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A Tripolar Model of Gas Price Formation in Germany. Does the Shale Revolution in the US Matter?

  • Anna Moenke ORCID logo EMAIL logo and Aleksander Welfe ORCID logo


Presented analysis of gas price formation mechanism in Germany was prompted by changes brought about by technological advancements and the liberalization and harmonization of natural gas markets in the European Union after the year 2000. Because the data used in the study is generated by nonstationary stochastic processes, the cointegrated vector autoregressive model was applied as the most appropriate. The analysis pointed out that the price of natural gas, oil and the USD/EUR exchange rate influence each other in the long run and thus should be modelled together. Gas price in Germany is driven by both fundamental and financial factors, and so it rises with economic expansion, oil price increases, and the depreciation of the USD. It also reacts to changes in short-term interest rates and the volume of gas production in the US, which confirms that the shale revolution in this country has been consequential for gas prices in Europe, like any other supply shock would have been.

JEL Classification: C32; C51; Q41

Corresponding author: Anna Moenke, Warsaw School of Economics, Al. Niepodleglosci 162, 02-554 Warszawa, Poland, E-mail:

Funding source: Narodowe Centrum Nauki

Award Identifier / Grant number: OPUS 21: DEC—2021/41/B/HS4/04317


The second author kindly acknowledges financial support from National Science Centre under OPUS 21: DEC—2021/41/B/HS4/04317.

Appendix A

A.1. Tables and figures

Table 2 presents the definitions of variables used in the empirical analysis. Figure 3 depicts the residuals of CVAR equations explaining prices of gas, oil and exchange rate. Table 3 presents the results of unit root tests.

Table 2:

The definitions of variables used in the empirical analysis.

Symbol Name Description Source
P g Natural gas price Import price index (excluding taxes, duties etc.) Federal statistical office –
P o Crude oil price To calculate real price of oil, nominal price of Europe brent spot price FOB (dollars per barrel) was deflated by the EU’s CPI Energy information administration (data on brent spot price); OECD (data on CPI)
ex t de USD/EUR real exchange rate The real USD/EUR exchange rate was calculated as: ex t de = p t   pe t   s t , where P t and PEt are the US and German CPIs, respectively. S t stands for the nominal USD/EUR exchange rate. Small letters denote natural logarithms (data on nominal interest rate), ECD – (data on CPIs)
Y t act Economic activity Y t act is a OECD’s industrial production index. It accounts for the output of the mining, manufacturing, electricity, gas and steam and air-conditioning sectors of the OECD’s countries OECD –
SI t The relative stock exchange index The stock exchange rate index in Germany was measured against the US′ stock exchange rate index SI t  = Rn t DJ/Rn t DAX (Rn t DAX, Rn t DJ stand for DAX and dow Jones indexes, respectively). The monthly average value of the indexes on closing was used
R t US US′ short term interest rate The real short-term interest rate in the US is calculated as nominal three-month treasury bill rate adjusted for inflation according to the equation: R t US = Rn t US − (P t  − P ts )/P t−1(Rn t US stands for nominal interest rate, P t is US′ CPI) OECD –
prod t us Gas production in the US U.S. Natural gas gross withdrawals (MMcf). The data were deseasonalized with TRAMO-SEATS procedure Energy information agency –
vol t Volume of futures and options contracts on energy products Total monthly volume of futures and options contract on the ICE futures europe market
  1. Year 2015 is the base period for indexes.

Figure 3: 
The residuals of CVAR equations explaining prices of gas, oil and exchange rate. In the case of the CVAR in I(1) domain, each equation is a linear combination of the variables; hence, the residuals must be stationary if each of the variables is I(0).
Figure 3:

The residuals of CVAR equations explaining prices of gas, oil and exchange rate. In the case of the CVAR in I(1) domain, each equation is a linear combination of the variables; hence, the residuals must be stationary if each of the variables is I(0).

Table 3:

Unit root tests results.

Variable ADF KPSS
H 0: y ∼ I(1) H 0: y ∼ I(0)
No intercept no trend With intercept With intercept and trend With intercept With intercept and trend
p g 0.64 −3.41 −3.21 0.3 0.17
Δp g −3.6 −3.61 −3.47
p o −0.21 −2.55 −3 0.63 0.2
Δp o −9.99 −9.97 −9.94
exde −0.92 −2.43 −2.87 0.69 0.16
Δexde −10.82 −10.79 −10.77
y akt 0.56 −2.22 −2.87 0.90 0.11
Δy akt −10.97 −10.97 −10.93
si −0.53 −2.29 −3.02 0.45 0.32
Δsi −16.39 −16.35 −16.6
r us −1.19 −1.44 −1.56 0.51 0.26
Δr us −9.48 −9.50 −9.47
produs 2.98 0.29 −3.10 1.74 0.16
Δprodus −12.36 −12.95 −12.97
vol 1.72 −2.06 −2.38 1.70 0.18
Δvol −3.37 −3.91 −4.17
  1. The ADF t-statistic and KPSS LM-statistic are compared with the 95th quantiles of asymptotic distributions (see Davidson and MacKinnon 1993; Kwiatkowski et al. 1992). The bolded values lead to the null hypothesis rejection at 5% level of significance.

A.2. Additional Empirical Results

The CVAR model presented in section 4 of the paper has 8 variables comprising the vector: y t T = p t g   p t o   ex t de  prod t us   y t akt   s i t   r t us   vol t . As before, the optimal lag length of 2 months was selected and two dummy variables were included (first with a value of 1 in September 2008, and the second one taking a value of 1 in November and December 2015). Assuming that the model has only two long-run relationships (see the cointegration test results, Table 1), in the next step, the existence of weakly exogenous variables was tested. Both economic activity and the volume of futures and options contracts on the ICE exchange were found to be weakly exogenous (LR = 4.82; p = 0.31). The repeated trace test and the maximum eigenvalue test confirmed the previous results (pointing to the existence of 4 and 2 long-term relationships, respectively). After imposing the necessary restrictions, the following results were obtained (the figures in the parentheses are t-Student statistics):

(10) A 1 B T y t 1 = [ 0.02 0.29 ( 2.73 ) 0.01 ( 0.98 ) 0.005 ( 1.47 ) 0.008 3.26 0 0.02 ( 4.42 ) 0.04 ( 1.98 ) 0 ( 3.33 ) 0.18 ( 1.13 ) 0.13 ( 3.41 ) 0.04 ( 1.33 ) 0 0.27 ( 4.31 ) 0.10 ( 0.46 ) 0 ]

p g 1.23 p o + 10.82 ex de + 4.06 prod us 3.62 y akt 0.63 si + 0.33 r us 15.91       2.69       8.37             3.44         1.41     0.45     2.65     1.69 ex de 0.12 p o 0.29 prod us + 0.55 si 0.01 r us + 0.06 vol + 1.17           3.22         1.67         3.59     0.8       2.34       1.22

The restrictions enabled all cointegrating vectors (LR = 5.09; p = 0.40) with full economic interpretation to be identified. The system adjusts to the equilibrium path as α 11 = −0.02, α 32 = −0.13 and the tests confirm that the residuals are stationary.

The key conclusions concerning gas price formation following from the above results and those presented in Section 4 are virtually the same. The price of gas in Germany goes up with a rising price of oil, expanding economic activity, and a depreciating US dollar. Increasing gas production in the US reduces the price of gas in Germany. A falling interest rate boosts investments in the commodity market, raising the price of gas. According to the second cointegrating vector, a rising price of oil increases the USD/EUR exchange rate and so does gas production in the US. Increases in the stock index ratio and in the volume of futures contracts and options on the ICE reduce the USD/EUR exchange rate.


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Received: 2022-01-10
Accepted: 2022-07-12
Published Online: 2022-08-19
Published in Print: 2022-08-26

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