Which Side of the Economy Is Affected More by Oil Prices: Supply or Demand?

Abstract

This chapter develops a New Keynesian model to examine a theoretical global economy with two basic macroeconomic components: an energy producer and an energy consumer. (From now on in this chapter whenever we refer to the “energy” or “energy prices”, we refer to “crude oil” and “crude oil price”, which is the main source of energy.) This simple economy uses these two components to evaluate how oil prices affect the consumer economy’s gross domestic product and inflation from 1960 to 2011. This model assumes that changes in the oil price transfer to macro variables through either supply (aggregate supply curve) or demand channels (aggregate demand curve). In order to examine the effects of this transfer, an IS curve is used to look at the demand side and a Phillips curve is used to analyze inflationary effects from the supply side. The empirical analysis concludes that movements in the oil price mainly affect the economy through the demand side (shifting the aggregate demand curve) by affecting household expenditures and energy consumption. This analysis provides several additional findings, among which is that easy monetary policies amplify energy demand more than supply, resulting in skyrocketing crude oil prices, which inhibit economic growth.

An earlier version of this chapter first appeared as F. Taghizadeh-Hesary and N. Yoshino. 2013. Which side of the economy is affected more by oil prices: Supply or demand? USAEE Research Paper No. 13-139. Reused with permission from the United States Association for Energy Economics.

Appendix

3.1.1 (a) Euler, Money Demand , Labor Supply Equations (Log-Linearized Version)

The log-linearized versions of Eqs. (3.5, 3.6, and 3.7) are shown as:

$$ \begin{array}{ll}{c}_t=-\frac{b}{\eta }+{E}_t{c}_{t+1}+\frac{1}{\eta }{E}_t{\pi}_{t+1};\hfill & b= Log\beta, {E}_t{\pi}_{t+1}={E}_t{p}_{t+1}^c-{p}_t^c\hfill \end{array} $$

(3.38)

$$ \begin{array}{ll}{m}_t=\frac{1}{\sigma }{p}_t^c+\frac{\eta }{\sigma }{c}_t+\frac{v}{\sigma };\hfill & v= Log\chi \hfill \end{array} $$

(3.39)

$$ {l}_t=\frac{1}{\kappa}\left({w}_t-{p}_t^c-\eta {C}_t\right) $$

(3.40)

The lowercase letters denote the logarithms of the corresponding upper case variables. By solving these three equations for c _t which is consumption in logarithmic form, the consumption equation yields:

$$ {c}_t=\frac{-b+v}{\eta }+{E}_t{c}_{t+1}+\frac{1}{\eta }{E}_t{\pi}_{t+1}-\frac{\sigma }{\eta }{m}_t+\frac{1}{\eta }{w}_t-\frac{\kappa }{\eta }{l}_t $$

(3.41)

3.1.2 (b) Household Energy Consumption

Since earlier in Eq. (3.38) of Sect. a of the Appendix we had written ${E}_t{\pi}_{t+1}={E}_t\left({p}_{t+1}^c\right)-{p}_t^c$, here we convert it back, and substitute the right hand side of it in Eq. (3.41) of Sect a of the Appendix in order to release energy prices and non-energy prices from p ^c _t . We log linearize the CPI equation (Eq. 3.39) as follows:

$$ \begin{array}{ll}{p}_t^c=\varepsilon -A\left(a-{p}_t^{NG}\right)+\left(A-1\right)\;\left(z-{p}_t^G\right);\hfill & \varepsilon = Log\lambda, a= Log A,z= Log\left(1-A\right)\hfill \end{array} $$

(3.42)

By substituting it and the expected value of Eq. (3.39) of Sect. a of the Appendix for t + 1 in Eq. (3.41) of Sect. a of the Appendix, the logarithmic form of the household consumption equation yields:

$$ {c}_t=\frac{-b-\varepsilon -\left(A-1\right)z+ Aa}{\eta }-\frac{A}{\eta }{p}_t^{NG}+\frac{\left(A-1\right)}{\eta }{p}_t^G+\frac{\sigma }{\eta }{E}_t{m}_{t+1}-\frac{\sigma }{\eta }{m}_t+\frac{1}{\eta }{w}_t-\frac{\kappa }{\eta }{l}_t $$

(3.43)

Substituting the anti-log of Eq. (3.43) of Sect. b of the Appendix into Eq. (2) of footnote 22, gives the demand of representative household for energy yields.

3.1.3 (c) Phillips Curve (Part 1)

Real marginal cost is written as follows:

$$ {s}_t=\left(\phi {W}_t+\varpi {P}_t^G\right) $$

(3.44)

Following Woodford’s (2003) analysis, we write the equation below, which shows the relationship between marginal cost of supply and output levels:

$$ {\widehat{s}}_t=\omega {\widehat{Q}}_t+{\sigma}^{-1}{\widehat{Y}}_t-\left(\omega +{\sigma}^{-1}\right){\widehat{Y}}_t^n $$

(3.45)

Where $\omega >0$ and $\sigma >0$. Letting $\overline{Y}$ be the constant level of output in a steady state, and be level of output in full employment, we define ${\widehat{Q}}_t= \log \left({Q}_t/\overline{Y}\right)$, ${\widehat{Y}}_t= \log \left({Y}_t/\overline{Y}\right)$, ${\widehat{Y}}_t^n= \log \left({Y}_t^n/\overline{Y}\right)$, and ${\widehat{s}}_t= \log \left(\mu {s}_t\right)$, where $\mu =\theta /\left(\theta -1\right)>1$ is the seller’s desired markup. Substituting Eq. (3.45) in Sect. c of the Appendix in the following inflation equation from Calvo (1983) produces the following results:

$$ {\pi}_t=\xi {\widehat{s}}_t+\psi {E}_t{\pi}_{t+1} $$

(3.46)

$$ {\pi}_t\left\lfloor \omega {\widehat{Q}}_t+{\sigma}^{-1}{\widehat{Y}}_t-\left(\omega +{\sigma}^{-1}\right){\widehat{Y}}_t^n\right\rfloor \xi +\psi {E}_t{\pi}_{t+1} $$

(3.47)

Dividing Eq. (3.15) by $\overline{Y}$ and obtaining the Log-linearization of this equation results in the following :

$$ {\widehat{Q}}_t= \log \left[\frac{Y_t}{\overline{Y}}\left(\frac{P_t^c}{P_t^{NG}}\right)\right]={\widehat{Y}}_t+{p}_t^c-{p}_t^{NG} $$

(3.48)

The corresponding log-linear approximation to the aggregate price index is as follows:

$$ {p}_t^c=\iota {p}_t^G+\left(1+\iota \right){p}_t^{NG} $$

(3.49)

Substituting the log linear aggregate price index (Eq. (3.49) of Sect. c of the Appendix) along with Eq. (3.48) of Sect. c of the Appendix into Eq. (3.47) of Sect. c of the Appendix yields a New-Keynesian Phillips curve:

$$ {\pi}_t=\xi \left\lfloor \left(\omega +{\sigma}^{-1}\right)\left({\widehat{Y}}_t-{\widehat{Y}}_t^n\right)+\omega \left(\iota {p}_t^G-\iota {p}_t^{NG}\right)\right\rfloor +\psi {E}_t{\pi}_{t+1} $$

(3.50)

We followed the Blanchard and Kahn (1980) method for rational expectations:

$$ {E}_t{\pi}_{t+1}=\frac{1}{\psi }{\pi}_t-\frac{\xi }{\psi}\left[\left(\omega +{\sigma}^{-1}\right)\left({\widehat{Y}}_t-{\widehat{Y}}_t^n\right)+\omega \left(\iota {p}_t^G-\iota {p}_t^{NG}\right)\right] $$

(3.51)

Then for the previous period we have:

$$ {E}_{t-1}{\pi}_t=\frac{1}{\psi }{\pi}_{t-1}-\frac{\xi }{\psi}\left[\left(\omega +{\sigma}^{-1}\right)\left({\widehat{Y}}_{t-1}-{\widehat{Y}}_{t-1}^n\right)+\omega \left(\iota {p}_{t-1}^G-\iota {p}_{t-1}^{NG}\right)\right] $$

(3.52)

This obtains the ${E}_{t-1}$ value of Eq. (3.50) of Sect. c of the Appendix, which we can write in for the ${E}_t{\pi}_{t+1}$ results :

$$ {E}_t{\pi}_{t+1}=\frac{1}{\psi }{E}_{t-1}{\pi}_t-\frac{\xi }{\psi }{E}_{t-1}\left[\left(\omega +{\sigma}^{-1}\right)\left({\widehat{Y}}_t-{\widehat{Y}}_t^n\right)+\omega \left(\iota {p}_t^G-\iota {p}_t^{NG}\right)\right] $$

(3.53)

After substituting ${E}_{t-1}{\pi}_t$ from Eq. (3.52) of Sect. c of the Appendix with Eq. (3.53) of Sect. c of the Appendix and then setting Eq. (3.51) of Sect. c of the Appendix and Eq. (3.53) of Sect. c of the Appendix as equal the Phillips curve yields, however, it becomes apparent that this is not the final version of it and we need to do some more work on it.

3.1.4 (d) Phillips Curve (Part 2)

Initial version of Phillips curve:

$$ {\pi}_t=\frac{1}{\psi }{\pi}_{t-1}-\frac{\xi }{\psi}\left[\left(\omega +{\sigma}^{-1}\right)\left[{\widehat{Y}}_{t-1}-{\widehat{Y}}_{t-1}^n\right]+\omega \left(\iota {p}_{t-1}^G-\iota {p}_{t-1}^{NG}\right)\right]+{\varepsilon}_t $$

(3.54)

From Eq. (3.49) of Sect. c of the Appendix, we write the inflation rate in t-1 and substitute it in Eq. (3.54) of Sect. d of the Appendix, making it so that the final Phillips curve yields the results in Eq. (3.17).

3.1.5 (e) Equation 20 Derivations

Considering the initial version of our Phillips curve (Eq. (3.54) of Sect. d of the Appendix) by solving for ${E}_t{\pi}_{t+1}-{E}_{t-1}{\pi}_t$:

$$ {E}_t{\pi}_{t+1}-{E}_{t-1}{\pi}_t=\frac{1}{\psi}\left({\pi}_t-{\pi}_{t-1}\right)-\frac{\xi }{\psi}\left(\begin{array}{l}\left[\left(\omega +{\sigma}^{-1}\right)\kern0.5em \left({\widehat{Y}}_t-{\widehat{Y}}_t^n\right)+\iota \omega \left({p}_t^G-\iota {p}_t^{NG}\right)\right]-\hfill \\ {}\left[\left(\omega +{\sigma}^{-1}\right)\left({\widehat{Y}}_{t-1}-{\widehat{Y}}_{t-1}^n\right)-\iota \omega \left({p}_{t-1}^G-\iota {p}_{t-1}^{NG}\right)\right]\hfill \end{array}\right) $$

(3.55)

We assume the equation:

$$ \left\lfloor \left(\omega +{\sigma}^{-1}\right)\left({\widehat{Y}}_t-{\widehat{Y}}_t^n\right)+\iota \omega \left({p}_t^G-\iota {p}_t^{NG}\right)\right\rfloor ={\vartheta}_t $$

(3.56)