## Background

Throughout 2022, the Canadian economy faced persistently high inflation. The Bank of Canada responded forcefully by increasing the target rate by 425 basis points between March 2022 and January 2023. These increases led investors to expect slower economic growth in Canada, and these expectations are evident in the drop in earnings forecasts for companies whose stocks are traded on the TSX. This provided policy-makers with an early sign that higher interest rates would be effective and slow economic growth because these forecasts fell more for companies that are more sensitive to interest rates.

Using the price-to-earnings ratios of stocks listed on the TSX, we construct a model to forecast future economic growth in Canada. The forecasts that we obtain for year-over-year growth of real gross domestic product (GDP) have declined from 5.6% at the start of January 2022 to 2.1% by February 2023. The lower price-to-earnings ratios for industries that are more sensitive to interest rates are the reason for this decline. The forecast for growth remained flat until the end of May 2023, which is the end of our sample period.

## Understanding the signals that valuation ratios send

We use the information from the one-year-ahead earnings forecasts and prices of TSX equities, in the form of price-to-earnings ratios. Valuation ratios such as these can reveal rich information about the effects of monetary policy on future GDP growth because monetary policy influences these valuation ratios in three ways:

- by lowering future economic growth and therefore the level of expected earnings
- by lowering the discounted value of expected earnings
- by increasing the compensation that investors require for taking on the risk of investing in equities

We gather the valuation ratios across industries using data for 2003–23 and then try to determine the combination of industry valuation ratios that provides the most accurate forecasts of one-year-ahead real GDP growth. Chernis and Luu (2018) find that higher interest rates lead some Canadian households to decrease their consumption of some categories of goods faster and by more than in other categories. We ask whether this higher sensitivity to interest rates extends to the valuation ratios of industries that are more exposed to these areas of consumption. Specifically, we ask whether changes in the valuation ratios of these industries that are sensitive to interest rates provide information about future GDP growth when compared with changes in the valuation ratios of other industries. To do this, we use the three-pass regression filter (TPRG) methodology (Kelly and Pruitt 2015)—a data-driven approach—to determine what linear combination of valuation ratios delivers the best forecasts throughout the sample. We then check whether the combination that results from the TPRG places greater weight on industries that are sensitive to interest rates.

## Finding value in the cross-section

We find that valuation ratios provide a useful signal about future economic growth. One single combination of these valuation ratios produces forecasts of GDP growth with accuracy that is as good as or better than that achieved using a variety of known leading indicators of GDP growth together, including:

- the yield spread between 2-year Government of Canada bonds and 10-year Government of Canada bonds
- year-over-year growth of the consumer price index
- year-over-year GDP growth
- changes in the monthly labour force participation rate
- aggregate TSX one-year-ahead price-earnings ratio
- the Canadian effective exchange rate

This degree of accuracy confirms that the cross-section of valuation ratios summarizes the information contained across several leading indicators of the Canadian economy, even though publicly traded firms produce only a fraction of Canadian GDP.

Looking into the weights given by this combination on the valuation ratios of different industries, we find that it puts more weight on industries that are more sensitive to interest rates (Chart 1).1 This pattern, which is driven by the data, shows that our sample foreshadowed the cyclical variations in real GDP growth based on the relative decline in valuation ratios in specific industries exposed to changes in interest rates.

### Chart 1: Forecasts place outsized weight on the valuation of interest-rate sensitive industries

## Looking back to the past

We review the forecasts of GDP growth that we estimate for the period of the 2008–09 global financial crisis to verify that the model’s signals about future growth provide valuable insights into sources of economic growth. The results show a decline of roughly 3% in the one-year-ahead GDP growth forecast over 2008 (Chart 2). Realized one-year-ahead GDP growth initially fell faster and deeper than the stock market had predicted, and it eventually recovered faster than predicted. This forecasting error likely reflects that, at the beginning of the year, investors did not anticipate that the crisis would reach the depths it eventually did in autumn 2008, which turned out to be unprecedented.

Chart 2 also shows that the decline was consistently led by the valuation ratios of:

- the primary goods sectors (i.e., energy and materials)
- highly cyclical sectors, including capital goods, media, transportation and banks

This pattern was especially apparent when the global financial crisis reached its worst point. Statistics Canada later identified the slowdown in primary resource sectors and business investment as key reasons for weaker Canadian GDP growth over the period (Cross 2010), which is consistent with this pattern. Boivin (2011) also highlighted the sensitivity of business investment to a sharp slowdown in global demand during that period.

### Chart 2: Canadian equity markets correctly identified sectors most important to the 2008–09 global financial crisis

## Gazing toward the future

After we establish that the Canadian stock market helped predict lower growth during past downturns, we ask what the cross-section of valuation ratios implies for the next year. The forecasts for year-over-year real GDP growth declined by just over 3 percentage points between the start of January 2022 and February 2023, from 5.6% to 2.1% (Chart 3). We also find that this decline is largely driven by the lower valuation ratios for banks, consumer durable goods, capital goods, and software and services. These cyclical industries are typically more sensitive to interest rates. The model forecasts for year-over-year growth have remained relatively flat between February 2023 and May 2023, a period when the overnight rate was unchanged in Canada.

### Chart 3: Valuation of interest-rate-sensitive equities forecasts a slowdown in real GDP growth

## Conclusion

Because the Bank has raised interest rates to bring inflation back to target, understanding the impact of higher interest rates on Canadian economic growth is important. This is because interest rate increases will likely slow future growth as they work through the economy. Furthermore, the effect of higher rates is expected to vary in timing and size across sectors, which means that studying how interest-rate-sensitive sectors respond to higher interest rates shows how interest rate increases are working to balance supply and demand and moderate inflation. Using a data-driven approach, we extract the information content of Canadian companies’ valuations for future GDP growth and provide an estimate of expected economic growth. More work is needed to extend this analysis further back in time to:

- capture the patterns of stock market responses across other business cycles
- analyze the implications for other macroeconomic variables that are crucial to understanding the evolution of the Canadian economy, such as inflation, oil prices or the exchange rate

## References

- Boivin, J. 2011. “The ‘Great’ Recession in Canada: Perception vs. Reality.” Speech at the Montréal CFA Society, Montréal, Quebec, March 28.
- Chernis, T. and C. Luu. 2018. “Disaggregating Household Sensitivity to Monetary Policy by Expenditure Category.” Bank of Canada Staff Analytical Note No. 2018-32.
- Cross, P. 2010.
*Year-End Review of 2009*. Ottawa: Statistics Canada. - Kelly, B. and S. Pruitt. 2015. “The Three-Pass Regression Filter: A New Approach to Forecasting Using Many Predictors.”
*Journal of Econometrics*186 (2): 294–316.

## Appendix

We use the three-pass regression filter (TPRF; Kelly and Pruitt 2015) to determine the combination of price-to-earnings ratios that best forecasts year-over-year growth of gross domestic product (GDP). The first step is a time-series regression of each industry’s price-to-earnings ratio \(\displaystyle X_{i,t}\) on one-year-ahead GDP growth \(\displaystyle y_{t+h},\) shown in equation (1):

\(\displaystyle X_{i,t}\) \(\displaystyle=\, A_{i,0}\) \(\displaystyle+\, A_{i,1} y_{t+h}\) \(\displaystyle+\,\epsilon_{i,t}.\)

This step measures how each industry’s price-to-earnings ratio correlates with future GDP growth. The second step is to conduct a cross-section regression of monthly price-to-earnings ratios on the industry-level coefficients, \(\displaystyle \hat A_{i,}\) from the first step. This regression produces a forecasting factor, \(\displaystyle F_{t,}\) shown in equation (2):

\(\displaystyle X_{i,t}\) \(\displaystyle=\, B_{0}\) \(\displaystyle+\, F_{t} \hat A_{i,1}\) \(\displaystyle+\,\epsilon_{i,t}.\)

Intuitively, the estimated forecasting factor \(\displaystyle F_{t}\) will be higher when the spreads of the price-to-earnings ratios mirror the spreads of their correlations with future GDP based on the correlations estimated by \(\displaystyle \hat A_{i,1}\). For example, this will occur when equities that have higher price-to-earnings ratios relative to other equities also tend to have larger correlations with future growth.

The last step is predictive time-series regression of GDP growth \(\displaystyle y_{t+h}\) on the estimated factor \(\displaystyle \hat F_{t,}\) shown in equation (3):

\(\displaystyle y_{t+h}\) \(\displaystyle=\, B_{0}\) \(\displaystyle+\, B_{1} \hat F_{t}\) \(\displaystyle+\,\varphi_{t}.\)

This regression resets the level and scale of the forecasting factor to estimate the factor’s relationship with future realized growth. Results from this regression can therefore be used to evaluate the accuracy of GDP growth forecasts.

We estimate the model using the weighted average of the one-year-ahead price-to-earnings ratios of MSCI Industry Classification Benchmark level 2 sector indexes from Refinitiv. Data on real GDP are from Statistics Canada, and GDP growth is measured as year-over-year real GDP growth. Financial data are from Bloomberg. The sample period ranges from January 2004 to May 2023.

## Endnotes

- 1. The combination of valuation ratios also places significant weight on energy and mining, which is unsurprising given the importance of the commodity sector for Canadian economic growth.[←]

## Disclaimer

Bank of Canada staff analytical notes are short articles that focus on topical issues relevant to the current economic and financial context, produced independently from the Bank’s Governing Council. This work may support or challenge prevailing policy orthodoxy. Therefore, the views expressed in this note 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.

DOI: https://doi.org/10.34989/san-2023-9