Public Finance Seminar Spring 2013, Professor Yinger

1. Public Finance SeminarSpring 2013, Professor Yinger Demand for Public Services: The Median Voter and Other Approaches

2. Demand for Public Services Class Outline • Household Demand for Public Services • The Median Voter Model • Estimating Household Demand

3. Demand for Public Services The Starting Point • An household’s demand for local public services, like its demand for private goods, depends on its income, the price of the services, the price of alternatives, and its preferences. • But with 2 big twists: • There is no market price. • The demand for services can be expressed in several different ways:

4. Demand for Public Services Lack of a Market Price • Most public services are funded by taxes, not prices. • Hence, the “price” is defined as the cost of an additional unit of service • And this price depends on the tax system. • Tax Price = How much would the individual pay if taxes were raised enough to provide one more unit of the service to everyone in the jurisdiction. • A more formal definition will be derived later.

5. Demand for Public Services How Is Demand Revealed? • The demand for services can be expressed: • Through voting (today’s class) • Through bidding for housing and choice of a community (the subject of later classes) • Through the purchase of private substitutes, such as private schools, security guards, or access to a gated community (not covered in any class)

6. Demand for Public Services Household Demand for Public Services • A Household’s Budget Constraint • Income (Y) must be spent on housing (H with price P), property taxes (tV=tPH/r) and other stuff (Z with price 1):

7. Demand for Public Services The Community Budget Constraint • In a community, sending per household (E) to achieve the desired service level (S) must equal property tax revenue per household (t multiplied by average V ). • We will skip state aid and other local revenue sources for now.

8. Demand for Public Services Solving for Tax Price, 1 • Solve the community budget constraint for t: • Substitute into the household budget constraint:

9. Demand for Public Services Solving for Tax Price, 2 • Tax price is the cost of one more unit of S, i.e., the derivative of the household budget constraint with respect to S, or, • where MCis the resource cost of another unit of S, and the ratio of V to average V is the tax share.

10. Demand for Public Services Estimating Household Demand • With TP defined, we can write down a household demand function: • The problem: How to estimate this function? • One answer: through surveys.

11. Demand for Public Services Survey Studies of Household Demand • Approach 1: Surveys of voting on a referendum. • The demand function defines a latent variable, which can be studied with a discrete-choice model, with Y and TPas explanatory variables. • This approach also can be applied to a survey of preferences for increasing, decreasing, or not changing spending.

12. Demand for Public Services Survey Studies of Household Demand, 2 • Approach 2: Surveys of spending preferences: “How much would you like to spend?” • Use a multiplicative form with desired spending (= (S)(AC)) as the dependent variable (assuming AC=MC):

13. Demand for Public Services The Median Voter Theorem • Although household voting is not observed, the outcomes of voting in a community are easy to observe—on referenda or in the form of spending or service levels. • The median voter model provides a way to estimate a demand model at the community level—where the data are!

14. Demand for Public Services Bergstrom and Goodman • This famous paper (AER 1973) starts with an obvious point (the voter in the middle of the demand distribution is always on the winning side) • It then adds assumptions about the structure of demand and taxes (that demand depends on Y and TP, that there is a property tax, and that the demand for H is a function of Y) • And shows that the voting outcome in a community is determined by the voter with the median Y and median TP.

15. Demand for Public Services Bergstrom and Goodman, 2 • In symbols: • This was revolutionary because it specified the demand for S using data just on median Y and median TP, which are readily observed. • Scholars can proceed “as if” voting outcomes depend only on the demand of this abstract median voter.

16. Demand for Public Services Problems with Median Voter Models • 1. Logical problems • If demand is not one-dimensional and preferences do not take certain forms, the public choice mechanism may not be well defined. This is Arrow’s impossibility theorem: it is impossible to write down a general model of public choice for complex decisions. • Example: private schools. Some people with a high demand for public services under some circumstances (no private alternative) may have a low demand under others (a good private school nearby).

17. Demand for Public Services Problems with Median Voter Models, 2 • 2. Institutional problems • The median voter model says institutions are neutral. Politicians and bureaucrats have no impact on observed spending or service quality (except perhaps through inefficiency—more later). Also, results are assumed not to be skewed by non-participation. This may not be true. • Example: renters. The tax price idea applies only to owners. But it is very hard to find a significant renter variable in a median voter model.

18. Demand for Public Services Problems with Median Voter Models, 3 • 3. Tiebout bias • More on this later. • Basically, this is a form of selection bias in which people with low incomes but high demand for services based on unobserved factors end up in jurisdictions with high-quality services.

19. Demand for Public Services The Budget Constraints • The Median Voter’s Constraint • The Community Constraint • The Combined Constraint

20. Demand for Public Services Components • Tax Price • Augmented Income • This term leads to the Oates equivalence theorem: $1 of aid weighted by tax share should have the same impact on demand as $1 of income. More later.

21. Demand for Public Services Constant Elasticity Demand • General Form • Linear Form to Estimate

22. Demand for Public Services The Big Problem: Endogeneity • Note that this equation includes MC, which depends on the level of S • It also includes e, which may depend on MC as well as on key explanatory variables, such as Y and tax share. • A solution: Model MCand e. • Most studies ignore these problems!

23. Demand for Public Services The Cost Function • A multiplicative form: • implies that

24. Demand for Public Services Efficiency • Assume demand for services other than S and monitoring incentives depend on augmented income, TP, and other factors, M:

25. Demand for Public Services The Full Expenditure Function • Also recall that E = C{S}/e. Substitute MC and e into this expression to obtain • which can be estimated in log form (with the above approximation).

26. Demand for Public Services The Demand Function • Now substitute MC and e into the demand function and solve for S to get an estimating equation: • where the expressions with asterisks can all be identified with the expenditure results. • Note that the simultaneity problem is solved with algebra, not econometrics.

27. Demand for Public Services Common Error • Most studies ignore e. • But if e is a function of augmented income and TP, then the coefficients of these variables in a demand function reflect efficiency effects as well as demand effects. • They do not just give demand elasticities!

28. Demand for Public Services Massachusetts (Phuong/Yinger) • Property tax limits with overrides • No independent school districts, so actions may depend on costs of other services • Observe 296 districts over 6 years • Year dummies, but no fixed effects • Service is measured with a state-defined Student Performance Index

29. Demand for Public Services

30. Demand for Public Services

31. Demand for Public Services Tax Price with Parcel Tax • The budget constraints • Solve for P and substitute

32. Demand for Public Services California Estimates (D/Y 2011) • About 900 school districts in two years (2003-04 and 2004-05) • Service is measured by an index (API) of several tests in several grades developed for the California school accountability system. • No fixed effects, but clustered errors.

33. Demand for Public Services Demand Results from California

34. Demand for Public Services California, 2

35. Demand for Public Services California, 3 • These variables are instruments in the cost equation.

36. Demand for Public Services Subject • Entry 1