Assessing the Impact of the Bank of Canada’s Government Bond Purchases

Introduction

In the wake of the 2008–09 global financial crisis, several central banks introduced large-scale asset purchase programs, commonly referred to as quantitative easing (QE). The goal of these QE programs is to address financial market strains and to provide additional monetary stimulus once policy interest rates are at, or close to, their effective lower bounds. QE has therefore become an important tool used by many central banks around the world to affect monetary conditions once traditional interest rate tools are constrained. Although the Bank of Canada did not employ QE in response to the global financial crisis, QE is nonetheless part of the Bank’s framework for conducting monetary policy at low interest rates (Bank of Canada 2015).

In March 2020, the Bank implemented a federal government bond purchase program to address the financial and economic strains caused by the COVID-19 pandemic. Known as the Government of Canada Bond Purchase Program (GBPP), it was introduced as the Bank lowered its policy interest rate to its lower bound of 25 basis points (bps).1^, 2 The program began by purchasing a minimum of $5 billion Government of Canada (GoC) securities in the secondary market each week. These purchases were financed by increasing the size of settlement balances (known as “reserves” in other jurisdictions).3 The GBPP’s stated goal at the time was “…to address strains in the GoC debt market and to enhance the effectiveness of all other actions taken so far…” (Poloz 2020a). The Bank committed to continuing its purchases “…until the economic recovery is well underway.” As financial strains subsided, the purpose of the GBPP transitioned away from addressing financial strains. Instead, it became a tool to provide “…the necessary degree of monetary policy accommodation required to achieve the inflation target” (Bank of Canada 2020).

The pace of the Bank’s QE program decreased as economic conditions improved:

• On October 28, 2020, the Bank recalibrated the QE program to shift purchases toward longer-term bonds and reduced the pace to at least $4 billion a week.
• On April 21, 2021, the Bank adjusted the weekly net purchases of GoC bonds to a target of $3 billion. This reduction in the amount of incremental stimulus being added each week reflected the progress made in Canada’s economic recovery.
• On July 14, 2021, the target pace was adjusted to $2 billion per week.
• On October 27, 2021, the Bank ended quantitative easing and entered a reinvestment phase. During this phase, the purchase of GoC bonds was solely to replace maturing bonds so that the Bank’s holdings remained relatively stable over time.
• On April 13, 2022, the Bank announced that it was ending its reinvestment phase and would begin the process of quantitative tightening (QT).

By the end of the reinvestment phase, the GBPP had purchased approximately $340 billion of government bonds with a weighted average maturity of about six years. To put the pace and scale of the Bank’s asset purchase programs in perspective, Chart 1 compares the Bank’s balance sheet as a percentage of gross domestic product (GDP) with that of the Federal Reserve, the European Central Bank and the Bank of England. The chart highlights four notable observations:

• Unlike the other central banks, the Bank of Canada did not engage in QE following the global financial crisis. As a result, its balance sheet was much smaller than the balance sheets of the other central banks when the pandemic began.
• The pace of the Bank’s asset purchases following the onset of the pandemic was faster than the pace of balance sheet expansion in other central banks, normalizing by GDP. However, although the pace was faster at the beginning of the pandemic, the total amount of the Bank’s balance sheet expansion during the pandemic was smaller than that of the other central banks. In addition, much of the fast pace of the increase was due to lending operations; when we exclude those operations, the pace is similar.
• At its peak, the Bank’s balance sheet, as a percentage of GDP, was about half the size of the comparable measure for the other central banks.
• The Bank’s balance sheet has declined more than the others’ since its peak, largely for two reasons:
  • Several assets the Bank purchased (including GBPP and non-GBPP assets) were short-term in nature and therefore matured soon after QT began.
  • The Bank wound down its lending operations, while those of the other central banks are ongoing.

Chart 1: Changes in components of central banks’ balance sheets as a percentage of nominal GDP

Chart 1: Changes in components of central banks’ balance sheets as a percentage of nominal GDP

Sources: Board of Governors of the Federal Reserve System, European Central Bank, Bank of England and Bank of Canada
Last observation: December 2022

This was the first time the Bank used QE, and the amount needed during the pandemic was considerable. Therefore, it is crucial that we understand the impact of this monetary policy tool not only on financial markets but also on the economy. Johnson (2023) reviews all the Bank’s market operations related to the pandemic and provides some recommendations on how their design and implementation could be changed in the future. Arora et al. (2021) analyze intraday movements in GoC bond yields in the hour after the Bank first announced the GBPP on March 27, 2020, at 9 a.m. They find that the announcement of the GBPP had a strong and immediate impact, with 10-year benchmark GoC bond yields declining by about 10 bps immediately after the announcement.

The rest of this paper is organized as follows. First, we extend Arora et al.’s (2021) evaluation of the financial market impact of the GBPP by:

• considering a larger set of GBPP-related announcements
• investigating the impact of the GBPP on a broader range of financial market assets

We find that, across a large set of announcements, 10-year bond yields declined by about 20 bps, with similar declines for other maturities. Since the impact of the GBPP is likely larger than the announcement-related returns, in a back-of-the-envelope counterfactual we estimate that the GBPP may have had an impact of almost 80 bps on 10-year bond yields.

Second, using Zhang’s (2021) model, we use this counterfactual to estimate the impact of the GBPP on inflation and output.4 With an 80 bps impact on 10-year bond yields, the model counterfactual suggests that the GBPP had a peak impact of about 3% on real GDP and 1.8 annualized percentage points on inflation. Meanwhile, a counterfactual with a 20 bps impact on 10-year bond yields suggests a peak impact of about 0.6% on real GDP and 0.6 annualized percentage points on inflation.

Theory of quantitative easing

The objective of QE is to support aggregate economic activity when the traditional instrument of monetary policy—the short-term nominal interest rate—cannot be reduced further because it is constrained by the effective lower bound. The general idea is that asset purchases can reduce longer-maturity interest rates while the overnight rate is near zero. From a theoretical perspective, there are three potential channels through which QE can impact financial market prices and the economy.

Signalling channel

In this channel, QE announcements signal to market participants that the central bank has changed its views on current or future economic conditions (Bauer and Rudebusch 2014). Alternatively, QE announcements may convey information about changes in the monetary policy reaction function or in policy objectives, such as the inflation target. In such cases, investors may alter their expectations for the future path of the policy rate, perhaps by lengthening the period they expect short-term interest rates to be near zero.5 Sometimes, market participants anticipate a future path of interest rates based on the timing or implied sequencing of QE or QT. For example, if participants believe that the central bank will not raise the overnight rate from its lower bound until it stops QE or starts QT, then any announcement related to QE or QT can change expectations for interest rates.

Likewise, implied sequencing means that interest rate announcements can also influence expectations for QE. If participants expect QE to begin once the overnight rate approaches the lower bound, then rate cuts near the lower bound may increase their expectations for QE. This makes it challenging to measure the impact of QE, since participants may already have expectations for QE by the time the central bank officially announces a QE program.

Sometimes, QE announcements are accompanied by forward guidance announcements where the central bank “…provides direct information about the probable state of monetary policy in the future” (Sutherland 2023). In this sense, a central bank’s QE program may be interpreted as a signal of its commitment to maintaining its forward guidance policy.

Portfolio balance channel

For this channel to be effective, financial markets need some friction or segmentation. Otherwise, QE purchases would be neutral and would have no impact on asset prices (Wallace 1981).6 In effect, QE is the swap of one asset for another (Melzer 2010). The central bank removes government bonds from the market and replaces them with settlement balances (an asset for payment system participants). Under the assumption of complete and competitive markets, this asset swap should have no impact on asset prices. This is analogous to Ricardian equivalence (for debt versus taxes) and the theorem of Modigliani-Miller (for choice of financing structure of firms). The implication is that, in the absence of frictions or segmentation, the demand curve for long-term bonds would be flat.

Several types of models have introduced segmentation and frictions to demonstrate how QE can increase asset prices. Vayanos and Vila (2021) are often cited as a prime example of the portfolio balance channel. In their model, preferred-habitat investors invest only in bonds of a specific maturity (e.g., 10-year bonds). In addition, risk-averse arbitrageurs may invest across the entire maturity spectrum. In doing so, they are exposed to duration risk—the risk that interest rates will change. Since they are risk averse, they require compensation for bearing that risk in the form of a term premium on longer-term bonds. In Vayanos and Vila’s (2021) model, QE removes duration risk from the market and reduces the risk exposure of arbitrageurs, thus reducing the term premium on all bonds. The impact of QE is stronger when arbitrageurs are more risk averse. Indeed, in their model, QE would have no impact if arbitrageurs were risk neutral.

Several other factors may influence the effectiveness of the portfolio balance channel of QE. For instance, if interest rates are near their lower bound and are expected to remain there for an extended period, there is less duration risk in the market and the impact of QE may be smaller (King 2019). As well, the impact of QE may be smaller in a small open economy if there is a high degree of substitutability between domestic and foreign assets (Kabaca 2016; Diez de los Rios and Shamloo 2017).

To put this theory in perspective, Chart 2 illustrates how the Bank of Canada’s QE changed the portfolio holdings of market participants. Given the fiscal policy response to support households and businesses at the onset of the pandemic, there was a sharp increase in the gross quantity of government bonds outstanding, especially bonds with less than five years of maturity. Absent QE, the portfolio balance theory suggests that this increase in government bonds outstanding would have increased both duration risk in the market and the term premium on government bonds. Chart 2 also shows that the Bank’s QE absorbed most of this increase in the gross supply of government bonds outstanding. The fiscal policy response and the Bank’s QE were reacting to the same worrisome economic and financial conditions, which is why government debt and QE both increased at the same time. However, because of the Bank’s QE, the market did not need to absorb the extra duration risk from the government’s issuance. If the market had had to absorb this extra risk, arbitrageurs would have demanded more compensation to hold long-term bonds, which means that the term premium would have been higher.

Chart 2: Ownership of Government of Canada bonds

Chart 2: Ownership of Government of Canada bonds

Source: Bank of Canada
Last observation: January 31, 2023

Liquidity channel or market functioning channel

QE purchases can increase asset prices by reducing the liquidity risk premium. This premium results in a higher yield and compensates investors for the risk that they would have to prematurely liquidate their long position in a security at an unfavourable price. Unlike the portfolio balance channel, in which QE impacts prices upon announcement, in the liquidity channel, prices (and liquidity metrics) generally move when the QE purchases are made (Vissing-Jorgensen 2021).

QE can help restore market functioning when the capacity of dealers to intermediate in the market is impaired and causes the liquidity risk premium to rise abruptly (Duffie and Keane 2023). Large-scale asset purchases for market functioning can occur even when the overnight rate is not at its lower bound. Duffie and Keane (2023) point out that, although monetary policy and market functioning goals are usually well aligned, this is not always the case. For example, in autumn 2022 the Bank of England purchased gilts at the same time that it was tightening monetary policy.

Christensen and Gillan (2022) posit that the liquidity risk premium is the result of a bargaining game between buyers and sellers, and that large-scale asset purchases increase the bargaining power of sellers by providing a committed buyer. They argue that this increase in bargaining power increases the price and thus lowers the yield of the bond (i.e., it reduces the liquidity risk premium) because those selling are less likely to be squeezed.

Transmission of quantitative easing

The ultimate goal of QE is to stimulate broader economic activity to help achieve the inflation target. Figure 1 illustrates how QE may transmit to the broader economy. In the first step of the transmission, all three channels increase financial market prices and reduce yields. Each channel may impact a different set of financial market prices. The signalling channel is more likely to have a greater impact on bonds with shorter maturities (i.e., less than two or three years). The portfolio balance channel, meanwhile, may have a greater impact on longer-maturity bonds when the central bank removes duration risk. QE may also impact the specific bonds being purchased if it helps to restore market liquidity. QE purchases not only increase the price of government bonds but also influence the prices of other assets, such as foreign bonds, corporate bonds and foreign exchange (e.g., Neely 2015; Diez de los Rios and Shamloo 2017; Krishnamurthy and Vissing-Jorgensen 2011). This rise in asset prices increases wealth and reduces borrowing costs for both households and firms. In turn, households and firms increase their investment and consumption, raising both GDP and inflation.

Figure 1: Stylized transmission of quantitative easing

It becomes more difficult to measure its impact as QE moves further along the transmission path. Changes in financial market prices in a short window around QE announcements can easily be observed, but the same cannot be said for changes in macroeconomic variables. Macroeconomic variables are reported less frequently (e.g., monthly or quarterly), and inflation and GDP respond to monetary policy with a lag. One approach to measuring the impact of QE on macroeconomic variables is to include asset purchases in a vector autoregression (VAR) model with sign and zero restrictions (e.g., Weale and Wieladeck 2022). Another approach is to incorporate financial market frictions directly into a dynamic stochastic general equilibrium (DSGE) model (e.g., Chen, Cúrdia and Ferrero 2012). As above, there is a risk with empirical work that estimates are averages of different state-dependent effects at different times. In DSGE models, a risk is that estimation or calibration is primarily reflective of “normal times” and that in periods of Knightian uncertainty, estimates could have particularly large error bands.

Financial market impact

At least two main challenges make measuring the impact of QE on financial markets difficult. First, understanding the impact of QE on government bond yields requires understanding the slope of the demand curve for long-term government bonds. That is, how much does a change in the quantity of government bonds impact the yield that the market demands to hold those bonds? The challenge is that the slope of the demand curve is not easily observed and likely not constant. The slope may be relatively flat when the outstanding quantity of bonds is moderate but become steeper when the quantity of bonds grows. Moreover, this demand curve may shift over time and become steeper in times of financial stress and increasing risk aversion. Krishnamurthy and Vissing-Jorgensen (2012), for instance, examine the aggregate demand curve for US Treasury debt and show that it does not have a constant slope. Further, in an update on his website, Krishnamurthy shows that this demand curve has shifted since the global financial crisis due to an increase in demand for safe assets.

Second, to understand the full impact of QE on financial markets, we need to understand the counterfactual scenario of how financial market prices would have evolved without QE. The effect of QE is the difference between actual prices and prices in this counterfactual scenario. Since this counterfactual scenario cannot be observed, most studies quantify the impact of QE on financial market prices by measuring how those prices respond to QE announcements made by the central bank. Measuring QE using this approach assumes that financial market prices just before the announcement are a good approximation of the counterfactual scenario of no QE. This implies that QE was completely unexpected, since financial market prices should reflect the market’s expectations for QE.

For example, it is unlikely that the GBPP was completely unexpected when the Bank first announced it, given that other countries had previously introduced QE programs, and given that the overnight rate had already been moved toward its lower bound. Further, market participants probably formed expectations about the size of the GBPP after these announcements were made. For instance, it may be the case that as long as purchases were being made (especially in the early period when the Bank was purchasing at least $5 billion per week), market participants were increasing their expectations for the duration (and hence the overall size) of the GBPP.

Figure 2 illustrates these challenges in a supply and demand framework. In this framework, the demand curve slopes upward since we are examining yields and not prices. Suppose that, before the pandemic, the supply of bonds is given by the vertical supply curve S_A. The equilibrium bond yield is given by its level at point A in the diagram. Given the pandemic programs, the market expects the government to expand supply so that the supply curve moves to the right to curve S_B. In the absence of any other measures, bond yields increase to the level at point B in the diagram. However, because market participants also expect that there is a high probability the central bank will implement a QE program that will offset some of this supply, the expected supply curve does not shift to curve S_B but instead shifts to curve S_C. So, we do not observe yields at the level at point B in the diagram, but only observe yields at the level at point C. Once the central bank officially announces a QE program, expectations for supply shift to the left to curve S_D.

The impact of QE we are interested in measuring is the difference between the counterfactual yields when there is no QE and the actual yields. In Figure 2, this means we are interested in the difference between the yields at point B and the yields at point D. Unfortunately, when we measure the yield changes around QE announcements, we measure only the difference between yields at point C and yields at point D. Further, it is a challenge to extrapolate the announcement impact to get the full impact because:

• We don’t know how much markets changed their expectation of QE when the announcement was made.
• The slope of the yield curve likely changes, so extrapolating from the flatter (steeper) part of the demand curve may underestimate (overestimate) the impact.

We employ three strategies to mitigate these challenges, each with advantages and disadvantages. In our first strategy, we examine changes in long-term bond yields that occurred around a much broader set of Bank of Canada communications, including some announcements before the Bank officially announced its QE program. These communications include not only our interest rate announcements but also speeches made by Governing Council members and reports on results of operations. This strategy is not perfect:

• Market expectations may still evolve outside these announcements.
• Some of the yield changes following the announcements may be due to non-QE factors.

However, these communications may have changed expectations for QE, and including this broader set allows us to potentially capture those changes.

Our second strategy looks at the reaction of US interest rates to the Federal Open Market Committee’s announcement of its first QE program following the 2008–09 global financial crisis. We take this second approach because this QE announcement was more unexpected and therefore has a better chance of measuring the full yield impact of a QE program. However, this is not an apples-to-apples comparison since the Federal Reserve’s first QE program was implemented in response to a different kind of crisis (i.e., a banking crisis, not a pandemic) and purchased mortgage-backed securities in addition to US Treasuries.7 Further, the impact of QE in a small open economy may be different from its impact in a large economy (Diez de los Rios and Shamloo 2017).

Our third strategy looks at three announcements in which the Bank of Canada reduced its QE program. Although these announcements were largely expected, we assume that each announcement got people to expect a $1 billion weekly increase in supply 13 weeks sooner than they otherwise would have started expecting it (the period of one Monetary Policy Report and interest rate decision cycle). A reduction in purchases of $13 billion per announcement resulted in a total reduction of $39 billion across the three announcements.8 We then scale up to get a yield impact for the total program size of about $340 billion.

Event study analysis

We conduct an event study by analyzing the reactions of financial markets to Bank of Canada policy announcements on dates between March 2020 until October 2021. Our sample covers three distinct periods:

• Pre-GBPP announcements, covering two announcements when the Bank made interest rate cuts on March 3, 2020, and March 14, 2020.
• GBPP-related announcements, which include five announcements between March 27, 2020, and September 9, 2020.
• Reduction-related announcements, including nine announcements between October 28, 2020, and October 27, 2021.

We include pre-GBPP announcement dates because market participants may have already developed expectations for QE before March 27, 2020, due to the severity of the economic shock and the fact that interest rates were approaching their lower bound.9 Analyzing reduction-related announcements allows us to assess the impact of a decrease in expectations for stimulus as economic conditions improved. We focus our analysis on announcements rather than operations, under the assumption that efficient financial markets should quickly incorporate the impact of the Bank’s news into prices.10

We look at the changes in various financial asset prices from 10 minutes before to 20 minutes after an announcement is made. Using a narrow event-study window ensures that the asset prices are less likely to be influenced by any other significant (non-QE) macroeconomic events, thereby enhancing the accuracy of our estimation. For example, Prime Minister Trudeau made a speech announcing a large fiscal package on March 27, 2020, at 11:15 a.m., which was just a few hours after the Bank’s GBPP announcement. The fiscal package announcement would have an impact on expected GoC bond supply and, consequently, bond yields. Furthermore, our methodology of using a narrow window is consistent with the literature analyzing the impact of central bank announcements on financial markets (Gürkaynak, Sack and Swanson 2005; Swanson 2017; Feunou et al. 2017).

To identify the impact of QE, we examine the changes in several financial instruments. The first financial asset we look at is the 90-day bankers’ acceptance futures (BAX) contracts that trade on the Montréal Exchange. We use BAX to measure market participants’ expectations of future short-term interest rates. Specifically, we calculate the change in the three-month Canadian BAX contract that expires between two and three quarters from the time of each individual announcement.11 Using a similar method, we also calculate the changes in the yields of 2-year, 5-year and 10-year GoC benchmark bonds obtained from the Market Trade Reporting System 2.0,12 the price of S&P TSX 60 standard futures that trade on the Montréal Exchange, and the USD/CAD exchange rate obtained from Refinitiv.

We start by examining the change in market prices around the Bank’s two interest rate announcements in early March 2020 (we label these announcements “pre-GBPP”). Although these announcements preceded the Bank’s initial GBPP announcement, market participants may have increased their expectations for QE when the Bank lowered its interest rate toward the effective lower bound. Further, the Bank stated in these announcements that it was ready to supply liquidity; this may also have increased market expectations for QE. These pre-GBPP announcements caused a reduction in bond and money market yields that was more pronounced at shorter maturities (Table 1, panel a). More specifically, the announcements on March 4, 2020, and March 13, 2020, led to decreases in BAX yields of approximately 18 bps.13 Moreover, 2-year, 5-year and 10-year GoC bond yields declined around these announcements by 8 bps, 17 bps and 10 bps, respectively. The decline in shorter maturities was likely due to decreased expectations for short-term rates because of the interest rate portion of the announcements. However, some of the decline in the longer-maturity yields may have been due to increased expectations for QE.

Next, we analyze market movements around the five GBPP-related announcements. There is a cumulative decrease of about 15 bps, 11 bps and 11 bps in 2-year, 5-year and 10-year yields, respectively, in the window around these announcements. The most important of these announcements in terms of market reaction was the initial announcement of the GBPP on March 27, 2020. It resulted in a decrease of 9–14 bps on benchmark GoC bond yields (Table 1, panel b). The decline in bond yields around this announcement is consistent with the decline observed in Arora et al. (2021). The announcement of the GBPP lowered equity prices by about 55 bps but had a negligible impact on the value of the Canadian dollar against the US dollar. Only minor changes in financial market prices occurred across the other four announcements in the GBPP period. This is not surprising because the Bank did not change the GBPP program in any of these announcements.14

Finally, we look at the market reaction to the Bank’s nine announcements during the reduction period. The overall impact on prices throughout the reduction period is the reverse of the impact over pre‑GBPP and GBPP-related sample periods (Table 1, panel c). This is intuitive—the Bank decreased its weekly QE purchases, and the announcements in this period likely reduced market expectations of the size of the QE program. The largest impact is observed on October 27, 2021, when the Bank announced the end of QE and entered the reinvestment phase. Following this announcement, the yield on BAX and GoC bonds increased. The increase was more pronounced for shorter maturities, reflecting an increase in expectations for short-term interest rates. Short-term rates increased by 37 bps, while long-term rates increased by 7 bps. The markets interpreted this announcement as signalling that the Bank would begin increasing interest rates sooner than the markets had previously thought, given that the Bank stated in its October 2021 Monetary Policy Report that economic slack would be absorbed by the middle quarters of 2022, earlier than its previous estimate of the second half of 2022.

Our event-study estimate of the impact of QE on financial markets depends on how narrowly we interpret announcements as being related to QE. If we look only at the GBPP period, GoC 10-year bond yields declined by a total of about 10 bps around the announcements. If we assume that the decline in 10-year yields around the announcements of March 4, 2020, and March 13, 2020, was due to increased expectations for QE, the estimated decline becomes larger, about 21 bps. On the one hand, our event-study analysis may underestimate the financial market impact of QE because it captures only how the announcements changed expectations for QE and not their full impact. On the other hand, it may overestimate the impact because it assumes that the decline in yields around the early-March announcements was due to QE and not due to the rate cuts themselves. On balance, we are likely still underestimating the impact on financial markets. The 12 bps increase in 10-year yields around the reduction announcements also suggests we may be underestimating QE.

To put our estimate of the impact of QE in Canada into perspective, Chart 3 compares the impact of QE on 10-year government bond yields and the size of purchases across different countries and programs. The circles represent QE programs announced in response to the global financial crisis, and the triangles represent QE programs announced during the COVID-19 pandemic period. The chart shows no clear relationship between the size of the purchases and the impact on 10-year bond yields. The lack of a relationship between size and impact could be due to several factors, such as the size of the economy, how unexpected the announcements were or whether the country was at the zero lower bound when it announced QE. For example, Japan’s QE was larger in size than that of other countries, but it likely had a small impact because it was announced when Japanese bond yields were already close to the effective lower bound. Unsurprisingly, the first large-asset purchase program (QE1) in the United States and the Asset Purchase Facility in the United Kingdom, the first QE program in each country, had the largest effects. The Bank of Canada’s GBPP program is in the middle in terms of impact.

Impact on the macroeconomy

In this section, we estimate the effects of the QE announcements on the macroeconomy. Various approaches have been used to estimate the macroeconomic effects of QE in different economies. The Committee on the Global Financial System (CGFS 2019) conducts a review of 25 studies using mostly DSGE and VAR models. Overall, the effects are estimated as positive for both real output and inflation. Depending on the specific methodology adopted, the central bank and the program, the estimates of the peak response of real GDP and inflation show a lot of variation. The estimates for the effects of QE on GDP and inflation are both in the range of between 0 and 4 percentage points.

The details for the model used in this paper can be found in Zhang (2021), whose framework is based on the model of Gertler and Karadi (2011, 2013). Gertler and Karadi (2011, 2013) modify a reasonably standard New Keynesian model to explicitly include a banking sector and banking sector balance sheets. The model makes three primary assumptions to incorporate the role of QE:

• Banks finance risky, long-term assets with riskless, short-term debt.
• The existence of an agency problem between households and banks constrains the borrowing ability of the latter and generates excess returns between long- and short-term debts.
• The central bank conducts long-term asset purchases during economic crises and boosts the economy by reducing the credit costs of the banking sector.

Building on Gertler and Karadi (2011, 2013), Zhang (2021) adds the following three features to the model. All three are needed to study forward guidance and asset purchase policies in one framework and the effects of the policies on the entire yield curve.

• First, the paper introduces a nominal shadow overnight interest rate that follows a Taylor rule. The shadow overnight rate is the same as the observed overnight rate when the zero lower bound is not binding and is negative when the zero lower bound is binding.
• Second, the paper outlines a forward guidance shock, in the form of an announcement of future shocks to the Taylor rule, as a modelling device for generating innovations in expected future interest rates.
• Third, the paper presents a flexible approximation to interpolate the full yield curve using the shadow rate and the rate on a perpetuity.

In the model, forward guidance and asset purchases influence the yield curve differently:

• When at the zero lower bound, a central bank can announce an easing forward guidance policy to keep the overnight rate low in the near future. The forward guidance policy lowers expectations for future policy rates, thus decreasing short- to medium-term yields more than long-term yields. This forward guidance shock can also represent the signalling component of asset purchases, as markets infer information about the future path of policy rates from the QE announcement.
• Asset purchases of long-term bonds, in contrast, reduce the term premium and will decrease long-term yields more than short-term yields.

These policies will also have indirect impacts on the yield curve that need to be accounted for. Since these policies raise the market’s expectations for output and inflation, there will be feedback from these policies onto shorter-term yields. For instance, the impact of a forward guidance shock on short- to medium-term rates may be reduced because the market will expect the economy to improve. Such improvement will temper expectations for the time of liftoff from the zero lower bound and the path for the overnight rate. And, given the direct and indirect effects of these policies on the yield curve, the model can infer how much of a given shock is related to forward guidance and how much is related to large-scale asset purchases.

We then combine the model with observed yield data. We estimate the model so that the changes in the yields that the structural model predicts from a linear combination of the two types of shocks will match the observed changes in 2-year, 5-year and 10-year yields around QE announcements. We provide the model with three different scenarios of yield changes. In the first scenario we look only at QE announcements on fixed interest rate announcement dates. In the second scenario we add the two pre-GBPP March announcements to the sample. Since the first two scenarios estimate only the surprise component of the impact, in the third scenario we do a back-of-the-envelope calculation to estimate the full impact of the program on yields.

For the third scenario, we consider the three reduction-related announcements in April, July and October 2021. There was a cumulative increase of about 8.8 bps of 10-year GoC yield around these announcements. We estimate the change in the market’s expectations for our balance sheet by assuming that market participants advanced their expectations of a $1 billion weekly reduction by a quarter of a year each time. Market participants were largely expecting these announcements, so this assumption may be a generous estimate of how much the market’s expectations for supply changed. This assumption implies a surprise of $1 billion a week for 13 weeks, for a total of $13 billion for each announcement, and a total of $39 billion over all three announcements. If we linearly scale the 8.8 bps 10-year yield impact for $39 billion up to $340 billion, it implies an impact of 77 bps for the full program. If we assume a smaller change in market expectations for the supply of bonds, it implies a larger impact for the full program. This estimate of 77 bps is roughly the same size as the estimated impact of QE1 in the United States. Their QE1 program was more of a surprise (since it was their first QE announcement), so the impact estimated by the event study is likely closer to the total impact of QE1.15

Then, given observed changes in 2-year, 5-year and 10-year yields around a central bank announcement, the model can disentangle how each component—large-scale asset purchases and forward guidance—will impact inflation and GDP. We then feed the total change in 2-year, 5-year and 10-year GoC bond yields in the first two scenarios into the model to estimate the sizes of the forward guidance and QE shocks and their impact on GDP and inflation. For the third scenario, we use only the 10-year GoC bond yield and attribute all the changes to large-scale asset purchases.

The dynamic effects of QE on real GDP and inflation for each of the three scenarios are shown in Chart 4. The figure provides the impulse response only for the large-scale asset purchase portion of each scenario and not for the forward guidance portion of the scenario. We ignore the forward guidance portion because we want to concentrate on the impact of QE only. Some of the QE announcements were accompanied by interest rate changes, which would be reflected in the impact of the forward guidance portion.

The peak impact of QE on real GDP, presented in Chart 4, panel a, occurs about three to four quarters after the shock and ranges from about 0.14% for scenario 1 to about 3% for scenario 3. Scenario 3, which is meant to capture both the expected and the surprise component of QE, is in the middle of the range CGFS (2019) provides for the estimated impact of QE on GDP in different countries. Similarly, Chart 4, panel b, shows that the peak impact for inflation is highest for scenario 3. The peak effect is around 1.8 percentage points. The inflationary impact of QE is in the lower end of the range of cross-country estimates provided in CGFS (2019), who find a range between 0 and 4 percentage points.

Chart 4: Dynamic effects of quantitative easing in three scenarios

Chart 4: Dynamic effects of quantitative easing in three scenarios

Conclusion

We provide an overview of the Bank’s GBPP and discuss the theories for how QE transmits to financial markets and the macroeconomy. We also discuss the challenges inherent in estimating QE’s impact. As a result of these challenges, the overall impact of QE is uncertain.

In this paper, we find that 10-year GoC bond yields decline by 10–20 bps around GBPP announcements. However, this change represents only the unexpected component of the total effect of QE, given that markets likely have expectations for QE before the announcements are made. While the counterfactual cannot be observed, and thus the impact of QE cannot be directly measured, the total effect of QE is likely much larger. In one scenario using back-of-the-envelope calculations, we estimate that the full QE effect is closer to 80 bps on the 10-year yield. We consider a range of scenarios to estimate the macroeconomic impact. We use a model that maps yield impacts into impacts on GDP and inflation to estimate the effect of QE on these two variables. In a scenario that considers the full impact of QE, the model suggests QE has a peak impact of about 3% on GDP and 1.8% on inflation.

There is considerable uncertainty around the impact of QE on bond yields, and likely more uncertainty about the impact of QE on GDP and inflation. Therefore, these estimates should be taken with a grain of salt. Moreover, models of QE do not capture the potential for QE to eliminate negative tail outcomes. For example, in the counterfactual model of the absence of QE, it is possible there could have been a much larger increase in yields than we consider in our 80 bps scenario because the market would have to absorb an extra $340 billion of issuance. And the model does not capture the possibility that QE helps avoid a large, negative macroeconomic outcome.

Several questions remain unexplored:

• The demand for government bonds could be nonlinear, and this nonlinearity is not directly observed. We assess the reactions of financial markets around the time of QE announcements; however, a great deal of uncertainty remains about the shape of the demand curve. This is because these announcements do not provide much information about the impact of large changes in government debt outstanding and, hence, the overall impact of QE.
• While we know that the impact of QE (and QT) depends on the institutional and economic environment, we do not have good estimates of how much different factors matter.
• Our estimate of the macroeconomic impacts of QE is based on a closed-economy macroeconomic model. The transmission of QE may be different in small open economies such as Canada.

We leave these questions to future research.

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Endnotes

Disclaimer

Bank of Canada staff discussion papers are completed staff research studies on a wide variety of subjects relevant to central bank policy, produced independently from the Bank’s Governing Council. This research may support or challenge prevailing policy orthodoxy. Therefore, the views expressed in this paper are solely those of the authors and may differ from official Bank of Canada views. No responsibility for them should be attributed to the Bank.