Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
16 March2009 Frank Cowell: EC426 Public Economics MSc Public Economics 2008/9 http://darp.lse.ac.uk/ec426 Fiscal Governance: Local Public Goods Frank Cowell: EC426 Public Economics Fiscal governance Overview... Introduction The basic intuition Clubs Local public goods Equilibrium Mode of provision Frank Cowell: EC426 Public Economics Public goods and the public sector Public and semi-public goods provide a challenge There are some standard answers how to ensure efficient allocation how to reveal willingness to pay should they be provided in private or public sector? only work for small communities? special mechanisms Here examine an alternative approach redefine the problem focus on the way people make choices… what kind of fiscal environment do they want? Frank Cowell: EC426 Public Economics Tiebout’s intuition Up to now the economy as a whole has been fixed Introduce the possibility of multiple jurisdictions no question of governance nor of “jurisdiction” of the fiscal system affects basket of goods provided zone in which it is possible to determine taxes crucial point: relationship amongst jurisdictions Tiebout (1956) virtually invented our topic changed context of the public-goods argument a new role for consumer choice: voting with your feet made an analogy with a private market place modern evidence that this choice mechanism works (Banzhaf and Walsh 2008) Frank Cowell: EC426 Public Economics Tiebout: questions What type of equilibrium? How are communities determined? Equilibrium concepts that take into account the endogenous structure of communities How does the economy work out of equilibrium? Depends upon the exact specification of the mechanism that is supposed to be operating Tiebout suggested a migration mechanism Will there be an efficient outcome from the Tiebout process? Is this more than just a demand-revealing mechanism? Frank Cowell: EC426 Public Economics Fiscal governance Overview... Introduction An extension of the public goods idea Clubs Local public goods Equilibrium Mode of provision Frank Cowell: EC426 Public Economics Endogenous structure The endogeneity of the community gives a nice clue Think of each community as privately determined The public good issues remain within each community But free choice between communities This suggests an analogy with the theory of clubs Originally developed by Buchanan (1965) Combines public and private elements See also Cornes and Sandler (1996) Frank Cowell: EC426 Public Economics Clubs: excludability and rivalness The good is like a public good within the club Excludability: club good is restricted to its members people can be excluded from membership can charge a membership fee membership entitles you to full consumption of the good without further charge Rivalness: could we assume that club good is non-rival? for realism, allow for the possibility of congestion cost of providing the club good may rise with the membership same may also be true of the marginal cost Frank Cowell: EC426 Public Economics Clubs: model of production A two good economy Notation: x – amount of private good, z – amount of club good, s – size of the of club C(z, s) – cost of producing the club good Standard assumptions about cost: measure values in terms of private good Cz(z, s) > 0 – MC of club good is positive Czz(z, s) 0 – MC of club good is nondecreasing in z Cs(z, s) 0 – possibility of congestion Examine this in an economy with fixed total output equivalent to assuming a given amount of income y Frank Cowell: EC426 Public Economics Clubs: production possibilities Club good versus total private good production frontier sx marginal rate of transformation xs + C(z, s) = sy curvature comes from increasing marginal cost of z z d (sx) – ——— = Cz(z, s) dz Frank Cowell: EC426 Public Economics Clubs: individual optimisation Use this in a model of individual choice Each individual has the utility function U(x, z) Assume that club costs are divided equally: C(z, s) / s So the problem becomes: maximise U(y C(z, s) / s , z) Differentiate with respect to z: so the budget constraint is: x + C(z, s) / s ≤ y 1 — Cz(z, s) Ux(x, z) + Uz(x, z) = 0 s Differentiate with respect to s: 1 — [C(z, s) s Cs(z, s)] Ux(x, z) = 0 s2 Frank Cowell: EC426 Public Economics Club model: individual’s equilibrium boundary of individual feasible set individual IC x equilibrium x + C(z, s) / s = y U(x, z) = const curvature from increasing MC comes from Czz > 0 A Cz(z, s) / s = Uz(x, z) / Ux(x, z) z Frank Cowell: EC426 Public Economics Clubs: basic results Optimal amount of club good must satisfy: Cz(z, s) = s Uz(x, z) ──── Ux(x, z) MRT= S MRS just as for public goods The optimal membership must satisfy: Cs(z, s) = C(z, s) / s MC of providing services = Access cost Frank Cowell: EC426 Public Economics Clubs: summary Model is a simple extension of classic public goods Novelty is to introduce a type of partial exclusion mechanism In the standard case we get two easily interpreted marginalist rules: On the level of provision of the club good On the access conditions to the club Frank Cowell: EC426 Public Economics Fiscal governance Overview... Introduction Using the club approach to model local jurisdictions Clubs Local public goods Equilibrium Mode of provision Frank Cowell: EC426 Public Economics Modelling local public goods Focus on a collection of communities Affinity with the club model an excludable non-rival good no exclusion within the jurisdiction local public good and private good may / may not be perfect substitutes there may or may not be congestion may also need to consider overall size of the “economy” People choose jurisdiction in the same way they choose a club think of them as tax jurisdictions each jurisdiction works a bit like a club have preferences over private, public goods migration mechanism: vote with their feet What would the outcome look like? Frank Cowell: EC426 Public Economics Stiglitz model of a community Assume simple linear technology Assume production depends on the size of the community: Community subject to diminishing returns in population Q = f (s) f is an increasing concave function Take tradeoff in (public,private)-space For a given size of community this is linear no congestion costs MRT in community is set at 1 total output is given by Q = xs + z All public: (f (s), 0) All private: (0, f (s) / s ) Consider the optimum for a given community size Frank Cowell: EC426 Public Economics Stiglitz model: single s max amount available of private good max amount available of local public good x linear tradeoff between two types of goods solution for given s note that this solution is conditional on a given s f(s)/s U(x, z) = const A f(s) z Frank Cowell: EC426 Public Economics Stiglitz model: solution Previous diagram is a “short-run” model Optimum determined in usual way MRS = 1 / s MRT = S MRS =1 However we ought to consider the possibility of multiple jurisdictions Each one may differ in size Overall production possibility determined as an envelope Frank Cowell: EC426 Public Economics Stiglitz model: multiple s linear tradeoff for low s linear tradeoff for medium s linear tradeoff for high s x the envelope for s {low, middle, high} the envelope for s [0, ∞) feasible set U(x, z) = const solution possibilities with just 3 sizes of jurisdiction possibilities with arbitrarily A many sizes of jurisdiction note the fundamental z nonconvexity of the problem Frank Cowell: EC426 Public Economics x Stiglitz model: types of solution x interior solution solution – no public good A solution – no private goods multiple solutions A z x x A z A B Frank Cowell: EC426 Public Economics Stiglitz model: questions Why the nonconvexity? Homogenous consumers? Follows from relationship between size and provision of goods An artefact of special assumptions? What if we used a conventional club-good model? Introduce rising marginal cost again Suppose people differ in their taste for public goods Will the demand-revelation mechanism work? Will an equilibrium always exist? Deal with each of these in turn… Frank Cowell: EC426 Public Economics Modified model: multiple s nonlinear tradeoff for low s nonlinear tradeoff for medium s x nonlinear tradeoff for high s the envelope for s {low, middle, high} shape is the same as for the club model clearly attainable set could be nonconvex, even with Czz > 0 z Frank Cowell: EC426 Public Economics Heterogeneous citizens A simple example to illustrate the point: Preferences are given by group i specialises in public good type i If the two are together: citizen type 1: U(x, z1 + kz3) where 0 < κ < 1 citizen type 2: U(x, z2 + kz3) If the two types are separated: three types of public goods two types of citizen may be economies of scale in the production of good 3 particularly important if κ is close to 1 So free allocation via migration may not be efficient analogous to the market failure of pure private goods where there is increasing returns Frank Cowell: EC426 Public Economics Equilibrium: the core Core: set of unblocked allocations Core of an economy with public goods existence theorem does not necessarily apply equilibrium mechanisms different The core may be empty unless a fundamental solution concept for equilibrium for private goods core is non-empty any competitive equilibrium must lie in the core equal sharing is enforced (Pauly 1970 ) all clubs are of uniform size (Pauly 1970 ) if individuals have the same tastes (Stiglitz 1977) Need to examine nature of Tiebout equilibrium more closely Frank Cowell: EC426 Public Economics Fiscal governance Overview... Introduction Using the club approach to model local jurisdictions Clubs Local public goods Equilibrium and Optimality Mode of provision Frank Cowell: EC426 Public Economics Basic questions on equilibrium What type of choice? What type of mechanism? Fixed number of jurisdictions? Freely set up jurisdictions (prairie model)? Fixed overall population Single type of public good usually assume simple migration people follow the money Will equilibrium be efficient? Frank Cowell: EC426 Public Economics Local public goods: fixed number of communities Assume that there are just two communities Allow for free choice between communities Two possibilities of equilibrium (1) Where only one community is settled: Overall size is given at N s1 + s2 = N u(N) 0 (2) Where both communities are settled: u(s1) = u(s2) Frank Cowell: EC426 Public Economics A model of social welfare Assume Benthamite objective function: For an interior welfare maximum the optimal size where: ∂W —— = 0 ∂ s1 which implies s1u'(s1) + u(s1) – [N – s1] u'(N – s1) – u(N – s1) = 0 But two complications Per-person utility is same for everyone in a given community of size s: u(s) Welfare is weighted sum of per-person utility in each community W = s1u(s1) + s2u(s2) = s1u(s1) + [N – s1] u(N – s1) we also have to take account of corners interior maximum may not be unique Need to derive utility-possibility set from equilibrium conditions Frank Cowell: EC426 Public Economics 2-jurisdiction U-possibility (1) utility in community 1 s2u2 utility in community 2 equality ray utility possibility set welfare contours unique interior welfare maximum two communities settled s1u1 Frank Cowell: EC426 Public Economics 2-jurisdiction U-possibility (2) utility possibility set s2u2 welfare contours two extreme welfare maxima only one community settled s1u1 Frank Cowell: EC426 Public Economics 2-jurisdiction U-possibility (3) utility possibility set s2u2 welfare contours two interior welfare maxima two communities settled s1u1 Frank Cowell: EC426 Public Economics Migration mechanism Will migration “work”? First case involves substantial economies of scale Get multiple equilibria Only extreme cases are stable Only extreme cases are efficient Second case also involves economies of scale yields stable equilibria? yields efficient equilibria? examine four cases combined diagram facilitates interpretation Only extreme cases are stable Only interior case is efficient Other cases show that multiple equilibria do not necessarily involve extremes Frank Cowell: EC426 Public Economics Pareto-efficient: extreme equilibria u1 u2 u(s2) u(s1) stable stable unstable s1 rising s1 falling s1 Frank Cowell: EC426 Public Economics 3 Equilibria: inefficient extremes u1 u2 u(s2) u(s1) unstable stable stable s1 rising s1 falling s1 Frank Cowell: EC426 Public Economics 3 interior eqa: efficient equality u1 u2 u(s2) u(s1) unstable stable stable s1 rising s1 falling s1 Frank Cowell: EC426 Public Economics 5 Equilibria: inefficient equality u1 u2 stable stable unstable unstable stable u(s2) s1 rising u(s1) s1 falling s1 Frank Cowell: EC426 Public Economics Equilibria May be multiple equilibria An equilibrium is bound to exist if alternation between stable and unstable equilibria two-community and single community equilibria may coexist stable equilibria may be inefficient if land values play no role everyone is identical the υ(·) functions are continuous Where individuals differ, will equilibrium exist? Need to examine specific models… Frank Cowell: EC426 Public Economics Fiscal governance Overview... Introduction Coercion or voluntarism? Clubs Local public goods Equilibrium Mode of provision Frank Cowell: EC426 Public Economics Role of the state Should the provision of public goods be based on voluntarism, or coercion? Local public goods models suggest more than one paradigm With heterogeneous individuals there is a conflict of interests Involuntary contributions: can overcome the free-rider problem do not resolve the conflict-of-interest problem Voluntarism Individuals will not agree on appropriate output and contributions: They may be compelled to contribute at tax rates that seem to be unfair avoids “unfairness” from compulsion may not be consistent with the absence of free riding Given the Tiebout adjustment mechanism, will one of these be eliminated? Frank Cowell: EC426 Public Economics An illustrative model To address “public or private?” question Utility of individual i u(xi, z) = [xi1–s + z1–s] / [1 – s ] private good xi public good z s is nonnegative elasticity of substitution Production construct a model of public good production model two provision modes allow Tiebout style choice between two modes private incomes yi are exogenous public goods produced from “contributions” of private good ci= yi – xi MRT = 1, so amount of public good is: z = Si ci Provision modes treated as two different models of a community… Frank Cowell: EC426 Public Economics Two provision modes Coercive provision: public good provided by taxation tax based on community aggregate income Y := Si yi so i has to contribute ci = tY tax rate t is selected by voting chosen tax rate: t = [1 + [ymedian/Y]b]1, b := [1 – s]/s Voluntary provision: based on individual contributions Like “conformity model” in tax compliance (Bergstrom et al 1986) optimal contribution decision depends on income ci = max {yi – Y / n*, 0}, n* := 1 + #{cj > 0} Frank Cowell: EC426 Public Economics Provision: endogenous choice Suppose two communities exist simultaneously Three possible types of equilibrium: people can “choose” public or private use Tiebout model to address choice between communities all individuals migrate to the voluntary-provision community all individuals migrate to the coercive-provision community ‘interior’ equilibria: collections of individuals in both communities The relevant type depends on degree of substitution (parameter s) income distribution see Glomm and Lagunoff (1998) Frank Cowell: EC426 Public Economics Which mode of provision? Results for three types Type 1: voluntary provision only Type 2: coercive provision only equilibrium always exists sometimes exists need conditions on preferences and income distribution Type-3: interior (mixed-mode) equilibria: exists if income is sufficiently polarised richer individuals migrate to the community with voluntary provision poorer individuals reside in the public provision community Frank Cowell: EC426 Public Economics Mode of provision – extension Extend the Glomm and Lagunoff (1998) analysis Individuals make repeated sequential decisions a dynamic economy congestion costs wealth accumulation Glomm and Lagunoff (1999) which community to inhabit? coercive community? voluntarist community? The essence of the static model persists: maybe voluntary provision exists as a within-period Nash equilibrium outcome but if there is convergence of the wealth distribution… …then coercive mechanism is selected in the perfect equilibrium result may not hold if there is no wealth convergence in the long run Frank Cowell: EC426 Public Economics A fundamental trade-off? Consider trade-off between fundamental effects of taxation and spending policies Analyse using a two-community economy: Tiebout mechanism interpreted as unrestricted migration between jurisdictions Kessler and Lülfesmann (2005) Individuals differ provision of public goods redistributive objectives in their incomes in their tastes for a local public good In each jurisdiction amount of public services determined by inhabitants (majority vote) local spending financed by linear income tax specific to the jurisdiction Frank Cowell: EC426 Public Economics A fundamental trade-off Individuals make a selection from this trade-off Kessler and Lülfesmann (2005) show that Tiebout-like sorting equilibria exist by choice of jurisdiction through migration by the voting mechanism if the spread in tastes is very large almost perfect sorting by preferences otherwise, a partial sorting prevails… …stratification into rich, poor communities is more pronounced Existence of sorting equilibria is robust independent of whether individuals can relocate after voting Frank Cowell: EC426 Public Economics Decentralisation? Is decentralisation a good idea? 1 Tiebout argument positive case for decentralisation revealed preference for public goods 2 Tax competition at the heart of fiscal governance debate contrast two types of model negative case against decentralisation intergovernmental competition relies on distortionary tax inefficient outcome? Main question in an economy with mobile, heterogeneous consumers… …where public goods financed by distortionary tax on mobile capital is decentralization desirable? see Brueckner (2004 ) Frank Cowell: EC426 Public Economics Decentralisation: recommendations 1 Tiebout argument for decentralisation 2 Tax competition against decentralisation allow sorting by migration (but will this lead to efficient equilibrium?) if governments agree common tax rate on capital can get efficient publicgood level remove fiscal autonomy of subnational governments a uniform tax on capital to provide a common public good national capital tax effectively lump sum: eliminate distortion Which dominates? Brueckner (2004 ) uses numerical simulation given dispersion of preferences… gains from Tiebout sorting are likely to outweigh the loss from the capital-tax distortions otherwise decentralization may be undesirable Frank Cowell: EC426 Public Economics References Banzhaf, H. S. and Walsh, R. P. (2008) “Do People Vote with Their Feet? An Empirical Test of Tiebout’s Mechanism,” American Economic Review, 98, 843-863 Bergstrom, T., L. Blume, and H. Varian (1986) “On the private provision of public goods,” Journal of Public Economics 29, 25-49. Brueckner, J. (2004 ) “Fiscal Decentralization with Distortionary Taxation: Tiebout vs. Tax Competition,” International Tax and Public Finance, 11, 133-153} Buchanan, J. M. (1965) “An economic theory of clubs.” Economica, 32, 1-14. Cornes, R. and T. Sandler (1996). The Theory of Externalities, Public Goods and Club Goods (second ed.). Cambridge University Press. Glomm, G. and R. Lagunoff (1998) “A Tiebout theory of public vs private provision of collective goods,” Journal of Public Economics, 68 , 91-112. Glomm, G. and R. Lagunoff (1999) “A dynamic Tiebout theory of voluntary vs involuntary provision of public goods,” Review of Economic Studies, 66, 659-677. Kessler, A. S. and C. Lülfesmann (2005) “Tiebout and redistribution in a model of residential and political choice,” Journal of Public Economics, 89, 501.528. Pauly, M. V. (1970) “Optimality, .public. goods and local governments: A general theoretical analysis,” Journal of Political Economy, 78, 572-585. Stiglitz, J. E. (1977) “The theory of local public goods, “in M. S. Feldstein and R. P. Inman (Eds.), The Economics of Public Services. London, UK: Macmillan. Tiebout, C. M. (1956) “A pure theory of local expenditures,” Journal of Political Economy, 64, 416-424.