## 1. Introduction

_{2}emissions in the US. Eisenmann et al. (2021) conducted a survey in Germany to understand the changes in people’s travel behavior during the COVID-19 pandemic and determined that public transport lost ground while private cars gained importance. Thus, it is probable that changes in human mobility during the COVID-19 period will also impact fuel prices, but up until now, no studies have investigated this issue.

## 2. Methods

_{1}and EMG

_{2}represent these variables. These variables are dummy variables taking 1 when the period belongs to the time when the first and second states of emergency were enforced in Tokyo. As Tokyo was under the first state of emergency from 7 April to 25 May 2020, EMG

_{1}is coded as 1 when the data contained this period. The second state of emergency started on 8 January 2021 and continued until the final data period obtained in this study, so EMG

_{2}is coded as 1 for periods later than 8 January 2021.

## 3. Results and Discussions

## 4. Conclusions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Indices for the number of visits to transit stations and workplaces between 17 February 2020 and 22 February 2021 in Japan. EMG1 indicates the starting (7 April 2020) and ending (25 May 2020) periods of the first state of emergency and EMG2 denotes the starting period (8 January 2021) of the second state of emergency enforced in Tokyo.

**Figure 2.**Fuel prices between 17 February 2020 and 22 February 2021. (

**a**) Premium and regular gasoline; (

**b**) diesel and kerosene. EMG1 indicates the starting and ending periods of the first state of emergency and EMG2 denotes the starting period of the second state of emergency.

**Figure 3.**CUSUM and CUSUMSQ tests for the linear ARDL models. (

**a**) Premium gasoline; (

**b**) regular gasoline; (

**c**) diesel; (

**d**) kerosene.

**Figure 4.**CUSUM and CUSUMSQ tests for the NARDL models. (

**a**) Premium gasoline; (

**b**) regular gasoline; (

**c**) diesel; (

**d**) kerosene.

Levels | First Differences | |||||
---|---|---|---|---|---|---|

t-Stat. | Breakpoint | t-Stat. | Breakpoint | |||

Premium | −3.46 | 21-December-20 | −5.25 | ** | 10-August-20 | |

Regular | −3.84 | 16-November-20 | −5.23 | ** | 1-January-20 | |

Diesel | −3.47 | 16-November-20 | −5.25 | ** | 10-August-20 | |

Kerosene | −2.44 | 4-April-20 | −5.14 | ** | 12-October-20 | |

Transit | −4.79 | 27-April-20 | −6.70 | *** | 20-April-20 | |

Workplace | −9.04 | *** | 27-April-20 | −8.02 | *** | 18-May-20 |

Fuel Prices | F-Stat. | |
---|---|---|

Premium | 6.63 | *** |

Regular | 5.23 | *** |

Diesel | 5.34 | *** |

Kerosene | 4.06 | ** |

Significance level | I(0) | I(1) |

1% level | 4.13 | 5.00 |

5% level | 3.10 | 3.87 |

10% level | 2.63 | 3.35 |

Premium | Regular | Diesel | Kerosene | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Variables | Coef. | t-Stat. | Coef. | t-Stat. | Coef. | t-Stat. | Coef. | t-Stat. | ||||

Constant | 146.13 | *** | 40.73 | 136.23 | *** | 33.99 | 118.94 | *** | 28.99 | 82.87 | *** | 11.98 |

Transit | −0.01 | −0.05 | 0.04 | 0.20 | 0.05 | 0.27 | −0.54 | −1.64 | ||||

Work | 0.05 | 0.64 | 0.05 | 0.68 | 0.20 | * | 1.95 | 0.30 | * | 1.91 |

ΔPremium | ΔRegular | ΔDiesel | ΔKerosene | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Variables | Coef. | t−Stat | Variables | Coef. | t−Stat | Variables | Coef. | t−Stat | Variables | Coef. | t−Stat | ||||

Constant | 30.34 | *** | 4.80 | Constant | 30.50 | *** | 4.31 | Constant | 25.76 | *** | 4.40 | Constant | 9.17 | ** | 2.38 |

Premium(-1) | −0.21 | *** | −4.96 | Regular(-1) | −0.22 | *** | −4.45 | Diesel(-1) | −0.22 | *** | −4.52 | Kerosene(-1) | −0.11 | *** | −2.76 |

Transit ^{a} | 0.00 | −0.04 | Transit ^{a} | 0.01 | 0.17 | Transit(-1) | 0.01 | 0.28 | Transit(-1) | −0.06 | ** | −2.28 | |||

Work ^{a} | 0.01 | 0.51 | Work ^{a} | 0.01 | 0.45 | Work ^{a} | 0.04 | 1.56 | Work ^{a} | 0.03 | * | 1.86 | |||

ΔPremium(-1) | 0.28 | ** | 2.06 | ΔRegular(-1) | 0.22 | 1.47 | ΔDiesel(-1) | 0.27 | * | 1.86 | ΔKerosene(-1) | −0.17 | −1.29 | ||

ΔPremium(-2) | −0.33 | ** | −2.05 | ΔRegular(-2) | −0.22 | −1.36 | ΔTransit | −0.06 | −1.09 | ΔTransit | −0.12 | *** | −3.05 | ||

EMG1 | −1.67 | −1.67 | EMG1 | −1.28 | −0.99 | EMG1 | −0.42 | −0.45 | EMG1 | −2.01 | *** | −3.39 | |||

EMG2 | 2.07 | *** | 3.57 | EMG2 | 2.22 | *** | 3.10 | EMG2 | 1.97 | *** | 3.07 | EMG2 | 0.07 | 0.18 |

^{a}Indicates the variable is interpreted as Z = Z(-1) + ΔZ.

Fuel Prices | F-Stat. | |
---|---|---|

Premium | 7.30 | *** |

Regular | 3.60 | ** |

Diesel | 3.64 | ** |

Kerosene | 3.22 | * |

Significance level | I(0) | I(1) |

1% level | 3.29 | 4.37 |

5% level | 2.56 | 3.49 |

10% level | 2.2 | 3.09 |

Premium | Regular | Diesel | Kerosene | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Variables | Coef. | t-Stat. | Coef. | t-Stat. | Coef. | t-Stat. | Coef. | t-Stat. | ||||

Constant | 171.34 | *** | 119.60 | 161.00 | *** | 26.98 | 138.99 | *** | 28.66 | 87.01 | *** | 7.24 |

Transit+ | −0.01 | −0.15 | −0.24 | ** | −2.12 | −0.21 | * | −1.97 | −0.42 | −1.62 | ||

Transit- | 0.91 | *** | 14.96 | 0.77 | *** | 4.12 | 0.71 | *** | 4.52 | −0.45 | −0.80 | |

Work+ | −0.14 | * | −1.93 | 0.13 | * | 1.86 | 0.11 | * | 1.75 | 0.30 | 1.65 | |

Work- | −0.53 | *** | −5.73 | −0.31 | ** | −2.68 | −0.29 | *** | −2.93 | 0.33 | 0.99 |

ΔPremium | ΔRegular | ΔDiesel | ΔKerosene | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Variables | Coef. | t-Stat. | Variables | Coef. | t-Stat. | Variables | Coef. | t-Stat. | Variables | Coef. | t-Stat. | ||||

Constant | −99.35 | *** | −3.09 | Constant | −65.53 | * | −1.83 | Constant | −63.90 | * | −1.96 | Constant | 11.28 | 0.98 | |

Premium(-1) | 0.58 | *** | 2.92 | Regular(-1) | 0.41 | * | 1.71 | Diesel(-1) | 0.46 | * | 1.85 | Kerosene(-1) | −0.13 | −1.15 | |

Transit+(-1) | 0.00 | 0.09 | Transit+(-1) | 0.10 | 1.34 | Transit+(-1) | 0.10 | 1.41 | Transit+ ^{a} | −0.05 | −1.54 | ||||

Transit-(-1) | −0.53 | *** | −4.31 | Transit-(-1) | −0.31 | ** | −2.43 | Transit-(-1) | −0.32 | ** | −2.52 | Transit-(-1) | −0.06 | −1.31 | |

Work+ ^{a} | 0.08 | 1.28 | Work+(-1) | −0.05 | −1.16 | Work+(-1) | −0.05 | −1.08 | Work+ ^{a} | 0.04 | * | 1.93 | |||

Work-(-1) | 0.31 | *** | 3.46 | Work- ^{a} | 0.12 | ** | 2.61 | Work- ^{a} | 0.13 | *** | 2.87 | Work- ^{a} | 0.04 | * | 1.78 |

ΔPremium(-1) | −0.39 | * | −1.89 | ΔRegular(-1) | −0.15 | −0.71 | ΔDiesel(-1) | −0.17 | −0.77 | ΔKerosene(-1) | −0.14 | −0.96 | |||

ΔPremium(-2) | −0.84 | *** | −4.36 | ΔRegular(-2) | −0.47 | ** | −2.24 | ΔDiesel(-2) | −0.46 | * | −2.00 | ΔTransit- | −0.15 | ** | −2.52 |

ΔTransit+ | 0.23 | ** | 2.17 | ΔTransit+ | 0.28 | 2.09 | ΔTransit+ | 0.25 | * | 1.93 | EMG1 | −2.00 | *** | −3.30 | |

ΔTransit+(-1) | 0.24 | ** | 2.70 | ΔTransit+(-1) | 0.20 | *** | 1.69 | ΔTransit+(-1) | 0.23 | * | 1.98 | EMG2 | 0.24 | 0.33 | |

ΔTransit+(-2) | 0.19 | ** | 2.25 | ΔTransit- | −0.41 | *** | −2.76 | ΔTransit- | −0.43 | *** | −2.97 | ||||

ΔTransit- | −0.40 | *** | −3.42 | ΔTransit-(-1) | 0.14 | * | 1.91 | ΔTransit-(-1) | 0.14 | * | 2.00 | ||||

ΔTransit-(-1) | 0.25 | *** | 3.27 | ΔTransit-(-2) | 0.10 | 1.55 | ΔTransit-(-2) | 0.11 | 1.69 | ||||||

ΔTransit-(-2) | 0.16 | ** | 2.34 | ΔWork+ | 0.03 | 0.53 | ΔWork+ | 0.04 | 0.93 | ||||||

ΔTransit-(-3) | 0.09 | 1.25 | ΔWork+(-1) | 0.05 | 1.29 | ΔWork+(-1) | 0.04 | 1.22 | |||||||

ΔWork- | 0.08 | * | 2.00 | ΔWork+(-2) | 0.06 | ** | 2.04 | ΔWork+(-2) | 0.06 | ** | 2.13 | ||||

ΔWork-(-1) | −0.14 | *** | −2.97 | EMG1 | 0.11 | 0.07 | EMG1 | −0.06 | −0.04 | ||||||

ΔWork-(-2) | −0.09 | ** | −2.74 | EMG2 | −2.30 | −1.23 | EMG2 | −2.45 | −1.38 | ||||||

ΔWork-(-3) | −0.05 | −1.57 | |||||||||||||

EMG1 | −0.83 | −0.80 | |||||||||||||

EMG2 | −4.78 | *** | −2.84 |

^{a}Indicates the variable is interpreted as Z = Z(-1) + ΔZ.

Model | BG F-Stat. | BP F-Stat. | ||
---|---|---|---|---|

ARDL for premium | 1.05 | 2.29 | ** | |

NARDL for premium | 2.24 | * | 2.27 | ** |

ARDL for regular | 1.35 | 1.38 | ||

NARDL for regular | 1.61 | 0.79 | ||

ARDL for diesel | 0.49 | 2.52 | ** | |

NARDL for diesel | 1.37 | 0.85 | ||

ARDL for kerosene | 0.71 | 2.26 | ** | |

NARDL for kerosene | 0.29 | 1.74 |

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