# Competition in a Wholesale Fuel Market—The Impact of the Structural Changes Caused by COVID-19

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

- magnitude asymmetry, in which the amount of downward price change differs depending on the direction of upstream price change, observed in a long-run horizon (Figure 1).
- pattern asymmetry, in which the speed of downward price change differs depending on the direction of upstream price change, detected in the short-run horizon (Figure 2).

## 3. Materials and Methods

^{3}, the wholesale price of an unleaded standard 95 octane gasoline reported by LOTOS in PLN per m

^{3}, the wholesale price of standard diesel oil for road transport (brand name of PKN: Ekodiesel) reported by PKN in PLN per m

^{3}, the wholesale price of standard diesel oil for road transport (brand name of LOTOS: Eurodiesel) reported by LOTOS in PLN per m

^{3}.

^{3}, New York Harbor Regular Gasoline spot price, published by EIA, in USD per m

^{3}(possible IPP benchmark price), New York Harbor Ultra-Low Sulfur No 2 Diesel spot price, in USD per m

^{3}(possible IPP benchmark price), USD/PLN average exchange rate, reported by Polish Central Bank.

^{3}. All of the series have been logarithmically transformed to allow interpretation of the multiplayer as a percent change. Transformed variables are named as: L_Diesel, L_Gas95, O_Diesel, O_Gas95, Brent, NYH_Gas, NYH_Diesel, USD_PLN, where prefix L stands for Lotos and O stands for Orlen. Domestic prices are not transformed to USD to allow examination of asymmetry in reaction to depreciation/appreciation of domestic currency (PLN). A similar approach was used in [46] and [47]. The phenomenon under examination is connected with inherently dynamic processes, though the author only focused on dynamic modeling. As a process-generating theoretical model, the nonlinear, autoregressive-distributed lag (NARDL) specification is used. The NARDL model was proposed in [46]. NARDL approach was used in a context of APT research previously (e.g., [24,26,27,30,47]). A NARDL unrestricted specification and bound testing of cointegration allow for asymmetries in both the short- and long-run parameters. The ability to simultaneously estimate both long and short-run asymmetries in a computationally simple and tractable manner is a very flexible approach and provides a straightforward means of testing both long- and short-run symmetry restrictions. In a visual layer, one can assess the asymmetry of dynamic adjustment using asymmetric, dynamic multipliers graph calculated on the basis of estimation of NARDL parameters.

_{t}is a scalar I(1) variable;

**x**

_{t}is a k × 1 vector of regressors defined such that ${\mathit{x}}_{t}={\mathit{x}}_{0}+{\mathit{x}}_{t}^{+}+{\mathit{x}}_{t}^{-}$ and ${\mathit{x}}_{t}^{+}={\displaystyle \sum}_{j=1}^{t}\Delta {\mathit{x}}_{j}^{+}={\displaystyle \sum}_{j=1}^{t}max(\Delta {\mathit{x}}_{j},0)$; and ${\mathit{x}}_{t}^{-}={\displaystyle \sum}_{j=1}^{t}\Delta {\mathit{x}}_{j}^{-}={\displaystyle \sum}_{j=1}^{t}min(\Delta {\mathit{x}}_{j},0)$ are partial sum processes of positive and negative changes in

**x**

_{t}around known threshold zero.

_{t}is a scalar dependent variable;

**x**

_{t}is a k × 1 vector of regressors decomposed as ${\mathit{x}}_{t}={\mathit{x}}_{0}+{\mathit{x}}_{t}^{+}+{\mathit{x}}_{t}^{-}$; ${\Phi}_{j}$ ‘s are the autoregressive parameters; ${\mathit{\theta}}_{j}^{+}$ and ${\mathit{\theta}}_{j}^{-}$ are the asymmetrically distributed lag parameters; and ${\epsilon}_{t}$ is an iid process with zero mean and constant variance ${\sigma}_{\epsilon}^{2}$.

_{BDM}statistic proposed by Banerjee et al. in [51] tests:

- H
_{0}: - $\mathsf{\rho}=0$ (no long-run level relationship)
- H
_{1}: - $\mathsf{\rho}<0$

_{PSS}statistics by Pesaran, Shin and Smith, described in [48], tests:

- H
_{0}: - $\mathsf{\rho}={\mathit{\theta}}^{+}={\mathit{\theta}}^{-}=0$
- H
_{1}: - $\mathsf{\rho}={\mathit{\theta}}^{+}={\mathit{\theta}}^{-}\ne 0$.

_{BDM}and F

_{PSS}test statistics are nonstandard under their respective null hypotheses, and their exact asymptotic distributions are generally complicated to derive. Therefore, Pesaran et al. in [48] proposed the “bound testing” approach for cointegration testing in ARDL/NARDL specification.

- long-run amount or “reaction asymmetry”, associated with ${\mathit{\beta}}^{+}\ne $ ${\mathit{\beta}}^{-}$;
- short-run amount or “impact asymmetry”, associated with the inequality of the coefficients on the contemporaneous first differences $\Delta {x}_{t}^{+}$ and $\Delta {x}_{t}^{-}$;
- speed asymmetry or “adjustment asymmetry”, captured by the patterns of adjustment from initial equilibrium to the new equilibrium following an economic perturbation (i.e., the dynamic multipliers). Adjustment asymmetry derives from the interaction of impact and reaction asymmetries in conjunction with the error correction coefficient, $\mathsf{\rho}$.

- H
_{0}: - ${\mathit{\beta}}^{+}={\mathit{\beta}}^{-}$ (restriction of long-run symmetric reaction)
- H
_{1}: - ${\mathit{\beta}}^{+}\ne {\mathit{\beta}}^{-}$

- H
_{0}: - ${{\displaystyle \sum}}_{j=0}^{q-1}{\mathit{\pi}}_{j}^{+}={{\displaystyle \sum}}_{j=0}^{q-1}{\mathit{\pi}}_{j}^{-}$ (additive symmetry)

- H
_{0}: - ${\pi}_{0}^{+}={\pi}_{0}^{-}$

_{t}. The cumulative dynamic multipliers can be calculated as follows from the NARDL-in-levels representation (3) or from CECM (4):

## 4. Results

_{t}= USD_PLN (important cost factor); and x

_{t}= Brent, NYH_Gas, NYH_Diesel (upstream prices). Following (6), ${\beta}_{u}^{+}=-\frac{{\theta}_{u}^{+}}{\mathsf{\rho}}$, ${\beta}_{u}^{-}=-\frac{{\theta}_{u}^{-}}{\mathsf{\rho}}$, ${\beta}_{x}^{+}=-\frac{{\theta}_{x}^{+}}{\mathsf{\rho}}$, and ${\beta}_{x}^{-}=-\frac{{\theta}_{x}^{-}}{\mathsf{\rho}}$are the asymmetric long-run parameters; ${\pi}_{uj}^{+},{\pi}_{uj}^{-},{\pi}_{xj}^{+},{\pi}_{xj}^{-}$parameters capture short-run asymmetries, especially ${\pi}_{u0}^{+},{\pi}_{u0}^{-},{\pi}_{x0}^{+},{\pi}_{x0}^{-}$, the impact parameters; and ρ is an error correction coefficient.

^{2}and Akaike criteria. The long-run coefficient values are all below 0.5 for both players, which indicates that wholesale consumers are fairly insulated from fluctuations in the prices of inputs in the long run. The estimated error correction term values are consistent with the theoretical structure of a model (all are negative). Speed of adjustment toward the long-run equilibrium is about 1.4 to 1.8 % in the case of crude oil and about 2.3 to 2.6 % in the case of benchmarks. This supports the possible IPP schema of pricing.

## 5. Discussion

## 6. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Study | Subject | Positive APT | Frequency of Data |
---|---|---|---|

[5] Bacon (1991) | U.K. gasoline market, retail | yes | biweekly |

[10] Karrenbrock (1991) | U.S. gasoline prices, retail | yes | monthly |

[11] Kirchgässner and Kübler (1992) | Germany gasoline prices, retail | mixed results | monthly |

[12] Shin (1994) | U.S. gasoline market, wholesale average products’ prices | no | monthly |

[13] Borenstein et al. (1997) | U.S. gasoline market, retail | yes | weekly |

[14] Duffy-Deno (1996) | regional gasoline market, wholesale and retail prices | mixed results | weekly |

[15] Reilly and Witt (1998) | U.K. gasoline market, retail | yes | monthly |

[16] Asplund et al. (2000) | Swedish gasoline market, retail | yes | monthly |

[17] Eckert (2002) | Canada (Ontario province gasoline market), retail | yes | weekly |

[18] Bejger and Bruzda (2002) | Polish wholesale prices, a dominant player | yes | weekly |

[19] Radchenko (2004) | U.S. gasoline market, retail | yes | weekly |

[20] Oladunjoye (2008) | three U.S. wholesale markets | yes | weekly |

[21] Meyler (2009) | 12 initial Euro-member countries | weak evidence of APT | weekly |

[22] Clerides (2010) | 27 E.U. countries | mixed results | weekly |

[23] Polemis (2012) | Greece | yes | weekly |

[24] Greenwood-Nimmo and Shin (2013) | U.K. gasoline market, retail | yes | monthly |

[25] Lamotte et al. (2013) | France diesel and gasoline market, retail | yes | weekly |

[26] Atil et al. (2014) | U.S. market spot prices | no | monthly |

[27] Chattopadhyay and Mitra (2015) | Indian gasoline market | yes | monthly |

[28] Siok Kun Sek (2017) | Malaysia macroeconomic indices—crude oil | yes | annual |

[29] Farkas and Yontcheva (2019) | Hungarian wholesale and retail prices | yes | weekly |

[30] Bejger (2019) | Polish wholesale market, two major players | mixed results | daily |

Statistics | Brent | L_Diesel | L_Gas95 | NYH_Gas | NYH_Diesel | O_Diesel | O_Gas95 | USD_PLN |
---|---|---|---|---|---|---|---|---|

mean | 5.806 | 8.185 | 8.192 | 6.011 | 6.057 | 8.185 | 8.192 | 1.336 |

median | 5.838 | 8.182 | 8.182 | 6.047 | 6.084 | 8.181 | 8.182 | 1.335 |

maximum | 6.294 | 8.375 | 8.377 | 6.374 | 6.465 | 8.371 | 8.376 | 1.451 |

minimum | 4.049 | 7.946 | 7.903 | 4.742 | 5.069 | 7.933 | 7.903 | 1.199 |

std. dev. | 0.271 | 0.094 | 0.083 | 0.237 | 0.236 | 0.094 | 0.083 | 0.047 |

skewness | −1.368 | −0.050 | −0.459 | −1.693 | −0.781 | −0.057 | −0.459 | −0.233 |

kurtosis | 6.873 | 2.252 | 3.574 | 7.967 | 3.244 | 2.259 | 3.575 | 3.502 |

Jarque–Bera | 1393.352 | 35.307 | 72.549 | 2238.746 | 154.786 | 34.803 | 72.664 | 29.049 |

observations | 1487 | 1487 | 1487 | 1487 | 1487 | 1487 | 1487 | 1487 |

Variable | Prob. * | Variable | Prob. * |
---|---|---|---|

Brent | 0.094 | Δ(Brent) | 0.000 |

L_Diesel | 0.243 | Δ(L_Diesel) | 0.000 |

L_Gas95 | 0.054 | Δ(L_Gas95) | 0.000 |

NYH_Gas | 0.092 | Δ(NYH_Gas) | 0.000 |

NYH_Diesel | 0.318 | Δ(NYH_Diesel) | 0.000 |

O_Diesel | 0.308 | Δ(O_Diesel) | 0.000 |

O_Gas95 | 0.077 | Δ(O_Gas95) | 0.000 |

USD_PLN | 0.037 | Δ(USD_PLN) | 0.000 |

Variable | Value of Test Statistics |
---|---|

Δ(Brent) | 0.0396 |

Δ(L_Diesel) | 0.0627 |

Δ(L_Gas95) | 0.0558 |

Δ(NYH_Gas) | 0.0319 |

Δ(NYH_Diesel) | 0.0633 |

Δ(O_Diesel) | 0.0621 |

Δ(O_Gas95) | 0.0583 |

Δ(USD_PLN) | 0.0648 |

Variable | Estimated Break Date | Zivot–Andrews Test Statistics | Integration |
---|---|---|---|

Brent | 1/07/2020 | −3.7864 | yes |

L_Diesel | 1/08/2020 | −4.0122 | yes |

L_Gas95 | 1/22/2020 | −3.9042 | yes |

NYH_Gas | 1/07/2020 | −3.5573 | yes |

NYH_Diesel | 1/07/2020 | −3.7869 | yes |

O_Diesel | 1/07/2020 | −4.0752 | yes |

O_Gas95 | 1/22/2020 | −3.9317 | yes |

USD_PLN | 4/24/2017 | −4.6356 | yes? |

Dependent Variable y | L_Gas95 | O_Gas95 | ||||

Regressor x | Brent | Brent | ||||

Model Estimated | NARDL (2, 3, 6, 1, 1) | NARDL (2, 3, 6, 2, 1) | ||||

Parameter | Value | t-Statistic | Prob. | Value | t-Statistic | Prob. |

ρ | −0.0184 | 4.6142 | 0.0000 | −0.0183 | −4.6289 | 0.0000 |

${\beta}_{x}^{+}$ | 0.3447 | 5.9610 | 0.0000 | 0.3388 | 5.8663 | 0.0000 |

${\beta}_{x}^{-}$ | 0.3327 | 7.0445 | 0.0000 | 0.3302 | 7.0074 | 0.0000 |

${\beta}_{u}^{+}$ | 0.4424 | 2.5902 | 0.0097 | 0.4650 | 2.7388 | 0.0062 |

${\beta}_{u}^{-}$ | 0.4922 | 2.7103 | 0.0068 | 0.4992 | 2.7616 | 0.0058 |

${\pi}_{x0}^{+}$ | 0.1015 | 14.7830 | 0.0000 | 0.1057 | 15.5825 | 0.0000 |

${\pi}_{x0}^{-}$ | 0.0460 | 8.6850 | 0.0000 | 0.0414 | 7.8978 | 0.0000 |

${\pi}_{u0}^{+}$ | 0.1709 | 4.8705 | 0.0000 | 0.1573 | 4.5288 | 0.0000 |

${\pi}_{u0}^{-}$ | 0.1742 | 4.4618 | 0.0000 | 0.1225 | 3.1735 | 0.0015 |

Cointegration tests | Stat. Value | Stat. Value | ||||

F_PSS | 4.4084 | 4.3978 | ||||

t_BDM | −4.6063 | −4.6288 | ||||

Symmetry restrictions * | Stat. Value | Prob. | Stat. Value | Prob. | ||

W_LR_x | 0.8047 | 0.4211 | 0.5774 | 0.5637 | ||

W_LR_u | −0.8020 | 0.4227 | −0.5516 | 0.5811 | ||

W_SRa_x | 0.0891 | 0.9290 | 0.0168 | 0.9865 | ||

W_SRa_u | - | - | 1.2112 | 0.2260 | ||

W_SRi_x | 5.5583 | 0.0000 | 6.5196 | 0.0000 | ||

W_SRi_u | −0.0532 | 0.9575 | 0.5664 | 0.5712 | ||

Diagnostics | Stat. Value | Stat. Value | ||||

Adjusted R-squared | 0.4626 | 0.47465 | ||||

Akaike criterion | −7.8763 | −7.9000 | ||||

Dependent variable y | L_Gas95 | O_Gas95 | ||||

Regressor x | NYH_Gas | NYH_Gas | ||||

Model Estimated | NARDL (5, 7, 7, 6, 1) | NARDL (2, 7, 7, 6, 1) | ||||

Parameter | Value | t-Statistic | Prob. | Value | t-Statistic | Prob. |

ρ | −0.0235 | −4.7419 | 0.0000 | −0.0255 | −5.2034 | 0.0000 |

${\beta}_{x}^{+}$ | 0.4076 | 8.6752 | 0.0000 | 0.3973 | 9.2056 | 0.0000 |

${\beta}_{x}^{-}$ | 0.4088 | 10.5452 | 0.0000 | 0.4023 | 11.2861 | 0.0000 |

${\beta}_{u}^{+}$ | 0.5157 | 3.9843 | 0.0001 | 0.5199 | 4.3534 | 0.0000 |

${\beta}_{u}^{-}$ | 0.4852 | 3.4795 | 0.0005 | 0.4738 | 3.6835 | 0.0002 |

${\pi}_{x0}^{+}$ | 0.0860 | 11.9715 | 0.0000 | 0.0888 | 12.3307 | 0.0000 |

${\pi}_{x0}^{-}$ | 0.0839 | 14.0467 | 0.0000 | 0.0743 | 12.4278 | 0.0000 |

${\pi}_{u0}^{+}$ | 0.1975 | 5.8268 | 0.0000 | 0.1911 | 5.6277 | 0.0000 |

${\pi}_{u0}^{-}$ | 0.1839 | 4.9148 | 0.0000 | 0.1302 | 3.4724 | 0.0005 |

Cointegration tests | Stat. Value | Stat. Value | ||||

F_PSS | 4.6027 | 5.5271 | ||||

t_BDM | −4.7419 | −5.2034 | ||||

Symmetry restrictions * | Stat. Value | Prob. | Stat. Value | Prob. | ||

W_LR_x | −0.0951 | 0.9242 | −0.4082 | 0.6832 | ||

W_LR_u | 0.5614 | 0.5746 | 0.9220 | 0.3567 | ||

W_SRa_x | 0.5465 | 0.5847 | 0.6168 | 0.5375 | ||

W_SRa_u | 4.2265 | 0.0000 | 5.0797 | 0.0000 | ||

W_SRi_x | 0.1976 | 0.8433 | 1.3517 | 0.1767 | ||

W_SRi_u | 0.2274 | 0.8201 | 1.0173 | 0.3092 | ||

Diagnostics | Stat. Value | Prob. | Stat. Value | Prob. | ||

Adjusted R-squared | 0.5179 | 0.5135 | ||||

Akaike criterion | −7.9667 | −7.9642 | ||||

Dependent Variable y | L_Diesel | O_Diesel | ||||

Regressor x | Brent | Brent | ||||

Model Estimated | NARDL (6, 7, 6, 5, 4) | NARDL (6, 7, 4, 5, 1) | ||||

Parameter | Value | t-Statistic | Prob. | Value | t-Statistic | Prob. |

ρ | −0.0145 | −3.2293 | 0.0013 | −0.0180 | −3.9953 | 0.0001 |

${\beta}_{x}^{+}$ | 0.2685 | 3.7197 | 0.0002 | 0.2962 | 5.3192 | 0.0000 |

${\beta}_{x}^{-}$ | 0.3045 | 5.1427 | 0.0000 | 0.3270 | 7.1528 | 0.0000 |

${\beta}_{u}^{+}$ | 0.4298 | 2.2871 | 0.0223 | 0.4646 | 3.0276 | 0.0025 |

${\beta}_{u}^{-}$ | 0.2485 | 1.1875 | 0.2352 | 0.3066 | 1.8294 | 0.0676 |

${\pi}_{x0}^{+}$ | 0.0842 | 14.7962 | 0.0000 | 0.0914 | 15.2815 | 0.0000 |

${\pi}_{x0}^{-}$ | 0.0473 | 10.8075 | 0.0000 | 0.0501 | 10.8846 | 0.0000 |

${\pi}_{u0}^{+}$ | 0.1896 | 6.6684 | 0.0000 | 0.1579 | 5.2730 | 0.0000 |

${\pi}_{u0}^{-}$ | 0.1119 | 3.5508 | 0.0004 | 0.0813 | 2.4530 | 0.0143 |

Cointegration tests | Stat. Value | Stat. Value | ||||

F_PSS | 3.0988 | 3.9556 | ||||

t_BDM | −3.2293 | −3.9953 | ||||

Symmetry restrictions * | Stat. Value | Prob. | Stat. Value | Prob. | ||

W_LR_x | −2.2093 | 0.0273 | −2.2677 | 0.0235 | ||

W_LR_u | 2.5808 | 0.0100 | 2.7004 | 0.0070 | ||

W_SRa_x | −0.6325 | 0.5271 | −0.0655 | 0.9477 | ||

W_SRa_u | 3.5810 | 0.0004 | 5.0124 | 0.0000 | ||

W_SRi_x | 4.4120 | 0.0000 | 4.7040 | 0.0000 | ||

W_SRi_u | 1.5481 | 0.1218 | 1.4506 | 0.1471 | ||

Diagnostics | Stat. Value | Prob. | Stat. Value | Prob. | ||

Adjusted R-squared | 0.5393 | 0.5023 | ||||

Akaike criterion | −8.3062 | −8.2045 | ||||

Dependent Variable | L_Diesel | O_Diesel | ||||

Regressor x | NYH_Diesel | NYH_Diesel | ||||

Model Estimated | NARDL (4, 5, 6, 3, 3) | NARDL (6, 5, 6, 5, 3) | ||||

Parameter | Value | t-Statistic | Prob. | Value | t-Statistic | Prob. |

ρ | −0.0237 | −4.1402 | 0.0000 | −0.0260 | −4.2966 | 0.0000 |

${\beta}_{x}^{+}$ | 0.3608 | 9.1020 | 0.0000 | 0.3477 | 9.0231 | 0.0000 |

${\beta}_{x}^{-}$ | 0.3900 | 14.1542 | 0.0000 | 0.3836 | 14.3144 | 0.0000 |

${\beta}_{u}^{+}$ | 0.5357 | 5.3596 | 0.0000 | 0.5354 | 5.5299 | 0.0000 |

${\beta}_{u}^{-}$ | 0.4072 | 3.5731 | 0.0004 | 0.3840 | 3.4447 | 0.0006 |

${\pi}_{x0}^{+}$ | 0.1035 | 13.9049 | 0.0000 | 0.1042 | 13.1859 | 0.0000 |

${\pi}_{x0}^{-}$ | 0.0988 | 14.3219 | 0.0000 | 0.1056 | 14.4689 | 0.0000 |

${\pi}_{u0}^{+}$ | 0.1571 | 6.0076 | 0.0000 | 0.1330 | 4.7955 | 0.0000 |

${\pi}_{u0}^{-}$ | 0.1499 | 5.1160 | 0.0000 | 0.1197 | 3.8509 | 0.0001 |

Cointegration tests | Stat. Value | Stat. Value | ||||

F_PSS | 3.6012 | 3.8066 | ||||

t_BDM | −4.1402 | −4.2966 | ||||

Symmetry restrictions * | Stat. Value | Prob. | Stat. Value | Prob. | ||

W_LR_x | −1.5487 | 0.1217 | −1.9532 | 0.0510 | ||

W_LR_u | 1.9250 | 0.0544 | 2.3293 | 0.0200 | ||

W_SRa_x | −0.1349 | 0.8926 | −0.2044 | 0.8380 | ||

W_SRa_u | 0.0375 | 0.9701 | 0.8145 | 0.4154 | ||

W_SRi_x | 0.3926 | 0.6946 | 1.4799 | 0.1391 | ||

W_SRi_u | 0.1539 | 0.8777 | 0.2683 | 0.7885 | ||

Diagnostics | Stat. Value | Prob. | Stat. Value | Prob. | ||

Adjusted R-squared | 0.5973 | 0.5696 | ||||

Akaike criterion | −8.4677 | −8.3487 |

**Table 7.**Aggregates of significant positive and negative short-run multipliers of USD/PLN exchange rate.

Additive Asymmetry Cases | ||||
---|---|---|---|---|

Dependent Variable y | L_Gas9 | O_Gas95 | L_Diesel | O_Diesel |

Regressor x | NYH_Gas | NYH_Gas | Brent | Brent |

${{\displaystyle \sum}}_{j=0}^{q-1}{\pi}_{uj}^{-}$ | 0.1840 | 0.1302 | 0.0864 | 0.0813 |

${{\displaystyle \sum}}_{j=0}^{q-1}{\pi}_{uj}^{+}$ | 0.5716 | 0.5856 | 0.4416 | 0.4440 |

Dependent Variable | L_Gas95 | O_Gas95 | ||||

Regressor x | Brent | Brent | ||||

Model Estimated | ARDL (6, 2, 5, 0, 3) | ARDL (6, 2, 5, 0, 1) | ||||

Parameter | Value | t-Statistic | Prob. | Value | t-Statistic | Prob. |

ρ | −0.0462 | 2.5828 | 0.0104 | −0.0486 | −2.9338 | 0.0037 |

${\beta}_{x}^{+}$ | 0.2495 | 3.3400 | 0.0010 | 0.2820 | 4.4925 | 0.0000 |

${\beta}_{x}^{-}$ | 0.2236 | 3.3332 | 0.0010 | 0.2504 | 4.4645 | 0.0000 |

${\beta}_{u}^{+}$ | 0.1881 | 0.3911 | 0.6961 | 0.0980 | 0.2375 | 0.8125 |

${\beta}_{u}^{-}$ | 0.3943 | 0.9253 | 0.3558 | 0.3418 | 0.9245 | 0.3563 |

${\pi}_{x0}^{+}$ | 0.0397 | 3.3883 | 0.0008 | 0.0526 | 4.7411 | 0.0000 |

${\pi}_{x0}^{-}$ | 0.0373 | 5.0291 | 0.0000 | 0.0246 | 3.5135 | 0.0005 |

${\pi}_{u0}^{+}$ | - | - | - | - | - | - |

${\pi}_{u0}^{-}$ | 0.4292 | 4.3122 | 0.0000 | 0.2263 | 2.4923 | 0.0134 |

Cointegration tests | Stat. Value | Stat. Value | ||||

F_PSS | 2.9956 | 2.8553 | ||||

t_BDM | −2.5922 | −2.9338 | ||||

Symmetry restrictions * | Stat. Value | Prob. | Stat. Value | Prob. | ||

W_SRa_x | −0.8379 | 0.4030 | 0.09758 | 0.9223 | ||

W_SRa_u | 3.1099 | 0.0021 ^{#} | - | - | ||

W_SRi_x | 0.1484 | 0.8820 | 1.8299 | 0.0686 | ||

W_SRi_u | 4.3121 | 0.0000 ^{#} | 2.4923 | 0.0134 | ||

Dependent Variable | L_Gas95 | O_Gas95 | ||||

Regressor x | NYH_Gas | NYH_Gas | ||||

Model Estimated | ARDL (6, 4, 7, 7, 1) | ARDL (6, 7, 7, 7, 1) | ||||

Parameter | Value | t-Statistic | Prob. | Value | t-Statistic | Prob. |

ρ | −0.0855 | −4.6819 | 0.0000 | −0.0701 | −3.5041 | 0.0006 |

${\beta}_{x}^{+}$ | 0.3100 | 10.1975 | 0.0000 | 0.3428 | 7.4012 | 0.0000 |

${\beta}_{x}^{-}$ | 0.2536 | 9.0014 | 0.0000 | 0.2839 | 7.3037 | 0.0000 |

${\beta}_{u}^{+}$ | −0.3228 | −1.3753 | 0.1705 | −0.3067 | −1.1416 | 0.2550 |

${\beta}_{u}^{-}$ | 0.1429 | 0.7430 | 0.4583 | 0.1663 | 0.7544 | 0.4514 |

${\pi}_{x0}^{+}$ | 0.0452 | 3.3190 | 0.0011 | 0.0517 | 3.7601 | 0.0002 |

${\pi}_{x0}^{-}$ | 0.1022 | 10.8636 | 0.0000 | 0.0880 | 9.6893 | 0.0000 |

${\pi}_{u0}^{+}$ | 0.0112 | 0.1297 | 0.8969 | 0.0360 | 0.4404 | 0.6601 |

${\pi}_{u0}^{-}$ | 0.3345 | 3.5947 | 0.0004 | 0.1446 | 1.6596 | 0.0985 |

Cointegration tests | Stat. Value | Stat. Value | ||||

F_PSS | 5.3190 | 3.8499 | ||||

t_BDM | −4.6819 | −3.5041 | ||||

Symmetry restrictions * | Stat. Value | Prob. | Stat. Value | Prob. | ||

W_SRa_x | −2.1276 | 0.0345 | −0.4210 | 0.6742 | ||

W_SRa_u | 1.8355 | 0.0678 | 2.6802 | 0.0080 | ||

W_SRi_x | −2.9530 | 0.0035 | −1.8721 | 0.0626 | ||

W_SRi_u | −2.2063 | 0.0284 | −0.7883 | 0.4314 | ||

Dependent Variable | L_Diesel | O_Diesel | ||||

Regressor x | Brent | Brent | ||||

Model Estimated | NARDL (4, 3, 6, 3, 0) | NARDL (2, 7, 6, 0, 0) | ||||

Parameter | Value | t-Statistic | Prob. | Value | t-Statistic | Prob. |

ρ | −0.0059 | −0.3117 | 0.7556 | −0.0155 | −0.8097 | 0.4190 |

${\beta}_{x}^{+}$ | −0.2080 | −0.1470 | 0.8833 | −0.1949 | −0.3417 | 0.7329 |

${\beta}_{x}^{-}$ | 0.0074 | 0.0086 | 0.9932 | −0.0605 | −0.1368 | 0.8913 |

${\beta}_{u}^{+}$ | 7.6790 | 0.3161 | 0.7523 | 3.5930 | 0.8075 | 0.4203 |

${\beta}_{u}^{-}$ | 4.9486 | 0.3098 | 0.7570 | 2.3159 | 0.7668 | 0.4440 |

${\pi}_{x0}^{+}$ | 0.0298 | 2.8343 | 0.0050 | 0.0263 | 2.3960 | 0.0174 |

${\pi}_{x0}^{-}$ | 0.0315 | 4.6786 | 0.0000 | 0.0377 | 5.3614 | 0.0000 |

${\pi}_{u0}^{+}$ | 0.1649 | 2.1591 | 0.0319 | - | - | - |

${\pi}_{u0}^{-}$ | - | - | - | - | - | - |

Cointegration tests | Stat. Value | Stat. Value | ||||

F_PSS | 3.1019 | 5.3472 | ||||

t_BDM | −0.3117 | −0.8097 | ||||

Symmetry restrictions * | Stat. Value | Prob. | Stat. Value | Prob. | ||

W_SRa_x | −2.7660 | 0.0062 | −3.0494 | 0.0026 | ||

W_SRa_u | 2.0877 | 0.0380 ^{#} | - | - | ||

W_SRi_x | −0.1115 | 0.9113 | −0.7400 | 0.4601 | ||

W_SRi_u | 2.1591 | 0.0319 ^{#} | - | - | ||

Dependent Variable | L_Diesel | O_Diesel | ||||

Regressor x | NYH_Diesel | NYH_Diesel | ||||

Model Estimated | NARDL (3, 3, 3, 0, 0) | NARDL (3, 2, 4, 7, 0) | ||||

Parameter | Value | t-Statistic | Prob. | Value | t-Statistic | Prob. |

ρ | −0.0654 | −2.8151 | 0.0053 | −0.0393 | −1.5343 | 0.1264 |

${\beta}_{x}^{+}$ | 0.4366 | 6.5535 | 0.0000 | 0.3249 | 2.7693 | 0.0061 |

${\beta}_{x}^{-}$ | 0.3764 | 8.2960 | 0.0000 | 0.3310 | 4.5467 | 0.0000 |

${\beta}_{u}^{+}$ | 0.4809 | 1.5299 | 0.1274 | 1.0687 | 1.2534 | 0.2114 |

${\beta}_{u}^{-}$ | 0.7260 | 2.2759 | 0.0238 | 0.9641 | 1.5069 | 0.1333 |

${\pi}_{x0}^{+}$ | 0.1241 | 7.0029 | 0.0000 | 0.1121 | 6.2631 | 0.0000 |

${\pi}_{x0}^{-}$ | 0.0716 | 5.3219 | 0.0000 | 0.0787 | 5.7187 | 0.0000 |

${\pi}_{u0}^{+}$ | - | - | - | 0.0035 | 0.0506 | 0.9597 |

${\pi}_{u0}^{-}$ | - | - | - | - | - | - |

Cointegration tests | Stat. Value | Stat. Value | ||||

F_PSS | 3.8007 | 3.2311 | ||||

t_BDM | −2.8151 | −1.5343 | ||||

Symmetry restrictions * | Stat. Value | Prob. | Stat. Value | Prob. | ||

W_SRa_x | 0.6069 | 0.5445 | 6.5847 | 0.0017 | ||

W_SRa_u | - | - | −0.1498 | 0.8810 * | ||

W_SRi_x | 1.9710 | 0.0499 | 0.6839 | 0.4947 | ||

W_SRi_u | - | - | 0.0506 | 0.9597 * |

^{#}For the null hypothesis that sum/value of short run parameters is equal to 0.

Wholesale Price | Input | Whole Sample APT | The Year 2020 APT |
---|---|---|---|

L_Gas95 | Brent | Positive impact APT | No significant APT |

L_Gas95 | USD/PLN (Brent) | No significant APT | Negative impact and additive APT |

L_Gas95 | NYH_Gas | No significant APT | Negative impact and additive APT |

L_Gas95 | USD/PLN (NYH_Gas) | Positive additive APT | Negative impact and additive APT |

O_Gas95 | Brent | Positive impact APT | Positive impact APT |

O_Gas95 | USD/PLN (Brent) | No significant APT | Negative impact APT |

O_Gas95 | NYH_Gas | No significant APT | Negative impact APT |

O_Gas95 | USD/PLN (NYH_Gas) | Positive additive APT | Positive additive APT |

L_Diesel | Brent | Positive impact APT | Negative additive APT |

L_Diesel | USD/PLN (Brent) | Positive additive APT | Positive impact and additive APT |

L_Diesel | NYH_Diesel | No significant APT | Positive impact APT |

L_Diesel | USD/PLN (NYH_Diesel) | No significant APT | No significant APT |

O_Diesel | Brent | Positive impact APT | Negative additive APT |

O_Diesel | USD/PLN (Brent) | Positive additive APT | No significant APT |

O_Diesel | NYH_Diesel | No significant APT | Negative additive APT |

O_Diesel | USD/PLN (NYH_Diesel) | No significant APT | No significant APT |

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## Share and Cite

**MDPI and ACS Style**

Bejger, S.
Competition in a Wholesale Fuel Market—The Impact of the Structural Changes Caused by COVID-19. *Energies* **2021**, *14*, 4211.
https://doi.org/10.3390/en14144211

**AMA Style**

Bejger S.
Competition in a Wholesale Fuel Market—The Impact of the Structural Changes Caused by COVID-19. *Energies*. 2021; 14(14):4211.
https://doi.org/10.3390/en14144211

**Chicago/Turabian Style**

Bejger, Sylwester.
2021. "Competition in a Wholesale Fuel Market—The Impact of the Structural Changes Caused by COVID-19" *Energies* 14, no. 14: 4211.
https://doi.org/10.3390/en14144211