1 School-Quality CapitalizationECN741, Urban Economics Professor John Yinger, The Maxwell School, Syracuse University, 2016

2 Methodological Challenges ExamplesSchool Quality Capitalization Class Outline Methodological Challenges Examples Recent Publications Cleveland Application Outline

3 Methodological Challenges ExamplesSchool Quality Capitalization Class Outline Methodological Challenges Examples Recent Publications Cleveland Application Outline

4 Methodological ChallengesSchool Quality Capitalization Methodological Challenges 1. Functional form 2. Defining School Quality (S) 3. Controlling for neighborhood traits 4. Controlling for housing characteristics Challenges

5 School Quality CapitalizationFunctional Form As discussed in previous classes, simply regressing V on S (with or without logs) is not satisfactory. Regressing ln{V} on S and S2 is pretty reasonable—but cannot yield structural coefficients. To obtain structural coefficients, one must use nonlinear regression or the Rosen 2-step method (with a general form for the envelope and a good instrument for the 2nd step)—or something fancier. Challenges

6 Defining School QualitySchool Quality Capitalization Defining School Quality Most studies use a test score measure. A few use a value-added test score. A few use a graduation rate. Some use inputs (spending or student/teacher ratio), which is not compelling to me. A few use multiple output measures—but more studies should do this! Challenges

7 Neighborhood ControlsSchool Quality Capitalization Neighborhood Controls Data quality varies widely; some studies have many neighborhood controls. Many fixed-effects approaches are used (sometimes inappropriately) to account for unobservables, e.g.: Border fixed effects (cross section) Neighborhood fixed effects (panel) Another possible approach is to use instrumental variables—for every amenity!!! Challenges

8 School Quality CapitalizationBorder Fixed Effects BFEs were popularized by Black (QJE, May 1999); they appear in at least 16 studies. BFEs define elementary school attendance zone boundary segments. Define a border fixed effect (BFE) for each segment, equal to one for houses within a selected distance from the boundary. Drop all observations farther from boundary. Challenges

9 Border Fixed Effects, 2 School Quality Capitalization SchoolHouse Sale Dropped Observations Boundary Segment Challenges

10 School Quality CapitalizationBorder Fixed Effects, 3 The idea is that the border areas are like neighborhoods, so the BFEs pick up unobservables shared by houses on each side of the border. The size of the relevant border area is not known, so it it a good idea to try several different distances. Challenges

11 School Quality CapitalizationBorder Fixed Effects, 4 As discussed in the previous class BFEs have three main weaknesses: First, they may do little to eliminate the bias from omitted neighborhood traits, Second, they greatly cut the sample size, Third, they change the question addressed by a hedonic regression and are therefore easy to misinterpret. Challenges

12 School Quality CapitalizationBFEs and Sorting Two recent articles (Kane, Riegg, and Staiger (American Law and Economics Review, Summer 2006, and Bayer, Ferreira, and McMillan, JPE, August 2007) find significant differences in demographics (e.g. average household income) across attendance-zone boundaries. They make the reasonable argument that these differences are products of sorting; higher-income households end up on the better-school side of the boundary. Challenges

13 School Quality CapitalizationBFEs and Sorting, 2 B/F/M then argue that these demographic differences become neighborhood traits and they include them as controls. This strategy (including average neighborhood income and perhaps other demographic traits) is used by the vast majority of school-quality hedonic studies. The justification is that the coefficient of school quality will be biased without controls for these sorting-induced neighborhood differences. Challenges

14 School Quality CapitalizationBFEs and Sorting, 3 The problem with this approach is that, as discussed in the previous class, demographic traits of small neighborhoods are measures of demand—which do not belong in an hedonic. As Rosen argued long ago, the envelope is not a function of demand variables. Including demand variables re-introduces the endogeneity problem and changes the meaning of the results. Challenges

15 School Quality CapitalizationBFE and Sorting, 4 In sum, the estimated impact of school quality on house values may be biased if neighborhood demographic traits are omitted from the regression, but including variables that are determinants of demand (even if they are also measures of neighborhood amenities) is not a solution. One cannot solve an omitted-variable problem by altering the meaning of a regression (in this case from a hedonic to bid functions). If the coefficient of school quality drops when neighborhood income is included, this just shows that the slope of the (mis-specified) bid function is lower than the slope of the (possibly biased) envelope. Challenges

16 School Quality CapitalizationBFE and Sorting, 5 This problem is more serious with very small neighborhoods (e.g. block groups) than with medium neighborhoods (e.g. tracts), and may not arise with large neighborhoods (e.g. zip codes). One relatively easy way to avoid this problem is to collect data on neighborhood traits that are correlated with income but are not demand determinants, such as the distance to parks, golf courses, or lakes. Challenges

17 School Quality CapitalizationOther Fixed Effects Other types of fixed effects are possible with panel data: Tract fixed effects School district fixed effects House fixed effects (with a panel large enough to observe double sales). These approaches account for some unobservable factors, but may also introduce problems. Challenges

18 Possible Problems with Fixed EffectsSchool Quality Capitalization Possible Problems with Fixed Effects These fixed effects limit the variation in the data for estimating school quality capitalization. The coefficients of school quality and other amenities must be estimated based on changes in these variables over time. School quality and other amenities may not change much over time, so it may be difficult to estimate their effects. The behavioral response to short-run changes in an amenity may be different from the long-run effects that determine cross-sectional variation; for example, people may not respond to a one-year increase in student test scores that does not alter a schools reputation. Challenges

19 The IV Approach School Quality CapitalizationWith omitted variables, explanatory variables are likely to be correlated with the error term. One possible correction is to use instrumental variables—and 2SLS. However, credible IVs are difficult to find. No study had identified an IV that provides a general correction for omitted variable bias in estimating school quality capitalization. Moreover, identification requires an instrument for every amenity—not just for one. An equation with more than one amenity possibly affected by omitted variable bias but with an instrument for only one amenity (school quality, say) is not identified! Challenges

20 Controlling for Housing TraitsSchool Quality Capitalization Controlling for Housing Traits A housing hedonic requires control variables for the structural characteristics of housing. Because housing, neighborhood, and school traits are correlated, good controls for housing traits are important (but surprisingly limited in many studies). As discussed later, the widely cited B/F/M article has only 2 housing traits: number of rooms and year built, plus one trait correlated with housing type: whether owner-occupied. Challenges

21 School Quality CapitalizationHousing Traits, 2 If good data on housing traits are available, one strategy for a cross-section is to estimate the hedonic in two stages. Stage 1: Define fixed effects for the smallest observable neighborhood type (e.g. block group or tract); in a sample of house sales, regress V on housing traits and these FE’s—with no neighborhood traits. Stage 2: Use the coefficients of the FE’s as the dependent variable in a second stage with neighborhood traits on the right side; the number of observations equals the number of neighborhoods. Challenges

22 Housing Traits, 3 This approach has two advantages:School Quality Capitalization Housing Traits, 3 This approach has two advantages: The coefficients of the housing traits cannot be biased due to missing neighborhood variables. The second stage need not follow the same form as the first, so this approach adds functional-form flexibility. Note that the standard errors in the 2nd stage must be corrected for heteroskedasticity. The coefficient of each FE is based on a different number of observations—with a different variance. Challenges

23 Methodological Challenges ExamplesSchool Quality Capitalization Class Outline Methodological Challenges Examples Recent Publications Cleveland Application Outline

24 Selected Recent ExamplesSchool Quality Capitalization Selected Recent Examples Epple, Peress, and Sieg (AEJ: Microecconomics, November 2010) Bayer, Ferriera, and MacMillan (JPE, August ) Clapp, Nanda, and Ross (JUE, March 2008) Bogin (Syracuse dissertation 2011, now Bogin/Nguyen-Hoang, JRS, November 2014), building on Figlio and Lucas (AER, June 2004) Yinger (JUE, March 2015) Recent Studies

25 School Quality CapitalizationE/P/S E/P/S have house sales data for the Pittsburgh area. Their strategy is to solve and estimate a general equilibrium model with variation in income and one taste parameter—both assumed to have a certain form. This allows them to have heterogeneity within a jurisdiction—a huge advantage of this approach. The big disadvantage is that they have a single amenity index (a linear combination of 3 variables). This method is also technically complex, although the first stage is the same is mine (discussed below). Recent Studies

26 B/F/M B/F/M have census data from the San Francisco area.School Quality Capitalization B/F/M B/F/M have census data from the San Francisco area. They estimate a linear hedonic with BFE’s, pooling sales and rental data. (They also estimate a fancy multinomial choice model, which is not considered here.) They find that adding the BFE’s cuts the impact of school quality on housing prices. They find that adding neighborhood income cuts the impact of school quality even more. Recent Studies

27 School Quality CapitalizationB/F/M Hedonic Recent Studies

28 School Quality CapitalizationB/F/M Issues They estimate a linear hedonic, which rules out sorting (in an article about sorting!). Their discrete-choice model implies linear bid functions, which in turn imply an infinite price elasticity of demand and a quadratic hedonic, not a linear one (see the notes from the last class). In addition to BFEs, they have only 2 housing traits, 1 sort-of housing trait, and 4 location controls, one of which is a set of land uses. Recent Studies

29 School Quality CapitalizationB/F/M Issues, 2 B/F/M acknowledge that sorting exists and complicates a BFE approach by leading to different amenities on different sides of a boundary—a possible source of bias. They claim to solve this problem by including neighborhood demographics, including income, as controls; this approach, they say, picks up higher bids in neighborhoods that, due to sorting, have higher-income residents. But neighborhood income is a demand factor, which belongs in a bid function, not an envelope. Because of sorting, income is endogenous and a regression that includes income estimates bid-functions, not the envelope! One cannot solve a bias problem with a method that changes the meaning of the regression! Recent Studies

30 School Quality CapitalizationC/N/R C/N/R use a panel of housing transactions in Connecticut between 1994 and 2004 They use tract fixed effects to control for neighborhood quality in their panel data. They look at math scores and cost factors (e.g. student poverty) They find that tract fixed effects have little impact on the estimate of capitalization when income and other demographics are included. Recent Studies

31 School Quality CapitalizationC/N/R Hedonic Recent Studies

32 They have only 4 housing traits and 2 non- demand neighborhood traits.School Quality Capitalization C/N/R Issues They use a semi-log form with only one term for S, which rules out sorting. They control for neighborhood demographics, which raises the same issue as B/F/M: Should demand variables be included? They have only 4 housing traits and 2 non- demand neighborhood traits. Recent Studies

33 School Quality CapitalizationDhar/Ross, JUE, January 2012 In a follow up, Dhar/Ross use data from Connecticut and fixed effects for district boundary segments. They pool across metropolitan areas, which does not make sense to me; each area has its own equilibrium. They estimate a time-trend in the boundary fixed effects, which introduces (inappropriately) demographic changes into their controls. They use a semi-log form with only one term for S, which rules out sorting. They have only 4 housing traits, and only neighborhood dummies and school quality for amenities. Recent Studies

34 School Quality CapitalizationBogin/ Nguyen-Hoang The Florida school accountability program hands out “failing” grades to some schools. The Figlio/Lucas article looks at the impact of this designation on property values. The national No Child Left Behind Act also hands out “failing” grades. The 2011 Bogin essay (and follow-up article) looks at the impact of this designation on property values around Charlotte, North Carolina. In both cases, the failing grades are essentially uncorrelated with other measures of school quality. Recent Studies

35 School Quality CapitalizationBogin/ Nguyen-Hoang, 2 B/N-H find that a failing designation lowers property values by about 6%. This effect peaks about 7 months after the announcement and fades out after one year. They provide a clear interpretation of results with this “change” set-up. Because of possible re-sorting, the change in house values cannot be interpreted as a willingness to pay. A failing designation might change the type of people who move into a neighborhood. Consider the following figure from Bogin’s thesis: Recent Studies

36 School Quality CapitalizationBogin/ Nguyen-Hoang, 3 Recent Studies

37 Specification SummarySchool Quality Capitalization Specification Summary Many studies estimate the following and interpret β as the average MWTP: Problems: A linear specification is not appropriate because it rules out sorting. Average MWTP is a limited concept, even with the correct specification; it cannot be compared across place or time because it is affected by the sorting equilibrium. Recent Studies

38 Specification, 2 With a panel:School Quality Capitalization Specification, 2 With a panel: With sufficient observations, this approach can use double-sales data to difference out individual house fixed effects. With fewer observations, it can still difference out tract fixed effects. Recent Studies

39 Specification, 3 Problems with panel applications:School Quality Capitalization Specification, 3 Problems with panel applications: A linear specification is still not appropriate. The β coefficient does not measure average MWTP unless S does not change (in which case β cannot be estimated!), or there is no change in the distribution of demand for S and no re-sorting! These problems are ignored in the literature. Recent Studies

40 Specification, 4 School Quality CapitalizationCross-Section with Demand Variables: Problems: This is a bid-function regression, not an envelope. The income term, Y, is endogenous. Without an interaction between S and Y, the slope of the bid function (dV/dS) is the same for everyone and there is no sorting!! Recent Studies

41 School Quality CapitalizationSummary A recent paper by Yinger and Nguyen-Hoang (Journal of Benefit-Cost Analysis, online in November 2015), catalogues the hedonic “vices” found in recent studies. Their findings are summarized in the following table. Recent Studies

42 Table 7. Hedonic Vices in Selected Recent Empirical Hedonic StudiesSchool Quality Capitalization Table 7. Hedonic Vices in Selected Recent Empirical Hedonic Studies Functional Form Control Variable Interpretation Linear Contradictory Demand Neighborhood Fixed Effects Average MWTP Difference Regression Border (Neighborhood) Fixed Effects School Quality Studies Bayer et al. 2007 X Black 1999 Clapp et al. 2008 (X) Dhar & Ross 2012 Fack & Grenet 2010 Gibbons et al. 2013 Kane et al. 2006 Ries & Somerville 2010 Air Quality Studies Anselin & Lozano-Gracia 2008 Bajari et al. 2012 Brasington & Hite 2005 Kim et al. 2003 Zabel & Kiel 2000 Notes: This table includes all the empirical hedonic articles in the Social Science Citation Index that (a) cover school quality, or air quality, (b) were published after 2000, and (c) that were cited at least 10 times. We also include a few articles published since 2010, because it may take some time for a paper to be cited, and selected other well-known papers. Capitalization

43 Methodological Challenges ExamplesSchool Quality Capitalization Class Outline Methodological Challenges Examples Recent Publications Cleveland Application Outline

44 Estimates with a Derived EnvelopeSchool Quality Capitalization Estimates with a Derived Envelope Finally, let’s consider some results for both the hedonic and the underlying bid functions from the application of the method Yinger developed using data from a large metropolitan area. This method has several advantages: It avoids the endogeneity problem in the Rosen 2-step approach. It avoids inconsistency between the bid functions and their envelope (the hedonic equation). It includes most parametric forms for a hedonic as special cases. It allows for household heterogeneity. It leads to tests of key sorting theorems. A New Approach

45 Estimates with a Derived Envelope, 2School Quality Capitalization Estimates with a Derived Envelope, 2 This approach applies only to continuous amenities, such as school quality or particulates in the air, not to discrete amenities, such as a good view. This approach is based on the assumption of one-to-one matching, that is, to an equilibrium with a unique amenity level for each household type. It cannot address heterogeneity in a large city. It may not be a good approximation in other places. This approach relies on the assumption of constant elasticity demand functions, which may not be appropriate. However, most other forms implicitly rely on this assumption, too. A New Approach

46 My Envelope The form derived in an earlier class:School Quality Capitalization My Envelope The form derived in an earlier class: and X(λ) is the Box-Cox form. A starting point is a quadratic form, which corresponds to μ = -∞ and σ3 = 1 A New Approach

47 School Quality CapitalizationThe Brasington Data All home sales in Ohio in 2000, with detailed housing characteristics and house location; compiled by Prof. David Brasington. Matched to: School district and characteristics Census block group and characteristics Police district and characteristics Air and water pollution data Yinger focuses on the 5-county Cleveland area and add many neighborhood traits. A New Approach

48 School Quality CapitalizationMy Two-Step Approach Step 1: Estimate the envelope using my functional form assumptions to identify the price elasticity of demand, μ. Step 1A: Estimate hedonic with neighborhood fixed effects Step 1B: Estimate PE{S, t} for the sample of neighborhoods with their coefficients from Step 1A as the dependent variable. Step 2: Estimate the impact of income and other factors (except price) on demand. A New Approach

49 Neighborhood Fixed EffectsSchool Quality Capitalization Neighborhood Fixed Effects Start with Census block groups containing more than one observation. Split block-groups in more than one school district. Total number of “neighborhoods” in Cleveland area sub-sample: 1,665. A New Approach

50 Step 1A: Run Hedonic Regression with Neighborhood Fixed EffectsSchool Quality Capitalization Step 1A: Run Hedonic Regression with Neighborhood Fixed Effects Dependent variable: Log of sales price in Explanatory variables: Structural housing characteristics. Corrections for within-neighborhood variation in seven locational traits. Neighborhood fixed effects. 22,880 observations in Cleveland subsample. A New Approach

51 School Quality CapitalizationTable 1. Variable Definitions and Results for Basic Hedonic with Neighborhood Fixed Effects Variable Definition Coefficient Std. Error One Story House has one story 0.0050 Brick House is made of bricks 0.0153*** 0.0052 Basement House has a finished basement 0.0308*** Garage House has a garage 0.1414*** 0.0067 Air Cond. House has central air conditioning 0.0254*** 0.0055 Fireplaces Number of fireplaces 0.0316*** 0.0038 Bedrooms Number of bedrooms *** 0.0028 Full Baths Number of full bathrooms 0.0601*** 0.0042 Part Baths Number of partial bathrooms 0.0412*** 0.0041 Age of House Log of the age of the house *** 0.0032 House Area Log of square feet of living area 0.4237*** 0.0086 Lot Area Log of lot size 0.0844*** 0.0037 Outbuildings Number of outbuildings 0.1320*** 0.0396 Porch House has a porch 0.0327*** 0.0073 Deck House has a deck 0.0545*** 0.0053 Pool House has a pool 0.0910*** 0.0180 Date of Sale Date of house sale (January 1=1, December 31=365) 0.0002*** 0.0000 A New Approach

52 School Quality CapitalizationTable 1. Variable Definitions and Results for Basic Hedonic with Neighborhood Fixed Effects Variable Definition Coefficient Std. Error Commute 1a Employment wtd. commuting dist. (house-CBG), worksite 1 *** 0.0272 Commute 2a Employment wtd. commuting dist. (house-CBG), worksite 2 *** 0.0321 Commute 3a Employment wtd. commuting dist. (house-CBG), worksite 3 *** 0.0302 Commute 4a Employment wtd. commuting dist. (house-CBG), worksite 4 *** 0.0295 Commute 5a Employment wtd. commuting dist. (house-CBG), worksite 5 *** 0.0344 Dist. to Pub. Schoola Dist. to nearest pub. elementary school in district (house-CBG) 0.0061 Elem. School Scorea Average math and English test scores of nearest pub. elementary school relative to district (house-CBG) 0.0170 0.0197 Dist. to Private School Distance to nearest private school (house-CBG) *** 0.0057 Distance to Hazard Dist. to nearest environmental hazard (house-CBG) 0.0332*** 0.0082 Distance to Eriea Dist. to Lake Erie (if < 2; house-CBG) ** 0.0010 Distance to Ghettoa Dist. to black ghetto (if < 5; house-CBG) *** 0.0331 Distance to Airporta Dist. to Cleveland airport (if < 10; house-CBG) 0.0259** 0.0122 Dist. to CBG Center Distance from house to center of CBG *** 0.0074 Historic Districta In historic district on national register (house-CBG) 0.0120 0.0178 Elderly Housinga Within 1/2 mile of elderly housing project (house-CBG) * 0.0194 Family Housinga Within 1/2 mile of small family housing project (house-CBG) 0.0836** 0.0403 Large Hsg Projecta Within 1/2 mile of large family housing project (>200 units; house-CBG) ** 0.0257 High Crime Distance to nearest high-crime location (house-CBG) 0.0701*** 0.0246 A New Approach

53 Step 1B: Run Envelope RegressionSchool Quality Capitalization Step 1B: Run Envelope Regression Dependent variable: coefficient of neighborhood fixed effect plus the constant. Explanatory variables: Public services and neighborhood amenities Commuting variables Income and property tax variables Neighborhood control variables A New Approach

54 School Quality CapitalizationSchool Variables Variable Definition Elementary Average percent passing in 4th grade in nearest elementary school on 5 state tests (math, reading, writing, science, and citizenship) minus the district average (for and ). High School The share of students entering the 12th grade who pass all 5 tests (= the passing rate on the tests, which reflects students who do not drop out, multiplied by the graduation rate, which indicates the share of students who stay in school) averaged over and Value Added A school district's sixth grade passing rate (on the 5 tests) in minus its fourth grade passing rate in Minority Teachers The share of a district’s teachers who belong to a minority group A New Approach

55 Cleveland and East ClevelandSchool Quality Capitalization Cleveland and East Cleveland The Cleveland School District is unique in because: It was the only district to have private school vouchers It was the only district to have charter schools (except for 1 in Parma). The private and charter schools tend to be located near low-performing public schools. The East Cleveland School District is unique in because: It received a state grant for school construction in that was triple the size of its operating budget. No other district in the region received such a grant. A New Approach

56 Table 2. Descriptive Statistics for Key VariablesSchool Quality Capitalization Table 2. Descriptive Statistics for Key Variables Mean Std. Dev. Minimum Maximum CBG Price per unit of Housing Relative Elementary Scorea 0.3148 0.0894 0.0010 0.6465 High School Passing Rate 0.3197 0.2040 0.0491 0.7675 Elementary Value Addeda 0.2400 0.0942 0.0100 0.4960 Share Minority Teachersb 0.1329 0.1548 0.6146 Share Non-Black in CBGb 0.8022 0.3226 1.0000 Share Hispanic in CBG 0.9623 0.0810 0.3673 Weighted Commuting Distance 7.4567 7.2660 Income Tax Ratec 0.0091 0.0012 0.0075 School Tax Rate 0.0309 0.0083 0.0172 0.0643 City Tax Rated 0.0578 0.0140 0.0227 0.1033 Tax Break Rated 0.0330 0.0121 0.0047 0.0791 No A-to-S 0.1339 0.3407 0.0000 Not a City 0.1393 0.3464 Crime Lowhigh 0.0252 0.1569 Crime Highlow 0.1291 0.3354 Crime Highhigh 0.1934 0.3951 Crime Hotspot1 0.0126 0.1116 Crime Hotspot2 0.0354 0.1849 Crime Hotspot3 0.0847 0.2785 Crime Hotspot4 0.2667 0.4423 A New Approach

57 Some Preliminary ResultsSchool Quality Capitalization Some Preliminary Results In their “Vices” article, Yinger and Nguyen-Hoang use this data set to look at some of the problems that arise with hedonic regressions. The following figure shows results for the high school variable based on: A full-controls quadratic (the best choice without nonlinear estimation) A limited-controls quadratic A limited-controls quadratic with CBG demographics (a mis-specified bid-function regression) A limited-controls quadratic with CBG demographics and an interaction between CBG income and the high school variable (a better bid-function regression, drawn for mean income). A New Approach

58 Some Preliminary Results, 2School Quality Capitalization Some Preliminary Results, 2 A New Approach

59 School Quality CapitalizationThe Main Results The following three tables and two graphs present the main results in my JUE article. Table 3. Results for Tax, Commuting, Crime, Pollution, and Ancillary School Variables Table 4. Results for Other Geographic Controls Table 5. Specification Tests and Results for Key School and Ethnicity Variables Envelope for Relative Elementary Score Envelope for High School Passing Rate A New Approach

60 School Quality CapitalizationTable 3. Results for Tax, Commuting, Crime, Pollution, and Ancillary School Variables Variable Definition Coefficient R.Std. Error Income Tax Rate School district income tax rate. 1.8818 5.1607 School Tax Rate School district effective property tax rate. 3.8335*** 1.2968 City Tax Rate Effective city property tax rate beyond school tax. 1.3896 Tax Break Rate Exemption rate for city property tax 4.0874* 2.1146 Not a City CBG not in a city 0.0673* 0.0385 Commute 1 Job-weighted distance to worksites *** 0.0072 Commute 2 (Commute 1) squared 0.0004*** 0.0002 Crime Lowhigh Low property, high violent crime *** 0.0333 Crime Highlow High property, low violent crime ** 0.0149 Crime Highhigh High property and violent crime *** 0.0214 Crime Hotspot1 CBG within ½ mile of crime hot spot *** 0.0500 Crime Hotspot2 CBG ½ to 1 mile from crime hot spot * 0.0392 Crime Hotspot3 CBG 1 to 2 miles from crime hot spot *** 0.0341 Crime Hotspot4 CBG 2 to 5 miles from crime hot spot * Village CBG receives police from a village ** 0.0493 Township CBG receives police from a township *** 0.0431 County Police CBG receives police from a county *** 0.0452 City Population Population of city (if CBG in a city) -2.09E-05*** 0.0000 Smog CBG within 20 miles of air pollution cluster *** 0.0701 Smog Distance (Smog)×Distance to cluster (not to the NW) 0.0080** 0.0039 Near Hazard CBG is within 1 mile of a hazardous waste site *** 0.0169 Distance to Hazard Distance to nearest hazardous waste site (if <1) 0.0749*** 0.0229 Value Added 1 School district's 6th grade passing rate on 5 state tests in minus its 4th grade passing rate in 1.1913*** 0.3924 Value Added 2 (Value Added 1) squared *** 0.6998 Minority Teachers 1 Share of district's teachers from a minority group 0.3260 0.2169 Minority Teachers 2 (Minority Teachers 1) squared * 0.3921 Cleveland SD Dummy for Cleveland & E. Cleveland Schl. Dists. 0.4755 0.3269 Near Public CBG is within 2 miles of public elem. school 0.0220 Distance to Public (Near Public) ×Distance to public school 0.0108 Near Private CBG is within 5 miles of a private school 0.0209 Distance to Private (Near Private) ×Distance to private school 0.0050 A New Approach

61 Table 4. Results for Other Geographic ControlsSchool Quality Capitalization Table 4. Results for Other Geographic Controls Variable Definition Coefficient Robust Std. Error Lakefront Within 2 miles of Lake Erie 0.070*** 0.0239 Distance to Lake (Lakefront) ×(Distance to Lake Erie) 0.0192 Snowbelt 1 (East of Pepper Pike) ×(Distance to Lake Erie) 0.0291*** 0.0066 Snowbelt 2 (Snowbelt 1) squared *** 0.0004 Ghetto CBG in the black ghetto 0.0439 Near Ghetto CBG within 5 miles of ghetto center 0.0246 Near Airport CBG within 10 miles of Cleveland airport 0.0292 0.0329 Airport Distance (Near Airport) ×(Distance to airport) 0.0038 Local Amenities No. of parks, golf courses, rivers, or lakes within ¼ mile of CBG 0.0189** 0.0081 Freeway CBG within ¼ mile of freeway 0.0123 0.0116 Railroad CBG within ¼ mile of railroad *** 0.0104 Shopping CBG within 1 mile of shopping center * 0.0094 Hospital CBG within 1 mile of hospital 0.0117 0.0098 Small Airport CBG within 1 mile of small airport 0.0295 0.0219 Big Park CBG within 1 mile of regional park 0.0037 0.0108 Historic District CBG within an historic district 0.0072 0.0183 Near Elderly PH CBG within ½ mile of elderly public housing 0.0237 Near Small Fam. PH CBG within ½ mile of small family public housing 0.0267 Near Big Fam. PH CBG within ½ mile of large family public housing (>200 units) ** 0.0420 A New Approach

62 Nonlinear, σ3 = 1, Split Eth.Vars.School Quality Capitalization Table 5. Specification Tests and Results for Key School and Ethnicity Variables Variable Linear Quadratic Nonlinear, σ3 = 1 Nonlinear, σ3 = 1, Split Eth.Vars. Relative Elementary Score First Term (=σ1) 0.1268** 0.2448 0.5676 0.6032 (0.0595) (0.2480) (0.3912) (0.5057) Second Term (=σ2) - (0.3584) (3.5516) (4.5470) First Term Cleveland (=σ1) *** 0.3903*** 0.3908*** (0.0722) (0.3911) (0.0230) (0.0229) Second Term Cleveland (=σ2) 1.6740*** 0.3004*** 0.2979*** (0.4876) (0.0885) (0.0875) μ -∞ High School Passing Rate 0.4826*** 0.2177*** 0.2166*** (0.0587) (0.2631) (0.0338) (0.0342) 0.6049** 1.3139** 1.3255** (0.2849) (0.5328) (0.5366) *** *** (0.2752) (0.2704) R-Squared 0.7046 0.7156 0.7167 0.7169 Test of Hypothesis that Model Adds to Explanatory Power Test statistic 6.66 2.04 n.a. P-value 0.000 0.042 A New Approach

63 School Quality CapitalizationA New Approach

64 School Quality CapitalizationA New Approach

65 Estimated Impacts School Quality CapitalizationIn the case of the High School variable, housing prices are about 30% higher in a district with the highest value (77% passing) compared to a district with a 20% passing rate. Prices are also about 3% higher at a 13 percent passing rate than at a 20% passing rate, but this result is not statistically significant (and involves only a few observations). The results for the Elementary variable in Cleveland are consistent with the view that parents care about elementary school quality, but also care about education opportunities, which are clustered in the neighborhoods with the worst regular public schools. A New Approach

66 Conclusions, Theory The envelope derived in my paper:School Quality Capitalization Conclusions, Theory The envelope derived in my paper: Is based on a general characterization of household heterogeneity. Makes it possible to estimate demand elasticities (and program benefits) from the first-step equation—avoiding endogeneity. Ensures consistency between the envelope and the underlying bid functions. Sheds light on sorting. A New Approach

67 Conclusions, Empirical ResultsSchool Quality Capitalization Conclusions, Empirical Results Willingness to pay for some aspects of school quality can be estimated with precision. The price elasticity of demand for high school quality is about and housing prices are up to 30% higher where high school quality is than where it is low. The theory of sorting is strongly supported in most cases. Household types with steeper bid functions for high school quality tend to live where school quality is higher. A New Approach

68 Conclusions, Empirical, ContinuedSchool Quality Capitalization Conclusions, Empirical, Continued Household seem to care about several dimensions of school quality, but precise demand parameters cannot be estimated in many cases. The price elasticity and other parameters cannot be precisely estimated for relative elementary scores. Results for elementary value added suggest a relationship that is too complex for current specifications; parents appear concerned about schools with low starting scores even when they improve. Results for percent minority teachers indicate that many households prefer teacher diversity, which calls for a specification different from any used up to now. A New Approach

69 Tests for Normal SortingSchool Quality Capitalization Tests for Normal Sorting Once the envelope has been estimated, one can recover its slope with respect to S, which is a function of income and other demand variables (for S and H). The theory says that the income coefficient is (-θ/μ - γ). Normal sorting requires this coefficient to be positive. Recall that the amenity price elasticity, μ, is negative. A New Approach

70 Direct and Indirect TestsSchool Quality Capitalization Direct and Indirect Tests Direct and indirect tests are possible. A direct test looks at the income coefficient controlling for all other observable demand determinants. An indirect test says that normal sorting for S may arise indirectly through the correlation between S and other amenities (and the impact of income on these other amenities). Based on the omitted variable theorem, the indirect test comes from the sign of the income term in a regression omitting all other demand variables. A New Approach

71 Table 7. Tests for Normal SortingSchool Quality Capitalization Table 7. Tests for Normal Sorting Type of Test Relative Elementary Score High School Passing Rate Indirect Test Income Coefficient 1.7699*** 1.0189*** Standard Error (0.5793) (0.0564) R-squared 0.0849 0.2028 Observations 142 1113 Conclusion Support Direct Test 1.3540* 0.6426*** (0.8059) (0.0906) 0.2236 0.3026 Weak Support A New Approach

72 Conclusions, Normal SortingSchool Quality Capitalization Conclusions, Normal Sorting Normal sorting is supported for relative elementary school, when only the positively-sloped envelope portions in Cleveland are considered. Normal sorting is strongly supported for high school quality. A New Approach