVNSA/PGNP) + 1.248 LOG (P/(JPXGUV * JE/E) (6.8) | (2.4)

R? = 0.615 SEE = 0.111 DW=1.86 9 = 0.853

Period 61:1 to 75:4

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-20

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

LOG (XECV/(EPXGUV * EE)) = - 0.734 - 0.128 Q1 + 0.039 Q2 - 0.093 Q3 (1.3) (4.0) (1.2) (3.0)

+ 0.153 L0G (GNPVNSA/PGNP) - 0.141 EDV41 - 0.150 EDV50 (1.2) (1.5) (1.7)

. . 4

~ 0.043 EDV30 + 0.064 EDV49 - 0.125 EDVS + E- a, (0.7) (0.7) (1.4) °° i-o 7+

LOG(P_; /(EPXGUV_; * EE_; / E_;))

—2 S

R= 0.604 SEE = 0.089 DW = 2.02 p= 0.329 )

Period 61:1 to 75:4

LY «

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-2]

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

LOG(XUCV/UPXGUV) = - 4.237 + 0.024 Q1 + 0.084 Q2 ~ 0.218 Q3 (16.1) (1.6) (5.5) (15.5) to _ + 1,460 LOG(GNPVNSA/PGNP) + Za, 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 a

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

A-22

BILATERAL, BRIDGE EQUATION: IMPORTS FROM GERMANY aa)! ncn a LAN

MCGV = ~ 0.004 + 0.974 xGCV + 0.172 xcCV , (0.3) (14.1) (2.3) - R* = 0.971 SEE = 0.042 DW = 1.95

Period 61:1 to 75:4

BILATERAL BRIDGE EQUATION: IMPORTS FROM JAPAN

MCJV = 0.004 + 0.518 xJCV + 0.564 XICV_, (0.4) (8.6) (9.2)

R* = 0.987 SEE = 0.057 DW = 3.27

Period 61:1 to 75:4

A-24

BILATERAL BRIDGE EQUATION: IMPORTS FROM THE REST-OF-THE-WORLD rE Ri PE WORLD

MCRV = 0.209 + 0.643 XRCV + 0,271 xRCV_, (3.8) (10.5) (4.3)

R = 0.991 SEE = 0.263 DW = 1.39

Period 61:1 to 75:4

A-25

BILATERAL BRIDGE EQUATION: IMPORTS FROM THE U.K. 224 aE EIN EE UR

MCEV = - 0.003 + 0.941 XECV + 0.155 XECV_, (0.1) (19.1) (3.1) :

R* = 0.967 SEE = 0.047 DW = 1.94

Period 61:1 to 75:4

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

A-27

EXPORT OF coops/

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

(5.5) (6.8) (0.1) (2.5) (10.1) 2 | 3 % ay LOG(PXGUV_s/UPXGUV_,) + © by LOG(E_,_,) + 0.054 QSCALE

i=0 i=0 (1.5)

+ 0.006 QAUTST (1.0)

R? = 0.9661 SEE = 0.045 DW=1.77. » = 0.418

Period 61:1 to 75:4

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

z (1.3) (1.3) (1.3) (1.3) b; “0.430 -0.322 -0.215 -0.197 1.075

(2.3) (2.3) (2.3) (2.3) (2.3)

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

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_1) + 0.202 LOG(FGNP) + 0.060 QEXPO (3.6) (2.3) (1.4) ,

+ 0.034 QAUTO + 0.197 LOG(FP/PXS) (2.0) (1.1)

Ro = 0.9681 .SEE = 0.061 DW = 2.34

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_ 1) + 0.450 LOG(GNP) + 0.388 1.06 (P/ PMS ) (6.6) (3. 9) (1.3)

= 0.9794. SEE = 0.042 Dw = a

Period 61:1 to 75:4

A-30

EXPORTS OF GOODS AND SERVICES: BRIDGE EQUATION (balance of payments basis aoe Ee ARDY ERV Cho: BRIDGE E to National Income Accounts basis)

XGSNIVS = - 0.003 + 1.000 (XGV + XSOV + XSYV) (0.2) (1578.4)

-R? = 0.999 SEE = 0.051 DW = 3.08

Period 61:1 to 75:4

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) .

R = 0.999 SEE = 0.038 DW = 2.17

Period 61:1 to 75:4

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

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-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_,/E) * NFAEOQ , * FRSC (4.2) (2.1) ~

+ 0.008 (E_,/E) * URL * LTDC_, (3.9)

R2 = 0.7934 SEE = 0.091 DW=1.9 9 = 0.315

Period 61:1 to 75:4

A-35

INVESTMENT 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 * CLIPL_1)).- 0.032 RL * (-LTDL_,) (7.0) (5.0)

_) - R = 0.9178 SEE = 0.155 DW= 1.95 p = 0.415

_ Period 61:1 to 75:4

DOMESTIC PRICE

LOG(P) = = 0.185 + 0.732 LOG(P_,) + 0.122 LOG(W) + 0.096 LOG(PMGSNT) . (4.5) (10.2) (3.9) (3.1)

+ 0.0004 CU + 0.017 LOG(PPC) (2.6) (3.7) R’ = 0.999 SEE = 4.09 E-3 DW = 2.30

Period 61:1 to 75:4

A~-37

EXPOR' 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)

R2 = 0.967 SEE = 0.012 DW = 1.76 p = 0.746

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° 9 = 0.798

Period 61:1 to 75:4

A-39

SERVICE DEFLATOR, EXPORTS

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

Re = 0.9675 SEE = 0.041 DW = 2.15

Period 61:1 to 75:4

A-40

SERVICE DEFIATOR, IMPORTS

ean a

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

R2 = 0.9856 SEE = 0.023 DW = 2.05

Period 61:1 to 75:4

A-41

CAPACITY UTILIZATION

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

R° = 0.933 SEE = 0.008 DW = 2.03 p = 0.637

. Period 61:1 to 75:4

A-42

WAGES

(W-W_,)/W_y, = - 0.001 + 0.069 QUI + 0.0003 TIME - 0.008 QCNTRL

(0.2) (2.4) (1.4) (0.9) 3 . : + 0.210 (2 (Py - Py_y)/P,_,)/4 - 0.0001 UN_, - 0.012 UN_1*QUI (2.2) ieo b BA And (0.1) b (2.7)

+ 0.737 (W_y - Wis5)/Ws (6.1)

R? = 0.9663 SEE = 0.007 DW= 2.19 -

Period 62:2 to 75:4

A-43 WAGE BILL

WB = - 10.667 + 1.019 LF * (1 - UN/100) *W* 2 4 0.104 cu (4.1) (168.7) . (3.7)

Re = 0.998 SEE = 0.438 DW = 1.83 p = 0,586 Period 61:1 to 75:4

A-44

EMPLOYMENT

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

4 > a, LOG(GNPV_,/(W_,)) 1=

R” = 0.9826° SEE = 0.005 Dw = 1.62 p= 0.768

Period 62:1 to 75:4

i 0 4 2 3 4 Sum a; 0.149 0.095 0.053 0.024 . 0.006 0.326 (3.6) (5.5) (2.9) (1.1) (0.3) (503)

A-45

LABOR FORCE PARTICIPATION ee RED

LOG(LF/POP15) = - 0.709 + 0.279 LOG(W_,/P_,) - 0.014 LOG(UN_,) (8.8) (5.9) (1.4)

- 0.001 NW, / Ply (1.3)

-R = 0.4371 SEE = 0.004 DW= 1.68 p = 0.906

Period 62:1 to 75:4

A-46

DEMAND _DEPOSiTS

DD/NWNSA = - 0.001 - 0.007 Q2 - 0.009 Q3 - 0.001 Q4 - 2.2E-04 TIME | ' (0.3) (6.0) (4.4) (0.8) (2.0)

+ 0.698 DD_,/NWNSA + 0.072 GNPVNSA/NWNSA - 0.001 RS (8.0) fo (3.6) . (4.5) R’ = 0.950 SEE = 0.002 DW = 1.21

Period 61:1 to 75:4

A-47

SAVING DEPOSITS

SD/NHNSA = = 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) | . 70 - 0.002 KFIX * DEFIXED + EZ a, RS_; (5.6) i=0

R = 0.981 SEE = 0.004 DW = 0.65

Period 61:1 to 75:4

4 ) 1 2 3 A 5 @, 708-04 6.0E-04 5.0E-04 4.1E-04 3.2E=04 2.3E-04 (3.2) (4.3) (5.4) (4.9) (3.5) (2.5) 6 7 SUM 1.5E-04 0.7E-04 7

3.0E-03 (1.9) (1.5) . . (5.4)

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)

RB’ = 0.957. SEE = 0.004 pw = 0.52

Period 61:1 to 75:4

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)

BR? = 0.941 SEE = 7.5E-04 DW = 0.80

Period 61:1 to 75:4

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

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) » G.6) (2.4) (1.0) .

~ 0.094 QBACTS * RD -.0.139 DEFIXED * KFIX (1.6) (3.1)

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

Bp sey

A-52

HORT T 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)

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

LONG-TERM INTEREST RATE

RL=1.735+ £

(3.3)

i=0

= 0.743 SEE = 01289 DW=1.58 p= 0.667

A-53

a RS + i ~ i=0

Period 61:1 to 75:4

i 0: a (0.079 (3.1)

8 ().050 (5.3)

4 Ob 15.076 (1.8)

1 0.077 (3.7)

0.045

(4.7)

9.804 (2.3)

2 0.074 (4.5)

10 ~

0.040 (4.2)

6.970

(1.5)

3. 0.071 (5.4)

11 0.034 (3.7)

4.572 (0.8)

4 0.068 (6.2)

12 0.028 (3.4)

2.611 ©

(0.5)

5 0.064 (6.7)

13 0.021 (3.1)

1.087 (0.3)

A (Loc(P_,))

6 0.597 (6.6)

‘0.015 (2.9)

7 0.055

_ (6.0)

15 0.007 (2.7)

SUM 0.789 (6.7)

SUM 8.120 (1.8)

A-54 -

ERRORS AND OMISSIONS

EANDO = - 1.123 + 1.531 Q2 + 2.192 Q3 + 0.930. Qh = 0.338 A (NNSA) (4.0) (4.4) (4.6) (2.6) CG: 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)

BR’ = 0.3805 SEE = 0.898 DW = 2.48

Period 61:1 to 75:4

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; A(UNW_,) (3.0) (1.9) - (1.6) i=0 ;

3 + E by 1/ER_, + 0.850 QSMITH i=0 (1.9) |

Re = 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)

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) (45) (1,4) (0.7)

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

R2 = 0.404 SEE = 0.771 DWe 2.18

Period 61:1 to 75:4

A-57

CHANGE IN LONG-TERM LIABILITIES

DLTPL = - 8.439 - 0.327 Q2 - 0.203 Q3 + 0.304 Q4 4 0.155 QMIDEA

(1.3) (0.9) © (0.5) (0.8) . (0.2)

+ 0.590 A(RL - URL) - 1.037 QIET1 - 1.261 QIET2 (1.0) (1.7) (2.8)

+ 0.009 QZEUROF + 1.019 QEREG69 - 0.579 QLOBO + 0.791 QEIETB © (1.5) (2.3) (0.8) (@. 8)

5 5 + 5 a, AQUNW,) + £ by WER, - 1.369 QSMITH i=0 i=0 . (1.3)

R? = 0.4442

Period 61:1 to 75:4

i 1

a 0,049 (3.4)

b 8,510

(1.5)

- 0.041

(3.4)

3.906

(1.9)

SEE = 1.001

3 0.033 (3 .4)

0.577 (0.4)

4 5 0.025 0.016 (3.4) (3.4)

-1.479 -2.260

(0.5) (0.7)

DW = 1.31

6 0.008 (3.4)

SUM 0.171

G -4)

7.486 (1.3)

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) (1.1)

Rr = 0.082. SEE = 0.174 “DW = 1.84 p= 0.774

Period 61:1 to 75:4

A-59

FORWARD EXCHANGE RATE ~

EF = 1).022 + 8.142E-05 Q2 + 1.108E-04 Q3 - 3.449E-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-60

LED EXCHANGE RATE

2 2° ELEAD = 0.588 - 0.241 KFIX+ 2% a, Els.) + 2 dy E.y.y (4.6) (0.6) ic0 i=0 . *KFIX+ 2 cy DNFA_, + d; DNFA_, * KFIX i=0 i=0 1 1 | + Eo e NGP, + gf f NGP_, * KFIX i=0 i=0 .

R2 = 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) (0.1) (0.5) (0.4) (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) f - 0.091 0.091

(3.1) (3.1)

A-61

NET FOREIGN ASSETS: FLOATING EXCHANGE RATE PERIOD

DNFAFI. = 1,219 (1 - KFIX) + 0.114 (E/E_,-1) * (1 - KFIX) (0.7) (3.8)

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

-R2 = 0.5011 SEE = 0.650 DW = 1.72

Period 70:3 to 75:4

8-62

CHANGE 1N NET GOVERNMENT POSITION: FIXED EXCHANGE RATE _PERTOD

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)

R = 0.5671 SEE = 0.444 DW-= 1.60

Period 61:1 to 70:2

A-63

LIS’ OF IDENTITIES

GNP identities Ll. GNP = C + IFP + IFG + II + G + XGSNI - MGSNI + RES 2. GNPV = CV + IFPV + IFGV + IIV + GV + XGSNIV - MCSNIV + RESV 3. GNPVNSA = GNPV / SAFGNEV 4. PCHGNP = A(LOG(GNP)) * 400 . Components of GNP 5. G=GvV/P

5. CV=C*P

7, IFPV = IFP * P

B. IFGV = IFG * P

9. IIV=II*P

10. MGSNIV = 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 - SCKG / 4) * KG.1 + IFG / 4

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

Private net_worth proxy . 19. DNWNSA = YDPVNSA - CVNSA + XTRANV - MTRANV ~ 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 = MG + (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. XCIV = XCJV + XCGV + XCEV + XCUV + XCRV + XCJUNK

Merchandise imports, balance of payments basis

29. MGV = GM * PMGUV

Merchandise imports, custons clearance basis (U.S.$)

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

1 .

Total tax revenue 31. TV = TPERV + TNRESV + TCORPV + TINDV

Wage Bill 32. WBNSA = WB / SAFWB

ee 1A pplied only to linked version of the model.

A-65 . ~

Trade balance

33. TB = XGV - MGV

Total world exports, excluding Canada

34, WIV = XGTV + XJTV + XUTV + XETV + XRTV

Canadian exports to trading partners 35. XUJEGV = XCUV + XCJV + XCEV + XCGV

Canajian imports to trading partners 36. MUJEGV = XUCV + XJCV + XECV + XGCV

eighted foreign averages of competitors price, capacity utilization ae nice of exports, gross national product, domestic deflator, and dis sposable income ; ;

37. PCOMP = (GE * spxquyyXGIV/NIV * (JE * JPXGUV)

XJTV/WIV

* (EE * EPXGUV)~=LY/NTV « ypxguyXUTV/WIV

38. cusTCU = UCUXCUV/XUJEGV x jseyXCJIV/XUJEGV

ECUXCEV/XUJEGV x ocyXCGV/XUJEGV

49. FPXGUVD = UpxcuVMCUV/MCTV % (spxcuy * JE) MCJV/MCTV

%* (EPXGUV * EE)MCEV/MCTIV » (Gpxguy * GE)MCGV/MCTV

& ROWPXCMCRV/MCTV 40. FGNP = UGNPXCUV/XUJEGV jgypXCJV/XUJEGV

XCEV/XUJEGV ,

* EGDP

* CONPXCSV/XUJEGV

Pron ener tnee se seta:

A-66

a " _ XUCV/MUJEGV XJEV/MUJEGV 41. FP = UP ‘ * (JP * JE) /

XGCV/MUJEGV & (EP * EE) ECV /MUJEGV * (GP * GE) / IE

42. FYDVNSA = vypy*CUV/XUJEGV sypyysqXCJV/XUJEGV

* EyDyNSAXCEV/XUJEGY 4 GypyygaXCGV/XUJEGY

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 + XSOV + XTRANV - MGV - MSYV - MSOV - MIRANV + DSTL + DLTPL + DSTC + DLTPC + DLIDL

+ DLTDC + EANDO + NGKA

48. NFAEOQ = NFAEOQ_, + DNFA / 4

(NFAEOQ - NFAEOQR) * ER

Net government position of the monetary authority

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

49. NFAFED

51. NGP = NGP_, + DNGP / 4

A-67

Short-term liabilities and claims, stocks 92. STL = STL, - DSTL / 4 53. STC = STC_.1 - DSTC / 4

Long-term direct liabilities and claims, stocks 54, LIDL = LTDL_] - DLTDL / 4

55. LIDC

LIDC_; ~ DLTDC / 4 Long-term protfolio liabilities and claims, stocks

56. LTPL = LTPL_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 b foreigners Claims Dy foreigners

59. FL = - (STL + LTPL + LTDL)

60. FC

STC + LIPC + LIDC + NFAEOQ + 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 64. DEFIXED = MGV_, / (NFAEOQ_, + NFAEOQ. 9) * 2 * | PXGUV_, / PCOMP_; | 65. DEFIXE2 = MGV_, / (NFAEOQ_, + NFAEOQ_5) * 2

Change in reserve requirement

66. DRR = A(A) * (DD_] ~ TD_y) / 100

A-68

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

Unborrowed monetary base, sources and uses 68. BU (NFAEOQ. 7 + NFAEOQQ) * 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)

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 MSA"). All balance of payments variables are expressed at annual 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

averages and are not seasonally adjusted. Where monetary stocks are measured at end of quarter, the suffix "E0Q" is employed. The letter "V" appended to a4 variable name indicates measure-

ment in billions of Canadian dollars. When the "Vv" is absent, the

. varlable 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-70

The following abbreviations are used:

STATCAN BOC DOT FRB WHARTON

IFS

Statistics Canada

Bank of Canada Direction of Trade (IMF) Federal Reserve Board

Wharton Econometric Forecasting Associates

International Financial Statistics

CCAV

CUR

CUSTCU

CVNSA

DEF “XED

DEF ‘LXE 2

DEF LOAT

DLTDC

DLTDL

DLT PC

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 fixedrate 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 fixedrate 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)

ltrade weighted average for Germany, Japan, the United Kingdom

and the United States.

9°

DLTPL DNFA

DNFAFL DNFAFX

DNGP

DNGPFL DNGPFX

_ DNW DNWNSA

DRR | DSTC DSTL E

EANDO ECU EDV30 EDV41

EDV49 EDVS

EDV50

A-72

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

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$/CS, (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)

EFL EFX EGDP ELEAD EP EPXGUV ER EYDVNSA

FGNP

FL .FP FPXGUVD

FRSC }

FRSL

FYDVNSA

A-73

Canadian forward exchange rate index, U.S.$/CS, (EFR/1.008)

E * (1-KFIX)

E * KFIX

U.K. gross domestic product, output estimates

Canadian led spot exchange rate index (E,4)

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

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

Canadian exchange rate, U.S.$/C$ (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.

‘

GCU

GGNP

GNP GNPV

GP GPXGUV

GYDVNSA IFG

IFGV IFGVNSA

IFP

IFPV IFPVNS

II IIV INTSHK

JCU

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 (IIV/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)

JGNP | JP JPXGUV JYDVNSA

KF IX

- LTDC

LTDL

LTPC

LTPL

MCEV

MCGV

MCIV

MCRV

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, cif. (DOT) merchandise imports from Japan, c.i.£. (DOT)

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

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

MCUV

MGSNI

MGSNINS

MGSNIV

MGSNIVS

MGV

MSOV

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

tthe monetary authorities, end of quarter

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

end of quarter

NGK

NGKA

NGP

winsa} NWNSA

OTH

PCHGNP PCHP PCHW PCOMP PGNP

PMGSNI

PMGUV

PMS

POP15

A-77

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

net government capital account (STATCAN)

net government position of the consolidated monetary

authorities (BOC)

stock of private net worth (cumulated value of DNW)

other assets of the Bank of Canada (BOC)

implicit deflator for domestic absorption ((cv + IFGV + IFPV + IIV + GV)/(C + IFG + IFP + II + G)) percentage: change in gross national product percentage change in domestic price level percentage change in wages

foreign weighted average of the price of exports! implicit deflator for GNP (GNPV/GNP)

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

unit value of merchandise imports (STATCAN)

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

Canadian population 15 years of age and older (STATCAN)

ltrade weighted average for Germany, Japan, the United Kingdom

and the United States.

PPC

PXGUV |

PXS

QAUTO QAUTST QBACTS QCNTRL QCRISIS QEIETB

QEREG69

QEXPO QFRID QIET1 QIET2

QLOBO

QMIDEA QNEP

QRD

A-78

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

unit value of merchandise exports (STATCAN)

implicit deflator of export services ((XGSNIVS - XGV) /(XGSNIVS - XG)) dumny to reflect Canadian-U.S. auto agreement

dummy to reflect U.S. auto strike |

dummy for enactment of bank acts of 1967

dummy to reflect Canadian wage and price controls dummy for exchange rate crises in 1962 and 1968

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

dummy for divergance of weighted foreign rate from true foreign rate

dummy to reflect effects of Expo 67

dummy to reflect end of quarter occurring on a Friday dummy to reflect interest equalization tax

dummy to reflect interest equalization tax

dummy for exchange rate uncertainty and federal policy discouraging foreign borrowing

dumny for Suez Canel closing

dummy for new economic program in U.S.

dumny for periods when the discount rate is greater than the

short tem interest rate

QSCALE

QSMITH

QTAXI

QUI

QZEUROE

era

* Q3,04 RD RED

RES RESNSA

RESV RL

ROWPMG

ROWPXG 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)

RSHD

RU SCRG SCRP SD SDRVAL

sTCc

STL

TCORPV

TD TIME TINDV TNRESV TPERV

TRANV

ucu

UGNP

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)

UNW

UPXGUV URL

UYDV

WB’ ny; WBNSA

WMGV

XCEV _XCGV

XCJUNK

XCIV |

XCRV

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£. (DOT)

merchandise exports to Germany, c.i.f, (DOT)

slack variable to insulate bilateral export variables when Canadian model is shocked in isolation (normal value = Q) 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. (DOL)

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

total U.K. merchandise exports

XG XGCV

XGSNI XGSNINS XCSNIV XGSNIVS

XGTV XGV XJCV XJTIV “xRCV XRTV

XSOV |

XUCV XUTV XSYV XTRANV

XUJEGV

A-82

export of goods (STATCAN)

German 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.o0.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-83

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

younsa} disposable income (STATCAN)

Cite this document

APA

Federal Reserve (1982, August 31). The Canadian Sector of the Multi-Country Model. Ifdp, Federal Reserve. https://whenthefedspeaks.com/doc/ifdp_1982-209

BibTeX

@misc{wtfs_ifdp_1982_209,
  author = {Federal Reserve},
  title = {The Canadian Sector of the Multi-Country Model},
  year = {1982},
  month = {Aug},
  howpublished = {Ifdp, Federal Reserve},
  url = {https://whenthefedspeaks.com/doc/ifdp_1982-209},
  note = {Retrieved via When the Fed Speaks corpus}
}