Due to the log penalty term, the Bayesian Information Criterion tends to select more parsimonious models than the AIC (penalty term<sup>2K</sup> �N), hence avoiding overfitting. Accordingly the VAR(q) in matrix notation follows the respective country’s lag length q as determined by BIC: Due to the evidence from Section 3.1. for an autoregressive conditional heteroskedasticity process for returns ρd, the coefficient φi,2,2 is expected to be significantly different from zero. Indeed, VAR estimates confirm that realized volatility is significantly (and positively) autocorrelated in all sample countries.

Crucial for the purposes of this study is that indeed lagged oil price volatility is found to be significant in explaining current Industrial Production. In other words, oil price volatility has a negative impact on economic growth in all sample countries. Furthermore, it is striking to which extent these elasticity measures vary significantly across countries: E.g. the elasticity of economic activity to a volatility shock in the previous period is estimated to be -0.211 in Malaysia, i.e. 6.6 times larger than in the USA (-0.032). The corresponding estimates (i.e. for φi,1,2) are presented in the lower panel of Table 4.

|||<br>|**VAR Outpu **<br>Realized Volat<br>|**t**<br>ility (RV)<br>|||
|---|---|---|---|---|---|---|
||USA|JPN|GER|IND|KOR|MYS|
|IP(-1)|0.103|0.021|-0.111|0.016|0.081|-0.563|
|_S.E._|_-0.078_|_-0.066_|_-0.081_|_-0.064_|_-0.147_|_-0.483_|
|_t-stat_|_[1.314]_|_[ 0.315]_|_[-1.375]_|_[ 0.256]_|_[ 0.550]_|_[-1.165]_|
|IP(-2)|-0.177|0.014|-0.09|0.08|--|-0.009|
|_S.E._|_-0.147_|_-0.066_|_-0.11_|_-0.063_|_--_|_-0.023_|
|_t-stat_|_[-1.203]_|_[ 0.215]_|_[-0.820]_|_[ 1.258]_|_--_|_[-0.406]_|
||||Economic Activ<br>|ity (IP)<br>|||
||USA|JPN|GER|IND|KOR|MYS|
|RV(-1)|-0.032*|-0.085**|-0.103*|-0.058**|-0.152*|-0.211*|
|_S.E._|_-0.01_|_-0.036_|_-0.037_|_-0.024_|_-0.047_|_-0.066_|
|_t-stat_|_[-3.109]_|_[-2.339]_|_[-2.759]_|_[-2.396]_|_[-3.252]_|_[-3.214]_|
|RV(-2)|-0.029*|-0.063**|-0.079**|-0.031|--|-0.074|
|_S.E._|_-0.011_|_-0.027_|_-0.038_|_-0.026_|_--_|_-0.066_|
|_t-stat_|_[-2.723]_|_[-2.365]_|_[-2.079]_|_[ -1.192]_|_--_|_[-1.115]_|

**Table 4.** VAR estimates for first and second lags. Degrees of freedom are based on 332 observations and respective lag length (selected by BIC). Coefficients which are significant at the 1%, 5% or 10% levels are marked by asterisks (*, ** and *** respectively).<sup>8</sup>

# **3.4. Granger Causality**

In order to determine whether the estimated coefficients represent a causal relationship between IPm and RVm, a Granger causality test is applied. As both variables have been found to be stationary, the test is based on the standard VAR(q), with q selected according to the Bayesian Information Criterion. Granger’s (1969) causality test investigates whether lags of RVm have explanatory power in forecasting IPm (and vice versa), i.e. whether φi,1,2 (or φi,2,1) is significantly different from zero. Thus the first null-hypothesis is formulated as Η0: _“IP does not Granger-cause RV”;_ i.e. Η0: φi,2,1 = 0. Table 5 shows that this null cannot be rejected in any of the countries in the given sample period, i.e. supporting earlier results that industrial production has no causal influence on realized volatility.

_′ ′_ More interesting is the second null-hypothesis Η0: _“RV does not Granger-cause IP”_ ; i.e. Η0: φi,1,2 = 0 , meaning that realized volatility has no causal effect on industrial production. However, as the right panel of Table 6. shows, this null hypothesis must be rejected for all countries except the USA at a 5% significance level.

> 8 Intuitively, the upper panel of Table 4 demonstrates that past industrial production is insignificant in explaining current oil price volatility. Rafiq et al. (2009) confirm that other macro indicators also fail to predict oil price variability.

8