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Incentivizing public transit to improve performance to meet the programmatic goal of a funding agency

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Abstract

This paper deals with incentivizing public transit systems to exert effort to improve their performance to meet a programmatic goal of a funding agency. It shows the relationship between organisational and employee effort, formulates a net benefit equation with and without user cost savings and derives equations for effort. From these equations it surmises that (a) the larger the incentive the larger the effort transit systems and employees will exert to improve organisational performance, (b) effort is large when user costs are considered and (c) the larger the wage rate the smaller is the effort. In addition, it specifies a labour compensation equation that includes effort and labour intensity as some of its arguments and estimates it with a derived cost function and share equations as a system. The coefficients from them are used to show that when employees are incentivized to exert additional effort to improve organisational performance it increases the incentives, revenue and user cost savings by large proportions and cost by a very small proportion.

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Notes

  1. https://www.liveabout.com/basics-of-transit-funding-2798674 (Accessed 7/27/20).

  2. http://www.t4america.org/wp-content/uploads/2015/02/James-Corless-Indy-academy-5-14-15.pdf (Accessed 7/17/2020).

  3. Guidebook for Evaluating Fuel Charging Strategies for public Transit. 2012. TCRP Report 156, TRB, Washington DC.

  4. http://www.dot.gov/funding/procurement/third-partyprocurement/cooperative-purchase. Accessed 05/01/2020.

  5. Transit systems automatically receive incentive subsidy allocated based on a legislated formula. It is the increase in the subsidy which requires voluntary effort on their part.

  6. Throughout this paper agent and transit system are used interchangeably.

  7. This is because labour resource consists of physical and mental ability, the latter being how to do a job or learning and retaining knowledge to do a job.

  8. We make this assumption to make the derivations hereafter tractable recognizing that transit employment is labour intensive involving mostly drivers and mechanics who work long hours in jobs that are physical and skills-oriented. Unreported mental effort is an addition to labour work hours.

  9. Simon (1990) treats effort as an economic variable dependent on the additional income that can be obtained from the effort and the need for additional income, and provides a formula which he argues can be used to analyze less understood phenomena. Clark and Tomlinson (2001) considered it a latent variable and developed instruments for it.

  10. The items in the scale can be used to construct a continuous variable representing effort.

  11. This assumes no cost increase from exerting effort to improve performance, which need not hold as there might be costs in developing and implementing actions resulting from this effort. If that is the case, the sign of \(H\) is negative making the whole term positive and implying that each action has an associated cost.

  12. https://www.bizjournals.com/philadelphia/stories/1998/03/16/story4.html Accessed 05/24/2022.

  13. An alternative formulation is that total effort is \({x}_{1}+\widehat{E}\) (i.e., the sum of physical and mental efforts) and if both are considered as similar, then the cost of total effort is \({w}_{1}({x}_{1}+\widehat{E}\)). However, if each hour of extra effort \(\widehat{E}\) is considered more arduous than \({x}_{1}\) then the total effort is \({x}_{1}+{\rho }_{1}\widehat{E}\) where \({\rho }_{1}>1\) is a premium weight on effort. From this, the total labour cost is \({w}_{1}{x}_{1}+{\rho }_{1}{w}_{1}\widehat{E}={w}_{1}\times \left({x}_{1}+{\rho }_{1}\widehat{E}\right)={w}_{1}{x}_{1}^{*}\left({x}_{1}, \widehat{E}\right).\) A difference between this and the one based on a wage premium is the unit of analysis. Later we show that this gives very large effort, hence our use of the former.

  14. The question arises if organisational value should be maximized subject to a production function constraint. Such an approach assumes fixed output so it is not used because effort-induced actions can affect both cost and output simultaneously, e.g., the agent can use fuel-price hedging to reduce cost simultaneously with quality-of-service improvements to increase ridership.

  15. If the wage rate increases from the premium matching benefits from the principal also increase, which is not so with one-time payment.

  16. Becker (1977) assumes that labour compensation is a function of effort and intensity; our model expands it to include other variables.

  17. The data source does not provide this information.

  18. To derive this equation, consider \({C}^{*}= {x}_{1}{w}_{1}^{*}+{w}_{2}{x}_{2}+{w}_{3}{x}_{3}={x}_{1}{w}_{1}\left(1+ \rho E\right)+{w}_{2}{x}_{2}+{w}_{3}{x}_{3}.\) Substituting gives \({C}^{*}=C\left(\rho {ES}_{1}+1\right).\)

  19. The after-effort labour cost share is \({S}_{1}^{*}=\frac{{x}_{1}{w}_{1}\left(1+ \rho E\right)}{{C}^{*}}.\) Substituting \({C}^{*}=C\left[1+\rho E{S}_{1}\right]\) into \({S}_{1}^{*}\) and solving for \({S}_{1}\) gives \({S}_{1}=\frac{{S}_{1}^{*}}{1+ \rho E\left(1-{S}_{1}^{*}\right)}.\) The other cost shares can be derived similarly.

  20. Also, since \({w}_{1}^{*}{x}_{1}={C}_{E}^{*}\left(\bullet \right),\) by Shepard’s lemma \({w}_{1}^{*}=\frac{\partial {C}_{E}^{*}}{\partial {x}_{1}}.\)

  21. Uber started in San Francisco in 2009 initially targeting wealthy people to hail limousine services. In 2011, it launched its services and app making it available to other users nationwide. Lyft launched its services in 2012. See https://medium.com/@bhbern/a-brief-history-of-ride-sharing-7d1eca9e4654 Accessed 03/29/2023.

  22. https://www.nationalacademies.org/trb/blog/changing-trends-in-public-transit Accessed 03/25/2023.

  23. https://www.bing.com/search?q=US%20worker%20wages&form=SWAUA2 and https://www.statista.com/statistics/243842/annual-mean-wages-and-salary-per-employee-in-the-us/, both accessed March 19, 2023.

  24. The same is true if output is vehicle miles since the two are highly correlated.

  25. Note that by construction the minimum value of this ratio is one.

  26. Interestingly, for this coefficient the converged value was its lower bound and it was statistically significant.

  27. See https://www.bizjournals.com/philadelphia/stories/1998/03/16/story4.html and https://www.mscklaw.com/blog/2018/06/work-a-split-shift-you-might-deserve-more-pay. May 2, 2022.

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  1. Department of Marketing and Supply Chain Management, College of Business and Economics, North Carolina A&T State University, Greensboro, NC, 27411, USA

    Kofi Obeng

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Obeng, K. Incentivizing public transit to improve performance to meet the programmatic goal of a funding agency. Public Transp 16, 187–212 (2024). https://doi.org/10.1007/s12469-023-00340-9

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