Crime doesn't pay (these days)
But the Victorian Government might spend a little bit too much trying to stop fare evasion.
When I went to school, everyone had their preferred methods of avoiding ticket inspectors. One friend of mine told me that he just pretended to fall asleep as soon as he saw them and would stay that way until they left, no matter how loudly they demanded to see a ticket. Another just ran as fast as he could.
In 2019 the Victorian the government estimated that fare evasion cost them approximately $30.7 million dollars a year as approximately 3.12% of passengers didn’t have a valid ticket for their journey.
This is an improvement on the pre-2013 days when almost one in ten passengers was fare evading. In those halcyon days you could sign up for fare invasion insurance, which would cover the cost of any fines you received for $20 a month - lower than the average price of travel. While this scheme was shut down fairly quickly, the fact that it was viable means that it was probably cost effective to fare evade!
So does crime still pay in the year-of-our-lord 2021? I don’t know, the data isn’t out yet. And COVID has probably thrown the whole thing out of whack. But we do have data for 2018-19 and the short answer for that year is no - you were on average worse off by fare evading. But you might be surprised to learn that at this rate, it is not cost effective for the government to inspect tickets either.
To understand why, we need to quantify the costs and benefits of fare evasion and of inspecting tickets.
Smart choices
Based on the figures for 2018-19 we can see that the average fee for travelling on the Victorian public transport network is $1.88 per trip,1 while the fine for being caught fare evading was $237 at the time. We also need to know the likelihood that we get caught. To do this, I have divided the number of tickets inspected2 by the number of trips made3 which comes out to 1.61%. Putting all these numbers together we can work out that by fare evading you end up $1.94 worse off per trip on average than if you’d just paid your fare.
But this is for the hypothetical average train rider! If you’re a fare-evading, otherwise concession paying passenger making a one way trip, you’re going to be $1.58 worse off, while fare evading full-fare passenger making the same trip would be $0.67 better off!4
We can estimate if Public Transport Victoria (PTV) makes money on each inspection. A ticket inspector makes between $70,000 and $101,000 per year, and performs roughly 14,000 inspections per year (or about 60 per working day). Assuming the average salary is $85,000 and an estimate for on-costs (superannuation, payroll tax, etc) of 25%, this comes out to a cost of $7.59 per inspection. Given that roughly 3.15% of passengers are fare evading, this nets out to an average revenue per inspection of $7.46. So for every inspection the government makes, they probably lose about $0.13. Given I’ve made some broad assumptions about costs and wages, this value is too small to conclusively say whether each inspection is profitable.
Theoretically smart choices
In economics, we determine the amount two parties should take a certain action like this using a Mixed-Strategy Nash Equilibrium (which I’ll call an MSNE). To work this out, we need to map out the possible decisions and payoffs for each party.
The above table shows the payoff for both the government and the passenger for all possible decisions. For example, if the passenger pays the fare and the government inspects their ticket, the passenger has paid the ticket, while the government gets the ticket revenue but have to pay the wage cost of the inspection. Plugging in the values I have calculated, we get the following payoff table:
We can see that if the government catches a fare evader, they will earn $229.41 (after wage costs), while a passenger will pay the $237 fine.
Using these payoffs, we can calculate the payoff maximising decisions for both parties under a MSNE:
The government should inspect 0.79% of all travellers. In 2019, they inspected 1.61% of all passengers.
Passengers should fare evade 3.20% of the time. In 2019, 3.15% of passengers fare evaded.
That it is not cost effective for passengers to fare evade, even though they are below the theoretical rate, is a direct result of the government over-inspecting.
Where theory meets reality
Now that we can see the theory and the reality, it is worth exploring why they might differ. The theory assumes that both passengers and the government act to maximise their payment, and we have good reason to believe that they don’t.
Passengers fare evade for a number of reasons - including being unable to afford the ticket, being unable to validate due to the amount of other travellers, rushing to board the train, leaving a wallet at home, and just not wanting to pay. Some of these groups would likely fare evade even when it was even less cost-effective to do so.
Government may have a variety of different incentives to inspect tickets, from wanting to create an impression of law and order or perhaps to shift societal norms. Further, the government may not be able to adjust their workforce rapidly or accurately enough to match changing and uncertain commuter behaviour.
In fact, government can actually get away with lower enforcement if it makes people think that there is more enforcement than there actually is. The converse of this is that if public believes there are less inspectors than there really are, then they will fare evade at a higher rate. Commuters fare evade at close to the rate of the MSNE, while government inspect at nearly double the rate. If you’re a believer in the model, this suggests that commuters believe government inspect at a rate half of what they really do. An alternate hypothesis may be that the Government is trying to establish a norm of compliance after a period where fare evasion was high.
In any case, due the high enforcement rates the fare-evasion ticket insurance is unlikely to be profitable today.
Appendix: how about some maths
In this bit I’ll quickly lay out my assumptions and my calculations for both the empirical and theoretical analysis.
Empirical calculations and assumptions
The values for inspections were calculated as follows:
There were about 600 authorised officers in 2019
The average inspector makes roughly $85,0005
On costs are about 25%, taking the average cost of an authorised officer to $106,250 per year
There were 700,000 inspections conducted a month, or roughly 8.4 million a year
Therefore the cost per inspection = $106,250 / (8.4 million / 600) = $7.59
There were 555.9 million trips (excluding regional bus services), 35.5 million of which were in the Free Tram Zone. Therefore there were approximately 520.4 million trips in 2019.
The cost for fares and fare evasion were calculated as follows:
The fare non-compliance rate was 3.15%, or 17.5 million trips per year
A fine cost $237
The revenue from fares was $949.14 million
Given there were 520.4 million trips, this equates to an average fare per trip of $1.88
The state government does not directly receive the GST from each fare, therefore the value received from each fare is $1.71
Theoretical calculations
The payout for each party for each decision is laid out below:
Under a MSNE, to solve for the inspection rate, the Payoff under both decisions should be equal. This is because if one decision were to be more profitable, rational actors would all choose that outcome. For example, if it were cost effective to fare evade, under this model everyone would do it. This would then incentivise government to inspect everyone’s ticket. The MSNE finds the equilibrium of these behaviours.
Given the values stated above, the inspection rate is as follows:
We can do the same for the evasion rate:
This was initially a bit of a surprise, as it was below even the concession rate for a single trip. But - this includes passengers who pay for yearly or monthly fares and trips that are taken after the daily fare-cap.
Using Figure 3, I have made a guesstimate that it’s approximately 700,000 inspections per month. I hope I’m reading that chart right. If you’re from PTV and you’re reading this please for the love of god make this more intelligible
The number of trips made also needs to account for journeys made in the free tram zone, which was estimated to be 35.5 million in the 2019 enquiry into the free tram zone. There are inviarably trips that are partially in the FTZ, but I’ve decided to ignore these.
This assumes analysis that the recorded inspections are the only way that tickets are checked. Your mileage may vary if you get on or off at a station with ticket barriers.
Inspectors make between $70,000 and $101,000. $85,000 just seemed like a nice midpoint.
Crime doesn't pay (these days)
Really interesting to read!
Yeah I think we should have more info like this, currently when we fare evade it's so focused on whether we'll get caught at each station that we don't think about the bigger picture of profitability over time. Would be nice to see info about how the ptv spreads their resources during the day/week as compared to rush hour, as well as which lines/stations they patrol, and whether it's better to fare evade on longer or shorter trips. Thanks a lot!