To analyze the international macroeconomic transmission of the US oil revolution shock, we need to model the oil–macroeconomy relationship in a global context. To this end, we integrate an oil price equation within a compact quarterly model of the global economy using the GVAR framework. The resulting GVAR-Oil model takes into account both the temporal and cross-sectional dimensions of the data; real and financial drivers of economic activity; interlinkages and spillovers that exist between different regions; and the effects of unobserved or observed common factors. This is crucial as the impact of the recent oil revolution cannot be reduced to just the USA (where the shock originates) but rather involves multiple regions, and may be amplified or dampened (through a number of channels) depending on the degree of openness of the countries, their trade structure, as well as the strength of global demand. Before describing our approach in modeling individual countries and the global oil market, we provide a short exposition of the GVAR methodology below.
The global VAR (GVAR) methodology
We consider N countries in the global economy, indexed by \(i=1,\ldots ,N\). With the exception of the USA, all other \(N-1\) countries are modeled as small open economies. This set of individual country-specific vector autoregressive models with foreign variables (VARX* models) is used to build the GVAR framework. Following Pesaran (2004) and Dees et al. (2007), a VARX* \(\left( p_{i},q_{i}\right) \) model for the ith country relates a \(k_{i}\times 1\) vector of domestic macroeconomic variables (treated as endogenous), \(\mathbf {x}_{it}\), to a \(k_{i}^{*}\times 1\) vector of country-specific foreign variables (taken to be weakly exogenous), \(\mathbf {x}_{it}^{*}\),
$$\begin{aligned} {\varvec{\Phi }}_{i}\left( L,p_{i}\right) \mathbf {x}_{it}=\mathbf {a}_{i0}+ \mathbf {a}_{i1}t+{{\varvec{\Lambda }} }_{i}\left( L,q_{i}\right) \mathbf {x} _{it}^{*}+\mathbf {u}_{it}, \end{aligned}$$
(1)
for \(t=1,2,\ldots ,T\), where \(\mathbf {a}_{i0}\) and \(\mathbf {a}_{i1}\) are \( k_{i}\times 1\) vectors of fixed intercepts and coefficients on the deterministic time trends, respectively, and \(\mathbf {u}_{it}\) is a \( k_{i}\times 1\) vector of country-specific shocks, which we assume are serially uncorrelated with zero mean and a non-singular covariance matrix, \( {{\varvec{\Sigma }}}_{ii}\), namely \(\mathbf {u}_{it}\thicksim i.i.d.\left( 0, {{\varvec{\Sigma }} }_{ii}\right) \). For algebraic simplicity, we abstract from observed global factors in the country-specific VARX* models. Furthermore, \( {{\varvec{\Phi }}}_{i}\left( L,p_{i}\right) =I-\sum _{i=1}^{p_{i}}{{\varvec{\Phi }}} _{i}L^{i}\) and \({{\varvec{\Lambda }} }_{i}\left( L,q_{i}\right) =\sum _{i=0}^{q_{i}}{{\varvec{\Lambda }} }_{i}L^{i}\) are the matrix lag polynomial of the coefficients associated with the domestic and foreign variables, respectively. As the lag orders for these variables, \(p_{i}\) and \(q_{i},\) are selected on a country-by-country basis, we are explicitly allowing for \({{\varvec{\Phi }}}_{i}\left( L,p_{i}\right) \) and \({{\varvec{\Lambda }} }_{i}\left( L,q_{i}\right) \) to differ across countries.
The country-specific foreign variables are constructed as cross-sectional averages of the domestic variables using data on bilateral trade as the weights, \(w_{ij}\)
$$\begin{aligned} \mathbf {x}_{it}^{*}=\sum _{j=1}^{N}w_{ij}\mathbf {x}_{jt}, \end{aligned}$$
(2)
where \(j=1,2,\ldots ,N\), \(w_{ii}=0,\) and \(\sum _{j=1}^{N}w_{ij}=1\). For empirical application, the trade weights are computed as 3-year averagesFootnote 7
$$\begin{aligned} w_{ij}=\frac{T_{ij,2007}+T_{ij,2008}+T_{ij,2009}}{ T_{i,2007}+T_{i,2008}+T_{i,2009}}, \end{aligned}$$
(3)
where \(T_{ijt}\) is the bilateral trade of country i with country j during a given year t and is calculated as the average of exports and imports of country i with j, and \(T_{it}=\sum _{j=1}^{N}T_{ijt}\) (the total trade of country i) for \(t=2007\), 2008, and 2009, in the case of all countries.Footnote 8
Although estimation is done on a country-by-country basis, the GVAR model is solved for the world as a whole, taking account of the fact that all variables are endogenous to the system as a whole. After estimating each country VARX*\(\left( p_{i},q_{i}\right) \) model separately, all the \( k=\sum _{i=1}^{N}k_{i}\) endogenous variables, collected in the \(k\times 1\) vector \(\mathbf {x}_{t}=\left( \mathbf {x}_{1t}^{\prime },\mathbf {x} _{2t}^{\prime },\ldots ,\mathbf {x}_{Nt}^{\prime }\right) ^{\prime }\), need to be solved simultaneously using the link matrix defined in terms of the country-specific weights. To see this, we can write the VARX* model in equation (1) more compactly as
$$\begin{aligned} \mathbf {A}_{i}\left( L,p_{i},q_{i}\right) \mathbf {z}_{it}={\varvec{\varphi }} _{it}, \end{aligned}$$
(4)
for \(i=1,\ldots ,N,\) where
$$\begin{aligned} \mathbf {A}_{i}\left( L,p_{i},q_{i}\right)= & {} \left[ {{\varvec{\Phi }} }_{i}\left( L,p_{i}\right) -{{\varvec{\Lambda }} }_{i}\left( L,q_{i}\right) \right] ,\quad \mathbf {z}_{it}=\left( \mathbf {x}_{it}^{\prime },\mathbf {x}_{it}^{\prime *}\right) ^{\prime }, \nonumber \\ {\varvec{\varphi }}_{it}= & {} \mathbf {a}_{i0}+\mathbf {a}_{i1}t+\mathbf {u}_{it}. \end{aligned}$$
(5)
Note that given Eq. (2) we can write
$$\begin{aligned} \mathbf {z}_{it}=\mathbf {W}_{i}\mathbf {x}_{t}, \end{aligned}$$
(6)
where \(\mathbf {W}_{i}=\left( \mathbf {W}_{i1},\mathbf {W}_{i2},\ldots ,\mathbf {W} _{iN}\right) \), with \(\mathbf {W}_{ii}=0\), is the \(\left( k_{i}+k_{i}^{*}\right) \times k\) weight matrix for country i defined by the country-specific weights, \(w_{ij}\). Using (6) we can write (4) as
$$\begin{aligned} \mathbf {A}_{i}\left( L,p\right) \mathbf {W}_{i}\mathbf {x}_{t}=\varphi _{it}, \end{aligned}$$
(7)
where \(\mathbf {A}_{i}\left( L,p\right) \) is constructed from \(\mathbf {A} _{i}\left( L,p_{i},q_{i}\right) \) by setting \(p=\max ( p_{1},p_{2},\ldots ,p_{N},q_{1},q_{2},\ldots ,q_{N}) \) and augmenting the \( p-p_{i}\) or \(p-q_{i}\) additional terms in the power of the lag operator by zeros. Stacking Eq. (7), we obtain the global VAR\(\left( p\right) \) model in domestic variables only
$$\begin{aligned} \mathbf {G}\left( L,p\right) \mathbf {x}_{t}=\varphi _{t}, \end{aligned}$$
(8)
where
$$\begin{aligned} \mathbf {G}\left( L,p\right) =\left( \begin{array}{c} \mathbf {A}_{1}\left( L,p\right) \mathbf {W}_{1} \\ \mathbf {A}_{2}\left( L,p\right) \mathbf {W}_{2} \\ . \\ . \\ . \\ \mathbf {A}_{N}\left( L,p\right) \mathbf {W}_{N} \end{array} \right) ,\quad \varphi _{t}=\left( \begin{array}{c} \varphi _{1t} \\ \varphi _{2t} \\ . \\ . \\ . \\ \varphi _{Nt} \end{array} \right) . \end{aligned}$$
(9)
For an early illustration of the solution of the GVAR model, using a VARX*\( \left( 1,1\right) \) model, see Pesaran (2004), and for an extensive survey of the latest developments in GVAR modeling, both the theoretical foundations of the approach and its numerous empirical applications, see Chudik and Pesaran (2016). The GVAR\(\left( p\right) \) model in Eq. (8) can be solved recursively and used for a number of purposes, such as forecasting or impulse response analysis.
Country-specific VARX* models
We include as many major oil exporters as possible in our multi-country setup, subject to data availability, together with as many countries in the world to represent the global economy. Thus, our version of the GVAR model covers 50 countries as opposed to the standard 33 country setups used in the literature, see Smith and Galesi (2014), and extends the coverage both in terms of major oil exporters and also by including an important region of the world when it comes to oil supply, the MENA region.Footnote 9
Table 1 Countries and regions in the GVAR model Of the 50 countries included in our sample, 18 are classified as major commodity exporters as primary commodities constitute more than 40% of their exports (these countries are denoted by \(^{*}\) in Table 1). Moreover, 15 are net oil exporters of which 10 are current members of the OPEC (denoted by \(^{1}\) in Table 1) and one is a former member (Indonesia left OPEC in January 2009). We were not able to include Angola and Iraq, the remaining two OPEC members, due to the lack of sufficiently long time-series data. This was also the case for Russia, the second largest oil exporter in the world, for which quarterly data are not available for the majority of our sample period.Footnote 10 Our sample also includes three OECD oil exporters (Canada, Mexico, and Norway) and the UK, which remained a net oil exporter for the majority of the sample (until 2006), and therefore is treated as an oil exporter when it comes to imposing sign restrictions (see the discussion in Sect. 3.1). These 50 countries together cover over 90% of world GDP, 85% of world oil consumption, and 80% of world proven oil reserves. Thus, our sample is rather comprehensive.
For empirical applications, we create two regions: one of which comprises the six Gulf Cooperation Council (GCC) countries: Bahrain, Kuwait, Oman, Qatar, Saudi Arabia, and the United Arab Emirates (UAE); and the other is the Euro Area block comprising 8 of the 11 countries that initially joined the euro on January 1, 1999: Austria, Belgium, Finland, France, Germany, Italy, Netherlands, and Spain. The time-series data for the GCC block and the Euro Area block are constructed as cross-sectionally weighted averages of the domestic variables (described in detail below), using purchasing power parity GDP weights, averaged over the 2007–2009 period. Thus, as displayed in Table 1, our model includes 38 country-/region-specific VARX* models.
Making one region out of Bahrain, Kuwait, Oman, Qatar, Saudi Arabia, and the United Arab Emirates is not without economic reasoning. The rationale is that these countries have in recent decades implemented a number of policies and initiatives to foster economic and financial integration in the region with a view to establishing a monetary union (loosely based on that of the Euro Area). Abstracting from their level of success with above objectives, the states of the GCC are relatively similar in structure, though in the short term they may face some difficulties in meeting the convergence criteria they have set for economic integration based on those of the European Union (EU). Inflation rates vary significantly across these countries, and fiscal deficits, which have improved since the start of the oil boom in 2003, are about to re-emerge in some countries. However, these economies already peg their currencies to the US dollar, except for Kuwait, which uses a dollar-dominated basket of currencies, and are accustomed to outsourcing their interest rate policy. They also have relatively open capital accounts, and hence, it is reasonable to group these countries as one region.Footnote 11
We specify two different sets of individual country-specific models. The first model is common across all countries, apart from the USA. These 37 VARX* models include a maximum of six domestic variables (depending on whether data on a particular variable is available), or using the same terminology as in equation (1)
$$\begin{aligned} \mathbf {x}_{it}=\left[ y_{it},~\pi _{it},~eq_{it},~r_{it}^{S},~r_{it}^{L},~ep_{it}\right] ^{\prime }, \end{aligned}$$
(10)
where \(y_{it}\) is the log of the real gross domestic product at time t for country\(\ i\), \(\pi _{it}\) is inflation, \(eq_{it}\) is the log of real equity prices, \(r_{it}^{S}\, (r_{it}^{L})\) is the short-term (long-term) interest rate, and \(ep_{it}\) is the real exchange rate. In addition, all domestic variables, except for that of the real exchange rate, have corresponding foreign variables computed as in Eq. (2)
$$\begin{aligned} \mathbf {x}_{it}^{*}=\left[ y_{it}^{*},~\pi _{it}^{*},~eq_{it}^{*},~r_{it}^{*S},~r_{it}^{*L}\right] ^{\prime }. \end{aligned}$$
(11)
Following the GVAR literature, the 38th model (USA) is specified differently, mainly because of the dominance of the USA in the world economy. First, given the importance of US financial variables in the global economy, the US-specific foreign financial variables, \(eq_{US,t}^{*}\) and \(r_{US,t}^{*L}\), are not included in this model. The appropriateness of exclusion of these variables was also confirmed by statistical tests, in which the weak exogeneity assumption was rejected for \(eq_{US,t}^{*}\) and \(r_{US,t}^{*L}\). Second, since \( e_{it}\) is expressed as the domestic currency price of a US dollar, it is by construction determined outside this model. Thus, instead of the real exchange rate, we included \(e_{US,t}^{*}-p_{US,t}^{*}\) as a weakly exogenous foreign variable in the US model.Footnote 12
The global oil market
To consider the macroeconomic effects of the US oil revolution, we also need to include nominal oil prices in US dollars in the country-specific VARX* models. If we follow the literature, we would include log oil prices, \( p_{t}^{o}\), as an endogenous variable in the US VARX* model and as a weakly exogenous variable in all other countries. See, for example, Cashin et al. (2014) and Chudik and Pesaran (2016). The main justification for this approach is that USA is the world’s largest oil consumer and a demand-side driver of the price of oil. However, it seems more appropriate for oil prices to be determined in global commodity markets rather in the US model alone, given that oil prices are also affected by, for instance, any disruptions to oil supply in the Middle East. Therefore, in contrast to the GVAR literature, we model the oil price equation separately and then introduce \(p_{t}^{o}\) as a weakly exogenous variable in all countries (including the USA), thereby allowing for both demand and supply conditions to influence the price of oil directly rather than using the US model as a transmission mechanism for the global economic conditions to the price of oil.Footnote 13
To add oil prices to the conditional country models, we simply augment the VARX* models (1) by \(p_{t}^{o}\) and its lag values
$$\begin{aligned} {{\varvec{\Phi }} }_{i}\left( L,p_{i}\right) \mathbf {x}_{it}=\mathbf {a}_{i0}+ \mathbf {a}_{i1}t+{{\varvec{\Lambda }} }_{i}\left( L,q_{i}\right) \mathbf {x} _{it}^{*}+\Upsilon _{i}\left( L,s_{i}\right) p_{t}^{o}+\mathbf {u}_{it}, \end{aligned}$$
(12)
where \(\Upsilon _{i}\left( L,s_{i}\right) =\sum _{i=0}^{s_{i}}\Upsilon _{i}L^{i}\) is the lag polynomial of the coefficients associated with oil prices, see Chudik and Pesaran (2013) for more details. Here, \(p_{t}^{o}\) can be treated (and tested) as weakly exogenous for the purpose of estimation and the marginal model for the oil price equation can be estimated with or without feedback effects from \(\mathbf {x}_{t}\). We incorporate the global oil market within the GVAR framework, by introducing an oil price equation
$$\begin{aligned} p_{t}^{o}=c_{p}+\sum \limits _{\ell =1}^{m_{p}}\alpha _{\ell }p_{t-\ell }^{o}+\sum \limits _{\ell =1}^{m_{y}}\beta _{\ell }y_{t-\ell }+\sum \limits _{\ell =1}^{m_{q}}\gamma _{\ell }q_{t-\ell }^{o}+u_{t}^{o}, \end{aligned}$$
(13)
which is a standard autoregressive distributed lag, ARDL(\( m_{p^{o}},m_{y},m_{q^{o}}\)), model in oil prices, world real income (\(y_{t}\) ) to proxy for global demand and world oil supplies (\(q_{t}^{o}\)), with all variables being in logs. Conditional (12) and marginal models (13) can be combined and solved as a complete GVAR model as explained earlier (see Sect. 2.1).
To take into account developments in the world economy, the oil price equation includes a measure of global output, \(y_{t}\), calculated as
$$\begin{aligned} y_{t}=\sum \limits _{j=1}^{N}w_{j}^{PPP}y_{jt}, \end{aligned}$$
(14)
where \(y_{jt}\) is the log of real GDP of country j at time t, \( j=1,2,\ldots ,N\), \(w_{j}^{PPP}\) is the PPP GDP weights of country j, and \( \sum _{j=1}^{N}w_{j}^{PPP}=1\). We compute \(w_{j}^{PPP}\) as a three-year average to reduce the impact of individual yearly movements on the weights
$$\begin{aligned} w_{j}^{PPP}=\frac{GDP_{j,2007}^{PPP}+GDP_{j,2008}^{PPP}+GDP_{j,2009}^{PPP}}{ GDP_{2007}^{PPP}+GDP_{2008}^{PPP}+GDP_{2009}^{PPP}}, \end{aligned}$$
(15)
where \(GDP_{jt}^{PPP}\) is the GDP of country j converted to international dollars using purchasing power parity rates during a given year t and \( GDP_{t}^{PPP}=\sum _{j=1}^{N}GDP_{jt}^{PPP}\).
To capture global oil supply conditions, we have also included a measure for the quantity of oil produced in the world in Eq. (13). A key question is how should \(q_{t}^{o}\) be included in our country-specific models? Looking at the 12 Organization of the Petroleum Exporting Countries (OPEC), of which some members are the largest oil producers in the world, we know that the amount of oil they produce in any given day plays a significant role in the global oil markets; however, they differ considerably from each other in terms of how much oil they produce (and export) and their level of proven oil reserves. Within OPEC, Saudi Arabia has a unique position as it is not only the largest oil producer and exporter in the world, but it also has the largest spare capacity and as such is often seen as a global swing producer. For example, in September 1985, Saudi production was increased from 2 million barrels per day (mbd) to 4.7 mbd (causing oil prices to drop from $57.61 to $29.62 in real terms)Footnote 14 and more recently following the US and the EU sanctions on Iran, Saudi Arabia has increased its production to stabilize the oil market. In fact, as is shown in Fig. 2 the relationship between Saudi Arabian oil production and total OPEC oil production is a very close one. In our application, Saudi Arabia and the other five GCC countries (Bahrain, Kuwait, Oman, Qatar, and the UAE) are grouped as one region, with this region then playing an important role when it comes to world oil supply.Footnote 15 Not only do these six countries produce more than 22% of world oil and export around 30% of the world total, the six GCC countries also possess 36.3% of the world’s proven oil reserves.Footnote 16 Therefore, given the status of the GCC countries with regards to OPEC oil supply, we include log of OPEC oil production, as an endogenous variable in the GCC block.
We now turn to non-OPEC oil supply. As Fig. 2 shows, the increase in non-OPEC production over the last decade is more or less the result of the oil revolution which has increased US production by 50% (from approximately 6–9 mbd). The recent technological advancements have not only reduced the costs associated with the production of tight oil, but also made the extraction resemble a manufacturing process in which the quantity produced can be altered in response to price changes with relative ease, which is not the case for conventional oil extraction which requires large capital expenditure and lead times. In other words, US oil production can play a significant role in balancing global demand and supply. Given the developments in the last decade, we model non-OPEC oil production within the US model.