Chapter 9. Canada: A Well-Established System

Tobias Adrian, Douglas Laxton, and Maurice Obstfeld
Published Date:
April 2018
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Rania Al-Mashat Kevin Clinton Douglas Laxton and Hou Wang

WHEREAS it is desirable to establish a central bank in Canada to regulate credit and currency in the best interests of the economic life of the nation, to control and protect the external value of the national monetary unit and to mitigate by its influence fluctuations in the general level of production, trade, prices and employment, so far as may be possible within the scope of monetary action, and generally to promote the economic and financial welfare of Canada. —Preamble to the Bank of Canada Act

For a quarter-century, the Bank of Canada has pursued flexible inflation targeting.1 The inflation-control targets, defined in agreements between the bank and the government of Canada, put the broad, multiple objectives defined by the preamble to the Bank of Canada Act into operational form. The mandate includes objectives for stabilizing output and inflation. Flexible inflation targeting, which accounts for the lagged effects of monetary policy on inflation and output and the short-term trade-offs between these goal variables, is squarely in line with this mandate.

The Canadian monetary framework is well tested and, without question, sound.2 And like any good arrangement for economic policy, the inflation- control-target agreements between the government and the central bank have a process for periodic review, assessment, and possible revision. This occurs every five years, and the current agreement is up for renewal in 2021.

Without questioning the success of the existing regime, the framework could be improved with greater transparency about the expected path of the policy rate—a step that in this book is called conventional forward guidance. Conventional forward guidance would involve routine publication of the forecast path of the policy rate and other relevant macroeconomic variables (such as the output gap and inflation) following the central bank’s policy decision meetings.

Before going further, it is worth drawing attention to the outstanding record of inflation control. Since 1994, headline consumer price index (CPI) inflation has averaged just under the 2 percent target. Expectations have been firmly anchored through the ups and downs of the business cycle and the exogenous price shocks that have occasionally driven the actual inflation rate off target. Thus, in 2016 the outlook for inflation remained remarkably stable despite the large impact of the recent oil price shock (Figure 9.1 and Table 9.1).

Figure 9.1.Inflation and Consensus Inflation Expectations for Canada, 1979–2017


Source: Consensus Economics.

Table 9.1.Inflation Expectations Are Better Anchored in Inflation-Forecast-Targeting Countries
201620172018Cumulative Deviations from Inflation Objectives (2017–18) (Percentage points)IFT Central Bank1



Czech Republic0.61.7


−0.2Yes (2002)
New Zealand0.71.7


−0.3Yes (1997)


−0.3Yes (2007)
United States21.32.3


0.0Yes (2012)
Euro Area0.31.3




Source: Consensus Economics, July 2016.Note: The numbers in parentheses represent percentage point deviations from the inflation targets.

Inflation-forecast-targeting (IFT) central banks use consistent macro forecasts to explain how they adjust their instruments to achieve their output-inflation objectives.

The implicit consumer price index (CPI) inflation objective for the United States is estimated by the authors at about 0.3 percentage point above the Fed’s official personal consumption expenditures (PCE) inflation objective of 2.0 percent. This is based on the difference in long-term CPI and PCE inflation forecasts from the Philadelphia Fed’s Survey of Professional Forecasters.

Source: Consensus Economics, July 2016.Note: The numbers in parentheses represent percentage point deviations from the inflation targets.

Inflation-forecast-targeting (IFT) central banks use consistent macro forecasts to explain how they adjust their instruments to achieve their output-inflation objectives.

The implicit consumer price index (CPI) inflation objective for the United States is estimated by the authors at about 0.3 percentage point above the Fed’s official personal consumption expenditures (PCE) inflation objective of 2.0 percent. This is based on the difference in long-term CPI and PCE inflation forecasts from the Philadelphia Fed’s Survey of Professional Forecasters.

The most transparent inflation-targeting central banks have adopted inflation-forecast targeting. The central bank’s forecast represents an ideal intermediate target that is used to communicate how it is managing the short-term output-inflation trade-off (Svensson 1997). That is, monetary policy targets the path of the central bank’s inflation forecast, which gradually converges to the 2 percent long-term target. The rationale is that this forecast embodies all relevant factors known to the central bank that may affect the future course of inflation. These factors include policymakers’ own preferences for the output-inflation trade-off, their assessments of the state of the economy, and their views on the transmission of monetary policy to output and inflation. Thus, the forecast embodies policymakers’ views of the best feasible path for the inflation rate from its current level to the long-term target rate. From this perspective, the central bank’s inflation forecast is itself an ideal operational target for monetary policy, over the medium and long term. Table 9.1 indicates, in an international comparison, that the inflation-forecast-targeting approach has had superior results in anchoring long-term inflation expectations to the announced targets.

Inflation-forecast-targeting central banks, Sveriges Riksbank, the Czech National Bank, and the Reserve Bank of New Zealand, ranked as the top three in the Dincer-Eichengreen index of central bank transparency (Figure 9.2). On this measure, they have overtaken the Bank of Canada, which was an early pioneer of inflation targeting and which, in conjunction with the IMF, provided advice on implementing the regime to several of them.

Figure 9.2.Dincer-Eichengreen Central Bank Transparency Index, 1998–2014

Several factors have contributed to the marked success of the framework in Canada. First, the exchange rate against the US dollar has been allowed to vary over a wide range, absorbing large shocks to the terms of trade and thereby buffering their impact on domestic output and inflation (Figure 9.3).

Figure 9.3.Oil Price and Canadian Exchange Rate, 2002–17

Source: Haver Analytics.

Second, fiscal policy has mainly played a supportive role, with surpluses during the pre-2008 expansion switching to large deficits after the global financial crisis, which reflect endogenous effects of the recession, and the 2009–10 fiscal stimulus. The budgetary consolidation during 2012–15, with smaller deficits, eventually restored a declining government-debt-to-GDP ratio.

After 2016, fiscal policy has been stimulative—appropriately in view of the macroeconomic circumstances.

Third, during 2010–13, Canada benefited from booming demand for oil and other commodities, driven by the expansion in China and other emerging markets, which stimulated domestic investment and output. This fortuitous development largely shielded Canada from the negative effects of the large drop of the global equilibrium real interest rate in the wake of the 2008 global financial crisis. In many advanced economies, chronic excess capacity and unduly low inflation rates have persisted despite extremely low interest rates. The global level of nominal rates consistent with maintaining output at potential is well below the pre-2008 level; currently the neutral rate may not be much higher than zero (Box 9.1).3 Since 2014, the weakness in world oil prices, the recession in the energy sector, and the weakness of other commodities markets has confronted Canadian monetary policy with the sharp end of the issue.

Box 9.1.Downward Trends in the Global Equilibrium Real Interest Rate

The equilibrium real interest rate can be defined as the rate that would be consistent with equality between actual output and potential (full-employment) output in the absence of any short-term or cyclical shocks. In a standard macroeconomic model, an inflation-forecast-targeting central bank would vary the policy rate from this level only to gradually return inflation to the target rate after some disturbance. This involves a medium-term concept of equilibrium. For Canada, a very open economy with high capital mobility, the global (or as an approximation, the US) equilibrium rate drives the domestic rate.

Inflation-adjusted bond yields have seen a trend decline since the early 1980s (Rachel and Smith 2015). A renewed drop after the onset of the 2008 global financial crisis, accompanied by low inflation and weak output growth, has led to substantial downward revisions of the equilibrium real interest rate. But there is no consensus on how far the rate may have declined since the crisis. IMF (2014), the Council of Economic Advisers (2015), and Holston, Laubach, and Williams (2016) discuss the causes of the decline. Summers (2015) cites a –3 to 1.75 percent range from a survey of US studies. Mendes (2014) puts the range at 1–2 percent for Canada. The main difference arises from definitions of shocks. Higher estimates, above 1 percent, classify as shocks the repeated headwinds that have resulted in a systematically disappointing recovery. Lower estimates, near or below zero, classify these headwinds as a permanent part of the medium-term environment rather than as shocks that have transitory effects on real interest rates.

The second approach is preferred. At some point, if negative headwinds persist, they are no longer shocks that have transitory effects. Repeated downgrades of forecasts (Table 9.2) and below-target inflation, along with declines in actual real rates, suggest that monetary policy has been confronting a decline in the neutral rate that can be perceived only with a recognition lag. In the meantime, policymakers overestimating the equilibrium real interest rate would attribute persistent surprisingly weak output to unexpected headwinds.

Moreover, because of the evident steep drop in the global equilibrium rate, encounters with the effective lower bound are likely to become more frequent and longer lasting.

Figure 9.1.1.Equilibrium Real Interest Rate for the United States


Sources: Authors’ calculations; Federal Reserve; Johannsen and Mertens 2016; Laubach and Williams 2015; Nomura; Obstfeld and others 2016.

Note: CBO = Congressional Budget Office; FOMC = Federal Open Market Committee; NAIRU = non-accelerating inflation rate of unemployment.

Table 9.2.Revision s to Bank of Canada Forecast for Attainment of Potential Output
2011:Q4Deleveraging, weak employment
2012:Q3Weak global, US fiscal tightening
2013:Q4Weak China, Europe, and Canada
2014:Q2Lagged revision for 2012:Q4
2015:Q4Weak global and Canada, commodity price collapse
2016:Q4Expected rebound slow to appear
Source: Bank of Canada Monetary Policy Reports, 2009–16.Notes: The first quarter in each shaded rectangle indicates when a revision was made. The last quarter in each shaded rectangle indicates when the output gap was expected to close, according to that revision. Rectangles do not always overlap exactly by one quarter, because small revisions are omitted.
Source: Bank of Canada Monetary Policy Reports, 2009–16.Notes: The first quarter in each shaded rectangle indicates when a revision was made. The last quarter in each shaded rectangle indicates when the output gap was expected to close, according to that revision. Rectangles do not always overlap exactly by one quarter, because small revisions are omitted.

Fourth, a sound system of financial regulation and supervision, which includes a five-year updating of banking legislation, helped the Canadian financial system avoid the excesses that preceded the global financial crisis. As a result, Canada was one of the few advanced economies to escape severe financial sector stress during the global financial crisis. The banks were well-capitalized and did not need public sector support. The postcrisis tightening of credit, due to heightened risk aversion, was less severe in Canada than in other countries.

The core measure of CPI inflation has remained near 2 percent, but the widening of the negative output gap since 2014 portended further reductions in inflation. In response, the Bank of Canada reduced the overnight interest rate. With the overnight interest rate at that time at 0.5 percent, some room remained for cuts—the bank has revised its estimate of the effective lower bound on the overnight rate down to –0.5 percent from 0.25 percent (Witmer and Yang 2015).

However, in view of the drop in the global equilibrium rate, policy rate cuts, even of the maximum feasible extent, might not give much of a boost to the economy—unless, that is, they are supplemented by other measures. The central bank, drawing on the experiences of other central banks, has signaled that it is prepared to adopt unconventional monetary policy measures, such as large-scale asset purchases and funding for credit. While these less conventional options remain open for future contingencies, their efficacy is uncertain (Poloz 2015). And questions have been raised about the implications of negative rates maintained over an extended period for the efficiency and stability of the financial system (Bech and Malkhozov 2016).

Conventional forward guidance would strengthen an already-strong framework by making the interest rate instrument more effective—a strategic modification that would pay off in good as well as bad times. The change would move Canada back to the forefront of the inflation-forecast-targeting economies on transparency. It would improve the Bank of Canada’s ability to manage the medium-term trade-offs as shocks drive the economy off course. In situations like a big downturn, it might obviate the need to consider a negative policy rate or the increased use of unconventional monetary instruments. And conventional forward guidance would be preferable to the suggestion to raise the inflation target from 2 percent, which raises issues of credibility (long-term inflation expectations have been very firm at 2 percent), effectiveness (a mere announcement would not do the job, the central bank would have to raise the actual inflation rate), and economic efficiency (such as inflation distortions caused by confusion between real and nominal changes, and by interactions with accounting and tax systems).

The essence of the argument is simple. In and of itself, the Bank of Canada’s setting of the overnight rate for the next six weeks (the interval between policy meetings) has limited impact on inflation or output. The policy rate has an effect only insofar as it moves the longer-term interest rates at which households and firms borrow and invest. In effect, the bank must ensure that public expectations of the future overnight rate move in line with the current setting.4

Conversely, the central bank must have a view of how its policy decisions will affect the medium-term path of the short-term rate, because the transmission to inflation and output depends on this path. Thus, underlying every interest rate policy decision is a forecast—indeed, the best-informed forecast—of the rate path that will get inflation back to the 2 percent target over the medium term. The forecast rate path, moreover, is endogenous—in the literal sense that inflation-forecast-targeting central banks use forecasting models with an endogenous policy rate, as well as in the logical sense that with an inflation target the policy rate must vary to keep inflation on target within the medium-term forecast horizon. The policy rate path therefore responds to observed economic conditions to get the inflation rate back to the target over time in a manner that efficiently manages the short-term output-inflation trade-off. If markets have similar policy interest rate forecasts as the central bank, longer-term interest rates, the exchange rate, and asset prices generally are likely to move in support of the objectives of monetary policy.

This point has been long accepted with respect to publication of the forecast inflation rate path. There is a duality, in that expected inflation and the actual nominal interest rate are the two components of the real interest rate. The published inflation rate forecast generally influences the expected real interest rate in support of monetary policy. When nominal interest rates are constrained by the effective lower bound, this is more important.5 The central bank might well envisage a strategy in which there is a temporary overshoot of inflation above the target. This would reduce the real interest rate and help move the economy away from a deflation or low-inflation dark corner. Under conventional forward guidance, the central bank would communicate the whole story underlying the strategy, allaying any risk to the credibility of the target that the planned overshoot might otherwise create.

The main objection to conventional forward guidance is the conditionality of the interest rate forecast. Monetary policy must allow the interest rate to vary to offset shocks. It cannot commit to a forecast path for the rate. Central bankers have worried that if it becomes necessary to deviate from a given path their credibility might be impaired. However, with effective communications, this issue need not arise: markets have readily adjusted in those countries where the central bank publishes its interest rate forecast (such as the Czech Republic, New Zealand, Norway, Sweden). Indeed, with a deeper understanding of the intentions of policymakers, markets are more likely to perform a strong buffering role against shocks. Model-derived confidence bands, and alternative forecasts based on shocks to the baseline forecast, are useful tools for communicating the conditionality of the projection and the impact of shocks should they materialize.

The analysis and policy simulations presented here indicate that a strong policy framework for avoiding macroeconomic quagmires would be provided by a loss-minimizing monetary policy, with a quadratic loss function, which puts an increasingly heavy penalty on deviations of inflation from the inflation target and of GDP from potential output; and full publication of the central bank forecast. In addition, near the effective lower bound, there is a clear role for a fiscal stimulus (Freedman and others 2009). These features could be more effective than unconventional monetary policy measures, or negative interest rates, or raising the target inflation rate, for avoiding the dark corner of the effective lower bound–deflation trap.

Expectations and a Threatening Dark Corner

In normal times, following a contractionary shock, policy would react with an interest rate cut that has its effects on inflation and output through the usual transmission mechanism. At the effective lower bound a somewhat weakened version of the mechanism could still apply, transmitted through real interest rates and the real exchange rate. That is, expected inflation provides a channel through which forward guidance can stimulate the economy. If monetary policy is active and credible, it could persuade the public that it will eventually get inflation back up to the long-term target. With the promise of a sufficiently vigorous policy, which commits to holding the interest rate at the effective lower bound for an extended future period, the public—and financial market participants in particular—would expect increased inflation. This would reduce longer-term real rates of interest even if the nominal rate were stuck at the effective lower bound. These movements buffer the shock. Under such circumstances, to respond strongly to the initially very weak economy, the central bank might show a stimulative forecast in which, over the medium term, inflation overshoots before returning to the long-term target.

Moreover, the real exchange rate would depreciate, and asset prices would rise immediately in line with the drop in the real interest rate. And the longer the expected period for the policy rate at the floor, the larger are these effects (Annex 9.1). This equilibrating response of the real price of foreign exchange is a normal aspect of the transmission mechanism. Thus, the real interest rate channel would be amplified in the open-economy case by the real exchange rate channel.6 A very similar argument to that for the real exchange rate applies to asset prices. An increase in the expected medium-term rate of inflation that reduces real interest rates would boost asset prices through the lower real discount rate and through the positive impact of exchange rate depreciation on profits. Increased asset prices would stimulate spending and help eliminate economic slack in the economy.

To achieve this result, the central bank has to persuade people that the nominal interest rate will remain at the floor for an extended period and that the rate of inflation will rise over the medium term, possibly above the long-term target, but that the rate of inflation will eventually return to target. Is this a realistic prospect? The exchange rate policy used by the Czech National Bank from November 2013 until April 2017, which has relied heavily on influencing expectations, suggests that, under a transparent inflation-forecast-targeting framework, it can be (Chapter 10).

Figure 9.4 provides an illustration. The economy is hit by some contractionary shocks that cause economic slack and inflation to fall below the target. The orange line indicates a passive policy, with actual inflation well below a noncredible target of 2 percent and the interest rate stuck at the effective lower bound. The blue line is for a credible framework: starting in period 4, policy smoothly achieves the 2 percent target in period 12. But policy could be more aggressive. With conventional forward guidance, monetary policy deliberately causes inflation to overshoot the target for several quarters—at the peak, inflation reaches 2.5 percent. The medium-term increase in the inflation rate (over the blue line), which peaks at 0.7 percentage point, translates into temporarily higher inflation expectations, and hence a decrease in real interest rates of 70 basis points. This positive feedback is part of the boost provided by the more aggressive policy, which achieves the inflation target at a lower overall cost: it involves a smaller cumulative output gap, and provides better risk management, in that it moves the economy more quickly from the dark corner where the effective lower bound risks allowing potential deflationary forces if new contractionary shocks were to hit the economy in the future.

Figure 9.4.Inflation Paths for Different Policy Frameworks


Source: Authors’ calculations.

Note: bps = basis points.

During a period in which the effective lower bound is binding, and where the main danger is on the deflation side, the forecast endogenous interest rate would be at the effective lower bound long enough to get inflation back on track (Eggertsson and Woodford [2003], with a different model, reach the same conclusion). To the extent that this forecast affects market expectations, it will result in medium- and long-term rates that are lower than their long-term equilibrium values. In this sense, publication of the forecast becomes an additional instrument, helping policy achieve its objectives, in the same way as the US Federal Reserve’s forward guidance since 2008.

Conventional forward guidance emerges from a systematic framework, but it so happens that its advantages become most clear in the zone around the effective lower bound. A transparent lower-for-longer interest rate strategy would have the positive impact of reducing real interest rates by more than the actual cut in the overnight rate. A published forecast would encourage a desirable movement in medium-term expectations for both the nominal interest rate (down) and for inflation (up). Thus, longer-term market interest rates, the exchange rate, and asset prices would play a reinforced shock-absorber role in support of the economy.

Different Types of Forward Guidance

Conventional Forward Guidance

Conventional forward guidance as practiced in the Czech Republic, New Zealand, Norway, and Sweden is a systematic part of the policy framework. It derives from the publication of a complete central bank macroeconomic forecast with an endogenous interest rate path and confidence bands around key variables. The endogenous policy rate moves to achieve the announced inflation target on a medium-term horizon in a way that reflects the policymakers’ preferences for short-term trade-offs between output, inflation, and interest rate variability. The policy rate path is clearly conditional on a range of assumptions and subject to a range of uncertainty, as indicated by the confidence bands. In general, publication of the path should help steer public expectations in a way that is helpful to the attainment of policy objectives, in particular through the effect on medium- and longer-term interest rates.

Under inflation-forecast targeting, a type of forward guidance takes place on an ongoing basis, in that the central bank provides a regular flow of information on its current policy actions and on its view of the medium-term macroeconomic outlook. The rationale is that markets are more likely to operate in support of monetary policy objectives if they are well-informed about the central bank’s view of the forces affecting inflation and output. At a minimum, under inflation-forecast targeting, forecast paths for inflation and the output gap or growth are published just after interest rate policy decisions are announced.

Systematic publication of the forecast interest rate path too would provide market participants with a seamless flow of information on how the changing state of the economy is likely to affect the monetary policy actions aimed at returning inflation to the target. This approach is robust in the sense that conventional forward guidance is a regular part of the policy framework—forward guidance is continuous in the routine format of the published forecast, not just in cases of major economic instability (Clinton and others 2015).

Publishing the path for the endogenous policy rate underlines that the policy action at any point in time involves more than just setting an interest rate until the next monetary policy meeting. In making any particular decision, policymakers must have in mind some view of the future interest rate path that will be necessary for the efficient achievement of the target over the medium term. A priori, releasing that path, along with a discussion of how it might change in response to new information that changes the outlook, would be the single most obvious way of clarifying for the public the central bank’s view of the policy implications of the economic outlook, and, more generally, for revealing how it intends to manage the short-term output-inflation trade-off.7 In contrast, a published forecast that shows a smooth return of inflation to target and output to potential, without the interest rate path, does not provide the public with a clear idea of the central bank’s perception of the outlook, such as how strong the economic headwinds may be or how it intends to deal with them.

It is important, however, that communication on the policy rate path should avoid creating the false perception that the path is a promise rather than a conditional forecast. In practice, this has not proved to be an insuperable difficulty in the Czech Republic, New Zealand, Norway, and Sweden, where the central banks publish their forecasts for the short-term interest rate (Clinton and others 2015). These central banks communicate to the public not just a forecast path for the future policy rate (and for unconventional instruments where these are a factor), but also a sense of how and why this path might change in response to a variety of developments. At the same time, the central bank should make clear its evaluation of the risks and uncertainties that lie ahead. Effective communications are the key to avoiding false perceptions about the precision of the forecast. To underline the degree of uncertainty in the projections, conventional-forward-guidance central banks publish confidence bands, as well as the central tendency, for the path of the policy interest rate. In addition, the publication of alternative scenarios to the baseline, embodying large shocks for which the probability cannot be calculated from historical data, can indicate the nonnormal range of uncertainty perceived by the central bank.

A central bank using conventional forward guidance does not have to give special guidance as to when its guidance will switch on and off, or as to the threshold values of inflation and unemployment (or the output gap) that might trigger a policy move. In contrast, forward guidance as practiced in the United States has involved ad hoc central bank statements about when in the future—at which calendar date—the policy interest rate might be changed, or about thresholds for the inflation rate and unemployment that might trigger a change in the rate (Alichi and others 2015).

Conventional forward guidance would generally influence expectations for the future policy rate, and for medium-term inflation, in a way that helps monetary policy—in good times as well as in times of heightened economic instability.8 That is, it would encourage the longer-term real market interest rates that affect business and household demand to move in line with developments in the state of the economy and the Bank of Canada’s output and inflation objectives. It would also improve the process of accountability, in that published forecast paths, confidence bands, and alternative scenarios provide a quantitative framework by which to account for central bank actions. Policymakers should be able to explain the events that caused deviations from the forecast path transparently, in terms of the specific deviations from forecast assumptions.

Unconventional Forward Guidance

Forward guidance on the policy interest rate was employed by the Bank of Canada, the Federal Reserve, the Bank of England, and the Bank of Japan, among others, after the global financial crisis. These central banks used forward guidance to talk down the expected policy rate path and term premium, and thereby to reduce longer-term interest rates. In this respect, it did succeed (Engen, Laubach, and Reifschneider 2015; Charbonneau and Rennison 2015). This is called unconventional forward guidance because it was introduced along with other unconventional measures as an ad hoc tool when the effective lower bound put constraints on reductions in the policy rate.

Unconventional forward guidance has encountered difficulties in communicating its conditionality, in particular the time horizon over which the guidance is to apply. In the immediate aftermath of the global financial crisis, with raised risk premiums, central banks wanted to assure markets that policy rates would remain at the floor for at least as long as it took to restore a semblance of order. Indeed, the Bank of Canada emphasized that its policy rate would be kept at the floor (estimated at the time to be 0.25 percent) from April 2009 to April 2010, but that this commitment was conditional on the outlook for inflation. As the economy recovered and inflation returned to the 2 percent target, the bank exited this unconventional forward guidance (more or less as initially planned).

As such, the experience turned out quite well and Canada avoided difficulties that surfaced in other advanced economies, as discussed below. However, this was in large part fortuitous, in that, after 2009, Canada benefited from the favorable shock of booming demand for oil and other commodities from China and other emerging markets.

In the United States and the United Kingdom, things were more complicated. As these economies emerged, sluggishly and unevenly, from the postcrisis recession, their central banks tried to communicate when, and under what conditions, the policy rate would rise from the floor (and quantitative easing would taper off). For this purpose, they announced threshold values for the unemployment rate and the inflation rate.

A risk in this kind of announcement is oversimplification. Policymakers do not themselves use a simple threshold rule for decision-making. Their view of the future path of the policy rate depends on a much more complex assessment of what may be necessary to return the inflation rate to target: they have a clear perception of the objectives of policy, which are given, and the conditional nature of their projections for the policy instrument. Within central banks, such assessments are informed by forecasts derived with macroeconomic models that take account of numerous factors influencing the outlook and the judgment of the forecasters. Announcing thresholds for inflation and unemployment risks misguiding financial markets about the scope of other considerations that may influence policymakers’ outlook for the interest rate.

This could lead financial market participants to underestimate the degree of uncertainty in the outlook, and hence make financial markets vulnerable to the arrival of unexpected news. For example, the strategy might misrepresent the amount of uncertainty in future long-term interest rates in the short term it might convince financial markets that short-term interest rates will stay low. A point will come, however, at which the interest rate has to be raised, upsetting market expectations and creating market volatility (as in the 2013 taper tantrum).

The Governor of the Bank of Canada has therefore expressed a concern that a conditional commitment to hold rates low might artificially reduce two-way rate volatility and prevent markets from properly assessing risks in the interest rate outlook, especially potential shocks of a size and nature in the distant tails of the statistical distributions (Poloz 2014). This risk is reduced with conventional forward guidance, which presents the central bank forecast as a conditional projection and is transparent about the underlying assumptions and their uncertain nature.

Country Experiences with Unconventional Forward Guidance

United Kingdom

The Bank of England announced a threshold rule (August 2013), declaring that it would not raise its policy interest rate (or reduce its quantitative easing) until the following occurred:

  • The unemployment rate fell below 7 percent or
  • CPI inflation 18 to 24 months ahead rose above 2.5 percent or
  • Inflation expectations became unhinged or
  • The low interest rate threatened financial stability

Within a few months the unemployment rate had fallen below the threshold, yet there was no economic case for a rate increase: inflation was below 2 percent and falling and the financial system looked stable. In February 2014 the central bank reverted to qualitative guidance with no numerical thresholds.

United States

The Federal Reserve has changed the form of its unconventional forward guidance several times since its inception in 2008 (from qualitative to date-based, to threshold-based, and back to qualitative). Until 2013 the guidance succeeded in the operational objective of reducing the term premium and expected future short-term rates—and, hence, bond yields.

These changes nevertheless looked like improvisation rather than a consistent strategy. In 2013, a change in perceptions about policy triggered the taper tantrum, an outbreak of financial market volatility. Bond yields and term premiums rose sharply, to an extent way out of line with the modest eventual tightening envisaged in the cautious public statements of the central bank. Continuing communication difficulties with unconventional forward guidance are illustrated by this clarification from Federal Reserve Chair Janet Yellen (March 2015): “just because we removed the word ‘patient’ ... doesn’t mean we are going to be impatient ...”

There is evidence that the communications difficulties have had material macroeconomic costs. The empirical study by Engen, Laubach, and Reifschneider (2015) concludes that if the public had understood beforehand the willingness of the Federal Open Market Committee (FOMC) to accommodate, the recession would have been less severe and the subsequent recovery more rapid (Figure 9.5).

Figure 9.5.Predicted US Unemployment Rate, 2008–20


Since January 2012, the Federal Reserve has released FOMC members’ interest rate projections following each meeting. But it is difficult to “connect the dots” from the individual projections to form a single consistent forecast (Alichi and others 2015).

Filardo and Hoffmann (2014) look at experience in the United States, Japan, and the United Kingdom. They find that forward guidance has had moderately beneficial results. Charbonneau and Rennison (2015) provide a somewhat more favorable assessment of the international experience (including Canada), finding lower expectations of the future path of policy rates, improved predictability of short-term yields over the near term, and reduced sensitivity of financial variables to economic news. Engen, Laubach, and Reifschneider (2015) suggest the net stimulus to real activity and inflation was limited by the gradual nature of the changes in expectations for the interest rate and term premiums. In view of the limited sample size and of the shifts in the nature of forward guidance, the lack of a strong positive macroeconomic effect should not be surprising. More systematic, and more explicit, interest rate guidance might well yield material gains.


The rate of inflation in September 2008, when the global financial crisis broke, was about 2 percent, and the Bank of Canada’s policy rate was above 4 percent. Over the next two years, the central bank exploited the ample room for action during the global recession, cutting the policy rate to near zero. The Canadian dollar depreciated. Exports fell sharply with the drop in US demand, but the decline in GDP was limited to 2.7 percent, as domestic demand held up quite well. Inflation remained positive. In the Canadian case, policy actions helped keep expectations up, and the exchange rate acted as a shock absorber. Despite the proximity of Canada to the US epicenter of the crisis, and the drop in commodity prices, the Canadian recession was relatively mild.

By 2010, the Canadian economy was recovering. Rising global oil prices gave output as well as inflation a boost, as investment and output in the energy sector began to expand strongly. Even so, a considerable degree of slack, with weak employment, persisted. One might question the management of the output-inflation trade-off. The bank’s forecasts for output were consistently overoptimistic. Over time, the forecasts in monetary policy reports repeatedly put back the date at which output was expected to reach potential, from the fourth quarter of 2011 in the July 2010 report, to the third quarter of 2017 in the April 2016 report (Table 9.2). In retrospect at least, such long-lasting headwinds, or negative output shocks, imply that the bank was overestimating the equilibrium real interest rate. An overestimate was to some extent inevitable, because this rate is not directly observable, and it would be impossible in real time to recognize a decline of the magnitude that now seems likely to have occurred.

Model Simulations of Alternative Policy Strategies

Simulation results based on a New-Keynesian model illustrate how conventional forward guidance might operate. The model used here for Canada bears similarities to those used at many central banks for forecasting and policy analysis. It has a standard core structure, with equations for the output gap, core inflation, the policy interest rate, and the exchange rate. Expectations are forward looking, consistent with the projections of the model itself, but the behavioral equations also embody lagged adjustments. In addition, the model has equations for headline inflation, food and energy inflation, the commodity terms of trade, trade and financial linkages with the rest of the world, and bond yields of various maturities.9 Nonlinearities are in the Phillips curve—which becomes quite flat when there is a negative output gap—the effective lower bound constraint, and the monetary policy reaction function.

Monetary policy follows a loss-minimizing strategy in which the loss function has a weight, 1, on the squared inflation gap (the deviation from 2 percent) and the squared output gap; there is a weight of 0.5 on the squared change in the policy interest rate, which implies a smoothed interest rate policy response; such smoothing is justified on theoretical grounds, and is a well-observed feature of actual central bank behavior. The quadratic loss function imposes an increasingly heavy loss as deviations from target increase; the loss-minimizing strategy would therefore be very averse to dark corners, in which the economy gets stuck in a bad equilibrium that is resistant to conventional policy instruments. In other words, the strategy takes a risk-avoidance approach to risk management.

It is interesting to see how a strategy of this nature, using conventional forward guidance, would have performed following the extreme event of the global financial crisis. A good place to start is in the second quarter of 2009. The dire situation then unambiguously called for maintaining the policy rate at the floor for some time and, in fact, the Bank of Canada provided forward guidance to this effect:

With monetary policy now operating at the effective lower bound for the overnight policy rate, it is appropriate to provide more explicit guidance than is usual regarding its future path so as to influence rates at longer maturities. Conditional on the outlook for inflation, the target overnight rate can be expected to remain at its current level until the end of the second quarter of 2010 in order to achieve the inflation target. (Bank of Canada, 2009).

The central bank forecast, that this policy would return inflation to the target of 2 percent in 2011, was not far off (Figure 9.6, dashed line). However, this was largely due to the one-off effect of a rise in global energy and food prices in 2010–11. The forecast that the output gap would be closed in 2011 was overoptimistic. Core inflation languished below 2 percent, and within a couple of years headline inflation fell back below target. One might ask whether monetary policy should have maintained an easier stance, especially after 2010 as the postcrisis fiscal stimulus was being withdrawn. More productive questions, however, concern systematic strategy rather than the particular response to the circumstances of the time.

Figure 9.6.Optimal Control versus IFB Reaction Function, 2009–13

Source: Authors’ simulations.

Notes: IFB = inflation-forecast-based; OPT = optimal control.

What would the macro forecast—the expected results—have looked like if a strategy combining conventional forward guidance with a loss-minimizing policy reaction function had been in place at the outset in the second quarter of 2009? How would the postcrisis economy, affected as it was by unexpected developments, have looked? What are the implications of other unconventional or supporting tools, such as a negative policy rate and a fiscal backstop?

In the simulations that follow, policymakers operate in quasi–real time: that is, the information available to them in any quarter is limited to what could have been available at the time. However, as vintage data sets are not used, the series employed contain revisions to the historical data. In other words, in these counterfactual reruns of history, the current historical data set unrolls one quarter at a time. The starting point, in the second quarter of 2009, had a large output gap, assumed to be –4.5 percent, an inflation rate of 1 percent, and a policy interest rate at the then-assumed effective lower bound of 0.25 percent. As for the real equilibrium interest rate, for the starting point, an estimate is assumed, based on historical information available at the time, of 1.7 percent; it is revised downward thereafter on the basis of incoming new data.10

Forecast as of the Second Quarter of 2009 Plan

Figure 9.6 compares a plan made in the second quarter of 2009 under the loss-minimization strategy (OPT, red line) with one based on a linear inflation-forecast-based (IFB) reaction function (IFB, blue line). Under both illustrative plans, the central bank practices conventional forward guidance, so the forecast interest rate path has a direct impact on interest rate expectations. The red and blue lines—for the policy rate, output gap, headline inflation, core inflation, exchange rate, and unemployment—can be interpreted as the forecasts the policymakers would have before them in the second quarter of 2009. They would of course differ from subsequent actual outcomes because of unexpected changes: the counterfactual comparison of policies is purely a model-based exercise. The dashed lines in the figure show the realized historical paths of the variables. Monetary policy is constrained by an effective lower bound of 0.25 percent, which the Bank of Canada at that time viewed as the effective floor.

Key aspects of these policy simulations are as follows:

  • 1. The derived loss-minimizing strategy (OPT) keeps the policy rate at the floor for two years, from the second quarter of 2009 to the same in 2011. The expectation under this plan, with the nominal interest rate held at the effective lower bound, is for the exchange rate to rise (the Canadian dollar to depreciate) about 4.5 percent for 2009 to the end of 2012. The wide output gap is closed quite quickly, to zero by the fourth quarter of 2010, and an excess demand gap opens. The unemployment rate comes down at the same pace. Inflation overshoots. Year-over-year core inflation peaks at 2.8 percent, from the fourth quarter of 2011 to the second quarter of 2012, before falling back to 2 percent. Headline inflation peaks slightly lower. One of the reasons for the strong stimulative impact of the policy is that the anticipated medium-term increase in inflation reduces real interest rates and causes the real exchange rate to rise (that is, a real depreciation).
  • 2. The IFB strategy implies that the policy rate stays at the floor for only about a year, from the third quarter of 2009 to the second quarter of 2010. The medium-term rise in the exchange rate (depreciation of the Canadian dollar) is relatively modest. The output gap is closed more slowly than with the OPT strategy, reaching zero in the third quarter of 2011 and staying there. Unemployment at that time is 1 percentage point higher than under OPT. Inflation (core and headline) does not get back to target until a year later. By most standards, OPT would be regarded as the better strategy.

OPT wants inflation to overshoot and the output gap to close fast, because, given the initial conditions, the below-target inflation, and the wide negative output gap in the second quarter of 2009, a quadratic loss function implies at the margin relatively high benefits from increases in both inflation and output. The constraint of the effective lower bound is an additional reason for the stimulative policy: given the loss function, forward-looking policymakers would be very averse to the bad equilibrium where deflation meets the effective lower bound. The idea is to put distance between the economy and that dark corner, fast.

Counterfactual History with Loss-Minimizing Strategy

The global financial crisis in fact had deeper and longer-lasting effects than anticipated in 2009. On top of this, additional negative shocks were to hit the Canadian economy. As a result, the history presents a much weaker picture than either of our two illustrative second-quarter 2009 policy strategies envisaged, and the negative output gap was never completely closed.

The simulations can be repeated, allowing the unanticipated shocks to affect the outcomes, including the loss-minimizing policy response (Figure 9.7).11 The quasi-real-time results can be compared with the history, since the hypothetical central bankers are dealing with the same shocks as the real ones.

Figure 9.7.Predicted Outcomes under Optimal Control with Historical Shocks, 2009–13

Source: Authors’ simulations.

Note: OPT = optimal control.

Key aspects of the results are as follows:

  • 1. The loss-minimizing response to the historical shocks results in the policy rate at the effective lower bound until the first quarter of 2013 (the whole period shown in Figure 9.7). In contrast, the Bank of Canada raised the policy rate to 1 percent in 2010. The Canadian dollar appreciates less with the counterfactual strategy.
  • 2. Under OPT, inflation overshoots the target by a substantial margin. Core inflation peaks above 3.5 percent in 2010, and headline inflation, driven by energy and food price shocks, peaks above 4 percent. The output gap closes to zero in the second half of 2011 before further negative shocks in 2012 reopen a gap.
  • 3. OPT delivers a considerably narrower output gap than the historical output gap and an unemployment rate consistently below the historical rate—as much as 0.8 percentage point lower in 2010 and 2011.
  • 4. In summary, OPT involves an aggressive response to the negative shocks in terms of the length of time the policy rate forecast is at the effective lower bound. It would quickly move the economy away from the deflation dark corner and closer to potential output and full employment.
  • 5. The overshoot in the inflation rate with OPT may be regarded as a drawback. And the 2010–11 increase in the prices of oil and food exacerbates the cycle in headline inflation. In our view, the prospect of a medium-term overshoot is acceptable, as, over time, the strategy would involve deviations on both sides of the target. Such a pattern is evident in Figure 9.7, and is in line with the Canadian experience of inflation targeting and the maintenance of a firm nominal anchor (see Kamenik and others 2013).

Fiscal Stimulus

The simulations in Figure 9.8 investigate the extent to which more expansionary policies in the aftermath of the global financial crisis might have helped achieve policy objectives. The assumed shock involves a fiscal stimulus equivalent to 1 percent of GDP and a cut in the policy rate from 0.25 to –0.5 percent (reflecting the Bank of Canada’s latest estimate of the effective lower bound). As before, each policy simulation refers to a forecast as of the second quarter of 2009. All cases considered are under the loss-minimizing strategy.

Figure 9.8.Optimal Control with Negative Interest Rate or Fiscal Backstop, 2009–13

Source: Authors’ simulations.

Note: OPT = optimal control.

Key aspects are as follows:

  • 1. Under the negative interest rate case (blue line), the policy rate is cut to the new floor and stays there a little less time than the base case with the 0.25 percent effective lower bound (red line). The lower rate causes a quick rise in the price of foreign exchange; these two changes close the output gap faster than the control. Because the nominal rate declines more, the decline in the real interest rates requires a smaller overshoot of inflation than in the base case. These changes are relatively modest compared with those achieved at the positive effective lower bound.
  • 2. Fiscal policy has a more direct impact on the economy than monetary policy. The results are shown in the cross-hatched lines. Because fiscal policy works through the demand channel more directly, and is less reliant on the expectations channel, the implied inflation overshoot is smaller than in the baseline. The fiscal stimulus does appreciate the Canadian dollar relative to the base case—in line with the classic Mundell-Fleming result for fiscal policy in a small economy with perfect capital mobility. However, in this model, unlike in Mundell-Fleming, fiscal policy is effective in increasing output because monetary policy keeps its focus on the objectives for inflation and the output gap and holds the interest rate at the effective lower bound. The exchange rate decrease relative to control is not large enough to choke off the stimulus. As Lane (2016) has pointed out, amid sustained weak aggregate demand, relying primarily on monetary policy to provide stimulus may lead to financial vulnerabilities that macroprudential policy cannot, or should not, offset. In such circumstances, fiscal policy may be called upon to provide stimulus, particularly since it is likely to be more effective at low interest rates.

Alternative Scenario: Linear Policy Reaction Function, Backward-Looking Expectations

This illustrative case shows investigation into a situation where monetary policy places less emphasis on the avoidance of large risks and where the credibility of the inflation target is not strong. The specific assumptions are the following:

  • Monetary policy follows an IFB reaction function
  • Expectations put a high weight on lagged inflation, such as because of imperfect credibility of the inflation target (Annex 9.2 gives detailed assumptions of this exercise).

The IFB reaction function does not have the same aversion to dark corners as the quadratic loss function, and will not lead to especially sharp corrective actions against negative shocks in the vicinity of deflation and the effective lower bound. Backward-looking expectations would reflect imperfect credibility of the announced inflation objective. If the target is not hit for a prolonged period, people are more likely to believe the rate they observe than the rate the central bank would like.

Negative shocks in this situation have bad results (Figure 9.9). Relative to history, starting in the second quarter of 2009 the output gap would have been wider, unemployment higher, and inflation lower. The counterfactual policy interest rate is lower for a couple of years. This does not reflect a more aggressive policy, but an endogenous response to the weaker economy.

Figure 9.9.Inflation-Forecast-Based Reaction Function and Backward-Looking Inflation Expectations, 2009–13

Source: Authors’ simulations.

Note: IFB = inflation-forecast-based.


Canada has a strong and well-proven inflation-forecast-targeting regime. Inflation expectations have been stable at the target rate of 2 percent for more than two decades. Core elements of this achievement have been the credibility of the target, which has been reinforced by sound monetary policy decisions, and the flexible exchange rate, which has helped stabilize the economy in the face of foreign disturbances, including large fluctuations in the commodity terms of trade.

However, the framework could be strengthened, especially in its capacity for avoiding dark corners. The case is strong for the Bank of Canada to use conventional forward guidance—that is, to publish its forecast of the short-term interest rate path as part of the information it releases following each of the eight annual policy decision meetings. Such an increase in transparency would strengthen the monetary policy framework for good times and times of greater economic instability. It would also improve accountability for monetary policy, in that the bank would be able to account openly for its interest rate decisions, against the guideline of the forecast path, justifying divergences from the path in terms of specific unexpected developments.

After the 2014–15 collapse of the boom in oil and other commodities, and the subsequent recession in the domestic energy industry, the Bank of Canada left open the options of unconventional policy instruments and a negative policy interest rate. However, these options have their own limitations and as yet uncertain effectiveness. Estimates of the equilibrium world real interest rate have been falling since the global financial crisis, in view of the lackluster performance of global output and low inflation. Various recent estimates are about zero (Summers 2015). This has implications for the framework of monetary policy and for fiscal policy.

If the 2 percent inflation target was right when the equilibrium real interest rate was 2 percent, is it still right when the equilibrium rate is near zero? The effective lower bound on the nominal interest rate would then impose a floor of about –2 percent on the gap between the actual and equilibrium real interest rate, which would not represent strong resistance to a downturn of typical cyclical amplitude. An increase of 1 percentage point in the inflation target, to 3 percent, would provide that much more space, still not a lot, for expansionary monetary policy.

However, merely announcing a higher target would not be enough—actions would be needed to get there—and the issue of how to achieve the more ambitious target would remain, especially given the firmness of expectations in Canada at 2 percent. Moreover, considering the price stability mandate for monetary policy, and the general performance of the economy over the past quarter-century, Canadian policymakers would reasonably be loath to recommend such a step.

From this viewpoint, an expansionary fiscal policy offers a better alternative for dealing with further negative shocks when monetary policy is constrained by the effective lower bound. And it would avoid any need to question the 2 percent inflation target, which has served well for a quarter-century as a firm nominal anchor to the economy.

Annex 9.1. Policy Credibility: Exchange Rate and Asset Prices as Shock Absorbers or Amplifiers

The risk-adjusted uncovered interest parity condition

This condition, under perfect foresight, may be written as

where it is domestic interest rate, itf is foreign interest rate, u t is domestic risk premium, st is nominal price of foreign exchange. That is, the future change in the exchange rate compensates for any interest differential, such that the return adjusted for change in the exchange rate and the risk premium is the same in either currency.

One period ahead:

Going forward:


such that this holds for any time t + k

Summing up all the equations from time t to t + k, yields

or equivalently,

Rearranging the equation gets

The same condition holds in real terms,

where rt is real interest rate, and zt is real exchange rate defined as nominal exchange rate adjusted for the foreign (ptf) and domestic (pt) price differential,

Real Exchange Rate as Shock Absorber

In normal times with active policy, a negative demand shock reduces inflation in the short term, but does not affect the long-term real exchange rate (zt+k+1). An inflation-forecast-targeting central bank is expected in normal times to reduce the policy rate sufficiently to steer inflation back to target. This expectation would, through the uncovered interest parity condition, lead to an immediate depreciation of the currency: the spot price of foreign exchange has to rise to the point that the expected decrease from then on compensates for the lower domestic interest rate.

Under a credible regime of aggressive policy responses, the expected medium-term inflation rate would also increase.12 The decline in real interest rates would be greater than that in nominal rates. At the effective lower bound, the current nominal interest rate cannot go any lower, but under the aggressive regime people would expect the future nominal interest rate to be at the effective lower bound for longer, and because of the anticipated increase in inflation, real interest rates would decline. Thus, in both normal times and at the effective lower bound, there is (Σj=0k+rt+j). Given that the long-term real exchange rate (zt+k+1) and expected paths for foreign real interest rates and domestic risk premium Σj=0k(rt+jf+ut+j) do not change, this would result in a real depreciation (↑zt),

This helps support demand, through both exports and domestic expenditure switching (from foreign goods to domestic goods).

Real Exchange Rate as Shock Amplifier

At the effective lower bound, the exchange rate can act as a shock amplifier. If policy is passive, and not credible, following a negative demand shock, people would expect the inflation rate in the future to be lower. Current and future short-term real interest rates could increase (Σj=0k+rt+j), resulting in a real appreciation (↓ zt):

This would reduce net exports and further deepen the recession.

Asset Prices as Shock Absorber or Amplifier

A similar argument holds for other asset prices such as equity prices. A credible aggressive policy response would cause increases in equity prices (through the positive impact on profits of currency depreciation, and the effect of a lower real discount rate on asset valuations). A noncredible, passive response would do the reverse. Thus, depending on the policy regime, asset prices too may act as an absorber or an amplifier of the impact of shocks.

Appendix 9.2. The New-Keynesian Model for Canada

1. IS Equation

The output gap (ŷt) is defined as the difference between the log-level of output (yt and potential output (y¯t). The investment-savings (IS) equation relates Canada’s output gap ŷt to past and expected future output gaps, the deviations of the lagged one-year real interest rate (r4t) and the real effective exchange rate (reert from their equilibrium values, and the-rest-of-the-world output gap (y¯tWorld) The terms-of-trade gap (tott^) also affects the output gap in a significant way.

2. Phillips Curve

In the Phillips curve, the core inflation rate (πtC) depends on inflation expectation (EπtC) and past year-on-year core inflation (π4t1C), with coefficients on both terms adding up to one. The lagged term reflects the intrinsic inflation inertia, resulting from contracts, costs of changing list prices and so on. Inflation expectation is pinned down by both the model-consistent solution of the year -over-year inflation one year ahead (π4t+4C), as well as the inflation target (π*), with the latter one having a small weight.13 Core inflation depends on lagged output gap in a nonlinear way.

Core inflation also depends on the rate of real effective exchange rate depreciation, as well as on the deviation of the real effective exchange rate from its equilibrium value, as a real depreciation raises the domestic cost of imported intermediate inputs and final goods, creating upward pressure on prices.

Finally, we allow some small pass-through from oil and food price inflation to core inflation. This is captured by adding the two terms on the real price of oil and food adjusted for real exchange rate effects.

3. Policy Interest Rate: Reaction Function Options

Linear Inflation-Forecast-Based (IFB) Reaction Function

The equation is a fairly standard IFB reaction function:

In contrast to the conventional Taylor rule, the inclusion of the three-quarter-ahead inflation projection (π4t+3Candπ4t+3H) in the IFB reaction function implies that it discounts shocks to the system that are expected to reverse within the three-quarter policy horizon. More generally, the reaction function allows the central bank to take account of all relevant information available to it on future developments over the three-quarter forecast horizon.

Loss Minimizing Strategy—Risk Management

This strategy chooses the interest rate path to minimize the discounted current and future losses from inflation deviations from the target, output gaps, and changes in the policy rate. The loss function incorporates the principal objectives of the central bank—expressing an aversion to deviations of output and inflation from desired values that grows ever larger as these deviations increase.

The quadratic formulation implies that large errors or deviations are more important in the thinking of central banks than small errors or deviations. The term with the squared change of the policy interest rate prevents very sharp movements in the policy interest rate, which would otherwise occur in the model on a regular basis in response to shocks. Central banks in practice do not typically change interest rates in large steps, and there are sound theoretical reasons for this. By taking account of both current and expected future values of output and inflation, this formulation has the central bank incorporate into its decisions any information currently available that may affect its objectives over the next few quarters.

Effective Lower Bound

Under both cases, the interest rate is subject to an effective lower bound constraint (ifloor), which is assumed to be 0.25 percent in the historical simulation.14

4. Real Interest Rates and Real Exchange Rates

The real interest rate (rt) is defined as the nominal interest rate minus the expected core inflation (πt+1C).

The bilateral real exchange rate between Canada and the United States (rt) is defined in terms of Canadian core CPI (ptC), and in such a way that an increase means a depreciation in the Canadian dollar. The real exchange rate is broken down into an equilibrium trend (z¯t) and deviation from that trend (z^t) The equilibrium real exchange rate is assumed to be determined by the equilibrium terms of trade (z¯ttot)

The real effective exchange rate that enters the output gap equation is the trade-weighted bilateral real exchange rates of Canada versus seven regions in the world (United States, euro area, Japan, China, emerging Asia, Latin America, and the rest of the world). The breakdown of the regions is consistent with the Global Projection Model.15

Risk-Adjusted Uncovered Interest Parity Condition

The risk-adjusted uncovered interest parity condition links the bilateral exchange rate between Canada and the United States with the interest rates in the two economies (itanditUS)

The equation allows the expected exchange rate (Est+1) to be a linear combination of the model-consistent solution (st+1) and backward-looking expectations (st-1) adjusted for the trend exchange rate depreciation (2[Δz¯t(π*,USπ*)/4]). The factor ¼, which multiplies the inflation differential (π*,us – π*), de-annualizes the inflation rates, which are expressed in annual terms, while the factor 2 is necessary as the nominal exchange rate in the past period (st-1) is extrapolated two periods into the future using the steady-state growth rate in the nominal exchange rate (Δz¯t(π*,USπ*)/4). Conversely, in the condition that links Canadian and US interest rates, the factor 4 before the expected depreciation (Est+1 – st) annualizes the expected quarterly depreciation rate, making it consistent with the interest rate quoted on the annual basis. A time-varying variable (σtctry) is included to account for shocks to country risk premium. Terms-of-trade shifts (σttot) is also an important factor that affects movements in the nominal exchange rate.

As the terms-of-trade premium should disappear when the economy is in the equilibrium, the following condition holds:

5. Relative Prices

Headline inflation is affected by the dynamics of relative price movements (core CPI (ptC) relative to headline CPI (ptH)). In the long term the overall (headline) inflation is assumed to be equal to the underlying (core) inflation, though it can diverge over prolonged periods, when there is a trend in the relative prices of noncore items (mortgage interest rates, unprocessed food, energy). The dynamics of relative prices (rpt) are modeled as the sum of the relative price trend (rp¯t) and the relative price gap (rp^t). The relative price gap depends on the real price of oil and food in the international markets adjusted for exchange rate effects, while the relative price trend growth is assumed to be an autoregressive process with mean zero. The parameters in the relative price gap equation are calibrated based on various information, such as the weights of energy and food in the CPI basket, and the degree and time profile of the pass-through from energy and food inflation to headline inflation.

6. Term Structure of Interest Rates

The model allows for long-term bond yields to shed light on the equilibrium real interest rates. Let itGov,k be the nominal government bond yield with a maturity of k quarters, where k could be 4, 8, 20, or 40. The bond yield is equal to the average expected short-term interest rates k quarters into the future plus a term (σtTerm,k) that captures both government bond premium (same for bonds with all maturity) and term premium (a premium that increases with the maturity). A shock at the end of each equation (ϵtGov,k) reflects measurement errors.

7. Unemployment Rate

The unemployment rate (ut) is characterized by a “gap version” of Okun’s law. The equation implies that a 1 percentage point increase in the unemployment gap (u^t) is associated with approximately 2 percentage point decrease in the output gap. The non-accelerating inflation rate of unemployment (NAIRU) (u¯t) is assumed to follow a stochastic process that has both shocks to the level and to the growth rate.

8. Potential Output

The potential growth rate (Δy¯t) is assumed to converge to its steady-state level (Δy¯ss) in the longer term. However, it can deviate from the steady-state level for prolonged periods.

9. The Rest of the World

The Canadian economy is linked to the rest of the world through both the trade linkage and the financial linkage. The rest-of-the-world output gap relevant for the Canadian economy is defined as a weighted average of output gaps in the seven regions (United States, euro area, Japan, China, emerging Asia, Latin America, and the rest of the world), using export shares as weights.

The equilibrium real interest rate in Canada is closely linked to that in the United States.

10. Commodity Terms of Trade

The real price of oil (rptOil) is defined as the global oil price (ptOil) in US dollars relative to the US CPI (ptUS). In the equilibrium, the real price of oil is assumed to grow at a rate of zero, although the actual growth rate can deviate from zero for long periods. The real price of oil gap (rp^tOil) defined as the difference between the real price of oil and its equilibrium value, is modeled as an autoregressive process with a shock.

A similar modeling strategy is followed for the real price of food.

The terms-of-trade gap (tott^) for Canada is determined by the real price of oil gap (rp^tOil) and the real price of food gap (rp^tFood). The coefficients of the two terms represent the shares of these two commodities in Canada’s GDP.

The real exchange rate depreciation consistent with changes in the terms of trade (Δzttot) is related to movements in the real price of oil (ΔrptOil) and food (ΔrptFood) adjusted for their relative size in total exports. The same condition holds for those variables at their respective equilibrium values.

The terms-of-trade premium that goes into the uncovered interest parity condition (σttot) is modeled as the “surprise” component in the real exchange rate movement consistent with the terms of trade.


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For a discussion of the history of inflation targeting in Canada, see Lane (2015).


Mendes (2014) estimates the neutral real interest rate in Canada at 1–2 percent, which translates to 3–4 percent in nominal terms. A neutral rate as high as 4 percent would imply that monetary conditions have been extremely expansionary since 2009, because the actual policy rate has not been above 1 percent. But this is difficult to square with subdued growth and inflation. If the latter are attributed to long-lasting economic headwinds, for operational purposes it would be simpler to regard these as part of the environment, rather than shocks, and to reduce the estimate of the neutral rate correspondingly.


Theory supporting this assertion can be found in Eggertsson and Woodford (2003) and Woodford (2005), for example.


In Canada, the effective lower bound has not been tested in practice, but a recent Bank of Canada estimate puts it at about –0.5 percent (Witmer and Yang 2015).


Svensson (2001) emphasizes these expectations mechanisms as a way to jump-start the economy in Japan.


This has been described by some policymakers as finding a path that “looks good” (Svensson 2002; Qvigstad 2005).


This corresponds to the observation by Eggertsson and Woodford (2003): “In fact, the management of expectations is the key to successful monetary policy at all times, not just in those relatively unusual circumstances when the zero bound is reached.” See also Woodford (2005).


Annex 9.2 outlines the model structure.


A rolling filter determines the estimates of latent variables.


The shocks are estimated from historical filtration of the model.


A regime that targets the path of the price level would systematically produce this kind of response (Svensson 1999).


The sensitivity analysis (Figure 9.9) looks at the implications of more inertia in the inflation process, in other words, a case where λ1 is reduced from 0.75 in the base case to 0.65, and at the same time the weight on the inflation target (1 – λ7) is reduced to 0.


Historically the effective lower bound is assumed to be 0.25 percent. Recently, the central bank revised its estimate of the effective lower bound down to –0.5 percent. In simulations, the implications of the new effective lower bound are examined.


See Carabenciov and others (2008) and Blagrave and others (2013) for the Global Projection Model.

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