Annex A - Econometric analysis
The full list of variables is as follows:
| Variable | Description |
|---|---|
| Constant | A standard constant or intercept |
| Trend | An overall trend growth rate - varies and choice has a strong influence on results. The preferred version is that in which demand stabilises pre-trial at 90% of pre-C19 demand in line with rail demand across the UK. From Scenarios M1 to M5 |
| PFT Dummy | A Peak Fares Trial Dummy - A variable that takes the value 1 from October 1 2023 and 0 before and allows a shift in demand from the Pilot to be estimated |
| PFT trend | A trend variable from October 1 2023 that allows the ongoing impact of the Pilot to be estimated |
| Day of the week variables | Wednesday is chosen as the base and Sunday, Monday, Tuesday, Thursday, Friday and Saturday variables take the value 1 on relevant day of the week to allow daily variations to be captured* |
| Month variables | Similar to the Day variables, September is chosen as the base* (All other months take the value 1 when applicable). This is a standard way of capturing seasonal impacts. |
| XmasNewYear | To account for distinctly different travel demand over the Christmas and New Year period. |
| Sport | 1 if there was a major sporting event that would be assumed to influence rail demand on the day |
| Concert | 1 if there was a major concert or cultural event on the day |
| Strike | 1 if strike action within Scotland. |
| Bad weather | 1 if yellow weather warning on day |
| Extreme weather | 1 if major weather event on day. |
| Travel demand difference | Proxy variable for general travel demand. Is the variation in road travel demand from the equivalent period in 2019 as percentage variation. Various specifications tested and make no difference to other results and just vary interpretation of this variable. |
| Fares Rise | A dummy variable to account for the rise in fares in April 24 |
*Note that the choice of the base has no impact on the overall results only the interpretation – for example, the Day variables show the impact of each day compared with the base (Wednesday).
Example results for the main Scenario (M2) are shown below.
| Variable | Coefficient | Std. Error | Star rating |
|---|---|---|---|
| const | 115161 | 8841.09 | *** |
| PFT_Dummy | 14177.6 | 2305.87 | *** |
| Trend_to_90PCD | 122.293 | 6.37062 | *** |
| Xmas_New_Year | -50897.1 | 4876.11 | *** |
| Sat | 16662.1 | 2599.02 | *** |
| Sun | -92459.4 | 2565.98 | *** |
| Mon_ | -16650.6 | 2559.99 | *** |
| Thur | 5670.76 | 2554.08 | ** |
| Fri | 21615.1 | 2562.89 | *** |
| Sport | 15248 | 3381.03 | *** |
| Concert | 17338.6 | 4457.12 | *** |
| Strike | -116852 | 5084.33 | *** |
| Weather | -26818.4 | 3801.96 | *** |
| Extreme_Weather | -74399.2 | 9352.31 | *** |
| Travel_Demand | 544.253 | 89.2585 | *** |
| Jan | -19605.7 | 3249.88 | *** |
| June | -9196.58 | 2650.52 | *** |
| July | -10861.2 | 3072.91 | *** |
| Aug | 16015.1 | 3154.37 | *** |
| Dec | 6586.5 | 3477.24 | * |
| R-squared | 0.84 | Adjusted R-Squared | 0.84 |
The approach used is a “General to Specific” methodology – all variables are initially included, and a model estimated. Then the most statistically insignificant variable is excluded and the model re-run. This is repeated until all remaining variables are significant.
The full results for the main scenarios are shown in the table below.
| Variable | All Basic | All T90 PCD | All T80 PCD | All T Oct24 | Express T90 | Intercity T90 | West Suburban T90 | East Suburban T90 | Scenic T90 | Revenue |
|---|---|---|---|---|---|---|---|---|---|---|
| const | 114767 | 115161 | 110084 | 114767 | 10184 | 11552 | 78381 | 11836 | 4319 | 565478 |
| PFT Dummy | - | 14178 | 15906 | - | 1700 | - | 9396 | - | - | -46275 |
| Trend | 122 | - | - | - | - | - | - | - | - | - |
| Trend to 90PCD | - | 122 | - | - | 10 | 13 | 76 | 18 | 6 | 523 |
| Trend to 80PCD | - | - | 157 | - | - | - | - | - | - | - |
| Trend to OCt23 | - | - | - | 122 | - | - | - | - | - | - |
| Peak Fares Trend | -85 | - | 105 | 37 | - | 5 | - | 24 | 4 | - |
| Xmas/New Year | -51627 | -50897 | -50230 | -51627 | -6197 | -4524 | -33263 | -5671 | -1436 | -204006 |
| Sat | 16636 | 16662 | 16648 | 16636 | 3386 | 1830 | 6845 | 2904 | 1767 | - |
| Sun | -92550 | -92459 | -92468 | -92550 | -5819 | -7612 | -63205 | -11780 | -3966 | -347206 |
| Mon | -16609 | -16651 | -16523 | -16609 | -2261 | - | -11638 | -2189 | -298 | -49177 |
| Tue | - | - | - | - | - | - | - | - | - | - |
| Thur | 5630 | 5671 | 5817 | 5630 | 917 | 513 | 3366 | 645 | 349 | 17879 |
| Fri | 21607 | 21615 | 21887 | 21607 | 1545 | 2769 | 13982 | 1890 | 1556 | 66359 |
| Sport | 15514 | 15248 | 16018 | 15514 | 2128 | 782 | 9928 | 2059 | 335 | 47833 |
| Concert | 17224 | 17339 | 16715 | 17224 | 2770 | - | 12226 | 1715 | - | 71306 |
| Strike | -117078 | -116852 | -117612 | -117078 | -7240 | -12842 | -77434 | -14257 | -4988 | -444002 |
| Weather | -23972 | -26818 | -25197 | -23972 | -2559 | -3678 | -15692 | -3111 | -1123 | -100841 |
| Extreme Weather | -73874 | -74399 | -74502 | -73874 | -5331 | -5372 | -51744 | -9458 | -2736 | -239081 |
| Travel Demand | 550 | 544 | 562 | 550 | 55 | 56 | 334 | 78 | 25 | 1853 |
| Jan | -19024 | -19606 | -27058 | -19024 | -2608 | -2938 | -11669 | -2921 | -1615 | -175744 |
| Feb | - | - | -12502 | - | -1038 | -1307 | - | -1209 | -728 | -110654 |
| Mar | - | - | -10700 | - | - | - | - | -1249 | -476 | -63056 |
| Apr | - | - | - | - | -739 | 2081 | -5477 | 881 | 1025 | -25636 |
| May | - | - | - | - | - | 1755 | -3800 | - | 888 | - |
| June | -10284 | -9197 | -9966 | -10284 | -643 | - | -9274 | -1104 | - | -38154 |
| July | -11145 | -10861 | -9330 | -11145 | -1245 | 1264 | -12548 | - | - | -39263 |
| Aug | 14858 | 16015 | 18061 | 14858 | 3617 | 2110 | - | 5901 | 2113 | 68262 |
| Oct | - | - | - | - | - | -752 | - | - | -356 | -40837 |
| Nov | - | - | - | - | - | - | - | - | -829 | -47239 |
| Dec | 8130 | 6587 | - | 8130 | 1166 | -1595 | 4553 | 1429 | -504 | -60871 |
| Fares Rise | - | - | -19685 | - | - | -1684 | - | -2442 | -724 | - |