State Education Aid, Tax Effort, and School District Efficiency

1. State Education Aid, Tax Effort, and School District Efficiency William Duncombe and John Yinger Center for Policy Research, The Maxwell School Syracuse University duncombe@maxwell.syr.edu, joyinger@maxwell.syr.edu EFRC Symposium October 23, 2009

2. Organization • Introduction • Empirical approach • Empirical estimates • Simulation

3. Introduction • One of the best known theorems in public finance is that a matching grant raises demand for public outputs more than does a lump sum grant. • Bradford and Oates: “[U]nder simple majority rule with fixed tax shares and a single public good, a matching grant will always lead to a larger public expenditure than will a lump-sum grant of the same amount.” (1971, p. 441)

4. Introduction • However, some research has found that open-ended matching grants do not always stimulate more demand than equal-cost lump-sum grants. • This paper updates the standard theorem to account for: • The “flypaper effect” • “Efficiency” • Interactions between different types of aid.

5. Example 1: Foundation Aid Versus District Power-Equalizing Aid • States have experimented with a number of aid operating aid formulas over the years. • While most states (40) use a lump-sum foundation aid program for operating aid, some states (12) use a matching grant (district power-equalizing aid, DPE) as a second tier of aid. • Second-tier matching aid programs are often designed to increase the demand for education in low-wealth school districts. While evidence is limited, low-wealth districts often slow to respond.

6. Example 2: New York Example • Two of New York’s main education programs are of these two types. • The Foundation Aid program is a lump-sum aid program. • New York’s Building Aid program is a wealth-equalized, open-ended matching grant. Despite very strong price incentives, high need urban districts have been slower to increase capital spending than other types of districts. • Our study analyzes what would happen to the demand for education outcomes and local expenditures if New York was to add a second-tier aid program that either was a lump-sum or an open-ended matching design.

7. Organization • Introduction • Empirical approach • Empirical estimates • Simulation

8. Approach Taken in This Study • In this paper we expand the education demand model to include: • A “flypaper effect”: We allow lump-sum aid to have a greater effect on demand and on efficiency than an equal-size increase in community income. • Grant interaction: A recognition that the stimulative impact of lump-sum grants may depend on whether a matching grants also exists. • Efficiency effects of grants: We allow for the possibility that lump-sum aid and matching aid programs may have different effects on efficiency.

9. Definition of Inefficiency • For this study we use a broad definition of “inefficiency” that includes: • Productive efficiency: Using more resources than necessary given the best available technology and school environment to “produce” a certain level of student performance. • Different objectives: Spending money on education outcomes other than the ones that policymakers (or researchers) select. We selected as performance measures the key components of New York’s accountability system—math and reading test scores. • We can’t separate the two in our analysis.

10. Theoretical Foundation • Our analysis combines: • A demand function for student performance • A cost function for student performance • An equation specifying the determinants of school district “efficiency”. • To make the modeling feasible, we use simple multiplicative functions.

11. Demand Function • Augmented income: • Family income • Lump-sum aid adjusted by the share of local taxes paid by the decisive voter. • Tax price: • Share of taxes paid by family with the median house value. • A cost index, which reflects the cost of producing one more unit of education. • An “efficiency” index. • Matching rate (state share of expenditure)

12. Cost Function • Math and reading test performance. • Price of resources (e.g., teacher salaries) • Size of the school district (e.g., economies of scale) • Characteristics of the students served: • Poverty rate • LEP rate • Share of students with significant special needs.

13. Efficiency Equation • We are hypothesize that “efficiency” is affected by school aid: • Higher lump-sum aid increases augmented income, which may lead to less incentive to monitor district operations and an incentive to spend money on outputs not in the accountability system. • A higher state matching rate lowers the tax price, which may provide local voters less incentive to monitor district operations.

14. How Does Increase in Lump-Sum Aid Affect Demand? • Direct effect: Raises augmented income, which increases demand for education. • Indirect effect: Increased income raises inefficiency, which raises the tax price. Demand for education goes down. • Overall effect: The direct effect is likely to be larger than indirect effect, so that increased lump-sum aid raises demand for education.

15. How Does Increase in State Matching Rate Affect Demand? • Direct effect: Reduces tax price, which increases demand for education. • First indirect effect: Reduces the value of lump-sum aid to the decisive voter, which could reduce demand for education. • Second indirect effect: Several possible effects on efficiency. Likely to reduce efficiency, which increases the tax price and reduces demand for education. • Overall effect: Likely to be an increase in demand but size of increase is sensitive to indirect effects.

16. Organization • Introduction • Empirical approach • Empirical estimates • Simulation

17. Methodology • Demand and cost models estimated using 8 years of data (2000-2007). • We use the most flexible function we could given the complexity of the model. • Steps were taken in estimating the regression models to minimize possible biases in the results.

18. Empirical Estimates • In general, the results fit expectations and are estimated with precision. • Similar to previous research we found demand for math and reading test scores was fairly unresponsive to: • Changes in tax prices • Changes in community income. • We found demand response to a lump-sum grant (demand flypaper effect) was much smaller than the effect on efficiency (efficiency flypaper effect). However, these results are not estimated with precision.

19. Organization • Introduction • Empirical approach • Empirical estimates • Simulation

20. Simulating the Impact of an Open-Ended Matching Grant and Lump-sum Grant • The approach we use in this paper is to simulate the impacts of adding a lump-sum or matching grant as a second tier aid program to an already existing lump-sum grant. • Use data on key variables from New York. We look at how results change for districts with different values for income, state aid, and tax share. • Use estimates of the key parameters from this study and examine how results are affected by different price elasticities, income elasticities, and flypaper effects.

21. The Simulation Process • We pick a matching rate (20%) • We then estimate the demand for math and reading performance in each hypothetical district. • Once the level of demand is found, we use it to find the corresponding spending level using the results of the cost model. • We then find the lump-sum grant which is equal in size. • Finally, we estimate the demand for math and reading performance with this lump-sum grant.

22. Basic Findings • Given our low estimates for price and income elasticities, we do not find that either type of grant has a significant effect on the demand for improved math and reading scores. • Using the results from our demand model, we find that open-ended matching grants are more stimulative than lump-sum grants. • However, these results are sensitive to our estimates of the flypaper effects, income elasticity and price elasticity.

23. Change in Flypaper Effect • We found that the impact of lump-sum aid on demand (f=1.83) is much smaller than the effect on efficiency (g=12.23). These estimates are not estimated with precision. • We also look at cases when: • Lump-sum aid does not have a different effect on demand or efficiency than income (f=1, g=1) • Lump-sum aid has four times as large an effect on demand and efficiency than income (f=4, g=4)

26. Response to Income Increase • We found that demand for math and reading performance is quite unresponsive to income increases (income elasticity = -.1) • We also look at cases when: • Response to income increase is twice what we estimated. • Response to income increase is half of our estimate.

29. Response to Tax Price Increase • We found that demand for math and reading performance is quite unresponsive to increases in the tax price (price elasticity = -.12) • We also look at cases when: • Response to tax price increase is twice our estimate. • Response to tax price increase is 25% higher than our estimate.

32. Conclusions from Simulation • Using the results from our cost and demand models, we find open-ended matching grants to be more stimulative than lump-sum grants. • However, these results are sensitive to our results for the flypaper effects, which we did not estimate precisely: • If no flypaper effect then lump-sum aid is more responsive in low-income and high tax share districts. • If flypaper effect on demand and efficiency is substantial, then lump-sum aid would be more stimulative in most districts.

33. Conclusions from the Simulation • There is variation across types of districts in the effects of matching vs. lump-sum aid. Districts most responsive to matching grants compared to a lump-sum grant are: • High income • Low tax share (large non-residential tax base) • Low existing state aid • While our approach is promising, we need to estimate more precisely the flypaper effects before we can make strong policy recommendations for New York.