Sources of pandemic-era inflation in Canada: an application of the Bernanke and Blanchard model

Overview and key messages

The surge in inflation during the COVID-19 pandemic has led to many debates about its causes and persistence. Among the questions driving these debates: Was the surge in inflation largely demand- or supply-driven? Is the pickup in wage growth merely a benign response to inflation shocks, or has it become a self-sustaining source of inflationary pressures?

In this note, we explore these questions by applying the model recently developed by Bernanke and Blanchard (2023) to Canadian data.1 Our analysis is part of a larger collaborative effort led by Bernanke and Blanchard that includes contributions from 11 central banks. The goal of this joint work is to analyze inflation across multiple economies using a common model and to identify similarities and differences between jurisdictions.

Our findings for Canada are broadly in line with Bernanke and Blanchard’s overall findings for the United States. We find that in 2021 and early 2022:

• supply shocks, including commodity prices and supply shortages, were the main drivers of the surge in inflation
• labour market pressures did not play a significant role in the surge in inflation

However, labour market pressures have become an increasingly important driver of inflation as supply shocks have started to fade. A scenario analysis suggests that inflation could become stuck around 3% over the forecast horizon if the labour market reverts to and remains at conditions seen in 2023.2 Labour market pressures may need to ease further to ensure that inflation returns to the 2% target by the end of 2025.

The remainder of this note is divided as follows. First, we give a brief overview of the model’s theoretical structure. We then describe the data used and discuss the estimation results for the three different versions of the model that we have tested. We also discuss the model’s impulse responses to price and labour market shocks. Next, we discuss how the model interprets the evolution of inflation and wage growth during the pandemic. We then share some model-based projections about how inflation may evolve in the future, conditional on certain assumptions. Finally, we summarize the results from other economies.

The Bernanke and Blanchard model

The Bernanke and Blanchard model consists of four equations that describe the behaviour of:

• wages
• prices
• short-run inflation expectations
• long-run inflation expectations

We discuss each of these equations in more detail below.

Prices

The growth rate in the price level, P, is a function of the growth in the aggregate wage, W, and other factors, Z_p (equation 1).3 Z_p includes non-labour input costs and price markups, as well as all other factors affecting prices. In the empirical version of the model, Z_p consists of commodity prices and a variable that measures supply disruptions during the pandemic. Additionally, the empirical version includes trend labour productivity because wage growth generally does not create inflationary pressures when it’s supported by productivity gains.

\(\displaystyle\, P_{t}-P_{t-1} \) \(\displaystyle=\, (W_{t}-W_{t-1}) \) \(\displaystyle+\, (Z_{p,t} - Z_{p,t-1}) \) \(\displaystyle\, (1) \)

\(\displaystyle\, W_{t}-W_{t-1} \) \(\displaystyle=\, (P_{t}^{e} - P_{t-1}) \) \(\displaystyle+\, \alpha(P_{t-1} - P_{t-1}^{e}) \) \(\displaystyle+\, \beta(X_{t} - \alpha X_{t-1}) \) \(\displaystyle+\, Z_{w,t} \) \(\displaystyle\, (2) \)

Inflation expectations

Short-run inflation expectations are a weighted average of long-run expectations, π^*, and past inflation (equation 3). Long-run expectations are a weighted average of their past values and of past inflation (equation 4). Inflation expectations play an important role in this framework. The parameters δ and γ determine the degree to which economic agents’ expectations are anchored. For example, long-run inflation expectations are perfectly anchored when δ = 1.

\(\displaystyle\, P_{t}^{e} - P_{t} \) \(\displaystyle=\, \delta \pi_{t}^{*} \) \(\displaystyle+\, (1- \delta) (P_{t-1} - P_{t-2}) \) \(\displaystyle\, (3) \)

\(\displaystyle\, \pi_{t}^{*} \) \(\displaystyle=\, γ \pi_{t-1}^{*} + (1-γ) (P_{t-1} - P_{t-2}) \) \(\displaystyle\, (4) \)

Note that this model does not incorporate an explicit inflation target. As a result, even temporary shocks can permanently raise inflation expectations and cause expectations to de-anchor. For instance, a positive demand shock may cause inflation to continue exceeding a central bank’s target, even after all the excess demand is eliminated. In such a situation, a period of excess supply would be needed to bring inflation back to target.

Data and estimation results

We estimated the empirical version of the analytical model using quarterly Canadian data. Following Bernanke and Blanchard, we incorporated four lags of all endogenous and exogenous variables to allow for gradual adjustments.4 The estimation sample for all four Canadian equations ends in the second quarter of 2023.5 We also added two dummy variables in the wage equation that are set to 1 in the second and third quarters of 2020. This addition aims to look through wage dynamics in these quarters early in the pandemic. Compositional effects and measurement errors, rather than genuine changes in the aggregate wage, drive dynamics in these quarters.6 Table 1 provides a full list of all the variables used and data sources.

Canada has several wage growth measures, each having various advantages and disadvantages. Therefore, we have estimated three different versions of the model with each using a different measure of wage growth. Table 3, Table 4, Table 5 and Table 6 present the estimation results for the four equations. The US specification column in each table shows the estimated coefficients for the US version (for comparison), while the following three columns show the estimation results for the Canadian specifications.

Wage equation

We provide a basic description of the three wage measures used in Table 2. In summary, we note the following observations:

• The Labour Force Survey (LFS) measure has the broadest coverage of the three measures and has several controls for worker characteristics. However, it relies on self-reported data, which may be less accurate.
• The wage settlements data are the least noisy of the three, but cover only unionized employees, which represent a small share of the overall workforce.7
• The Survey of Employment, Payrolls and Hours (SEPH) measure is based on data reported by firms, which may be more accurate than self-reported data. However, the measure has fewer controls for worker characteristics and a more limited industry coverage.

We use and report results for all three wage measures given that no single measure is clearly preferable in all areas. Chart 1 shows that the year-over-year growth rate of wages for each of the three measures display different short-run dynamics and quantitative differences. However, the measures generally exhibit similar trends over the long run.

Like Bernanke and Blanchard, we use the job vacancy-to-unemployment (V/U) ratio to capture wage pressures arising from imbalances between labour supply and demand. Compared with the unemployment rate, the V/U ratio is a more complete indicator of labour market tightness because it incorporates information from the perspectives of both workers and firms.

Compared with the unemployment rate, the V/U ratio provides a different account of the degree of tightness of the Canadian labour market during the pandemic (Chart 2). While the unemployment rate suggests that the labour market was only modestly tighter than pre-pandemic levels in 2022, the V/U ratio shows an unprecedented degree of tightness during the same period. The latter is arguably more consistent with survey-based evidence, such as results from the Bank of Canada’s Business Outlook Survey.8

Table 3 provides the estimation results for the wage equation. Across all wage measures, the coefficient on the V/U ratio in Canada is not statistically significant. This is possibly because the estimation sample for Canada is shorter than that for the United States.9 Additionally, like the finding for the US economy, we do not find evidence of a catch-up effect on wage growth.

On balance, the version of the model that uses the LFS-based wage measure appears to be the most consistent with Bernanke and Blanchard’s results for the United States. While the coefficient on the V/U ratio is much higher than in the United States, this is largely because the standard deviation of the Canadian V/U ratio is only one-third that of the US ratio.

The estimations with the other wage measures show larger differences compared with the US result. As reflected by the low R-squared value, the SEPH-based measure is not well explained by economic fundamentals. This may be due to the measure’s volatile nature and limited set of controls for workforce composition. The wage settlements measure has a high R-squared value but suggests an unusually weak relationship with inflation expectations, as evidenced by the small coefficient.

Price equation

The rate of price growth is modelled as a function of its past values, nominal wage growth and some non-labour input costs. Prices are measured using the consumer price index (CPI). For non-labour input costs, we include the relative prices of both food and energy. Like Bernanke and Blanchard, we capture the effects of global supply chain disruptions using an index based on the number of Google searches in Canada for the word “shortage.” Finally, we include trend productivity growth to capture the fact that wage increases do not generally cause inflationary pressure when supported by improvements in productivity growth. All versions of the model fit the inflation data quite well (Chart 3).

Table 4 shows the estimation results. Qualitatively, the results are similar to those for the United States, regardless of the wage measure used. However, we find a generally slower pass-through from wage growth to inflation. Additionally, unlike the United States, the coefficients on the variables for shortages and trend productivity growth are not statistically significant. Finally, the results show that no wage measure explains inflation materially more than the others.

Looking at the LFS measure as an example, the estimated long-run effect of an energy price shock on the price level is about 12%, other things being equal.10 By comparison, energy’s weight in the CPI basket is only about 7%, suggesting a strong pass-through from energy to non-energy prices.

Similarly, the long-run effect of a food price shock on the price level is about 47% in the LFS measure, which is much higher than food’s share in the CPI basket of about 17%. This long-run effect is also much larger than that measured for the United States (19%). As a result, the long-run effect appears to be exaggerated in Canada. We believe this is likely caused by the omission of import prices in the model. In the Appendix, we propose expanding Bernanke and Blanchard’s core model to incorporate the relative price of imports. Our expanded version has model properties that are nearly identical to the Bernanke and Blanchard version, except for the coefficient on food prices, which is halved.

Short-run and long-run inflation expectations equations

To estimate equations (3) and (4), we use short- and long-term inflation expectations measures developed by Bank staff using a dynamic factor model similar to that of Ahn and Fulton (2020). Short-run inflation expectations are defined as expectations of up to 2 years ahead, while long-run expectations refer to expectations from 3 to 10 years ahead.

We find that short-run inflation expectations in Canada are somewhat more responsive to long-run expectations than in the United States (Table 5). However, from the results in Table 6 we conclude that long-term inflation expectations in Canada have remained relatively well anchored over the estimation sample, with the coefficient being close to 1 for the past lagged long-run expectations. This is naturally consistent with recent data on long-run inflation expectations, which have remained close to the 2% target despite the elevated inflation over the past three years.

Impulse response functions

We use the estimated model to show how inflation reacts over time to changes in the main exogenous variables. The shocks are calibrated to correspond to a permanent increase of one standard deviation in these variables. This analysis enables us to compare the dynamic properties of the models used in the Canadian analysis with the US version.

In general, all three Canadian specifications yield plausible results, with model properties that are consistent with economic theory (Chart 4). Regardless of the specification used, the effects on inflation from the three price shocks (the relative price of energy, the relative price of food and the shortage index) are quite short-lived in both economies. However, the effects of the food price shock on inflation seem to be stronger and more persistent in Canada than in the United States. Except for the specification using wage settlements as a measure of nominal wages, the shock to the V/U ratio contributes less to inflation in Canada than in the United States.

Note: ECI is the US Employment Cost Index. LFS is the Labour Force Survey; SEPH is the Survey of Employment, Payrolls and Hours; WAGSET is the average negotiated wage adjustment in collective bargaining agreements.
Sources: US Bureau of Labor Statistics, Statistics Canada and Bank of Canada calculations

Drivers of price and wage inflation in Canada during the pandemic

Using the estimated model, we can break down the dynamics of inflation during the pandemic into its various drivers. This sheds light on what the model suggests as being responsible for the surge in inflation.

Price inflation

Chart 5 shows the breakdown of quarter-over-quarter inflation rates from the fourth quarter of 2019 to the second quarter of 2023 based on the solution of the full models and their implicit impulse response functions. We provide the decomposition for the US version of the model for comparison (Chart 5, panel a) and the Canadian decomposition in the remaining panels, each based on a different wage measure.

Chart 5: Labour market tightness contributed less to the pandemic-era inflation surge than other factors

Chart 5: Labour market tightness contributed less to the pandemic-era inflation surge than other factors

Decomposition of quarter-over-quarter CPI inflation, annualized

Note: ECI is the US Employment Cost Index. LFS is the Labour Force Survey; and SEPH is the Survey of Employment, Payrolls and Hours. Major wage settlements is the average negotiated wage adjustment in collective bargaining agreements. Initial conditions refers to the contribution of pre-pandemic data.
Sources: Bernanke and Blanchard (2023), Statistics Canada and Bank of Canada calculations
Last observation: 2023Q2

The results suggest that non-labour input cost shocks largely drove the surge in inflation in Canada from 2021 to early 2022, specifically:

• food prices
• energy prices
• global supply chain disruptions that were more persistent than anticipated

These results mirror the findings of Bernanke and Blanchard for the United States. However, food price shocks have played a more important role in Canada than in the United States.11

The contribution of labour market imbalances, as measured by the V/U ratio, to inflation was negative during the early part of the pandemic as the unemployment rate surged. However, as the economy bounced back, labour market pressures began to exert positive pressure and became an increasingly important driver of inflation.

The contribution of the labour market tightness was relatively small compared with other exogenous factors (Chart 5). Interestingly, a wage-price spiral did not materialize as some had feared even after inflation remained high and the labour market tight. This was largely because long-run inflation expectations remained well anchored. Although the high degree of anchoring is a feature of the data and is therefore reflected in the model, it is likely endogenous to monetary policy actions and was likely bolstered by the Bank’s forceful policy responses to the steep rise in inflation.12

Wage inflation

Chart 6 shows the various drivers of wage inflation dynamics. Like in the United States, labour market imbalances (as measured by the V/U ratio) have been an important driver of wage inflation in Canada. In all three versions of the model, labour market pressures started contributing positively to wage growth sometime in 2022. In the model version using the LFS wage measure, labour market imbalances contributed about 1.3 percentage points (pps) to quarter-over-quarter wage growth in the second quarter of 2023. They were also the single most important driver in that quarter.

Note: ECI is the US Employment Cost Index. LFS is the Labour Force Survey; and SEPH is the Survey of Employment, Payrolls and Hours. Major wage settlements is the average negotiated wage adjustment in collective bargaining agreements. Initial conditions refers to the contribution of pre-pandemic data.
Sources: Bernanke and Blanchard (2023), Statistics Canada and Bank of Canada calculations
Last observation: 2023Q2

Non-labour input costs have also contributed to higher wage growth. They contributed about 1.1 pps to quarter-over-quarter wage growth in the second quarter of 2023. Although the model has no direct channel between non-labour input costs and wages, there is an indirect link. For instance, a surge in energy prices leads to an increase in headline inflation, which raises short- and long-run inflation expectations and thus influences wage growth.

Overall, the model suggests that elevated wage growth seen recently in Canada has been driven by a roughly equal mix of a strong demand for labour and other price shocks that have contributed to a rise in short-run inflation expectations.

Model-based projections

Following Bernanke and Blanchard, we provide some insight into how the model predicts inflation will evolve in the future. The model can explain the evolution of inflation over history reasonably well, but cannot provide a forecast—or prediction—of what will happen in the future. The model offers only projections that are conditional on the assumptions provided. Therefore, the projections we present show how inflation could theoretically evolve if all the assumptions provided were to materialize.

For this exercise we make the following simplifying assumptions:

• Food and energy prices grow at the same rate as wages. In other words, the relative price of food and energy is assumed to be constant.
• Supply disruptions are immediately resolved, with the shortage indicator returning to a steady-state index value of 15 (by construction, it has a peak value of 100).
• Productivity grows quarter-over-quarter at an annualized pace of 1%, which is close to its sample average.
• A steady-state value of 0.45 for the V/U ratio. Following Bernanke and Blanchard, the constant in the wage equation is thus modified to ensure that the labour market is in balance at a ratio of 0.45.13
• There are no further shocks to the endogenous variables in the model, including prices, wages and inflation expectations.

To simplify, we use the LFS-based wage measure, which is our preferred version of the model. For the evolution of the labour market, we consider three alternative paths for the V/U ratio:

• Path 1: the V/U ratio converges toward its historical pre-pandemic average of 0.3 by the second quarter of 2025.
• Path 2: the V/U ratio converges toward 0.45, its value in the fourth quarter of 2019, by the second quarter of 2025.
• Path 3: the V/U ratio remains roughly stable, staying at its July 2023 value of about 0.6.

Chart 7 shows that if labour market imbalances remain at July 2023 levels, the inflation rate is likely to remain well above the 2% target by the end of 2025. In contrast, the model suggests that inflation could return to close to target over the same period if labour market conditions normalize back to pre-pandemic averages.  

Comparing results between economies

The surge in inflation during the pandemic was not isolated to the United States and Canada—it rose across major economies.

Our work is part of a joint effort among 11 central banks to understand the drivers and mechanisms of this global rise in inflation. Participants have applied the empirical framework using national or regional data for each participating country or region, doing so in collaboration with Bernanke and Blanchard. Participating central banks include:

• the Bank of Canada
• the Bank of England
• the Bank of Japan
• the European Central Bank
• several national central banks in the euro area14

In this section, we highlight what we have learned from this experience, emphasizing the similarities and differences between each country’s results.15

Overall, the estimated country-specific models fit the national data relatively well.

Despite some quantitative differences between the estimated coefficients, the results of the analysis in each country suggest that the second-round effects of energy and food price shocks were limited in almost all countries. Also, to some extent, short-term inflation expectations in each country responded to both past inflation and long-term expectations. However, and importantly for monetary policy-makers, this analysis has shown that long-term inflation expectations were broadly well anchored as inflation and short-term expectations rose.

The wage specification has proven the worst fit in each country’s version of the model. This may partly reflect the different ways that countries measure wage and job vacancies. As well, each country’s labour market operates differently, which could also reflect a different wage dynamic than that proposed by Bernanke and Blanchard in their framework. That said, the wage Phillips curve appears to be relatively flat, with the effect of the V/U ratio on wage inflation being small in almost all economies.16 Interestingly, the results of the analysis in each country revealed little evidence of a catch-up effect.

The dynamic effects of price shocks and supply shortages on overall inflation were short-lived in most economies. This reflected the surprisingly weak second-round effects of price shocks combined with well-anchored inflation expectations and limited wage catch-up effects by workers. In contrast, the dynamic effects of increased labour market tightness on headline inflation were relatively heterogeneous but quite small in many jurisdictions, reflecting the flatness of each country’s Phillips curves. For example, the labour shock had an almost insignificant impact on inflation in Japan. In contrast, the shock took longer to drive up inflation in the United States and participating countries in the euro area, while inflation in the United Kingdom increased faster and more jaggedly.

Finally, the historical decomposition leads to a similar narrative across the 11 economies. The results of this analysis across all participating countries show that price inflation was, to some extent, completely driven by food, energy and sectoral (shortages) price shocks before inflation reached its peak. However, the relative contribution of each of these shocks varies:

• Energy, food and sectoral price shocks played the largest role, particularly in the euro area and in the United Kingdom. This partly reflects these countries’ greater exposure to the impacts of the war in Ukraine.
• Food price shocks were a major contributor to inflation in Japan, characterizing the more moderate surge there as being predominantly driven by external factors.

As the pressure of price shocks eased, the small contribution of labour market shocks increased as inflation began to run out of steam. Since then, labour market shocks have remained persistent in virtually all countries, apart from Belgium, Japan and Italy where the impact has been almost nil. That said, the contribution of labour market tightness to elevated inflation has been greater in the United States than in the euro area. However, if we consider the European results separately, labour market shocks have played a greater role in France and the United Kingdom than in the United States or Canada.

Conclusion

The surge in inflation experienced during the pandemic has highlighted the importance of better modelling developments in the labour market, which is a key supply-side element of the economy. The joint effort of 11 central banks, inspired by Bernanke and Blanchard, provides valuable insights. Our contribution to this effort also adds to the Bank’s work to sharpen its modelling by focusing on how labour market dynamics influence wages and inflation (Coletti 2023). We are continuing this journey with ongoing research that we hope will improve understanding of the drivers of inflation in Canada.

Appendix: Expanding the model to incorporate import prices

The model developed by Bernanke and Blanchard (2023) does not include a role for import prices, likely because the United States is a fairly closed economy. However, the price of imported goods plays a more pivotal role in small open economies such as Canada. Therefore, we propose expanding the original framework by Bernanke and Blanchard to incorporate import prices.

Practically, this expansion entails adding a variable, grpm, and its first four lags into the price growth equation. This variable represents the annualized log-difference of total import prices relative to the aggregate wage measure.

Table A-1 summarizes the results of the expanded model and compares them with the results of the baseline model that does not include import prices.

The results show that expanding the model with import prices yields largely similar coefficients for the rest of the variables. The one noteworthy exception is the significant decline in the coefficient on food prices, from 0.127 in the baseline model to 0.072 in the expanded model. The coefficient in the expanded model is more closely in line with food’s weight in the consumer price index (CPI) basket. Further, the expanded model yields a 26% long-run effect of a food price shock, compared with 47% in the version without import prices. In our view, the response to food price shocks is more reasonable in the expanded model, and more generally in line with food’s weight in the CPI basket.

Therefore, while import prices are not found to be statistically significant, we prefer the augmented version of the model on theoretical grounds.

References

Ahn, H. J. and C. Fulton. 2020. "Index of Common Inflation Expectations."  FEDS Notes, September 2. Washington: Board of Governors of the Federal Reserve System.

Aldama P., H. Le Bihan and C. Le Gall. Forthcoming. “What Caused Inflation in the Post-Pandemic-Era? Replicating Bernanke and Blanchard (2023) on French Data.” Bank of France Technical Report.

Arce Ó., M. Ciccarelli, A. Kornprobst and C. Montes-Galdón. 2024. “What Caused the Euro Area Post-Pandemic Inflation?” European Central Bank Occasional Papers Series No. 343.

Bernanke B. S. and O. J. Blanchard. 2023. “What Caused the US Pandemic-Era Inflation?” Paper prepared for the Hutchins Center on Fiscal & Monetary Policy at the Brookings Institution conference, "The Fed: Lessons Learned from the Past Three Years,” May 23.

Bernanke B. S. and O. J. Blanchard. 2024. “An Analysis of Postpandemic Inflation in 11 Economies.” Peterson Institute for International Economics Working Paper No. 24-11.

Bonam, D., G. Hebbink and B. Pruijt. 2024. “Drivers of Dutch Inflation During the Pandemic Era.” De Nederlandsche Bank Analysis, March 22.

Coletti, D. 2023. “A Blueprint for the Fourth Generation of Bank of Canada Projection and Policy Analysis Models.” Bank of Canada Staff Discussion Paper No. 2023-23.

De Walque, G. and T. Lejeune. 2024. “What Caused the Post-Pandemic Era Inflation in Belgium? Replication of the Bernanke-Blanchard Model for Belgium.” National Bank of Belgium Working Paper Document No. 447.

Ghomi, M., S. Hurtado and J. M. Montero. 2024. "Analysis of Recent Inflation Dynamics in Spain. An Approach Based on the Blanchard and Bernanke (2023) Model." Banco de España Occasional Paper No. 2404.

Haskel, J., J. Martin and L. Brandt. 2023. “Recent UK Inflation: An Application of the Bernanke-Blanchard Model.” Bank of England paper, November 27.

Lam, A. 2022. “Canada’s Beveridge Curve and the Outlook for the Labour Market.” Bank of Canada Staff Analytical Note No. 2022-18.

Menz, J.-O. 2024. “Sources of Post-Pandemic Inflation in Germany and the Euro Area: An Application of Bernanke and Blanchard (2023).” Deutsche Bundesbank Technical Paper No. 02/2024.

Nakamura K., S. Nakano, M. Osada and H. Yamamoto. 2024. “What caused the Pandemic-Era Inflation? Application of the Bernanke-Blanchard Model to Japan.” Bank of Japan Working Paper No. 24-E-1.

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Endnotes

Acknowledgements

We thank Ben Bernanke, Olivier Blanchard, Gino Cateau, Jing Yang, Russell Barnett, Mikael Khan, Corrine Luu, Rodrigo Sekkel, Stefano Gnocchi, Jonathan Haskel, Carlos Montes Galdón, Sam Boocker, Josh Martin, Lennart Brandt, Philip Lane, Matteo Ciccarelli, Oscar Arce, Mitsuhiro Osada, Hiroki Yamamoto, Kouji Nakamura, Shougo Nakano, Ekaterina Peneva, Daniel Leigh, Hervé Le Bihan, Olivier Garnier, Jan-Oliver Menz, Thomas Lejeune , Massimiliano Pisani, Samuel Hurtado and Dennis Bonam for their insightful discussions and constructive feedback at the Bank of Canada seminar and the working group meeting series. We have also benefitted from Alex Lam and Paul Corrigan for their assistance and suggestions on constructing vacancy data for Canada. We are grateful to Jordan Press and Leanne Rancourt for their assistance in enhancing the readability of the paper, and to Guylaine Létourneau and Marie-Lou Lachance for their help translating this note into French. Yena Joo has provided excellent research assistance. Opinions expressed in this paper are those of the authors and do not necessarily reflect those of the Bank of Canada or its staff. Any remaining errors are ours.