Have European natural gas prices decoupled from crude oil prices? Evidence from TVP-VAR analysis

3.1 The model

We start our investigation of the European natural gas market by considering a structural VAR model for the trivariate vector y t = p t OIL , p t NGUS , p t NGEU ′ , where p = log(P). This is the most parsimonious specification to analyze the dynamic interactions among the three markets. The structural VAR process with the lag length l is:

where B ₀ is a 3 × 1 vector of constant terms, B _i for i = 1, 2, …, l denote 3 × 3 matrices of autoregressive coefficients, D is a 3 × 3 identification matrix and η _t is a 3 × 1 vector of structural shocks. It contains innovations to US oil (η ^OIL), US natural gas (η ^NGUS) and EU natural gas (η ^NGEU) prices. In model identification, we impose the recursive identification scheme, in which D is a lower triangular matrix as:

Based on the Schwarz information criterion, we set the maximum lag to l = 2 and estimate the reduced-form VAR on the main sample with the least squares method. Next, we use the estimated covariance matrix of residuals to compute the elements * of matrix D. Finally, we calculate impulse response functions to structural shocks, forecast error variance decomposition as well as historical decomposition for the three series.

3.2 The results

Impulse response functions. Figure 2 presents the impulse response functions (IRFs) of endogenous variables to one standard deviation of structural shocks along with the 90 % confidence bands. The left top panel illustrates that an oil market innovation immediately leads to an increase in crude oil prices by 9 %, which in the subsequent two months reaches a peak of almost 11 %. After the initial jump, oil prices slowly return to equilibrium, but even after five years their level is still around 3 % above the level observed before the occurrence of the shock. The center top panel demonstrates that oil prices are not significantly affected by shocks to US natural gas prices, which confirms the earlier results in the surveyed literature (e.g. Jadidzadeh and Serletis 2017). The right top panel shows that oil prices are also insensitive to unexpected changes in EU gas prices, though the maximum mean response is estimated at roughly 2 % after two years. This kind of result is at odds with the studies surveyed in the Introduction and it is driven by the large variation in oil and natural gas prices observed after 2020. In fact, throughout 2021 the relative price of power generation in Europe from natural gas has increased so much that it prompted a switch to oil, increasing global demand for oil by approximately half a million barrels a day (estimated by IEA 2021).

Figure 2:

Impulse response functions in the constant coefficient SVAR model. The figure presents the impulse response functions to structural shocks in the constant coefficient SVAR model estimated on the main sample. The black solid lines represent the mean value, whereas the shaded area denote the upper and lower 90 % bootstrapped confidence bounds. All values are multiplied by 100 so that they are expressed as per cents.

The reaction of natural gas prices in the US to the structural shocks is presented in the middle row of Figure 2. It can be seen that an oil price shock initially leads to an increase in natural gas prices by around 3–4%. Next, prices revert to the pre-shock level relatively quickly, so that three years after the occurrence of the shock they are almost back to equilibrium. The center panel indicates that the idiosyncratic shock causes an initial jump in prices by roughly 13 % and its gradual reversion to equilibrium, which lasts 5 years. Finally, the reaction to a shock originating in the European gas market, which is depicted in the right panel, is positive and significant, but short-lived. It can be added that this result is driven by observations from the last two years of the sample.

The bottom row of Figure 2 presents the reaction of the main variable of our interest: European natural gas prices. The left panel indicates that an oil shock does not initially trigger their sizeable reaction. However, after two years it becomes significant and amounts to around 6 %, which is comparable to the response of oil prices at this horizon. As a result, following an oil shock, the decoupling of European natural gas prices from oil prices is short-lived and broadly disappears after two years. The center panel shows that European natural gas prices are not significantly affected by the development in the US gas market in the statistical sense. The reaction is not sizeable and visibly weaker from the reaction of P ^NGUS to this shock. The comparison of both variables reaction illustrates how shocks in the US market lead to the decoupling of natural gas prices across the Atlantic. Finally, the right bottom panel shows that idiosyncratic shocks to the European natural gas market lead to a persistent upward shift in prices, where the initial reaction amounts to about 8 %, with peak at around 10 % shortly after the occurrence of the shock.

Forecast error variance decomposition. How important are the three shocks for the dynamics of the real energy commodity prices? Figure 3 quantifies their contribution to the forecast error variance for individual variables at different horizons. The left panel shows that fluctuations in oil prices are to a dominant extent determined by shocks specific to the oil market. This confirms that the situation in the natural gas market has a limited impact on crude oil price developments. We note that the contribution of EU natural gas shocks to oil prices variation, amounting to roughly 8 % in the long-term, is driven by most recent observations in the sample. Next, the center panel shows that US natural gas prices are predominantly driven by shocks specific to the US natural gas market. The contribution of oil shocks to the forecast error variance increases along the horizon, but stabilizes at 15 % after two years. The contribution of the European natural gas market shocks is hardly discernible. Finally, the right panel demonstrates that in the short run European natural gas prices are almost entirely determined by idiosyncratic shocks. However, for further horizons there is a notable increase in the contribution of oil shocks, which rises to over 55 %. In turn, the contribution of shocks originating in the US natural gas market is relatively small.

Figure 3:

Forecast error variance decomposition in the constant coefficient SVAR model. The figure presents FEVD for selected horizons for the log level in real oil and natural gas prices. The dark gray, light gray and medium gray colors represent the contribution of oil, US natural gas and EU natural gas market shocks (in per cents), respectively.

Historical decomposition. We continue the SVAR analysis by computing the contribution of the three shocks to real energy commodity price developments. The upper panel of Figure 4 illustrates that, apart from the most recent period, oil prices are hardly affected by natural gas markets shocks. The middle panel shows that major fluctuations in the US natural gas prices before the shale gas revolution as well as their subsequent rapid decline have been driven by shocks specific to the US natural gas sector. However, for this variable there is also a visible and non-negligible contribution of oil market shocks, especially following the outburst of the great financial crisis as well as during the period of abundant oil supply throughout 2015 and 2016. It is also discernible that recent increases in US natural gas prices are partly driven by shocks originating in the EU market. Finally, the bottom panel summarizes well the dependence of European natural gas prices on crude oil market developments, especially up until the end of 2016. It unambiguously shows that till that date most of European natural gas price fluctuations have closely followed crude oil market dynamics, with only a temporal impact of shocks specific to the US and European natural gas markets. However, the chart also shows that since 2018 they have been predominantly driven by idiosyncratic shocks, specific to the EU market.

Figure 4:

Historical decomposition for the log  annual growth rate in real oil and natural gas prices in the constant coefficient SVAR model. The black solid line represents the logarithmic annual rate of change in the real prices of oil and natural gas (in per cent). The dark gray, light gray and medium gray colors represent the contribution of oil, US natural gas and EU natural gas market shocks (in pp), respectively.

3.3 Key takeaways

The above SVAR analysis allows us to make few observations. First, the comparison of IRFs for crude oil and US natural gas prices indicates that after the occurrence of η ^OIL and η ^NGUS innovations, both variables behave differently. This illustrates the observed decoupling of the US natural gas and crude oil markets. Second, the comparison of IRFs for crude oil and European natural gas prices indicates that after η ^OIL and η ^NGEU shocks there is only a temporary decoupling of both markets. However, after two years from the occurrence of shocks the reactions of both variables are almost the same. Moreover, after the η ^NGUS shock both variables behave similarly from the initial period onwards. This would indicate that the dynamics of these two markets are closely linked over medium and long-term horizons, but not over the short-term one. Next, the FEVD analysis shows that developments in the natural gas markets, both in the US and in Europe, affect crude oil prices only to a very limited extent. It also illustrates that US natural gas prices are not linked to oil prices neither in the short nor in the long horizon. Finally, FEVD confirms that European natural gas prices are linked to oil prices over the medium and long term. All the above results confirm findings presented in studies surveyed in Table 1, which do not account for the recent extreme market events. The new result of our SVAR analysis, which is driven by the most recent observations, is that at short-term horizon European natural gas market shocks significantly affect natural gas prices in the US as well as are exert an upward pressure on oil prices.

4.1 The model

In the time-varying framework the dynamics of the dependent variable y _t is given by a VAR process of order l = 2 according to the following rule of motion:

Note that now we allow all parameters, i.e. the vector of constant terms B _0,t , the coefficients of the autoregressive matrices { B i , t } i = 1 l and the identification matrix D _t to change over time. The drift in the lagged coefficients is designed to capture possible nonlinearities and time variation in the lag structure of the model, which affects the propagation mechanism of shocks. In turn, the variability in the identification matrix reflects heteroscedastic structure of innovations in the system. By allowing for the variation in both parts of the model, we leave it up to data to determine whether it results from changes in the magnitude of economic shocks (i.e. the impulse) or the changes in the propagation mechanism (i.e. the response).

To estimate the model efficiently we assume that D t = A t − 1 Σ t , where A _t is a lower triangular matrix that models the contemporaneous relations between endogenous variables, while Σ _t is the diagonal matrix of standard deviations. In our case, i.e. for the recursive identification scheme and trivariate system, they are as follows:

Given the above decomposition, we perform common VAR analysis in the time-varying framework by drawing from the posterior distribution. For that purpose we write down model (3) as:

where β _t is a vector that collects all parameters from { B i , t } i = 0 l and X t ′ = I 3 ⊗ 1 , y t − 1 ′ , … , y t − l ′ , with ⊗ being the Kronecker product.

Following Primiceri (2005), the time-varying parameters from vector β _t and the free elements of matrix A _t , which are stacked into α _t = [a _21,t , a _31,t , a _32,t ]′, are governed by the standard random walk. In turn, the vector of standard deviations σ _t = [σ _1t , σ _2t , σ _3t ]′ follows the geometric random walk. Consequently, they are specified as follows:

All innovations in the system are assumed to be mutually independent and normally distributed with the variance-covariance matrix:

where Q, S and W are positive definite, time-invariant matrices.

To estimate the model we rely on Bayesian methods, in particular the Markov Chain Monte Carlo (MCMC) approach and the Gibbs sampler proposed by Del Negro and Primiceri (2015). As regards the prior, we follow the procedure as well as choices described by Primiceri (2005), which is a standard approach in the literature (e.g. Anand and Paul 2021; Bjørnland et al. 2019; Chatziantoniou et al. 2021; Czudaj 2019; Lubik et al. 2016; Lyu et al. 2021). In the first step, we need to set the prior for the initial value of model parameters, i.e. β ₀, α ₀ and logσ ₀. We do it by estimating the time-invariant VAR model of the form (1) using pre-sample observations. The point estimates ( β ̂ , α ̂ and σ ̂ ) as well as the respective variance matrices ( V ̂ β ̂ and V ̂ α ̂ ) are taken as parameters of the prior distribution, namely:

As regards the hyperparameters specifying the tightness of the prior, we set them to the standard values from the literature, i.e. k _β = 4, k _α = 4, k _σ = 1.

In the second step, we impose a prior on matrices Q, S and W by assuming that:

where I W denotes the inverse Wishart distribution. In equation (15) S ₁ and S ₂ denote two blocks of matrix S, sized 1 × 1 and 2 × 2, and corresponding to parameters belonging to separate equations of the TVP-VAR-SV model (see Primiceri 2005, for details). As regards the hyperparameters, we use the standard values of k _Q = 0.01, k _W = 0.01 and k _S = 0.10, which are also chosen in most studies enumerated at the beginning of this section. However, as robustness, we have also checked how a sensible change in our prior assumptions affects our results. To this end, in the sensitivity analysis we multiply parameters k _Q and k _S and divide k _W by a factor of 4. Next, we choose p _Q = 120 to accounts for the number of observations in the pre-sample and set p _W = n + 1 and p S j = j + 1 , as is usually done in the empirical literature. Finally, we set the number of MCMC draws to initialize the sampler to 5 × 10³ and the number of MCMC draws to 5 × 10⁴. Since we employ a thinning factor of 10, in the end we retain 5 × 10³ draws. In presenting our results we report the median estimates along with 90 % credible sets. For the detailed and critical description of the TVP-VAR-SV model, including estimation issues, we refer the reader to Lubik and Matthes (2015).

4.2 The results

The evolution of model parameters. We start our investigation of the TVP-VAR-SV model by inspecting the evolution of model parameters over time. The top and middle rows of Figure 5 present the posterior median for autoregressive coefficients along with the 90 % credible sets. The overwhelming impression is that for the baseline prior there is virtually no time variation for these parameters. On the contrary, the bottom row of the figure points to high variation in stochastic volatility parameters. It should be noted that this kind of outcome is typical for studies applying the TVP-VAR-SV framework (e.g. Anand and Paul 2021; Amir-Ahmadi et al. 2016; Cogley and Sargent 2005; Corsello and Nispi Landi 2020; Koop and Korobilis 2013; Lubik et al. 2016; Papiez et al. 2022; Primiceri 2005; Wiggins and Etienne 2017).

Figure 5:

The evolution of selected coefficients in the TVP-VAR-SV model. The black solid line represents the posterior median, whereas the shaded area denotes the 90 percent posterior credible sets. The red line represent the posterior median in the model with hyperparameters k _Q and k _S multiplied and k _W divided by a factor of 4.

The time-stability of the lag coefficients combined with large movements in stochastic volatility means that the propagation of shocks remains rather constant, whereas the strength of the impulse varies over time. In our case, there are several, occasional and short-lived increases in the time-varying standard deviation of shocks. The most pronounced spike in stochastic volatility occurred in the period following the outbreak of the Covid-19 pandemic, while smaller variation is also discernible during the global financial crisis. In the former case, this is especially visible for the European natural gas prices. Our reading of this result is that depending on the event, the initial reaction of energy commodity prices should differ, but their further development in time remains similar.

Impulse response functions. Given the evidence provided in Figure 5, we inspect market reaction during several specific time periods. These pertain to the:

• Mar. 1996: cold winter in the US,

• Dec. 2000: high US natural gas prices during the California crisis,

• Sep. 2005: record high US natural gas prices due to the Katrina hurricane,

• Jun. 2008: record high oil prices,

• Feb. 2009: collapse in energy commodity prices during the global financial crisis (GFC),

• Feb. 2014: cold winter in the US coupled with massive natural gas withdrawals,

• Mar. 2018: the cold snap in Europe due to the impact of the “Beast from the East”,

• Apr. 2020: most severe economic restrictions across the globe due to Covid-19,

• Aug. 2022: record high European natural gas prices.

For all the above periods, in Figure 6 we present the posterior median impulse response. It illustrates that the propagation mechanism has indeed remained stable across the sample, while changes in IRFs originate mostly from the movements in stochastic volatility, i.e. the strength of the impulse. It can be seen that in seven episodes that occurred before 2020 the initial response of energy commodity prices is quite similar, despite different economic events. For instance, the top left panel illustrates that oil market shocks increase crude oil prices, with the standard magnitude of the response from around 7 % in winter 2014 to around 10 % throughout the deep recession during the GFC. However, most recently, following the outbreak of the Covid-19 pandemic, the reaction of oil prices to the oil shock almost doubled, amounting to over 15 % on impact and peaking at around 20 % shortly after the occurrence of shocks. The panel also shows that the pace of the return of oil prices to the pre-shock level remained broadly the same, with half-life amounting to about 5 years, in line with the literature on real commodity price persistence (e.g. Ghoshray et al. 2014; Rubaszek 2021). The remaining two top panels of the figure show that the sensitivity of oil prices to natural gas market shocks in the US and in Europe is limited. Again, we observe two grouped sets of IRFs, before and during Covid-19. Interestingly, the peak of the impact of the US natural gas market shock on oil prices realizes far later after the occurrence of the shock than in the case of the EU shock.

Figure 6:

Impulse response functions in the TVP-VAR-SV model. The solid lines represent the posterior median impulse responses at various points in time. Market events are described in Section 4.2. All values are multiplied by 100 so that they are expressed as per cents.

The middle row of Figure 6 describes the reaction of US natural gas prices to the three structural shocks. In the first year after the oil price shock the reaction of US natural gas prices varies from around 4 % to almost 9 %. It can be noticed that the pace of reversion is considerably slower than in the constant coefficient VAR. The center panel shows that during most recent events US natural gas prices reaction to market-specific shock amounted to as much as 20 %, visibly more than during the cold winter of 1996, the California crisis, the Hurricane Katrina episode or the record withdrawals in 2014.

The bottom row of Figure 6 illustrates how the reaction of European natural gas prices to the structural shocks evolves over time. Following oil shocks there is a sizable, although lagged, response of EU natural gas prices. The peak response takes place around two years after the shock and is estimated to amount between 6 % and 14 %, depending on the episode. The central panel shows that the situation on the US natural gas market does not influence EU prices in a significant way, leading to the decoupling of gas prices across the Atlantic. Instead, EU market specific shocks tend to significantly impact European natural gas prices, with the response amounting even to around 23 % for selected episodes and horizons. It should be emphasized that in this case the pace of reversion to pre-shock level is relatively quick, with half-life of about one year.

A careful look at Figure 6 leads to the observation that at longer horizons the responses of oil and European natural gas prices to all shocks are almost the same, which is not the case for shorter horizons. In the case of the oil shock, this is illustrated in detail in Figure 7. Specifically, it presents the ratio of oil to European natural gas price response, at various horizons and for different moments in time, so that a value of 1 means that the reactions of both variables are the same. The figure delivers strong evidence that the decoupling of European natural gas prices from oil prices is short-lived. At horizons above 2 years, the reaction of both variables is almost exactly the same, without any restrictions imposed on VAR model parameters. Moreover, this result is valid across the sample, which covers almost three last decades.

Figure 7:

The short-term divergence and long-term convergence of oil and EU natural gas prices. Each bar represents the ratio of the median reaction of oil prices and EU natural gas prices to the oil shock at a specific horizon and for a certain market event. A value of one means that the change in prices of both commodities is the same.

We continue our investigation by checking how the use of the TVP-VAR-SV framework influences our perception about the dynamics of the analyzed trivariate system for energy commodity prices compared to the broadly used constant coefficient structural VAR model. In Figure 8 we compare posterior median IRF obtained from the TVP-VAR-SV approach for the last period of the sample to the IRF obtained from the structural VAR. This allows us to study how both models behave if estimated using information available at the end of our sample. In general, we observe that in the TVP-VAR-SV model the response of energy commodity prices to shocks is more pronounced and sometimes more persistent than in the structural VAR model. However, both models are unanimously pointing to the segmentation of gas markets and to the link between European natural gas and crude oil prices in the longer horizons. This would suggest that, despite the changes in the structure of the European natural gas market, including a shift from the oil price indexation towards gas-on gas competition, European prices are still linked to oil prices over the long-term horizon.

Figure 8:

The comparison of impulse response functions in the SVAR and TVP-VAR-SV model. The black solid line represents the posterior median, whereas the shaded area denotes the 90 percent posterior credible sets for the last period in the sample from the time-varying parameters SVAR model (i.e. October 2022). The dashed line illustrates the impulse response function from the constant coefficient SVAR model. All values are multiplied by 100 so that they are expressed as per cents.

Forecast error variance decomposition. We conclude the TVP-VAR-SV analysis by quantifying time-varying contribution of the three shocks to the forecast error variance of endogenous variables at four selected horizons, i.e. on impact, after one year, three years and five years ahead. The top row of Figure 9 shows that in the very short-term energy commodities prices are almost exclusively driven by market-specific shocks. The left column of the figure indicates that for oil prices the contribution of idiosyncratic shock to variance remains dominant also at longer horizons. Specifically, in the long run around 90 % of their variability stems from the shock specific to the oil market, while the contribution of US and EU natural gas market shocks are negligible. As regards natural gas prices, we observe sizeable discrepancies between the US and EU markets. For the former, the role of idiosyncratic shocks is dominant for all horizons and periods. The contribution of oil and European gas market shocks is usually below 25 % and 5 %, respectively. In the case of European natural gas prices the situation is different. The contribution of oil market shocks to forecast error variance at the five-year horizon stands approximately at 80 % throughout the majority of the sample, which points to the strong link between both energy commodity prices over the long-run. However, the figure also shows that there has been a gradual increase in the contribution of idiosyncratic shocks to the forecast error variance to around 33 % at the end of the sample, which might reflect the changing structure of the European natural gas market. Finally, it can be seen that the developments in the US natural gas market play a minor role in the evolution of EU natural gas prices.

Figure 9:

Forecast error variance decomposition in the TVP-VAR-SV model. The figure presents the evolution of the forecast error variance decomposition for the log level in real oil and natural gas prices. The dark gray, light gray and medium gray colors represent the contribution of oil, US natural gas and EU natural gas markets shocks (in per cents), respectively. As median contributions are reported, their sum is normalized to add up to 100.

4.3 Sensitivity analysis

In the baseline specification of the prior for the TVP-VAR-SV model we fix hyperparameters k _Q , k _S and k _W at values most commonly used in the literature. As a robustness check, we rescale them by a factor of 4, so that k _Q = 0.04, k _W = 0.0025 and k _S = 0.40. This modification introduces more freedom in the evolution of autoregressive parameters and, at the same time, constrains changes in stochastic volatility components.

The impact of this change on the posterior median of model parameters is hardly visible, which is illustrated in Figure 5. Rescaling the prior has very small effect on the shape of impulse-response functions (Figure 10) and forecast error variance decomposition (Figure 11). Thus, we conclude that our results are robust to reasonable changes in prior assumptions.

Figure 10:

IRF in the TVP-VAR-SV model with hyperparameters rescaled by 4. The solid lines represent the posterior median impulse responses at various points in time from the model with hyperparameters k _Q and k _S multiplied and k _W divided by a factor of 4. Market events are described in Section 4.2. All values are multiplied by 100 so that they are expressed as per cents.

Figure 11:

FEVD in the TVP-VAR-SV model with hyperparameters rescaled by 4. The figure presents the evolution of the forecast error variance decomposition for the log level in real oil and natural gas prices based on the model with hyperparameters k _Q and k _S multiplied and k _W divided by a factor of 4. The dark gray, light gray and medium gray colors represent the contribution of oil, US natural gas and EU natural gas markets shocks (in per cents), respectively. As median contributions are reported, their sum is normalized to add up to 100.

4.4 Key takeaways

The TVP-VAR analysis allows us to infer the following. An important new result of our investigation is that on energy commodity markets shocks propagation mechanism is stable, whereas the strength of structural impulses turned out to be volatile. In particular, we observe its multi-fold increase throughout the Covid-19 pandemic and since the onset of the Russian invasion of Ukraine. Secondly, we have delivered updated evidence to the literature surveyed in Table 1 by showing that even despite recent extreme market events the decoupling of European natural gas prices from oil prices remains short-lived as there exists a long-term link of both commodities at horizons above 2 years. It should be emphasized that this result, which is stable throughout the entire sample, was derived using unrestricted VAR model. Finally, using a very flexible estimation framework, in this section we have confirmed previous evidence on low sensitivity of oil prices to natural gas market shocks as well as the decoupling of gas prices across the Atlantic.