Public Finance Seminar Spring 2013, Professor Yinger

1. Public Finance SeminarSpring 2013, Professor Yinger Bidding and Sorting

2. Bidding and Sorting Class Outline • Bidding • Sorting • Allocative Efficiency and Equity

3. Bidding and Sorting Three Related Questions • How do households select a community in which to live? • =The subject of this class. • How do communities select the levels of local public services and the property tax rate? (= Demand!) • Under what conditions is the community-choice process compatible with the local voting process? (=General Equilibrium)

4. Bidding and Sorting Tiebout • Charles Tiebout argued in a famous 1956 JPE article that people shop for a community, just as they shop for other things. • This process came to be known as “shopping with one’s feet.” • The Tiebout model became very influential both because it identified an important type of behavior to be studied • and because it concluded that the community-choice process is efficient. • Although Tiebout’s model has neither a housing market nor a property tax, many people still accept his efficiency claim, at least to a first approximation.

5. Bidding and Sorting The Consensus Model, Assumptions • 1. Households care about housing, public services, and other goods. • 2. Households fall into distinct income/taste classes. • 3. Households are mobile (i.e. can move costlessly across jurisdictions). • So an equilibrium cannot exist unless all people in a given income/taste class achieve the same level of satisfaction. • 4. All households who live in a jurisdiction receive the same level of public services.

6. Bidding and Sorting The Consensus Model, Assumptions, 2 • 5. Residence in a jurisdiction is a precondition for the receipt of public services there. • 6. Public services are financed through a local property tax. • 7. An urban area has many local jurisdictions, which have fixed boundaries and vary in their local public service quality and property tax rates. • 8. Households are homeowners(or else they are renters and the property tax is shifted fully onto them through rents).

7. Bidding and Sorting Bidding • These assumptions describe a housing market in which households compete for access to the most desirable locations, i.e., those with the best combinations of public services and property tax rates. • This competition takes the form of housing bids, with different bids for different types of household.

8. Bidding and Sorting Bidding, 2 • An analysis of bidding is based on 4 concepts: • Housing is measured in units of housing services, H, which can be thought of as quality-adjusted square feet. • The associated housing price, labeled P, is what a household bids per unit of Hper year. • The rent for a housing unit, R, equals PH. If the unit is an apartment, R = PH is equivalent to the annual rent. • If the unit is owner-occupied, Ris not observed but is implicit. The value of a housing unit, V,is the amount someone would pay to own that unit; it equals the present value of the flow of net rental services associated with ownership or V = PH/r = R/r.

9. Bidding and Sorting The Bid Function • P is the amount a household is willing to pay per unit of H in a jurisdiction with service quality S and property tax rate t: P = P{S, t}. • A bid function is defined for all values of S and t, regardless of whether or not these values are the ones a household actually experiences. • We will have to do some more work to figure out market prices.

10. Bidding and Sorting The Bid Function, 2 • This logic is expressed in the following two figures. • Figure 1 shows how bids (P) change as S changes (holding t constant). • Figure 2 shows how bids change as t changes (holding S constant) • These curves hint at the idea that housing prices reflect S and t but we are not quite there yet.

11. Bidding and Sorting Figure 1: Housing Bids as a Function of Public Service Quality(Holding the Property Tax Rate Constant)

12. Bidding and Sorting Figure 2: Housing Bids as a Function of the Property Tax Rate(Holding Public Service Quality Constant)

13. Bidding and Sorting Sorting • If all household are alike, then Figures 1 and 2 describe market outcomes; in equilibrium housing prices will adjust to exactly compensate households who end up in low-S or high-t jurisdictions. • But obviously households are not all alike, and different types of households must sort across jurisdictions.

14. Bidding and Sorting Sorting and Slopes • The key idea in the consensus model is that households sort according to the steepness of their bid functions. • The slope is ∂P/∂S; a steeper slope corresponds to a greater willingness to pay (WTP) for an increment in S. • Housing sellers prefer to sell to the highest bidder, so a steeper slope wins where S is higher.

15. Bidding and Sorting Figure 3: Consensus Bidding and Sorting

16. Bidding and Sorting The Price Envelope • In Figure 3, the observed market price function is the envelope of the underlying bid functions, say PE. • This function shows how S and t show up in housing prices. • This phenomenon is known as capitalization, because it has to do with the impact of annual flows S and t ) on the value of a capital asset (a house). • As we will see, many studies estimate capitalization!

17. Bidding and Sorting Sorting and Bid-Function Heights • One subtle point in Figure 3 is that the heights of the bid functions adjust so that each type of household has enough room. • To get the logic right, start with a point at which the bid functions of two groups intersect—i.e., their heights are the same. • From this starting point, it is obvious that the group with the steeper bid function bids more where S is higher. • It is impossible to shift the heights around so that (a) both groups live somewhere and (b) the group with the flatter slope lives where S is higher.

18. Bidding and Sorting Sorting and Empirical Research • Figure 3 has 2 key implications for empirical work. • Any estimate of the impact of S on P (or on R or V) blends willingness to pay (movement along a bid function) and sorting (shifting across bid functions). • In Figure 3, for example, (P3– P1) does not measure any group’s WTP for S3 versus S1. • The relationship between S and P is very unlikely to be linear (or even log-linear).

19. Bidding and Sorting The Marginal Household • When examining values for S (in the data), the difference in bids can be interpreted as the valuation of the marginal household, i.e., the household just indifferent between the two jurisdictions. • Some scholars have introduced this approach into formal models with a continuous distribution of household preferences—and even estimated these models (more later). • But a focus on the marginal household does not help interpret the empirical result of most studies.

20. Bidding and Sorting Normal Sorting • Under normal circumstances, higher-income households will pay more for an increment in S. See Figure 4, where MB = MWTP (and a 2 subscript indicates high-income). • So high-income households will normally win the competition in high-S jurisdictions. • Low-income households win the competition in low-S jurisdictions because they are willing to accept low H, e.g. by doubling up.

21. Bidding and Sorting Figure 4: The Demand for Local Public Services D2 = MB2

22. Bidding and Sorting Normal Sorting, 2 • The formal condition for normal sorting is that the ratio of the income and elasticities of demand for S must exceed the income elasticity of demand for H . • Note that αmatters because a household’s willingness to pay for S (and hence its bid) is spread out over the number of units of H it buys.

23. Bidding and Sorting Sorting and Inequality • Sorting results in a system of local governments in which some jurisdictions are much wealthier than others. • Moreover, as discussed earlier in the class, the cost of public services is often linked to poverty. • The overall result is a federal system in which both resources and costs are unevenly distributed—and in which higher-income people receive higher levels of S. • The key normative tradeoff: community choice versus equality of opportunity.

24. Bidding and Sorting Heterogeneity Within a Jurisdiction • Sorting implies a tendency for jurisdictions to be homogeneous by income. • But this homogeneity is not complete: • Other factors influence demand. • Heterogeneous communities arise where bid functions cross. See Figure 3. Many household types could live in a large jurisdiction.

25. Bidding and Sorting Sorting and Tax Rates • Figure 3 holds t constant. • In fact, t does not affect sorting. • Any household is willing to pay $1 to avoid $1 of property taxes (or to bid 1% more in a location where t is 1% lower). • Sorting only involves S. • Nevertheless, sorting is sometimes shown with net bids that reflect both S and t. See Figure 5.

26. Bidding and Sorting Figure 5: Consensus Bidding and Sorting Net of Taxes

27. Bidding and Sorting The Hamilton Approach • Bruce Hamilton (Urban Studies 1975) developed a model with three additional assumptions: • Housing supply is elastic (presumably by movement in jurisdiction’s boundaries). • Zoning is set at exactly the optimal level of housing for the residents of a jurisdiction. • Government services are produced at a constant cost per household.

28. Bidding and Sorting Hamilton, 2 • The striking implication of the Hamilton assumptions is that capitalization disappears. See Figure 6. • Everyone ends up in their most-preferred jurisdiction, so nobody bids up the price in any other jurisdiction. • This prediction (no capitalization) is rejected by all the evidence (to be covered in future classes).

29. Bidding and Sorting Figure 6: Hamilton Bidding and Sorting

30. Bidding and Sorting Is a Federal System Efficient? • Tiebout (with no housing or property tax) said picking a community is like shopping for a shirt and is therefore efficient (in the allocative sense). • This result is replicated with a housing market and a property tax under the Hamilton assumptions. • These assumptions are extreme and the model is rejected by the evidence.

31. Bidding and Sorting Sources of Inefficiency • 1. Heterogeneity • Heterogeneity leads to inefficient levels of local public services. • Outcomes are determined by the median voter; voters with different preferences experience “dead-weight losses” compared with having their own jurisdiction. • See Figure 7.

32. Bidding and Sorting Figure 7: Inefficiency Due to Heterogeneity

33. Bidding and Sorting Heterogeneity in Services? • The consensus model assumes that all households in a jurisdiction receive the same services. • This is not true; higher-income neighborhoods have better police protection and probably better elementary schools, for example. • This eliminates some of the inefficiency in Figure 7—but adds to inequality. • This topic is poorly understood; research is needed!

34. Bidding and Sorting Sources of Inefficiency • 2. The Property Tax • Producers of housing base their decisions on P, whereas buyers respond to P(1 + t/r), (which, as we will see is constant across jurisdictions). • This introduces a so-called “tax wedge” between producer and consumer decisions, which leads to under-consumption of housing.

35. Bidding and Sorting Hamilton and Inefficiency • These two sources of inefficiency disappear in Hamilton’s model: • Boundaries adjust so that all jurisdictions are homogeneous (despite extensive evidence that boundaries do not change for this reason). • Zoning is set so that housing consumption is optimal (despite the incentives of residents to manipulate zoning).

36. Bidding and Sorting Conclusions on Efficiency • The Hamilton model shows how extreme the assumptions must be to generate an efficient outcome. • Nevertheless, most scholars defend our federal system as efficient, • Instead of identifying policies, such as intergovernmental aid programs, to improve its efficiency.