UNDERSTANDING A MONETARY CONDITIONS INDEX

Neil R. Ericsson, Eilev S. Jansen, Neva A. Kerbeshian and Ragnar Nymoen.

November 1997Abstract

Numerous central banks, governmental organizations, and businesses now calcu-late a Monetary Conditions Index (or MCI) as an indicator of the stance of monetarypolicy. Two central banks, for Canada and New Zealand, use their MCIs as op-erational targets. This paper describes and defines this concept, summarizes howcentral banks implement MCIs in practice, reviews some of the. operational and con-ceptual issues involved, and evaluates the sensitivity of MCIs to an inherent sourceof uncertainty in their calculation. Empirically, this uncertainty typically rendersMCIs uninformative for their ostensible purposes, so some possible alternatives areconsidered.

Keywords: inflation, MCI, monetary conditions index, monetary policy, output,prices, uncertainty.

JEL classifications: E52, C52.

Preliminary. Comments welcome.All correspondence. should be addressed to the first author (NRE).

Neil R. EricssonStop 24, Division of International Finance, Federal Reserve Board2000 C Street, N.W., Washington, D.C. 20551 U.S.A.(202) 452-3709 (office) . (202) 736-5638 (fax) eicsson@frb.gov (Internet)

Eilev S. JansenResearch Department, Norges Bank, Bankplassen 2P.O. Box 1179 Sentrum, N-0107 Oslo 1 Norway(47) (22) 42 61 60 (office) (47) (22) 42 40 62 (fax)eilev.jansen@norges-bank.no (Internet)

Neva A KerbeshianStop 22,Division of International Finance, Federal Reserve Board2000 C Street, N.W., Washington, D.C. 20551 U.S.A.(202) 452-6489 (office) (202) 736-5638 (fax) kerbeshn@frb.gov (Internet)

Ragnar NymoenDepartment of Economics, University of OsloP.O. Box 1095 Blindern, N--0317 Oslo, Norway(47) (22) 85 51 54 (office) (47) (22) 85 50 35 (fax)ragnar.nymoen@econ.uio.no (Internet)and Norges Bank (address above) ragnar.nymoen@norges-bank.no (Internet)

Underst an ding a Monetary Conditions Index .

Neil R. Ericsson, Eilev S. Jansen, Neva A. Kerbeshian , and Ragnar Nymoen*

Introduction

I

Several central banks now calculate a Monetary Conditions Index (or MCI). for use inmonetary policy.. Empirically, an MCI.is a weighted average of changes in an interestrate and an exchange rate relative to their, values in a base period. The weights on theinterest rate and exchange rate reflect the estimated relative effects of those variableson aggregate demand over some period, often approximately two years.. MCIs arecurrently used as indicators of monetary conditions and as operational short-run

targets for monetary policy. .

A Monetary Conditions Index has several attractive features.. Its motivation issimple: exchange rates influence. aggregate demand, especially insmall open economies.

Thus, focusing on exchange rates as well-as interest rates may be important in un-derstanding an economy's behavior, and so in policymaking. Also, an MCI is easy tocalculate. For central banks, an. MCI is an intuitively appealing operational target formonetary policy. It generalizes interest-rate targeting to include effects of exchange

rates on an. open economy, and it serves as a model-based policy guide between formalmodel forecasts. For institutions other than central banks, an MCI as an index per semay capture both domestic and foreign influences on the general monetary conditions

of a country.MCIs are gaining widespread use. The central banks of Canada, New Zealand,

The first and third authors are a staff economist and a research assistant in the Division of.International Finance, Federal Reserve Board, Washington, D.C., U.S.A. The second author isthe director of the Research Department, Norges Bank, Oslo, Norway; and the fourth author isan associate professor of economics at the University of Oslo, Oslo, Norway. The authors may,be reached on the Internet at ericsson©frb.gov, eilev.jansen@norges-bank.no, kerbeshn@frb.gov,'and ragnar.nymoenQ .on.uio .no, respectively. The views expressed in this paper are solely theresponsibility of tie authors and should not be interpreted as reflecting those of Norges Bank, theBoard of Governors of the Federal Reserve System, or other members of their staffs. The firstauthor gratefully acknowledges the generous hospitality of Norges Bank, where he was visiting whenhe became involved in this research. We wish to thank Carol Bertaut, Richard Dennis, JurgenDoornik, Pierre Duguay, Dick Freeman, Dale Henderson, David Hendry, Karen Johnson, AnneSofie Jore, David Longworth, Cathy Mann, David Mayes, Sunil Sharma, Ralph Smith, and LarsSvensson for helpful discussions and comments; Richard Dennis, Bengt Hanson, and Anne SofieJore for providing the.data in Dennis (1996a, 1996b), Hanson (1993), and Jore (1994); and'TheodorSchoneberg, John Simpson, and Carl Strong for providing the MCI weights used by Deutsche Bank,Goldman Sachs, and JP Morgan respectively. All numerical results were obtained using PcGiveProfessional Versions 8.00, 8.10, and 9.00; cf. Doornik and Hendry '(1994, 1996).

1

Norway, and Sweden each publish an MCI and, to varying degrees, use their respectiveindexes in the conduct of monetary policy. Additionally, the IMF and the OECDcalculate MCIs for evaluating the monetary policies of many countries, and firmssuch. as Deutsche Bank,

lPMorgan puua b' sh MCrL_Goldman Sacis, and lla to ascertain

the general monetary environment in various countries.. An MCI assumes an underlying model relating economic activity and inflation

to the variables in the MCI, with the weights in the MCI reflecting the effects ofthe interest rate and exchange rate on aggregate demand. Being model-based, those

variables'' effects are' estimated, and the corresponding coefficients have an associateduncertainty from estimation. This paper shows that, empirically, this uncertainty

typically renders MCIs uninformative for their ostensible purposes.Sections 2 and 3 provide a foundation for understanding MCIs in practice, and

hence for understanding how estimation uncertainty impinges on their use. Section 2describes and,defines the Bank of Canada's Monetary Conditions Index, summarizes

how the Bank. utilizes its MCI in. conducting monetary policy,, reviews some opera-tional considerations, and documents MCI usage by other institutions and for othercountries. Section 3 analyzes two facets in the design of an MGI: the choice of weightsand variables, and the assumptions of the underlying empirical model. Section 4.eval-uates the robustness of MCIs to the uncertainty arising from the estimated weightsin the model, focusing on MCIs for Canada, New Zealand, Norway, Sweden, andthe United States. In light of the (often) .extreme uncertainty present in calculat-

ing MCIs, Section 4 then considers some possible alternatives. Section 5 concludes.While intuitively appealing, an MCI appears fraught with difficulties as an indicatorof monetary stance and as an operational target for monetary policy.

A previous paper, Eika, Ericsson, and Nymoen (1996b), derives analytical and

empirical properties of MCIs in an attempt to ascertain their usefulness in mone-tary policy. The current paper' complements Eika, Ericsson, and Nymoen (1996b)

by focusing on the practical implementation of an MCI and the degree- to whichimplementation is affected by uncertainty in the estimated weights.

2 Construction and Use of MCIs

The concept of a Monetary Conditions Index was developed at the Bank of Canadaand is used there more extensively than elsewhere, so this section begins by describ-

ing the Bank's MCI (Section 2.1), its implementation in practice (Section 2.2), andoperational considerations (Section 2.3). Section 2.4 considers MCIs used by otherinstitutions and for other countries. The discussion in the first three subsections relies

heavily on Duguay and Poloz (1994), Poloz, Rose, and Tetlow (1994), and Longworth

and Freedman (1995) for the role of the Bank's quarterly model in monetary policy;on the Bank of Canada (1994, 1995), Barker (1996), and Zelmer (1996) for details on

the MCI itself; on Freedman (1994) for the justification of an MCI in monetary policy;and especially on Freedman (1995) and Thiessen (1995) for an overview encompassingall of these issues.

2.1 Construction of the Bank of Canada's MCI

For the last several years, the Bank of Canada has used an MCI as an operationaltarget.in setting monetary policy. This - subsection defines the construction of the

MCI, briefly describes its empirical underpinnings; and interprets the generated index.The Bank's MCI is .a weighted sum of changes in the nominal 90-day commercial

paper interest rate (R) and a nominal G-10 bilateral trade-weighted exchange rate.index (E), where both variables are relative to. values in a .base period. The weights

on the interest rate and exchange rate reflect their. estimated relative effects on out-put. For Canada, the weights are 3 to 1, interest rate to exchange rate. That is; aone percentage point increase in. the interest rate induces. three times the change inthe Bank's MCI as would a one percent appreciation of the Canadian dollar. Alge-braically, it is convenient to write the MCI as:

MCIt = . 8R•(Rt-Ro) + 8e. (et-eo), (1)

where t is a time index, t = 0 is the base period, OR and 0e are the respective weights onthe interest rate and the exchange rate, and variables in lower case denote logarithms.Thus, the calculated MCI depends upon the weights 9R and 0, the measures of theexchange rate and the interest rate, and the base- period. Usually, the exchange ratein (1) is in logarithms or in percent deviations from its baseline value, whereas theinterest rate is in levels: Below, logarithms of the exchange rate generally are used,.and the choice makes little difference for the countries and sample periods involved.

The relative weight of 3 is. derived from a range of econometric. evidence on thedeterminants of-aggregate demand. As discussed in Freedman (1994, pp. 469-470 and afootnote 27), Duguay's (1994) results are typical of that evidence, so we focus on arepresentative regression from that paper, Duguay (1994, p. 51, Table 1, column 7):

Ayt = + 0.13 -;- 0.52 Ayt + 0.45 'A yz 1

(0.13) (0.11) (0.11)

0.40 [A$RRt/ 8] .0.15 [A12gt/12] (2)(0.22) (0.12)

T = 44 [1980(1) - 1990(4)) R2 = 0.64 & = 0.62% dw = 1.96.

3 . N

The series are all quarterly and include real Canadian GDP (Y) and real U.S. GDP(Y*), and A is 'the first difference operator.' The real interest rate (RR) is con-structed as the nominal 90-day commercial paper interest rate (R) minus the one-quarter lag in the annual rate of change of t e Canadian GDP deflator (P). Thatis, RRt = Rt - 1 Opt-1. ' The real exchange rate (Q) is the product of .the' nom-inal bilateral Canada-U .S. exchange rate (E, in U.S. dollars per Canadian dollar)

and the ratio of the Canadian. GDP deflator to the U.S. GDP deflator (P*): i.e.,Q = E E. (PIP*). Thus, an increase in Q represents an.appreciation of the Canadian.real exchange rate. The symbols T, : R2 R2, d, and dw'denote the sample size of theestimation period, the squared multiple correlation' coefficient, the adjusted versionthereof, the estimated equation standard error, and the Durbin-Watson statistic re-spectively . The coefficients are estimated by least squares, and estimated standarderrors are in parentheses.2

The ratio of the coefficients on the interest rate _ and the exchange rate is(-0.40)/(-0 :15) or 2.67, which is virtually the relative weight Qf 3 used by the Bank'of Canada. While the relative weight is based on estimated relations with real interest

.rates and exchange rates, the Bank applies the weight to ark- index with the corre-sponding nominal variables. Switching from real to nominal variables is convenientoperationally, and it has been defended by the short horizon for MCI-based monetarypolicy and the near constancy of inflation and relative prices over that horizon.

Figure 1 plots the Bank's Monetary Conditions Index. A decline in the interestrate increases aggregate demand and lowers the MCI, as does a depreciation of'theCanadian dollar, so a fall in the index is interpreted as a loosening of. monetary

conditions. As a policy indicator, the MCI aims to keep track of both interest rate and

exchange rate movements and their effects on aggregate demand. From 1990 through1993, the MCI fell steadily, signaling a general loosening of monetary conditions. In1994 and early 1995, conditions tightened. Thereafter, the index resumed falling.

In Figure 1 and in all other figures of MCIs herein,- each MCI.is scaled such that its

weights sum to unity, i.e., BR+Be = 1. A plotted MCI is thus always in units equivalentto the *interest rate, measured as a fraction, thereby permitting easy interpretation

'The difference operator A is defined as (1 - L), where the lag operator L shifts a variable oneperiod into the past. Hence, for xt (a variable x' at time t), Lxt = xt_1 and so Att = xt - xt_1.More generally, A1xt = (1- V )ixt. If i (or j) is undefined, it is taken to be unity.

2A minor notational and empirical discrepancy exists between (1) and (2), in that. E in theformer is the 0-10 trade-weighted exchange rate whereas E (through Q) in the latter is the bilateral.U.S.-Canadian exchange rate. This distinction is maintained below. MCIs for Canada use the G-10 trade-weighted exchange rate, whereas regressions' for Canada use the. bilateral U.S.-Canadianexchange rate.. Choice between the two exchange rates should make only a minor difference: the

U.S.-Canadian exchange rate dominates the G-10 trade-weighted exchange rate, With the formerrecieving a weight of over 80% in the latter.

4

of and comparison across different MCIs. For instance, the decline in the CanadianMCI from 1990 to 1994 is interpreted as the equivalent of a 12 percentage point (1200

basis point) , d6cline in the interest rate. Roughly half of this decline is due to: the20% depreciation of the Canadian dollar over that period, leading to Figure 2.

Figure 2 shows the two components of the MCI: the nominal 90-day commercialpaper rate and the logarithm of the nominal G-10. trade-weighted Canadian dollar.During 1990 and 1991, the Canadian dollar remained relatively constant while theinterest rate declined, with the latter variable being primarily responsible for the fall inthe MCI. In 1992 and 1993, both variables moved downward, with both contributingto the MCI's continued fall. From 1994 onward, the two variables have moved inopposite directions, offsetting each other's movements to some extent.

2.2 The Bank of Canada's MCI as an Operational Target

For the past several years, the Bank of.Canada has used its MCI as an operational1 a

target. This subsection describes how the Bank has done so, focusing on the roleplayed by the Bank's econometric model.

The Bank of Canada calculates a desired or target path for. the MCI from interest

rate and exchange rate forecasts from the'Bank's Quarterly Projection Model (orQPM). The QPM includes equations for output growth (similar to (2)), inflation,and the exchange rate. In the model, interest rates and exchanges rates influenceoutput, which in turn influences inflation through a Phillips curve relationship. Theexchange rate is determined through an uncovered interest rate parity condition with

a risk premium. Additionally, the model incorporates a monetary response function,

which is designed to bring inflation back to the midpoint of the Bank's inflation. target

range within a specified time, and subject to smoothness .constraints on the path of.the interest rate. Currently, the Bank has an inflation target range of 1 to 3 percent

at 6 to 8 quarters out. From the model, the Bank derives a solution for the future

paths of the interest rate and exchange rate, consistent with the inflation target.. Thedesired path for the MCI is then calculated from those paths on the interest rate andexchange rate.3

If, in the short term from week to week - the actual MCI rises above (orfalls below) its target path, this is interpreted as a tightening (or loosening) of mon-etary conditions relative to those anticipated and desired, and the Bank considersresponding. In effect, the MCI is a convenient short-hand calculation for how to

3In practice, the Bank controls the overnight interest rate, which is closely linked to the 90-daycommercial paper interest rate. For the most part, the discussion below ignores the distinction

between the Bank's actual policy instrument and what constitutes a very short-term operationaltarget. 0

N5

adjust interest rates if the exchange rate moves sometime between adjacent formal(quarterly) forecast rounds with the QPM. Operationally, at weekly and mid-quarter

meetings, the MCI serves as a starting point in policy discussions, in which the Bark

looks at developments that have occurred since the beg a irig of the quarter in de-ciding whether to adjust policy. The Bank then may also make adjustments to the

desired path. of the MCI.Gordon Thiessen, Governor of the Bank of Canada, summarizes the role of the

MCI at the Bank, as follows.

... we [at the Bank of.Canada] aim at a path for monetary conditionsthat would bring about a path for aggregate: demand and prices consistentwith the control of inflation. Thiessen (1995, p. 54) .

Charles Freedman, Deputy Governor of the' Bank of Canada, provides additional

details.

In the last few' years, the Bank of Canada has used the concept ofmonetary conditions (the. combination of the movement of interest ratesand the exchange rate) as the operational target of policy, in much thesame way as short-term interest rates were used in the past.

... The objective of monetary policy over the next three years or sois to .maintain the rate, of inflation within a band of 1 to 3 per cent. Thequarterly Bank of Canada staff projection takes into account such factorsas the movements in foreign variables and domestic exogenous variables aswell as the momentum of the economy, and sets out a path for monetary

conditions that will result in the rate of inflation six to eight quarters

ahead being within the Bank's target band. .... One can think of thispath [of.the MCI] as the desired or target path for monetary' conditions.

Freedman (1995, pp. 53, 54, 56)

Three qualifications should be noted. First, while the QPM is the foundation forgenerating the forecasts, additional analyses of the domestic .and foreign -economiesalso play a role, with iterations between sectoral specialists and the QPM resulting injudgmentally adjusted forecasts. Second, the forecasts are conditional; both on theBank's'views of future domestic monetary and fiscal policy and on its views of future-foreign economic outcomes. Third, there are operational considerations, as described

in.the next subsection.

6 N

2.3 Operational Considerations

Implementing an MCI as a target involves practical, operational considerations, whichare reflected by the Bank of Canada's experience. These considerations include boththe timing of policy adjustments and the role of additional information in the policyprocess.. Timing, or "tactical" considerations, have sometimes made an MCI a difficultoperational target to achieve.

The Bank has a desired path for the MCI. If the actual MCI is "off course,"then the Bank tries to move it back on track as quickly as' is tactically possible."Tactically" is the operational word here, in that the Bank sometimes has. allowedactual and desired MCIs to differ for considerable periods - of a quarter or more. TheBank has explained such episodes by arguing, for example, that observed exchangerates were out of line relative to fundamentals, as the Bank believed happened with

transitory reactions to the Quebec problem. In such. situations., the calculated index

may not accurately reflect intended or actual monetary conditions. Freedman (1995)

provides a lucid account of this problem..

... Suppose. an easing. of monetary conditions was appropriate, but

there was.a great deal of uncertainty and nervousness in the exchange

market. ... In such circumstances, the Bank would delay any decisionto ease monetary conditions because of the risk that an action to reducethe overnight rate, could result in significant weakness in the exchangemarket and lead to the buildup of extrapolative expectations in that mar-ket, followed, as we have so often seen in Canada in recent years, by anincrease in interest rates in the money market and the bond market. Ineffect, an attempt to ease monetary conditions could, via the interactionof. developments in the exchange market and domestic financial markets,

result in an outcome where monetary conditions ended up tighter and noteasier. Thus, the tactical aspect involves. choosing the timing of changes

to. avoid undesired market-driven outcomes. (p. 58) '

Timing is clearly an issue. Further, market conditions and the market's responses toBank actions may simply prevent the Bank .from achieving its target, at least in the

short or medium term.The MCI is central to. the Bank's decision process,. in which use of the MCI is

viewed as interest-rate targeting, adjusted for exchange-rate effects on aggregate de-.

mand in a small open economy. That said, inputs additional to the MCI do influence

the Bank's policy decisions, as Freedman (1995) indicates. .

... While the [model-based path for the MCI] recommended by the

staff is A 'crucial input into the views of senior management on the desired

7

path for monetary conditions, senior management may also incorporateinto its thinking the possible effects of a broad range of outcomes withrespect to the movements of exogenous variables or the momentum of the

Canadian economy. Indeed, the staff prepares alternative "risk scenarios"that incorporate some of these factors. Management may also decide inwhich direction to take or avoid risks (e.g., that. it is appropriate to bees-pecially vigilant about a resurgence of inflation). If, following this type ofanalysis, there is .a divergence between actual and desired monetary condi=tions)

the Bank will look for' the right time to make adjustments. Among

the factors that enter into the timing decision are. market uncertainty. and

market nervousness.' (p. 59)

Thus, even for a stable developed economy like Canada; achieving targeted levels of

the MCI has sometimes proven infeasible because of tactical difficulties. For countries

with much more volatile economies and larger swings 'in the exchange rate, tacticalconsiderations are likely to make an MCI operationally infeasible.

2.4 General Usage of MCIs

While much discussion in the literature focuses on the Bank of Canada's use of its

Monetary Conditions Index, MCIs have widespread use among other institutions and

for other countries. The central banks -of New Zealand, Norway, and Sweden eachpublish an MCI and (to varying degrees) use it in conducting monetary policy. TheReserve Bank of New Zealand (starting in late 1996) uses an MCI as an operational

target in much the. way that the Bank of Canada does; see the Reserve Bank of, NewZealand (1996a). The central banks of Norway. and Sweden use MCIs in a more lim-ited fashion'- as indicators of monetary conditions when formulating their monetarypolicies; see Norges Bank (1995) and Hansson and Lindberg (1994). Additionally, the

IMF and OECD use MCIs in evaluating monetary policies. across countries, and busi-nesses such as Deutsche Bank, Goldman Sachs, and JP Morgan calculate MCIs to

evaluate different countries' monetary conditions.

Table 1 compiles alternative relative weights for MCIs across selected countries,

as published or made available. by the institutions just mentioned. This table isindicative of the range of countries and sources, rather than being exhaustive. While

MCIs are' about monetary conditions, institutions other than the central bank of a

given country may well calculate an MCI for that country, even if that central bank

does not publish or use an MCI in policy. For many countries,. several estimates of

the relative weights are available, and the estimates vary considerably. The' range of

estimated weights in part reflects large confidence intervals for the weights and the

8

use of different models and sample periods.In light of the range in available weights, Section 3.1 considers inter alia the

empirical consequences of using different weights. Section 4 then examines in detail

the uncertainty of the estimated weights. and the empirical consequences that thatuncertainty has for using an MCI as an indicator. or target..

3 Two Facets of MCI Design

I

This section analyzes two facets in, the design' of an MCI: the choice of weights andvariables (Section 3.1), and the assumptions of the underlying empirical model (Sec-tion 3.2), with the latter leading directly into Section 4 on coefficient uncertainty.Empirically, MCIs appear very sensitive to even minor changes in weights, variables,and assumptions.

3.1 'Choice of Weights and Variables

The choice of weights and variables in an MCI. is central to%onstructing the indexitself, and MCIs can be empirically sensitive to that choice. For example, Figure 3

plots three: alternative MCIs for Canada: one using the Bank of Canada's relativeweight of 3, and the other two using the smallest and largest Canadian weightsappearing in Table 1(weights-of 2 and 4.3 respectively). In 1986 and 1987, the MCI

is nearly invariant to. the relative weight because the exchange rate was virtuallyconstant; see Figure 2. From 1988 through 1994, weights matter considerably because

the Canadian dollar appreciated and then depreciated. In late 1996, some versions

of the index actually move in different directions. To focus on this phenomenon,Figure 4 plots the MCIs from the beginning of 1994 onwards. The MCI with thesmallest relative weight indicates a moderate tightening of monetary policy in theautumn of 1996, whereas. the indexes with larger weights on the interest rate show

a moderate or considerable loosening. Similar episodes occur in 1983-1984, whilenoting. that the extreme scale of Figure 3 necessary' for capturing 17 years of datadoes dwarf the discrepancies in the various MCIs' behavior. In general, the weightscan and do affect the magnitude and the sign of changes in the index. Notably,

the Bank of Canada initially used weights of 2:1 and then switched to 3:1, with asubstantial effect on the measured MCI.

The selection of variables in the MCI is-an open-issue as well. MCIs in this paper'sfigures are calculated from only a single interest rate and a single exchange rate fora given country. Many possible interest rates and exchange rates are available, and

using different variables in the MCI can induce differences in movement similar to

those encountered in the choice of weights.

For example, the Bank of Canada currently uses a nominal' G-10 bilateral trade-

weighted exchange rate. Such an exchange rate is appealing in trade equations, and

.hence in an aggregate output equation such as (2). Howeyer, for. short- to medium-term monetary policy, international exchange markets may be more speculative and

financial in nature, in which case bilateral trade weights are less germane . A conflictmay well exist between the data appropriate for the underlying econometric model

and those appropriate for policy analysis.

A range of alternative interest rates also exists. Numerous short-term rates areavailable, and MCIs need not be restricted to short-term rates alone.. Deutsche Bank

and Goldman Sachs in particular use weighted averages of long-term- and short-terminterest rates in calculating their MCIs. Further, an MCI may be calculated from real(rather than nominal) variables, with the measurement of expected inflation implying

yet a further.choice in variables. Without substantially better information on the

choice of weights and variables, currently calculated MCIs may well ' be misleadingabout underlying changes in monetary stance, both in magnitude and in sign.

The choice of variables also can be viewed as an issue in-a.ggregation, with four

forms of aggregation occurring . First, an MCI includes only exchange rates and in

terest rates , to the exclusion of other potential variables ; see Section 3.2 below. Thatexclusion constitutes aggregation , with weights.of zero on those other variables..Sec-ond, bilateral exchange rates are aggregated into a single exchange rate index. Third,

available interest rates are aggregated , often into a single interest rate. Fourth, com-

bining a given exchange rate index and a given interest rate into an MCI constitutesaggregation. All four senses * of aggregation involve losses of information, and useof an MCI. implicitly assumes that the'information lost is not important for policy..

Specifically, because many combinations of an interest rate and an exchange rate give'rise to the same value of the index , the lost information is important if the mix ofthe two variables is of concern.

In practice, the Bank of Canada does look at the two variables separately, espe-cially when considering how to alter monetary conditions; see Freedman (1995, p. 58),as quoted above. For example, rapid depreciation of the exchange rate can translate'into risk.premia.across the yield spectrum, in which case the exchange rate may beweaker in conjunction with higher interest rates,-but overall monetary conditions canbe unaffected. As Figures 1-4 show, episodes exist (such as early 1994) when the

interest rate increased but the exchange rate weakened even more, with the MCImoving in the opposite direction from the interest rate.

10

3.2 Assumptions of the Underlying Empirical Model

The use and interpretation of an MCI rests upon the assumptions of the underlying

model. Several issues arise for that model, including dynamics, data nonstationarityand differencing, exogeneity and feedback, parameter constancy, 'the choice of modelvariables, and the uncertainty arising from estimating the model. This. subsection-summarizes these six issues, relating them to the corresponding model assumptions.

These assumptions are often testable . and, if violated, directly affect the economicinterpretation of the MCI. Eika, Ericsson, and Nymoen (1996b) present, a more de-tailed analytical assessment, and their empirical evaluation confirms such difficultiesin models for the Canadian, * Swedish, and Norwegian MCIs. Gerlach and Smets

(1996) and Alexander (1997) discuss possible .economic theoretical underpinnings ofan MCI and the associated, rather stringent assumptions required for an MCI to be

an optimal policy target.

First, the relationships between the policy instruments, the exchange rate, the

short-term interest rate, output, and inflation generally are dynårnic, implying differ-

ent short-, medium-, and, long-run multipliers. Thus, the policy horizon inay affectthe relative weight. If policy is concerned with several horizons, the weight for' a'single horizon may not be adequate.

Second, the temporal properties of the data themselves bear on the constructionof an MCI. In particular, nonstationarity of the data (e.g., as in a series with drift)may affect the distribution of the error terms in the associated model and therebyaffect statistical inference. Nonstationary data also may be cointegrated. If so,- therelevant equations should include levels of the series, and calculations of multipliers.*should account. for those levels. By contrast, output equations for calculating MCI

weights are typically estimated with differenced or detrended data, with no testing

for cointegration. Further, the MCI itself is calculated on the levels of the data.Adjustment of the MCI relative to a base period simply subtracts a constant from

an unbased MCI and does not constitute working with differenced data: The mixed

use of differences and levels affects the interpretation of the weights: short run fordifferences, contrasting with long run for levels.

Third, the postulated :exogeneity of the policy instruments and other variables ispotentially misleading. In the MCI itself, the weights are interpreted as elasticities

of aggregate demand with respect to the interest rate and the exchange rate. Thisinterpretation assumes no feedback from aggregate demand or inflation onto exchangerates and interest 'rates over the relevant policy horizon. Such feedback may occurunder any policy regime and seems likely to occur under inflation targeting by design.

With feedback, the estimated weights need not reflect the total effects of the exchange

rate and interest. rate on aggregate demand. As an alternative, the feedback could

11

be estimated and subsequently incorporated into the elasticities from which an MCIis derived.

Fourth, parameter constancy is critical to the interpretation of an MCI, and. it

turns on all three of the aforementioned issues. Statistically nonconstant weights mayarise empirically from mis-specified dynamics, improper treatment, of nonstationarity,or incorrect exogeneity assumptions. Because the MCI is designed for policy, it is

important to establish the invariance of. the weights to, changes in policy, yet this

conjectured invariance generally.has not been investigated empirically. With noncon-stant parameters, estimation over different sample periods would result in differentestimates of the weights, and so different choices of weights. Eika, Ericsson, andNymoen (1996b, Section IV) illustrate how that choice.of weights can affect policyinferences with an MCI.

Fifth, the choice of model variables determines the variables omitted from the

model. Significant omitted variables in the model's relationships may affect dynamics,

cointegration, exogeneity, and parameter constancy in the model.More generally, the use and interpretation of an MCI in policy assumes the exis-

tence of direct and unequivocal relationships between the variables involved... Possible

additional influences in those- relationships can confound the .strict interpretation of.an MCI as an index of monetary conditions.

One such relationship is that between, the actual policy instrument (such as thecentral bank's overnight interest rate) and the exchange rate and short-term interest

rate. If variables other than the policy instrument play an. important role in de-termining the exchange rate and. interest rate, neglect of those other variables hassubstantive implications for policy with an MCI. For example, changes in world oiland commodity prices may alter a country's terms of trade, thereby affecting theexchange.rate. The MCI would then change, even if monetary stance remained un-'changed. Likewise, changes in world interest rates and inflation rates and changesin domestic asset portfolio preferences may alter 'the domestic short-term interest

rate, and so the MCI. The variables' from which the MCI is constructed may reflectphenorhena other than just direct monetary policy, so movements in the MCI arenot tied unequivocally to changes in monetary stance. Conversely, by following ortargeting an MCI, a central bank could be misled into adopting an overly tight or

loose monetary policy, simply because some external shock affected the exchange rateor the domestic short-term interest rate.

An additional relationship is the one between exchange rates, interest rates, and

output growth, which is.the basis. for. calculating the relative weight in the MCI.

Exchange rates have other effects on the economy, such as influencing domestic pricesdirectly; cf. Root and Rogoff (1995), 3uselius (1992), and de Brouwer and Ericsson

12 1

(1995) for examples of theoretical and empirical research supporting such a channel.The interest rate also may have other channels to inflation. Specifically, interest.rates may affect'mortgage payments and hence inflation through the calculated costof housing. Neglect of these transmission mechanisms is likely to result in the MCIbeing a misleading index of monetary conditions per se, particularly if the MCI is'being used by the central bank in targeting inflation. An MCI focuses on only one ofmany potential channels and on only two of many potential variables in the monetarytransmission mechanism.

Sixth, the relative weight in an. MCI is based on an estimated empirical model;and so is subject to coefficient uncertainty from that estimation. Thus, the estimatedweight may be numerically nonconstant, even if it is statistically constant. Numer-ically nonconstant weights -may arise from the lack of information content in thedata, leading to large standard errors. Section 3.1 above shows that the calculation

of an MCI can be sensitive to the choice of weights.. Uncertainty from estimationhas not been previously examined for MCIs, so the next section (Section 4) turnsto quantifying that uncertainty and assessing its consequences for using an MCI in

practice.

4 Uncertainty of MCI Weights and Its Consequences

This section develops and applies a framework for assessing the statistical uncertaintyfrom estimating the MCI weights. Section 4.1 provides the statistical background.Sections 4.2, 4.3, 4.4, 4.5, and 4.6 apply the framework to MCI models for Canada,

New Zealand, Norway, Sweden, and the United States. Section 4.7 summarizes thepolicy consequences of uncertainty in an MCI's relative weight, and Section 4.8 con-siders some alternatives.

Throughout, the notation of variables parallels that for Canada in Section 2. Inparticular, variables with an asterisk correspond to. the foreign country (or countries)and those without correspond to the home, country. That said, specifics of the datadefinitions may differ, country by country. .

4.1 Measuring the Uncertainty of MCI Weights

This subsection describes three approaches for measuring the uncertainty that arisesfrom estimating MCI relative weights. The three approaches respectively use theWald, Fieller, and likelihood ratio statistics to construct confidence intervals for theweights. The Fieller and likelihood ratio forms appear preferable because of their

finite sample properties.

13

The first and most intuitive approach is based on the associated standard errorand t ratio for the estimated relative weight, and thus corresponds to a Wald statistic;see Wald (1943) and Silvey (1975, pp. 115-118). This method may be characterized.as follows. An equation is estimated in the form:

Ayt ='a • A.RRt + b •'I .qt + other variables + error. (3)

The relative weight p is a/b, and its estimated value is a/b, where a circumflexdenotes estimation. Also, (3) is conveniently rewritten as:

L yt = b • (p • ARRt + Aqt) + other variables +, error. (4)

The relative weight p enters (4) explicitly, where p may be estimated directly by

(say) nonlinear least squares. The result is numerically equivalent to the ratio å/bderived from the linear estimates (d, b) in (3). In either case, a standard error forcan be computed, from which confidence intervals are directly obtained.

A confidence interval includes the unconstrained estimate of µ, which is å./b, andsome region around that value. Intuitively, the confidence inte;val contains each value

po of the relative weight that does not violate the hypothesis

Hw: alb = ILO (5)

too strongly in the data, noting that p = alb. More formally, let Fw(po) be the Wald-based F statistic for testing Hw, and let Pr(•) be the probability of its argument.Then, a confidence interval of (1- a)% is (plower, puppper],where the lower and upper

bounds (plower and purr) are calculated as satisfying Pr(Fw(po)) < 1- a for p E

[plower, y,,ppper]• Equivalently, the confidence interval is defined by Fw(po)) < c(a),where c(a) is a critical value generating the size a. This second formulation of aconfidence interval has a convenient graphical representation, as discussed below.

If b, the coefficient on the exchange rate, is precisely estimated,.the Wald approach

is usually quite satisfactory. However, if b is imprecisely estimated (i.e., not verysignificant statistically), then this approach can be highly misleading. Specifically,the Wald approach ignores how å/b behaves for.values of b relatively close to zero,where "relatively" reflects the uncertainty in the estimate of b. Empirically, estimates

of b often are not very significant statistically, so this concern is germane to calculatingMCIs. In essence, the problem arises because ,4 is a nonlinear function of estimators(et, b) that are (approximately) jointly nQtmally distributed; see Gregory and Veall

(1985) for details.

The second approach avoids this problem by.transforming the nonlinear hyp o-thesis (5) into a linear one: namely,

14

Hp : a - b/io 0 . (6)

This approach is due to Fieller (1940, 1954), so the hypothesis in (6) and correspond-ing F statistic are denoted HF and FF(yo). Because the hypothesis (6) is linear in

the parameters a and b, tests of this hypothesis are typically well-behaved, even ifb is close to zero. Determination of confidence intervals is exactly as for the Waldapproach, except that the F statistic is constructed for a.- bµo = 0. See Kendall andStuart (1973, pp. 130-132) for a summary.

The third approach uses the likelihood ratio (LR) statistic to calculate the confi-

dence interval for the' hypothesis Hw. That is, (3), is estimated both unrestrictedlyand under the restriction Hw, corresponding likelihoods (or residual sums of squares,for single equations) are obtained, and the confidence interval is constructed fromvalues of yo for which the LR statistic is less than a given critical value.

Several comments Are of note. First, the LR statistic and the confidence. intervalsgenerated from it are invariant to the choice of Hw or . HF- because the likelihood-isinvariant to nonsingular transformations of its parameters.. Second, if the originalmodel (3) is linear in its parameters, then Fieller's solution is numerically equivalent

to the LR one, giving the former a generic justification. Third, if (3) is nonlinear inits parameters, then the LR, Fieller, and Wald confidence intervals are all different.In particular, the LR and Fieller confidence intervals differ because inter alia the like-.lihood ratio requires an iterative numerical procedure to estimate the model underthe null hypothesis that µ = µo, whereas the Fieller solution is non-iterative, once

(3) is estimated. The LR confidence interval is probably the most appealing of thethree for nonlinear models because of its invariance property. For this reason, andbecause the LR and Fieller statistics are equivalent in linear models, discussion belowof empirical confidence intervals focuses on the LR form. Fourth, the Fieller statistic

is technically a "Wald" statistic in that it is constructed from only unrestricted es-timates, albeit-of (3) rather than of (4). However, for ease of distinction below, thestatistics for testing (5) and (6) on the unrestricted estimates are called Wald andFieller statistics. Finally, constructing confidence intervals for ratios of estimates is

a common problem. For example, it arises in calculating the estimated uncertainty

of NAIRUs; see Staiger, Stock,. and Watson (1997).Sections 4.2, 4.3, 4.4, 4.5, and 4.6 below obtain and analyze confidence intervals

of MCI relative weights for Canada, New. Zealand, Norway, Sweden, and the UnitedStates. Each subsection presents an estimated equation for calculating the MCI

relative weight. From that equation, LR, Fieller, and Wald confidence intervals of

the estimated relative weight are derived for the 67.5% (i.e., "±1 standard error"),

90%, and 95% levels. Table 2 lists those confidence intervals for all five countries.

N15

Additionally, for each country, four graphs characterize the estimation uncertaintyfrom several perspectives. The first graph for each country plots the LR, Fieller,

and Wald F statistics as a function of the hypothesized relative weight µ0.. This

graph provides an overall view of the estimation uncertainty. A conafidence interval

corresponds to the region of po for which an F statistic remains below a given critical

value, so this ' graph simplifies, comparison of the LR, Fieller, and Wald confidence . .intervals. The second graph plots the MCI evaluated at its unrestricted estimate andat the upper and lower bounds from an LR 95% confidence interval. In an obviousnotation, this graph contains MCI (µ) t, .MCI (pu eT) t, and MCI (pj, ,,,er) t. The thirdand fourth graphs aim to characterize the implications over one-quarter and one-year

horizons of choosing one relative weight rather than. another. The third graph plotsMCI (µ)t, MCI(µ)t_1 + L MCI (iiuppper)t,and MCI(µ)t-i + AMCI (µtower)t, andthe fourth graph plots MCI (µ)t, MCI (µ)t_4 + A4MCI (pupppeT)t,and MCI(µ)t_4 +A4MCI( iijower)t• That is, these two graphs show how-much an MCI might differ

over fixed horizons from any particular starting point, noting that the base period of

an MCI is arbitrary. For computational convenience, calculations are based on thelong-run relative weights, although these weights do not typically differ much (if at

all) from the interim relative weights at the policy horizons. of interest.For each country, the interest rate is measured as a fraction and the exchange rate

is in logarithms. Following the various central banks' practices, the Canadian MCI isnominal,' whereas those for New Zealand,. Norway, and Sweden are real. The Federal

Reserve Board does not publish an MCI, so the choice of a nominal MCI versus a

real MCI is open for the United States. Below, the nominal MCI is plotted for theUnited States.

4.2 Canada

Equation (2) reports the estimates and implied standard errors for the regression

in Duguay (1994, p. 51, Table 1, column 7). Using data from the Federal ReserveBoard's INTL database, we could closely replicate that regression:

Ayt = + 0.14 + 0.44 Dyi + 0.55 Ayt 1(0.13) (0.12) A0.12) f

0.648 [tsRRt/8] - 0.181 [Al2gt/12] (7)(0.231) (0.109)

T = 44 [1980(1) 1990(4)] R2 = 0.67 &= 0.628% dw = 1.82 .

The derived estimated relative MCI weight is (-0.648)/(_0.181) or 3.56, somewhat

larger numerically than the estimate of 2.67 from Duguay's equation, but well within

the range of estimates typically obtained for Canada (see Table 1).The LR 95% confidence interval is enormous: [0.74, oo]. It includes equal weights

on the interest rate and exchange rate (µ = 1), as well as a zero weight on theexchange rate (µ = cc). Even 'the 67.65% eonfi ence interval, equivalent to a plus-or-minus one standard error band for single coefficient estimates, is large: [1.80,9.601;see Table 2. This high degree of uncertainty is unsurprising, given the marginallysignificant coefficient on the exchange rate in (2) and (7).

Figure 5 shows just how uncertain the estimate of the MCI relative weight is byplotting the LR F statistic. for various hypothesized values µo of the relative weightµ. Small values of the F statistic correspond to relative weights that are statisti-cally acceptable, whereas large values do not. To measure the degree of statisticalacceptability, Figure 5 also plots the critical values of the F statistic for 32.35%, 10%,and 5%: that is, for 67.65%, 90%, and 95% confidence intervals. For example, for

µo greater than about unity, all values of the LR F statistic lie under the line cor-

responding to the 5% critical value (95% confidence region). That visually portras

the actual 95% confidence interval of [0.74, oo]. Only numerically small values and.negative values of µo are clearly rejected by the data. Negative weights would likelybe ignored if obtained in a,policy framework, given their counter-intuitive sign. The

Wald statistic gives a distorted picture, particularly when the hypothesized relativeweight µo is far away from the unconstrained estimate of 3.56.,

The observed empirical uncertainty has immediate repercussions for the CanadianMCI in policy, as shown in Figures 6-8. These figures demonstrate how statisticallyreasonable estimates of the relative weight can obtain completely different outcomes

for the MCI as an index. For instance, depending upon whether the MCI is calculated

from plower or µu,, monetary policy either loosens substantially (by roughly 500basis points) or tightens substantially (by 300 basis points) over the period 1993Q1-1995Q1: see Figure 6. The empirical consequences of these two scenarios are clearly

very different.Figures 7 and 8 derive the implications of using µ10111er or µfl rather than the

unconstrained MCI relative weight µ for short horizons that are likely to be of interestin policy.- specifically, for one-quarter and one-year horizons. Discrepancies of over

100 basis points are common at a one-quarter horizon, and of over 500 basis points at

a one-year horizon. Which such large differences in MCIs calculated'from empiricallyreasonable relative weights, policy based on an MCI must be problematic.

4.3 New Zealand

Much recent work has appeared on MCIs for New Zealand: see Mayes and Riches

(1996), Nadal-De Simone, Dennis, and Redward (1996), Dennis (1996a, 1996b), Den-

It17

nis and Roger (1997), and the Reserve Bank of New Zealand (1996b). As withCanada, we focus on a single, representative equation: here, Dennis (1996a, p. 15,Table 2, Equation A). Using data provided by Dennis, .we have replicated that equa-tion:

A(Vy)t --

0.011 + 0.34 A(Qy)t- j - 0.155 ORRt-3(0.006) (0.16) (0.062)

- 0.089 Agt.-s - 1.22 A2pt_3 - 0.53 A2pt_4(0.033) . (0.32) (0.14)

-}- 0.65"Ayi 3 + 0.72 Ayt-5 + 0.815 ut_1 (8)(0.22) . (0.23) (0.129) -

T = 40 [1986(2) -1996(1) 1 o = 0.675%

The equation is estimated by first-order autoregressive least squares, with ut_1 beingthe lagged error.- The dependent variable is the change in an output gap, where thegap is obtained using the Hodrick-Prescott filter. The operator n.ablaV denotes thatfilter and Vy the corresponding output gap, where this notation is selected because.the HP filter has effects similar to differencing. Here, the HP* smoothing parameterA is 1600. The relative MCI weight is, estimated as the ratio of the coefficients onARRt_3 and Agt_5, which is (-0.155)/(-0.089) or 1.75.

The LR 95% confidence interval is large, [0.30, 7.31]. Differences between LRand Fieller statistics are minor, whereas both differ sharply from the Wald statisticoutside the range µ E [-2, +3]; see Figure 9.

The confidence intervals for New Zealand are not as large as those for Canada.However, the presence of small relative weights in the confidence interval has a markedeffect on the calculated MCIs, as seen in Figures 10-12.. Discrepancies at the one-year

horizon (Figure 12) exceed 1000 basis points during 1987-1988 and are over 500 basispoints for the most recent observation (1996Q1).

4.4 Norway

The Norwegian MCI is based on Jore (1994). Eika, Ericsson, and Nymoen (1996b,Section IV.3) analyze the model in Jore (1994); details on the data appear in Eika,Ericsson, and Nymoen (1996a, Appendix B). Jore uses an HP filter on output, with asmoothing parameter A of 100, 000 - effectively a linear trend-. We replicated Jore's

(1994) Equation 2:

18 . l%

(Vy)t .= + 0.028 - 0.124 (V.y)t_1 -- 0.30 A 2gt(0.013) (0.087) (0.11)

- 0.349 RRt_2 - 0.163 gt-1 (9)(0.171) (0.088)

T = 36 [1985(1) - 1993(4)] R2 = 0.32 & = 1,16%... dw = 2.23 ;

see also Eika, Ericsson, and Nymoen (1996b, p. 782, Table 1). The long-run relative

MCI weight is estimated as the ratio of the coefficients on RRt_2 and qt_1, which is(-0.349)/(-0.163) or 2.14.

The LR 95% confidence interval is [0.00, oo], even larger than those calculatedfor Canada and New Zealand. All non-negative weights fall within the 95% confi-

dence interval, and Figure 13 reflects that. From Figures 14-16, completely different

accounts of monetary conditions are feasible with different empirically acceptable es-

timates of the MCI relative weight. In the three figures, typical deviations acrossMCIs are 400, 200, and 300'basis points. respectively. The different MCIs also cresseach other frequently - that implies that their directions of movement often differin sign for a given period. . ,'

1

4.5 Sweden

The Swedish MCI is based on a model in Hansson (1993), which is further discussedin Hansson and Lindberg (1994) and Eika, Ericsson, and Nymoen (1996b, pp. 779-

781 and the Appendix therein). Details of the data appear in Eika, Ericsson, and

Nymoen (1996a, Appendix B). The Swedish model is one of output and inflationjointly, contrasting with the single-equation models of output alone for.Canada, NewZealand, and Norway. The Swedish model takes the form:

log(VY)t = al log(VY)t_1 + a21og(VY)t_2 -{- a3pt

+ a4RRt_1+ a5gt-1 + Eit

Apt = biA Pt-1 + . . . + b40pt-4 + b51og(VY)t

+ bsOPe+ . . . + blsQP.i 1o+ E2t ,

where the HP smoothness parameter is infinite (i.e.', corresponding to linear detrend-ing); and VY denotes the ratio of the unfiltered to filtered data, as Y is in levels,not logs. Estimates of the coefficients in (10)-(11) appear in Table 3. The estimatedlong-run- relative MCI weight is the ratio of the coefficients on RRt_1 and qt_1, whichis (-0.154)/(-0.076) or 2.02.

19 %1

The LR 95% confidence interval is relatively small: [1.06, 2.96]. The Fieller andWald confidence intervals are similar , with the three statistics differing only for values

of µo rejected by all statistics: see Figure 17. However, the calculated confidence inter-vals are probably unreliable, given that the over-identifying restrictions in (10)-(11)are rejected against the corresponding unrestricted reduced form. The test statisticof over-identifying restrictions is X2 (32 ) = 48.1 with a p value of 3.4%.; see Eika,

Ericsson, and Nymoen (1996b, Appendix).Even if a 95% confidence interval of [1.06, 2.96] is assumed, MCIs still can differ

by a few hundred-basis points, depending upon which value of the relative weightis chosen from .that interval: see Figure 18. One-quarter perturbations are genera llysmall (Figure 19), but one-year perturbations are not (Figure 20)..

4.6 United States

The Federal Reserve Board does not publish an MCI for the United States. However,as Table I shows, other institutions do. To calculate the uncertainty of an estimat dMCI weight for the United States; we estimate a model for the- growth rate of realU.S. GDP similar to the Canadian equation (7) and the Norwegian equation (9). ThisU.S. equation is:

L1yt = - 0.041 + 0 .309 Ayt-1 + 0.269 L1RRt(0.032) (0.095) (0.060)

- 0.035 RRt + 0.0094 qt(0.044) (0.0066)

T = 84 [1976(2) -1996 (4)] R2 = 0.30 - & = 0.670% dw = 2.10

(12)

Equation (12) is a statistically satisfactory simplification of a fourth-order auto-regressive distributed lag in Ayt, RRt, and qt. The corresponding F statistic isF(10, 70) = 0.49, with a p value of 0.89.

Because the real interest rate RRt enters (12) with a negative coefficient whereas

the real exchange rate qt has a positive coefficient, the estimated relative MCI weightis negative: (-0.035)/(+0.0094), or. -3.69. However, the LR 95% confidence in-terval is the entire real line [-oo, oo]. Even the 67.5% confidence interval is large:[-8.45,1.84]. Because of the substantial coefficient uncertainty, marked differences

exist between the LR and Wald statistics: see Table 2 and especially Figure 21. Anegative relative weight presents some interpretive difficulties, so the MCIs in Fig-ures 22-24 are *evaluated at /2 = +10 (regarded-as a "reasonable" value, in light ofTable 1), and at lower and upper bounds of µ = 0 and µ = oo respectively. The MCIs

are little affected by whether p = 10 or j = oo, as would be expected from giving the

20 1

I

1

exchange rate a relative weight of one tenth or of zero. However, the MCIs for µ = 0(i.e., the exchange rate itself) differ substantially from those for p = 10 or µ = oo.Deviations of 200, 25, and 100 basis points are common for the standard, 1-quarter,and 4-quarter calculations.

The positive (albeit insignificant) coefficient on q is a puzzle. Table 4 providesa numerical explanation through the sample correlations of the variables in (12).Specifically, Lyt and qt are positively correlated, and qt has only small or moder-ate correlations with the other regressors. Figure 25 characterizes this informationthrough time-series plots and cross-plots for (Lyt, 4RRt), (Lyt, RRt), and (Lyt, qt).The high positive correlation between Lyt and LRRt arises from a few large obser-vations in the early 1980s, as seen in the 'first pair of graphs in the figure. The slightpositive correlation between Lyt and qt comes from their coincident larger values justprior to 1985 (bottom pair of graphs). The United States was exiting a. recession,with output growing at a rate higher than average. At the same time, the U.S. dollarappreciated to an all-time high for'the sample.

Because (12) is very much a reduced-form equation, the results for the estimatedMCI are unlikely to be robust to the choice of sample period: Even for. the sampleused, (12) shows some evidence of mis-specification. Tests of normality and heterosce-dasticity in the residuals are strongly rejected, even while the dynamic simplificationis statistically acceptable. Thus, the MCI weight, confidence intervals, and MCI seriesderived from (12) should be viewed with caution because of that equation's empiricalproblems. Other MCIs for the United States are likely to be based on similar modelsand data, so those MCIs also should be treated with caution, at least until theirempirical underpinnings are clarified.

4.7 Consequences of Uncertainty in an. MCI's Weights

For Canada, New Zealand, Norway, Sweden, and the United States, the large esti-mation uncertainty associated with the MCI weights renders calculated.MCIs unin-

formative for policy. The model for the Swedish MCI is itself mis-specified, so it isdifficult to interpret MCIs based on that model. For all five countries, the estimationuncertainty often implies discrepancies in the MCI of 100 basis points or more forstatistically acceptable choices of the relative weight. Such discrepancies occur evenat one quarter ahead, which is a short horizon for policy based on an MCI. Further-

more, the choice of weight often affects the MCI's direction of movement, and notjust the magnitude of its movement. That feature is particularly problematic, in. sofar as an MCI is interpreted as an indicator of monetary stance.

21

4.8 Alternatives to MCIs

While MCIs as such appear impractical for use in policy,. their motivation is sensible.In a small open economy, foreign economic activity is likely to affect the domesticeconomy through the exchange rate; and empirical models are a potentially sensibleway of capturing the exchange rate's effects.

That said, tools other than MCIs are available for policy input in this context.In the conduct of monetary policy, central banks historically have considered a widerange of economic variables, including but not limited to interest rates and exchangerates. Central banks have changed their emphasis across those variables over time,for instance, in light of financial innovation. Instead of summarizing model-based.calculations in a single index such as an MCI, those calculations may be presented

directly, as time-dependent effects across a variety of economic aggregates. Suchmodel-based calculations also may then be part of the economic information feedinginto the policy process itself. - -

Policy-oriented examples of model-based calculations for Canada, Norway, andthe -United States appear in Poloz, Rose, and Tetlow • (1994), Norges Bank (1996),

and Mauskopf (1990). Good graphical and tabular techniques can ease the burden incommunicating inherently multivariate results; see Tufte (1983, 1990, 1997). Further-

more, better design of empirical models for policy appears possible, using econometric

tools and corresponding software developed over the last decade or so. Spanos (1986),Banerjee, Dolado, Galbraith, and Hendry (1993), and Hendry (1995) describe some ofthose tools; Doornik and Hendry (1994, 1996) exemplify the software available; andthe papers in Ericsson and Irons (1994) inter alia show how such tools and softwarecan aid empirical modeling.

5 Concluding Remarks

An MCI is an appealing operational target for monetary policy - it broadens aninterest- rate target to include effects of the exchange rate on an open economy. Indoing so, an MCI also incorporates model-based estimates of the effects of monetarypolicy on the economy. Notwithstanding the intuitive attraction of a Monetary Con-

ditions Index, substantive limitations in the index' s use arise from tactical difficulties,the choice of weights and variables, the underlying model's assumptions, and the as-sociated uncertainty of the estimated relative weight. The latter three issues pertainto summary indicators and model-based calculations generally, but they appear par-ticularly important empirically for MCIs. As a policy target and as an indicator of

monetary conditions, an MCI focuses on only two of many potential variables in the

22 «

monetary transmission mechanism. While the Bank of Canada and the Reserve Bankof New Zealand currently use MCIs as operational targets, they are well aware of theshortcomings involved. This paper has clarified one specific shortcoming, estimationuncertainty, and drawn its implications for the practical implementation of MCIs inmonetary policy.

23

Table 1. Selected Alternative Relative Weights for MCIs

CentralSource

Deutsche Goldman JPCountry Ba`:l :s

IMF OECDBank Sachs Morgan

Australia 2.3 4.3Austria 3.3Belgium 0.4

Canada 213: 4 2.3 4.3 2.7Denmark 1.9

Finland 2.5France 3 4 " - 3.4. 2.1 3.5

Germany 2.5, 4 4 2.6 ' 4.2 2.3'Italy 3 4 6.6 6 4.1

Japan 10 4 8.8 .. 7.9Netherlands 3.7 0.8New Zealand 2

Norway 1.41 5 2 5 24Spain . . .

Sweden 3-4 1.5 0.5 2.1Switzerland 6:4 1.7

United Kingdom 3 4 14.4 5 2.9

United States 10 39 10.1--

Note: Weights are those on interest rates relative to those on exchange rates.

Sources: Bank of Canada (1995, p. 14), Reserve Bank of New Zealand (1996a, pp. 22-23), Norges Bank (1995, p. 33), Hansson and Lindberg (1993, p. 16), InternationalMonetary Fund (1996a, p. 16; 1996b, p: 19), Organization for Economic Co-operationand Development (1996, p. 31), Graf and Schonebeck (1996), Davies and Simpson(1996), and Suttle (1996), with -additional information on'specific MCI weights forDeutsche Bank, Goldman Sachs, and JP Morgan from personal communications withTheodor Schoneberg, John Simpson, and Carl Strong.

24 '

Table 2. MCI Relative Weights and Their Estimated Confidence Intervals

Calculation CountryCanada New Zealand Norway Sweden United States

Estimationsample

80Q1-90Q4 86Q2-96Q1 85Q1-93Q4 73Q3-92Q4 76Q1-96Q4

MCI Relative WeightsMultiplier

Interim - 2.0 3-4(horizon) (6-8 quarters) (medium-term) (8 quarters) (4 quartets) (-)

Long-run 3.56 1.75 2.15 2.02 -3.69Published 3 2 3 3-4 -

Estimated Confidence Intervals for the Longrun Relative. Weights.Statistic

95%11

LR [0.74, oo] [0-30,7'31] (0.00, 00] [1.06,2.96] [-oo, oo]Fieller Same as LR . [0.32, 7.53] Same as LR [0.92,3.05] Same as LRWald [-1.72,8.85] [-0.16,3.66) [-0.94,5.23] [1.17,2.87] [-11.02,3.65]

90%

LR (1.06, oo] [0.52, 5.05] [0.36, 26.6] [1.27,2.76] t-00,001Fieller Same as LR [0.53, 5.12] Same as LR [1.17, 2.82] Same as LRWald [-0.84,7.96] [0.16, 3.33] [-0.42,4.71] [1.31,2.73] [-9.82,2.461

67 5%*.

LR [1.80, 9.60] • [0.97, 3.04] [1.00, 4.98] [1.61, 2.43] [-8.45,1.84]Fieller Same as LR [0.97, 3.05] Same as LR [1.56, 2.47] Same as LRWald [0.95, 6.18] [0.811'2.68] ' [0.63, 3.66] [1.59,2.45]- [-7.37,0.00]

I

*This confidence interval is calculated such that the corresponding F (or x2) statistic equalsunity, equivalent to a f.1 standard error band in a classical setting. Because the statistic'sdegrees of freedom vary across country, the associated p values ålso vary, albeit onlyslightly. The value 67.5% is approximate, with actual values ranging from 67.5%-to.68.3%.

25 1

Table 3. The Swedish Output and Inflation Equations

Variable : Output Equation laflation Equation

Coefficient t ratio Coefficient t ratio

log(VY)t -1 - 0.124 ' 2.4

log(VY)t_1 0.467 3.8

l0g(VY)t_2 0.469 3.8

Apt -0 .374 -3.0 -1 -

Apt-1 0.100 -

Opt-2 0.043 0.4

Apt-3 0.105 0.9

A Pt-4 0.309 2.8

RRt_1 -0.154 -2.5 '

qt_i -0 .076 -3.1

Apt* 0.132 2.0

Apt-1 0.029 0.6

A pt 2 0,093 2.1

A p7-3 0.044 0.9

Opi_4 0.020 0.4

,N-kpi_5 -0 .071 -1.5

L1p7_6 0.015 0.3

4 pi_7 , 0.034 0.7

A pt-8 -0 .023 -0 .5

Op7_9 0.022. . M,

pi-lo 0.149 3.4

& 1.267% 0.934%

't26

Table 4. Data Properties of the U.S. Variables

Calculation

Variable StandardVariance-covariance Matrix

Deviation

Variable

dyt Ayt-1 ARRI RRt qt

0 yt 0.0078 1

Dyt-i 0.0078 0.33 1

ORRt 0.0130 0.42 0.01 1

RRt 0.0221 0.16 0.15 0.25 1

qt 0.1438 0.16 0.16 -0.01 `0.60 1

Note: The sample period is 1976Q1-1996Q4.

1

.16

-.02

.3

.2

.15

- MC130.14

.12

.1

.08

.06

.04

.02

0

-.04

-.061980 1982 1984 1986 1988 1990 1992 1994 1996 1998

Figure 1: The Canadian MCI evaluated at a relative weight of 3.

- R90Cflac

ll--- cangl0

la t.25

t `i ! r,.

.05

01980 1982 1984

nIlii ;tl

1

I 1 (^V

. tlb,yI

1986 1988 1990 1992 1994 1996 1998

Figure 2: The components of the Canadian MCI: the 90-day commercial paper inter-est rate (-) and the log of the exchange rate (- -).

28 • 't

--- MCI30---•• MC120--- MC143

.02

0

-.02

-.04

D61980 1982 1984 1986 1988

t!\\! ,'

i

1994 1996 1998

i

Figure -3: The Canadian MCI evaluated at relative weights of 2, 3, and 4.3.

-.01

-.02

--- MCI30------ MCI20--- MCI43

1990 1992

! Nji ,• ,

'I • 1

1

-.03

1995 1996 1997

Figure 4: The Canadian MCI evaluated at relative weights of 2, 3, and 4.3 over arecent subsample.

29

,.:1 • t !., \;i .!\ f -\ i •

.J •

't

. 12

10

2

- FLR x MCtwt----- Wald x MClwt--- F05pc x MCIwt--- F10pc x MClwt--- F32pc x MClwt

8

6

4 -

LR statistic(= Fieller statistic)

--------------95%----=--- -----------T----------------,1 11,t 1190% 1 .1

67.65%

420 -15 -10 -5 0 5 10 15 g 0 20

Figure 5: F statistics for testing that the MCI relative' weight p equals. some hypoth-esized value yo, with critical values: Canada.

.15

.1

Ji -----• MCInoSI i - MCIun

i t\ --- MCIp05 -

I \

y I\

.05/

- ' i \\ Ij I\ \/ ! % /

0

-.05

i

1982 1984 1986 1988 1990 1992 1994 1996 1998

Figure 6: The MCI evaluated at the unrestricted estimate (-), and at that estimate'supper and lower 95% critical values (- - and - -): Canada.

30 N

.15

.1

.05

A

0

-.o5

- MCIun----- XMCInO5--- XMCIp05

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998

Figure 7: The MCI evaluated at the unrestricted estimate (-), and with 1-quarter,,perturbations at that- estimate's 95% critical values (- _ and - -

.15 ,

.1

.05

0

1982 1984 ' 1986

: Canada.

1988 1990 1992 1994 1996 1998

Figure 8: The MCI evaluated at the unrestricted estimate (-), and with 4-quarterperturbations at that estimate's 95% critical values (- - and - -): Canada.

11 - MCIunIt1 •---- X4MCin05

11 --- X4MCIp05

1 \1 .

-.05

I31

14

12

10

- FLR x FMCIwt- -- FFstat x FMCI:wt

•---- WFstat x FMCIwt--- F05pc x FMCIwt--- F10pc x FMCIwt--- F32pc x FMCIwt

8

LR statistic

4

2

Fidfler statistic95%-------------------- --- ---------- ------------------

90%--------- ---------- ----- ---------------------

67.5%

20 -15 -10 -5 0 5 10 15 Ftp 20 '

Figure 9: F statistics for testing that the MCI relative weight p equals some hypoth-esized value µo, with critical values: New Zealand.

2.4----- MCInO5- MCIun

2.35 --- MCip05

2.3r

t . /\ ;N t2.25 ! t ! t _ `:

r 1 ! .,! t 1!

2.2r ', f 11

. !:

. 2.15

2.1

2.05

!

i

:/

i`; v ..

. ' .i= •••/

/ '•/---•-/.i i

1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997

Figure 10:- The MCI evaluated at the unrestricted estimate (-), and at that esti-mate's upper and lower 95% critical values (- and - -): New Zealand.

32 't

2.4- MC1un----- XMCInOS

2.35 --- XMCIØ5

2.3

2.25

2.2

2.15

2.1

2.05

V 21984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997

Figure 11: The MCI evaluated at the unrestricted estimate (-), and with 1-quarterperturbations at that estimate's 95% critical values (- - and - -): New Zealand.

2.4

2.35

2.3

2.25

2.2

. 2.15

2.1

2.05

- MCIunX4MCInO5

--- X4MCIpOS

;

' 1\I \

.-` - ,,`-.' %

`1 ••.:

, ,.,

21984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997

Figure 12: The MCI evaluated at the unrestricted estimate (-), and with 4-quarterperturbations at that estimate's 95% critical values (- - and - -): New Zealand.

33 N

12

10

4

2

- FLR x MCIwtWald x MCIwt

--- F05pc x MCiwt--- FIOpc x MCiwt--- F32pc x MCFwt

8

6 LR statistic(= Fieller statistic)

95%

Wald statistic

90%------------------°-------- ----- ------------------

67 50%--------------------------- --- -- '

-20 -15 -10. -5 . 0 5 10 15 90 20

•

Figure 13:.F statistics for testing, that the MCI relative weight is equals some hy-pothesized value u0i with critical values: Norway.

.12- MCInO5----• MCIun--- MCIp05

.08

.064

.04;i

'-- .r .

.02

0

-.02

-.04

-.061985 1986 1987 1988 1989 1990 • 1991 1992 1993 1994 1995

Figure 14: The MCI evaluated at the unrestricted estimate (-), and at that esti-mate's upper and lower 95% critical values (- - and - -): Norway.

34 ,t

.12- MClun .----- XMC1n05--- XMCIp05

.08

.06 -.. 11 ':• ' , i1 \\/ ;1 : ..- • 1 : _ .

r.04

. . • ' '` // .

.02

Q

-.02

-.04

-.061985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995

Figure 15: The MCI evaluated at the unrestricted estimate (-), and with 1-quarterperturbations at that estimate 's 95% critical values ( and - -): Norway.

.12- MClun

....... X4MCInO5--- X4MCIp05

.08

/

/

• ^``J/ `I

( \ •.06' \ // \' ^\

`

.04 V11 1./

• . • /

1 /

.•.02

0

-.02

-.04

-.Ø1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995

Figure 16 : The MCI evaluated at the unrestricted estimate (-), and with 4-quarterperturbations at that estimate 's 95% critical values (- - and - -): Norway.

35 1

14

10

12

- Chi2LR x MCIwtF--- Chi2F x MCIwtF

-----• Chi2W x MCIwtF--- Chi05pc x MCIwtF--- ChilOpc x MCIwtF--- Chi32pc x MCIwtF

-----------------------------

2

LR statistic

Fieller statistic

4 ------=----------------------'•-- -------------95%----

Wald statistic

90%

68.27%

0-20 -15 -10 -5 0 5 10 t 15 9 0 20 -

Figure 17: Chi-squared statistics for testing that the MCI.relative weight µ equalssome hypothesized value po, with critical values: Sweden.

.06--•--• MCInO5

MCIun.04 -} -- MCIp05

I

.02

v• 1. , /.

0

''; 1 \ 1 \II.•

.1 \ I \t ^ \

t-.02

r ; t '

`•:

1\

\`

' itlt

1 1 I\ ! ' ;1 ". j.1

t1'1 ` ,

1

1i ". / ` •

04- 1

`

\ j I I. 1 I \ i I

,

i i •1 I `t

r1-.06 1 I

\ I

-.08

-.11970 1975 1980 1985 1990 1995

Figure 18: • The MCI evaluated at the unrestricted estimate (-), and at that esti-mate's upper and lower 95% critical values (- - and - -):' Sweden.

36 1

.06- MCiun----- XMCInO5

.04 --- XMCIp05

.02 -

0

-.02

-.04

-.06

-.08

I

•t

1970 1975 1980 1985 1990 1995

i•

Figure 19: The MCI evaluated at the unrestricted estimate (-), and with 1-quarterperturbations at that estimate 's 95% critical values (- - and - -): Sweden.

. .06- MCIun----- X4MCInO5

.04 --- X4MCIp05

.02

1

1975 1980 1985 1990 1995

Figure 20: The MCI evaluated at the unrestricted estimate (-), and with 4-quarterperturbations at that estimate's 95% critical values (- - and - -): Sweden.

0

-.02

- -.04

-.06

-.08

37

12

10

4

8

6

- FFstat x MCIwtFWFstat x MC1wtF

--- F05pc x MCIwtF--- F1Opc x MC1wtF--- F32pc x MCIwtF

1 Wald statistic

95%------------ -------------------- -,=------- ----------------

2

90%-------------='r------------------ -------------------------

LR statistic (= Fjellet statistic

---------------

20 -15 -10 -5 0 5 10 15 µ0 20

Figure 21: F statistics for testing that.the MCI, relative weight p equals some.hy-pothesized value µo, with critical values: United States.

I

.6

.5

.4

- MCInO5- MCIun

.9 --- MCIp10

.8

.7

.3

r'

i-'••.--_

1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998

Figure 22: The MCI evaluated . at p = 10 (-), and at p = oo and p = 0 (- - and --): United States.

38

I- MCIun

XMCInO5•4 --- XMCip05

.8

.7

.6

.4

.3

'- ; 11

, . , „ •

. . • - , . ,'111,'I '

;;

;,

.2 .1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998

Figure 23: The MCI evaluated at µ = 10 (--), and with 1-quarter perturbations. atµ = oo and p = 0 (- - and - =): United States.

1- MCIun----- X4MCInO5

.9 --- X4MC1p05

.8

.7

.3

1976 1978 1980 1982 1984 1986 198$ 1990 1992 1994 1996 1998

Figure 24: The MCI evaluated at µ = 10 (-), and with 4-quarter perturbations atp = oo and µ == 0 (- - and - -): United States.

; •; •

N-,

I39

0

-.02

, •,, 11 , 1, 1,1 •,' ,,- '

II ,

.025

1975 1980 1985 1990 1995 -.05 0 .05

Dyus.04 ------ RR

, •.,

.02111 .

0

-.02

' , ,

1975 1980 1985 1990

Dyus f.04 ......

q

,.02 ', •' ;,., ., .'.

0

-.02

ll

.025

0

0

ø o Dyus x DRR

00 0O 0

CD

0

0

O o Dyus x Ø

i 0

0 000

0OOø 000

RD8 O OCS

0

00

080

0

0 0

1995 0 .05

.025

0. ,.•

.1 ,0

0

()

0 o Dyus x q

0

00. 0

000 0

0

0 0

1975 1980 1985 1990 1995 4.75 5 ' 5.25

Figure 25: -Time-series plots and cross-plots for (Ayt, LRRt), (/yt, RRt), and(oyt)qt): United States.

40 1

References

Alexander, L. S. (1997). "Dotes on the Poole Model and MCIs", memo, Divisionof International Finance, Board of Governors of the Federal Reserve System,Washington, D.C., January.

Banerjee,- A., Dolado, J. J., Galbraith; J. W., and Hendry, D. F. (1993). Co-integration, Error Correction, and the Econometric Analysis of Non-stationaryData. Oxford University Press, Oxford.

Bank of Canada (1994). "Monetary Conditions - Les Conditions Monetaires", Bank.of Canada Review Revue de la Banque du Canada, 1994 (Autumn), 18-20.

Bank of Canåda (1995). Monetary Policy Report, 1995 (May). Bank of Canada,Ottawa, Canada.

Barker, W. (1996). "The Relationship Between Daily Bank of Canada Operations. and the Monetary Conditions Index",. In Zelmer, M. (ed.),, Money.Markets av.d

Central Bank Operations, 169-209 (with discussion). Bank of Canada, Ottawa.

de Brouwer, G., and Ericsson, N. R. (1995). "Modelling Inflation in Australia",International Finance Discussion Paper No. 530, Board of Governors of theFederal Reserve System, Washington, D.C., November.

Davies, G., and Simpson, J. (1996). "Summary", The Internnational EconomicsAnalyst (Goldman Sachs), 11(7/8), iii-xviii.

Dennis, R. (1996a). "A Measure of MonetaryConditions", memo, Reserve Bank ofNew Zealand, Wellington, December.

Dennis, R. (1996b). "Monetary Conditions and the Monetary Policy TransmissionMechanism", Øenlo, Reserve Bank of New Zealand, Wellington, November.

Dennis, R., and Roger, S. (1997). "The Role of.Monetary Conditions Indicator Bandsin Monetary Policy Implementation", memo, Reserve Bank of New Zealand,Wellington, January.

Doornik, J. A., and Hendry, D. F. (1994). PcGive Professional 8.0: An InteractiveEconometric Modelling System. International Thomson Publishing, London.

Doornik, J. A., and Hendry, D. F. (1996). PcGive Professional for Windows, Ver-sion 9.0. International Thomson Publishing, London.

Duguay, P. (1994).. "Empirical Evidence on the Strength of the Monetary Transmis-sion Mechanism in Canada: An Aggregate Approach",. Journal of MonetaryEconomics, 33(1), 39-61.

41

Duguay, P., and Poloz, S. (1994). "The Role of Economic Projections in CanadianMonetary Policy Formulation", Canadian Public Policy - Analyse de Poli-tiques, 20(2), 189-199.

Eika,' K. H., Ericsson, N. R., and Nymoen, R. (1996a). "Hazards in Imple-menting a Monetary Conditions Index", International Finance Discus-sion Paper No. 568, 'Board of Governors of the Federal Reserve System,Washington, D.C.; October; also available on the World Wide 'Web a thttp://www.bog.frb.fed.us/pubs/ifdp/1996/568/ifdp568.pdf.

Eika, K. H., Ericsson, N.. R., and Nymoen, R. (1996b).. "Hazards in Implementinga Monetary Conditions Index", Oxford Bulletin of Economics and Statistics,58(4), 765-790.

Ericsson, N. R., and Irons, J. S. (eds.) (1994). Testing Exogeneity. Oxford University.Press, Oxford.

Fieller, E. C. (1940). "The Biological Standardisation of Insulin", Journal of theRoyal Statistical Society, Supplement , 7, 1-64.

Fieller, E. C. (1954). "Some Problems in Interval Estimation", Journal of the RoyalStatistical Society, Series B, 16(2), 175-185.

Freedman, C. (1994). "The Use of Indicators and of the Monetary Conditions Indexin Canada",' In Balino, T. J. T., and Cottarelli, C. (eds.) , Frameworks forMonetary Stability: Policy Issues and Country Experiences, Chapter 18, 458-476. International Monetary Fund, Washington, D.C.

Freedman, C. (1995). "The Role of Monetary Conditions and the Monetary Condi-tions Index in the Conduct of Policy -- Le Role des Conditions Monetaires etde l'Indice des Conditions Monetaires dans la Conduite de la Politique", Bankof Canada Review. - Revue de la Banque du Canada, 1995 (Autumn), 53-59.

Froot, K. A., and Rogoff, K. (1995). "Perspectives on PPP and Long-run RealExchange Rates", In Grossman, G., and Rogoff, K. (eds.) , Handbook ofInternational Economics, Chapter 32, Volume 3, 1647-1688. North-Holland,Amsterdam.

Gerlach, S., and Setets, F. (1996). "MCIs and Monetary Policy in Small OpenEconomies under Floating Rates", memo, Bank for International Settlements,Basle, November.

GrS.f, B., and Schonebeck, T. (1996). "DBR MCI in August: Little Change", MarketIssues: Economics (Deutsche Morgan Grenfell), (October 7), 2-3; also availableon the World Wide Web at http://Ø.rdt.com/rdt/dmg.

42 . I

Gregory, A. W., and Veall, M. R. (1985). "Formulating Wald Tests of NonlinearRestrictions", Econometrica, 53(6), 1465-1468.

Hansson, B. (1993). "A Structural Model", In Franzen, T., Andersson, K., Alexius,A., Berg, C., Hansson, B., Nilsson, C., and Nilsson, J. (eds.) , Monetary PolicyIndicators, Chapter 5, 55-64. Sveriges Riksbank, Stockholm, Sweden.

Hansson, B., . and Lindberg, H. (1994). "Monetary Conditions Index - A MonetaryPolicy Indicator", Quarterly Review (Sveriges Riksbank - Swedish Central.Bank), 1994 (3), 12-17.

Hendry, D. F. (1995). Dynamic Econometrics.. Oxford University Press, Oxford.

International Monetary Fund (1996a). World Economic Outlook: May 1996. Inter-national Monetary Fund, Washington, D.C.

International Monetary Fund (1996b). World Economic Outlook: October 1996.International Monetary Fund, Washington, D.C. . ,

Jore, A. S. (1994). "Beregning av en Indikator for Pengepolitikken" (Calculation ofan Indicator for Monetary Policy), Penger og Kreditt, J4 (2), 100-105. .

Juselius, K. (1992). "Domestic and Foreign Effects on Prices in an Open Economy;The Case of Denmark", Journal o f Policy Modeling, L (4), 401-428.

Kendall, M. G., and Stuart, A. (1973): The Advanced Theory of Statistics: Volume 2,Inference and Relationship. Charles Griffin and Company, London, Third Edi-tion.

Longworth, D., and Freedman, C. (1995). "The Role of the Staff Economic Projectionin Conducting Canadian Monetary Policy" , In Haldane, A. G. (ed.) , TargetingInflation, 101-112. Bank of England, London.

Mauskopf,. E. (1990). "The. Transmission Channels,of Monetary Policy: How HaveThey Changed?", Federal Reserve Bulletin, 76(12), 985-1008.

Mayes, D. G., and Riches, B. (1996). "The Effectiveness of Monetary Policy in NewZealand", Reserve Bank Bulletin (Reserve Bank of New Zealand); 59(1), 5-19.

Nadal-De Simone, F., Dennis, R., and Redward, P. (1996). "A Monetary ConditionsIndex for New Zealand", Reserve Bank of New Zealand Discussion PaperNo. G96/2, Reserve Bank of New Zealand, Wellington, July.

Norges Bank (1995). Economic Bulletin, 1995/1. Norges Bank, Oslo.

Norges Bank (1996). "'Projections for the Norwegian Economy in the Years to 2000",Economic Bulletin, 1996/4, 264-281..

't43

Organization for Economic Co-operation and Development (1996). OECD EconomicOutlook 59: June 1996. Organization for Economic Co-operation and Develop-ment, Paris.

Poloz, S., Rose, D., and Tetlow, R. (1994). "The Bank of Canada's New QuarterlyProjection Model (QPM): An Introduction --Le Nouveau Modele Trimestrielde Prevision (MTP) de la Banque du Canada: Un Apercu", Bank of CanadaReview - Revue de la Banque du Canada, 1994 (Autumn), 23-38.

Reserve Bank of New Zealand (1996a). Monetary Policy Statement, December, Re=serve Bank of New Zealand, Wellington; also available on the World Wide Web'at http://www.rbnz.govt.nz/monetary/mpspdf.htm.

Reserve Bank of New Zealand (1996b). "Summary Indicators of Monetary Condi-tions", Reserve Bank Bulletin (Reserve Bank of New Zealand), 39(3), 223-228.

Silvey, S. D. (1975). Statistical Inference. Chapman and Hall, London.

Spanos, A. (1986). Statistical Foundations of I Econometric Modelling. CambridgeUniversity Press, Cambridge.

Staiger, D., Stock, J. H., and Watson, M. W. (1997). "The NAIRU, Unemploymentand Monetary Policy", Journal of Economic Perspectives , 11(1), 33-49.

Suttle, P:- (1996 ). "Monetary Conditions Worldwide ", World Financial Markets(JP Morgan ), (March 29), 26.

' Thiessen, G. G. (1995). "Uncertainty and the Transmission of Monetary Policyin Canada - L'Incertitude et la Transmission de la Politique .Monetaire auCanada", Bank of Canada Review - Revue de la Banque du Canada, 1995(Summer ), 41-58.

Tufte, E. R . (1983). The Visual Display of Quantitative Information. Graphics Press,Cheshire, Connecticut.

Tufte,-E. R. (1990). Envisioning Information . Graphics Press, Cheshire, Connecticut.

Tufte, E. R. (1997). Visual- Explanations: Images and Quantities, Evidence andNarrative . Graphics Press, Cheshire, Connecticut.

Wald, A. (1943).' "Tests of Statistical Hypotheses Concerning Several ParametersWhen the Number of Observations Is Large", Transactions of the AmericanMathematical Society , 54 (3), 426-482.

Zelmer, M. (1996). "Strategies Versus Tactics for Monetary Policy Operations", InZelmer, M. (ed.) , Money Markets and Central B ank Operations , 211-278 (withdiscussion). Bank of Canada, Ottawa.

44 `