Do oil prices predict economic growth? New global evidence

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Author's personal copy Energy Economics 41 (2014) 137–146

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Do oil prices predict economic growth? New global evidence Paresh Kumar Narayan a,⁎, Susan Sharma a, Wai Ching Poon b, Joakim Westerlund a a b

Centre for Financial Econometrics, School of Accounting, Economics and Finance, Deakin University, Australia School of Business, Monash University, Malaysia Campus, Malaysia

a r t i c l e

i n f o

Article history: Received 11 June 2013 Received in revised form 7 October 2013 Accepted 7 November 2013 Available online 21 November 2013 JEL classification: C22 E31 E37 F43

a b s t r a c t In this paper, we test whether oil price predicts economic growth for 28 developed and 17 developing countries. We use predictability tests that account for the key features of the data, namely, persistency, endogeneity, and heteroskedasticity. Our analysis considers a large number of countries, shows evidence of more out-of-sample predictability with nominal than real oil prices, finds in-sample predictability to be independent of the use of nominal and real prices, and reveals greater evidence of predictability for developed countries. © 2013 Elsevier B.V. All rights reserved.

Keywords: Economic growth Predictability Oil price

1. Introduction That there is a relationship between oil price and economic growth is well-known. Two strands of the literature have reinforced this. Consider first the studies that have estimated the effects of oil prices on economic growth.1 The main findings of this literature are two-fold: (a) oil price generally has a negative effect on economic growth (Kilian, 2008; Kilian and Vigfusson, 2011a); and (b) the oil price effect need not be linear (Hamilton, 2003; Kilian and Vigfusson, 2011b). The latter finding implies that oil prices tend to affect countries differently depending on their stage of development. The second strand of literature owes much to the early work of Hamilton (1983), and tests whether oil prices have any predictive content. Typically, these studies fit a predictive regression model of economic growth in which oil price appears as a predictor variable; see also Hamilton (2011). As much as this literature is growing and is attractive, given the gradual rise in oil prices over the last decade and the ramifications for economic performance, a key limitation is also rather obvious. Much of the research on the economic growth–oil price nexus focuses on the US economy. Outside of the US, not much is known on whether or ⁎ Corresponding author at: Alfred Deakin Professor, School of Accounting, Economics and Finance, Faculty of Business and Law, Deakin University, 221 Burwood Highway, Burwood, Victoria 3125, Australia. Tel.: +61 3 9244 6180; fax: +61 3 9244 6034. E-mail address: [email protected] (P.K. Narayan). 1 Indeed there are studies, such as Ferderer (1996), Elder and Serletis (2010), Rahman and Serletis (2012), that have considered the effects of oil price volatility on economic growth. 0140-9883/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.eneco.2013.11.003

not the oil price predicts economic growth. In light of this research gap, we test whether oil price predicts economic growth in 45 countries, of which 28 are developed and 17 are developing. We use quarterly time series data. Our predictive regression model is familiar in that economic growth (proxied by either growth in real gross domestic product or industrial production) is regressed on the one-period lagged oil price variable. The contribution of our paper is three-fold. First, our paper not only focuses on the US, which has previously been the main subject of this literature, but also includes as many as 44 additional developed and developing countries. A multi-country study of whether or not oil price predicts economic growth allows us to better understand the role of oil prices on a more global level. At this stage, it is fair to claim that the role of oil prices in economic growth is very much unknown from a global point of view. Our proposed empirical investigation narrows this research gap. Our second contribution is relatively more methodological in that we pay particular attention to the salient features of data, namely, persistency, endogeneity, and heteroskedasticity, that matter directly for the performance of predictive regression models. The first issue relates to the persistent nature of the predictor variable. Specifically, the existence of persistent predictors has been shown to lead to the failure of conventional asymptotic theory for exogenous regressors (see Elliot and Stock, 1994), leading to deceptive inference. We find that oil price is highly persistent; not only do we accept the unit root null hypothesis, we also find the autoregressive coefficient of the oil price variable to be close to one. Then there is the issue of endogeneity of the predictor

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variable. It would be bold to claim that oil price is purely exogenous. For example, by generating higher demand for oil, growth could also influence oil price. Therefore, formally testing whether or not oil price is endogenous is a matter of prerequisite, for, as already alluded, endogeneity of the predictor variable has been shown to bias the results on predictability. The final issue is that of heteroskedasticity. Westerlund and Narayan (2012) show that if heteroskedasticity is present and it is correctly accounted for in predictive regression models, then the properties of the resulting predictability test are better compared to when heteroskedasticity is ignored. Our approach to addressing these three issues is to use the bias-adjusted ordinary least squares (OLS) estimator of Lewellen (2004), and the Westerlund and Narayan (2012) generalised least squares (GLS) estimator. The main difference between the two is that while the former estimator accounts for only persistency and endogeneity, the latter estimator is flexible enough to cater for all three features of the data. To put these issues into perspective, let us at the outset acknowledge that while the literature has been mindful of the issue of persistent predictors, the issue of endogeneity has received little attention, while that of heteroskedasticity has been completely ignored. Ignoring these features of the data comes at a cost as they have direct implications for the outcome on predictability. Third, we establish the robustness of our findings by undertaking both in-sample and out-of-sample predictability analyses. This approach is not common in the literature, and some studies (Ashley et al., 1980; Rapach and Wohar, 2006) suggest that perhaps an out-ofsample analysis is relatively more important to policy makers than insample evidence. A related group of studies (Foster et al., 1997; Lo and MacKinlay, 1990) claim that in-sample tests suffer from data mining. Inoue and Kilian (2004), however, show that in-sample and out-ofsample tests of predictability are equally reliable against data mining under the null hypothesis of no predictability. What is clear from this literature is that there is no shortage of tension when it comes to the choice between in-sample and out-of-sample evaluations and we are avoiding being caught in this debate. The best way forward is to undertake both in-sample and out-of-sample evaluations. Doing so not only makes the predictability analysis complete but it also allows us to gauge the robustness of our results. Briefly foreshadowing the main findings, we find that nominal oil price predicts economic growth for 37 of the 45 countries and for around 70% of the countries there is evidence of out-of-sample predictability. When we use real oil price, like with nominal oil price, we discover strong evidence of in-sample predictability (for 36 countries). However, evidence on out-of-sample predictability is weak. At best, only for around 55% of the countries there is evidence of out-ofsample predictability. Finally, we find that with nominal oil price both in-sample and out-of-sample evidence of predictability are found for 33 countries while for real oil price this evidence is only found for 30 countries. We organise the balance of the paper as follows. In Section 2, we discuss the data and methodology. In Section 3, we discuss the results. In the final section, we provide concluding remarks. 2. Data and methodology 2.1. Data This paper is based on a quarterly data set that includes 45 countries. Of these 45 countries, 17 are developing countries and the balance is developed countries. The sample size is dictated by data availability. We have quarterly data. For 68% of the countries in our sample the data span the period 1983Q2 to at least 2010Q4. Therefore, for most countries we have no less than 113 quarterly observations. The specific dates of data for each country are reported in the last column of Table 1. The world average crude oil price and industrial production index are obtained from the International Financial Statistics (IFS) published by the International Monetary Fund, while data on quarterly

real GDP growth rate are obtained from the World Development Indicators published by the World Bank. The nominal crude oil price was converted into the real crude oil price by using the country-specific consumer price index, which was obtained from the IFS. 2.2. Estimation approach A typical predictive regression model, where oil price is considered as a predictor of economic growth, has the following form: yt ¼ α þ βOP t−1 þ εy;t :

ð1Þ

Here, yt is the economic growth in quarter t proxied by either the growth rate in real GDP or industrial production, and OPt is the average world crude oil price in US dollars in the same quarter. The null hypothesis of no predictability is H0 : β = 0. As explained earlier, in the above specification, it is possible that oil price is endogenous. If it is, one can expect a bias, leading to deceptive inference on the no predictability null. Given that in our empirical analysis we have relatively small sample sizes, the implications of endogeneity could be serious. To avoid this, we follow Westerlund and Narayan (2012) and model oil price as follows: OP t ¼ μ ð1−λÞ þ λOP t−1 þ εop;t

ð2Þ

where εop,t is mean zero and with variance σ2op. If the error terms from Eqs. (1) and (2) are correlated, then oil price is said to be endogenous. In order to allow for this possibility, we assume that the error terms are linearly related in the following way: εy;t ¼ θε op;t þ t

ð3Þ

where t is again mean zero and with variance σ2 . We use two estimators, bias-adjusted OLS and GLS. Both estimators are based on making Eq. (1) conditional on Eq. (2), thereby removing the effect of the endogeneity. The resulting conditional predictive regression can be written as2: yt ¼ α−θμ ð1−λÞ þ β

adj

OP t−1 þ θOP t þ t

ð4Þ

where t is independent of εop,t by construction and βadj = β − θ(λ − 1). The bias-adjusted OLS estimator of Lewellen (2004) is basically the OLS estimator of βadj = β − θ(λ − 1) in Eq. (4). The key difference between this estimator and the one of Westerlund and Narayan (2012) is the accounting for potential conditional heteroskedasticity in t. Lewellen (2004) uses OLS, which means that any information contained in the heteroskedasticity is ignored. The GLS estimator, on the other hand, exploits this information and is therefore expected to be more precise.3 In particular, it is assumed

2 The literature on predictability models has moved away from treating a predictor variable as purely stationary because in practice it is not. Although the null hypothesis of unit root can be comfortably rejected for many predictors, they are still very highly persistent. In other words, many predictors are shown and, as a result, known to be only slowly mean-reverting. Let us see this. Denote the predictor variable by yt, such that we have yt = ρyt − 1 + εt. Standard asymptotic theory, which presumes that |ρ| b 1, is likely to be inappropriate because predictors are shown to be persistent even though the unit root null hypothesis can be comfortably rejected (see Campbell and Yogo, 2006; Elliot and Stock, 1994; Lewellen, 2004; Westerlund and Narayan, 2012). In particular, Elliot and Stock (1994) show that even if {tt}Tt = 1 is stationary, if ρ ≈ 1, the standard asymptotic theory is likely to provide a poor approximation in small samples. As a response to this, researchers have considered alternative frameworks based on ‘local asymptotic theory’ (see Campbell and Yogo, 2006; Cavanagh et al., 1995; Lanne, 2002; Lewellen, 2004; Torous et al., 2004; and Westerlund and Narayan, 2012). This theory allows one to model a highly persistent predictor variable. 3 The size adjusted power gain from using the GLS test statistic over the OLS test statistic in small sample sizes is estimated to be around 20% (Westerlund and Narayan, 2012).

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Table 1 Results for unit-root test, mean and standard deviation (nominal oil price as predictor). No.

Country

IPg/GDPg

Oil price (OP)

Mean

Std deviation

Dates

Test stat[LL]

p-Value

Test stat[LL]

p-Value

IPg/GDPg

OP

IPg/GDPg

OP

Panel A: Developed countries 1 Australia 2 Belgium 3 Canada 4 Czech Republic 5 Denmark 6 Finland 7 France 8 Germany 9 Greece 10 Hong Kong 11 Hungary 12 Iceland 13 Ireland 14 Israel 15 Italy 16 Japan 17 Malta 18 Netherlands 19 New Zealand 20 Norway 21 Portugal 22 Singapore 23 South Korea 24 Spain 25 Sweden 26 Switzerland 27 UK 28 US

−2.943[7] −4.297[3] −10.273[0] −3.843[3] −5.241[3] −10.505[0] −4.995[5] −9.582[0] −4.284[3] −3.086[7] −3.590[4] −1.816[4] −13.830[0] 3.827[0] −4.442[4] −6.485[4] −9.201[0] −4.825[7] −3.836[4] 1.739[7] −2.336[7] −5.105[0] −3.226[7] −4.563[5] −4.481[5] −4.514[3] −9.231[0] −4.592[4]

0.044 0.001 0.000 0.003 0.000 0.000 0.000 0.000 0.000 0.030 0.008 0.368 0.000 0.003 0.000 0.000 0.000 0.000 0.004 0.409 0.163 0.0003 0.021 0.000 0.000 0.000 0.000 0.000

−1.741[2] −2.167[2] −1.848[2] −2.561[2] −1.741[2] −2.166[2] −1.741[2] −1.848[2] −1.741[2] −2.167[2] −1.848[2] −4.105[1] −1.848[2] −1.741[2] −1.741[2] −1.848[2] −3.758[1] −1.741[2] −1.930[2] −1.741[2] −1.848[2] −3.161[1] −2.167[2] −1.741[2] −1.741[2] −1.741[2] −1.848[2] −1.848[2]

0.726 0.503 0.675 0.299 0.726 0.503 0.726 0.675 0.726 0.503 0.675 0.012 0.675 0.726 0.726 0.675 0.025 0.726 0.631 0.726 0.675 0.113 0.503 0.726 0.726 0.726 0.675 0.675

0.667 0.640 0.450 2.365 0.753 5.012 0.615 0.360 0.121 1.149 1.092 4.050 1.939 −2.340 0.787 0.312 0.677 1.245 0.506 0.802 0.506 2.842 2.322 0.541 1.744 0.858 0.167 0.602

33.806 33.054 34.495 37.069 33.806 33.054 33.806 34.495 33.806 33.054 34.495 48.377 34.495 33.806 33.806 34.495 38.636 33.806 35.611 33.806 34.495 64.000 33.054 33.806 33.806 33.806 34.495 34.495

4.760 4.184 1.579 8.906 8.266 39.009 9.715 2.413 6.082 6.208 8.739 20.231 4.783 10.105 11.588 3.973 11.183 13.063 5.766 8.549 7.244 5.630 12.778 8.477 16.452 6.890 1.547 1.392

25.525 24.363 26.445 26.792 25.525 24.363 25.525 26.445 25.525 24.363 26.445 28.693 26.445 25.525 25.525 26.445 27.617 25.525 27.192 25.525 26.445 24.772 24.363 25.525 25.525 25.525 26.445 26.445

83q2-11q1 83q2-10q4 83q2-11q2 90q2-10q4 83q2-11q1 83q2-10q4 83q2-11q1 83q2-11q2 83q2-11q1 83q2-10q4 83q2-11q2 98q2-10q4 83q2-11q2 83q2-11q1 83q2-11q1 83q2-11q2 92q2-10q4 83q2-11q1 87q3-11q1 83q2-11q1 83q2-11q2 03q2-10q3 83q2-10q4 83q2-11q1 83q2-11q1 83q2-11q1 83q2-11q2 83q2-11q2

Panel B: Developing countries 29 Argentina 30 Brazil 31 Chile 32 China 33 Colombia 34 Croatia 35 India 36 Indonesia 37 Malaysia 38 Mexico 39 Philippines 40 Poland 41 Russia 42 South Africa 43 Sri Lanka 44 Thailand 45 Turkey

−3.521[4] −7.918[1] −9.955[2] −17.674[0] −4.999[4] −3.899[0] −4.887[3] −7.802[0] −8.729[0] −11.510[0] −3.865[7] −3.301[3] −6.867[1] −4.308[2] −16.065[2] −8.263[0] −3.717[7]

0.010 0.000 0.000 0.000 0.000 0.004 0.000 0.000 0.000 0.000 0.003 0.017 0.000 0.000 0.000 0.000 0.005

−3.821[1] −3.500[1] −4.150[1] −2.367[2] −1.847[2] −4.186[1] −1.747[2] −2.246[2] −1.741[2] −1.848[2] −2.167[2] −1.848[2] −3.888[1] −2.167[2] −3.862[1] −3.853[1] −1.741[2]

0.021 0.046 0.009 0.394 0.674 0.009 0.726 0.458 0.726 0.675 0.503 0.675 0.018 0.503 0.023 0.020 0.726

0.893 0.772 0.6775 11.479 3.181 1.770 1.975 0.603 2.026 0.671 0.195 1.011 −1.270 −0.426 1.537 0.959 1.536

43.308 39.537 46.680 38.890 34.494 50.870 33.806 38.024 33.806 34.495 33.054 34.495 41.184 33.054 59.728 39.724 33.806

6.084 2.948 8.159 66.110 7.546 5.145 6.726 11.842 5.275 2.893 11.689 5.531 16.551 7.841 9.435 7.664 7.588

30.348 29.462 30.756 28.986 26.445 30.879 25.525 28.031 25.525 26.445 24.363 26.445 28.152 24.363 29.538 27.994 25.525

94q2-11q2 91q2-11q2 96q2-11q2 90q2-11q2 83q2-11q2 98q2-11q2 83q2-11q1 90q2-11q1 83q2-11q1 83q2-11q2 83q2-10q4 83q2-11q2 94q2-10q4 83q2-10q4 01q2-11q2 93q2-10q4 83q2-11q1

that t has the following autoregressive conditional heteroskedastic (ARCH) structure:

2

σ t ¼ ψ0 þ

q X

sampling, which can be viewed as a special kind of bootstrapping. We do this. 2.3. Preliminary results

2

ψ j t− j

ð5Þ

j¼1

where σ2t = var(t|It − 1) and It is the information available at time t. The ARCH model in Eq. (5) can be mimicked in-sample by fitting an autoregressive (AR) model to the squared OLS residuals obtained ^ þ ^2 þ ψ from Eq. (4), ^ say. The fitted value from this AR model, σ t

t

0

q ^ 2 ∑ j¼1 ψ t− j , is a consistent estimator of σ2t and can, therefore, be used j^ as a weight when performing GLS. The Westerlund and Narayan (2012) test for predictability (or rather the absence thereof) is the resulting GLS t-statistic for testing H0 : βadj = 0 in Eq. (4). The main problem with the above approaches is that they are not equipped to handle cases in which oil price has an AR root that are “local to unity”, which means that while highly persistent the root is less than one. One way to circumvent this problem is to use sub-

We begin by considering the three main features of the data, namely, persistency, endogeneity, and heteroskedasticity, which all matter for the accuracy of the estimated predictive regression model. Proper understanding of the extent of these issues in the data at hand is therefore essential in interpreting the results. Before we begin with this, we read Table 1, where we report results on basic features of the data. In columns 3 and 4, we report results from a test of the null hypothesis of a unit root in economic growth and in oil prices for each of the 45 countries in our sample. The unit root test that we use is the familiar augmented Dickey-Fuller (ADF, 1981) test, which, in the case of oil price, includes a time trend and an intercept, while in the case of economic growth, includes only an intercept. The test statistic and the p-value are reported for each series, as is the estimated lag length, obtained by using the Schwarz Information Criteria (starting with a maximum of eight lags). According to the ADF test, the unit root null is not rejected

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for the economic growth series of three of the countries, namely, Iceland, Norway, and Portugal. For the rest of the countries, economic growth is found to be stationary. As for the (world) oil price, while this is just the one series, because of the different sample sizes for the different countries, the ADF test results differ across countries. The unit root null is accepted for all but nine countries (Iceland, Malta, Argentina, Brazil, Chile, Croatia, Russia, Sri Lanka, and Thailand). However, since the rejection of the null does not imply that oil price is not persistent, in Table 2 we also report the estimated first-order AR coefficient of oil price. What we notice immediately is that for all those nine countries for which the null is rejected, and similar to the 36 countries for which the null is not rejected, the AR coefficient is very close to one. Moreover, given the multiplicity of the testing problem, nine rejections out of 45 are actually not that unlikely, even if the null is true. We, therefore, proceed as if oil price is in fact unit root non-stationary in all regressions. In the final two columns of Table 1, we report the mean and standard deviation of economic growth and oil price for each country. Table 2 Results for AR(1), autocorrelation, and ARCH effects. No.

Country

AR(1)

Ljung-Box Q-statistic 2

OP Panel A: Developed countries 1 Australia 0.973 2 Belgium 0.949 3 Canada 0.968 4 Czech Republic 0.939 5 Denmark 0.973 6 Finland 0.949 7 France 0.973 8 Germany 0.968 9 Greece 0.973 10 Hong Kong 0.949 11 Hungary 0.968 12 Iceland 0.901 13 Ireland 0.968 14 Israel 0.973 15 Italy 0.973 16 Japan 0.968 17 Malta 0.945 18 Netherlands 0.973 19 New Zealand 0.970 20 Norway 0.973 21 Portugal 0.968 22 Singapore 0.740 23 South Korea 0.949 24 Spain 0.973 25 Sweden 0.973 26 Switzerland 0.973 27 UK 0.968 28 US 0.968

68.925⁎⁎⁎ 73.521⁎⁎⁎ 76.134⁎⁎⁎ 53.892⁎⁎⁎ 68.925⁎⁎⁎ 73.521⁎⁎⁎ 68.925⁎⁎⁎ 76.134⁎⁎⁎ 68.925⁎⁎⁎ 73.521⁎⁎⁎ 76.134⁎⁎⁎ 30.505⁎⁎⁎ 76.134⁎⁎⁎ 68.925⁎⁎⁎ 68.925⁎⁎⁎ 76.134⁎⁎⁎ 48.583⁎⁎⁎ 68.925⁎⁎⁎ 57.980⁎⁎⁎ 68.925⁎⁎⁎ 76.134⁎⁎⁎ 13.563⁎⁎⁎ 73.521⁎⁎⁎ 68.925⁎⁎⁎ 68.925⁎⁎⁎ 68.925⁎⁎⁎ 76.134⁎⁎⁎ 76.134⁎⁎⁎

Panel B: Developing countries 29 Argentina 0.956 30 Brazil 0.966 31 Chile 0.947 32 China 0.959 33 Columbia 0.968 34 Croatia 0.926 35 India 0.973 36 Indonesia 0.964 37 Malaysia 0.973 38 Mexico 0.968 39 Philippines 0.949 40 Poland 0.968 41 Russia 0.936 42 South Africa 0.949 43 Sri Lanka 0.888 44 Thailand 0.941 45 Turkey 0.973

44.916⁎⁎ 53.732⁎⁎⁎ 38.908⁎⁎⁎ 56.283⁎⁎⁎ 76.134⁎⁎⁎ 32.680⁎⁎⁎ 68.925⁎⁎⁎ 50.584⁎⁎⁎ 68.925⁎⁎⁎ 76.134⁎⁎⁎ 73.521⁎⁎⁎ 76.134⁎⁎⁎ 42.680⁎⁎⁎ 73.521⁎⁎⁎ 23.068⁎⁎⁎ 45.658⁎⁎⁎ 68.925⁎⁎⁎

⁎⁎⁎ p-Value is zero. ⁎⁎ p-Value is b0.05. ⁎ p-Value is b0.10.

2

ARCH (F-stat) 2

IPg /GDPg 0.738 2.059 0.005 0.542 4.961⁎⁎ 0.011 0.028 7.348⁎⁎ 0.177 20.152⁎⁎ 0.516 2.910⁎ 0.048 79.724⁎⁎⁎ 1.352 3.012⁎ 0.214 4.710⁎⁎ 0.001 7.233⁎⁎ 4.063⁎⁎ 0.988 0.074 0.478 0.642 0.008 9.481⁎⁎ 30.875⁎⁎⁎ 2.925⁎ 5.676⁎⁎ 0.443 0.000 11.241⁎⁎ 6.477⁎⁎ 9.461⁎⁎ 51.105⁎⁎⁎ 0.053 0.581 0.455 0.809 4.383⁎⁎ 0.078 3.481⁎ 12.220⁎⁎⁎ 0.123

OP 23.510⁎⁎⁎ 20.771⁎⁎⁎ 21.605⁎⁎⁎ 17.696⁎⁎⁎ 23.510⁎⁎⁎ 20.771⁎⁎⁎ 23.510⁎⁎⁎ 21.605⁎⁎⁎ 23.510⁎⁎⁎ 20.771⁎⁎⁎ 21.605⁎⁎⁎ 7.019⁎⁎⁎ 21.605⁎⁎⁎ 23.510⁎⁎⁎ 23.510⁎⁎⁎ 21.605⁎⁎⁎ 15.080⁎⁎⁎ 23.510⁎⁎⁎ 20.300⁎⁎⁎ 23.510⁎⁎⁎ 21.605⁎⁎⁎ 0.862 20.771⁎⁎⁎ 23.510⁎⁎⁎ 23.510⁎⁎⁎ 23.510⁎⁎⁎ 21.605⁎⁎⁎ 21.605⁎⁎⁎ 13.188⁎⁎⁎ 16.847⁎⁎⁎ 10.871⁎⁎⁎ 18.209⁎⁎⁎ 21.605⁎⁎⁎ 8.0333⁎⁎⁎ 23.510⁎⁎⁎ 20.079⁎⁎⁎ 23.510⁎⁎⁎ 21.605⁎⁎⁎ 20.771⁎⁎⁎ 21.605⁎⁎⁎ 12.446⁎⁎⁎ 20.771⁎⁎⁎ 4.453⁎⁎⁎ 13.649⁎⁎⁎ 23.510⁎⁎⁎

IPg/GDPg 1.893 3.152⁎⁎ 0.354 0.335 0.616 0.010 8.980⁎⁎⁎ 1.989 2.332⁎ 3.009⁎⁎ 5.041⁎⁎ 0.694 0.391 0.683 4.790⁎⁎ 4.215⁎⁎ 0.077 7.869⁎⁎⁎ 4.189⁎⁎ 0.257 0.660 1.502 6.126⁎⁎⁎ 5.355⁎⁎ 5.153⁎⁎ 3.732⁎⁎ 2.098⁎ 10.680⁎⁎⁎

1.281 0.131 5.401⁎⁎ 3.325⁎⁎ 0.392 1.332 0.300 21.158⁎⁎⁎ 0.159 0.221 1.891 0.511 0.131 1.605 1.498 2.152⁎ 1.662

Considering the evidence for developed countries, we notice that economic growth ranges from as low as 0.12% in the case of the Greece to as high as 5% in the case of Finland. For five countries (the Czech Republic, Finland, Iceland, Singapore, and South Korea), economic growth has averaged over 2% per quarter. By comparison, the most volatile economic growth, based on the coefficient of variation, has been experienced by Belgium, Finland, Iceland, Sweden, and the Netherlands. The US, the UK, and Canada have had the least volatile economic growth. When we consider developing countries, we find the economic growth rate to be much higher compared to developed countries. The growth ranges from as low as −1.3% in the case of Russia to as high as 11.5% in the case of China. We now turn to the results for heteroskedasticity reported in Table 2. With regard to autocorrelation, we report the Ljung-Box Q-statistic at the lag length of four for the squared oil price and economic growth. The results for oil price suggest that the null hypothesis of no autocorrelation must be rejected at the 1% level for all countries. The results for economic growth are mixed, with the null being rejected in 40% of the cases. While the evidence of autocorrelation in squared variables is indicative of ARCH, we also perform a formal Lagrange multiplier (LM) test for heteroskedasticity. Our approach here is as follows. We filter each of the two series through a fourth-order AR model. The LM test is then applied to the resulting filtered variables. According to the results (see Table 2), except for Singapore, the null hypothesis of no ARCH in the oil price is strongly rejected for all countries. The results for economic growth are more mixed, with the no ARCH null being rejected for 40% of countries. As a final preliminary, we search for any evidence that oil price is endogenous. This is done in Table 3 where we report the OLS estimates of θ in model (3) after replacing εy,t and εop,t with the estimated OLS residuals from Eqs. (1) and (2), respectively. We find, unlike the strong evidence that oil price is persistent and that oil price and economic growth for almost half of the countries are characterised by ARCH, that oil price is only endogenous for four countries, Canada, Germany, Norway, and Brazil. The main message emerging from the preliminary analyses of the data is that while endogeneity is not a serious concern, oil price is strongly persistent and heteroskedastic, and, for around 45% of the countries in our sample, there is also strong evidence that economic growth is heteroskedastic. This implies the need for addressing these issues in estimating predictive regression models, and it is these features that motivate us to use the procedure of Westerlund and Narayan (2012), and to some extent also the one of Lewellen (2004). 2.4. Predictability test results We now turn to the results for in-sample predictability. While we compute results for four horizons, h say, to conserve space in Table 4 we only report results for h = 1. We report the asymptotic GLS and Lewellen 95% confidence intervals for β. For the GLS test, we also report sub-sample based confidence intervals. Looking first at the results from the Lewellen (2004) test, we find little evidence of predictability. In fact, except for four countries, Ireland, the UK, the US and Russia, the confidence intervals include the value zero, suggesting that the null hypothesis of no predictability cannot be rejected. This is true regardless of the horizon. One possible explanation for this weak evidence is the inability of the Lewellen (2004) OLS-based approach to account for heteroskedasticity, which, as we documented earlier, is a strong feature of our data. Indeed, Westerlund and Narayan (2012) show that in the presence of heteroskedasticity the performance of the Lewellen test (in terms of its power to reject the null) weakens substantially. When we consider results from the GLS-based test, according to the asymptotic confidence intervals, there is evidence of predictability for all countries. However, as mentioned earlier in Section 2.2, perhaps the most suitable confidence intervals with which to judge predictability are the sub-sample ones. While weaker than the results based on the

Author's personal copy P.K. Narayan et al. / Energy Economics 41 (2014) 137–146 Table 3 Results for endogeneity test. No.

Country

141

Table 4 95% confidence intervals for beta-nominal oil price, h = 1. θ

t-Stat

Countries

tsub FGLS

p-Value

No.

tFGLS

tLEW

[0.025, 0.021] [1.328, 1.485] [0.017, 0.011] [0.051, 0.075] [0.047, 0.052] [0.134, 0.159] [0.097, 0.099] [0.030, 0.023] [0.313, 0.312] [0.001, 0.006] [0.097, 0.101] [0.054, 0.066] [−0.002, −0.004] [0.084, 0.108] [0.016, 0.031] [0.021, 0.017] [0.109, 0.127] [0.096, 0.116] [0.015, 0.017] [0.007, 0.030] [0.001, 0.011] [0.027, 0.042] [0.052, 0.066] [0.043, 0.043] [0.048, 0.058] [0.044, 0.043] [−0.003, −0.004] [−0.005, −0.008]

[−0.048, 0.023] [−3.938, 1.442] [−0.010, 0.011] [−0.078, 0.067] [−0.074, 0.053] [−0.455, 0.157] [−0.079, 0.069] [−0.013, 0.020] [−1.482, 0.088] [−0.044, 0.054] [−0.061, 0.066] [−0.209, 0.191] [−0.071, −0.003] [−0.023, 0.126] [−0.108, 0.069] [−0.038, 0.019] [−0.059, 0.126] [−0.091, 0.108] [−0.056, 0.034] [−0.075, 0.053] [−0.071, 0.034] [−0.114, 0.045] [0.063, −0.137] [−0.089, 0.040] [−0.139, 0.112] [−0.051, 0.055] [−0.026, −0.004] [−0.023, −0.004]

[0.077, 0.072] [0.027, 0.018] [0.046, 0.051] [0.154, 0.094] [0.011, 0.009] [0.071, 0.053] [0.010, 0.014] [0.088, 0.101] [0.009, 0.012] [0.020, 0.016] [0.057, 0.068] [0.053, 0.049] [0.259, 0.301] [0.079, 0.094] [1.025, 1.092] [0.097, 0.099] [0.080, 0.073]

[−0.029, 0.069] [−0.018, 0.023] [−0.087, 0.050] [−0.397, 0.123] [−0.049, 0.007] [−0.076 0.066] [−0.044, 0.058] [−0.043 0.144] [−0.069, 0.010] [−0.024, 0.018] [−0.040, 0.144] [−0.029, 0.051] [0.027, 0.303] [−0.036, 0.086] [−0.613, 1.297] [−0.038, 0.093] [−0.060, 0.055]

Panel A: Developed countries 1 Australia 2 Belgium 3 Canada 4 Czech Republic 5 Denmark 6 Finland 7 France 8 Germany 9 Greece 10 Hong Kong 11 Hungary 12 Iceland 13 Ireland 14 Israel 15 Italy 16 Japan 17 Malta 18 Netherlands 19 New Zealand 20 Norway 21 Portugal 22 Singapore 23 South Korea 24 Spain 25 Sweden 26 Switzerland 27 UK 28 US

0.027 −0.016 0.069*** −0.025 −0.004 0.022 −0.080 0.083*** 0.077 −0.008 −0.038 0.032 0.025 −0.047 −0.069 0.035 0.056 −0.163 −0.032 −0.176** −0.083 −0.009 0.040 −0.037 −0.087 −0.010 0.017 0.021

0.583 −0.388 4.968 −0.441 −0.052 0.381 −0.840 3.760 1.311 −0.129 −0.439 0.138 0.536 −0.379 −0.587 0.913 0.820 −1.275 −0.555 −2.141 −1.171 −0.181 0.361 −0.448 −0.538 −0.146 1.148 1.611

0.561 0.699 0.000 0.661 0.958 0.704 0.403 0.000 0.193 0.897 0.662 0.891 0.593 0.706 0.559 0.363 0.415 0.205 0.580 0.035 0.244 0.858 0.719 0.655 0.592 0.885 0.253 0.110

Panel A: Developed countries 1 Australia [0.011, 0.005] 2 Belgium [0.557, 2.323] 3 Canada [0.022, 0.005] 4 Czech Republic [0.041, 0.110] 5 Denmark [0.039, 0.031] 6 Finland [0.074, 0.223] 7 France [0.069, 0.091] 8 Germany [0.032, 0.028] 9 Greece [−0.003, 0.119] 10 Hong Kong [−0.003, 0.008] 11 Hungary [0.086, 0.122] 12 Iceland [−0.026, 0.174] 13 Ireland [−0.003, -0.026] 14 Israel [0.107, 0.148] 15 Italy [−0.009, 0.001] 16 Japan [0.008, 0.016] 17 Malta [0.107, 0.124] 18 Netherlands [0.036, 0.101] 19 New Zealand [0.001, 0.010] 20 Norway [−0.023, 0.024] 21 Portugal [−0.027, −0.016] 22 Singapore [0.123, 0.256] 23 South Korea [0.019, 0.053] 24 Spain [0.035, 0.035] 25 Sweden [−0.009, 0.022] 26 Switzerland [0.032, 0.034] 27 UK [−0.003, −0.009] 28 US [−0.010, 0.006]

Panel B: Developing countries 29 Argentina 30 Brazil 31 Chile 32 China 33 Columbia 34 Croatia 35 India 36 Indonesia 37 Malaysia 38 Mexico 39 Philippines 40 Poland 41 Russia 42 South Africa 43 Sri Lanka 44 Thailand 45 Turkey

0.001 0.096*** −0.035 0.494 0.036 −0.002 −0.008 0.047 −0.024 0.036 −0.071 0.031 0.053 −0.011 −0.061 0.030 0.113

0.023 3.450 −0.404 1.444 0.494 −0.036 −0.121 1.069 −0.480 1.267 −0.669 0.562 0.408 −0.780 −0.577 0.771 1.521

0.982 0.000 0.688 0.153 0.622 0.971 0.904 0.288 0.632 0.208 0.505 0.576 0.685 0.437 0.567 0.444 0.131

Panel B: Developing countries 29 Argentina [0.063, 0.101] 30 Brazil [0.013, 0.021] 31 Chile [0.028, 0.027] 32 China [0.419, 0.006] 33 Colombia [0.003, 0.020] 34 Croatia [0.038, 0.033] 35 India [0.010, 0.002] 36 Indonesia [0.084, 0.088] 37 Malaysia [−0.003, 0.006] 38 Mexico [0.008, 0.011] 39 Philippines [0.065, 0.074] 40 Poland [0.048, 0.047] 41 Russia [0.166, 0.294] 42 South Africa [0.071, 0.088] 43 Sri Lanka [0.781, 0.978] 44 Thailand [0.080, 0.084] 45 Turkey [0.051, 0.105]

**, *** denote statistical significance at the 5% and 1% levels, respectively.

asymptotic confidence intervals, the sub-sample based evidence is still quite encouraging, with evidence of predictability for all but eight countries (Greece, Hong Kong, Iceland, Italy, Malaysia, Norway, Sweden, and the US) It follows that for 37 countries—16 developing and 21 developed—there is evidence that oil price predicts economic growth. We now consider the out-of-sample forecasting evaluation. Here, the performance of the oil price-based forecast is tested against the historical average-based forecasts, which is Eq. (1) with β set to zero. Following, for example, Rapach and Wohar (2006), we use half the sample to generate the first forecast. The results are reported in Tables 5 and 6. We begin by examining the relative Theil U statistic, which is the ratio of the Theil U from the unrestricted (oil pricebased) model to the restricted (historical average) model. This implies that when the relative Theil U is less than one the forecasts from the unrestricted model are better than those obtained from the restricted model. We report results for h = 1, …, 4. When h = 1, we find that for 31 countries (69%) there is evidence that the historical average outperforms the oil price-based forecast. We consider two other measures of forecasting performance, namely, the out-of-sample R2 (OR2) statistic of Campbell and Thompson (2008), and the MSE-F statistic of McCracken (2007). The OR2 statistic is given by OR2 = 1 − (MSEUR /

MSER), where MSEUR and MSER are the mean square error (MSE) of the out-of-sample predictions from the unrestricted and restricted models, respectively. Hence, OR2 N 0 suggests that the unrestricted model outperforms the restricted model. The results reported in Table 5 suggest that this is true only for seven countries (Argentina, Colombia, Ireland, South Korea, South Africa, the UK, and the US). The MSE-F statistic tests the null hypothesis that restricted and unrestricted models have equal forecasting ability. The null is tested against the one-sided alternative hypothesis that the MSE for the unrestricted model forecasts is less than the MSE for the restricted model forecasts. The results reported in Table 5 suggest that if h = 1, the null hypothesis cannot be rejected for 29% of the countries. Therefore, for those countries, the restricted and unrestricted models have the same forecasting abilities. However, for the rest of the countries (71%), the null is comfortably rejected, suggesting that the unrestricted model beats the restricted model. Therefore, on the whole, two of the three out-of-sample evaluation techniques suggest that for around 70% of the countries in our sample, the oil price-based predictive regression model outperforms the historical average. In view of the above results for h = 1 we ask: what about the performance at higher horizons? To answer this question, in Tables 5 and 6 we consider three additional horizons, h = 2, 3, 4. The results suggest that

Author's personal copy 142

P.K. Narayan et al. / Energy Economics 41 (2014) 137–146

Table 5 Out-of-sample forecasting evaluation. No.

Countries

Table 6 Out-of-sample forecasting evaluation.

h=1 Rel. Theil U

h=2

No.

OOS_R

MSE-F, p-value

Rel. Theil U

OOS_R

MSE-F, p-value

Panel A: Developed countries 1 Australia 0.8558 2 Belgium 0.8979 3 Canada 1.0662 4 Czech Republic 1.1112 5 Denmark 0.9002 6 Finland 1.0516 7 France 0.7853 8 Germany 0.8594 9 Greece 0.9343 10 Hong Kong 1.1442 11 Hungary 0.7249 12 Iceland 0.8652 13 Ireland 1.0376 14 Israel 1.3167 15 Italy 0.8169 16 Japan 0.8564 17 Malta 0.8876 18 Netherlands 0.7770 19 New Zealand 0.7936 20 Norway 0.8447 21 Portugal 0.8485 22 Singapore 0.9818 23 South Korea 1.0917 24 Spain 0.8343 25 Sweden 0.8128 26 Switzerland 0.7994 27 UK 0.8022 28 US 1.0254

−0.2243 −0.2338 −0.0320 −1.1031 −0.0450 −0.0736 −0.6278 −0.2410 −0.0220 −0.2017 −0.2599 −0.6913 0.0189 −5.1754 −0.5205 −0.1192 −0.1245 −0.6467 −0.7474 −0.7145 −0.4525 −0.0229 0.0157 −0.6835 −0.5168 −0.1221 0.0642 0.0739

0.0000 0.0000 0.6335 0.0000 0.1952 0.0039 0.0000 0.0000 0.9642 0.0000 0.0000 0.0000 0.9896 0.0000 0.0000 0.0000 0.0047 0.0000 0.0000 0.0000 0.0000 0.9992 0.9987 0.0000 0.0000 0.0000 0.0120 0.0028

0.8054 1.0506 0.9738 1.0738 0.9702 0.9369 0.9837 0.7677 0.6751 1.0775 0.7585 0.9435 1.0379 1.3187 0.8970 0.8982 1.0556 1.0078 0.8399 0.9300 0.9383 0.9785 1.0887 0.9834 1.0151 0.8781 0.8568 0.9481

−0.3079 −0.0601 −0.1577 0.0828 −0.0028 −0.2488 −0.0012 −0.6175 −0.1129 −0.2645 −0.5569 −0.0806 −0.0053 −5.2542 −0.0509 0.0479 −0.6558 −0.0063 −1.6907 −0.0796 −0.0470 0.0200 −0.2484 0.0093 0.0034 −0.0753 0.1572 0.1427

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Panel B: Developing countries 29 Argentina 0.7502 30 Brazil 0.8326 31 Chile 0.7434 32 China 1.2694 33 Colombia 0.9315 34 Croatia 0.9322 35 India 0.9165 36 Indonesia 2.0811 37 Malaysia 1.0088 38 Mexico 1.0680 39 Philippines 0.8622 40 Poland 0.7838 41 Russia 1.5856 42 South Africa 1.0441 43 Sri Lanka 0.7989 44 Thailand 0.8893 45 Turkey 0.8474

0.0411 −0.3641 −0.3385 −1.8492 0.0042 −0.0657 −0.6930 −0.7337 −0.0953 −0.0049 −0.4369 −0.0160 −0.9018 0.0302 −0.0218 −0.4102 −0.6072

0.8494 0.0000 0.0000 0.0000 1.0000 0.6208 0.0000 0.0000 0.0002 1.0000 0.0000 0.9982 0.0000 0.7347 0.9993 0.0000 0.0000

0.7956 0.9134 0.7238 1.0080 0.8227 0.8311 0.8482 1.5958 0.9692 0.9113 1.0818 0.8851 1.6082 1.1190 0.9260 0.9165 0.8980

−0.2298 −0.3648 −0.5649 0.2830 −0.0227 −0.4022 −0.1526 −1.7282 0.1520 −0.1818 −0.0219 −1.2171 −2.3123 −0.1922 0.0029 −0.0666 −0.0601

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

at horizons greater than one, the unrestricted model outperforms the restricted model for all countries. The MSE-F test provides the greatest evidence in favour of the unrestricted model. While with h = 1 only 70% of the countries had the null of equal predictive ability rejected in favour of the unrestricted model, at higher horizons, the null is rejected for all 45 countries. The Theil U statistic provides the second strongest evidence in favour of the restricted model, with U b 1 for as much as 69% of the countries. The least evidence is provided by the OR2. 2.5. Robustness tests The question of whether or not oil price predicts economic growth is so intensely investigated that the use of real versus nominal oil price has become a source of tension in the recent literature. In Fig. 1, we plot the nominal and real oil price data for the period 1983–2011. While the trend in the data is the same, some differences are obvious. This is exemplified in the works of Hamilton (2011) and Kilian and Vigfusson (2011a,b). For example, Kilian and Vigfusson (2011b) argue that one should use real oil price; they write: “The focus on real oil price

Countries

h=3 Rel. Theil U

h=4 OOS_R

MSE-F, p-value

Rel. Theil U

OOS_R

MSE-F, p-value

Panel A: Developed countries 1 Australia 0.8832 2 Belgium 0.9464 3 Canada 1.0069 4 Czech Republic 1.0350 5 Denmark 0.8543 6 Finland 0.9692 7 France 0.7625 8 Germany 0.9107 9 Greece 0.7816 10 Hong Kong 0.9744 11 Hungary 0.7392 12 Iceland 0.9449 13 Ireland 1.0796 14 Israel 1.3105 15 Italy 0.7838 16 Japan 1.0257 17 Malta 0.9259 18 Netherlands 0.8093 19 New Zealand 0.7787 20 Norway 0.8262 21 Portugal 0.7896 22 Singapore 1.0148 23 South Korea 0.9790 24 Spain 0.7557 25 Sweden 0.8585 26 Switzerland 1.0105 27 UK 0.9779 28 US 1.0128

−0.2024 −0.0756 −0.0991 −0.4205 −0.3173 −0.0243 −0.3265 −0.0578 −0.2941 −0.2526 −0.4277 −0.1606 0.0002 −4.8829 −0.2301 0.0094 −0.3152 −0.3337 −0.0366 −0.2561 −0.3172 −0.1068 −0.1808 −0.3023 −0.1213 −0.0031 0.0994 0.0479

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.8832 0.9464 1.0069 1.0350 0.8543 0.9692 0.7625 0.9107 0.7816 0.9744 0.7392 0.9449 1.0796 1.3105 0.7838 1.0257 0.9259 0.8093 0.7787 0.8262 0.7896 1.0148 0.9790 0.7557 0.8585 1.0105 0.9779 1.0128

−0.2111 −0.0085 −0.1234 −0.0466 −0.0466 −0.0468 0.0109 −0.0183 −0.3414 −0.3173 −0.0018 −0.0968 −0.0736 −3.8189 −0.0589 −0.0303 −0.1949 0.0052 −0.2277 0.0232 −0.1176 −0.0473 −0.3763 −0.0373 0.0081 −0.1457 0.0578 0.1060

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Panel B: Developing countries 29 Argentina 0.7665 30 Brazil 0.9177 31 Chile 1.0062 32 China 1.2634 33 Colombia 0.6592 34 Croatia 0.9093 35 India 1.2265 36 Indonesia 1.0642 37 Malaysia 1.0699 38 Mexico 0.9412 39 Philippines 1.0040 40 Poland 0.8486 41 Russia 1.5707 42 South Africa 1.1307 43 Sri Lanka 0.8064 44 Thailand 1.2751 45 Turkey 0.9919

−0.7626 −0.1112 0.0023 0.2895 −0.0603 −0.0729 −1.7000 −0.2205 −0.2761 −0.0863 −0.0017 −0.6253 −2.0313 −0.2007 −0.0231 −1.0167 −0.0092

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.7665 0.9177 1.0062 1.2634 0.6592 0.9093 1.2265 1.0642 1.0699 0.9412 1.0040 0.8486 1.5707 1.1307 0.8064 1.2751 0.9919

0.0057 −0.8108 −0.2565 0.2530 −0.0762 −0.0417 −0.0157 −0.8717 −0.2944 −0.3328 −0.0077 −0.0332 −1.0208 −0.0567 −0.0123 −0.5894 −0.5571

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

innovations … makes sense because theoretical models that imply asymmetries in the transmission of oil price shocks are expressed in terms of real price of oil” (page 9). Hamilton (2011) challenges this on the grounds that the use of real oil price induces measurement errors. More specifically, he writes: “… deflating by a particular number, such as the CPI, introduces a new source of measurement error, which could lead to a deterioration in the forecasting performance. In any case, it is again quite possible that there are differences in the functional form of forecasts based on nominal instead of real prices” (page 370).4 In light of this debate, our results seem incomplete even though we, like Hamilton (2011), believe that nominal oil price is a better predictor of economic growth. This belief is not sufficient to ignore the role that real oil price may have in explaining economic growth. Therefore, for the sake of completeness, in this section we repeat all analysis based on real oil price. Our main findings from the descriptive statistics of the 4 Moreover, we notice from a forecasting evaluation undertaken by Kilian and Vigfusson (2011b: Table 2) that nominal oil price has lower mean squared percentage error compared to real oil price in three out of five proxies for oil prices.

Author's personal copy P.K. Narayan et al. / Energy Economics 41 (2014) 137–146 Table 7 95% confidence intervals for beta, real oil price. No.

Countries

tsub FGLS

tFGLS

tLEW

Panel A: Developed countries 1 Australia [0.015, 0.012] 2 Belgium [0.352, 2.457] 3 Canada [0.023, 0.008] 4 Czech Republic [0.048, 0.106] 5 Denmark [0.051, 0.045] 6 Finland [0.035, 0.207] 7 France [0.066, 0.088] 8 Germany [0.028, 0.027] 9 Greece [0.012, 0.020] 10 Hong Kong [−0.008, −0.006] 11 Hungary [0.001, 0.004] 12 Iceland [0.926, 1.929] 13 Ireland [−0.007, −0.035] 14 Israel [−0.013, −0.018] 15 Italy [0.009, 0.035] 16 Japan [0.012, 0.014] 17 South Korea [0.005, 0.063] 18 Malta [0.142, 0.153] 19 Netherlands [0.052, 0.125] 20 Norway [−0.006, 0.046] 21 New Zealand [0.000, 0.012] 22 Portugal [0.007, 0.013] 23 Singapore [0.086, 0.034] 24 Spain [0.025, 0.017] 25 Sweden [0.062, 0.104] 26 Switzerland [0.039, 0.043] 27 UK [−0.005, −0.013] 28 US [−0.013, 0.009]

[0.033, 0.027] [1.147, 1.327] [0.019, 0.012] [0.063, 0.098] [0.064, 0.070] [0.109, 0.137] [0.097, 0.099] [0.031, 0.024] [0.022, 0.020] [−0.004, 0.006] [0.005, 0.006] [1.177, 1.020] [−0.004, −0.007] [−0.018, −0.021] [0.058, 0.082] [0.023, 0.019] [0.060, 0.078] [0.152, 0.131] [0.116, 0.141] [0.030, 0.057] [0.018, 0.021] [0.019, 0.027] [0.051, 0.035] [0.028, 0.037] [0.123, 0.139] [0.052, 0.052] [−0.005, −0.006] [−0.006, −0.009]

[−0.047, 0.035] [−4.876, 1.284] [−0.009, 0.015] [−0.076, 0.106] [−0.077, 0.068] [−0.544, 0.142] [−0.086, 0.080] [−0.014, 0.023] [−0.020, 0.021] [−0.039, 0.062] [−0.013, 0.010] [0.999, 0.999] [−0.086, −0.003] [0.006, 0.009] [−0.111, 0.084] [−0.037, 0.021] [−0.122, 0.099] [−0.063, 0.151] [−0.098, 0.128] [−0.074, 0.069] [−0.065, 0.040] [−0.058, 0.030] [−0.124, 0.117] [−0.091, 0.052] [−0.143, 0.133] [−0.052, 0.062] [−0.026, 0.000] [−0.023, 0.000]

Panel B: Developing countries 29 Argentina [0.091, 0.131] 30 Brazil [0.000, 0.000] 31 Chile [0.044, 0.031] 32 China [0.001, 0.000] 33 Colombia [0.073, 0.120] 34 Croatia [0.006, 0.004] 35 India [0.051, 0.052] 36 Indonesia [0.016, 0.038] 37 Malaysia [0.010, 0.019] 38 Mexico [0.000, 0.000] 39 Philippines [0.030, 0.015] 40 Poland [0.000, 0.000] 41 Russia [−0.018, 0.007] 42 South Africa [0.000, −0.008] 43 Sri Lanka [0.024, 0.041] 44 Thailand [0.052, 0.057] 45 Turkey [0.000, 0.000]

[0.123, 0.117] [0.000, 0.000] [0.057, 0.064] [0.000, 0.000] [0.086, 0.092] [0.006, 0.006] [0.061, 0.061] [0.005, 0.009] [0.023, 0.033] [0.000, 0.000] [0.025, 0.021] [0.000, 0.000] [0.020, −0.011] [−0.005, −0.003] [0.002, 0.064] [0.050, 0.046] [0.000, 0.000]

[−0.049, 0.123] [0.000, 0.000] [−0.110, 0.062] [0.000, 0.000] [−0.010, 0.250] [−0.019, 0.006] [−0.028, 0.051] [−0.096, 0.080] [−0.074, 0.021] [0.000, 0.001] [−0.103, 0.007] [0.000, 0.000] [−0.012, 0.065] [−0.062, −0.005] [−0.251, 0.163] [−0.031, 0.043] [0.000, 0.000]

data can be summarised as follows. First, the estimated first-order AR coefficient of real oil price is close to one for all 45 countries. Second, the LM test for the null of no ARCH leads to a rejection for all but 13 countries. The evidence of ARCH is supported by the Ljung-Box test of the squared residuals, leading to a rejection of the null hypothesis of no autocorrelation for all 45 countries. Finally, the test of endogeneity reveals that real oil price is endogenous in the case of Canada, Germany, Israel, Norway, Brazil, Croatia, and Russia. On the whole, then, as for the nominal oil price, persistency and heteroskedasticity are important issues that need to be appropriately accounted for, while endogeneity is still an issue, but applies to only seven of the 45 countries in our sample. The details of all preliminary results are available from the authors upon request. We begin by considering the in-sample evidence, which, just as with nominal prices, is strong (see Table 7). In fact, focusing on the GLS subsample-based test,5 the no predictability null is rejected for all but 5 The subsample length, s, is fine as long as s → ∞ with s/T → 0 as T → ∞. However, one should not choose s too small as this will make the FGLS test statistic will not be wellbehaved. Similarly, a choice of s too large—that is too close to T will lead to little variation in the series, rendering the distribution of the FGLS test an underestimation of the true dispersion of FGLS.

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nine countries. Of these nine, two are developed countries (Norway and the US), while the remaining (Brazil, China, Mexico, Poland, Russia, South Africa, and Turkey) are developing countries. This compares with seven countries when we used nominal oil price. We also note that the countries for which the null is rejected for the real oil price are also among the ones for which the null is rejected when using nominal prices. As before, the out-of-sample evidence of predictability based on real oil price (see Table 8) is weaker than the in-sample evidence. Based on the Theil U statistic, for instance, only for around 55% of the countries there is evidence of out-of-sample predictability. This compares with around 70% of the countries when using the nominal oil price. Finally, with real oil price evidence for both in-sample and out-of-sample predictability appears in only 30 countries, while with nominal oil price evidence was found for 33 countries. What do we conclude from this analysis? There are two main conclusions. First, the existing Hamilton versus Kilian–Vigfusson debate on whether one should use nominal or real oil price is not something for which we find support when exploring international data covering 45 countries, as both nominal and real oil price based models produce very similar results in-sample but very different results out-of-sample. Second, one strength of our investigation is that it is based on 45 countries, and there are some cases where nominal and real oil prices give different results. In light of the existing debate and the claim by Kilian and Vigfusson (2011b, page 10) that: “… the use of the nominal price of oil is not consistent with economic theory and requires a behavioural motivation”, we infer that the choice of predictor and, indeed, the interpretation of the results should be left to the policy makers of the respective countries. It is safe to claim that it is the policy makers who have a better understanding of the behavioural nature of their economies, and of the relevance and implications of real versus nominal oil price shocks. 2.6. Parameter stability One aspect of our estimation which we have left unattended is that of parameter stability. To assume that the coefficient on oil price is stable would be ambitious in light of structural shocks to oil prices. Indeed, a feature of the literature, at least in the works of Hooker (1996) and Hamilton (1996, 2003), is that they test whether the estimated coefficient on oil price is stable. Following Hamilton (2003), we test the null hypothesis of no change in the oil price coefficient using the SupF, AvgF and ExpF tests. For details on these tests, see Hamilton (2003, page 284). The results are reported in Table 9. We report results for the null of no change in both the nominal and the real oil price. Results from all three tests suggest that the null hypothesis of no change in oil price, regardless of whether it is the real or nominal price, cannot be rejected. The only exceptions are Israel, Colombia, Croatia, and South Africa in the case of the nominal oil price, and Israel, the UK, the US, Croatia, China and Poland in the case of real oil prices. Therefore, only for these eight countries do we find some evidence that the oil price coefficient is unstable. 2.7. Additional results As we discussed earlier, there is an active related strand of the literature that examines the effect of oil price uncertainty or volatility on economic growth. In this section, our goal is to examine whether nominal and real oil price volatilities affect economic growth. We proxy oil price volatility by the standard deviation of the one-step-ahead forecast error and apply a bivariate GARCH VAR model, similar to the one proposed by Elder and Serletis (2010), where details on the methodology can be found. We report the effects of oil price volatility on output growth for each of the 45 countries in Table 10; column 2 contains results when volatility is computed using the nominal oil price and column 3 contains results based on the real oil price measure of volatility. The results are as follows. First, for 23 out of 45 countries, both nominal and real oil price volatilities have a negative effect on

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160 140 120 100 80 R e a l o il p ric e

60 40 20 N o m in a l o il p ric e

0 84

86

88

90

92

94

96

98

00

02

04

06

08

10

Fig. 1. A plot of real and nominal oil prices, 1983–2011.

Table 8 Out-of-sample forecasting evaluation — real oil price. No.

Countries

h=1 Rel. Theil U

Table 9 Test for stability of coefficient on real and nominal oil price. h=2

Countries

OOS_R

MSE-F, p-value

Rel. Theil U

OOS_R

MSE-F, p-value

Panel A: Developed countries 1 Australia 1.0377 2 Belgium 1.0003 3 Canada 1.0272 4 Czech Republic 0.8147 5 Denmark 0.8831 6 Finland 0.9893 7 France 0.8222 8 Germany 0.8560 9 Greece 1.0151 10 Hong Kong 1.0092 11 Hungary 1.0233 12 Iceland 0.8250 13 Ireland 1.0056 14 Israel 1.0211 15 Italy 0.9467 16 Japan 0.8502 17 Malta 0.7402 18 Netherlands 0.7826 19 New Zealand 0.7869 20 Norway 0.8839 21 Portugal 0.9961 22 Singapore 0.9703 23 South Korea 1.0118 24 Spain 0.9636 25 Sweden 0.9038 26 Switzerland 0.8756 27 UK 1.0011 28 US 1.0028

0.0065 0.0001 0.0032 −0.1777 −0.0685 0.0020 −0.1053 −0.2693 −0.0005 −0.0131 −0.0037 −0.4678 0.0307 0.2866 −0.0238 −0.1318 −1.0251 −0.1645 −0.2324 −0.0718 −0.0019 −0.0486 0.0043 −0.0257 −0.0436 −0.0297 −0.0007 −0.0004

1.0000 1.0000 1.0000 0.0000 0.0081 1.0000 0.0000 0.0000 1.0000 0.9999 1.0000 0.0000 0.6912 0.0000 0.9334 0.0000 0.0000 0.0000 0.0000 0.0050 1.0000 0.9703 1.0000 0.8885 0.2286 0.7519 1.0000 1.0000

1.0270 0.9973 1.0394 0.9046 0.8897 0.9644 0.9173 0.7589 1.0078 0.9811 0.9502 1.0695 1.0067 1.0471 0.9389 1.0204 0.8376 0.9609 0.7750 0.9864 0.9685 1.0084 0.9975 0.9560 0.9337 1.0195 1.0110 0.9907

0.0206 0.0004 0.0021 −0.0632 −0.0527 0.0025 −0.0179 −0.5256 −0.0011 −0.0024 0.0080 0.0181 0.0250 0.3472 −0.0248 0.0203 −0.0726 −0.0018 −0.7695 −0.0084 −0.0224 −0.1031 0.0144 −0.0241 −0.0232 0.0031 0.0029 0.0584

1.0000 1.0000 1.0000 0.0000 0.0081 1.0000 0.0000 0.0000 1.0000 0.9999 1.0000 0.0000 0.6912 0.0000 0.9334 0.0000 0.0000 0.0000 0.0000 0.0050 1.0000 0.9703 1.0000 0.8885 0.2286 0.7519 1.0000 1.0000

Panel B: Developing countries 29 Argentina 0.9649 30 Brazil 1.0132 31 Chile 0.7456 32 China 1.0785 33 Colombia 0.9972 34 Croatia 0.9278 35 India 1.0164 36 Indonesia 1.0138 37 Malaysia 1.0106 38 Mexico 0.9870 39 Philippines 0.9305 40 Poland 1.0431 41 Russia 1.0675 42 South Africa 1.0545 43 Sri Lanka 0.8913 44 Thailand 0.8548 45 Turkey 1.0676

−0.0139 0.0002 −0.3252 0.2554 0.0055 −0.0782 −0.0014 0.0110 −0.0564 −0.0028 −0.0138 −0.0087 0.0831 0.0272 −0.0284 −0.2671 0.0026

0.9999 1.0000 0.0000 0.0000 1.0000 0.4440 1.0000 1.0000 0.0450 1.0000 0.9998 1.0000 0.1595 0.8444 0.9961 0.0000 1.0000

0.8528 0.9690 0.7226 1.0989 1.0108 0.8355 0.9950 1.0005 1.0053 0.9999 0.9037 1.0253 1.0729 1.0509 0.9180 0.8543 1.0622

−0.0845 −0.0019 −0.5856 0.2875 0.0023 −0.4520 0.0020 0.0278 0.0204 −0.0001 −0.0049 −0.0051 0.1338 0.0400 0.0041 −0.2174 0.0026

0.9999 1.0000 0.0000 0.0000 1.0000 0.4440 1.0000 1.0000 0.0450 1.0000 0.9998 1.0000 0.1595 0.8444 0.9961 0.0000 1.0000

Nominal oil price Max. F-stat

Real oil price

Exp F-stat

Ave F-stat

Max. F-stat

Exp F-stat

Ave F-stat

Panel A: Developed countries Australia 1.000 (06Q2) Belgium 1.000 (00Q1) Canada 0.351 (04Q1) Czech Republic 0.653 (95Q3) Denmark 1.000 (03Q1) Finland 0.417 (99Q1) France 0.950 (05Q1) Germany 0.910 (03Q4) Greece 0.921 (06Q3) Hong Kong 1.000 (03Q3) Hungary 0.771 (06Q1) Iceland 0.406 (07Q1) Ireland 0.816 (06Q1) Israel 0.000 (87Q4) Italy 1.000 (00Q3) Japan 0.600 (91Q1) Malta 0.905 (07Q4) Netherlands 0.827 (05Q1) New Zealand 0.627 (03Q1) Norway 0.462 (00Q2) Portugal 0.958 (01Q2) Singapore 0.763 (09Q2) South Korea 1.000 (03Q2) Spain 1.000 (06Q3) Sweden 1.000 (01Q1) Switzerland 0.992 (01Q1) UK 0.425 (88Q4) US 0.432 (88Q2)

1.000 1.000 0.477 0.488 0.869 0.234 0.670 0.690 1.000 1.000 0.752 0.278 0.682 0.000 0.756 0.457 0.768 0.558 0.645 0.207 0.672 0.698 0.934 0.844 0.779 0.988 0.387 0.347

1.000 1.000 0.484 0.478 0.825 0.179 0.620 0.644 1.000 1.000 0.736 0.286 0.660 0.000 0.705 0.396 0.744 0.495 0.632 0.145 0.624 0.707 0.880 0.800 0.730 0.920 0.402 0.388

1.000 (88Q1) 1.000 (00Q1) 0.960 (95Q4) 0.640 (05Q1) 0.981 (01Q1) 0.849 (99Q1) 0.986 (05Q1) 0.864 (03Q4) 0.724 (06Q3) 1.000 (89Q1) 0.810 (92Q4) 0.334 (07Q1) 1.000 (02Q2) 0.030 (91Q2) 1.000 (06Q3) 0.574 (91Q1) 0.920 (07Q4) 0.832 (05Q1) 0.735 (03Q1) 0.593 (05Q1) 1.000 (91Q1) 0.825 (08Q1) 0.946 (91Q1) 0.957 (06Q3) 1.000 (06Q3) 1.000 (07Q1) 0.055 (88Q4) 0.086 (88q2)

0.927 1.000 0.714 0.386 0.665 0.502 0.734 0.638 0.465 1.000 0.905 0.189 1.000 0.008 0.722 0.360 0.827 0.583 0.660 0.232 0.654 0.685 0.715 0.664 0.805 1.000 0.026 0.050

0.869 1.000 0.678 0.350 0.603 0.441 0.684 0.588 0.380 1.000 0.889 0.172 1.000 0.002 0.664 0.281 0.800 0.522 0.612 0.158 0.587 0.682 0.670 0.602 0.753 0.950 0.013 0.040

Panel B: Developing countries Argentina 0.456 (02Q2) Brazil 0.974 (03Q3) Chile 1.000 (02Q4) China 0.125 (94Q1) Colombia 0.018(07Q2) Croatia 0.000(07Q3) India 0.940 (91Q2) Indonesia 0.344 (98Q3) Malaysia 0.368 (88Q4) Mexico 0.943 (00Q4) Philippines 0.471 (87Q4) Poland 0.559 (91Q4) Russia 0.325 (05Q1) South Africa 0.000 (02Q1) Sri Lanka 0.929 (03Q4) Thailand 0.491 (01Q3) Turkey 0.832 (04Q3)

0.676 0.968 1.000 0.150 0.051 0.000 0.758 0.653 0.249 1.000 0.232 0.521 0.176 0.000 0.904 0.328 0.473

0.729 0.915 1.000 0.243 0.074 0.002 0.712 0.746 0.246 0.969 0.166 0.529 0.158 0.011 0.886 0.300 0.392

0.503 (02Q2) 1.000 (95Q2) 1.000 (02Q4) 0.076 (94Q1) 0.567(91Q4) 0.000(07Q3) 1.000 (91Q2) 0.548 (98Q3) 0.221 (90Q1) 1.000 (92Q4) 0.562 (04Q4) 0.002 (90Q1) 0.240 (99Q2) 0.480 (02Q1) 0.892 (03Q4) 0.612 (01Q3) 1.000 (94Q3)

0.733 1.000 1.000 0.027 0.556 0.000 1.000 0.496 0.099 0.950 0.179 0.011 0.185 0.508 0.858 0.418 1.000

0.793 1.000 1.000 0.027 0.556 0.000 1.000 0.434 0.056 0.888 0.106 0.264 0.169 0.522 0.846 0.378 0.974

Author's personal copy P.K. Narayan et al. / Energy Economics 41 (2014) 137–146 Table 10 Bivariate GARCH results of the effects of oil price volatility on economic growth. Countries

Nominal oil price volatility

Real oil price volatility

Coefficient

p-Value

Coefficient

p-Value

Panel A: Developed countries Australia 0.6549*** Belgium 0.3948*** Canada −0.2495*** Czech Republic −0.2681*** Denmark 0.1564*** Finland 0.0714* France 0.1813*** Germany −0.2562*** Greece 0.1940*** Hong Kong 0.5921*** Hungary −0.2515*** Iceland −0.2632*** Ireland −0.2431*** Israel 0.1703*** Italy 0.1728*** Japan −0.2539*** Malta −0.2983*** Netherlands 0.7489*** New Zealand −0.2601*** Norway 0.1215*** Portugal −0.2486*** Singapore −0.2667*** South Korea 0.7402*** Spain 0.7409*** Sweden 0.4979*** Switzerland 0.7469*** UK −0.2475*** US −0.2569***

0.0000 0.0000 0.0000 0.0000 0.0000 0.0716 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.4870*** −0.2592*** −0.2403*** −0.3174*** −0.2440*** 0.5876*** −0.2581*** 0.8646*** −0.1687*** −0.2406*** −0.3002*** −0.2625*** −0.2532*** −0.4409*** 0.2121*** −0.2486*** −0.2714*** 0.7045*** −0.2528*** −0.2528*** −0.2154*** −0.2648*** −0.2597*** −0.2444*** −0.2597*** −0.2502*** −0.2480*** −0.2557***

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Panel B: Developing countries Argentina −0.2458*** Brazil −0.2896*** Chile −0.2257*** China −0.2480*** Colombia −0.2308*** Croatia −0.2991*** India 0.0754* Indonesia −0.3411*** Malaysia 0.7019*** Mexico −0.2696*** Philippines 0.7395*** Poland −0.2626*** Russia −0.2582*** South Africa 0.2181*** Sri Lanka −0.2676*** Thailand −0.2724*** Turkey 0.6468***

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0866 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

−0.2256*** −0.4675*** −0.2380*** −0.1616*** −0.2677*** −0.2924*** −0.2389*** −0.3679*** −0.2422*** 0.7434*** −0.2704*** −0.3477*** −0.2523*** −0.2597*** −0.2582*** −0.2893*** −0.2779***

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

*, *** denote statistical significance at the 10% and 1% levels, respectively.

economic growth. Of these, 11 out of 17 developing countries and 12 out of 28 developed countries experience that both nominal and real oil price volatilities negatively affect economic growth. Second, for the Netherlands, Italy, Finland, and Australia—all developed countries— both nominal and real oil price volatilities have a statistically significant positive effect on economic growth. Third, for another 16 countries, we find that while nominal oil price volatility has a positive effect on economic growth, real oil price volatility has a negative effect on growth. On the other hand, for Germany and Mexico while nominal oil price volatility has a negative effect on economic growth, real oil price volatility has a positive effect on growth. On the whole then in only 60% of countries in our sample both nominal and real oil price volatilities exert the same effects (in terms of sign) on economic growth. For the remaining countries, the effect on economic growth is very much dependent on whether one uses nominal or real oil prices. The key implication of these findings is that the use of oil and real oil price matters and this is the very issue which is at the heart of the debate in the literature as alluded to in Section 2.5. In short, while theoretical models appeal to

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real oil price, Hamilton argues that deflating oil price introduces an additional source of measurement error. Our goal here is not to propose or claim that one of these measures of oil price is superior than the other; rather, we intend to simply highlight the fact that the choice of nominal versus real oil prices goes beyond the predictability literature, including where one simply examines the effect of the second moment of oil prices on economic growth. 3. Concluding remarks In this paper, we undertake an in-sample and out-of-sample predictability analysis of economic growth based on oil price and covering a wide range of developed and developing countries. Our contributions are two-fold. First, we undertake an extensive analysis of economic growth predictability using oil price and a predictive regression model that accounts for the often-ignored statistical features of the data, in particular, the issue of heteroskedasticity. We find evidence that the nominal oil price predicts economic growth for 37 countries—16 developing and 21 developed countries. There is greater evidence of in-sample predictability compared to out-of-sample predictability. For 33 countries, we discover evidence of both in-sample and out-ofsample predictability. Second, we undertake a robustness test of economic growth predictability by using the real oil price. From this exercise, we find that while the in-sample evidence of predictability is consistent with those obtained using nominal prices, out-of-sample evidence is around 15% less at best. However, for no less than 30 countries both in-sample and out-of-sample evidence of predictability are found. We conclude with what we believe should form the direction for future research on this subject. A related branch of studies (Hamilton, 2011; Herrera et al., 2011; Rahman and Serletis, 2011; Serletis and Istiak, 2013) have identified that oil price and output growth relationship is nonlinear or asymmetric. Future research, using our results as a motivation, should test for predictability using nonlinear models. References Ashley, R., Granger, C.W.J., Schmalensee, R., 1980. Advertising and aggregate consumption: an analysis of causality. Econometrica 48, 1149–1167. Campbell, J.Y., Thompson, S.B., 2008. Predicting excess stock returns out of sample: can anything beat the historical average? Rev. Financ. Stud. 21 (4), 1509–1531. Campbell, J.Y., Yogo, M., 2006. Efficient tests of stock return predictability. J. Financ. Econ. 81, 27–60. Cavanagh, C., Elliott, G., Stock, J., 1995. Inference in models with nearly integrated regressors. Econ. Theory 11, 1131–1147. Dickey, D.A., Fuller, W.A., 1981. Distribution of the estimators for autoregressive time series with a unit root. Econometrica 49, 1057–1072. Elder, J., Serletis, A., 2010. Oil price uncertainty. J. Money Credit Bank. 42, 1137–1159. Elliot, G., Stock, J.H., 1994. Inference in time series regression when the order of integration of a regressor is unknown. Econ. Theory 10, 672–700. Ferderer, J.P., 1996. Oil price volatility and the macroeconomy. J. Macroecon. 18, 1–26. Foster, F.D., Smith, T., Whaley, R.E., 1997. Assessing goodness-of-fit of asset pricing models: the distribution of the maximal. J. Finance 53, 591–607. Hamilton, J.D., 1983. Oil and the macroeconomy since World War II. J. Polit. Econ. 91 (2), 228–248. Hamilton, J.D., 1996. This is what happened to the oil price-macroeconomy relationship. J. Monet. Econ. 38, 215–220. Hamilton, J.D., 2003. What is an oil shock? J. Econ. 113 (2), 363–398. Hamilton, J.D., 2011. Nonlinearities and the macroeconomic effects of oil prices. Macroecon. Dyn. 15, 472–497. Herrera, A.M., Lagalo, L.G., Wada, T., 2011. Oil price shocks and industrial production: is the relationship linear? Macroecon. Dyn. 15, 472–497. Hooker, M.A., 1996. What happened to the oil price-macroeconomy relationship? J. Monet. Econ. 38, 195–213. Inoue, A., Kilian, L., 2004. In-sample or out-of-sample tests of predictability: which one should we use? Econ. Rev. 23, 371–402. Kilian, L., 2008. Exogenous oil supply shocks: how big are they and how much do they matter for the U.S. economy? Rev. Econ. Stat. 90 (2), 216–240. Kilian, L., Vigfusson, R.J., 2011a. Are the responses of the US economy asymmetric in energy price increases and decreases? Quant. Econ. 2, 419–453. Kilian, L., Vigfusson, R.J., 2011b. Nonlinearities in the oil price–output relationship. Macroecon. Dyn. 15, 337–363 (July, 1–27).

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