blic Economics

1. MSc Public Economics 2008/9http://darp.lse.ac.uk/ec426 Fiscal Governance: Local Public Goods Aim of this lecture Local public goods How are jurisdictions determined? Should there be public or private provision? V103 http://darp.lse.ac.uk/presentations/ec426/FiscalAdministration.ppt Leila: 6674 6300 (or 7437 or 6460). A31 Audio Visual Unit DESMOND Mr George 6271 g.desmond@lse.ac.uk FLOOD Mr Ray 7694 r.flood@lse.ac.uk GALE Mr Adam 6520 a.gale@lse.ac.uk HEAD Mr Chris 6417 c.head@lse.ac.uk Aim of this lecture Local public goods How are jurisdictions determined? Should there be public or private provision? V103 http://darp.lse.ac.uk/presentations/ec426/FiscalAdministration.ppt Leila: 6674 6300 (or 7437 or 6460). A31 Audio Visual Unit DESMOND Mr George 6271 g.desmond@lse.ac.uk FLOOD Mr Ray 7694 r.flood@lse.ac.uk GALE Mr Adam 6520 a.gale@lse.ac.uk HEAD Mr Chris 6417 c.head@lse.ac.uk

2. Overview...

3. Public goods and the public sector Public and semi-public goods provide a challenge how to ensure efficient allocation how to reveal willingness to pay should they be provided in private or public sector? There are some standard answers 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?

4. Tiebout’s intuition Up to now the economy as a whole has been fixed no question of governance nor of “jurisdiction” of the fiscal system Introduce the possibility of multiple jurisdictions 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) Tiebout: “Just as the consumer may be visualised as walking to a private market place to buy his goods we place him in the position of walking to a community where the prices (taxes) of community services are set “Both trips take the consumer to the market. “ There is no way in which the consumer can avoid revealing his preferences in a spatial economy” Banzhaf-Walsh: Using a locational equilibrium model, we derive formal tests of his premise. The model predicts increased population density in neighborhoods experiencing exogenous improvements in public goods and, for large improvements, increased relative mean incomes. We test these hypotheses in the context of changing air quality. Our results provide strong empirical support for the notion that households “vote with their feet” for environmental quality.Tiebout: “Just as the consumer may be visualised as walking to a private market place to buy his goods we place him in the position of walking to a community where the prices (taxes) of community services are set “Both trips take the consumer to the market. “ There is no way in which the consumer can avoid revealing his preferences in a spatial economy” Banzhaf-Walsh: Using a locational equilibrium model, we derive formal tests of his premise. The model predicts increased population density in neighborhoods experiencing exogenous improvements in public goods and, for large improvements, increased relative mean incomes. We test these hypotheses in the context of changing air quality. Our results provide strong empirical support for the notion that households “vote with their feet” for environmental quality.

5. Tiebout: questions What type of equilibrium? Depends upon the exact specification of the mechanism that is supposed to be operating How are communities determined? Equilibrium concepts that take into account the endogenous structure of communities How does the economy work out of equilibrium? Tiebout suggested a migration mechanism Will there be an efficient outcome from the Tiebout process? Is this more than just a demand-revealing mechanism?

6. Overview...

7. 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)

8. 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 Exclusion: no exclusion of individual services no specialised “packages” Exclusion: no exclusion of individual services no specialised “packages”

9. Clubs: model of production A two good economy measure values in terms of private good 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: 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

10. Clubs: production possibilities This is the diagram for the economy as a wholeThis is the diagram for the economy as a whole

11. 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 budget constraint is: x + C(z, s) / s = y So the problem becomes: maximise U(y ? C(z, s) / s , z) Differentiate with respect to z: 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

12. Club model: individual’s equilibrium This is the diagram for the individual This is the diagram for the individual

13. Clubs: basic results Optimal amount of club good must satisfy: Uz(x, z) Cz(z, s) = s ---- 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

14. 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

15. Overview...

16. Modelling local public goods Focus on a collection of communities think of them as tax jurisdictions each jurisdiction works a bit like a club 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 have preferences over private, public goods migration mechanism: vote with their feet What would the outcome look like?

17. Stiglitz model of a community Assume simple linear technology no congestion costs MRT in community is set at 1 total output is given by Q = xs + z 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 All public: (f (s), 0) All private: (0, f (s) / s ) Consider the optimum for a given community size

18. Stiglitz model: single s

19. 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

20. Stiglitz model: multiple s

21. Stiglitz model: types of solution

22. Stiglitz model: questions Why the nonconvexity? 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 Homogenous consumers? 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…

23. Modified model: multiple s

24. Heterogeneous citizens A simple example to illustrate the point: three types of public goods two types of citizen Preferences are given by citizen type 1: U(x, z1 + kz3) where 0 < ? < 1 citizen type 2: U(x, z2 + kz3) If the two types are separated: group i specialises in public good type i If the two are together: may be economies of scale in the production of good 3 particularly important if ? 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 Two of the goods are special to the two types; third good is common Good 3 is attractive to both groups But it is less attractive than good i to type i, i = 1, 2Two of the goods are special to the two types; third good is common Good 3 is attractive to both groups But it is less attractive than good i to type i, i = 1, 2

25. Equilibrium: the core Core: set of unblocked allocations a fundamental solution concept for equilibrium for private goods core is non-empty any competitive equilibrium must lie in the core Core of an economy with public goods existence theorem does not necessarily apply equilibrium mechanisms different The core may be empty unless 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

26. Overview...

27. Basic questions on equilibrium What type of choice? Fixed number of jurisdictions? Freely set up jurisdictions (prairie model)? Fixed overall population Single type of public good What type of mechanism? usually assume simple migration people follow the money Will equilibrium be efficient?

28. Local public goods: fixed number of communities Assume that there are just two communities Overall size is given at N s1 + s2 = N Allow for free choice between communities Two possibilities of equilibrium (1) Where only one community is settled: u(N) ? 0 (2) Where both communities are settled: u(s1) = u(s2)

29. A model of social welfare Assume Benthamite objective function: 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) 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 we also have to take account of corners interior maximum may not be unique Need to derive utility-possibility set from equilibrium conditions

30. 2-jurisdiction U-possibility (1)

31. 2-jurisdiction U-possibility (2)

32. 2-jurisdiction U-possibility (3)

33. Migration mechanism Will migration “work”? yields stable equilibria? yields efficient equilibria? examine four cases combined diagram facilitates interpretation 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 Only extreme cases are stable Only interior case is efficient Other cases show that multiple equilibria do not necessarily involve extremes

34. Pareto-efficient: extreme equilibria Involves substantial economies of scale Get multiple equilibria Only extreme cases are stable Only extreme cases are efficient Involves substantial economies of scale Get multiple equilibria Only extreme cases are stable Only extreme cases are efficient

35. 3 Equilibria: inefficient extremes also involves economies of scale Only extreme cases are stable Only interior case is efficient also involves economies of scale Only extreme cases are stable Only interior case is efficient

36. 3 interior eqa: efficient equality

37. 5 Equilibria: inefficient equality

38. Equilibria May be multiple equilibria alternation between stable and unstable equilibria two-community and single community equilibria may coexist stable equilibria may be inefficient An equilibrium is bound to exist if if land values play no role everyone is identical the ?(·) functions are continuous Where individuals differ, will equilibrium exist? Need to examine specific models…

39. Overview...

40. 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 Individuals will not agree on appropriate output and contributions: They may be compelled to contribute at tax rates that seem to be unfair Involuntary contributions: can overcome the free-rider problem do not resolve the conflict-of-interest problem Voluntarism 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?

41. An illustrative model To address “public or private?” question construct a model of public good production model two provision modes allow Tiebout style choice between two modes 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 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… s = 0, total inflexibility s = 8, perfect substitutess = 0, total inflexibility s = 8, perfect substitutes

42. 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} cannot be an individual income tax (would imply lump-sum taxation) chosen tax rate based on what the median voter would select Income ratio ymedian/Y decreases with greater inequality t decreases with b: so it increases with sigma t increases in inequality if s < 1 decreases in inequality if s > 1 cannot be an individual income tax (would imply lump-sum taxation) chosen tax rate based on what the median voter would select Income ratio ymedian/Y decreases with greater inequality t decreases with b: so it increases with sigma t increases in inequality if s < 1 decreases in inequality if s > 1

43. Provision: endogenous choice Suppose two communities exist simultaneously people can “choose” public or private use Tiebout model to address choice between communities Three possible types of equilibrium: 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)

44. Which mode of provision? Results for three types Type 1: voluntary provision only equilibrium always exists Type 2: coercive provision only 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

45. Mode of provision – extension Extend the Glomm and Lagunoff (1998) analysis a dynamic economy congestion costs wealth accumulation Glomm and Lagunoff (1999) Individuals make repeated sequential decisions 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

46. A fundamental trade-off? Consider trade-off between fundamental effects of taxation and spending policies provision of public goods redistributive objectives Analyse using a two-community economy: Tiebout mechanism interpreted as unrestricted migration between jurisdictions Kessler and Lülfesmann (2005) Individuals differ 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

47. A fundamental trade-off Individuals make a selection from this trade-off by choice of jurisdiction through migration by the voting mechanism Kessler and Lülfesmann (2005) show that Tiebout-like sorting equilibria exist 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

48. Decentralisation? Is decentralisation a good idea? at the heart of fiscal governance debate contrast two types of model 1 Tiebout argument positive case for decentralisation revealed preference for public goods 2 Tax competition 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 )

49. Decentralisation: recommendations 1 Tiebout argument for decentralisation allow sorting by migration (but will this lead to efficient equilibrium?) 2 Tax competition against decentralisation if governments agree common tax rate on capital can get efficient public-good 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

50. 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.