Oil prices and economic policy uncertainty: Evidence from a nonparametric panel data model
Abebe Hailemariam *
Russell Smyth †
Xibin Zhang‡
Abstract We examine the relationship between oil prices and economic policy uncertainty in G7 countries. To do so, we employ a novel nonparametric panel data technique that allows the trend and coefficient functions to evolve as unknown time-varying functional forms. We also estimate country-specific and common trend functions allowing them to evolve over time. Using monthly data from G7 countries over the period 1997:012017:07, we find that the effect of oil prices on economic policy uncertainty is timevarying. Our results show that the estimated time-varying coefficient function of the oil price was negative in years in which increases in oil prices were driven by a surge in global aggregate demand. Further, our nonparametric local linear estimates show that the country-specific and common trend functions are increasing over time. Our findings are robust to endogeneity and alternative nonparametric specifications.
Keywords: oil prices; economic policy uncertainty; time-varying coefficient function; nonparametric panel data.
* Department of Economics, Monash Business School. †
E-mail:
[email protected] Department of Economics, Monash Business School. E-mail:
[email protected] ‡ Department of Econometrics and Business Statistics, Monash Business School.
[email protected]
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E-mail:
1 Introduction We ask two important questions that are of interest to policy makers. Do changes in oil prices drive economic policy uncertainty? Does the relationship between oil prices and economic policy uncertainty vary over time? Beginning with the seminal work of Hamilton (1983), it is well established that oil price shocks affect several macroeconomic activities including GDP, inflation and stock returns (Alquist et al., 2013; Balke et al., 2010; Blanchard and Riggi, 2013; Christoffersen and Pan, 2017; Cologni and Manera, 2008; Cunado and Gracia, 2005; Feng et al., 2017; Filis, 2010; Kilian and Park, 2009; Lippi and Nobili, 2012; Sadorsky, 1999; Tang et al., 2010). Existing studies on the macroeconomic impact of oil prices have largely focused on the business cycle channel via which oil price shocks negatively affect macroeconomic performance. For example, Hamilton (2003) shows that every recession in the US is preceded by oil price fluctuations. In a recent paper, Barrero et al. (2017) find that oil price volatility has a significant effect on short-term uncertainty. Thus, changes in oil prices may also be among the most important drivers of economic policy uncertainty. Since the work of Bloom (2009), a large number of papers have examined the macroeconomic effects of uncertainty (see Bloom et al., 2014, for a survey). Substantial evidence shows that policy uncertainty is negatively correlated with business cycles and that uncertainty amplifies the effect of recessions through delaying firms’ investment and hiring decisions and by undermining the effectiveness of economic policies. Therefore, investigating the factors that drive economic policy uncertainty is important in order to facilitate effective macroeconomic management. Baker, Bloom, and Davis (2016) construct media-based indices of economic policy uncertainty for the US and a number of other countries. They show that economic policy uncertainty has intensified following the global financial crisis (GFC) and that it remains high today in Western Europe and North America with significant and persistent adverse effects on real economic activities. A growing strand of the literature provides evidence that changes in economic policy uncertainty indices are associated with changes in a number of macroeconomic variables, such as industrial production and employment (Baker et al., 2016), the unemployment rate (Caggiano et al., 2014; 2017) and stock market returns and volatility (Kang and Ratti, 2013; You et al., 2017). Other strands of the literature find that economic policy uncertainty may be correlated with asset prices (Brogaard and Detzel, 2015) and bank loan growth (Bordo et al., 2016). Given the importance of economic policy uncertainty following the GFC, surprisingly, little is known on how economic policy uncertainty serves as a channel through which oil price
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shocks transmit to the macroeconomy. There are a few studies that examine the relationship between oil prices and economic policy uncertainty (see e.g., Antonakakis et al., 2014; Degiannakis et al. 2018; Kang and Ratti, 2013; Kang et. al, 2017; Rehman, 2018). These studies, however, employ parametric models with restrictive functional form assumptions. The limitation of parametric models is that the estimates may be biased and inconsistent, due to misspecification when there is no prior knowledge of the functional form. There are no studies that use non-parametric modelling. Moreover, each of these studies apply a structural VAR framework, based on Kilian (2009), to time series data for a single country or group of countries. There are no panel studies that examine the effect of oil prices on economic policy uncertainty. Another common limitation of these studies is that long-term trends in economic policy uncertainty are ignored. It is important to account for these trends as long-term movements in economic policy uncertainty can shed light on long-term policy directions (Duca and Saving, 2018). We address this gap in the literature by adopting a non-parametric panel data model with time-varying coefficients to examine the effect that changes in oil prices have on economic policy uncertainty in G7 countries using monthly data for January 1997 to July 2017. We relax the restrictive functional form assumptions in the existing literature. We also contribute to the literature by estimating the country-specific and common trend functions that are largely ignored in the literature. The existing literature on the relationship between oil prices and economic uncertainty has ignored that real oil prices may be endogenous. Another feature of our study is that we specifically address this issue in a nonparametric framework. Motivating the relevance of varying-coefficient non-parametric modelling, some studies, employing Markov switching models and time-varying parameter VARs, have found that the oil price — economic policy uncertainty relationship is time varying (Antonakakis et. al, 2014; Degiannakis et al. 2018) and non-linear (Rehman, 2018). The relationship between oil prices and economic policy uncertainty has become complex and unstable, meaning that parametric models may not uncover the underlying relationship between the two variables, nor the manner in which this relationship has evolved over time. While Markov switching models or time-varying parameter VARs have been used in a few studies to capture the effect of structural breaks and instability, we contend that such approaches are too restrictive to capture the complexity of the underpinning relationship (see also Silvapulle et al., 2017). There are also advantages in applying a non-parametric framework to panel data over employing time series data for a single country or group of countries as the extant literature does. Panel data can exploit variation both over time and across cross-sectional units. Use of panel data provides additional observations which enhances degrees of freedom and allows one to address the presence of cross-section correlation. Thus, coefficient estimates
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are consistent and efficient. In addition to being the first to model the relationship between oil prices and economic policy uncertainty in a nonparametric framework, we contribute to the small literature that has employed nonparametric panel data modelling in energy economics in other contexts. Related non-parametric panel data models examine energy demand (Karimu and Brännlund, 2013), the environmental Kuznets curve (Paudel and Poudel, 2012), convergence of pollutants (Runar et al., 2017), and CO2 -growth nexus (Shahbaz et al., 2017). But, the study that comes closest in modelling approach to that employed here is Silvapulle et al. (2017) who examine the effect of oil prices on stock prices in oil importing countries. Nonparametric panel data methods are increasingly popular tools for economic modelling when researchers lack prior knowledge on the specific functional form(s) that govern the relationship between variables. As argued in Ruckstuhl et al. (2000), nonparametric panel data estimation techniques are appropriate and asymptotically justified when the size of the cross-sectional units is fixed and the length of time series increases as in our case. We adopt a novel non-parametric varying-coefficient panel data model with fixed effects that employs a local linear dummy variable estimation (LLDVE) method to estimate the trend and coefficient functions in a highly nonlinear fashion. The local linear method has become increasingly popular for nonparametric regression in recent years due to several appealing features; namely, effective bias reduction, mathematical efficiency, and adaptation of edge effects (e.g see Fan and Gijbels, 1996). Our non-parametric panel data approach relaxes the restrictive functional form assumptions underpinning parametric models employed in the existing literature. In addition, our method allows the common trend functions to evolve over time to capture common global shocks. More importantly, the non-parametric panel data model also allows for time-varying coefficient functions, as well as country-specific and common trend functions to capture nonlinearity and heterogeneity across time and countries. We find that the relationship between oil prices and economic policy uncertainty is timevarying. While the relationship between oil prices and economic policy uncertainty is negative for much of the period, we find that the oil price has a strong positive effect on economic policy uncertainty in the aftermath of the GFC. Moreover, we find that the country-specific and common trend functions are increasing over time. The remainder of this paper is organized as follows. Section 2 briefly discuses the parametric model and sets out the nonparametric panel data technique. We discuss the local linear dummy variable estimator and the procedures for constructing optimal bandwidth and bootstrapping confidence intervals. Section 3 describes the data and Section 4 contains a discussion of the results derived from the parametric and nonparametric estimators.
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Section 5 concludes the paper.
2 A panel data model with time-varying coefficients 2.1 Nonparametric estimation Following the modelling strategy in Li et al. (2011) and Silvapulle et al. (2017), our econometric model that relates the economic policy uncertainty index to oil prices is of the form: Yi t = f t + βt ,1 rpoilt + βt ,2 spreadi t + βt ,3 mindexi t + αi + e i t .
(1)
Let X i t = (rpiolt , spreadi t , mindexi t ) and βt = (βt ,1 , βt ,2 , βt ,3 ). This model is written in matrix form as Yi t = f t + X i>t βt + αi + e i t ,
for i = 1, 2, · · · , N ,
and t = 1, 2, · · · , T ,
(2)
where Yi t is the log of the economic policy uncertainty index, f t = f i ( Tt ) are unknown countryspecific trend functions, rpoilt denotes the real price of oil, spreadi t is sovereign credit spread relative to the benchmark and mindexi t denotes the economic misery index, defined as the sum of inflation and unemployment. αi denote unobserved individual effects and e i t is the error term, which is stationary and independent of the regressors. βt , j = β j (t /T ) and f t = f i (t /T ) are vectors of time-varying coefficient and trend functions, where f (·) and β j (·) P are unknown smooth functions. For identification purpose, we assume that iN=1 αi = 0. To estimate the trend functions, f t , and the vector of time-varying coefficients of interest, βt , j , that measure the effects of oil prices on economic policy uncertainty in equation (2), we use the LLDVE method. To explain the LLDVE estimator in detail, we introduce the following notations. Y = (Y1 > , · · · , YT > )> with Yi = (Yi 1 , · · · , Yi t )> , > > β1 , · · · , X 1T βT , · · · , X N>1 β1 , · · · , X N>T βT )> , B (X , β) = (X 11 > > e = (e 1> , · · · , e N ) with e = (e i 1 , · · · , e i T )> fori = 1, · · · , N ,
f = I¯N ⊗ ( f 1 , · · · , f T )> ,
α = (α1 , · · · , αN )> , D = I N ⊗ I¯N ,
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where I¯k is a k × 1 vector of ones, and ⊗ represents the Kronecker product. The model given by (2) is re-written in matrix notation as Y = f + B (X , β) + Dα + e. Given that
PN
i =1 αi
(3)
= 0, we modify (3) as Y = f + B (X , β) + D ∗ α∗ + e,
(4)
where α∗ = (α2 , · · · , αN )> and D ∗ = (− I¯N −1 , I N −1 )> ⊗ I¯T . ¡ ¢> We assume that f t = f i (t /T ) and βt = β1 (t /T ), β2 (t /T ), · · · , βd (t /T ) are unknown smooth functions of τ with τ = t /T ∈ (0, 1). To estimate the varying coefficient and trend functions by the LLDVE method, we define the £ ¤> augmented time-varying vector as β∗ (τ) = f (τ), β1 (τ), · · · , +βd (τ) , where β∗ is assumed to have first and second order derivatives. After Taylor expansion, we have β∗ (t /T ) ≈ β∗ (τ) + β0∗ (τ)(t /T − τ), where β0∗ (τ) is the first derivative of β∗ (τ). It follows that 0
> > f + B (x, β) ≈ M (τ)[β> ∗ (τ)(β∗ (τ)) ] , > where M (τ) = [M 1> (τ), M 2> (τ), · · · , M N (τ)]> with
1 X i>1 . .. . M i (τ) = . . 1 X i>T
1−τT Th
.. .
T −τT Th
1−τT Th
.. .
T −τT Th
X i>1 X i>T
,
for i = 1, 2, · · · , N . Estimation of parameter is formulated to minimize the weighted least squares given in (5) ¡ ¢> 0 with respect to α∗ and β∗ (τ), hβ∗ (τ) . Thus, we have £ ¡ ¢> ¤> £ ¡ ¢> ¤ 0 0 min Y − M (τ) β∗ (τ), hβ∗ (τ) − D ∗ α∗ W (τ) Y − M (τ) β∗ (τ), hβ∗ (τ) − D ∗ α∗ , where W (τ)= I N ⊗ w(τ) is the kernel weight matrix with µ ¶ µ ¶¾ 1 − τT 1 1 − τT 1 w(τ) = diag K ,··· , K , h Th h Th ½
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(5)
and K (·) is a kernel function. The solution to the minimization problem given by (5) leads to the LLDVE estimates, βˆ∗ (τ) of β∗ (τ), which are explicitly expressed as ¡ ¢ βˆ∗ (τ) = (I d +1 , 0d +1 ) M > (τ)W ∗ (τ))M (τ) M > (τ)W ∗ (τ)Y ),
(6)
where I d ×1 is a (d + 1) × (d + 1) identity matrix, 0d ×1 is a (d + 1) × (d + 1) matrix of zeros, and £ ¤> βˆ∗ (τ) = fˆ(τ), βˆ1 (τ), · · · , βˆd (τ) , W ∗ (τ) = K > (τ)W (τ)K (τ), with K (τ) = I N T − D ∗ (D ∗>W (τ)D ∗ )−1 D ∗W (τ). Note that W (τ)D ∗ α∗ = 0 for any τ. The fixed effects are estimated using least squares. Following the estimation strategy of Su and Ullah (2006), Chen et al. (2012), and Silvapulle et al. (2017), we have ¡ ¢ ¡ ¢ ˆ − D ∗ α∗ > Y − fˆ − B (X , β) ˆ − D ∗ α∗ , αˆ ∗ = argmin Y − fˆ − B (X , β) α
(7)
where fˆ = I¯N ⊗ ( fˆ(1/T ), · · · , fˆ(T /T ))> , ¡ ¢ ˆ = X > βˆ1 , · · · , X > βˆT , · · · , X > βˆ1 , · · · , X > βˆT > , B (X , β) 11 1T N1 NT ˆ /T ), · · · , βˆd (t /T ))> . The solution to the minimization problem of (7) yields the with βˆ t = (β(t fixed effect estimates: N X ¡ ¢−1 ¡ ¢ ˆ , and αˆ 1 = 1 − αˆ ∗ ≡ αˆ 2 , · · · , αˆ N )> = (D ∗> D ∗ D ∗> Y − fˆ − B (X , β) αˆ i . i =2
We estimate individual trend functions from the vector of residuals eˆi t = Yi t − fˆ(t /T ) − X i>t βˆ t − αˆ i . ˆ i (t /T ), is estimated by a local Specifically, for the i th cross-section, the trend function, m linear regression of eˆi t on τ = t /T : eˆi t = m i (t /T ) + εi t , where εi t , for t = 1, 2, · · · , T , are independent errors with a zero mean.
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(8)
2.2 Bandwidth selection Our next step is to select the bandwidth for the LLDVE method. Since the performance of nonparametric models depends on the choice of bandwidth selection, we follow a leaveone-unit-out cross-validation method proposed by Sun et al. (2009) and Silvapulle et al. (2017). The leave-one-unit-out least square cross-validation automatically chooses the optimal bandwidth such that: h¡ ¢> > ¡ ¢i ˆ ˆ ˆ ˆ ˆ h opt = argmin Y − f (−) − B (X , β(−) M D M D Y − f (−) − B (X , β(−) , h
(9)
where ¡ ¢> fˆ−i = fˆ(−i ) (1/T ), · · · , fˆ(−N ) (1/T ), · · · , fˆ(−N ) (T /T ) , ¡ ¢> βˆ∗(−i ) (t /T ) = βˆ1(−i ) (t /T ), · · · , βˆd (−i ) (t /T ) , ¡ > ¢> > ˆ βˆ1(−1) , · · · , X 1T βT (−1) , · · · , X N>1 βˆ1(−2) , · · · , X N>T βˆT (−N ) , B (X , βˆ(−i ) ) = X 1T ¡ ¢ with M D = I N T − T −1 I N ⊗ I¯T I¯T> ) satisfying M D D = 0 so as to eliminate unknown fixed effects. Therefore, we have ¡ ¢ ˆ − B (X , βˆ(−) )> M > M D (B (X , β) ˆ − B (X , βˆ(−) ) hˆ opt = argmin B (X , β) D h
ˆ − B (X , βˆ(−) )> M > M D e + e > M > M D e, + (B (X , β) D D
(10)
whose first term is used to choose an optimal bandwidth, whereas the last term has a zero expectation when e is independent of X i t .
2.3 Bootstrapping confidence intervals We use a bootstrapping method to construct nonparametric confidence bands for the timevarying trend and coefficient functions following Wu (1986), Mammen (1993) and Silvapulle ˆ i (τ; b), et al (2017). The first step is to obtain the detrended residuals from (8), εˆ i t = eˆi t − m where εˆ i = (ˆε1t , · · · , εˆ N t ) for i = 1, 2, · · · , N .. Next, we re-sample the detrended residuals εˆ ∗t = εˆ k , where k is randomly selected from {1, · · · , T } with replacement and generate a bootstrapping sample of Yi t through ˆ i (τ; b) + εˆ ∗t , Yi∗t = fˆ(1/T ) + X i>t βˆ t + αˆ i + m
for
t = 1, 2, · · · , T .
Using the bootstrapped sample of {Yi∗t , X i t }, we get the estimates of time-varying common
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trend functions fˆ(t /T ), the coefficient functions βˆ∗t and the individual trend functions by the LLDVE method. The final step is to repeat the above procedure 1000 times and obtain the 90% confidence bands for the estimates of the common trend and coefficient functions.
2.4 Endogeneity Oil prices and economic policy uncertainty might be simultaneously determined, which poses a challenge to pin down the direction of causality. To address this issue, we employ a procedure for consistent estimation of nonparametric simultaneous equations models proposed by Su and Ullah (2008). The basic idea of the proposed nonparametric estimator is similar to standard two-stage least-squares. In the first stage, we run a nonparametric regression of the endogenous variable on all the exogenous regressors. In the second stage, we run a nonparametric regression of the dependent variable on each of the regressors, including the endogenous variable and the residuals from the first stage regression. The third stage involves marginal integration to ensure that the assumption of a zero mean error term holds. To briefly explain the Su and Ullah (2008) estimator consider a model that treats the real price of oil as the endogenous regressor:
Yi = m(X i , Z1i ) + εi
and
X i = g (Zi ) + u i
where Yi is economic policy uncertainty, m(.) is the unknown smooth function of interest, X i is the endogenous regressor (real price of oil), Zi = (Z1i , Z2i ) where Z1i and Z2i are d 1 × 1 and d 2 ×1 vectors of instrumental variables respectively, g (.) is an unknown smooth function of the instruments Z and u are disturbances. We assume that E (u|Z ) = 0 and E (ε|Z , u) = E (ε|u). The model allows for both u and ε to be heteroscedastic. Su and Ullah (2008) show that the local linear least square (LLLS) estimation of m(.) is feasible and can be estimated as follows. E (Y |X , Z , u) = m(X , Z1 ) + E (ε|X , Z , u) = m(X , Z1 ) + E (ε|X − g (Z ), Z , u) = m(X , Z1 ) + E (ε|Z , u) = m(X , Z1 ) + E (ε|u)
By the law of iterated expectations, and since Z1 ∈ Z , we have w(X , Z1 , u) ≡ E (Y |X , Z1 , u) = E (Y |X , Z1 , u) = m(X , Z1 ) +E (ε|u). Since u are unobserved, Su and Ullah (2008) propose that they can be replaced by the residuals obtained by regressing X on Z nonparametrically to provide consistent estimates of m(X , Z1 ) without further restrictions. Assuming that E (ε) = 0, the procedure for the Su and Ullah (2008) estimator is as follows:
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Step 1. Run a local-constant regression of X on Z with kernel function K 1,h (.) and bandwidth vector h 1 to get a consistent estimate, gˆ (Z ) of g (.) and obtain the residuals uˆ i = X i − gˆ (Zi ), for i = 1, 2, · · · , n. Step 2. Run a local-linear regression of Y on X , Z1 and uˆ with kernel function K 2,h (.) and ˆ , Z1 , u) of w(.). bandwidth vector h 2 to get a consistent estimate, w(X Step 3: Obtain a consistent estimate of m(.) as ˆ , Z1 ) = m(X
n 1X ˆ , Z1 , uˆ i ) w(X n i =1
ˆ , Z1 , uˆ i ) is the counterfactual estimate of w(X ˆ , Z1 , u) obtained using the bandwhere w(X widths from the local linear regression in step 2 and assuming that E (ε) = 0. The derivatives of m(.) are given by ˆ 0 (X , Z1 ) = m
n 1X wˆ 0 (X , Z1 , uˆ i ) n i =1
where wˆ 0 (X , Z1 , uˆ i ) is the counterfactual derivative of w(.). As outlined in the application of the method by Henderson et al. (2013), the instrumental variable estimator of Su and Ullah (2008) is an appropriate applied nonparametric econometric tool to deal with potential endogeneity in kernel based nonparametric methods.
2.5 Parametric panel data model To determine which parametric estimator is suitable to model economic policy uncertainty, we first test for cross-sectional dependence (CD) in our data. Consider the standard panel-data model Yi t = αi + β0 Xi t + u i t , for i = 1, 2, · · · , N and t = 1, 2, · · · , T
(11)
where Yi t is the logarithm of economic policy uncertainty, Xi t is a 3 × 1 vector of regressors including the logarithm of real oil price, the logarithm of the misery index and the sovereign credit spread, while u i t is the error term. To test for CD in the data series, we consider a statistic that captures an average pairwise
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correlation coefficient given as PT N NX −1 X 2 t =1 z i t z j t ρ i j with ρ i j = PT ρ¯ = , P 2 N (N − 1) i =1 j =i +1 ( t =1 z i t )1/2 ( Tt=1 z 2j t )1/2 where z i t is either the logarithm of economic policy uncertainty or any of the regressors or residuals from the regression in Equation (11). The null hypothesis for the CD test is stated as H0 : ρ i j = 0 for i 6= j , that is no cross-section dependence, against the alternative hypothesis of H1 : ρ i j 6= 0 for some i 6= j . For fixed N and large T, as in our case (N=7, T=247), the Breusch and Pagan (1980) CD test based on the Lagrange Multiplier (LM) statistic is appropriate. The test statistic is given by P −1 PN ˆ 2i j , where ρˆ i j is the estimated pairwise correlation. We also conC D LM = T iN=1 j =i +1 ρ q PN −1 PN 2T ˆ i j . The CD test sider the CD test proposed by Pesaran (2004); C D p = N (N j =i +1 ρ −1) i =1 results reported in Table 1 show the rejection of the null of cross-sectional independence. That is, the data are correlated across countries. Table 1: Cross-sectional dependence test results.
log(Economic policy uncertainty) log(Economic misery index) Sovereign credit spread
C D LM
C Dp
ρ¯
441.18 587.11 1997.32
40.75 15.10 10.65
0.57 0.21 0.15
Note: Under the null hypothesis of no cross-section dependence, C D ∼ N (0, 1). The P-values are zero indicating that the data are correlated across countries.
To account for CD in our panel, we employ the dynamic common correlated effects (CCE) estimator proposed by Chudik and Pesaran (2015). Consider the dynamic heterogeneous panel data model version of Equation (11) with a multifactor error term that accommodates an unobserved factor structure.
Yi t = αi + φi Yi ,t −1 + βi Xi t + u i t ,
u i t = γ 0 ft + e i t
(12)
where ft denotes a vector of m-dimensional unobserved common factors, γi is an m × 1 vector heterogeneous factor loading and e i t is a country-specific error term. Chudik and Pesaran (2015) propose that Equation (12) can be consistently estimated using the dynamic CCE based on pooled mean group (PMG) estimator by including sufficient number of lags
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of cross-section averages as follows. Yi t = αi + φi Yi ,t −1 + βi Xi t +
p X i =0
δ0i l Z¯ t −l + ²i t ,
(13)
¯ t ), with Y¯t and X ¯ t denoting simple cross-sectional averages of Yi t and Xi t where Z¯ t = (Y¯t , X P in year t . The mean group estimates are given by θˆMG = 1 N θˆi with θˆi = (φˆ i , βˆi ). This N
i =1
estimator allows the error term to to be correlated serially, as well as cross-sectionally, and it is robust to endogeneity. The error correction model (EC M ) corresponding to Equation (13) is given by: ∆Yi t = λ(Yi ,t −1 − θi Xi t ) + δ0,i + δ1i ∆Xi t + ²i t ,
(14)
where δi are heterogeneous short-run coefficients and θi are the long-run coefficients assumed to be homogeneous across countries. The coefficient of EC M , λi , measures the speed of adjustment to long-run equilibrium after a shock. As outlined in Pesaran et al (1999), the PMG estimator based on the authoregressive distributed lag approach is suitable for long-run analysis and it is robust to endogeneity of regressors. In addition, they show that the estimator is valid irrespective of whether the series are I (0) or I (1).
3 Data To measure economic policy uncertainty, we use the monthly indices constructed by Baker and colleagues as described in Baker et al. (2016), but since updated beyond 2016. Baker and colleagues constructed policy-related economic uncertainty indices for a number of countries based on newspaper coverage frequency. The indices capture uncertainty related to the decision makers, economic policy actions and the timing and effect of economic policies. To construct the indices in each country, they consider major newspapers for each country and search the digital archives of each newspaper to obtain a monthly count of articles that contain terms describing the economy, policy and uncertainty. To account for variations in the overall volume of articles across newspapers and time, they scale the raw counts by the total number of articles in the same newspaper/month and standardize each monthly paper series to unit standard deviation over the period under consideration. They then compute the average across the newspapers considered by month and normalize the series by the mean (for full details on construction of the indices see Baker et al. (2016)). Following the empirical literature (see e.g Kilian, 2009), we use refiners’ acquisition cost (RAC) for imported crude oil, obtained from the U.S. Energy Information Administration. We transformed RAC crude oil prices to real terms using the U.S. CPI to obtain the real price
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of oil. As noted in Alquist et al. (2013), the RAC for imported crude oil provides a good proxy for global oil price fluctuations compared to other alternative oil price series, such as West Texas Intermediate (WTI). We constructed the economic misery index as a sum of CPI inflation and the unemployment rate from the OECD database as a control variable following Duca and Saving (2018). Sovereign credit spread is computed as a 10-year bond yield spread from the benchmark (or the excess yields to the US 10-year bond yield that is considered as risk-free government bonds) using data from the OECD database. Sovereign credit spread is used to proxy credit risk and associated fiscal policy uncertainty. Controlling for fiscal policy uncertainty is important given that, for instance, Arbatli et al. (2017) suggest that fiscal matters are the leading source of economic policy uncertainty in Japan. They show that, on average, 57 percent of the newspaper articles on which the economic policy uncertainty index is based contain one or more fiscal policy terms. Table 2 shows the summary statistics for the series. As shown in Table 2, economic policy uncertainty indices vary significantly in the G7 countries, with overall standard deviation of 83. The maximum value of economic policy uncertainty index in the sample is recorded for the UK, reflecting the uncertainty generated by the Brexit referendum. The economic misery index also varies significantly ranging from 2.5 to 14.3 with overall standard deviation of 2.7. Meanwhile, the real price of oil is a global variable common to all countries. Table 2: Summary statistics: monthly data (1997:01-2017:07, Observations=1729).
Variable Economic policy uncertainty Real price of oil Index of economic misery Sovereign credit spread
Mean
Overall standard deviation
Between standard deviation
Within standard deviation
Min
Max
130.00 0.54 8.68 -0.37
83.18 0.28 2.67 1.28
21.32 — 2.29 1.11
80.80 0.28 1.62 0.76
11.29 0.12 2.50 -4.97
1141.80 1.27 14.26 5.05
Figure 1 shows that economic policy uncertainty index increases sharply with the onset of the GFC and intensified with the increase in oil prices and the euro area debt crisis in 2011.
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Figure 1: Trends in oil price and economic policy uncertainty indices
Economic policy uncertainty remained elevated even after the GFC, except the rollback in the trend between 2012 and 2014. The uncertainty index hit a new all-time high in 2016 with the Brexit referendum where the index was almost five times the value just before the GFC. The economic policy uncertainty index also increased sharply in the US following the last presidential election due to uncertainties surrounding various policies to be undertaken by the new administration. The economic policy uncertainty indices for Europe and the US exhibit similar trends with some common peaks, such as during the 2008/2009 GFC and during the European debt crisis in the second half of 2011. Oil prices also significantly increased during these periods before they plunged from 2014 onwards.
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4 Results and discussion 4.1 Baseline parametric estimates Table 3 presents the baseline results from the dynamic CCE estimators, based on the PMG panel data model. Our results provide evidence of a time-varying relationship between economic policy uncertainty and oil prices. The coefficient on real oil price is negative and statistically significant for the full sample and the pre-GFC sample. The effect of oil price on economic policy uncertainty in the post-GFC period is positive, but statistically insignificant. More precisely, our estimates show that the point elasticity of economic policy uncertainty with respect to changes in oil prices is about -0.32 for the full sample, -0.85 for the pre-GFC sample and 0.10 in the post-GFC period. The interpretation of the coefficient -0.32 is that, on average, a 1% increase in real oil prices is associated with a 0.3% decrease in economic policy uncertainty. The condition for the existence of a dynamically stable long-run relationship between economic policy uncertainty and oil prices is that the coefficient on the EC M term be negative and within the unit circle. As shown in Table 3, the coefficients on the EC M falls within the dynamically stable range. The estimate of the EC M coefficient captures the speed of adjustment to long-run equilibrium. For example, the interpretation of the EC M coefficient of -0.3 in column (1) is that the system is converging to equilibrium by 30% and that the estimated model is stable. The CD test rejects the null hypothesis of weak cross-sectional dependence. The R 2 shows that a sizeable proportion of the variations in economic policy uncertainty is explained by our model. For example, the R 2 in column (2) shows that about 48% of the variation in economic policy uncertainty is explained by our model.
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Table 3: Baseline parametric estimates
log(Real price of oil) log(Economic misery index) Sovereign credit spread ECM R2 Observations CD test
(1) Full sample
(2) Pre-GFC
(3) Post-GFC
-0.320*** (0.073) 0.319 (0.266) 0.176** (0.075) -0.301*** (0.049) 0.163 1645 -6.085
-0.852*** (0.117) 0.413 (0.621) 0.110 (0.102) -0.478*** (0.050) 0.271 798 -3.932
0.102 (0.146) -0.0682 (0.451) 0.114** (0.045) -0.383*** (0.085) 0.229 679 -2.935
Note: The dependent variable is the log of economic policy uncertainty. Standard errors are given in parenthesis with *** indicating p values being less than 0.01. The CD test is based on Pesaran (2015) with the null hypothesis being weak cross-section dependence. The p-value for the CD test rejects the null hypothesis of weak cross-sectional dependence.
A potential shortcoming of the parametric panel data estimator is that the estimates may be inconsistent if the model is misspecified. To address this issue, and to capture the smooth time-varying relationship between oil prices and economic policy uncertainty, we employ local linear estimators of a varying coefficient nonparametric panel data technique.
4.2 Nonparametric estimation of varying coefficients and trend functions Before we estimate the trend and coefficient functions, we pre-test for the existence of countryspecific and global trends in section 4.2.1.
4.2.1 Nonparametric trend tests We adopted the Mann-Kendall (MK) nonparametric trend test (Mann, 1945; Kendall, 1975) which is the most common test employed to detect monotonic trends in energy and climate data series. An advantage of the nonparametric MK test is that it does not require the data to be normally distributed. In addition, the MK test is robust to abrupt breaks in data series and invariant to transformations, such as logs. Thus, it is a superior test to detect the existence
16
of linear or non-linear trends. The null hypothesis is that the data series are independent and identically distributed, whereas the alternative hypothesis is that the data series follow a monotonic trend. If X i and X j are the sequential data values of the time series at time i and j, the MK test statistic is computed as:
S=
n−1 X
n X
sgn(X j − X i )
i =1 j =i +1
1, with sgn(x) = 0 −1
if
x >0
if
x =0.
if
x i , and assigns values of 1 to positive differences, 0 to no differences and -1 to negative differences. The S statistic is calculated as the sum of these integers. Large positive values of S indicate an upward trend, while large negative values of S suggest a downward trend. The statistic S has an approximate normal distribution with the following Z-transformation. S−1 , σ Z= 0 S+1 σ
where σ =
³
1 18
if
S >0
if
S =0
if
S 0, trends are increasing, while if Z < 0 trends are decreasing. The null hypothesis of no trends is rejected if |Z | > Z1−α/2 , suggesting that a significant trend exists in the time series. Table 4 presents the nonparametric MK test results. The Table shows that economic policy uncertainty exhibits a positive and significant trend in all countries except for Japan. The global trend in economic policy uncertainty is also positive and significantly different from zero.
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Table 4: Nonparametric country-specific and global trend tests
log(EPU) log(Misery index) Credit spread log(Real price of oil)
CA
DEU
FRA
GBR
ITA
JPN
USA
Global
10.560 -8.157 -6.727
8.788 -12.691 -4.906
14.110 -6.357 -0.529
13.656 2.314 -4.266
2.991 -2.671 4.845
0.041 -4.169 15.345
5.403 4.122 4.906
9.956 -7.197 2.345 11.747
Note: The critical value, Z1−α/2 , for the 5% significance level is 1.96. Therefore, |Z | > 1.96 indicates the rejection of the null hypothesis of no trend in the data series. Country codes: CA=Canada, DEU=Germany, GBR= United Kingdom, ITA=Italy, JPN=Japan, USA=United States.
Oil price is a global variable common to all countries. The nonparametric trend test indicates that oil prices exhibit a significant positive trend. The trends in the misery index and sovereign credit spread are positive in some countries and negative in others. Each are statistically significantly different from zero, except for the spread series for France. Having confirmed the existence of trends in our series, we proceed to a more rigorous nonparametric analysis of the time varying coefficient and trend functions.
4.2.2 Local linear estimates In this section we present the estimates of f (.) and β j (.) for the observed data, {(Yi , X i )}, using the LLDVE method discussed in section 3. Figure 2 presents the results from the local linear dummy variable estimations along with 90% confidence intervals. Compared to the parametric point estimates, our nonparametric panel data estimation captures the time-varying relationship between oil prices and economic policy uncertainty. Specifically, oil prices and economic policy uncertainty have a negative relationship before 2010, which becomes positive thereafter, before reversing again in 2015. The coefficient on oil prices increased sharply between 2006 and 2010, then leveled off until 2012 before increasing sharply again in 2014. The main reason for the negative relationship between oil prices and economic policy uncertainty is that the main driver of oil prices since the late 1990s has been the surge in aggregate demand, rather than supply shocks (Kilian, 2009). The nonparametric estimates in Figure 2 also shows that the effect of oil prices on economic policy uncertainty is downward trending from around 2014 and that there is a negative correlation between the two variables at the end of our sample period. In sum, our local linear estimates show that the coefficient function on the oil price was largely negative for most of the period under consideration, except for the relatively short period following the GFC.
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Common trend
Coefficient of oil price
5.2
0.4
5
0.2
0 4.8 -0.2 4.6 -0.4 4.4 -0.6 4.2
-0.8 2000
2005
2010
2000
2015
Coefficient of economic misery
2005
2010
2015
Coefficient of sovereign credit spread 0.3
2 1.5
0.2
1 0.1 0.5 0 0 -0.1
-0.5
-0.2
-1 -1.5
-0.3 2000
2005
2010
2015
2000
2005
2010
2015
Figure 2: Estimates of common trend and coefficient functions with 90% confidence bands What drives the time-varying relationship between oil prices and economic policy uncertainty? Several factors can be behind the underlying time-varying relationship between the two variables over time. First, the increase in the price of oil can be driven by either a dis-
19
ruption in crude oil supply or by the surge in aggregate demand driven by a booming world economy. The main reason for the negative effect of an increase in oil prices on economic policy uncertainty in the period 1997 to 2007 was that the surge in oil prices in this period was driven by an increase in aggregate demand for global commodity prices. As Kilian (2009) shows, the increase in oil prices after 1979, and particularly after 2003, has not resulted in recessions since oil price rises in this period were driven primarily by strong global aggregate demand stemming from a booming world economy. In particular, the high demand for crude oil from emerging-market economies in recent decades has been the primary source of increases in oil prices. Studies subsequent to Kilian (2009) by several authors, who have used structural VAR models (see e.g., Peersman and Van Robays, 2012; Lippi and Nobili, 2012), show that an increase in oil prices has an adverse effect on the economy when induced by supply shocks, rather than aggregate demand shocks. Studies that examine the direct relationship between oil prices and economic policy uncertainty (e.g., Antonakakis et. al, 2014; Kang and Ratti, 2013) also show that the effects of an increase in oil prices that arise from an unanticipated increase in global aggregate demand shocks are very different from those caused by a disruption in oil supply or an unanticipated increase in oil prices due to precautionary demand, resulting from fears about future shortages in crude oil supply. As noted in Kilian (2008), economic growth in Japan was above the normal rate following the surge in oil prices between 2002 and the GFC, due to the expansion of the global economy driven by an increase in aggregate demand that counteracted the negative effects of higher oil prices and reduced economic policy uncertainty. Our findings with respect to the time-varying relationship between oil prices and economic policy uncertainty is consistent with the argument in Kilian (2009) that the effect of an increase in oil price in a particular period depends on the underlying reason for the oil price increase. Our findings are consistent with recent studies that have applied time-varying parameter VARs and concluded that prevailing economic conditions in each period matter for the oil priceeconomic policy uncertainty relationship (Degiannakis et al. 2018). Specifically, the surge in global demand for industrial commodities from the early 2000s until the GFC, stemming from a boom in global economic activity, dampened the effect of the oil price increase on economic policy uncertainty during this period. Another explanation for the negative relationship between oil prices and economic policy uncertainty could be changes in the transmission mechanism of shocks. Specifically, some of the negative effects of higher oil prices on the economy are mitigated by the substitution to high quality fuels and continued technological advancement that have given rise to energy efficiency gains over past decades. Blanchard and Gali (2007) and Blanchard and Riggi (2013) suggest that the mechanism by which oil price shocks transmit to macroeconomic effects can change with the structure of the economy and policy framework. Substantial oil
20
price declines since the summer of 2014 were driven by large-scale investment and technological innovation that gave rise to the shale oil and gas revolution in the U.S. The fracking boom in the U.S has increased the supply of oil, which has contributed to the lower oil price (Bataa and Park, 2017; Kilian, 2017). Substitution to natural gas, associated with the shale gas revolution has also contributed to the decline in oil prices since 2014 (Middleton et al., 2017). The natural gas market is the biggest competitor of crude oil, especially in the transportation sector. This reflects global concerns over the long-term impact of carbon emissions from crude oil and the fact that natural gas is the cleanest energy source among fossil fuels.
4.2.3 Common and country-specific trend functions The LLDVE estimates of country-specific trend functions, along with the common trend function, are plotted in Figure 3. We present the country-specific economic policy uncertainty trend functions and the common trend functions together for comparison. The dotted lines represent the 90% confidence bands around the common trend functions. As shown in Figure 3, the common trend increases sharply in the period between 1999 and 2012 and leveled out thereafter. Different patterns are observed for the country-specific economic policy uncertainty trend functions. Figure 3 shows that the trend function for the economic policy uncertainty index in Canada has increased since 2005 and was above the global trend at the onset of the GFC. The trend function for France has been above the global trend since 2003 and continued to be upward trending to the end of the study period. For Italy, the trend function has been below the global trend since the GFC. For the US and Japan, the country-specific trend functions jump above the global trend at the onset of the GFC, but this is reversed after 2010, while in Germany the country-specific and global trend functions overlap for most of the periods after the GFC. Overall, the country specific trend function for economic policy uncertainty has been largely following the global trend function for each of the countries in the G7.
21
Germany
Canada 5.2
5.2
5
5
4.8
4.8 4.6
4.6
4.4
4.4
4.2
4.2
1997 2000 2002 2005 2007 2010 2012 2015
1997 2000 2002 2005 2007 2010 2012 2015
France
UK
5.5
5.5
5
5
4.5 4.5 4 4
3.5 1997 2000 2002 2005 2007 2010 2012 2015
1997 2000 2002 2005 2007 2010 2012 2015
Italy
Japan
5.2
5.2
5
5
4.8
4.8
4.6
4.6
4.4
4.4
4.2
4.2
1997 2000 2002 2005 2007 2010 2012 2015
1997 2000 2002 2005 2007 2010 2012 2015
US 5.2 5 4.8 4.6 4.4 4.2 1997 2000 2002 2005 2007 2010 2012 2015
Figure 3: Estimates of country-specific trend functions (black) and common trend functions (blue) with 90% confidence bands for the common trend estimates.
22
4.3 Robustness checks, endogeneity and nonlinearity The effects of changes in oil prices might be different for net oil exporters and importers. Higher oil prices are expected to have a positive effect for net oil exporting economies, resulting in lower uncertainty. This is because of the potential improvement in terms of trade from boosting oil revenue. In addition, if the increase in oil price is being driven by a demand shock, we would expect a decrease in economic policy uncertainty in oil importers and exporters, but if it is a supply shock, an oil price rise might increase economic policy uncertainty in oil importers. Since Canada is the only net oil exporter among the G7 countries, we conduct a sensitivity check by re-estimating our model excluding Canada from our sample. Figure 4 presents the estimated coefficient of oil price and the common trend functions. Our results remain robust to the exclusion of Canada. This is plausible result because the increase in oil prices since the late 1990s has been mainly driven by a positive aggregate demand shock.
Figure 4: Estimates of coefficient of oil price and common trend functions excluding Canada from the sample.
We conduct a further sensitivity check on our results by separating out inflation and unemployment, rather than aggregating them in the economic misery index .The rationale for so doing is that inflation and unemployment could have differential effects on economic policy uncertainty in booms and busts. The estimated coefficients of oil price and the common trend function, reported in Figures 5 and 6, show that our results are robust. As expected, the coefficients of inflation and unemployment move in opposite directions during ’good times’ before the GFC, while both increase during the GFC.
23
Figure 5: Estimates of coefficient of oil price, inflation and common trend functions.
24
Figure 6: Estimates of coefficient of oil price, unemployment rate and common trend We conduct alternative estimations to check for endogeneity and nonlinearity, employing functions. the Su and Ullah (2008) estimator outlined in Section (2.4). We model economic policy uncertainty allowing for the real oil price to be the endogenous regressor instrumented by its
25
lagged value. Following Henderson and Parmeter (2015), we compare the 45◦ gradient plots (Figure 7) for the local linear estimates that ignore endogeneity of real oil prices and the instrumental variable local linear estimates to visualize the effect of accounting for endogeneity and to detect nonlinearity in our estimates. The basic idea of the 45◦ plots is as follows. Each point on the dark black line represents the estimated gradient, one for each observation. Each point on the red and blue lines in Figure 7 represents the upper and lower bounds of a 95% bootstrapped confidence interval for the specific point estimates, respectively. The estimated gradient for an observation is positive and statistically significant if the upper and lower confidence bands for that estimate are both in the upper right quadrant. If the confidence bands for a given estimate are both in the lower left quadrant, then the estimate for that observation is negative and statistically significant. The gradient estimate is statistically insignificant if the upper or lower confidence bands straddle the horizontal axis (see Henderson et al., 2012). As shown in Figure 7, there is no significant difference between the local linear estimates that ignore endogeneity (panel (a)) and the instrumental variable local linear estimates that account for endogeneity (panel (b)). The estimated gradients are statistically significant at 5%. They are evenly distributed in the negative and positive quadrant, indicating that oil prices have negative and positive effects on economic policy uncertainty. That is, the relationship between real oil prices and economic policy uncertainty is nonlinear. Our results suggest that failure to account for nonlinearity may lead to inconsistent estimates.
26
0.5 1.0 1.5 2.0 −1.5
−0.5
Estimated Gradient
0.5 1.0 1.5 2.0 −0.5 −1.5
Estimated Gradient
−1.5
−0.5
0.5 1.0 1.5 2.0
Estimated Gradient a) Local Linear
−1.5
−0.5
0.5 1.0 1.5 2.0
Estimated Gradient b) Su and Ullah IV Local Linear
Figure 7: 45◦ plot of the estimated gradients for real price of oil
In sum, our results are robust to alternative specifications and endogeneity. More, importantly our results show that it is crucial to account for nonlinearity in modeling the relationship between oil prices and economic policy uncertainty.
27
5 Concluding remarks We have examined the effect of oil prices on economic policy uncertainty in the G7 countries using a time-varying nonparametric panel data model. Specifically, we employed a data-driven local linear method to empirically examine the time-varying trend and coefficient functions that govern the relationship between the oil price and economic policy uncertainty. We allow these functions to evolve over time in the form of unknown functional forms with confidence bands constructed using a bootstrapping method. Our approach has several advantages over parametric models used in the extant literature to model the relationship between the oil price and economic policy uncertainty. First, unlike the commonly adopted restrictive parametric specifications that have the risk of misspecification, our nonparametric panel data technique does not impose assumptions on the functional forms. Instead, we allow the data to tailor the shape of the functional form. Second, we allow the effect of oil price on economic policy uncertainty to evolve over time as an unknown functional form. We also allow the common global trend of to evolve over time as an unknown functional form. Third, we estimate the country specific trend functions to evaluate the pattens of individual trend functions against the common global trend function. Using monthly data for the period January 1997 to July 2017, our LLDVE estimates reveal that the relationship between oil prices and economic policy uncertainty is time-varying. The coefficient function of the oil price is negative and relatively flat for the period between 1998 and 2006, then it increased sharply until 2010. The coefficient function was positive between 2010 and 2015. Overall, our results show that the coefficient function of the oil price was largely negative for most of the period under consideration. We attribute this finding to the main driver of oil prices in recent decades being the surge in aggregate demand which has had a positive effect on economic outlook and reduced policy uncertainty. We show that the country-specific trend functions follow the global common trend function for most countries. The parametric point estimates represent an ’average’ snapshopt at a point in time. In this sense, the nonparametric estimates capture more information by accounting for the entire distribution of economic policy uncertainty and the nonlinear effect of oil prices.
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References Alquist, R., Kilian, L., & Vigfusson, R. J. (2013). Forecasting the price of oil. In Handbook of economic forecasting (Vol. 2, pp. 427-507). Elsevier. Antonakakis, N., Chatziantoniou, I., & Filis, G. (2014). Dynamic spillovers of oil price shocks and economic policy uncertainty. Energy Economics, 44, 433-447. Arbatli, E. C., Davis, S. J., Ito, A., Miake, N., & Saito, I. (2017). Policy Uncertainty in Japan (No. w23411). National Bureau of Economic Research. Baker, S. R., Bloom, N., & Davis, S. J. (2016). Measuring economic policy uncertainty. The Quarterly Journal of Economics, 131(4), 1593-1636. Balke, N. S., Brown, S., & Yucel, M. (2010). Oil price shocks and US economic activity: an international perspective. Working Papers 1003, Federal Reserve Bank of Dallas, Dallas Fed WP. Barrero, J. M., Bloom, N., & Wright, I. (2017). Short and long run uncertainty (No. w23676). National Bureau of Economic Research. Bataa, E., & Park, C. (2017). Is the recent low oil price attributable to the shale revolution?. Energy Economics, 67, 72-82. Blanchard, O. J., & Gali, J. (2007). The Macroeconomic Effects of Oil Shocks: Why are the 2000s so different from the 1970s? (No. w13368). National Bureau of Economic Research. Blanchard, O. J., & Riggi, M. (2013). Why are the 2000s so different from the 1970s? A structural interpretation of changes in the macroeconomic effects of oil prices. Journal of the European Economic Association, 11(5), 1032-1052. Bloom, N.,(2009). The impact of uncertainty shocks. Econometrica, 77(3), 623-685. Bloom, N. (2014). Fluctuations in uncertainty. Journal of Economic Perspectives, 28(2), 153-76. Bordo, M. D., Duca, J. V., & Koch, C. (2016). Economic policy uncertainty and the credit channel: Aggregate and bank level US evidence over several decades. Journal of Financial Stability, 26, 90-106. Breusch, T. S., & Pagan, A. R. (1980). The Lagrange multiplier test and its applications to model specification in econometrics. The Review of Economic Studies, 47(1), 239-253. Brogaard, J., & Detzel, A. (2015). The asset-pricing implications of government economic policy uncertainty. Management Science, 61(1), 3-18. Caggiano, G., Castelnuovo, E., & Groshenny, N. (2014). Uncertainty shocks and unemploy-
29
ment dynamics in US recessions. Journal of Monetary Economics, 67, 78-92. Caggiano, G., Castelnuovo, E., & Figueres, J. M. (2017). Economic policy uncertainty and unemployment in the United States: A nonlinear approach. Economics Letters, 151, 31-34. Chen, J., Gao, J., & Li, D. (2012). Semiparametric trending panel data models with crosssectional dependence. Journal of Econometrics, 171(1), 71-85. Christoffersen, P., & Pan, X. N. (2017). Oil volatility risk and expected stock returns. Journal of Banking & Finance. Chudik, A., & Pesaran, M. H. (2015). Common correlated effects estimation of heterogeneous dynamic panel data models with weakly exogenous regressors. Journal of Econometrics, 188(2), 393-420. Cologni, A., & Manera, M. (2008). Oil prices, inflation and interest rates in a structural cointegrated VAR model for the G-7 countries. Energy economics, 30(3), 856-888. Cunado, J., & De Gracia, F. P. (2005). Oil prices, economic activity and inflation: evidence for some Asian countries. The Quarterly Review of Economics and Finance, 45(1), 65-83. Degiannakis, S., Filis, G., & Panagiotakopoulou, S. (2018). Oil Price Shocks and Uncertainty: How stable is their relationship over time?. Economic Modelling. Duca, J. V., & Saving, J. L. (2018). What drives economic policy uncertainty in the long and short runs: European and US evidence over several decades. Journal of Macroeconomics, 55, 128-145. Fan, J., & Gijbels, I. (1996). Local polynomial modelling and its applications: monographs on statistics and applied probability 66 (Vol. 66). CRC Press. Filis, G. (2010). Macro economy, stock market and oil prices: Do meaningful relationships exist among their cyclical fluctuations?. Energy Economics, 32(4), 877-886. Feng, J., Wang, Y., & Yin, L. (2017). Oil volatility risk and stock market volatility predictability: Evidence from G7 countries. Energy Economics, 68, 240-254. Hamilton, J. D. (1983). Oil and the macroeconomy since World War II. Journal of political economy, 91(2), 228-248. Hamilton, J. D. (2003). What is an oil shock?. Journal of econometrics, 113(2), 363-398. Henderson, D. J., Kumbhakar, S. C., & Parmeter, C. F. (2012). A simple method to visualize results in nonlinear regression models. Economics Letters, 117(3), 578-581. Henderson, D. J., Papageorgiou, C., & Parmeter, C. F. (2013). Who benefits from financial development? New methods, new evidence. European Economic Review, 63, 47-67.
30
Henderson, D. J., & Parmeter, C. F. (2015). Applied nonparametric econometrics. Cambridge University Press. Kang, W., & Ratti, R. A. (2013). Structural oil price shocks and policy uncertainty. Economic Modelling, 35, 314-319. Kang, W., & Ratti, R. A. (2013). Oil shocks, policy uncertainty and stock market return. Journal of International Financial Markets, Institutions and Money, 26, 305-318. Kang, W., Ratti, R. A., & Vespignani, J. L. (2017). Oil price shocks and policy uncertainty: New evidence on the effects of US and non-US oil production. Energy Economics, 66, 536546. Karimu, A., & Brännlund, R. (2013). Functional form and aggregate energy demand elasticities: A nonparametric panel approach for 17 OECD countries. Energy Economics, 36, 19-27. Kendall, M.G., (1975). Rank correlation methods. Griffin, London Kilian, L. (2008). Exogenous oil supply shocks: how big are they and how much do they matter for the US economy?. The Review of Economics and Statistics, 90(2), 216-240. Killian, L., (2009). Not All Oil Price Shocks Are Alike: Disentangling Demand and Supply Shocks in the Crude Oil Market. American Economic Review, 99(3), 1053 -1069 Kilian, L., (2017). The Impact of the Fracking Boom on Arab Oil Producers. The Energy Journal, International Association for Energy Economics, 38(6), 137-160. Kilian, L., & Park, C. (2009). The impact of oil price shocks on the US stock market. International Economic Review, 50(4), 1267-1287. Li, D., Chen, J., & Gao, J. (2011). Nonparametric time-varying coefficient panel data models with fixed effects. The Econometrics Journal, 14(3), 387-408. Lippi, F., & Nobili, A. (2012). Oil and the macroeconomy: a quantitative structural analysis. Journal of the European Economic Association, 10(5), 1059-1083. Mammen, E. (1993). Bootstrap and wild bootstrap for high dimensional linear models. The annals of statistics, 255-285. Mann, H. B. (1945). Nonparametric tests against trend. Econometrica: Journal of the Econometric Society, 245-259. Middleton, R. S., Gupta, R., Hyman, J. D., & Viswanathan, H. S. (2017). The shale gas revolution: Barriers, sustainability, and emerging opportunities. Applied energy, 199, 88-95. Paudel, K. P., & Poudel, B. N. (2012). Functional form of water pollutants-income relationship under the environmental Kuznets curve framework. American Journal of Agricultural
31
Economics, 95(2), 261-267. Peersman, G., & Van Robays, I. (2012). Cross-country differences in the effects of oil shocks. Energy Economics, 34(5), 1532-1547. Pesaran, M. H., Shin, Y., & Smith, R. P. (1999). Pooled mean group estimation of dynamic heterogeneous panels. Journal of the American Statistical Association, 94(446), 621-634. Pesaran, M. H. (2004). General diagnostic tests for cross section dependence in panels. University of Cambridge, Cambridge Working Papers in Economics No. 0435. Pesaran, M. H. (2015). Testing weak cross-sectional dependence in large panels. Econometric Reviews, 34(6-10), 1089-1117. Rehman, M. U. (2018). Do oil shocks predict economic policy uncertainty?. Physica A: Statistical Mechanics and its Applications. Ruckstuhl, A. F., Welsh, A. H., & Carroll, R. J. (2000). Nonparametric function estimation of the relationship between two repeatedly measured variables. Statistica Sinica, 51-71. Runar, B., Amin, K., & Patrik, S. (2017). Convergence in carbon dioxide emissions and the role of growth and institutions: a parametric and non-parametric analysis. Environmental Economics and Policy Studies, 19(2), 359-390. Shahbaz, M., Shafiullah, M., Papavassiliou, V. G., & Hammoudeh, S. (2017). The CO2 growth nexus revisited: A nonparametric analysis for the G7 economies over nearly two centuries. Energy Economics, 65, 183-193. Sadorsky, P. (1999). Oil price shocks and stock market activity. Energy economics, 21(5), 449-469. Silvapulle, P., Smyth, R., Zhang, X., & Fenech, J. P. (2017). Nonparametric panel data model for crude oil and stock market prices in net oil importing countries. Energy Economics, 67, 255-267. Su, L., & Ullah, A. (2006). More efficient estimation in nonparametric regression with nonparametric autocorrelated errors. Econometric Theory, 22(1), 98-126. Su, L., & Ullah, A. (2008). Local polynomial estimation of nonparametric simultaneous equations models. Journal of Econometrics, 144(1), 193-218. Sun, Y., Carroll, R. J., & Li, D. (2009). Semiparametric estimation of fixed-effects panel data varying coefficient models. In Nonparametric econometric methods (pp. 101-129). Emerald Group Publishing Limited. Tang, W., Wu, L., & Zhang, Z. (2010). Oil price shocks and their short-and long-term effects on the Chinese economy. Energy Economics, 32, S3-S14.
32
Wu, C. F. J. (1986). Jackknife, bootstrap and other resampling methods in regression analysis. the Annals of Statistics, 1261-1295. You, W., Guo, Y., Zhu, H., & Tang, Y. (2017). Oil price shocks, economic policy uncertainty and industry stock returns in China: Asymmetric effects with quantile regression. Energy Economics, 68, 1-18.
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