Oil price shocks and macroeconomic dynamics: How important is the role of nonlinearity?

Abstract

This study examines the state-dependent effects of crude oil price shocks on the US aggregate economy. Using a smooth transition vector autoregressive model, we assess the effects of normalized supply and demand shocks in the global oil market over the different phases of the business cycle. Our findings show that the link between oil prices and macroeconomic dynamics is nonlinear and that structural shocks in the oil market conditional on recessions have a greater and more persistent contractionary impact on macroeconomic variables including industrial production, employment, and consumer price inflation. Forecast error variance decomposition confirms that oil prices have much stronger stagflationary effects during recessions.

Appendix

1.1 Linearity test at a multivariate level

Following Caggiano et al. (2014, 2017), to test nonlinearity at the multivariate level, we perform the Lagrange multiplier (LM) linearity test proposed by Terasvirta and Yang (2014). The p-dimensional 2-regime first-order Taylor approximation of a logistic STVAR with a single transition variable takes the following form:

$$\begin{aligned} X_{t} =\Theta _{0}^{ \prime } Y_{t} +\Theta _{1}^{ \prime } Y_{t} z_{t} +\varepsilon _{t} \end{aligned}$$

(A1)

where $X_{t} =[\Delta p r o d_{t},r e a_{t},r p o_{t},\pi _{t}, \Delta e m p l_{t}, \Delta i p_{t}]^{ \prime }$ is the $(p \times 1)$ vector of endogenous variables, $Y_{t} =[X_{t -1} \vert \ldots X_{t -k}\vert \alpha ]^{ \prime }$ is the $((k \times p +q) \times 1)$ vector of exogenous variables, $z_{t}$ is the transition indicator variable, and $\Theta _{0}$ and $\Theta _{1}$ are matrices of parameters. In this case, the number of endogenous variables is $p =6$, the number of exogenous variables is $q =1$, and the number of lags is $k =1$ (via (Terasvirta and Yang 2014)). Under the null hypothesis of linearity, $\Theta _{1} =0.$ This LM-type test is performed as follows:

• 1. Estimate the restricted model ($\Theta _{1} =0$) by regressing $X_{t}$ on $Y_{t}$ and collect the residuals ${\tilde{E}}$ and the matrix residual sum of squares $R S S_{0}$ = ${\tilde{E}}^{ \prime } {\tilde{E}}$.

• 2. Run an auxiliary regression of ${\tilde{E}}$ on the unrestricted model (A1) and collect the residuals ${\tilde{\Xi }}$ and the matrix residual sum of squares $R S S_{1} ={\tilde{\Xi }}^{ \prime } {\tilde{\Xi }}$.

• 3. Compute the test statistic $L M =T \times t r a c e (R S S_{0}^{ -1} (R S S_{0} -R S S_{1}))$, where T is the sample size. The test statistic is distributed as a $\chi ^{2}$ with $p \times (k p +q)$ degrees of freedom.

For this model, a value of the LM-test statistic is 104.6 (d.f. = 42) and its corresponding p value is 0.00. Thus, the p value rejects the null hypothesis of linearity, $\Theta _{1} =0$ at any conventional confidence level.

1.2 Nonlinearity inherent in the global oil market

We examine how the effect of different structural oil price shocks on oil prices themselves varies over the different phases of the business cycle. The first block $X_{1 t} =[\Delta p r o d_{t},r e a_{t},r p o_{t}]^{ \prime }$, which constitutes the structural global oil market model, is forced apart and re-estimated via the STVAR. Our finding indicates that the effect of aggregate demand shock on oil prices is business-cycle dependent, while the remaining two shocks have no considerable heterogeneous effects on variations in oil prices over the business cycle (see the Figure 7). The aggregate demand shock triggers the peak in the eighth month (0.45%), but it rises a little bit in the fourth month (0.24%) and then dies out quickly during recessionary periods. It states that a strong decline in US domestic industrial activity substantially attenuates a global boom that tends to lift the real price of oil. This implies that the expansionary effect of aggregate demand shock might be weakened during recessions, but the output response is likely to bounce back via the downward pressure of such shock on the price of oil.

Fig. 7

Responses of the real price of oil to structural shocks in the global oil market: 1973–2018. Note Responses of the real price of oil to one standard-deviation supply and demand shocks in the global oil market. Three structural shocks are normalized to represent that each shock tends to raise the real price of oil following Kilian (2009). Our model features the vector of three endogenous variables: $X_t = [\Delta prod_t; rea_t; rpo_t]^\prime$

Table 3 Descriptive statistics and data sources for robustness checks

Table 4 60 Month-ahead FEVDs the six-variable models with the substitution variables: unemployment

Table 5 60 Month-ahead FEVDs the six-variable models with the substitution variables: WTI spot price

Table 6 60 Month-ahead FEVDs the seven-variable models including a monetary policy variable

1.3 Extra tables for robustness

Table 3 presents the descriptive statistics and data sources for additional variables we used in robustness checks. Tables 4, 5 and 6 reports the 60-month ahead forecast error variance decomposition for robustness checks. Table 4 shows that US unemployment vs. employment qualitatively displays a very similar pattern across different phases of the business cycle. In Table 5, the contribution on headline inflation conditional on recession is fairly muted from 57.6% (our baseline) to 46.6% due to the fact that WTI spot price was under control of the US government partially in our sample. Finally, in Table 6, we confirm that the money-supply growth has much stronger effects on all the variables in recessions than in non-recessions. However, the variation by adding the monetary policy variable is milder for the total explaining power of oil price shocks.