Oil Demand and Supply Shocks in Canada’s Economy

Abstract

This paper investigates how oil supply shocks, aggregate demand shocks, and speculative oil demand shocks affect Canada’s economy, within an estimated Dynamic Stochastic General Equilibrium (DSGE) model. The estimation is conducted using Bayesian methods, with Canadian quarterly data from 1983Q1 to 2021Q4. The results suggest that the dynamic effects of oil price shocks on Canadian macroeconomic variables vary according to their sources. In particular, a 10 percent increase in the real price of oil driven by positive foreign aggregate demand shocks has a positive effect of about 1.2 percent on Canada’s real GDP upon impact and the effect remains positive over time. In contrast, an increase in the real price of oil driven by negative foreign oil supply shocks or by positive speculative oil demand shocks causes a small effect of about 0.15 percent on Canada’s real GDP upon impact but causes a slightly decline afterwards. At the same time, an oil price increase that originates from aggregate demand shock causes an increase in consumption and investment, while an oil price increase that originates from oil supply shocks or from speculative oil demand shocks cause a decline in consumption and investment. Furthermore, among the identified oil shocks, aggregate demand shocks have been by fare more important in explaining the variations of most of Canadian macroeconomic variables over the estimation period. In contrast, speculative oil demand shock appears to be the first source of variations in real oil price.

Appendix

A. The Log-Linearized Model

Variables with hats correspond to their log-deviation from their steady state level, except debt.

• 1. Euler equation for consumption:

  $${\widehat{\Lambda }}_{t}=\frac{1}{(1-\hslash )(1-\hslash \beta )}\left(-({\widehat{C}}_{t}-\hslash {\widehat{C}}_{t-1})+\hslash \beta ({\widehat{C}}_{t+1}-\hslash {\widehat{C}}_{t})\right)+\frac{1}{1-\hslash \beta }\left({\widehat{\zeta }}_{u,t}-\hslash \beta {\widehat{\zeta }}_{u,t+1}\right)$$
  $${\widehat{\Lambda }}_{t}={\widehat{\Lambda }}_{t+1}+{\widehat{r}}_{t}$$

• 2. Labor supply:

  $${\widehat{w}}_{t}={\widehat{\zeta }}_{u,t}+\left(\frac{N}{1-N}\right){\widehat{N}}_{t}-{\widehat{\Lambda }}_{t}$$
  $${\widehat{N}}_{t}={\left(\frac{{N}_{o}}{N}\right)}^{\frac{\varsigma +1}{\varsigma }}{\widehat{N}}_{o,t}+{\left(\frac{{N}_{d}}{N}\right)}^{\frac{\varsigma +1}{\varsigma }}{\widehat{N}}_{d,t}$$
  $${\widehat{w}}_{o,t}={\widehat{w}}_{t}+\frac{1}{\varsigma }({\widehat{N}}_{o,t}-{\widehat{N}}_{t})$$
  $${\widehat{w}}_{d,t}={\widehat{w}}_{t}+\frac{1}{\varsigma }({\widehat{N}}_{d,t}-{\widehat{N}}_{t})$$

• 3. Log-linearized capital first-order condition

  $${\widehat{r}}_{t}=\left(1-\beta (1-\delta )\right){E}_{t}{\widehat{r}}_{s,t+1}^{k}+\beta (1-\delta ){E}_{t}{\widehat{q}}_{s,t+1}-{\widehat{q}}_{s,t}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}{\text{for}}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}s\in \{o,d\}$$

• 4. Log-linearized investment first-order condition

  $${\widehat{q}}_{s,t}={\kappa }_{s}\left(\Delta {\widehat{I}}_{s,t}-\beta {E}_{t}\Delta {\widehat{I}}_{s,t+1}\right)\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}{\text{for}}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}s\in \{o,d\}$$

• 5. Capital accumulation:

  $${\widehat{K}}_{s,t}=(1-\delta ){\widehat{K}}_{s,t-1}+\delta {\widehat{I}}_{s,t}+\delta \hspace{0.33em}\hspace{0.33em}\hspace{0.33em}{\text{for}}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}s\in \{o,d\}$$

• 6. Uncovered interest parity condition:

  $${\widehat{r}}_{t}={\widehat{r}}_{t}^{\star }+{\widehat{\Phi }}_{{B}_{t}^{\star }}+{E}_{t}\Delta {\widehat{s}}_{t+1}$$

• 7. The Risk premium of borrowing abroad is:

  $${\widehat{\Phi }}_{{B}_{t}^{\star }}=-\varrho \left(\frac{s.{b}^{\star }}{Y}\right)({\widehat{s}}_{t}+{\widehat{b}}_{t}^{\star }-{\widehat{Y}}_{t})$$

• 8. Final good composition:

  $${\widehat{Y}}_{d,t}^{z}={\widehat{Z}}_{t}-\theta {\widehat{p}}_{d,t}$$
  $${\widehat{Y}}_{m,t}={\widehat{Z}}_{t}-\theta {\widehat{p}}_{m,t}$$
  $$0=(1-{\omega }_{m}){\widehat{p}}_{d,t}+{\omega }_{m}{\widehat{p}}_{m,t}$$

• 9. Production sector of crude oil:

  $${\widehat{Y}}_{o,t}={\widehat{A}}_{o,t}+\left(\frac{{W}_{o}{N}_{o}}{{e}_{t}{P}_{o}^{\star }{Y}_{d}}\right){\widehat{N}}_{o,t}+\left(\frac{{R}_{o}^{k}{K}_{o}}{{e}_{t}{P}_{o}^{\star }{Y}_{o}}\right){\widehat{K}}_{o,t-1}+\left(\frac{{P}_{X}X}{{e}_{t}{P}_{o}^{\star }{Y}_{o}}\right){\widehat{X}}_{t}$$
  $${\widehat{w}}_{o,t}={\widehat{s}}_{t}+{\widehat{p}}_{o,t}^{\star }-\frac{1}{{\xi }_{o}}{\widehat{N}}_{o,t}+\frac{1}{{\xi }_{o}}{\widehat{Y}}_{o,t}+\left(1-\frac{1}{{\xi }_{o}}\right){\widehat{A}}_{o,t}$$
  $${\widehat{r}}_{o,t}^{k}={\widehat{s}}_{t}+{\widehat{p}}_{o,t}^{\star }-\frac{1}{{\xi }_{o}}{\widehat{K}}_{o,t-1}+\frac{1}{{\xi }_{o}}{\widehat{Y}}_{o,t}+\left(1-\frac{1}{{\xi }_{o}}\right){\widehat{A}}_{o,t}$$
  $${\widehat{p}}_{X,t}={\widehat{s}}_{t}+{\widehat{p}}_{o,t}^{\star }-\frac{1}{{\xi }_{o}}{\widehat{X}}_{t}+\frac{1}{{\xi }_{o}}{\widehat{Y}}_{o,t}+\left(1-\frac{1}{{\xi }_{o}}\right){\widehat{A}}_{o,t}$$
  $${\widehat{p}}_{o,t}={\widehat{s}}_{t}+{\widehat{p}}_{o,t}^{\star }$$

• 10. Supply of oil reserves:

  $${\widehat{X}}_{t}=0$$

• 11. Production sector of domestic good:

  $${\widehat{Y}}_{d,t}={\widehat{A}}_{d,t}+\left(\frac{{W}_{d}{N}_{d}}{{P}_{d}{Y}_{d}}\right){\widehat{N}}_{d,t}\left(\frac{{R}_{d}^{k}{K}_{d}}{{P}_{d}{Y}_{d}}\right){\widehat{K}}_{d,t-1}+\left(\frac{{P}_{o}O}{{P}_{d}{Y}_{d}}\right){\widehat{O}}_{t}$$
  $${\widehat{w}}_{d,t}={\widehat{p}}_{d,t}-\frac{1}{{\xi }_{d}}{\widehat{N}}_{d,t}+\frac{1}{{\xi }_{d}}{\widehat{Y}}_{d,t}+\left(1-\frac{1}{{\xi }_{d}}\right){\widehat{A}}_{d,t}$$
  $${\widehat{r}}_{d,t}^{k}={\widehat{p}}_{d,t}-\frac{1}{{\xi }_{d}}{\widehat{K}}_{d,t-1}+\frac{1}{{\xi }_{d}}{\widehat{Y}}_{d,t}+\left(1-\frac{1}{{\xi }_{d}}\right){\widehat{A}}_{d,t}$$
  $${\widehat{p}}_{o,t}={\widehat{p}}_{d,t}-\frac{1}{{\xi }_{d}}{\widehat{O}}_{t}+\frac{1}{{\xi }_{d}}{\widehat{Y}}_{d,t}+\left(1-\frac{1}{{\xi }_{d}}\right){\widehat{A}}_{d,t}-{\phi }_{o}\left(({\widehat{O}}_{t}-{\widehat{Y}}_{d,t})-({\widehat{O}}_{t-1}-{\widehat{Y}}_{d,t-1})\right)$$

• 12. Price of imported good:

  $${\widehat{p}}_{m,t}={\widehat{s}}_{t}+{\zeta }_{m,t}$$

• 13. Foreign oil demand:

  $${\widehat{O}}_{t}^{\star }={\widehat{Y}}_{t}^{\star }-{\varphi }_{o}^{\star }{\widehat{p}}_{o,t}^{\star }$$

• 14. Foreign real interest rate

  $${\widehat{r}}_{t}^{\star }={\varphi }_{r}({E}_{t}{\widehat{Y}}_{t+1}^{\star }-{\widehat{Y}}_{t}^{\star })$$

• 15. Exports of domestic good:

  $${\widehat{Y}}_{d,t}^{ex}={\widehat{Y}}_{t}^{\star }-{\theta }_{ex}({\widehat{p}}_{d,t}-{\widehat{s}}_{t})$$

• 16. Speculative or Precautionary demand of crude oil

  $${\widehat{OS}}_{t}={\Theta }_{OS}\left[\beta ({E}_{t}{\widehat{p}}_{o,t+1}^{\star }-{\widehat{r}}_{t}^{\star })-{\widehat{p}}_{o,t}^{\star }\right]+{\widehat{Z}}_{os,t}$$

• 17. Net foreign asset dynamic:

  $$\left(\frac{s.{b}^{\star }}{Y}\right)\left({\widehat{s}}_{t}+{\widehat{b}}_{t}^{\star }\right)={\beta }^{-1}\left(\frac{s.{b}^{\star }}{Y}\right)\left({\widehat{\Phi }}_{{B}_{t-1}^{\star }}{\widehat{R}}_{t-1}^{\star }-{\widehat{\pi }}_{t}^{\star }+{\widehat{s}}_{t}+{\widehat{b}}_{t-1}^{\star }\right)+\left(\frac{{P}_{d}{Y}_{d}^{ex}}{P.Y}\right)\left({\widehat{p}}_{d}+{\widehat{Y}}_{d}^{ex}\right)+\left(\frac{e{P}_{o}^{\star }{O}^{ex}}{P.Y}\right)\left({\widehat{s}}_{t}{\widehat{p}}_{o,t}^{\star }+{\widehat{O}}_{t}^{ex}\right)-\left(\frac{e.{Y}_{m}}{Y}\right)\left({\widehat{s}}_{t}+{\widehat{Y}}_{m,t}\right)$$

• 18. Real gross domestic product (GDP):

  $$\begin{array}{ccc}{\widehat{Y}}_{t}& =& \left(\frac{P.C}{P.Y}\right){\widehat{C}}_{t}+\left(\frac{P.I}{P.Y}\right){\widehat{I}}_{t}+\left(\frac{P.G}{P.Y}\right){\widehat{G}}_{t}+\left(\frac{e{P}_{o}^{\star }{O}^{ex}}{P.Y}\right)\left({\widehat{s}}_{t}+{\widehat{p}}_{o,t}^{\star }+{\widehat{O}}_{t}^{ex}\right)+\left(\frac{{P}_{d}{Y}_{d}^{ex}}{P.Y}\right)\left({\widehat{p}}_{d,t}+{\widehat{Y}}_{d,t}^{ex}\right)-\left(\frac{e.{Y}_{m}}{P.Y}\right)\left({\widehat{s}}_{t}+{\widehat{Y}}_{m,t}\right)\end{array}$$

• 19. Markets clearing:

  $${\widehat{I}}_{t}=\left(\frac{{I}_{o}}{I}\right){\widehat{I}}_{o,t}+\left(\frac{{I}_{d}}{I}\right){\widehat{I}}_{d,t}$$
  $${\widehat{Y}}_{d,t}=\left(\frac{{Y}_{d}^{z}}{{Y}_{d}}\right){\widehat{Y}}_{d,t}^{z}+\left(\frac{{Y}_{d}^{ex}}{{Y}_{d}}\right){\widehat{Y}}_{d,t}^{ex}$$
  $${\widehat{Z}}_{t}=\left(\frac{C}{Z}\right){\widehat{C}}_{t}+\left(\frac{I}{Z}\right){\widehat{I}}_{t}+\left(\frac{G}{Z}\right){\widehat{G}}_{t}$$
  $${\widehat{Y}}_{o,t}=\frac{O}{{Y}_{o}}{\widehat{O}}_{t}+\frac{{O}^{ex}}{{Y}_{o}}{\widehat{O}}_{t}^{ex}$$
  $$\left(\frac{OS}{{Y}_{o}^{\star }}\right)({\widehat{OS}}_{t}-{\widehat{OS}}_{t-1})={\widehat{Y}}_{o,t}^{\star }+\left(\frac{{Y}_{o}}{{Y}_{o}^{\star }}\right){\widehat{Y}}_{o,t}-\left(\frac{{O}^{\star }}{{Y}_{o}^{\star }}\right){\widehat{O}}_{t}^{\star }-\left(\frac{O}{{Y}_{o}^{\star }}\right){\widehat{O}}_{t}$$

• 20. Exogenous processes:

  $${\widehat{\lambda }}_{t}={\rho }_{\lambda }{\widehat{\lambda }}_{t-1}^{\star }+{\epsilon }_{\lambda ,t}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\text{for }\lambda =\left\{{Y}_{o}^{\star },{Y}^{\star },{Z}_{os},{A}_{o},{A}_{d},{\zeta }_{u},{\zeta }_{m},G\right\}$$

B. Data Sources

This appendix lists the time series used to construct the observable variables for the estimation. All series consist of 156 quarterly observations from 1983Q1 to 2021Q4.

Statistics Canada, Gross domestic product, expenditure-based (Table 36–10-0104–01), seasonally adjusted at annual rate:

• 1. Gross Domestic Product, Chained 2012 dollars.

• 2. Gross Domestic Product, current dollars.

• 3. Household final consumption expenditure, current dollars.

• 4. Business gross fixed capital formation, current dollars.

• 5. General governments final consumption expenditure, current dollars.

• 6. General governments gross fixed capital formation, current dollars.

• 7. Labor force. Statistics Canada (Table: 14–10-0017–01).

Federal Reserve Bank of St. Louis Databank:

• 8. Canadian Dollars to U.S. Dollar Spot Exchange Rate. (Identification code: EXCAUS)

• 9. Spot Crude Oil Price: West Texas Intermediate, Dollars per Barrel. (Identification code: WTISPLC)

• 10. U.S. Personal Consumption Expenditures. (Identification code: GDPDEF)

U.S. Energy Information Administration (EIA)

• 11. Oil Production in Canada, thousand barrels per day.

• 12. Oil Production in World, thousand barrels per day.

Personal Transformations:

• 13. GDP Deflator = (2)/(1).

• 14. Real Per Capita GDP (1)/(7)

• 15. Real Per Capita Consumption = (3)/(13)/(7).

• 16. Real Per Capita Investment = (4)/(13)/(7).

• 17. Real Per Capita Government Expenditure = [(5) + (6)]/(13)/(7).

• 18. Per Capita Oil Production in Canada = (11)/(7).

• 19. Per Capita Oil Production in the Rest Of World = [(11)-(12)]/(7).

• 20. Real Exchange Rate = [(10)*(8)])/(13).

• 21. Real Price of Oil = (9)/(10).