UNDERSTANDING
A MONETARY
CONDITIONS
INDEX
Neil R. Ericsson, Eilev S. Jansen, Neva A. Kerbeshian and Ragnar Nymoen. November 1997 Abstract Numerous central banks, governmental organizations, and businesses now calculate a Monetary Conditions Index (or MCI) as an indicator of the stance of monetary policy. Two central banks, for Canada and New Zealand, use their MCIs as operational targets. This paper describes and defines this concept, summarizes how central banks implement MCIs in practice, reviews some of the. operational and conceptual issues involved, and evaluates the sensitivity of MCIs to an inherent source of uncertainty in their calculation. Empirically, this uncertainty typically renders MCIs uninformative for their ostensible purposes, so some possible alternatives are considered. 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. Ericsson Stop 24, Division of International Finance, Federal Reserve Board 2000 C Street, N.W., Washington, D.C. 20551 U.S.A. (202) 452-3709 (office) . (202) 736-5638 (fax)
[email protected] (Internet) Eilev S. Jansen Research Department, Norges Bank, Bankplassen 2 P.O. Box 1179 Sentrum, N-0107 Oslo 1 Norway
(47) (22) 42 61 60 (office) (47) (22) 42 40 62 (fax)
[email protected] (Internet) Neva A Kerbeshian Stop 22,Division of International Finance, Federal Reserve Board 2000 C Street, N.W., Washington, D.C. 20551 U.S.A. (202) 452-6489 (office) (202) 736-5638 (fax)
[email protected] (Internet) Ragnar Nymoen Department of Economics, University of Oslo P.O. Box 1095 Blindern, N--0317 Oslo, Norway (47) (22) 85 51 54 (office) (47) (22) 85 50 35 (fax)
[email protected] (Internet) and Norges Bank (address above)
[email protected]
(Internet)
Underst an ding a Monetary
Conditions
Index .
Neil R. Ericsson, Eile v S. Jansen, Neva A. Kerbeshian , and Ragnar Nymoen*
Introduction Several central banks now calculate a Monetary Conditions Index (or MCI).for use in monetary policy.. Empirically, an MCI.is a weighted average of changes in an interest rate and an exchange rate relative to their, values in a base period. The weights on the interest rate and exchange rate reflect the estimated relative effects of those variables on aggregate demand over some period, often approximately two years.. MCIs are currently used as indicators targets for monetary policy.
I
of monetary .
conditions
and as operational
A Monetary Conditions Index has several attractive simple: exchange rates influence. aggregate
demand,
short-run
features.. Its motivation is
especially insmall open economies.
Thus, focusing on exchange rates as well-as interest rates may be important in understanding an economy's behavior, and so in policymaking. Also, an MCI is easy to calculate. For central banks, an. MCI is an intuitively appealing operational target for monetary
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 formal model forecasts. For institutions other than central banks, an MCI as an index per se may 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 is the director of the Research Department, Norges Bank, Oslo, Norway; and the fourth author is an associate professor of economics at the University of Oslo, Oslo, Norway. The authors may, be reached on the Internet at ericsson©frb.gov,
[email protected],
[email protected],' and ragnar.nymoenQ .on.uio .no, respectively. The views expressed in this paper are solely the responsibility of tie authors and should not be interpreted as reflecting those of Norges Bank, the Board of Governors of the Federal Reserve System, or other members of their staffs. The first author gratefully acknowledges the generous hospitality of Norges Bank, where he was visiting when he became involved in this research. We wish to thank Carol Bertaut, Richard Dennis, Jurgen Doornik, Pierre Duguay, Dick Freeman, Dale Henderson, David Hendry, Karen Johnson, Anne Sofie Jore, David Longworth, Cathy Mann, David Mayes, Sunil Sharma, Ralph Smith, and Lars Svensson for helpful discussions and comments; Richard Dennis, Bengt Hanson, and Anne Sofie Jore for providing the.data in Dennis (1996a, 1996b), Hanson (1993), and Jore (1994); and'Theodor Schoneberg, 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 PcGive Professional 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 respective indexes in the conduct of monetary policy. Additionally, the IMF and the OECD calculate MCIs for evaluating the monetary policies of many countries, and firms lP b' sh MCrL_ to ascertain such. as Deutsche Bank, Goldman Sacis, and llaMorgan puua 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 of the interest rate and exchange rate on aggregate demand.
Being model-based, those
variables'' effects are' estimated, and the corresponding coefficients have an associated uncertainty
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 2 describes and,defines the Bank of Canada's
Monetary Conditions Index, summarizes
how the Bank. utilizes its MCI in. conducting monetary policy,, reviews some operational considerations, and documents MCI usage by other institutions and for other countries. Section 3 analyzes two facets in the design of an MGI: the choice of weights and variables, and the assumptions of the underlying empirical model. Section 4.evaluates the robustness of MCIs to the uncertainty arising from the estimated weights in the model, focusing on MCIs for Canada, New Zealand, Norway, Sweden, and the 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 indicator of 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 monetary policy.
The current paper' complements
Eika, Ericsson, and Nymoen (1996b)
by focusing on the practical implementation of an MCI and the degree- to which implementation 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 Canada and 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), and operational considerations (Section 2.3). Section 2.4 considers MCIs used by other institutions 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 encompassing all 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 operational target.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 output. For Canada, the weights are 3 to 1, interest rate to exchange rate. That is; a one percentage point increase in. the interest rate induces. three times the change in the Bank's MCI as would a one percent appreciation of the Canadian dollar. Algebraically, 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, ORand 0eare the respective weights on the 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 the exchange rate and the interest rate, and the base- period. Usually, the exchange rate in (1) is in logarithms or in percent deviations from its baseline value, whereas the interest 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 the determinants of-aggregate demand. As discussed in Freedman (1994, pp. 469-470 and a footnote 27), Duguay's (1994) results are typical of that evidence, so we focus on a representative 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] (0.22)
T = 44 [1980(1) - 1990(4))
R2 = 0.64 3
.0.15 [A 12gt/12] (0.12) & = 0.62%
(2)
dw = 1.96. .
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 constructed as the nominal 90-day commercial paper interest rate (R) minus the onequarter lag in the annual rate of change of t e Canadian GDP deflator (P). That is, RRt = Rt - 1 Opt-1. ' The real exchange rate (Q) is the product of .the'nominal 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 the estimation period, the squared multiple correlation'coefficient, the adjusted version thereof, the estimated equation standard error, and the Durbin-Watsonstatistic respectively . The coefficients are estimated by le ast squares, and estimated standard errors 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 Qf3 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 corresponding nominal variables. Switching from real to nominal variables is convenient operationally, and it has been defended by the short horizon for MCI-based monetary policy 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 interest rate increases aggregate demand and lowers the MCI, as does a depreciation of'the Canadian 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 through 1993, the MCI fell steadily, signaling a general loosening of monetary conditions. In 1994 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 equivalent to 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 one period 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 the former 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 G10 trade-weighted exchange rate, whereas regressions' for Canada use the. bilateral U.S.-Canadian exchange
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 former recieving
a weight of over 80% in the latter.
4
of and comparison across different MCIs. For instance, the decline in the Canadian MCI 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: the 20% 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 commercial paper rate and the logarithm of the nominal G-10. trade-weighted Canadian dollar. During 1990 and 1991, the Canadian dollar remained relatively constant while the interest rate declined, with the latter variable being primarily responsible for the fall in the MCI. In 1992 and 1993, both variables moved downward, with both contributing to the MCI's continued fall. From 1994 onward, the two variables have moved in opposite directions,
2.2
The
Bank
offsetting each other's movements
of Canada's
MCI
to some extent.
as an Operational
Target
For the past several years, the Bank of.Canada has used its MCI as an operational 1 a target. This subsection describes how the Bank has done so, focusing on the role played 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 (or QPM). The QPM includes equations for output growth (similar to (2)), inflation, and the exchange rate. In the model, interest rates and exchanges rates influence output, which in turn influences inflation through a Phillips curve relationship. The exchange 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.. The desired path for the MCI is then calculated from those paths on the interest rate and exchange rate.3
If, in the short term from week to week - the actual MCI rises above (or falls below) its target path, this is interpreted as a tightening (or loosening) of monetary conditions relative to those anticipated and desired, and the Bank considers responding.
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-day commercial
paper
interest
rate.
For the most part,
between the Bank's actual policy instrument target.
the discussion
below ignores the distinction
and what constitutes a very short-term operational
0
5
N
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 deciding 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 conditions that would bring about a path for aggregate: demand and prices consistent with the control of inflation. Thiessen (1995, p. 54) . Charles Freedman, details.
Deputy
Governor of the' Bank of Canada,
provides additional
In the last few' years, the Bank of Canada has used the concept of monetary conditions (the. combination of the movement of interest rates and the exchange rate) as the operational target of policy, in much the same way as short-term interest rates were used in the past. ... The objective of monetary policy over the next three years or so is to .maintain the rate, of inflation within a band of 1 to 3 per cent. The quarterly Bank of Canada staff projection takes into account such factors as the movements in foreign variables and domestic exogenous variables as well 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 this path [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 for generating the forecasts, additional analyses of the domestic .and foreign -economies also play a role, with iterations between sectoral specialists and the QPM resulting in judgmentally adjusted forecasts. Second, the forecasts are conditional; both on the Bank's'views of future domestic monetary and fiscal policy and on its views of futureforeign 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, which are reflected by the Bank of Canada's experience. These considerations include both the timing of policy adjustments and the role of additional information in the policy process.. Timing, or "tactical" considerations, have sometimes made an MCI a difficult operational
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. allowed actual and desired MCIs to differ for considerable periods - of a quarter or more. The Bank has explained such episodes by arguing, for example, that observed exchange rates 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 decision to ease monetary conditions because of the risk that an action to reduce the overnight rate, could result in significant weakness in the exchange market and lead to the buildup of extrapolative expectations in that market, followed, as we have so often seen in Canada in recent years, by an increase in interest rates in the money market and the bond market. In effect, an attempt to ease monetary conditions could, via the interaction of. developments in the exchange market and domestic financial markets,
result in an outcome where monetary conditions ended up tighter and not easier. 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 to Bank 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 mand in a small open economy. That said, inputs additional
effects on aggregate de-. 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 incorporate into its thinking the possible effects of a broad range of outcomes with respect 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 in which direction to take or avoid risks (e.g., that. it is appropriate to beespecially vigilant about a resurgence of inflation). If, following this type of analysis, there is .adivergence 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, tactical considerations 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 each
publish an MCI and (to varying degrees) use it in conducting monetary policy. The Reserve 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,New Zealand (1996a). The central banks of Norway. and Sweden use MCIs in a more limited fashion'- as indicators of monetary conditions when formulating their monetary policies; see Norges Bank (1995) and Hansson and Lindberg
(1994). Additionally,
the
IMF and OECD use MCIs in evaluating monetary policies. across countries, and businesses 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 is
indicative 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 that uncertainty has for using an MCI as an indicator. or target..
3
Two Facets
of MCI Design
This section analyzes two facets in, the design' of an MCI: the choice of weights and variables (Section 3.1), and the assumptions of the underlying empirical model (Section 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.
I 3.1 'Choice
of Weights
and Variables
The choice of weights and variables in an MCI. is central to%onstructing the index itself, 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 relative weight of 3, and the other two using the smallest and largest Canadian weights appearing
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 virtually constant; 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 the smallest relative weight indicates a moderate tightening of monetary policy in the autumn
of 1996, whereas. the indexes with larger weights on the interest rate show
a moderate or considerable loosening. Similar episodes occur in 1983-1984, while noting. that the extreme scale of Figure 3 necessary' for capturing 17 years of data does dwarf the discrepancies in the various MCIs' behavior. In general, the weights can 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 a substantial effect on the measured MCI. The selection of variables in the MCI is-an open-issue as well. MCIs in this paper's figures are calculated from only a single interest rate and a single exchange rate for a 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 mediumterm monetary
policy, international
exchange markets
may be more speculative and
financial in nature, in which case bilateral trade weights are less germane . A conflict may well exist between the data appropriate and those appropriate for policy analysis.
for the underlying
econometric model
A range of alternative interest rates also exists. Numerous short-term rates are available, 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-term interest 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 misleading about 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. That exclusion constitutes aggregation , with weights.of zero on those other variables..Second, 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 constitutes aggregation. All four senses *of aggregation involve losses of information, and use of 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 of the two variables is of concern. In practice, the Bank of Canada does look at the two variables separately, especially 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 be weaker in conjunction with higher interest rates,-but overall monetary conditions can be 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 MCI moving in the opposite direction from the interest rate.
10
3.2
Assumptions
The use and interpretation
of the Underlying
Empirical
of an MCI rests upon the assumptions
Model of the underlying
model. Several issues arise for that model, including dynamics, data nonstationarity and differencing, exogeneity and feedback, parameter constancy, 'the choice of model variables, and the uncertainty arising from estimating the model. This. subsectionsummarizes these six issues, relating them to the corresponding
model assumptions.
These assumptions are often testable .and, if violated, directly affect the economic interpretation of the MCI. Eika, Ericsson, and Nymoen (1996b) present, a more detailed analytical assessment, and their empirical evaluation confirms such difficulties in models for the Canadian,
*Swedish,
and Norwegian
MCIs.
Gerlach and Smets
(1996) and Alexander (1997) discuss possible .economic theoretical underpinnings of an 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 affect the 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 construction of 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 thereby affect statistical inference. Nonstationary data also may be cointegrated. If so,- the relevant 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 for differences, contrasting with long run for levels. Third, the postulated :exogeneity of the policy instruments and other variables is potentially
misleading.
In the MCI itself, the weights
are interpreted
as elasticities
of aggregate demand with respect to the interest rate and the exchange rate. This interpretation assumes no feedback from aggregate demand or inflation onto exchange rates and interest 'rates over the relevant policy horizon. Such feedback may occur under 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 MCI is 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 may arise 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 nonconstant parameters, estimation over different sample periods would result in different estimates of the weights, and so different choices of weights. Eika, Ericsson, and Nymoen (1996b, Section IV) illustrate how that choice.of weights can affect policy inferences 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 existence 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 the central 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 determining the exchange rate and. interest rate, neglect of those other variables has substantive implications for policy with an MCI. For example, changes in world oil and commodity prices may alter a country's terms of trade, thereby affecting the exchange.rate. The MCI would then change, even if monetary stance remained un-' changed. Likewise, changes in world interest rates and inflation rates and changes in 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 reflect phenorhena other than just direct monetary policy, so movements in the MCI are not tied unequivocally to changes in monetary stance. Conversely, by following or targeting
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 rate or 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 prices directly; 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 cost of housing. Neglect of these transmission mechanisms is likely to result in the MCI being 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 of many potential channels and on only two of many potential variables in the monetary transmission
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 estimated weight may be numerically nonconstant, even if it is statistically constant. Numerically nonconstant weights -may arise from the lack of information content in the data, 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 estimation has not been previously examined for MCIs, so the next section (Section 4) turns to quantifying practice.
4
that uncertainty
Uncertainty
and assessing its consequences
of MCI Weights
for using an MCI in
and Its Consequences
This section develops and applies a framework for assessing the statistical uncertainty from 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 the policy consequences of uncertainty in an MCI's relative weight, and Section 4.8 considers some alternatives. Throughout, the notation of variables parallels that for Canada in Section 2. In particular, variables with an asterisk correspond to. the foreign country (or countries) and those without correspond to the home, country. That said, specifics of the data definitions may differ, country by country. .
4.1
Measuring
the Uncertainty
of MCI
Weights
This subsection describes three approaches for measuring the uncertainty that arises from estimating MCI relative weights. The three approaches respectively use the Wald, Fieller, and likelihood ratio statistics to construct confidence intervals for the weights.
The Fieller and likelihood
ratio forms appear
finite sample properties. 13
preferable
because of their
The first and most intuitive approach is based on the associated standard error and 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 circumflex denotes estimation. Also, (3) is conveniently rewritten as: L yt = b • (p • ARRt
+ Aqt) + other variables
The relative weight p enters (4) explicitly,
+, error.
(4)
where p may be estimated directly by
(say) nonlinear least squares. The result is numerically equivalent to the ratio å/b derived from the linear estimates (d, b) in (3). In either case, a standard error for can be computed, from which confidence intervals are directly obtained. A confidence interval includes the unconstrained estimate of µ, which is å./b, and some 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 Waldbased 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
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 a [plower, y,,ppper]•
confidence 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 very significant 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 calculating MCIs. 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 thesis (5) into a linear one: namely,
14
the nonlinear hyp o-
0.
Hp : a - b/io
(6)
This approach is due to Fieller (1940, 1954), so the hypothesis in (6) and corresponding 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 if b is close to zero. Determination of confidence intervals is exactly as for the Wald approach, except that the F statistic is constructed for a.- bµo= 0. See Kendall and Stuart
(1973, pp. 130-132) for a summary.
The third approach uses the likelihood ratio (LR) statistic to calculate the confidence interval for the' hypothesis Hw. That is, (3), is estimated both unrestrictedly and under the restriction Hw, corresponding likelihoods (or residual sums of squares, for single equations) are obtained, and the confidence interval is constructed from values 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. intervals generated from it are invariant to the choice of Hw or . HF-because the likelihood-is invariant to nonsingular transformations of its parameters.. Second, if the original model (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 in its 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 under the 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 the three for nonlinear models because of its invariance property. For this reason, and because the LR and Fieller statistics are equivalent in linear models, discussion below of 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 estimates, albeit-of (3) rather than of (4). However, for ease of distinction below, the statistics for testing (5) and (6) on the unrestricted estimates are called Wald and Fieller 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 United States. 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. 15
N
Additionally, for each country, four graphs characterize the estimation uncertainty from 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 and at the upper and lower bounds from an LR 95% confidence interval. In an obvious notation, this graph contains MCI (µ) t, .MCI (pu eT)t, and MCI (pj, ,,,er)t. The third and 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 plots MCI (µ)t, MCI(µ)t_1 + L MCI (iiuppper)t,and MCI(µ)t-i + AMCI (µtower)t, and the fourth graph plots MCI (µ)t, MCI (µ)t_4 + A4MCI (pupppeT)t,and MCI(µ)t_4 + iijower)t• That is, these two graphs show how-much
A4MCI(
over fixed horizons from any particular
an MCI might differ starting point, noting that the base period of
an MCI is arbitrary. For computational convenience, calculations are based on the long-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 is nominal,' 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 the United 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 Reserve Board's INTL database, we could closely replicate that regression: Ayt =
+ 0.14
(0.13)
+ 0.44 Dyi + 0.55 Ayt 1
0.648 [tsRRt/8] (0.231)
T = 44 [1980(1) 1990(4)]
A0.12)
(0.12)
R2 = 0.67
-
f
0.181 [Al2gt/12]
(0.109)
& = 0.628%
(7)
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 the exchange rate (µ = cc). Even 'the 67.65% eonfi ence interval, equivalent to a plus-orminus 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 marginally significant coefficient on the exchange rate in (2) and (7). Figure 5 shows just how uncertain the estimate of the MCI relative weight is by plotting the LR F statistic. for various hypothesized values µo of the relative weight µ. Small values of the F statistic correspond to relative weights that are statistically acceptable, whereas large values do not. To measure the degree of statistical acceptability, 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 corresponding 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 likely be ignored if obtained in a,policy framework, given their counter-intuitive
sign. The
Wald statistic gives a distorted picture, particularly when the hypothesized relative weight µo is far away from the unconstrained estimate of 3.56., The observed empirical uncertainty has immediate repercussions for the Canadian MCI in policy, as shown in Figures 6-8. These figures demonstrate how statistically reasonable 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
monetary policy either loosens substantially (by roughly 500 from plower or µu,, basis points) or tightens substantially (by 300 basis points) over the period 1993Q11995Q1: see Figure 6. The empirical consequences
of these two scenarios are clearly
very different. Figures 7 and 8 derive the implications of using µ10111e r or µfl rather than the unconstrained MCI relative weight µ for short horizons that are likely to be of interest in 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 empirically reasonable 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-
17
It
nis and Roger (1997), and the Reserve Bank of New Zealand (1996b). As with Canada, 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 equation:
A(Vy)t -
0.011 0.34 A(Qy)t- j - 0.155 ORRt-3 (0.062) - (0.006) + (0.16) - 0.089 Agt.-s (0.033)
1.22 A2pt_3
. (0.32)
- 0.53 A2pt_4 (0.14)
-}- 0.65 "Ayi 3 + 0.72 Ayt-5 + 0.815 ut_1
(0.22) .
T = 40 [1986(2)-1996(1) 1
(0.23)
(0.129) -
(8)
o = 0.675%
The equation is estimated by first-order autoregressive least squares, with ut_1 being the lagged error.- The dependent variable is the change in an output gap, where the gap is obtained using the Hodrick-Prescott filter. The operator n.ablaV denotes that filter and Vy the corresponding output gap, where this notation is selected because. the HP filter has effects similar to differencing. Here, the HP*smoothing parameter A is 1600. The relative MCI weight is, estimated as the ratio of the coefficients on ARRt_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 LR and Fieller statistics are minor, whereas both differ sharply from the Wald statistic outside 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 marked effect 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 basis points for the most recent observation
4.4
(1996Q1).
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 a smoothing parameter (1994) Equation 2:
A of 100, 000 -
effectively a linear trend-. We replicated Jore's
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 (0.171) (0.088) T = 36 [1985(1)- 1993(4)]
R2 = 0.32
(9)
& = 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 calculated for Canada and New Zealand. All non-negative weights fall within the 95% confidence 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, MCIs are 400, 200, and 300'basis points. respectively. The each other frequently - that implies that their directions in sign for a given period.
4.5
typical deviations across different MCIs also cress of movement often differ . ,'
Sweden
The Swedish MCI is based on a model in Hansson (1993), which is further discussed in Hansson and Lindberg (1994) and Eika, Ericsson, and Nymoen (1996b, pp. 779781 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 inflation jointly, contrasting with the single-equation models of output alone for.Canada, New Zealand, and Norway. The Swedish model takes the form: log(VY)t = al log(VY)t_1 + a21og(VY)t_2 -{-a3pt 1
+ 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 detrending); 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 estimated long-run- relative MCI weight is the ratio of the coefficients on RRt_1 and qt_1, which is (-0.154)/(-0.076)
or 2.02.
19
%1
The LR 95% confidenceinterval is relatively small: [1.06, 2.96]. The Fieller and Wald confidence intervals are similar , with the three statistics differing only for values
of µo rejected by all statistics: see Figure 17. However, the calculated confidenceintervals are probably unreliable, given that the over-identifying restrictions in (10)-(11) are rejected against the corresponding unrestricted reduced form. The test statistic of over-identifying restrictions is X2(32 ) = 48.1 with a p v al ue of 3.4%.; see Eika, Ericsson, and Nymoen (1996b, Appendix). Even if a 95% confidenceinterval of [1.06, 2.96] is assumed, MCIs still can differ by a few hundred-basis points, depending upon which value of the relative weight is chosen from .that interval: see Figure 18. One-quarter perturbations are genera lly sma ll (Figure 19), but on e-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 d MCI weight for the United States; we estimate a model for the- growth rate of real U.S. GDP similar to the Canadian equation (7) and the Norwegian equation (9). This U.S. equation is: L1yt = - 0.041 + 0.309 A yt-1 + 0.269 L1RRt (0.032) (0.095) (0.060) (12)
- 0.035 RRt + 0.0094 qt (0.044) (0.0066) T = 84 [1976(2) -1996 (4)]
R2 = 0.30 -& = 0.670%
dw = 2.10
Equation (12) is a statistically satisfactory simplification of a fourth-order autoregressive distributed lag in Ayt, RRt, and qt. The corresponding F statistic is F(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 weight is negative: (-0.035)/(+0.0094), or. -3.69. However, the LR 95% confidence interval 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. A negative relative weight presents some interpretive difficulties, so the MCIs in Figures 22-24 are *evaluated at /2 = +10 (regarded-as a "reasonable" value, in light of Table 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
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 provides a numerical explanation through the sample correlations of the variables in (12). Specifically, Lyt and qt are positively correlated, and qt has only small or moderate correlations with the other regressors. Figure 25 characterizes this information through 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 observations in the early 1980s, as seen in the 'first pair of graphs in the figure. The slight positive correlation between Lyt and qt comes from their coincident larger values just prior 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. dollar appreciated to an all-time high for'the sample. Because (12) is very much a reduced-form equation, the results for the estimated MCI are unlikely to be robust to the choice of sample period: Even for. the sample used, (12) shows some evidence of mis-specification. Tests of normality and heteroscedasticity in the residuals are strongly rejected, even while the dynamic simplification is statistically acceptable. Thus, the MCI weight, confidence intervals, and MCI series derived from (12) should be viewed with caution because of that equation's empirical problems. Other MCIs for the United States are likely to be based on similar models and data, so those MCIs also should be treated with caution, at least until their empirical 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 esti1
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 is difficult to interpret MCIs based on that model. For all five countries, the estimation uncertainty often implies discrepancies in the MCI of 100 basis points or more for statistically acceptable choices of the relative weight. Such discrepancies occur even at 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 not just the magnitude of its movement. That feature is particularly problematic, in. so far 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 domestic economy through the exchange rate; and empirical models are a potentially sensible way 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 wide range of economic variables, including but not limited to interest rates and exchange rates. 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. Such model-based calculations also may then be part of the economic information feeding into the policy process itself. Policy-oriented examples of model-based calculations for Canada, Norway, and the -United States appear in Poloz, Rose, and Tetlow •(1994), Norges Bank (1996),
and Mauskopf (1990). Good graphical and tabular techniques can ease the burden in communicating inherently multivariate results; see Tufte (1983, 1990, 1997). Furthermore, 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 of those tools; Doornik and Hendry (1994, 1996) exemplify the software available; and the papers in Ericsson and Irons (1994) inter alia show how such tools and software can aid empirical modeling.
5
Concluding
Remarks
An MCI is an appealing operational target for monetary policy - it broadens an interest- rate target to include effects of the exchange rate on an open economy. In doing so, an MCI also incorporates model-based estimates of the effects of monetary policy 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 associated uncertainty of the estimated relative weight. The latter three issues pertain to summary indicators and model-based calculations generally, but they appear particularly 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 Bank of New Zealand currently use MCIs as operational targets, they are well aware of the shortcomings involved. This paper has clarified one specific shortcoming, estimation uncertainty, and drawn its implications for the practical implementation of MCIs in monetary policy.
23
Table 1. Selected Alternative Relative Weights for MCIs
Country
Central Ba`:l:s
IMF
OECD
Goldman Sachs
JP Morgan
2.3
Australia
4.3
3.3
Austria Belgium Canada Denmark
Source Deutsche Bank
0.4 213:
Finland France
4
3
2.3
4 "
4.3
- 3.4.
2.5, 4
4
2.6
Italy
3
4
6.6
Japan Netherlands New Zealand
10
4
Germany
2.7 1.9
2.1 ' 4.2
2.3'
6
4.1
3.7
8.8 ..
7.9 0.8
1.5
2.5
1.4 4.2
1.5
0.5
2.1
6:4
1.7
2
Norway
Spain Sweden
2.5 3.5
3-4
Switzerland United Kingdom
3
United States
10
4
14.4
5
2.9
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. 2223), Norges Bank (1995, p. 33), Hansson and Lindberg (1993, p. 16), International Monetary Fund (1996a, p. 16; 1996b, p: 19), Organization for Economic Co-operation and Development (1996, p. 31), Graf and Schonebeck (1996), Davies and Simpson (1996), and Suttle (1996), with -additional information on'specific MCI weights for Deutsche Bank, Goldman Sachs, and JP Morgan from personal communications with Theodor Schoneberg, John Simpson, and Carl Strong. 24
'
Table 2. MCI Relative Weights and Their Estimated Confidence Intervals Calculation Canada Estimation sample
80Q1-90Q4
New Zealand 86Q2-96Q1
Country Norway 85Q1-93Q4
Sweden 73Q3-92Q4
United States 76Q1-96Q4
MCI Relative Weights Multiplier Interim (horizon) Long-run Published
(6-8 quarters) 3.56 3
(medium-term) 1.75 2
2.0 (8 quarters) 2.15 3
3-4 (4 quartets) 2.02 3-4
(-) -3.69 -
Estimated Confidence Intervals for the Longrun Relative. Weights. Statistic 95% LR Fieller W ald
[0.74,oo] Same as LR . [-1.72,8.85]
[0-30,7'31] [0.32, 7.53] [-0.16,3.66)
(0.00, 00] Same as LR [-0.94,5.23]
11
[1.06,2.96] [0.92,3.05] [1.17,2.87]
[-oo, oo] Same as LR [-11.02,3.65]
90% (1.06,oo]
[0.52,5.05]
[0.36,26.6]
[1.27,2.76]
t-00,001
Fieller
Same as LR
[0.53, 5.12]
Same as LR
[1.17, 2.82]
Same as LR
Wald
[-0.84,7.96]
[0.16, 3.33]
[-0.42,4.71]
[1.31,2.73]
[-9.82,2.461
LR
67.5%*
I LR
[1.80,9.60] •
Fieller
Same as LR
Wald
[0.95, 6.18]
[0.97,3.04]
[1.00,4.98]
[1.61,2.43]
[-8.45,1.84]
[0.97, 3.05]
Same as LR
[1.56, 2.47]
Same as LR
[0.811'2.68]
' [0.63, 3.66]
[1.59,2.45]-
[-7.37,0.00]
*This confidence interval is calculated
such that the corresponding
F (or x2) statistic equals
unity, equivalent to a f.1 standard error band in a classical setting. Because the statistic's degrees of freedom vary across country, the associated p values ålso vary, albeit only slightly. 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 Coefficient
t ratio
laflation Equation
Coefficient t ratio 0.124 '
2.4
-1
-
Apt-1
0.100
-
Opt-2
0.043
0.4
Apt-3
0.105
0.9
A Pt-4
0.309
2.8
log(VY)t
-1
-
log(VY)t_1
0.467
3.8
l0g(VY)t_2
0.469
3.8
-0 .374
-3.0
Apt
RRt_1
-0.154
-2.5
qt_i
-0 .076
-3.1
'
Ap t*
0.132
2.0
Apt-1
0.029
0.6
0,093
2.1
A p7-3
0.044
0.9
Opi_4
0.020
0.4
,N-k pi_5 L1p7_6
-0 .071
-1.5
0.015
0.3
0.034
0.7
pt-8 Op7_9
-0 .023
-0 .5
pi-lo &
0.149
A pt
4
2
,
pi_7
A
0.022. . M, 1.267%
26
3.4
0.934%
't
Table 4. Data Properties of the U.S. Variables
Calculation Variable
Standard Deviation
Variance-covariance Matrix
Variable dyt
Ayt-1
ARRI
0 yt
0.0078
1
Dyt-i ORRt
0.0078
0.33
1
0.0130
0.42
0.01
1
RRt
0.0221
0.16
0.15
0.25
qt
0.1438
0.16
0.16
-0.01
Note: The sample period is 1976Q1-1996Q4.
1
RRt
qt
1 `0.60 1
.16 -
MC130
.14 .12 .1 .08 .06 .04 .02 0 -.02 -.04 -.06 1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
Figure 1: The Canadian MCI evaluated at a relative weight of 3.
.3
.25
--ll la
t
R90Cflac cangl0 t
,. `i
! r
.2
n .15
Ilii;tl 1
I
1 (^V
.05
. 0 1980
1982
1984
1986
1988
tlb ,yI 1990
1992
1994
1996
1998
Figure 2: The components of the Canadian MCI: the 90-day commercial paper interest rate (-) and the log of the exchange rate (- -).
28
• 't
--- MCI30 ---•• MC120 --- MC143
.02 0
-.02 -.04
D6
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
i
Figure -3: The Canadian MCI evaluated at relative weights of 2, 3, and 4.3.
-.01 --- MCI30 ------ MCI20 --- MCI43
t!\\!
i
-.02
!
i
Nj
I
,.:1
t
•
i .!\
,'
!., f
,• •' 1
,
\; -\
i
•
-.03
.J
•
1
1995
Figure 4: The Canadian recent subsample.
MCI evaluated
1997
1996
at relative weights of 2, 3, and 4.3 over a
29
't
. 12
-
FLR x MCtwt
-----------
Wald x MClwt F05pc x MCIwt F10pc x MClwt F32pc x MClwt
10
LR statistic (= Fieller statistic)
8
6
--------------95%----=--, 1,t 90% 1
4 -
-----------T---------------11 11 .1
2 67.65%
420
-15
-10
-5
0
5
10
g 0 20
15
Figure 5: F statistics for testing that the MCI relative' weight p equals.some hypothesized value yo, with critical values: Canada. .15 Ji
-----• MCInoS
I i i t\ --.1
I
MCIun MCIp05
\
y
.05
-
-
I\
'
i
\
i/
\\
Ij
\
!%
I
/
/
0
-.05
1982
1984
1986
1988
1990
1992
1994
Figure 6: The MCI evaluated at the unrestricted estimate (-),
1996
and at that estimate's
upper and lower 95% critical values (- - and - -): Canada.
30
1998
N
.15 MCIun ----- XMCIn O5 --- XMCIp05
A
.1
.05
0
-.o5
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 - - : Canada. .15
, 11 It
1 .1
1 1
1
-
MCIun
•---- X4MCin05 1 --- X4MCIp05 \ .
.05
0
-.05
1982
1984 '
1986
1988
1990
1992
1994
1996
1998
Figure 8: The MCI evaluated at the unrestricted estimate (-), and with 4-quarter perturbations at that estimate's 95% critical values (- - and - -): Canada.
31
I
14 - -•----------
12
FLR x FMCIwt FFstatx FMCI:wt WFstat x FMCIwt F05pc x FMCIwt F10pc x FMCIwt F32pc x FMCIwt
10
8 LR statistic Fidflerstatistic 4 --------------------
95%
---
----------
90% ----------
---------
------------------
-----
---------------------
2 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 hypothesized value µo, with critical values: New Zealand. 2.4 2.35
----- MCInO5 MCIun --- MCip05
2.3
r
2.25
N
!
t
r ! !
r 2.2
.
!:
',
t !
1
!
t
1 f
t . /\ ; t _ `:
:
., `;
i /
v
..
11
!
.
2.15
.
' .i
/
.i= ••• /
'•/---•-/ i
i
2.1 2.05
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 estimate's upper and lower 95% critical values (- and - -): New Zealand.
32
't
2.4 MC1un ----- XMCInOS --- XMCIØ5
2.35 2.3 2.25 2.2 2.15 2.1 2.05
V
2 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
Figure 11: The MCI evaluated
perturbations
at the unrestricted
estimate
(-),
and with 1-quarter
at that estimate's 95% critical values (- - and - -): New Zealand.
2.4 2.35
-
MCIun
---
X4MCIn O5 X4MCIpOS
2.3 ;
2.25
' `1
I 1\ -`
-. ,,
\
`-.'
% ••.:
2.2 , .,
,
. 2.15
2.1 2.05 2 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
Figure 12: The MCI evaluated at the unrestricted estimate (-), perturbations
at that estimate's
and with 4-quarter
95% critical values (- - and - -): New Zealand.
33
N
12 10
FLR x MCIwt Wald x MCIwt F05pc x MCiwt FIOpcx MCiwt F32pc x MCFwt
-------
8 Wald statistic LR statistic (= Fiellerstatistic)
6
95% 4 90% ------------------°--------
-----
------------------
2
67-50%
--------------------------20
-15
-10.
-5
---
.
0
-- ' 5
10
90
15
20
•
Figure 13:.F statistics for testing, that the MCI relative weight is equals some hypothesized value u0i with critical values: Norway. .12 MCIn O5 ----• MCIun ---
MCIp05
.08 4 .06 .04
'--
;i .r .
.02 0
-.02 -.04 -.06
1985
1986 1987
1988
1989
1990 • 1991
1992
1993
1994
1995
Figure 14: The MCI evaluated at the unrestricted estimate (-), and at that estimate's upper and lower 95% critical values (- - and - -): Norway.
34
,t
.12
-
MClun .
----XMC1n05 --- XMCIp05 .08
,i
.06 -.. 11 ':• '1 1 .•
\\/
:
1:
;
_
.
.
r
.04 .
.
•
'
'` //
.
.02 Q -.02 -.04
-.06
1985
1986
1988
1987
1989
1990
1991
1992
1993
1994
1995
Figure 15: The MCI evaluated at the unrestricted estimate (-), and with 1-quarter perturbations at that estimate's 95% critical values ( and - -): Norway.
.12 -
MClun
....... X4MCInO5 ---
X4MCIp05
.08
.06 (
\
•
'\ .04
11 •
.
\'
//
1.
^\
`
•
/
^``J/
`I
/
V
/
•
/ 1
/
.•
.02 0 -.02 -.04 -.Ø
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
Figure 16: The MCI evaluated at the unrestricted estimate (-), and with 4-quarter perturbations at that estimate 's 95% critical values (- - and - -): Norway. 35
1
14
Wald statistic LR statistic
12 Fieller statistic 10 -
Chi2LR x MCIwtF
--- Chi2Fx MCIwtF -----• -------
Chi2W x MCIwtF Chi05pc x MCIwtF ChilOpc x MCIwtF Chi32pc x MCIwtF
4 ------=----------------------'•--
-------------95%---90%
----------------------------2
68.27% 0-20
-15
-10
-5
0
5
10
t
15
90
20
-
Figure 17: Chi-squared statistics for testing that the MCI.relative weight µ equals some hypothesized value po, with critical values: Sweden. .06 .04
--•--• MCInO5 MCIun -} -- MCIp05 I
.02 v• 1
.
0
/.
,
''; I -.02 1
- .04 -.06
• 1\ ". : 1 ` j. i 11 1 \ j 1 I 1 I \ I
1 \I
1 \
1 \
.• r \` lt 1
' i
t1
t` t 1 I\
1 ". I\ i
`t
' ^I
; tt
'1
I I I i i
!
`
/
,
.
\\ '
;
, `
•
•
r1
-.08 -.1 1970
1975
1980
1985
1990
Figure 18: •The MCI evaluated at the unrestricted estimate (-),
1995
and at that esti-
mate's upper and lower 95% critical values (- - and - -):' Sweden. 36
1
.06 MCiun ----- XMCInO5 --- XMCIp05
.04 .02
-
0 -.02 •t -.04
I
-.06 -.08
1970
1975
1980
1985
1990
1995
i•
Figure 19: The MCI evaluated at the unrestricted estimate (-), and with 1-quarter perturbations at that estimate 's 95% critical values (- - and - -): Sweden.
. .06 .04
MCIun ----- X4MCIn O5 --- X4MCIp05
.02 0
1
-.02 - -.04
-.06 -.08
1975
1980
1985
1990
Figure 20: The MCI evaluated at the unrestricted estimate (-), perturbations
at that estimate's
1995
and with 4-quarter
95% critical values (- - and - -): Sweden.
37
12
10
-
FFstat x MCIwtF WFstat x MC1wtF
---
F05pcx MCIwtF
-----
F1Opcx MC1wtF F32pc x MCIwtF
8 1 Wald statistic 6
4 ------------
--------------------
-,=-------
95% ---------------90%
-------------='r------------------
-------------------------
LR statistic (= Fjellet statistic
2 --------------20
-15
-10
-5
0
5
10
15
µ0
20
Figure 21: F statistics for testing that.the MCI, relative weight p equals some.hypothesized
value µo, with critical values: United States.
I .9
---
- MCIn O5 MCIun MCIp10
.8 .7 .6 r'
.5 i-'••.--_
.4 .3
1976
1978
1980
1982
1984
1986
1988
Figure 22: The MCI evaluated .at p = 10 (-), -): United States.
38
1990
1992
1994
1996
1998
and at p = oo and p = 0 (- - and -
I •4
---
MCIun XMCInO5 XMCip05
.8 .7 .6 '-
,;
, . .
.4
; . ,' ' ' I 111
11
„ •
-
• , .
,
;
;,
.3 .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. at µ = oo and p = 0 (- - and - =): United States.
1 .9
MCIun ----- X4MCInO5 --- X4MC1p05
.8 .7
; ;
•
•
N-,
.3
1976
1978
1980
1982
1984
1986
198$
Figure 24: The MCI evaluated at µ = 10 (-), p = oo and µ ==0 (- - and - -): United States.
39
1990
1992
1994
1996
1998
and with 4-quarter perturbations
I
at
ø
o Dyus x DRR
.025 0
0 0 O 0
0
CD
, •, ,1 •,' ' ,
,
11
,-
, 1,
1
II
,
0
0
-.02 1975
1980
1985
1990
1995
-. 05
0
Dyus
0
.04 ------ RR
111
'
,
o Dyus
x Ø
0
•.,
i 0
.
0 00
80
0
0
000
OOø RD8
0
0
O
.025 ,
.02
.05
0
0 0
O OCS 0 0
,
0
-.02 1975 .04 ......
.02 ,
1980 Dyus
1985
1995
1990
0
.05
f
0 .025
q , •'' ,. ,
0 0
, ;
0.
. '. .
0
000
0
ll
0
o Dyus x q
.1 ,
.
,.•
0
0
0
0 ()
00
-.02 1975
Figure
1980
1985
1990
25: -Time-series plots (oyt)qt): United States.
1995
and cross-plots
40
4.75
5 '
for (Ayt, LRRt),
5.25
(/yt, RRt), and
1
References Alexander, L. S. (1997). "Dotes on the Poole Model and MCIs", memo, Division of 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-stationary Data. Oxford University Press, Oxford. Bank of Canada (1994). "Monetary Conditions - Les Conditions Monetaires", Bank. of Canada Review Bank of Canåda
(1995).
Revue de la Banque du Canada, 1994 (Autumn), Monetary
Policy Report,
18-20.
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 the Federal Reserve System, Washington, D.C., November. Davies, G., and Simpson, J. (1996). "Summary", Analyst (Goldman Sachs), 11(7/8), iii-xviii.
The Internnational Economics
Dennis, R. (1996a). "A Measure of MonetaryConditions", New Zealand, Wellington, December.
memo, Reserve Bank of
Dennis, R. (1996b). "Monetary Conditions and the Monetary Policy Transmission Mechanism", Øenlo, Reserve Bank of New Zealand, Wellington, November. Dennis, R., and Roger, S. (1997). "The Role of.Monetary Conditions Indicator Bands in Monetary Policy Implementation", memo, Reserve Bank of New Zealand, Wellington, January. Doornik, J. A., and Hendry, D. F. (1994). PcGive Professional 8.0: An Interactive Econometric
Modelling System.
International
Thomson
Publishing,
London.
Doornik, J. A., and Hendry, D. F. (1996). PcGive Professional for Windows, Version 9.0. International Thomson Publishing, London. Duguay, P. (1994).. "Empirical Evidence on the Strength of the Monetary Transmission Mechanism in Canada: An Aggregate Approach",. Journal of Monetary Economics, 33(1), 39-61.
41
Duguay, P., and Poloz, S. (1994). "The Role of Economic Projections in Canadian Monetary 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 Implementing a Monetary Conditions Index", International Finance Discussion Paper No. 568, 'Board of Governors of the Federal Reserve System, Washington, D.C.; October; also available on the World Wide 'Web a t http://www.bog.frb.fed.us/pubs/ifdp/1996/568/ifdp568.pdf. Eika, K. H., Ericsson, N.. R., and Nymoen, R. (1996b).. "Hazards in Implementing a Monetary Conditions Index", Oxford Bulletin of Economics and Statistics, 58(4), 765-790. Oxford University
Ericsson, N. R., and Irons, J. S. (eds.) (1994). Testing Exogeneity. .Press, Oxford. Fieller, E. C. (1940). "The Biological Standardisation
of Insulin",
Journal of the
Royal Statistical Society, Supplement , 7, 1-64. Fieller, E. C. (1954). "Some Problems in Interval Estimation",
Journal of the Royal
Statistical Society, Series B, 16(2), 175-185.
Freedman, C. (1994). "The Use of Indicators and of the Monetary Conditions Index in Canada",' In Balino, T. J. T., and Cottarelli, C. (eds.) , Frameworks for Monetary 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 Conditions Index in the Conduct of Policy -- Le Role des Conditions Monetaires
et
de l'Indice des Conditions Monetaires dans la Conduite de la Politique", Bank of 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 Real Exchange Rates", In Grossman, G., and Rogoff, K. (eds.) , Handbook of International Economics, Chapter 32, Volume 3, 1647-1688. North-Holland, Amsterdam. Gerlach, S., and Setets, F. (1996). "MCIs and Monetary Policy in Small Open Economies under Floating Rates", memo, Bank for International Settlements, Basle, November. GrS.f, B., and Schonebeck, T. (1996). "DBR MCI in August: Little Change", Market Issues: Economics (Deutsche Morgan Grenfell), (October 7), 2-3; also available on 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 Nonlinear Restrictions", 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 Policy Indicators, Chapter 5, 55-64. Sveriges Riksbank, Stockholm, Sweden. Hansson, B., . and Lindberg, H. (1994).
"Monetary
Conditions
Index -
Policy Indicator", Quarterly Review (Sveriges Riksbank Bank), 1994(3), 12-17.
A Monetary
Swedish Central.
Hendry, D. F. (1995). Dynamic Econometrics.. Oxford University Press, Oxford. International Monetary Fund (1996a). World Economic Outlook: May 1996. International 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 of an 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 of 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 Edition.
Longworth, D., and Freedman, C. (1995). "The Role of the Staff Economic Projection in Conducting Canadian Monetary Policy" , In Haldane, A. G. (ed.) , Targeting Inflation, 101-112. Bank of England, London. Mauskopf,. E. (1990). "The. Transmission Channels,of Monetary Policy: How Have They Changed?", Federal Reserve Bulletin, 76(12), 985-1008. Mayes, D. G., and Riches, B. (1996). "The Effectiveness of Monetary Policy in New Zealand", Reserve Bank Bulletin (Reserve Bank of New Zealand); 59(1), 5-19. Nadal-De Simone, F., Dennis, R., and Redward, P. (1996). "A Monetary Conditions Index for New Zealand", Reserve Bank of New Zealand Discussion Paper No. 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.. 43
't
Organization for Economic Co-operation and Development (1996). OECD Economic Outlook 59: June 1996. Organization for Economic Co-operation and Development, Paris. Poloz, S., Rose, D., and Tetlow, R. (1994). "The Bank of Canada's New Quarterly Projection Model (QPM): An Introduction --Le Nouveau Modele Trimestriel de Prevision (MTP) de la Banque du Canada: Un Apercu", Bank of Canada Review - 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 Conditions", 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 IEconometric Modelling. Cambridge University Press, Cambridge.
Staiger, D., Stock, J. H., and Watson, M. W. (1997). "The NAIRU, Unemployment and Monetary Policy", Journal of Economic Perspectives , 11(1), 33-49. Suttle, P: - (1996 ). "Monetary Conditions Worldwide ", (JP Morgan ), (March 29), 26.
World Financial Markets
' Thiessen, G. G. (1995). "Uncertainty and the Transmission of Monetary Policy in Canada - L'Incertitude et la Transmission de la Politique .Monetaire au Canada", Bank of Canada Review - Revue de la Banque du Canada, 1995 (Summer ), 41-58.
Tufte, E. R. (1983). The Visual Display of Quantitative Information. GraphicsPress, Cheshire, Connecticut. Tufte,-E. R. (1990). Envisioning Information . Graphics Press, Cheshire, Connecticut. Tufte, E. R. (1997). Visual- Explanations: Images and Quantities, Evidence and Narrative . Graphics Press, Cheshire, Connecticut. Wald, A. (1943).' "Tests of Statistical Hypotheses Concerning Several Parameters When the Number of Observations Is Large", Transactions of the American Mathematical Society , 54(3), 426-482. Zelmer, M. (1996). "StrategiesVersus Tactics for Monetary Policy Operations", In Zelmer, M. (ed.) , Money Markets and Central B ank Operations , 211-278 (with
discussion). Bank of Canada, Ottawa.
44
`
