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Lecture Outline Methodological Challenges Examples Recent Publications My Cleveland Application

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

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Functional Form As discussed in previous classes, simply regressing V on S (with or without logs) is not satisfactory. Regressing ln{ V } on S and S 2 is pretty reasonable—but cannot yield structural coefficients. To obtain structural coefficients, one must use either nonlinear regression or the Rosen 2-step method (with a general form for the envelope and a good instrument for the 2 nd step). Both approaches are difficult!

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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). A few use both, but the use of multiple output measures is rare (but sensible!).

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Neighborhood Controls Data quality varies widely; some studies have many neighborhood controls. Many fixed-effects approaches are possible to account for unobservables, e.g.: Border fixed effects (cross section) Neighborhood fixed effects (panel) Another approach is to use an instrumental variable.

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Border Fixed Effects Popularized by Black (1999); appears in at least 16 studies. Define elementary school attendance zone boundary segments. Define a border fixed effect (BFE) for each segment, equal to one for housings within a selected distance from the boundary. Drop all observations farther from boundary.

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Border Fixed Effects, 2 School House Sale Boundary Segment

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Border 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. But bias comes from un-observables that are correlated with S ; by design, BFEs are weakly correlated (i.e. take on the same value for different values of S ).

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Border Fixed Effects, 4 BFEs have three other weaknesses: They shift the focus from across-district differences in S to within-district differences in S, which are smaller and less interesting. They require the removal of a large share of the observations (and could introduce selection bias). They ignore sorting; that is, they assume that neighborhood traits are not affected by the fact that sorting leads to people with different preferences on either side of the border bid.

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BFE and Sorting Two recent articles (Kane et al. and Bayer et al.) find significant differences in demographics across attendance-zone boundaries. Bayer et al. then argue that these demographic differences become neighborhood traits and they include them as controls. I argue that these differences are implausible as neighborhood traits, but 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.

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Other Fixed Effects Other types of fixed effects are possible, e.g., Tract fixed effects (with a large sample or a panel) School district fixed effects (with a panel). House fixed effects (with a panel). These approaches account for some unobservable factors, but may also introduce problems.

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Problems with Fixed Effects They all limit the variation in the data for estimating capitalization. School district fixed effects, for example, imply that the coefficient of S must be estimated based only on changes in S. They may account for demand factors, such as income, that should not be included in a hedonic. Because household and tract income are highly correlated, including tract dummies effectively controls for household income, resulting in the same problems as those caused by BFEs. My interpretation is not popular. Economists seem to prefer more controls even if they do not make theoretical sense.

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The IV Approach With omitted variables, the included explanatory variables are likely to be correlated with the error term. A natural correction is to use an instrumental variable— and 2SLS. However, credible IVs are difficult to find. For example, the well-known 2005 Chay/Greenstone article in the JPE estimates a hedonic for clean air using a policy announcement as an instrument. But many studies (some mentioned below) show that announcements affect house values so the C/G instrument fails the exogeneity test.

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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).

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Housing 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); 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.

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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 this stage must be corrected for heteroskedasticity. The coefficient of each FE is based on a different number of observations.

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Selected Recent Examples Bayer, Ferriera, and MacMillan (JPE 2007) Clapp, Nanda, and Ross (JUE 2008) Bogin (Syracuse dissertation 2011), building on Figlio and Lucas (AER 2004) Yinger (working paper 2012)

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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 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.

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B/F/M Hedonic

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B/F/M Problems They estimate a linear hedonic, which rules out sorting (in an article about sorting!) and is inconsistent with their own bid functions. They control for neighborhood income (implausible theoretical basis). They have only 3 housing traits and 3 other location controls (+ BFE’s). One neighborhood control (density) is a function of the dependent variable; I guess they never took urban economics!

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C/N/R They use a panel of housing transactions in Connecticut between 1994 and 2004 They use tract fixed effects to control for neighborhood quality. They look at math scores and cost factors (e.g. student poverty) They find that tract fixed effects lower the estimate of capitalization even below its level with income and other demographics.

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C/N/R Hedonic

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C/N/R Problems They use a semi-log form with only one term for S, which rules out sorting. They control for neighborhood demographics and tract FEs, 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. They include fraction owner-occupied, which appears to be endogenous.

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Bogin The Florida school accountability program hands out “failing” grades to some schools. The Figlio/Lucas paper (AER 2004) 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 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.

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Bogin 2 Bogin finds 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. Bogin also provides 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:

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Bogin 3

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Estimates with a Derived Envelope Finally, I would like to present some results for both the hedonic and the underlying bid functions from the application of the method I have 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.

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My Envelope The form derived in my last lecture: and X (λ) is the Box-Cox form. A starting point is a quadratic form, which corresponds to μ = -∞ and σ 3 = 1

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The 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 I focus on the 5-county Cleveland area and add many neighborhood traits.

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My 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 P E {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.

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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.

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Step 1A: Run Hedonic Regression with Neighborhood Fixed Effects Dependent variable: Log of sales price in 2000. Explanatory variables: ◦ Structural housing characteristics. ◦ Corrections for within-neighborhood variation in seven locational traits. ◦ Neighborhood fixed effects. 22,880 observations in Cleveland subsample.

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Table 1. Variable Definitions and Results for Basic Hedonic with Neighborhood Fixed Effects VariableDefinitionCoefficientStd. Error One StoryHouse has one story- 0.00720.0050 BrickHouse is made of bricks 0.0153***0.0052 BasementHouse has a finished basement 0.0308***0.0050 GarageHouse has a garage 0.1414***0.0067 Air Cond.House has central air conditioning 0.0254***0.0055 FireplacesNumber of fireplaces 0.0316***0.0038 BedroomsNumber of bedrooms- 0.0082***0.0028 Full BathsNumber of full bathrooms 0.0601***0.0042 Part BathsNumber of partial bathrooms 0.0412***0.0041 Age of HouseLog of the age of the house- 0.0839***0.0032 House AreaLog of square feet of living area 0.4237***0.0086 Lot AreaLog of lot size 0.0844***0.0037 OutbuildingsNumber of outbuildings 0.1320***0.0396 PorchHouse has a porch 0.0327***0.0073 DeckHouse has a deck 0.0545***0.0053 PoolHouse has a pool 0.0910***0.0180 Date of SaleDate of house sale (January 1=1, December 31=365) 0.0002***0.0000

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Table 1. Variable Definitions and Results for Basic Hedonic with Neighborhood Fixed Effects VariableDefinitionCoefficientStd. Error Commute 1 a Employment wtd. commuting dist. (house-CBG), worksite 1- 0.0952***0.0272 Commute 2 a Employment wtd. commuting dist. (house-CBG), worksite 2- 0.0991***0.0321 Commute 3 a Employment wtd. commuting dist. (house-CBG), worksite 3- 0.1239***0.0302 Commute 4 a Employment wtd. commuting dist. (house-CBG), worksite 4- 0.1012***0.0295 Commute 5 a Employment wtd. commuting dist. (house-CBG), worksite 5- 0.0942***0.0344 Dist. to Pub. School a Dist. to nearest pub. elementary school in district (house-CBG)- 0.00320.0061 Elem. School Score a Average math and English test scores of nearest pub. elementary school relative to district (house-CBG) 0.01700.0197 Dist. to Private SchoolDistance to nearest private school (house-CBG)- 0.0168***0.0057 Distance to HazardDist. to nearest environmental hazard (house-CBG) 0.0332***0.0082 Distance to Erie a Dist. to Lake Erie (if < 2; house-CBG)- 0.0021**0.0010 Distance to Ghetto a Dist. to black ghetto (if < 5; house-CBG)- 0.1020***0.0331 Distance to Airport a Dist. to Cleveland airport (if < 10; house-CBG) 0.0259**0.0122 Dist. to CBG CenterDistance from house to center of CBG- 0.0239***0.0074 Historic District a In historic district on national register (house-CBG) 0.01200.0178 Elderly Housing a Within 1/2 mile of elderly housing project (house-CBG)- 0.0327*0.0194 Family Housing a Within 1/2 mile of small family housing project (house-CBG) 0.0836**0.0403 Large Hsg Project a Within 1/2 mile of large family housing project (>200 units; house-CBG)- 0.0568**0.0257 High CrimeDistance to nearest high-crime location (house-CBG) 0.0701***0.0246

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Step 1B: Run Envelope Regression Dependent variable: coefficient of neighborhood fixed effect. Explanatory variables: ◦ Public services and neighborhood amenities ◦ Commuting variables ◦ Income and property tax variables ◦ Neighborhood control variables

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School Variables VariableDefinition ---------------------------------------------------- ElementaryAverage percent passing in 4 th grade in nearest elementary school on 5 state tests (math, reading, writing, science, and citizenship) minus the district average (for 1998-99 and 1999-2000). High School The share of students entering the 12 th 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 1998-99 and 1999-2000. Value Added A school district's sixth grade passing rate (on the 5 tests) in 2000-2001 minus its fourth grade passing rate in 1998- 99. Minority Teachers The share of a district’s teachers who belong to a minority group

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Cleveland and East Cleveland The Cleveland School District is unique in 2000 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 2000 because ◦ It received a state grant for school construction in 1998- 2000 that was triple the size of its operating budget. ◦ No other district in the region received such a grant.

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Table 2. Descriptive Statistics for Key Variables MeanStd. Dev.MinimumMaximum CBG Price per unit of Housing84835.6823331.2532215.83345162.50 Relative Elementary Score a 0.31480.08940.00100.6465 High School Passing Rate0.31970.20400.04910.7675 Elementary Value Added a 24.00219.41641.000049.6000 Share Minority Teachers b 0.13290.15480.00100.6146 Share Non-Black in CBG b 0.80220.32260.00101.0000 Share Non-Hispanic in CBG0.96230.08100.36731.0000 Weighted Commuting Distance13.20467.45677.266039.5236 Income Tax Rate c 0.00910.00120.00750.0100 School Tax Rate0.03090.00830.01720.0643 City Tax Rate d 0.05780.01400.02270.1033 Tax Break Rate d 0.03300.01210.00470.0791 No A-to-S0.13390.34070.00001.0000 Not a City0.13930.34640.00001.0000 Crime Lowhigh0.02520.15690.00001.0000 Crime Highlow0.12910.33540.00001.0000 Crime Highhigh0.19340.39510.00001.0000 Crime Hotspot10.01260.11160.00001.0000 Crime Hotspot20.03540.18490.00001.0000 Crime Hotspot30.08470.27850.00001.0000 Crime Hotspot40.26670.44230.00001.0000

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Table 3. Definitions for Tax, Commuting, Crime, Pollution, and Ancillary School Variables VariableDefinition Income Tax RateSchool district income tax rate School Tax Rate***School district effective property tax rate City Tax RateEffective city property tax rate beyond school tax Tax Break Rate*Exemption rate for city property tax No A-to-SDummy: No A/V data Not a CityCBG not in a city Commute 1***Job-weighted distance to worksites Commute 2**(Commute 1) squared Crime Lowhigh***Low property, high violent crime Crime Highlow**High property, low violent crime Crime Highhigh***High property and violent crime Crime Hotspot1***CBG within ½ mile of crime hot spot Crime Hotspot2*CBG ½ to 1 mile from crime hot spot Crime Hotspot3***CBG 1 to 2 miles from crime hot spot Crime Hotspot4***CBG 2 to 5 miles from crime hot spot Village**CBG receives police from a village Township***CBG receives police from a township County Police***CBG receives police from a county City Population***Population of city (if CBG in a city) City Pop. Squared***City population squared/10000 City Pop. Cubed***City population cubed/10000 2 City Pop. to 4th***City pop. to the fourth power/10000 3 Smog***CBG within 20 miles of air pollution cluster Smog Distance**(Smog) × Distance to cluster (not to the NW) Near Hazard***CBG is within 1 mile of a hazardous waste site Distance to Hazard***Distance to nearest hazardous waste site (if <1) Value Added 1***School district's 6th grade passing rate on 5 state tests in 2000-01 less its 4th grade rate in 1998-99 Value Added 2***(Value Added 1) squared Minority Teachers 1Share of district's teachers from a minority group Minority Teachers 2*(Minority Teachers 1) squared Rel. Elem. Cle. 1*** Average 4th grade passing rate on 5 state tests in nearest elem. school minus district average (1998-99 and 1999- 2000) for Cle. and E. Cle. only Rel. Elem. Cle. 2***(Rel. Elem. Cle. 1) squared Cleveland SDDummy for Cleveland & E. Cleveland School Districts Near PublicCBG is within 2 miles of public elem. school Distance to Public*(Near Public) × Distance to public school Near PrivateCBG is within 5 miles of a private school Distance to Private(Near Private) × Distance to private school

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Table 4. Definitions for Other Geographic Controls VariableDefinition Lakefront***Within 2 miles of Lake Erie Distance to Lake(Lakefront) × (Distance to Lake Erie) Snowbelt 1***(East of Pepper Pike) × (Distance to Lake Erie) Snowbelt 2***(Snowbelt 1) squared GhettoCBG in the black ghetto Near GhettoCBG within 5 miles of ghetto center Near AirportCBG within 10 miles of Cleveland airport Airport Distance(Near Airport) × (Distance to airport) Local Amenities***No. of parks, golf courses, rivers, or lakes within ¼ mile of CBG FreewayCBG within ¼ mile of freeway RailroadCBG within ¼ mile of railroad ShoppingCBG within 1 mile of shopping center HospitalCBG within 1 mile of hospital Small AirportCBG within 1 mile of small airport Big Park***CBG within 1 mile of regional park Historic DistrictCBG within an historic district Near Elderly PHCBG within ½ mile of elderly public housing Near Small Fam. PH***CBG within ½ mile of small family public housing Near Big Fam. PH***CBG within ½ mile of large family public housing (>200 units) Worksite 2**Fixed effect for worksite 2 Worksite 3***Fixed effect for worksite 3 Worksite 4*Fixed effect for worksite 4 Worksite 5Fixed effect for worksite 5 Geauga CountyFixed effect for Geauga County Lake County***Fixed effect for Lake County Lorain County***Fixed effect for Lorain County Medina CountyFixed effect for Medina County

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Table 3A. Results for Ancillary School Variables Variable DefinitionCoefficient Std. Error Value Added 1 School district's 6th grade passing rate on 5 state tests in 2000-2001 minus its 4th grade passing rate in 1998-99 0.0120***0.0039 Value Added 2 (Value Added 1) squared- 0.0002***0.0001 Minority Teachers 1 Share of district's teachers from a minority group 0.33790.2177 Minority Teachers 2 (Minority Teachers 1) squared- 0.7334*0.3967 Rel. Elem. Cle. 1 Average 4th grade passing rate on 5 state tests in nearest elementary school minus district average (1998-99 and 1999-2000) for Cleveland and E. Cleveland only - 1.5045***0.4066 Rel. Elem. Cle. 2 (Rel. Elem. Cle. 1) squared 1.8398***0.4951 Cleveland SD Dummy for Cleveland & E. Cleveland School Districts 0.14140.2232

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Table 5A. Specification Tests and Results for Key School Variables VariableLinearQuadratic Nonlinear Estimation of μ’s with σ 3 = 1 Nonlinear Estimation of μ’s, Various σ 3 ’s Relative Elementary Score First Term0.1268** 0.2448 0.0022***- 0..0034 (0.0581)(0.2480)(0.0008)(0..0041) Second Term-- 0.208689.4295 0.3161 (0.3584)(163.9870)(0.2099) μ-∞ - 0.3694***- 0.8141*** (0.1342)(0.687) σ 3 ∞111/5 High School Passing Rate First Term0.4826***- 0.0862 0.2168*** 0.7375*** (0.0600)(0.2631)(0.0339)(0.0692) Second Term- 0.6049** ~ 1.3087** 0.4636*** (0.2849)(0.5294)(0.1758) μ-∞ - 0.7564***- 1.0752** (0.2762)(0..4899) σ 3 ∞11 5

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Estimated Impacts The Impact of Amenities on Housing Prices (Along Envelope) Change in Price of House Due to Raising the Amenity from: Amenity Selected Value of Amenity Minimum to Selected Value Selected Value to Maximum Relative Elementary Score0.10015.8%6.7% High School Passing Rate0.221-3.5%32.6% The Impact of Amenities on Housing Bids (Along Illustrated Bid Function) Change in Price of House Due to Raising the Amenity from: AmenityMinimum to Maximum Value Relative Elementary Score*7.5% High School Passing Rate17.7% * Minimum set at 0.1.

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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.

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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 -1.0 and housing prices are up to 30% higher where high school passing rates are high than where they are low. The theory of sorting is strongly supported in some cases. ◦ Household types with steeper bid functions for high school quality tend to live where school quality is higher.

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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.

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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.

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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.

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Table 6. Tests for Normal Sorting Type of Test Relative Elementary Score High School Passing Rate Indirect Test Income Coefficient 0.0702 0.8243*** Standard Error(0.0479)(0.0471) Observations12221113 ConclusionInconclusiveSupport Direct Test Income Coefficient 0.0218 0.5088*** Standard Error(0.0855)(0.0759) R-squared0.02540.2796 Observations 12221113 ConclusionInconclusiveSupport

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Conclusions, Normal Sorting Normal sorting is neither supported nor rejected for relative elementary school. Normal sorting is strongly supported for high school quality. So normal sorting appears to be strong across districts if not within them.

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