Back Matter
  • 1, International Monetary Fund
  • | 2, International Monetary Fund


  • Alichi, A., J. Benes, J. Felman, I. Feng, C. Freedman, D. Laxton, E. Tanner, D. Vavra, and H. Wang, 2015a, “Frontiers of Monetary Policymaking: Adding the Exchange Rate as a Tool to Combat Deflationary Risks in the Czech Republic,IMF Working Paper No. 15/74.

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  • Bank of England, 2013, “Monetary Policy Trade-Offs and Forward Guidance,August.

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  • Charbonneau, K. and L. Rennison, 2015, “Forward Guidance at the Effective Lower Bound: International Experience,Bank of Canada Staff Discussion Paper 2015–15.

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  • Clinton, K., C. Freedman, M. Juillard, O. Kamenik, D. Laxton, and H. Wang, 2015, “Inflation-Forecast Targeting: Applying the Principle of Transparency.IMF Working Paper No.15/132.

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  • Eggertsson, G. B., and M. Woodford, 2003, “The Zero Bound on Interest Rates and Optimal Monetary Policy,Brookings Papers on Economic Activity, 1:2003.

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  • Engen, E., T. Laubach, and D. Reifschneider, 2015, “The Macroeconomic Effects of the Federal Reserve’s Unconventional Monetary Policies,Finance and Economic Discussion Series 2015-005, Federal Reserve Board.

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  • Filardo, A. and B. Hoffmann, 2014, “Forward Guidance at the Zero Lower Bound,BIS Quarterly Review, March.

  • FOMC, 2012, Board of Governors of the Federal Reserve Press Release, January 25.

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  • Kamenik, O., H. Kiem, V. Klyuev, and D. Laxton, 2013, “Why is Canada’s Price Level So Predictable?Journal of Money Credit and Banking, 45(February), pp. 7185.

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  • Johannsen, B. K. and E. Mertens, 2016, “The Expected Real Interest Rate in the Long Run: Time Series Evidence with the Effective Lower Bound,FEDS Notes.

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  • Lane, T., 2015, “Inflation Targeting—A Matter of Time,Bank of Canada. Conference presentation, Halifax, Nova Scotia October.

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  • Mendes, R.R., 2014, “The Neutral Rate of Interest in Canada,Bank of Canada Discussion Paper 2014–5.

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  • Rachel, L. and T. D. Smith, 2015, “Secular Drivers of the Global Real Interest Rate,Bank of England Staff Working Paper No. 571.

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  • Svensson, L. E. O., 1997, “Inflation Forecast Targeting: Implementing and Monitoring Inflation Targets,European Economic Review, Vol. 41.

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  • Svensson, L. E. O., 2002, “Monetary Policy and Real Stabilization,” in Rethinking Stabilization Policy, A Symposium Sponsored by the Federal Reserve Bank of Kansas City, Jackson Hole, Wyoming.

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Appendix I. Policy Credibility: Exchange Rate and Asset Prices as Shock Absorbers or Amplifiers

The risk-adjusted uncovered interest parity (UIP) condition

This condition, under perfect foresight, may be written as


where it is domestic interest rate, itf is foreign interest rate, ut 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 we have


Going forward we have


such that this holds for any time t


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


or equivalently,


Rearranging the equation, we get


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

Under normal times with active policy, a negative demand shock reduces inflation in the short run, but does not affect the long-run real exchange rate (zt+k+1). An IFT central bank is expected in normal times to reduce the policy rate sufficiently to steer inflation back to target. This expectation would, through the UIP 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 ELB, the current nominal interest rate cannot go any lower, but under the aggressive regime people would expect that the future nominal interest would be at the ELB for longer, and because of the anticipated increase in inflation, real interest rates would decline. Thus in both normal times, and during the ELB, we have (Σj=0krt+j). Given that the long-run real exchange rate (zt+k+1) and expected paths for foreign real interest rates and domestic risk premium Σj=0k(rt+jf+μt+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 ELB, 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=0krt+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 lower real discount rate on asset valuations). A non-credible, passive response would do the reverse. Thus depending on the policy regime, asset prices too may act as an absorber or an amplifier for the impact of shocks.

Appendix II. The New-Keynesian Model for Canada

A.II.1. IS Equation

The output gap (yt) is defined as the difference between the log-level of output (yt) and potential output (y¯t). The IS equation relates Canada’s output gap (yt) to past and expected future output gaps, the deviations of the lagged one-year real interest rate (r 4t) and the real effective exchange rate (reert) from their equilibrium values, and the-rest-of-the-world output gap (ytWorld). The terms-of-trade gap (tott) also affects the output gap in a significant way.


A.II.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, etc. Inflation expectation is pinned down by both the model-consistent solution of the year-on-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 non-linear way. Core inflation also depends on the rate of real effective exchange rate depreciation, as well as 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.


A.II.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+3C and π4t+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 inflations deviation 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 chocks. 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.


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


A.II.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 (zt) 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 (U.S., 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 (GPM).15

Risk-adjusted UIP Condition

The risk-adjusted uncovered interest parity condition links the bilateral exchange rate between Canada and the U.S. with the interest rates in the two economies (it and itUS).


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*,USπ*) de-annualizes the inflation rates which are expressed in annual terms, while the factor 2 is necessary as we extrapolate the nominal exchange rate in the past period (st-1) 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 U.S. 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:


A.II.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 run the overall (headline) inflation is assumed to be equal to the underlying (core) inflation, though it can diverge over prolonged periods of time, when there is a trend in the relative prices of non-core 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 (rpt). 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.


A.II.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 which increases with the maturity). A shock at the end of each equation (ɛtGov,k) reflects measurement errors.


A.II.7 Unemployment Rate

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


A.II.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 of time.


A.II.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 (U.S., 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 U.S.


A.II.10. Commodity Terms of Trade

The real price of oil (rptOil) is defined as the global oil price (ptOil) in U.S. dollars relative to the U.S. 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 of time. The real price of oil gap (rptOil), defined as the difference between the real price of oil and its equilibrium value, is modeled as an autoregressive process with a shock.


We follow similar modeling strategy for the real price of food.


The terms-of-trade gap (tott) for Canada is determined by the real price of oil gap (rptOil) and the real price of food gap (rptFood). 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 (ΔrptOit) and food (ΔrptF00d), adjusted for their relative size in the total export. The same condition holds for those variables at their respective equilibrium values.


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


Kevin Clinton and Ondra Kamenik are visiting scholars in the Research Department. We thank Cheng Hoon Lim for useful comments as well as participants at seminars at the IMF and the Department of Finance Canada. We also thank Yiqun Li for his excellent research assistance.


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 the 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, e.g., Eggertsson and Woodford (2003) and Woodford (2005).


In Canada, the ELB has not been tested in practice, but a recent Bank of Canada estimate puts it at about -0.5 percent (Witmer and Yan, 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, and 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).


Appendix II 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).


In the sensitivity analysis (Figure 11), we look 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 reduce to 0.


Historically the effective lower bound is assumed to be 0.25 percent. Recently the Bank has revised down its estimate of the effective lower bound to be -0.5 percent. In simulations we look at the implications of the new effective lower bound.