A major feature of the school finance landscape over the last two decades has been the reform of state school finance systems. Using the case of Maryland's Bridge to Excellence in Public Schools Act, this paper extends the current literature by developing a conceptual framework for residential bidding and sorting and using it to estimate housing market responses to the Maryland state aid reform. With repeat-sales data and many control variables, we find that an increase of $1,000 in current state aid per pupil induced by the reform is associated with an increase of 5 percent to 13 percent in property values. Moreover, within a district the property-value increases are greater in higher-income tracts, where the demand for school quality is likely to be greater. ## 1. Introduction A major feature of the school finance landscape over the last two decades has been the reform of state school finance systems in a number of states, often prompted by state court decisions. Most of these reforms have involved changes in the state school aid system to improve educational equity or adequacy. Along these lines, the State of Maryland initiated a significant school finance reform without direct judicial prodding, which resulted in the implementation of the Bridge to Excellence in Public Schools Act of 2002 (Senate Bill 856). The financing system for public education in Maryland changed substantially beginning in fiscal year (FY) 2004, and the act was fully phased in by FY 2008. This reform required an additional$1.3 billion above the amount that local school districts would have received from the state under the previous state aid formula, an increase of approximately 75 percent between FY 2002 and FY 2008.

One potentially important unintended effect of school finance reform is on residential bidding and sorting (e.g., Dee 2000; Hoxby 2001; Roy 2004). Because households decide jointly where to live and where to send their children to school, people can respond to any educational reforms affecting property tax rates and the quality of schools by moving to another school district (Aaronson 1999) or placing their children in private schools (Hoxby 2001). In turn, this residential sorting can affect the property tax base of school districts and the student composition of schools, which could substantially undermine or amplify the intended impacts of reforms. Increases in housing prices in some locations due to education finance reform, for example, give capital gains to current homeowners but increase housing costs for renters (Wyckoff 1995, 2001; Dee 2000; Yinger 2004). Thus, understanding the impacts of reform on residential sorting is important for assessing the longer-term equity impacts of school aid reforms.

This paper extends the current literature by developing a conceptual framework for residential bidding and sorting and using it to estimate housing market responses to the state aid reform. On the national-level analysis, Dee (2000) finds the capitalization of education finance reforms but state-level analyses reveal the heterogeneous impacts of reforms (e.g., California in Brunner, Murdoch, and Thayer 2002; Michigan in Chakrabarti and Roy 2015; and Vermont in Downes 2010). Significant redistribution of aid in Maryland provides a unique opportunity to examine the complex impact of education finance reform on property values. To be specific, this paper uses panel data for individual house sales, which allows us to identify repeat sales, and difference out time-invariant fixed effects at each house, thereby minimizing problems associated with omitted variables. We also add the series of control variables explaining the different trajectories of housing prices over time. We find that an increase of $1,000 in current state aid per pupil induced by the reform is associated with an increase of 5 percent to 10 percent in property values. Because educational costs vary across school districts,$1,000 of aid will not go as far in some districts as in others. We find that an increase of $1,000 in cost-adjusted state aid per pupil is associated with an increase of 11 percent to 14 percent in housing prices, which suggests that home buyers are aware of these cost differences. The underlying assumption for identifying the effect of school finance reform is that the trend of housing prices in a district before the reform continues into subsequent years, after controlling for heterogeneous housing market trends in neighborhoods with different income levels. Subsequently, changes in this trend after reform can be interpreted as being a result of the reform's effects. To determine whether our findings hold up under alternative assumptions, we also estimate the model with census tract time-trend variables with all sales data, instead of just with repeat sales. Both approaches yield results similar to those from our baseline model. The rest of the paper is structured as follows. The next section reviews the literature on the impact of education finance reform on property values. We then provide an overview of the Maryland school finance system and its state aid reform in section 3. Section 4 introduces our conceptual framework. We then present the empirical strategy and data sources used in the analysis. Finally, the last section provides results and policy implications from the empirical analysis. ## 2. Literature Review Studies on the impact of education finance reform on property values have been conducted using reduced form estimates (e.g., Guilfoyle 1998; Dee 2000; Hoxby 2001; Brunner, Murdoch, and Thayer 2002; Roy 2004; Downes 2010) or simulation models designed to capture the general equilibrium effects (e.g., Nechyba 2004; Epple and Ferreyra 2008; Ferreya 2009). In the earliest empirical study, Dee (2000) investigates the impact of state aid reforms on median housing prices at the school district level using national data. By treating all education finance reforms as a single event, he finds that median housing values increase by 11–20 percent in the poorest school districts, which receive the largest aid increases.1 Other studies explore diverse state responses to education reforms (Hoxby 2001; Downes 2010). Empirical studies with a focus on a single state have documented that the capitalization effect of education finance reform varies depending on the characteristics of the reform (Guilfoyle 1998; Brunner, Murdoch, and Thayer 2002; Downes 2010; Chakrabarti and Roy 2015). For example, using house-level data, Brunner, Murdoch, and Thayer (2002) investigate the impact of school finance reform on property values in California. They examine whether reform-induced changes in school spending are capitalized, whether equalization of resources between school districts leads to equalization of housing price differences, and whether spending and housing price convergence works through leveling up or leveling down. They find that a$1 increase in spending per pupil is associated with a $6 increase in property value. Guilfoyle (1998) investigates the impact of state aid reform on property values in Michigan using two samples of housing prices: the median housing price at the district level and the individual housing price with repeated sales data. With dual sales data, he estimates that a$100 increase in per pupil spending increases house prices by 0.51 percent, and a decrease of $1 in annual property taxes raises housing prices by a$4.23. Chakrabarti and Roy (2015) also find a positive relation between Michigan school finance reform and school district property values.

By contrast, Downes (2010) investigates the impact of school finance reform in Vermont (Act 60) on housing price by using individual property sales data. He takes advantage of repeat sales data to avoid possible bias caused by the correlation between neighborhood quality and state aid. He finds little evidence for capitalization of school finance reform.

## 3.  Maryland's Education Finance Reform

Prior to school finance reform, the education finance system in Maryland relied more heavily on local revenue sources than did the vast majority of states. In 2001, for example, the national average for the share of revenue from state governments was 49.9 percent, whereas in Maryland the state government provided only 37.3 percent. Local governments provided 56.8 percent of total funding in Maryland; only two states, Connecticut and Nebraska, had a higher local government revenue share (Huang 2004). This financing arrangement led to wide variation in local funding for education and undoubtedly contributed to disparities in education quality across school districts.

In 1999, the Commission on Education Finance, Equity and Excellence (Thornton Commission) was created under Chapter 601 Laws of Maryland. Its task was to restructure the state's education finance system. Based on the recommendation from the Thornton Commission, the legislature passed Chapter 288 in 2002, commonly called the Bridge to Excellence in Public Schools Act, or BTE. It changed dramatically the components of Maryland's education financing system starting in 2004.2 The legislation eliminated or phased out twenty-seven aid programs and consolidated them into four broad categories: (1) the Foundation Program; (2) three programs for special needs students; (3) a general matching grant to encourage local tax effort; and (4) several other types of aid programs for noninstructional purposes.

Table 1 summarizes differences between the main state aid programs on several key features before and after the implementation of BTE. One of the biggest changes in the state aid formula involves the foundation amount, which increased 31 percent, from $4,291 to$5,634 per pupil (in 2003 dollars), when fully phased in. In addition, school districts with a large share of low-income students are major beneficiaries of BTE because the new state aid formula provides more funding for these students. The additional state aid per low-income pupil was $1,073 under the previous formula but rose to$6,197 under BTE. With regard to limited English proficiency (LEP) students, $1,350 in additional state aid per pupil was provided under the old formula, compared with$5,634 with BTE. Moreover, the additional aid for a pupil requiring special education rose from $774 per pupil to$4,169 per pupil under the new formula.

Table 1.
Major Differences in State Aid Schemes Before and After Reform
Foundation ProgramPre-reformPost-reform
Foundation amount $4,291 in$2003 $5,634 in$2003
GCEI No Yes
Minimum state aid No 15% of foundation amount
Special Needs Students
Special education Ad hoc Weight of 0.74* per pupil foundation
Compensatory 25% of per pupil foundation amount Weight of 1.10* per pupil foundation
LEP $1,350 per pupil Weights of 1.00* per pupil foundation Guaranteed Tax Base Program None Only if less than 80% avg. wealth per pupil and only for the local tax effort above that required in the foundation program; no more than 20% of per pupil foundation amount Foundation ProgramPre-reformPost-reform Foundation amount$4,291 in $2003$5,634 in $2003 GCEI No Yes Minimum state aid No 15% of foundation amount Special Needs Students Special education Ad hoc Weight of 0.74* per pupil foundation Compensatory 25% of per pupil foundation amount Weight of 1.10* per pupil foundation LEP$1,350 per pupil Weights of 1.00* per pupil foundation
Guaranteed Tax Base Program
None Only if less than 80% avg. wealth per pupil and only for the local tax effort above that required in the foundation program; no more than 20% of per pupil foundation amount

Source: Authors’ calculations based on Maryland State Department of Education and Maryland Department of Legislative Services (2002).

LEP = limited English proficiency students.

Finally, a form of matching grant called a guaranteed tax base (GTB) program was included in BTE to encourage tax effort in districts with below average wealth. However, it restricts the maximum amount of aid a district can receive to 20 percent of per pupil foundation amount. Moreover, scholars have shown that add-on guaranteed tax base programs of this sort have little impact on school district behavior (Yinger 2004).

Figure 1 and table 2 summarize the impact of state aid reform on different types of districts. School districts with larger concentrations of students from poor families receive a larger increase, and more rapid growth, state aid than did other types of district.

Figure 1.

State Aid Per Pupil at Different Level of Share of FRPL Students

Notes: Adjusted to 2005 dollars using the Implicit Price Deflator for State and Local Government Purchases (IPD). State aid is measured as the current state aid per pupil without the state contribution to teacher retirement cost. FRPL = free or reduced-price lunch eligible.

Figure 1.

State Aid Per Pupil at Different Level of Share of FRPL Students

Notes: Adjusted to 2005 dollars using the Implicit Price Deflator for State and Local Government Purchases (IPD). State aid is measured as the current state aid per pupil without the state contribution to teacher retirement cost. FRPL = free or reduced-price lunch eligible.

Table 2.
Average Characteristics of School Districts by FRPL% for Change in Per Pupil State Aid
QuintilePercentage FRPL-Eligible StudentsChange in State Aid per Pupil ($)Change in State Aid per Pupil ($)Percent Change in State Aid per Pupil (%)Percent Change in State Aid per Pupil (%)Median Household Income
FY2001FY02—FY08FY03—FY08FY02—FY08FY03—FY08FY2001
Group 1 10.4% $2,100$1,842 66.7% 54.1% $66,898 Group 2 16.1%$2,014 $1,789 61.5% 51.1%$57,231
Group 3 22.0% $2,356$2,063 72.7% 58.3% $58,226 Group 4 30.8%$2,255 $1,782 84.6% 56.8%$43,221
Group 5 40.5% $2,300$2,098 52.8% 46.1% $36,540 Group 6 52.3%$4,022 $3,737 78.4% 69.0%$36,181
QuintilePercentage FRPL-Eligible StudentsChange in State Aid per Pupil ($)Change in State Aid per Pupil ($)Percent Change in State Aid per Pupil (%)Percent Change in State Aid per Pupil (%)Median Household Income
FY2001FY02—FY08FY03—FY08FY02—FY08FY03—FY08FY2001
Group 1 10.4% $2,100$1,842 66.7% 54.1% $66,898 Group 2 16.1%$2,014 $1,789 61.5% 51.1%$57,231
Group 3 22.0% $2,356$2,063 72.7% 58.3% $58,226 Group 4 30.8%$2,255 $1,782 84.6% 56.8%$43,221
Group 5 40.5% $2,300$2,098 52.8% 46.1% $36,540 Group 6 52.3%$4,022 $3,737 78.4% 69.0%$36,181

Notes: Quintiles are based on percentage of free or reduced-price lunch eligible students. State aid per pupil includes the current state aid without the state contribution to retirement cost and inflation is adjusted with Implicit Price Deflator on the basis of 2005 dollars.

FRPL = free or reduced-price lunch eligible.

## 4.  Conceptual Framework

This paper draws on the literature concerning hedonic regressions and their application to housing.3 In the standard model, households bid for housing in different jurisdictions based on public services levels and local tax rates, and compete for entry into the jurisdictions with the best public services. Observed housing prices (the hedonic envelope) equal the bids of the households who win this competition in each jurisdiction. Moreover, the households with the steepest bid functions, that is, with the largest willingness to pay for an increment in public services, win the competition for housing in the locations where the public services are the best. The same logic applies to neighborhood amenities.

A hedonic equation for public services or neighborhood amenities should have a nonlinear specification. Consider the case in which a household's willingness to pay for housing services (on the vertical axis) increases linearly with public service quality (on the horizontal axis). These bid functions have different slopes for different household types—a steeper slope indicates a greater willingness to pay for service-quality improvement. Now consider a service level, S*, at which the bid functions of household type A and household type B cross, and suppose that household type A has the steeper function. Under these circumstances, the (flatter) bid function for household type B will be higher to the left of S* and the (steeper) bid function for household type A will be higher to the right. A house seller obviously wants to sell to the household that bids the most, so sellers to the left of S* (that is, in jurisdictions with relatively low public service quality) will sell to household type B and sellers to the right will sell to type A. This behavior results in a nonlinear hedonic envelope. Panel A of figure 2 illustrates a nonlinear envelope with nonlinear bid functions. With many household types, the bid-function envelope can be approximated with a quadratic specification.4

Figure 2.

Conceptual Framework: Impact of State Aid Reform on Property Values. a. Sorting Pre-Reform. b. Impact of State Aid Reform on Property Values with Re-sorting

Notes: The x-axis is school quality and y-axis is the bidding price for two income taste groups (A and B). Specifically, S1 indicates school quality at a community during pre-reform years and S2 represents school quality at a community during post-reform years. Pij refers to the price that income taste group i bids at time j (i = A,B and j = 1 during pre-reform years or j = 2 during post-reform years). Note that there is another round of adjustments to reach equilibrium because the re-sorting expands the set of locations for group A even though its population does not change.

Figure 2.

Conceptual Framework: Impact of State Aid Reform on Property Values. a. Sorting Pre-Reform. b. Impact of State Aid Reform on Property Values with Re-sorting

Notes: The x-axis is school quality and y-axis is the bidding price for two income taste groups (A and B). Specifically, S1 indicates school quality at a community during pre-reform years and S2 represents school quality at a community during post-reform years. Pij refers to the price that income taste group i bids at time j (i = A,B and j = 1 during pre-reform years or j = 2 during post-reform years). Note that there is another round of adjustments to reach equilibrium because the re-sorting expands the set of locations for group A even though its population does not change.

An extensive empirical literature (reviewed in Nguyen-Hoang and Yinger 2011) estimates the impact of school quality on house values. Virtually all of these studies confirm that housing prices are higher in school districts (or school attendance zones) with higher-quality schools. This literature includes studies that investigate the impact of a change in school outcomes on the change in house values. Figlio and Lucas (2004), for example, estimate how much house values change when the local elementary school receives a failing grade from Florida's school accountability program. Bogin and Nguyen-Hoang (2014) extend this analysis to consider the impact on house values in Charlottesville of a failing grade in the federal No Child Left Behind accountability system. Drawing on the conceptual literature, these two studies recognize that the impact of a failing grade on house values operates through two channels. First, the types of households attracted to the neighborhood before the announcement of the failing grade may bid less for housing because of the negative information about the local school provided by this announcement. Second, the announcement may change the types of households moving into the neighborhood, and these households may have different bids for school quality than the households living there before the announcement. As shown by Bogin and Nguyen-Hoang, the second possibility implies that the observed change in house values after a failing grade is announced may understate how much the original residents are willing to pay to have a non-failing school.

This paper also draws on another branch of local public finance, namely, the specification and estimation of cost functions and demand functions for local public education.5 The key findings from this literature on which we draw are (1) the cost of education in a school district depends on several student traits, including the poverty level and the share of students who speak English as a second language; (2) the demand for education increases with income and decreases with tax price; and (3) increases in state aid induce voters to demand some combination of school quality improvements and local property tax cuts.

This literature implies that BTE could affect house values through three channels. First, the additional aid provided by BTE loosens a district's budget constraint and allows voters to select a school service–tax package more to their liking. People moving into the district who have school-quality demands similar to the voters already in the district will therefore bid more for housing there than they would have before BTE.

Because BTE does not have the same impact in every school district, it also could lead to a new pattern of household sorting.6 Re-sorting caused by BTE leads to the second and third channels for possible house-value impacts. The second channel is the one discussed by Figlio and Lucas (2004) and Bogin and Nguyen-Hoang (2014), namely, that the people moving into a district after BTE is implemented may have different demands for education than the people moving in before BTE. This channel is illustrated in panel B of figure 2. A district with a relatively large BTE-induced increase in school quality, from S1 to S2, for example, might attract new residents with a higher demand for school quality than the pre-BTE residents. In this case, the change in house values (PB1 to PA2) will reflect not only the BTE-induced improvement in school quality (PB1 to PB2) as seen by the original type of households, but also the increase in bids for housing associated with the BTE-induced shift to homebuyers with a higher demand for school quality (PB2 to PA2). The third channel is that changes in the types of students in a district, which also might result from re-sorting, may change educational costs.7 A BTE-induced increase in school quality might attract higher-income residents, for example, thereby lowering the share of neighborhood residents in poverty and lowering the cost of education in the district. This decrease in the cost of education will lead, in turn, to a higher demand for school quality. To the best of our knowledge, this channel has not been recognized in previous research.

It is not possible to estimate the impact of BTE on house values through each of these channels. Moreover, it is not possible to distinguish between changes in school characteristics that are induced by BTE from changes in school characteristics that have other causes, such as demographic trends within the state. Our strategy, therefore, is to focus on the impact of BTE through the first channel by controlling for observable changes in school and neighborhood characteristics. This strategy cannot shed light on the second two channels, but it has the virtue that it minimizes potential bias in estimating the first channel caused by a correlation between changes in a school district's state aid and district or neighborhood changes that have nothing to do with BTE.

## 5.  Empirical Strategy

Consider the following simple hedonic model to explain house price, V, in a panel setting. Let X stand for housing characteristics, N stand for neighborhood amenities, Dd be a fixed effect for school district or school-district type d, and Rt be a binary variable that equals 1 in years after school finance reform and 0 before. Reform takes place in year t*. The term (tt*) defines the post-reform time trend. In this specification, the post-reform shifts in both the intercept and the time trend are estimated for each d. Moreover, let μ be unobservable time-invariant house factors, υ be unobservable neighborhood effects, and ε be a random error. Then a hedonic model for house h in neighborhood type j at time t that accounts for district-type-specific trends with a possible shift after reform is:8
$ln{Vhjtd}=∑iαiXiht+∑kβkNkht+∑dγdDdh+∑dδdtDdh+∑dγd'RtDdh+∑dδd'Rt(t-t*)Ddh+μh+υjht+ϵht.$
(1)

This model is difficult to estimate without bias because it requires many Xs and many Ns and key house-specific factors and neighborhood amenities may not be observed. With double-sales data, however, we can estimate a differenced version of the model that is much simpler and that greatly minimizes the potential for omitted variable bias. Our main versions of this model assume that the variables in X and N are constant over time (as are their coefficients). However, we also present results that add time-varying controls for these variables.

Now suppose we observe house h selling at two different times, t and t′, where t′ > t. Then differencing equation 1 eliminates time invariant variables: the Xs, the Ns, the first term with district fixed effects, and the house fixed effect.9 The result is
$lnVhjt'dVhjtd=∑dγd'(Rt'-Rt)Ddh+∑dδd(t'-t)Ddh∑dδd'[Rt'(t'-t*)-Rt(t-t*)]Ddh+(υjht'-υjht)+(ϵht'-ϵht).$
(2)

We define neighborhood types based on census tract income. The resulting neighborhood-income-by-year fixed effects ensure that our estimates of the impacts of BTE control for underlying housing market trends that may differ for neighborhoods at different income levels (Glaeser, Gottlieb, and Tobio 2012). These controls are particularly important in our sample, which includes the recession years of 2001 and 2002. Our sample does not include the housing market crash, which began in 2008 but nevertheless controls for housing market trends leading up to that event. In other words, the identification strategy in our interrupted time analysis is not simply to assume that the trend of housing prices within school districts prior to the reform provides a valid counterfactual for what would have happened to housing prices within school districts had state aid reform not been implemented. Instead, we recognize that different types of neighborhoods might experience different housing price trends after reform for reasons that are separate from but correlated with changes in state education aid reform (Morgan and Winship 2007). These fixed effects minimize the bias from this possibility.

Equation 2 applies to cases in which both sales occur before reform $(Rt'=Rt=0)$, both sales occur after reform $(Rt'=Rt=1)$, or the first sale occurs before reform and the second one occurs after $(Rt=0;Rt'=1)$. As a result, all double sales observations can be used, regardless of whether they straddle the reform. In the first and second case the first term, $[(Rt'-Rt)Dhd]$, drops out, and in the first case the third term, $[Rt'(t'-t*)-Rt(t-t*)]Dhd$, drops out.10

We estimate equation 2 for two different school district definitions. First, we follow Chakrabarti and Roy (2015), henceforth CR, by defining categories of districts based on a pre-reform trait that is related to the magnitude of the reform in a district, and hence to the expected impact on property values. In the Michigan case analyzed by CR, the reform was designed to bring per pupil spending up to $6,000 in all districts, with a grandfather clause for districts spending more than that amount already. As a result, CR based their analysis on quintiles of the pre-reform per pupil spending distribution, which define the reform-based change in spending. They expected (and found) larger impacts in the lowest quintile, where the impacts of the reform were largest. However, it is not appropriate for us to define district types based on pre-reform spending levels because, in the Maryland case, the change in spending induced by the reform is not exogenous. We can, however, take advantage of the fact that one of the main features of Maryland's reformed education aid formula was a large increase in the weight placed on pupils eligible for a free or reduced-price lunch (FRPL). Hence, the pre-reform share of FRPL-eligible students predicts the magnitude of the aid change in a given district, and we define district types based on this share (see figure 1). Because of the link between the pre-reform FRPL share and the state aid change, we expect that the impact of the reform as estimated by equation 2 will be larger in districts with a higher pre-reform FRPL share. Second, we estimate equation 2 with d as a school-district indicator; that is, we estimate the pre-reform and post-reform time trends separately for each district. This approach has the advantage of allowing for a different price impact from BTE in each district, not just in a type of district. A district's γ′ coefficient indicates how much the district's property values shift when the reform is initiated. A district's δ′ coefficient indicates the change in the slope of a district's time trend during the post-reform years. A district's δ coefficient captures the underlying time trend for each district. To identify the impact of BTE with this approach, we estimate a second-stage regression to determine whether the estimated changes in the path of house values in a district after the implementation of BTE are correlated with the aid changes associated with this reform. This change in house value in a given district in year t′ equals $γd'+δd'(t'-t*)$. We estimate a regression with this change in house value as the dependent variable and with the change in aid as the explanatory variable. We also explore the extent to which this dependent variable can be explained by reform-induced changes in student test scores and tax rates or by reform-induced changes in sorting outcomes, as measured by changes in household incomes.11 ## 6. Data We have ten years of data on residential sales (1998 to 2007) and housing characteristics from two different databases produced by the Maryland State Department of Assessments and Taxation (SDAT): Real Property Sales File (RPSF) and Computer Assisted Mass Appraisal (CAMA). House sale prices come from the RPSF.12 After data cleaning, we have 772,566 sales records from 603,258 houses. This leads to 314,395 repeat sales records for 144,955 houses. School district variables are used in the second step of our analysis, which links the predicted change in housing price (compared with pre-reform trend) with the change in school district traits. School districts in Maryland are coterminous with counties. Total state aid per pupil (from Maryland Department of Education) includes aid recorded in any school district fund, including current expenses fund, food service fund, school construction fund, and debt service fund. Current state aid refers to state aid recorded only in the current expenses fund without the state's contribution to teacher retirements. Student performance measures include dropout rates, and passing rates in Reading and Math for third and fifth grades from the Maryland School Assessment (MSA) and the Maryland School Performance Assessment Program (MSPAP). One possible limitation that arises when using student test scores is that to conform to the requirements of No Child Left Behind, Maryland changed its tests in 2003 from MSPAP (school-based reporting system and essay exams) to MSA (multiple choice, short-answer questions, and individual student reporting system). We estimate Cronbach's alpha to check the reliability of measurement in each test score over our sample period (1997–2007).13 The results show that Cronbach's alphas are 0.96 and 0.98 in third and fifth grade reading, respectively, and 0.95 and 0.97 in third and fifth grade math, respectively. Because an alpha of 0.70 or higher is sufficient for modest reliability (Nunnally and Bernstein 1994), these results provide evidence that the test does not substantially change during our sample period. The effective tax rate (ETR) in each county is the product of the county's nominal tax rate and average assessment to sales ratios in residential properties drawn from Assessment Ratio Surveys in SDAT. Following Clapp, Nanda, and Ross (2008), the final property tax variable equals log{r + ETR}, where the discount rate (r) is 0.03, which is the standard rate in the literature.14 A variety of amenities and disamenities variables are included in the analysis. Data on the crime rate at the school district level come from the Uniform Crime Reporting Program in the Federal Bureau of Investigation, measuring the total and violent crime rates per 100,000 inhabitants. In addition, Geographic Information System software was used to bring in other neighborhood characteristics. Table 3 describes the summary statistics for repeated sales data in our baseline model. Appendix tables A.2 and A.3 list and define our school district variables and our neighborhood amenities or disamenities. Table 3. Summary Statistics for Sales Price Difference and Variables used in Hedonic Analysis for Repeated Sales Data VariablesMeanStandard DeviationMinMax Difference in sales price 113110 110763.9 −3509000 4837132 House characteristics Story 4.8 3.07 13 Square feet 1,608 719 22,932 Good condition 0.0045 0.067 Age 33.3 23.79 316 Rail station 0.245 0.43 Change in state aid per pupil ($1,000)
Percent change in state aid per pupil
Neighborhood characteristics
%Hispanic 0.069 0.065 0.0008 0.207
%Black 0.304 0.228 0.002 0.889
%LEP 0.035 0.03 0.102
%FRPL 0.259 0.137 0.06 0.778
%Special 0.118 0.017 0.084 0.186
Crime rate 4027.1 1723 1619 11657
VariablesMeanStandard DeviationMinMax
Difference in sales price 113110 110763.9 −3509000 4837132
House characteristics
Story 4.8 3.07 13
Square feet 1,608 719 22,932
Good condition 0.0045 0.067
Age 33.3 23.79 316
Rail station 0.245 0.43
Change in state aid per pupil ($1,000) Unadjusted 1.09 0.87 −0.43 3.58 Cost-Adjusted 0.49 0.335 −0.84 1.52 Percent change in state aid per pupil Unadjusted 36.06 26.4 −12.88 104.2 Cost-adjusted 27.9 21.13 −3.48 101.6 Neighborhood characteristics %Hispanic 0.069 0.065 0.0008 0.207 %Black 0.304 0.228 0.002 0.889 %LEP 0.035 0.03 0.102 %FRPL 0.259 0.137 0.06 0.778 %Special 0.118 0.017 0.084 0.186 Crime rate 4027.1 1723 1619 11657 FRPL = free or reduced-price lunch eligible; LEP = limited English proficiency. ## 7. Empirical Results Our empirical strategy leads to two estimating methods. The first method implements equation 2 with school district types defined by FRPL share. The second method implements this equation with a separate impact of BTE for each school district, and then estimates the link between housing trend shifts and state aid. ### Method 1 The results for the first method are presented in table 4. This method estimates equation 2 with six district classes defined by the share of FRPL-eligible students. We omit class 1 so that the coefficients measure differences from the lowest-FRPL districts. BTE substantially changed the aid formula starting in FY2004, so property that was sold after September 2003 was considered to be affected by state aid reform. Both columns in this table indicate that in the districts with the highest share of FRPL-eligible students, housing prices shifted downward relative to those in the lowest-FRPL districts in the year BTE was implemented but then grew significantly faster in later years.15 These effects are highly significant. The downward shift is slightly smaller and the increase in the trend is slightly greater when the neighborhood income-by-year fixed effects are included (column 2). The same pattern exists for houses in district class 4, which received a larger boost in state aid than did the districts in class 5 (see figure 1), although the effects are smaller than the ones for class 6. The effects are not significant for districts with other FRPL shares. Table 4. Impact of State Aid Reform on Property Values Change in(1)(2) Group 2*Reform −0.0150 −0.0205 (0.0131) (0.0130) Group 3*Reform 0.0179 0.0092 (0.0134) (0.0093) Group 4*Reform −0.0382** −0.0502*** (0.0126) (0.0114) Group 5*Reform −0.0098 0.0051 (0.0248) (0.0222) Group 6*Reform −0.0721** −0.0699*** (0.0222) (0.0164) Group 2*Reform*Trend 0.0130 0.0106 (0.0109) (0.0113) Group 3*Reform*Trend 0.0132 0.0024 (0.0147) (0.0142) Group 4*Reform*Trend 0.0348** 0.0265* (0.0098) (0.0097) Group 5*Reform*Trend 0.0300** 0.0068 (0.0106) (0.0123) Group 6*Reform*Trend 0.0614*** 0.0513*** (0.0098) (0.0106) Group 2*Trend −0.0020 0.0003 (0.0067) (0.0057) Group 3*Trend −0.0062 −0.0045 (0.0092) (0.0078) Group 4*Trend −0.0303** −0.0189** (0.0091) (0.0057) Group 5*Trend −0.0170 −0.0132 (0.0130) (0.0099) Group 6*Trend −0.0464*** −0.0402*** (0.0095) (0.0066) Reform 0.1487*** 0.0897*** (0.0155) (0.0111) Trend 0.0772*** 0.0713*** (0.0054) (0.0050) Reform*trend 0.0128 0.0066 (0.0081) (0.0119) Housing and neighborhood characteristicsa Yes Yes Income level / year fixed effect No Yes R2 0.864 0.876 N 157,859 157,859 Change in(1)(2) Group 2*Reform −0.0150 −0.0205 (0.0131) (0.0130) Group 3*Reform 0.0179 0.0092 (0.0134) (0.0093) Group 4*Reform −0.0382** −0.0502*** (0.0126) (0.0114) Group 5*Reform −0.0098 0.0051 (0.0248) (0.0222) Group 6*Reform −0.0721** −0.0699*** (0.0222) (0.0164) Group 2*Reform*Trend 0.0130 0.0106 (0.0109) (0.0113) Group 3*Reform*Trend 0.0132 0.0024 (0.0147) (0.0142) Group 4*Reform*Trend 0.0348** 0.0265* (0.0098) (0.0097) Group 5*Reform*Trend 0.0300** 0.0068 (0.0106) (0.0123) Group 6*Reform*Trend 0.0614*** 0.0513*** (0.0098) (0.0106) Group 2*Trend −0.0020 0.0003 (0.0067) (0.0057) Group 3*Trend −0.0062 −0.0045 (0.0092) (0.0078) Group 4*Trend −0.0303** −0.0189** (0.0091) (0.0057) Group 5*Trend −0.0170 −0.0132 (0.0130) (0.0099) Group 6*Trend −0.0464*** −0.0402*** (0.0095) (0.0066) Reform 0.1487*** 0.0897*** (0.0155) (0.0111) Trend 0.0772*** 0.0713*** (0.0054) (0.0050) Reform*trend 0.0128 0.0066 (0.0081) (0.0119) Housing and neighborhood characteristicsa Yes Yes Income level / year fixed effect No Yes R2 0.864 0.876 N 157,859 157,859 aHousing and neighborhood characteristics include all control variables used in Table 3. **p < 0.05; ***p < 0.01. These results appear to indicate either uncertainty about the impacts of the reform or some type of adjustment costs at the time of BTE implementation in September 2003, with a drop in housing prices of almost 7 percent in the highest-FRPL districts relative to those in the lowest-FRPL districts. This drop was quickly reversed, however, and, based on the results in column 2, it had disappeared by the end of 2004. By September 2007, housing prices in these districts were 13 percent above the class-1 baseline (see figure 3). In short, the post-reform housing price increases were highest in the districts with the highest concentrations of FRPL-eligible students, which are precisely the districts where BTE is predicted to have the greatest impact. Neither this figure nor any of our other results predicts, of course, what happened after 2007. Figure 3. Impact of State Aid Reforms on Housing Values Notes: The graph is based on the results from the second column of table 4. FRPL = free or reduced-price lunch eligible. Figure 3. Impact of State Aid Reforms on Housing Values Notes: The graph is based on the results from the second column of table 4. FRPL = free or reduced-price lunch eligible. ### Method 2 Table 5 shows regression results based on equation 2 with separate estimates for each school district in Maryland. All regressions are estimated with standard errors clustered at the school district level. This is the first stage of our second method, which allows for heterogeneous effects of reform on property values at the school district level. Because our empirical specification is the differenced version of a hedonic model with repeat-sales data, neighborhood and housing traits are included in the model as changes during the repeat sales period. The inclusion of neighborhood variables changes the interpretation of the estimated impact of state aid reform as a whole on property values. Because state aid reform may change sorting, controlling for variables (such as the crime rate, which may be influenced by sorting) implies that we may not be capturing all impacts of state aid reform. Coefficients in this hedonic model should be interpreted as partial effects of aid reform after controlling for possible changes in sorting that the reform induced. Table 5. Impact of State Aid Reform on Property Values Using Repeat Sales Data with Time Variant Controls School DistrictDistrict's Intercept Shift after the ReformDistrict's Time TrendChange in the Slope of a District's TimeControl Variables: Housing and Neighborhood Allegany −0.0746*** 0.0518*** 0.0599*** Story −0.0180 Anne Arundel 0.0825*** 0.0925*** 0.028*** Square feet 0.00012*** Baltimore city 0.0123 0.1315*** 0.0077 Good cond −0.078*** Baltimore county 0.0514*** 0.0951*** 0.0461*** Age −0.00016 Calvert 0.1029*** 0.0706*** 0.0504*** Brick −0.1093*** Caroline 0.1198*** 0.0635*** 0.0298*** Rail Station −0.0255* Carroll 0.0781*** 0.0785*** 0.0199*** %Hispanic 2.015 Cecil 0.0326*** 0.0779*** 0.0228** %Black −1.688 Charles 0.0617*** 0.1073*** 0.081*** %LEP −0.3817 Dorchester 0.0767*** 0.0884*** 0.0082 %FRPL 0.2074 Frederick 0.1083*** 0.0857*** 0.0085 %Special 0.6857 Garrett 0.069*** 0.0654*** −0.0084 (%Hisp)2 −3.8339 Harford 0.057*** 0.0674*** 0.0589*** (%Black)2 −0.4534 Howard 0.0824*** 0.0928*** 0.0263*** (%LEP)2 11.593** Kent 0.0412*** 0.0852*** −0.0018 (%FRPL)2 −0.8189*** Montgomery 0.0923*** 0.1134*** −0.0179 (%Special)2 −1.631 Prince Georges 0.0384*** 0.0778*** 0.0438*** Crime 4.20E—06 Queen Anne 0.0566*** 0.093*** −0.0046 (Crime)2 −7.70E—10 Somerset 0.0781*** 0.048*** 0.0781*** St Mary 0.0351** 0.0712*** 0.0261** Talbot 0.0477*** 0.0894*** −0.0183* Washington 0.1102*** 0.0802*** 0.0233** Wicomico 0.0096 0.069*** 0.0397*** Worcester 0.0277*** 0.1122*** −0.0443*** School DistrictDistrict's Intercept Shift after the ReformDistrict's Time TrendChange in the Slope of a District's TimeControl Variables: Housing and Neighborhood Allegany −0.0746*** 0.0518*** 0.0599*** Story −0.0180 Anne Arundel 0.0825*** 0.0925*** 0.028*** Square feet 0.00012*** Baltimore city 0.0123 0.1315*** 0.0077 Good cond −0.078*** Baltimore county 0.0514*** 0.0951*** 0.0461*** Age −0.00016 Calvert 0.1029*** 0.0706*** 0.0504*** Brick −0.1093*** Caroline 0.1198*** 0.0635*** 0.0298*** Rail Station −0.0255* Carroll 0.0781*** 0.0785*** 0.0199*** %Hispanic 2.015 Cecil 0.0326*** 0.0779*** 0.0228** %Black −1.688 Charles 0.0617*** 0.1073*** 0.081*** %LEP −0.3817 Dorchester 0.0767*** 0.0884*** 0.0082 %FRPL 0.2074 Frederick 0.1083*** 0.0857*** 0.0085 %Special 0.6857 Garrett 0.069*** 0.0654*** −0.0084 (%Hisp)2 −3.8339 Harford 0.057*** 0.0674*** 0.0589*** (%Black)2 −0.4534 Howard 0.0824*** 0.0928*** 0.0263*** (%LEP)2 11.593** Kent 0.0412*** 0.0852*** −0.0018 (%FRPL)2 −0.8189*** Montgomery 0.0923*** 0.1134*** −0.0179 (%Special)2 −1.631 Prince Georges 0.0384*** 0.0778*** 0.0438*** Crime 4.20E—06 Queen Anne 0.0566*** 0.093*** −0.0046 (Crime)2 −7.70E—10 Somerset 0.0781*** 0.048*** 0.0781*** St Mary 0.0351** 0.0712*** 0.0261** Talbot 0.0477*** 0.0894*** −0.0183* Washington 0.1102*** 0.0802*** 0.0233** Wicomico 0.0096 0.069*** 0.0397*** Worcester 0.0277*** 0.1122*** −0.0443*** Notes: Dependent variable is change in the log of housing price, compared to pre-reform trend. Equation is estimated with ordinary least squares (no constant term) and standard errors clustered at the school district level. Specification is based on equation 2 with repeat sales data. The number of observations is 157,859. R2 is 0.878. Districts are sorted by median household income, low to high. All housing and neighborhood variables are in change form. The quadratic terms are the change in the square of the variable. FRPL = free or reduced-price lunch eligible; LEP = limited English proficiency. *p < 0.10; **p < 0.05; ***p < 0.01. In the first column of table 5, the coefficients indicate each school district's γ′, which measures how much property values in the district shift after BTE was implemented compared to the pre-reform trend. For example, BTE increased property values in the Howard and Calvert districts by 8.2 percent and 10.3 percent, respectively. In contrast, the reform lowered property values by about 7.5 percent in the Allegany school district. The third column of table 5 provides the impact of reform on the change in the time trend in housing prices after controlling for time-varying housing traits and neighborhood characteristics. For example, the Allegany and Calvert school districts had positive, statistically significant changes in their trends; the rate of increase in property values rose by 6.0 and 5.0 percentage points, respectively, after the reform compared to pre-reform trend. All housing and neighborhood variables are in change form. To capture the nonlinearity in the hedonic, we include the change in the level and the change in the square of each variable.16 The second step with this method is to investigate the relationship between the change in house value associated with education finance reform and the change in state aid at the district level. This step addresses the question: Did the BTE aid changes lead to changes in house values? Each school district has its own coefficients derived from empirical specification 2, which allows us to provide the predicted reform-induced change in house value at the school district level for each post-reform year. Each district's predicted change in the log of housing price, which equals $γd'+δd't'-t*$, is regressed on the district's change in state aid between time $t'$ and $t*$.17 The measure of the change in state aid used in the analysis should reflect the change in state aid that bidders in the housing market are most apt to perceive. Because little is known about these perceptions, we examined several aid measures. We find that absolute and percent change measures in per pupil spending yield qualitatively similar results and, for conciseness, focus on the former. Table 6 presents results of ordinary least squares (OLS) regressions of predicted change in property values on the change in state aid. To account for heteroskedasticity and autocorrelation in the second step, we use Newey–West standard errors. Except for the quadratic term in columns 3 and 6, the regression coefficients are all positive and significant at the 1 percent level. These results support the hypothesis that post-reform changes in property values reflect the changes in state aid associated with BTE. To be specific, results from the first column of table 6 indicate that an increase of$1,000 in current state aid per pupil is associated with an increase of about 5.1 percent in property values. Because different districts face different educational costs, homebuyers may recognize that aid does not go as far in some districts as in others. The results in table 6 (columns 4, 5, and 6) support this view—when changes in state aid are adjusted for educational cost differences, the coefficients are even larger.18 An increase of $1,000 in cost-adjusted state aid per pupil is associated with a 11.3 percent increase in housing prices in column 4. Table 6. Results of a Regression Between Predicted Change in Housing Prices and Change in State Aid per Pupil (1)(2)(3)(4)(5)(6) Change in 0.051*** 0.046*** 0.105** 0.113*** 0.038*** 0.02 state aid (0.01) (0.009) (0.052) (0.029) (0.011) (0.17) Change in −0.0048 0.0165 (state aid)2 (0.0046) (0.03) Measure of state aid change Absolute change in state aid per pupil Ln (absolute change in state aid per pupil) Absolute change in state aid per pupil Absolute change in cost-adjusted state aid per pupil Ln (absolute change in cost-adjusted state aid per pupil) Absolute change in cost-adjusted state aid per pupil N 120 117 120 120 117 120 Adj R2 0.244 0.198 0.265 0.174 0.126 0.181 (1)(2)(3)(4)(5)(6) Change in 0.051*** 0.046*** 0.105** 0.113*** 0.038*** 0.02 state aid (0.01) (0.009) (0.052) (0.029) (0.011) (0.17) Change in −0.0048 0.0165 (state aid)2 (0.0046) (0.03) Measure of state aid change Absolute change in state aid per pupil Ln (absolute change in state aid per pupil) Absolute change in state aid per pupil Absolute change in cost-adjusted state aid per pupil Ln (absolute change in cost-adjusted state aid per pupil) Absolute change in cost-adjusted state aid per pupil N 120 117 120 120 117 120 Adj R2 0.244 0.198 0.265 0.174 0.126 0.181 Notes: Dependent variable is predicted change in the log of housing price, compared to pre-reform trend from results in table 5. The unit for the absolute change in state aid per pupil ($) is rescaled to $1,000. Equation is estimated with pooled ordinary least squares with Newey–West standard errors. **p < 0.05; ***p < 0.01. Homebuyers may be more attuned to changes in school quality and property tax rates than they are the associated changes in state aid. Table 7 looks into this possibility with both the linear and the quadratic form. We find that the state aid coefficients are still positive and statistically significant after controlling for changes in student performance and the effective tax rate. Specifically, when a school district (i.e., the school district receiving the median level of state aid prior to the reform) receives a$1,000 increase in state aid per pupil through state aid reform, its property values increase by about 6.5 percent to 7.8 percent (columns 1 and 3 in table 7). Cost-adjusted aid (column 2) has an even larger effect. The variables for change in student performance and tax rate have mixed findings. These results suggest that voters interpret aid changes as a reasonably complete summary of the impact of reform. The exception is that an increase in the test scores for fifth graders has a small negative and significant impact on house values, which is not the expected sign.

Table 7.
Results of a Regression between Predicted Change in Housing Prices and Change in School District Characteristics
(1)(2)(3)(4)
Change in state aid 0.065*** 0.147*** 0.078* −0.1426
(0.011) (0.037) (0.046) (0.15)
Change in test score for 3rd grade 0.0022 0.0027* 0.001 0.0011
(0.0014) (0.001) (0.003) (0.0023)
Change in test score for 5th grade −0.0045*** −0.0046*** −0.009 −0.012**
(0.002) (0.0016) (0.006) (0.006)
Change in dropout rate −0.002 0.0056 0.018 0.0085
(0.009) (0.01) (0.03) (0.022)
Change in effective tax rate 0.031 0. 0237 −0.29 −0.597
(0.347) (0.361) (0.46) (0.493)
Quadratic Form (All terms are squared)
Change in (state aid)2   −0.0014 0.0461*
(0.004) (0.0245)
Change in (test score for 3rd grade)2   −0.000014 −0.00001
(0.000029) (0.00002)
Change in (test score for 5th grade)2   0.000045 0.0008*
(0.00004) (0.00005)
Change in (dropout rate)2   −0.0014 0.0051*
(0.0021) (0.002)
Observations 120 120 120 120
Measure of State Aid State aid per pupil Cost-adjusted state State aid per pupil Cost-adjusted state
aid per pupil  aid per pupil
Adjusted R2 0.188 0.145 0.349 0.418
(1)(2)(3)(4)
Change in state aid 0.065*** 0.147*** 0.078* −0.1426
(0.011) (0.037) (0.046) (0.15)
Change in test score for 3rd grade 0.0022 0.0027* 0.001 0.0011
(0.0014) (0.001) (0.003) (0.0023)
Change in test score for 5th grade −0.0045*** −0.0046*** −0.009 −0.012**
(0.002) (0.0016) (0.006) (0.006)
Change in dropout rate −0.002 0.0056 0.018 0.0085
(0.009) (0.01) (0.03) (0.022)
Change in effective tax rate 0.031 0. 0237 −0.29 −0.597
(0.347) (0.361) (0.46) (0.493)
Quadratic Form (All terms are squared)
Change in (state aid)2   −0.0014 0.0461*
(0.004) (0.0245)
Change in (test score for 3rd grade)2   −0.000014 −0.00001
(0.000029) (0.00002)
Change in (test score for 5th grade)2   0.000045 0.0008*
(0.00004) (0.00005)
Change in (dropout rate)2   −0.0014 0.0051*
(0.0021) (0.002)
Observations 120 120 120 120
Measure of State Aid State aid per pupil Cost-adjusted state State aid per pupil Cost-adjusted state
aid per pupil  aid per pupil
Adjusted R2 0.188 0.145 0.349 0.418

Notes: Dependent variable is predicted change in the log of housing price, compared to pre-reform trend from results in table 5. Equation is estimated with a pooled ordinary least squares and Newey–West standard errors. The unit for the absolute change in state aid per pupil ($) is rescaled to$1,000.

*p < 0.10; **p < 0.05; ***p < 0.01.

These impacts of state aid provide similar estimates from previous studies. For instance, Dee (2000) shows that state aid reform leads to an 11 percent to 20 percent increase in median housing prices, and Guilfoyle (1998) provides evidence that a $1,000 increase in per pupil spending is associated with a 5.1 percent increase in housing prices. In absolute dollar terms, our results imply that a$1 increase in state aid per pupil leads to an increase in median housing price (in 2000) of approximately $8 to$17. In a similar vein, Barrow and Rouse (2004) estimate that a $1 increase in state aid per pupil is associated with a$30 increase in housing prices, and Brunner, Murdoch, and Thayer (2002) find that housing prices increase by $6 for every$1 increase in spending per pupil.

## 8.  Heterogeneous Impacts Caused by Sorting

As discussed earlier, the sorting of households across locations could result in heterogeneous impacts of an education finance reform on housing prices. The school districts in Maryland are not homogeneous, and even within a given district, higher-income households might place more value on educational improvements than do lower-income households. As a result, BTE might lead to a greater increase in housing prices in high-income neighborhoods than in low-income neighborhoods in the same district.

An additional complication arises in Maryland, however, because the impact of BTE on housing prices depends on homebuyers’ perceptions about the way additional state aid would be used. Because education finance reform is designed to help low-performing students, households may expect that the additional aid their district receives will go to the lowest-performing elementary schools in the district. The lowest-performing elementary schools tend to be located in low-income neighborhoods, so this possibility can lead to the opposite prediction from the one in the previous paragraph—namely, that the impact of an aid increase could be smaller in high-income neighborhoods because people buying housing in those neighborhoods do not expect much of the aid to be directed toward the associated elementary schools.

Table 8 shows the relationship between our estimate of the reform-induced change in housing price and household median income during pre-reform years. The dependent variable is based on a regression like the one in table 4, except that the shifts in the intercept and trend are estimated for each census tract, not for each school district. The explanatory variables in column 1 include tract median income and an interaction between the district-level change in state aid per pupil and tract income. In other words, this regression determines whether the impact of higher state aid on house values in a census tract depends on that tract's median income. The other columns provide the same type of test for other variables that might influence the demand for education, such as education, age, and family composition. The last column includes all of these variables and their interactions with the change in state aid.

Table 8.
Results of Relation between Predicted Change in Housing Prices and Household Demands at the Census Tract Level
(1)(2)(3)(4)(5)(6)(7)
Change in state aid per pupil 0.0463*** 0.0419*** 0.0341*** 0.0362*** 0.0385*** 0.0418*** 0.0357***
(0.0050) (0.0059) (0.0062) (0.0061) (0.0060) (0.0055) (0.0049)
Interaction with state aid
Median income 0.0127***      0.0357***
(0.0030)      (0.0049)
High school  0.0010     0.0178**
(0.0008)     (0.0054)
Bachelor   −0.0001    −0.0015
(0.0004)    (0.0012)
English    −0.0002   −0.0013*
(0.0005)   (0.0006)
Old     −0.0034***  0.0006
(0.0008)  (0.0005)
Child      0.0028** −0.0038*
(0.0011) (0.0018)
Median income −0.0075***      −0.0004
(0.0022)      (0.0021)
High school  0.0002     −0.0044
(0.0007)     (0.0038)
Bachelor   −0.0008**    0.0049***
(0.0003)    (0.0013)
English    0.0014***   −0.0021***
(0.0003)   (0.0006)
Old     −0.0004  −0.0001
(0.0006)  (0.0004)
Child      0.0007 0.0005
(0.0008) (0.0014)
Observations 4,386 4,386 4,386 4,386 4,386 4,386 4,386
R2 0.1411 0.1292 0.1566 0.1359 0.1463 0.1404 0.2234
(1)(2)(3)(4)(5)(6)(7)
Change in state aid per pupil 0.0463*** 0.0419*** 0.0341*** 0.0362*** 0.0385*** 0.0418*** 0.0357***
(0.0050) (0.0059) (0.0062) (0.0061) (0.0060) (0.0055) (0.0049)
Interaction with state aid
Median income 0.0127***      0.0357***
(0.0030)      (0.0049)
High school  0.0010     0.0178**
(0.0008)     (0.0054)
Bachelor   −0.0001    −0.0015
(0.0004)    (0.0012)
English    −0.0002   −0.0013*
(0.0005)   (0.0006)
Old     −0.0034***  0.0006
(0.0008)  (0.0005)
Child      0.0028** −0.0038*
(0.0011) (0.0018)
Median income −0.0075***      −0.0004
(0.0022)      (0.0021)
High school  0.0002     −0.0044
(0.0007)     (0.0038)
Bachelor   −0.0008**    0.0049***
(0.0003)    (0.0013)
English    0.0014***   −0.0021***
(0.0003)   (0.0006)
Old     −0.0004  −0.0001
(0.0006)  (0.0004)
Child      0.0007 0.0005
(0.0008) (0.0014)
Observations 4,386 4,386 4,386 4,386 4,386 4,386 4,386
R2 0.1411 0.1292 0.1566 0.1359 0.1463 0.1404 0.2234

Notes: Dependent variable is predicted change in housing price after the reform at the census tract level. Equation is estimated with ordinary least squares, and cluster standard errors in the district level are in parentheses. All demand variables are recorded as mean-centered variables. The unit of median income is rescaled to $10,000. *p < 0.10; **p < 0.05; ***p < 0.01. The key result in table 8 is that the impact of higher state aid on property values is higher in high-income census tracts, even within the same school district. This effect persists when other demand variables are included. The last column also indicates that the impact of aid increases with education (at least up to a high school degree). These results suggest that pre-reform sorting influences the property-value impacts of school finance reform, and that people buying housing expect the benefits of higher aid will be spread throughout a school district. ## 9. Robustness Checks Several robustness checks are presented in an online appendix that can be accessed on Education Finance and Policy’s Web site at www.mitpressjournals.org/doi/suppl/10.1162/edfp_a_00230. To begin, we used our first method to see if the effects of reforms were anticipated. Second, we conducted a separate analysis using our second method with just the school districts in the Baltimore metropolitan area. A hedonic equation represents the sorting equilibrium for the households competing against each other for housing in a given urban area, so using an entire state, even a relatively small one like Maryland, might produce misleading results. Third, we added a quadratic term to the trends in equation 2. Fourth, we reestimated equation 2 with all sales, not just repeat sales. Each of these robustness checks supports our conclusion that the relatively large increases in state aid to education in some school districts associated with BTE resulted in relatively large increases in house values in those school districts. ## 10. Conclusions and Discussion One major feature of the U.S. education system is disparities in funding across school districts. Many states have made efforts to reduce these funding gaps through education finance reforms. This study contributes to the debate by examining the unintended impact of Maryland state aid reform on property values. Our approach is to use repeat-sales data to isolate the impact of education finance reform on property values over time in the intercept and slope of housing prices in affected school districts. This approach minimizes the problem of omitted variable bias, which is a key challenge in the hedonics literature. We find that all school districts except Allegany have a positive intercept shift, and the change in slope of the time trend is positive in most districts. In the second step, we explore the link between the reform-induced change in housing price and the change in state aid. We find a strong association between these two variables, even after controlling for changes in student performance and in the property tax rate. Homebuyers appear to recognize that state aid reform will boost student performance. In addition, we extend the results by determining the extent to which changes in cost-adjusted aid influences property values. The positive relationship between these two variables implies that homeowners recognize that high poverty levels lead to the need for additional state aid. Our main conclusion is that homebuyers are aware of major reforms to state education aid, believe that an increase in aid associated with such a reform will lead to a better service-tax package, and, as a result, bid more for housing in locations with relatively large aid increases. Moreover, homeowners appear to be aware that what matters is cost-adjusted aid, not simply dollars of aid per pupil. In the long run, when the aid reforms are not fresh in homebuyers’ minds, the impact of aid on house values may diminish and be replaced by the impact of changes in school quality and tax rates. Within our sample period, however, the impacts of aid dominate. Post-reform house-value increases represent some combination of higher bids by households similar to the ones who lived in districts with aid increases before the reform was passed, a replacement of those households with others who place a higher value on the post-reform school-tax package, and changes in bids due to changes in education costs associated with reform-induced household re-sorting. We focus on the first of these components. We find that reform-induced changes in property values in a given district are higher in high-income tracts than in low-income tracts. We interpret this result as a reflection of the demand for education—high-income households are willing to pay more than low-income households for the school quality improvements expected from higher education aid. A full analysis of all three components of house-value increases remains a challenge for future research. Our results, with a focus on Maryland education finance reform, are similar to previous case studies in California, Texas, and Michigan, but not one in Vermont. Downes (2010) argues that the unique result in Vermont could be due to the prominence of vacation homes or expectations of overturning reform. Understanding the heterogeneous effect of the reform at the state level is a task for future research. A secondary conclusion of this paper, as discussed by Wyckoff (1995, 2001) and Yinger (2004), is that capitalization of state aid reform leads to winners and losers with regard to changes in property wealth across school districts. Those who own property in school districts with large increases in state aid, for example, will experience an increase in their housing price compared with those who own property in districts with small increases. These wealth changes affect people who own homes at the time of the reform, but not people who buy homes in the future, because they must pay a higher price to enter a district in which reform has improved school performance. Although we do not examine effects on renters, they are also likely to have to pay more to live in a district with reform-induced educational improvements. Of course, these effects are secondary to the main purpose of the reform, which is to help children, but they may make it difficult for some low-income families to afford housing in newly improved school districts. ## Acknowledgments The authors are grateful for comments from participants in presentations at the annual meetings of both the Association for Education Finance and Policy and the Association for Public Policy Analysis and Management, from the editors, and from two anonymous referees. Bill Duncombe passed away in May 2013, before the final revisions on this paper were carried out. However, Bill played a critical role in designing this project and preparing the original draft, and his insights appear throughout the paper. ## REFERENCES Aaronson , Daniel . 1999 . The effect of school finance reform on population heterogeneity . National Tax Journal 52 ( 1 ): 5 30 . Barrow , Lisa , and Cecilia Elena Rouse . 2004 . Using market valuation to assess public school spending . Journal of Public Economics 88 ( 9 ): 1747 1769 . doi:10.1016/S0047-2727(03)00024-0. Bogin , Alexander , and Phuong Nguyen-Hoang . 2014 . Property left behind: The unintended consequences of a No Child Left Behind “failing” school designation . Journal of Regional Science 54 ( 5 ): 788 805 . doi:10.1111/jors.12141. Brunner , Eric J. , James Murdoch , and Mark Thayer . 2002 . School finance reform and housing values: Evidence from Los Angeles . Public Finance and Management 2 ( 4 ): 535 565 . Chakrabarti , Rajashri , and Joydeep Roy . 2015 . Housing markets and residential segregation: Impacts of the Michigan school finance reform on inter-and intra-district sorting . Journal of Public Economics 122 : 110 132 . doi:10.1016/j.jpubeco.2014.08.007. Clapp , John M. , Anupam Nanda , and Stephen L. Ross . 2008 . Which school attributes matter? The influence of school district performance and demographic composition on property values . Journal of Urban Economics 63 ( 2 ): 451 466 . doi:10.1016/j.jue.2007.03.004. Cortina , Jose M. 1993 . What is coefficient alpha? An examination of theory and applications . Journal of Applied Psychology 78 ( 1 ): 98 104 . doi:10.1037/0021-9010.78.1.98. Cronbach , Lee J. 1951 . Coefficient alpha and the internal structure of tests . Psychometrika 16 ( 3 ): 297 334 . doi:10.1007/BF02310555. Dee , Thomas S. 2000 . The capitalization of education finance reforms . Journal of Law & Economics 43 ( 1 ): 185 214 . doi:10.1086/467452. Downes , Thomas . 2010 . Centralization of school finance and property values: Lessons from Vermont . Working Paper No. WP10RTDI . Cambridge, MA : Lincoln Institute of Land Policy . Duncombe , William , and Dan Goldhaber . 2003 . Adjusting for geographic differences in the cost of educational provision in Maryland . Available http://dlslibrary.state.md.us/publications/exec/msde/agdcepm_2003.pdf. Accessed 10 December 2017 . Duncombe , William , and Dan Goldhaber . 2009 . Adjusting for geographic differences in the cost of educational provision in Maryland: Revisions to the original report . Available https://marylandassociationofcounties.files.wordpress.com/2015/10/2009-update.pdf. Accessed 18 December 2017 . Duncombe , William , and John Yinger . 1998 . School finance reform: Aid formulas and equity objectives . National Tax Journal 51 ( 2 ): 239 262 . Duncombe , William D. , and John Yinger . 2001 . Alternative paths to property tax relief . In Property taxation and local government finance , edited by W. E. Oates , pp. 243 294 . Cambridge, MA : Lincoln Institute of Land Policy . Duncombe , William , and John Yinger . 2011 . Making do: State constraints and local responses in California's education finance system . International Tax and Public Finance 18 ( 3 ): 337 368 . doi:10.1007/s10797-010-9159-3. Epple , Dennis , and Maria Marta Ferreyra . 2008 . School finance reform: Assessing general equilibrium effects . Journal of Public Economics 92 ( 5–6 ): 1326 1351 . doi:10.1016/j.jpubeco.2007.11.005. Ferreyra , Maria Marta . 2009 . An empirical framework for large-scale policy analysis, with an application to school finance reform in Michigan . American Economic Journal: Economic Policy 1 ( 1 ): 147 180 . doi:10.1257/pol.1.1.147. Figlio , David N. , and Maurice E. Lucas . 2004 . What's in a grade? School report cards and the housing market . American Economic Review 94 ( 3 ): 591 604 . doi:10.1257/0002828041464489. Fisher , Ronald C. , and Leslie E. Papke . 2000 . Local government responses to education grants . National Tax Journal 53 ( 3 ): 153 168 . Glaeser , Edward L. , Joshua D. Gottlieb , and Kristina Tobio . 2012 . Housing booms and city centers . American Economic Review 102 ( 3 ): 127 133 . doi:10.1257/aer.102.3.127. Guilfoyle , Jeffrey P. 1998 . The incidence and housing market effects of Michigan's 1994 school finance reforms . Proceedings: Annual Conference on Taxation and Minutes of the Annual Meeting of the National Tax Association 91 : 223 229 . Hilber , Christian A. L. , Teemu Lyytikäinen , and Wouter Vermeulen . 2011 . Capitalization of central government grants into local house prices: Panel data evidence from England . Regional Science and Urban Economics 41 ( 4 ): 394 406 . doi:10.1016/j.regsciurbeco.2010.12.006. Hoxby , Caroline M. 2001 . All school finance equalizations are not created equal . Quarterly Journal of Economics 116 ( 4 ): 1189 1231 . doi:10.1162/003355301753265552. Huang , Yao . 2004 . A guide to state operating aid programs for elementary and secondary education . In Helping children left behind: State aid and the pursuit of educational equity , edited by John Yinger , pp. 331 349 . Cambridge, MA : MIT Press . Maryland Department of Legislative Services . 2002 . The Bridge to Excellence in Public Schools Act of 2002: Its origins, components, and future . Available http://dlslibrary.state.md.us/publications/opa/i/cefee_2002_pres.pdf. Accessed 20 December 2017 . Morgan , Stephen L. , and Christopher Winship . 2007 . Counterfactuals and causal inference: Methods and principles for social research . New York : Cambridge University Press . doi:10.1017/CBO9780511804564. Nechyba , Thomas J. 2004 . Prospects for achieving equity or adequacy in education: The limits of state aid in general equilibrium . In Helping children left behind: State aid and the pursuit of educational equity , edited by John Yinger , pp. 111 143 . Cambridge, MA : MIT Press . Nguyen-Hoang , Phuong , and John Yinger . 2011 . The capitalization of school quality into house values: A review . Journal of Housing Economics 20 ( 1 ): 30 48 . doi:10.1016/j.jhe.2011.02.001. Nguyen-Hoang , Phuong , and John Yinger . 2014 . Education finance reform, local behavior, and student performance in Massachusetts . Journal of Education Finance 39 ( 4 ): 297 322 . Nunnally , Jum C. , and Ira H. Bernstein . 1994 . Psychometric theory , 3rd ed. New York : McGraw-Hill, Inc. Rosen , Sherwin . 1974 . Hedonic prices and implicit markets: Product differentiation in pure competition . Journal of Political Economy 82 ( 1 ): 34 55 . doi:10.1086/260169. Ross , Stephen , and John Yinger . 1999 . Sorting and voting: A review of the literature on urban public finance. In Handbook of regional and urban economics , edited by Paul Cheshire and Edwin S. Mills , pp. 2001 2060 . New York : Elsevier North-Holland . Roy , Joydeep . 2004 . Effect of a school finance reform on housing and residential segregation: Evidence from Proposal A in Michigan . Available http://dx.doi.org/10.2139/ssrn.630122. Accessed 13 December 2016 . Taylor , Laura O. 2008 . Theoretical foundations and empirical developments in hedonic modeling . In Hedonic methods in housing markets , edited by Andrea Baranzini , José Ramirez , Caroline Schaerer , and Philippe Thalmann , pp. 15 37 . New York : Springer . doi:10.1007/978-0-387-76815-1_2. Wyckoff , Paul Gary . 1995 . Capitalization, equalization, and intergovernmental aid . Public Finance Review 23 ( 4 ): 484 508 . doi:10.1177/109114219502300404. Wyckoff , Paul Gary . 2001 . Capitalization and the incidence of school aid . Journal of Education Finance 27 ( 1 ): 585 607 . Yinger , John . 2004 . State aid and the pursuit of educational equity: An overview . In Helping children left behind: State aid and the pursuit of educational equity , edited by John Yinger , pp. 3 57 . Cambridge, MA : MIT Press . Yinger , John . 2015 . Hedonic markets and sorting equilibria: bid-function envelopes for public services and neighborhood amenities . Journal of Urban Economics 86 ( March ): 9 25 . doi:10.1016/j.jue.2014.12.001. Yinger , John , Howard S. Bloom , Axel Börsch-Supan , and Helen F. Ladd . 1988 . Property taxes and house values: The theory and estimation of intrajurisdictional property tax capitalization . San Diego : Academic Press . Zabel , Jeffrey , and Dennis Guignet . 2012 . A hedonic analysis of the impact of LUST sites on house prices in Frederick, Baltimore, and Baltimore City counties . Resource and Energy Economics 34 : 549 564 . doi:10.1016/j.reseneeco.2012.05.006. ## Notes 1. Hoxby (2001) estimates the impacts of parameters in school finance reform schemes on property values, but she does not estimate the overall impact on property values of specific reform plans. Some studies also look at the general relation between state aid and housing prices (Barrow and Rouse 2004; Hilber, Lyytikäinen, and Vermeulen 2011). 2. BTE provides “bridge funding” in FY 2003 between the old and new systems, which was financed with a 34-cent increase in the tobacco tax. Up to$64.7 million among the $80.5 million is distributed “in a way that is proportionate to the amount of funding that the school systems would have received in fiscal 2003 under Senate Bill 856 if the phase-in of the new financing system had started in fiscal 2003” (Maryland Department of Legislative Services 2002, pp. 15–16). 3. Hedonic studies, which build on Rosen (1974), are reviewed in Taylor (2008); the relevant literature in local public finance is reviewed in Ross and Yinger (1999). The connections between these two literatures are explored in Yinger (2015). 4. Yinger (2015) derives a more general version of this approach based on constant elasticity demand functions for public services and housing. He shows that the quadratic case corresponds to the assumption that the price elasticity of demand for public services is infinite, which corresponds in turn to a public service demand curve that is horizontal. He also shows that a linear specification for the hedonic is inconsistent with the standard sorting theorem. 5. The literature on cost functions is reviewed in Duncombe and Yinger (2001 and 2011); studies of the impact of state aid on the demand for local services are reviewed in Fisher and Papke (2000); other aspects of this demand are examined in Duncombe and Yinger (1998, 2011) and Nguyen-Hoang and Yinger (2014). 6. Any re-sorting will be associated with BTE-induced changes in school quality—not with BTE-induced changes in school property taxes. Ross and Yinger (1999) show that property tax differences across communities are capitalized into house values but do not result in sorting because all households are willing to pay$1 for a $1 lower property-tax payment. 7. Changes in sorting might also lead to changes in housing characteristics, such as the addition of new rooms when richer households move in. However, we only observe changes in housing characteristics between sales, which, by definition, are made by the pre-BTE buyer, not the post-BTE buyer. 8. For simplicity, equation 1 expresses the N variables in linear form—following the earlier discussion, however, our equation actually uses a quadratic form for these variables when they are continuous. For readability, the h subscript is omitted from the time variables. 9. Without the assumption that Ns and Xs are constant over time, a differenced version of our model includes the changes in N and X. In cases of houses being sold more than three times, we used each pair of repeated sales. 10. The growth rate can be estimated with months as the unit of time (instead of years) but is written here with the year indicator to simplify the notation. If months are used, then double sales within a single year can be included, even though the district-based variables all equal zero for these observations. It increases the number of observations that can be used in the analysis, but some care needs to be taken in using sales data within a year because it is possible that repeated sales data within a year might just reflect changes in the property records, not actual sales of houses. 11. Aside from the tobacco tax mentioned in footnote 2, the BTE reforms were funded by state general revenue, which comes largely from income and sales taxes. The connection between these taxes is not very salient, so the effect on household bids is likely to be small. Nevertheless, both of our methods net out any tax-related changes. Method 1 nets them out by expressing results relative to type-1 districts. Method 2 nets them out by including neighborhood income-by-year fixed effects. 12. Appendix table A.1 summarizes our data-filtering process. 13. Cronbach's alpha is one of the common statistics for test construction and use. It mainly checks the reliability of tests based on split-half reliability concepts (Cronbach 1951; Cortina 1993). 14. We do not know the assessment for an individual house, so we cannot examine the capitalization of within-district variation in the effective tax rate, as in Yinger et al. (1988). 15. Prices and price trends shifted upward in all district classes relative to the pre-reform trend. Following our theoretical predictions, we focus on changes relative to the lowest-FRPL districts. 16. The quadratic form is not used for the Rail station variable because it is a dichotomous variable representing whether the closest rail station is located less than five miles away from the property (and appears or disappears between sales). 17. We use pre-reform pupil measures when calculating state aid per pupil. For example, change in state aid per pupil between FY 2003 and FY 2007 is measured as the difference between (aid for FY 2007 / enrollment for FY 2003) and (aid for FY 2003 / enrollment for FY 2003). Thus, we are able to exclude any possible effects of re-sorting that reform induced (due to change in enrollment or education cost) on housing price. This allows us to estimate the impact of change in the state aid formula on housing prices. 18. Cost-adjusted state aid refers to Geographic Cost Education Index (GCEI)-adjusted state aid per pupil. The calculation process was as follows: first, current inflation-adjusted state aid was divided by the GCEI for the state of Maryland (developed by Duncombe and Goldhaber 2003, 2009). Then, aid per pupil was generated using weights that had been used in Maryland school finance reform for special education, LEP, and FRPL-eligible students. To be specific, the weights of students with special needs (e.g., special education, LEP, and FRPL) are 1.16, 1.10, and 1, respectively. 19. However, cleaning a dataset based on the dependent variables could generate biased estimates. To check any possible bias arising from omission of sales data with extreme value, several versions of the dataset were utilized in the analysis. The use of different versions of the data does not change the main results. ## Appendix A: Data Description Appendix table A.1 presents the data-filtering process conducted in order to eliminate house sales observations that may be inaccurate. Our initial sales data about houses from 1998 to 2007 is 796,887. When combining two datasets (e.g., CAMA and RPSF) using account information on the property, the matching rate is 99.78 percent. Table A.1. Data Filtering Process ItemsNumber of Observations Raw data set (arm's length sales data, land use of residential, townhouse, and townhouse condominium) 796,887 Dropped one of sales if sales of houses repeated within the 6-month period 7,221 Dropped samples when houses are boat slips, mobile homes, or rental dwellings 16,006 Dropped samples when houses cannot be projected on the map 229 Dropped samples when sales price <$20,000 or >$5,000,000a 865 All sales data after data filtering processb 772,566 Dropped nonrepeated sales data 458,171 Repeat sales after data filtering processc 314,395 ItemsNumber of Observations Raw data set (arm's length sales data, land use of residential, townhouse, and townhouse condominium) 796,887 Dropped one of sales if sales of houses repeated within the 6-month period 7,221 Dropped samples when houses are boat slips, mobile homes, or rental dwellings 16,006 Dropped samples when houses cannot be projected on the map 229 Dropped samples when sales price <$20,000 or >$5,000,000a 865 All sales data after data filtering processb 772,566 Dropped nonrepeated sales data 458,171 Repeat sales after data filtering processc 314,395 aTo check any possible bias arising from omission of sales data with extreme value, several versions of the dataset were utilized in the analysis. The results show a consistent pattern. bTotal number of houses is 603,258. cTotal number of houses is 144,955. Table A.2. Variables for Neighborhood Amenities/Disamenities NameDescriptionData Source Boat ramp Dichotomous variable equals one if distance to nearest boat ramp is less than 0.25 miles, otherwise zero MDSHA BWI airport Dichotomous variable equals one if distance to nearest BWI airport road is less than 10 miles, otherwise zero MDSHA Commuter/subway/metro station Dichotomous variable equals one if distance to nearest station is less than 5 miles, otherwise zero MDSHA Court Dichotomous variable equals one if distance to nearest court is less than 0.25 miles, otherwise zero MDSHA Environmental hazard Dichotomous variable equals one if distance to nearest environmental hazard is less than 1 miles, otherwise zero EPA Fire station Dichotomous variable equals one if distance to nearest post office is less than 0.25 miles, otherwise zero MDSHA Golf course Dichotomous variable equals one if distance to nearest golf course is less than 0.25 miles, otherwise zero MDSHA Government office Dichotomous variable equals one if distance to nearest government office is less than 0.25 miles, otherwise zero MDSHA Highway Dichotomous variable equals one if distance to nearest highway road is less than 0.25 miles, otherwise zero MDSHA Historic site Dichotomous variable equals one if distance to nearest boat ramp is less than 0.25 miles, otherwise zero MDSHA Hospital Dichotomous variable equals one if distance to nearest hospital road is less than 0.25 miles, otherwise zero MDSHA Small airport (landing strip) Dichotomous variable equals one if distance to nearest small airport is less than 1 miles, otherwise zero MDSHA Library Dichotomous variable equals one if distance to nearest library is less than 0.25 miles, otherwise zero MDSHA Museum Dichotomous variable equals one if distance to nearest museum road is less than 0.25 miles, otherwise zero MDSHA Park Dichotomous variable equals one if distance to nearest park is less than 0.25 miles, otherwise zero MDP Park & ride Dichotomous variable equals one if distance to nearest park & ride is less than 0.25 miles, otherwise zero MDSHA Police station Dichotomous variable equals one if distance to nearest police station is less than 0.25 miles, otherwise zero MDSHA Post office Dichotomous variable equals one if distance to nearest post office is less than 0.25 miles, otherwise zero MDSHA Prison Dichotomous variable equals one if distance to nearest prison is less than 0.25 miles, otherwise zero MDSHA Railroad Dichotomous variable equals one if distance to nearest railroad is less than 0.25 miles, otherwise zero MDSHA Shopping center Dichotomous variable equals one if distance to nearest shopping center is less than 1 miles, otherwise zero MDSHA Total crime rate total crime rate per 100,000 inhabitants FBI Town hall Dichotomous variable equals one if distance to nearest town hall is less than 0.25 miles, otherwise zero MDSHA Water Dichotomous variable equals one if distance to nearest lake or sea is less than 0.25 miles, otherwise zero MDP Distance to BWI airport Distance to nearest BWI airport if less than 10 miles MDSHA Distance to boat ramp Distance to nearest boat ramp if less than 0.25 mile MDSHA Distance to commuter/subway/metro stations Distance to nearest station if less than 5 miles MDSHA Distance to highway Distance to nearest Highway if less than 1 mile MDP Distance to water Distance to nearest lake or sea if less than 0.25 mile MDP NameDescriptionData Source Boat ramp Dichotomous variable equals one if distance to nearest boat ramp is less than 0.25 miles, otherwise zero MDSHA BWI airport Dichotomous variable equals one if distance to nearest BWI airport road is less than 10 miles, otherwise zero MDSHA Commuter/subway/metro station Dichotomous variable equals one if distance to nearest station is less than 5 miles, otherwise zero MDSHA Court Dichotomous variable equals one if distance to nearest court is less than 0.25 miles, otherwise zero MDSHA Environmental hazard Dichotomous variable equals one if distance to nearest environmental hazard is less than 1 miles, otherwise zero EPA Fire station Dichotomous variable equals one if distance to nearest post office is less than 0.25 miles, otherwise zero MDSHA Golf course Dichotomous variable equals one if distance to nearest golf course is less than 0.25 miles, otherwise zero MDSHA Government office Dichotomous variable equals one if distance to nearest government office is less than 0.25 miles, otherwise zero MDSHA Highway Dichotomous variable equals one if distance to nearest highway road is less than 0.25 miles, otherwise zero MDSHA Historic site Dichotomous variable equals one if distance to nearest boat ramp is less than 0.25 miles, otherwise zero MDSHA Hospital Dichotomous variable equals one if distance to nearest hospital road is less than 0.25 miles, otherwise zero MDSHA Small airport (landing strip) Dichotomous variable equals one if distance to nearest small airport is less than 1 miles, otherwise zero MDSHA Library Dichotomous variable equals one if distance to nearest library is less than 0.25 miles, otherwise zero MDSHA Museum Dichotomous variable equals one if distance to nearest museum road is less than 0.25 miles, otherwise zero MDSHA Park Dichotomous variable equals one if distance to nearest park is less than 0.25 miles, otherwise zero MDP Park & ride Dichotomous variable equals one if distance to nearest park & ride is less than 0.25 miles, otherwise zero MDSHA Police station Dichotomous variable equals one if distance to nearest police station is less than 0.25 miles, otherwise zero MDSHA Post office Dichotomous variable equals one if distance to nearest post office is less than 0.25 miles, otherwise zero MDSHA Prison Dichotomous variable equals one if distance to nearest prison is less than 0.25 miles, otherwise zero MDSHA Railroad Dichotomous variable equals one if distance to nearest railroad is less than 0.25 miles, otherwise zero MDSHA Shopping center Dichotomous variable equals one if distance to nearest shopping center is less than 1 miles, otherwise zero MDSHA Total crime rate total crime rate per 100,000 inhabitants FBI Town hall Dichotomous variable equals one if distance to nearest town hall is less than 0.25 miles, otherwise zero MDSHA Water Dichotomous variable equals one if distance to nearest lake or sea is less than 0.25 miles, otherwise zero MDP Distance to BWI airport Distance to nearest BWI airport if less than 10 miles MDSHA Distance to boat ramp Distance to nearest boat ramp if less than 0.25 mile MDSHA Distance to commuter/subway/metro stations Distance to nearest station if less than 5 miles MDSHA Distance to highway Distance to nearest Highway if less than 1 mile MDP Distance to water Distance to nearest lake or sea if less than 0.25 mile MDP Notes: All variables about distance between amenities and houses are measured in meters. Distances between houses and amenities are calculated on the basis of the Near function and Distance function in ArcGIS 9.3. Near function identifies the nearest amenities from house and Distance function calculates the straight-line distance between two points such as houses and amenities. When amenities variables are described as point variables in the map, distance between amenities and house is calculated along a straight line between two points. On the other hand, when amenities variables are represented as a line features such as a river or a set of line features for polygons such as parks, then the distance between amenities and house is calculated along a straight line to the nearest point on the line features. MDP = Maryland Department of Planning; MDSHA = Maryland State Highway Administration. Table A.3. School District Characteristics VariablesDefinitionData Source Total state aid per pupil All types of funds (e.g., current expenses, food service, school construction, and debt service) divided by total enrollment in a school district MSDE Current state aid per pupil The current expenses fund without the state's contribution to teacher retirements, divided by total enrollment in a school district MSDE Effective tax rate Nominal school district tax rates are multiplied by average assessment ratios in residential properties MSDAT Dropout rates The share of dropouts in school district i MSDE 3rd grade elementary passing rate The share passing in Reading and Math for third grade from MSA and MSPAP in school district i MSDE 5th grade elementary passing rate The share passing in Reading and Math for fifth grade from MSA and MSPAP in school district i MSDE High school passing rate The share passing in English 2, Government, Algebra, and Biology from High School Assessment in school district i MSDE African American The share of African American students in a school district MSDE Hispanic The share of Hispanic students within a school district MSDE Free and reduced-price lunch eligible The share of students eligible for free or reduced-price lunch programs within a school district MSDE Special education The share of students with special education within a school district MSDE Limited English proficiency The share of students with limited English proficiency within a school district MSDE VariablesDefinitionData Source Total state aid per pupil All types of funds (e.g., current expenses, food service, school construction, and debt service) divided by total enrollment in a school district MSDE Current state aid per pupil The current expenses fund without the state's contribution to teacher retirements, divided by total enrollment in a school district MSDE Effective tax rate Nominal school district tax rates are multiplied by average assessment ratios in residential properties MSDAT Dropout rates The share of dropouts in school district i MSDE 3rd grade elementary passing rate The share passing in Reading and Math for third grade from MSA and MSPAP in school district i MSDE 5th grade elementary passing rate The share passing in Reading and Math for fifth grade from MSA and MSPAP in school district i MSDE High school passing rate The share passing in English 2, Government, Algebra, and Biology from High School Assessment in school district i MSDE African American The share of African American students in a school district MSDE Hispanic The share of Hispanic students within a school district MSDE Free and reduced-price lunch eligible The share of students eligible for free or reduced-price lunch programs within a school district MSDE Special education The share of students with special education within a school district MSDE Limited English proficiency The share of students with limited English proficiency within a school district MSDE Notes: To check any possible bias arising from omission of sales data with extreme value, several versions of the dataset were utilized in the analysis. The results show a consistent pattern. MSA = Maryland School Assessment; MSDAT = Maryland State Department of Assessments and Taxation; MSDE = Maryland State Department of Education; MSPAP = Maryland School Performance Assessment Program. To clean the dataset of inaccurate observations, we eliminated sales with the following procedure. Because neighborhood amenities will be attached to houses based on their geographic location (e.g., latitude and longitude), 229 sales of houses that could not be projected on the map were dropped. Sales records are dropped (7,221 sales records) if sales of houses are repeated within a six-month period because it could simply reflect the transition of a sale record and not the actual sale. Sales of houses that are boat slips, rental dwellings, or mobile homes are dropped because this paper focuses on residential property (16,006 sales records). Like Zabel and Guignet (2012), who use the same source of property value data in Maryland, we exclude houses for which the sales price is lower than$20,000 or higher than \$5,000,000. This results in another 865 sale records being dropped from the base dataset.19 In total, approximately 24,000 sales are dropped from the dataset.

As a result of this cleaning process, we have total sales records of 772,566 from 603,258 houses. When focusing on only repeated sales data, there are 314,395 repeated sales records, from samples of 144,955 houses.

**

Deceased.