Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives

Fabbri, Daniele Working Paper Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives Quaderni - Working Paper DSE, No. 220 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Fabbri, Daniele (1995) : Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives, Quaderni - Working Paper DSE, No. 220, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/5095 This Version is available at: https://hdl.handle.net/10419/159063 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/3.0/ PUBLIC TRANSIT SUBSIDY: FROM THE ECONOMICS OF WELFARE TO THE THEORY OF INCENTIVES Daniele Fabbri Department of Economics, University of Bologna, Piazza Scaravilli 2, 40126-Bologna, Italy. tel.: 0039-51-258126 fax: 0039-51-221968 June 1995 ABSTRACT: Public Transit is publicly managed almost all over Europe. Public intervention in this sector is due to market failures: economies of scale and misperceptions of social and private costs may cause an insufficient supply of transit services. These arguments have been thouroughly analyzed within the standard welfarist approach to the theory and practice of subsidization. Ramsey rules and cost-benefit analysis emerged as useful devices for the definition of subsidy allocation. However remedies to market failures should be traded-off against government failures. Lack of incentives, X-inefficiency, regulatory capture, bureaucracy power are common facts in the internal organization of public administration. If a public sector utility, for some reasons, can not be completely privatized, it may be "almost" privatized by means of quasi-market mechanisms. Auctioning, yardistick competition, incentive schemes, auditing, regulation through competition are the keywords for the renewed public involvment in public transit. All these mechanisms can be properly studied within the theoretical format of the incentives theory. This approach helps us to understand past experiences of transit firms incentives scheme and to appreciate the relevance of the empirical analysis of performance indicators. An important question that emerges is the definition of operational incentive contracts. In this paper we will discuss this problem by referring to past and recent experiments with performance based subsidization programs. J.E.L.: H71, R38. Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives 1 CONTENTS INTRODUCTION 1. THE STANDARD WELFARIST APPROACH 1.1. Cost-benefit analysis of public transit subsidy 1.2. Transit subisidization as a pricing problem 1.3. Some criticism of the standard welfarist approach 2. THE ORGANIZATIONAL CONCERN 2.1. Optimal commercial criteria for public transit firms 2.2. Positive analysis of transport firms 2.3. Why does organization matter? 3. THE INCENTIVES THEORY APPROACH 3.1. Incentives theory of regulation: the Laffont and Tirole framework 3.2. A model of transit firm regulation 4. INCENTIVE PROGRAMS IN PRACTICE 4.1. General rules for incentive contracts in the public transit sector 4.1. Some experiments with performace-based transit subsidization 4.3. Open issues 5. CONCLUSIONS APPENDIX REFERENCES Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives 2 INTRODUCTION A subsidy is the difference between production costs of a good and revenues from sales to final users. Its aim is to restore profitability in the production of a good, in order to make it available in quantities and qualities otherwise not provided by the normal functioning of the market. Therefore subsidization is deliberately performed by an agent in order to let some activities exist and grow. Good reasons for subsidizing public transit have been repeatedly suggested by economists. Standard arguments are: economies of scale, second-best problems, redistribution in kind, option value, imperfect information. For all these reasons it might be socially useful to sustain the production of public transit. But to what extent should we provide this support? Standard welfarist approach gave the answers. These answers will be analyzed in section 1. Among the several limitations of the standard welfarist approach we find that what makes it an "outdated" framework is its complete disregard of organizational concerns. In section 2 we show how these issues have been normatively treated by the former advocates of the standard welfarist approach and how relevant they are in terms of positive explanations of public firms' behaviour. Once we explicitly introduce organizational issues we should find new theoretical paradigms allowing another answer to be answered: how to subsidize a public transit firm in order to reach some specific goals and given that it has its own rationality? The theory of incentives provides such a paradigm. In section 3 we provide a model of regulation that fits very well into the typical situations we face. Then, in the last section, it will be quite easy to analyze past and recent experiences of performance-based subsidization. 1. THE STANDARD WELFARIST APPROACH In the welfarist approach the optimal level of subsidy is defined through a welfare calculus of costs and benefits. Its comprehensiveness is limited only by the extent that direct and indirect effects, which pass through final users of the transport system, can be measured. The literature reports two ways of performing this welfare calculus: costbenefit analysis and approaches based on optimal pricing of public utilities. 1.1. Cost-benefit analysis of public transit subsidy Cost-benefit analysis allows us to define subsidization rules on the basis of a welfare comparison between alternative uses of subsidies. The alternative uses are given by Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives 3 different combinations of adjustments in tariff and quality of transit service with respect to the initial situation. Therefore cost-benefit analysis identifies the adjustments in tariff and quality of service that maximizes social welfare given a budget constraint on the total amount of subsidy. The main difficulty in these calculations is the presence of a quality index both in the demand and cost functions1. Let D(b,q) and C(D(b,q,),q) be respectively the demand and the short-run cost function of transit, where b is the tariff and q is the quality index2. For any initial situation (b0,q0), define the consumer surplus S, and the producer surplus P, by: SDvqdv b =∞ z(, ) 0 0 (1) PbDbq CDbqq=− 000 000 (,) (,), bg (2) Given this initial situation (b0,q0), it is possible to calculate the net benefit for each amount of money spent alternatively to lower the tariff or to improve the quality of service. In the first case, the net benefit per unit of subsidy will be given by the equation: dB dT W b P b bC bbC b b Db Db == −− +− ∂ ∂ ∂ ∂ ε ε () () 0 00 (3) where dBb is the net benefit due to a tariff reduction, measured by the variation in total surplus W=S+P, dTb is the required increase in subsidy, given by the variation of producer surplus and b represents tariff elasticity of transit demand. Equation (3) is quite easy to calculate since it is made of known ingredients: tariff, tariff elasticity of demand and marginal cost of service3. This is not so in the case of subsidization of an improved quality of service. In this case we have: 1These circumstances justify a "transportation" treatment of public transit subsidy. 2q might be either a scalar or a vector. 3If the tariff is initially set at marginal cost there is no space for increasing net social surplus. Otherwise if marginal cost is zero the increase in net social benefit will depend only on tariff elasticity of demand. Subsidizing a tariff reduction will be more welfare improving the more initial tariff exceed marginal cost and demand is elastic to the tariff. Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives 4 dB dT W q P q Dvqdv b C D qC CbC D q q q q bDq q qDq == +− − −− ∞ z ∂ ∂ ∂ ∂ ε ε (, ) ( ) () 00 0 0 0 0(4) The numerator of equation (4) contains an integral term. It measures the variation of consumer surplus due to an increase in quality of service. No small experiment with price and quality will generate the information required to evaluate this integral term. The reason for this is that quality changes affect the welfare of the entire set of inframarginal consumers. The data generated by local changes in the parameters will not yield such estimates. Therefore in order to calculate equation (4) it is necessary to build a model that replicates the reactions of the entire set of inframarginal consumers4. Moreover we must rescale these effects in terms of welfare measures. At this point the problem becomes transport-specific. In the generalized travel cost approach the problem is the building of behavioural models explaining the impact of quality of service on walking, waiting, boarding and travel time. The impact on this time requirements of the whole set of inframarginal consumers might then be translated into monetary terms by means of value of time coefficients5. Once made operational, equations (3) and (4) provide a sound basis for allocating public transit subsidies to different towns in the same region6. An improved version of this simple model has been made operational in England by Stephen Glaister. METS (Model for Evaluating Transport Subsidies)7, was able to calculate equations (3) and (4) by solving quite complicated local mobility simulation models. It considered a multiplicity of transport modes: car, bus, rail and metro. Consumers choose on the basis of the generalized travel cost of each alternatives. Generalized travel costs are calculated through speed-flow relationships evaluated at equilibrium points. In this way METS allows to estimate modal impacts produced by pricing and quality policies by measuring their effect on congestion reduction and other second-best concerns. 4Spence (1975) realizes that this is the main problem faced by the regulator of a monopolist "with quality". The regulator should provide the non-market informations needed in order to evaluate total willingness to pay for quality improvements. 5This is the approach followed by Dodgson (1987). He solves equation (5) in terms of a relationship between vehicles-km and waiting-time. See also Tisato (1992) for an improved user cost model. 6See Evans (1985) for the definition of different equalization schemes in transit transfers. Dodgson (1987), by referring to a sample of Australian cities, suggested that an increase in vehicle-km would not be welfare improving in most of the towns. 7For a detailed description of METS see Glaister (1987). Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives 5 Even though METS is probably the most ambitious operational model for allocating subsidies it nevertheless suffers from several internal limitations. Gwilliam (1987) provides the following ordered list of criticisms8: •With respect to the objectives encompassed it has been pointed out that the use of the cost-benefit framework does not provide for any environmental or distributional objectives. •The model is not disaggregated by time of day and therefore it does not properly assess welfare effects due to peak shifting policies. •The high level of spatial aggregation of the model and the lack of explicit geographical content result in an uncertain estimate of the real effect of congestion. •The short-term nature of the model does not enable the impact of subsidy over cost structure and supply capacity to be evaluated. 1.2. Transit subsidization as a pricing problem In Welfare Economics we do not find a direct definition of subsidy. We could say that it is a derived concept. Subsidy emerges as the difference between an opportune unit price and the unit cost for producing the quantity of service demanded at that price. Therefore welfare economists are mainly concerned with the extension of the concept of opportune price. This has usually been accomplished through the definition of second and third best solution to first-best deficiencies. Production costs usually do not play any relevant role. With given technology and perfectly elastic supply of inputs it could be assumed that the service demanded is produced at minimum costs. Therefore the standard pricing problems contain a traditional cost function. The model developed by Glaister and Lewis (1978) moves within this framework. It identifies optimal pricing schemes of urban public transit in presence of congestion and defines the second-best subsidy that allows its social costs to be internalised. The authors consider three means of transport: car, bus and train. Each mode is considered at peak (p) and off-peak time (f). Individual utility depends on personal use level and on time losses associated with each modes. Since these depend, through speed-flow relationships, on the levels of collective use of each one of the six means, it follows that individual utility functions could be written as uh(xh,X), where xh and X are respectively the vectors of individual and collective use for each modes considered. Therefore individual expenditure functions can be written as gh(ph,X,uh) leading to the aggregate expenditure: 8All the limits listed are escapable in theory. Dodgson and Topham (1987) introduced distributional elements in the cost-benefit calculus. Bly and Oldfield (1987) extended the model in order to consider environmental impact, capacity optimization and optimal mixing of tariff reduction and quality improvement policies. However all these extensions would imply higher costs of model building. Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives 6 GpXu u g nh h n ( , , ,..., ) 11 = = ∑(5) In order to obtain optimal tariffs Glaister and Lewis solved the following maximization problem9: Max G X X p u Gp p X p p X p p pu CXX pX CX pX pp Bp Bf Ap Bp Bf Bp Bp Bf Bp Bf Ap Bp Bf Bp Bp Bf Bp Ap Bp Bp Bp Bf Af Bf Bf Bp Bf ,, , ( , ), ( , ), $ , ,, (,), (,), $ , (,) () αα αα αα di odi t − −− −−−− (6) where CBp, peak bus service production cost, is dependent on its own level of use, XBp, and, because of congestion, on car use during the same period, XAp; αBp and αBf are a set of base prices, considerably higher than those under consideration. Thus the difference between the expenditure function evaluated at the two points is the compensating variation, i.e. the amount of money that would be required to compensate for an increase in tariffs from p to α. The remaining two terms in square brackets are the operating subsidies required on the peak and off-peak bus services. The sum of the compensating variation and the gross revenues is the total willingness to pay from which must be subtracted the various operating costs. Differentiating (6), equating to zero and rearranging terms we obtain the following expressions for the optimal bus tariffs: pSSX X Bp Bp Ap Ap Bp Bp Ap Bp Bp Bp Bf Bf Ap Bp Bp Bf Bf =+ −− R S | T |U V | W | 1ρ η η ηη ηη (7) pSSX X Bf Bf Ap Ap Bf Bf Ap Bf Bf Bp Ap Bf Bp Bp Bp Bf Bf =+ −− R S | T |U V | W | 1ρ η η ηη ηη (8) where ηji represent the direct and cross elasticities of compensated demand, SAp is the marginal social cost of a peak car passenger per mile and ρ is a combination of elasticities of demand reasonably positive and smaller than 1. Assuming that the modes are substitutes, (7) and (8) indicate that both peak and off-peak prices will be below respective marginal social costs by an amount proportional to marginal social cost of car use, both because of the possibilities of attracting peak car users directly and reallocating 9We removed rail modes in order to simplify formal treatment. Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives 7 demand between periods. Simulations performed do not bring any unexpected results. For a quite broad range of values of the parameters and marginal costs, second-best subsidy should be higher during off-peak periods. De Borger et al. (1993) recently applied an improved version of Glaister and Lewis model of urban transport in Belgium. Social cost includes congestion costs, environmental costs and accidents. In this way the model provides an exhaustive treatment of second-best arguments for transit subsidy. Results, obtained also considering car user price as a policy variable, indicate that each tariff should be set at the corresponding marginal social cost. With a binding budget constraint optimal tariffs will be fixed on the basis of a Ramsey rule and will be higher than the respective marginal social cost, both in peak and off-peak. In the simulations performed by De Borger et al. the extent of this increase for bus is quite surprising, especially if compared to that of private cars. 1.3. Some criticisms of the standard welfarist approach As we mentioned before the welfarist approach has been criticized for several reasons. The high level of spatial aggregation, insufficient time disaggregation, a simplified treatment of cost functions and the lack of explicit geographic content are some of the more relevant internal limits of models strictly based on this approach. Moreover we should not diseregard external limits due to the narrow definition of the mobility system. The welfarist approach focuses only on direct and indirect effects which pass through final users, identifying mobility needs with transport demand. In this way the empirical relevance of the approach may be quite limited in scope. In the following we will not discuss approaches coping with these types of limitations10. We do believe that the standard welfarist approach has merits that largely exceed its limits. However there is one more typical external limit, concerning the organizational contents, that we consider interesting to focus on here. This is the limit that makes the approach "out-of-date". The standard welfarist approach deliberatly disregards any references to the organizations governing supply of public transit services. It assumes that organization is simplified to a single decision maker that is a social welfare maximizer. It could be a regulator, as implicitly assumed in the cost-benefit analysis approach, or the transit firm, as is done in the second-best pricing problem. This drastic reduction changes the standard welfarist models to simple tools for evaluating transport policy options, but leaves important questions concerning the real implementation of those policy options completely unanswered. 10Two examples of such approaches are the application of Activity Analysis to public transit subsidization provided by Goodwin et al. (1983) and that of the so-called Lewes Approach, see Searle (1987). Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives 14 has the socially optimal incentive to reduce cost as it receives all the money it saved. However, a cost-plus transfer offers no incentive for cost reduction, as long as the firm does not appropriate of its cost savings. In the case of rent extraction the logic is reversed. Under a fixed-price transfer any exogenous reduction in cost is received by the firm. The firm's rent therefore is very sensitive to the technological environment. On the other hand, a cost-plus contract is ideal for rent extraction because any exogenous variation in cost is received by the government and not by the firm. When the regulator has perfect information about the techonology (there is moral hazard but no adverse selection), the optimal regulatory contract is a fixed-price transfer20. When the firm has private information about its technology optimal contracts are incentive contracts trading off effort inducement, which calls for fixed-fee transfers, and rent extraction, which calls for a cost-plus transfer. In general it is optimal for the regulator to offer a menu of incentive transfers, since the transfer should be tailored to the firm's information. An inefficient firm should not be regulated with the same contract as an efficient firm. The regulator discriminates among the different potential types of firm in the same way the monopolist price discriminates among consumers with different valuation for quantity or quality. The regulatory contract emerges as the solution of a mechanism design game, that is a three step game of incomplete information, where the agent's type is private information. In step 1 the regulator designs a contract [t(µ),C(µ)] that specifies for each announced value of the signal µ sent by the firm a net transfer to the firm t(µ), and a cost to realize C(µ). In step 2 the firm decides to accept or reject the contract. In step 3, the firm which accepts the contract plays the game specified in the contract. The revelation principle21 shows that, to obtain the highest expected payoff, the principal can restrict attention to contracts that are accepted by the firm at step 2 and in which at step 3 the firm truthfully reveal its type. As we will show, the revelation principle allows the regulatory problem to be solved in terms of standard optimal control techniques. 3.2. A model of transit firm regulation We saw that as long as organization matters, public transit subsidization should be treated as a regulation problem22. Organizational concern emerges in the public transit sector because of the following typical circumstances: 20In this case the fixed fee is optimally set at the lowest level consistent with the firm's partecipation provided that the firm chooses the effort that minimizes C+ψ(e). 21We are referring here to the textbook treatment contained in Fudenberg and Tirole (1991), ch. 7. 22See the paper by Pedersen (1994) for the first attempt, to my knowledge, in this direction. Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives 15 1. The transit firm maximizes its own rent while the regulator is concerned with social welfare. This latter circumstance is justified in that we are assuming the (normative) point of view of the regulator. That the transit firm maximizes its own monetary rent seems a good positive assumption at least for private companies. In the case of a public enterprise it could be intepreted as a typical managerial objective. 2. There is an asymmetry of information between the firm and the regulator in that: a) The firm is better informed than the regulator about technology and about local demand conditions. If we think of a regional authority in charge of subsidizing a multiplicity of local transit suppliers these circumstances seem quite plausible. There will be always some local specific features affecting technology and demand, that can not be properly detected by the regional authority. b) The firm cost-reducing effort can not be directly observed and quality standard is not easily verifiable by the regulator. While the first point seems obvious the second is worth some comments. Quality of transit is difficult to check as long as it depends on local conditions (demographic, geographic, social, ...). Therefore even if quality could be observed23, in principle, it would be difficoult to quantify and to include in a formal contract. Given these circumstances, the regulatory problem appears quite complicated as long as it is one of two-dimensional adverse selection and two-dimensional moral hazard. An important simplifying feature is that quality of transit service can usually be observed by users before use. Thus the regulator might recreate the incentives of an unregulated firm to provide quality by rewarding the regulated firm on the basis of sales. Laffont and Tirole (1993), ch. 4, provide a thorough analysis of this regulatory problem. In the following we give a brief overview of their model. We report some details in an appendix. The transit firm, which is a local monopoly, produces the service in quantity q with quality, which can be observed by users but not by regulator, s. Cost function is given by: Cseq=+−()β(12) where β is the technological parameter and e is cost-reducing effort. Firm's rent is given by: Ut e=−ψ( ) (13) 23This implies in any case high costs of minitoring and auditing. Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives 16 Users derive from the consumption of the transit service a gross surplus: Sqs AkshqBqks h g(,,) ( ) () θθ θ =+− − − − 22 22(14) where A, B, h e k are known positive constants and θ is a demand parameter24. The users'/taxpayer net surplus Sn, given by gross surplus net of individual expenditure and social cost of providing the service, is: SS pq Cpqt ng =− ++ −+()( )1λ(15) 3.2.1. The complete information case Under complete information a utilitarian regulator maximizes the sum of consumer and producer surpluses under the constraint that the firm be willing to partecipate: Max W q s e S U qse n (,,) (,,)=+ mr (16) s.c. U≥0 (17) Interior maximum is characterized by the first-order conditions25: pC p q −=+ λ λη1 1(18) ∂ ∂λ∂ ∂λ S s P sqC g s +=+()1 (19) ψ'( )eq=(20) U=0 (21) where η=p/Bq. Equation (18) says that service is produced up to the point where the Lerner index is equal to a Ramsey index time the inverse of elasticity of demand. The 24Quantity and quality are net complements if k>1 and net substitutes if k<1. Quantity and quality are net complements if an increase in quality raises the net marginal willingness to pay, that is the difference between price and marginal cost. 25For B large enough the program [(16), (17)] is concave and its interior maximum is fully characterized by the first-order conditions. Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives 17 optimal level of quality equates the marginal gross surplus plus the shadow cost of public funds times the increase in revenue to the social marginal cost of quality. Equation (20) equates the marginal disutility of effort to its marginal utility q, and equation (21) says that no rent is left to the firm. 3.2.2. Optimal regulation with asymmetric information Now we take into account the asymmetry of information. The regulator knows neither β nor θ and cannot observe e and s. However he observes C, p and q. We assume that the regulator maximizes expected social welfare and has a prior cumulative distribution F1 on βββ∈, , and F2 on θθθ∈, . The firm knows β and θ before contracting. The regulator knows that users equate their marginal utility of service to the price: pAksh Bq =+− −θ (22) By using equation (22) it is possible to eliminate the unobservable quality level s in the users' gross surplus (14), which becomes: Spq Bqpq pABq g(,)=+−−+ 2 1 2 22 bg (23) Similarily the cost function becomes: Ch keq q pABq k =+− FHGIKJ +−+ FHGIKJ βθ(24) The firm objective function will be: Ut e t h k pABq k C q =− =− + + −+ − FHGIKJ ψψβ θ () (25) β and θ enter the cost function and the firm's objective function only through the linear combination γ =β+hθ/k. This feature, which holds also for the regulator's objective function, reduces the model to a one-dimensional adverse selection model. We note at this point that high (low) values of β and θ, which are due respectively to a low (high) cost efficiency and a low (high) demand, imply high (low) values of γ . The regulator wishes to maximize social welfare. From the revelation principle we can restrict the problem to the analysis of direct and truthful revelation contracts. The individual rationality constraint of the firm is: Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives 18 U( γ )≥ 0 for any γ (26) while truth telling is guaranteed by the following first- and secondorder conditions of incentive compatibility (see appendix A.1.): ∂∂γ ψUe/'()=− (27) ∂∂γe/−≤1 0 (28) Thus the regulator designs the contract [t( γ ),c( γ ),p( γ ),q( γ )] that specifies for each value of γ announced by the firm a net transfer to the firm t( γ ), an average cost to realize c( γ ), a price to charge p( γ ) and a quantity to sell q( γ ), by solving the following optimal control problem26: max , , ( ) (), (), (), ()pqeU Wpqe dFz ⋅⋅⋅ ⋅ z lq bgmr γ γ(29) under constraints (26), (27) and (28), where the welfare function W is a obtained by substituing out quality from the social welfare function (16), and the cumulative distribution F(γ) is the convolution of F1 and F2. Maximizing the hamiltonian with respect to q and p we obtain conditions which correspond to (18) and (19), i.e., for a given effort e, the price, quantity and quality are the same as under complete information about technology and demand parameter. Moreover from (27) we see that p and q do not affect the rate at which the rent must be given up to the firm. Maximizing the hamiltonian with respect to e we get: ψλ λ γ γψ'( ) () () ''( )eq F fe=−+1(30) If we compare (30) with (20) we see that in order to extract part of the firm's rent the effort is distorted downward for a given output level, except for the most efficient type γ = γ 27. Equation (30) has a straightforward interpretation. If we raise effort of types in [ γ , γ 26For A and B large enough the program is concave and the optimum is characterized by its first-order conditions [see Laffont and Tirole (1993) appendix A4.3.]. 27Laffont and Tirole show that the level of quality is lower under incomplete information than under complete information if and only if quantity and quality are net complements. Incomplete information Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives 19 +d] (in number f( γ )d γ ) by de, productive efficiency increases by [1-ψ'(e( γ ))]de for these types, which yields social gain (1+λ)[q-ψ'(e( γ ))]def( γ )dγ. However this also raise the rent of types in [ γ , γ ] (in number F( γ )). From (27) the rent of type γ is increased by ψ ''(e( γ ))ded γ , and so is the rent of types γ °< γ . The social cost of the extra rents is λ ψ ''(e( γ ))(de)(d γ )F( γ ). At the optimum the marginal cost must equal the marginal benefit, which yields (30). Differentiating (30) we get: ∂∂γ λλψγ γγγ ψγ λ λ γ γψ γ eeddFf eFfe //( ) ''( ( ))( / ) ( )/ ( ) ''( ( )) /( ) ( )/ ( ) '''( ( )) =− + ++ 1 1(31) As long as the distribution F satisfies the monotone hazard rate property28 (d/dγ )[dF/df]>0 and ψ '''>0 it follows that the condition (28) is confirmed, that is in the optimal allocation the effort is decreasing in the firm's type. The same is true for the rent function that is given in the optimum by: Ued*( ) '( *( % )) % γψββ γ γ =z(32) where e* is the solution of (30). Therefore the less efficient types, those with an high cost inefficiency and low demand exerts a lower effort and receives a lower rent than the more efficient types, that is those with low cost inefficiency and high demand29. To implement the optimal regulatory contract the regulator must define an appropriate transfer t( γ ) offered to the firm in order to induce truthful behaviour. This transfer can be intepreted as a function T(.) of the variable z=C/q-(p-A-Bq)/k. The firstorder conditions for truthful revelation are (see appendix A.1): ∂ ∂γ ψγ ∂ ∂γ tzz +− ='( ) 0 (33) This implies that: makes rent extraction difficult, reduces power of incentives and leads to a decrease of effort. This raises marginal cost and reduces output. If quantity and quality are net complements, lower services are desirable, and conversly for net substitutes. Asymmetric information lowers quality when the unregulated monopolist oversupply quality. 28This property amounts to say that as long as the firm's type is getting "better" (more efficicient+higher demand) it is increasingly less probable that it could become even better. 29Type γγ= will receive U=0 and exert low effort; type γ = γ will receive the maximum rent and will exert the effort e* such that ψ '(e*)=q. Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives 20 ∂ ∂ψγ T zz=− − <'( ) 0 (34) Therefore the transfer is a decreasing function of z. Moreover it can be demonstrated (see Laffont and Tirole (1993), appendix A4.3) that differentiating (34) the transfer as a function of z is also a convex function. Since T(z) is convex it can be replaced by the family of its tangents. These tangents represent a menu of contracts that are linear in the observed value of z. t( γ °,z)=t*( γ °)+T'[z-z( γ °)]=t*( γ °)+ψ'(e*( γ °))[z( γ °)-z] (35) where γ ° is a firm's announcement and γ * denotes solutions to the optimal regulatory contract. Thus the transfer function t( γ ) can be replaced by the menu of linear contracts: t( γ ,z)=a( γ )+b( γ )[z( γ )-z] (36) where z( γ ) is the announced value of C/q-[p-A+Bq]/k, z is the observed ex-post value. The transfer is therefore a function of a performance index that subtracts from the realized cost an approximation of the service quality inferred from market data. In other words, the firm is offered a choice in a menu of linear contracts and is rewarded or penalized according to deviations from an index aggregating cost data and service quality data inferred from observation of market price and quantity and from a priori knowledge of the demand function. The menu of linear contracts (36) induces truth telling and the optimal level of effort. The firm is in fact solving the following problem: max *( ) '( *( )) ( ) ( ) ,eUt e z e e γγψ γ γγ ψ °=°+ ° °−+− lq mr (37) which implies that ψ '(e*( γ °))= ψ '(e) and therefore e=e*( γ °) and (∂t*/∂ γ °)+ ψ ''(∂e*/∂ γ °)[z( γ °)-z]+ ψ '(e*( γ °)(∂z/∂ γ °)=0. From (33) it follows that (∂t*/∂ γ °)+ ψ '(e*( γ °)(∂ z/∂ γ °)=0 and then for any γ the firm reveals γ °= γ in order to have z( γ °)=z. Moreover from this follows that the optimal conditions for q and p hold. Therefore the direct revelation contract [t( γ ),c( γ ),p( γ ),q( γ )] can be replaced by a contract such as [t(z, γ ),p(z),q(z)]. That is, the regulator, instead of assigning the direct mechanism by asking to the firm for its type, γ , offers a contract t(z, γ ) that induces the firm to implement the truthful value of C/q-[p-A+Bq]/k and the right level of effort. Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives 21 It is interesting to note that the menu of linear contracts can be alternatively decomposed into a linear sharing of total cost overruns with a coefficient b1( γ )= ψ '(e*( γ ))/q*( γ ) and a linear sharing of overruns in the service quality index with coefficient b2( γ )=ψ'(e*( γ )), or ta b C Cb pBq k pBq k =+ −+ +−+ LNMOQP () () () () () () γγγ γ γγ 12 (38) Moreover it can be demonstrated (see Laffont and Tirole (1993) that: 1) The fixed payment a(z) is a concave, increasing function of the parameters characterizing the power of the incentive schemes, b1 and b2. 2) The parameters characterizing the power of the incentive schemes b1 and b2, are positively correlated over the sample of types. The more "efficient" type , faces a fixed price transfer, with b1=ψ'(e*( γ ))/q=1/q, b2= ψ '(e*( γ ))=1 and a set at the highest level, and is therefore residual claimant for its cost savings and sales increases. The other types will face incentive contracts that are intermediate between the fixed-price and the cost-plus contract. 4. INCENTIVE PROGRAMS IN PRACTICE In this last section we wish to provide some general guidelines for the adoption of incentive schemes in public transit subsidization. We will not deal with the difficult questions regarding the design of "real" incentive contracts30. This is out of the scope of the paper and might be the subject of further research. We prefer here just to define some requirements from the previous treatment of the incentive approach. These criteria might be useful to understand old and current experiments with performance-based public transit subsidization. 4.1. General rules for incentive contract in the public transit sector The publicly managed transit sector typically suffers from high deficits associated with low performance. It is thus quite obvious that incentive subsidization has been repeatedly advocated, and will be increasingly promoted, by local government in charge of financing these deficits. Therefore it is very important to understand, especially for the publicly managed transit firms, what makes an incentive subsidization scheme successful. 30See the paper by Reichelstein (1992) for a rare example of numerical computation of the incentive schemes for a government contract. Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives 22 As long as we are explicitly referring to the theory of incentives as a normative paradigm, we identify conditions for the success of such schemes with the assumptions and normative prescriptions of that theory. In order to be successful, the contract set by a regulator must be voluntarily accepted by the regulated firm. Moreover the regulator should not be able to withdraw his initial offer once it is accepted by the firm. Once these conditions have been met, the regulator and the regulated firm enter in a mechanism design game that can be solved in the way we showed in the previous section. The firm voluntarily accepts the contract as long as the regulator sets it in a way to leave her at least as well as she would have been if she had not accepted it. In order to exclude renegotiation the regulator should have a reputation incentive, i.e. it should be better for him not to reject the contract once accepted by the firm as long as he wishes to have the reputation for respecting agreements. Therefore, as a first set of prescriptions the theory suggests that the regulator: 1) quantifies the firm's reservation level of utility and considers it carefully while defining the contract; 2) invests in a reputation for respecting agreements. In this way the regulator will be commited to a non-renegotiation behaviour and will therefore be able to propose credible contracts, i.e. contracts that may induce truthful revelation. A second general guideline is to give each firm its own contract, i.e. a contract properly tailored to the firm's information. Therefore there should be one contract for each firm. A properly defined contract induces truthful revelation, i.e. solves problems due to asymmetry of information. This implies that it should have a particular structure. We have seen that it might be defined as a transfer, linear in the realized, observed performance index, with a target rent, or fixed price component, plus a penalty, or bonus component, for performance overruns. Moreover we have seen that each contract must be defined as a menu of linear transfers, so that each firm might choose its own incentive transfer out of a menu of such transfers. The firm selects the target fixed price and the corresponding reward (penalty) rate by announcing its performance target. If the regulator properly calibrates these two parameters both conditional on the performace target announced by the firm, he might induce the firm to self-select, i.e. to announce the truthful performance target. In relation to the specific regulation problem faced in the transit sector, we argue that a fundamental concern is quality. As long as transfers can not be made to depend on quality, since it cannot be oserved by the regulator, we have seen that the regulation problem can be represented as a two-dimensional moral hazard and two-dimensional adverse selection model. However we have shown that as long as the service is a search good, i.e. its quality is observed by users before use, this fairly complicated regulation Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives 23 problem might be solved quite easily. As long as the firm has the incentive to boost current sales, consumption is a signal of quality. In this situation, incentives to provide quality might be disconnected from those to reduce cost, if the firm is rewarded also on the basis of sales. We have seen therefore that an important role might be played by observed performance indicators directly linked to consumption. Moreover we have shown that the power of the incentive scheme should be determined by the regulator depending on the a-priori probabilistic knowledge of unobservable cost and demand parameters. High powered schemes should be given to firms with lower productive inefficiency and high demand parameters. This implies that high powered schemes should be dependent on low cost and high sales announced performance. An important question is to identify the more appropriate ex-post observable performance measures. An obvious choice would be to use only indicators that are easy to audit31. An alternative would be to introduce performance assessment on the basis of information provided by a third party (panel of users, firm's input suppliers, ..). These general rules can be immediately applied by a regulator dealing with a private transit firm. On the contrary, some complications arise if the regulator wants to apply these rules to the design of performance-based subsidization for a system of publicly owned transit firms. We will briefly discuss these problems after having presented some of these experiences. 4.2. Some experiments with performance-based transit subsidization Fielding (1992) surveys some of the experiments with performance-based transit subsidization carried out in the United States. All the cases he explicitly refers to were unsuccessful. In Michigan the state transit authority calculated 47 indicators of transit performance. The mean, range and standard deviation for each indicator was calculated and each transit firm rewarded on the basis of its relative status in these rankings. The scheme failed because the use of so many indicators created confusion. The state of Pennsylvania32 was a very interesting example. Four indicators were calculated for each firm to cover the efficiency and effectiveness dimensions: cost per hour, revenue per hour, ridership per hour and the revenue-to-cost ratio. The state awarded 8.33% of the permissable deficit of each firm as a perfomance incentive, if the firm had maintained or improved performance over the previous year on the first three measures. To qualify for the incentive, a firm had to exceed a statewide revenue-to-cost 31See Pedersen (1994) on this regard. 32 See Miller (1980). Public Transit Subsidy: from the Economics of Welfare to the Theory of Incentives 30 Tisato, P., 1992, "User cost minimization and transport subsidy", Economic Letters, 39, pp. 241-247. Tulkens, H., 1986, "The performance approach in public enterprise economics", Annals of Public and Cooperative Economics, 57, pp. 429-443. Turvey, R. and Mohring, H., 1975, "Optimal bus fares", Journal of Transport Economics and Policy, 9, pp. 280-286.