AN ECONOMIC MEASURE OF THE MARGINAL COST OF TRANSPORTATION

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1 AN ECONOMIC MEASURE OF THE MARGINAL COST OF TRANSPORTATION Presenta(on to the 2012 Mid- Con(nent Transporta(on Research Forum By: Michael A. Rodriguez, AICP Associate Transporta(on Planner & Economist Strategic Consul(ng Group of Parsons Brinckerhoff

2 AGENDA 9/11/12

3 Agenda 1. Overview & Uses for a Marginal Cost 2. What is a Marginal Cost? 3. Data Source & Model 4. Results 5. Discussion & Further Research 6. QuesQons AGENDA

4 USES FOR A MARGINAL COST 9/11/12

5 Examples of Uses for Marginal Cost Goal of paper is to develop an esqmate of cost given a Qme series of data. Can demonstrate that costs per VMT vary depending on what the exisqng traffic condiqons are. Examples of uses of such a calculaqon: Toll Pricing Benefit- Cost Analysis USES FOR MARGINAL COST

Can demonstrate that costs per VMT vary depending on what the exisqng

6 WHAT IS MARGINAL COST? 9/11/12

7 Defini(ons of Cost Cost Value of Qme of users (autos) Value of Qme for commodiqes (trucks) Vehicle operaqng costs (fuel) Types of Costs Private Time Fuel Public Maintenance / DepreciaQon Emissions Safety risk Effects on oil market CongesQon effects on everyone else Concept shown by Vickrey (1955) TransportaQon congesqon grows non- linearly. Every new car adds more to traffic than the car before it. WHAT IS MARGINAL COST

risk Effects on oil market CongesQon effects on everyone else Concept shown by Vickrey (1955)

8 Average vs Marginal Cost

9 DATA & MODEL 9/11/12

10 Data Source Texas TransportaQon InsQtute Urban Mobility Study Costs only include private costs, not externaliqes. Data for 101 CiQes, from Used measures for: Total congesqon costs Arterial VMT Freeway VMT Arterial Lane- Miles Freeway Lane- Miles PopulaQon DATA & MODEL

Data for 101 CiQes, from 1982-2009 Used measures for: Total congesqon

11 Model But we have control variables DATA & MODEL

12 Model Specifica(on Model was specified in non- linear form DATA & MODEL As a result, to calculate marginal costs, parqal derivaqves were needed:

13 RESULTS 9/11/12

14 Regression Output Dependent Variable: LN(COST) Method: Panel Least Squares Sample (adjusted): Periods included: 26 Cross- secqons included: 101 Total panel (balanced) observaqons: 2626 Convergence achieved afer 6 iteraqons RESULTS Variable Coefficient Std. Error t- StaQsQc Prob. C LN(AVMT) LN(FVMT) LN(ALM) LN(FLM) LN(POP) AR(1) AR(2) R- squared Mean dependent var Adjusted R- squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan- Quinn criter F- staqsqc Durbin- Watson stat Prob(F- staqsqc) 0 Inverted AR Roots

000 LN(ALM) - 0.567679 0.0610-9.31 0.000 LN(FLM) - 0.82154 0.0590-13.93 0.000 LN(POP) 0.342992 0.0726 4.72 0.000 AR(1) 1.038293 0.0202 51.43 0.000 AR(2) - 0.07656 0.0198-3.87 0.000 R- squared 0.

15 Results RESULTS 2010 Dollars marginal cost per marginal cost per Arterial VMT Freeway VMT at sample mean $ $ at sample minimum $ $ at sample maximum $ $ NCHRP report idenqfies average cost between $ $0.21 per VMT FHWA report idenqfies an average cost of about $0.08 per urban VMT

16 DISCUSSION AND FURTHER STUDY 9/11/12

17 Discussion & Further Research These results are for all ciqes, and at the sample mean When parqal derivaqve is taken at sample maximum, the value is much higher To calculate a specific marginal cost for a facility: Depends on highway type (arterial vs. freeway) Marginal effects should be taken at the most recent level of congesqon Forecasts can show increasing marginal costs. Based on traffic projecqons Based on populaqon projecqons Based on Further research: To separate data by individual ciqes Examine against revealed preference data in tolling DISCUSSION & FURTHER RESEARCH

freeway) Marginal effects should be taken at the most recent level of congesqon Forecasts can show increasing marginal costs.

18 Sources Schrank, D., T. Lomax, and S. Turner. Urban Mobility Report Texas TransportaQon InsQtute, Texas A&M University System, College StaQon. hkp://l.tamu.edu/documents/ mobility_report_2010_wappx.pdf. Accessed July 31, SOURCES Vickrey, W. Pricing in TransportaQon and Public UQliQes: Some ImplicaQons of Marginal Cost Pricing for Public UQliQes. The American Economic Review, Vol. 45, No. 2, 1955, pp Vickrey, W. In Highway Research Record, No. 476, TransportaQon Research Board of the NaQonal Academies, Washington, D.C., 1973, pp Walters, A.A. The Theory and Measurement of Private and Social Cost of Highway CongesQon. Econometrica, Vol. 29, 1961, pp Lomax, T., S. Turner, G. Shunk, H.S. Levison, R.H. Prak, P.N. Bay, G.B. Douglas. Quan2fying Conges2on: Volume 1 Final Report. Project 7-13 FY 92. NaQonal Highway CooperaQve Research Project, TransportaQon Research Board, U.S. Federal Highway AdministraQon. Management and Opera2ons Toolbox. hkp:// ops.pwa.dot.gov/tdm/toolbox.htm. Accessed July 31, 2011.

The American Economic Review, Vol. 45, No. 2, 1955, pp. 605-620. Vickrey, W. In Highway Research Record, No. 476, TransportaQon Research Board of the NaQonal Academies, Washington, D.C., 1973, pp.

19 QUESTIONS? 9/11/12

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