Transcript X h

“A Unified Framework for Measuring
Preferences for Schools and
Bayer, Ferreira, McMillian
Research Question
• How to measure households value for good
schools and neighborhood characteristics?
• Why do we care?
– School quality affects economically important
outcome like earnings (important topic in labor
– Public policy: property taxes fund education,
policy evaluation e.g. cost benefit analysis of
desegregation programs
Literature Review
• Black (QJE, 1999)
-Typical approach look at effect of school
quality on test scores and earnings
-Alternative approach: estimate households
willingness to pay for better school
• Basic idea: when agent purchases a home, she is also pay for:
– Type of house she buys
– the schools that her children go to
– Neighborhood characteristics
Willingness to Pay
• Hedonic Model:
– X- characteristics of house e.g. size, type, # rooms
– Z- neighborhood socio-demographics
– ε – error term
• ID problem: endogeneity of neighborhood
• Solution: Boundary Discontinuity Design
– Instrument for socio-demographics
Boundary Discontinuity Design:
Ideal Experiment
School Attendance Zone A
School Attendance Zone B
Boundary Discontinuity Design
• Socio-demographics of neighborhoods the
• Difference in Quality of school depending on
school attendance zone  paying for school
• In practice, need to consider housed in narrow
bands (0.1-0.3 miles)
– Statistical Power to make inferences
• Need to control for socio-demographics
Ownership and # of Rooms
Test Scores and Housing Prices
• Addresses endogeneity of neighborhood
– Produced more consistent estimates of willingness
to pay for good school
• Limitation of Study
– Does not control for socio-demographics above on
beyond boundary instrument
Bayer, Ferreira, McMillian
– Improve on Black by
• Using richer data set
– Unrestricted Census Data
» Contains block level information
• Embedding Boundary Discontinuity Design within
discrete choice heterogeneous sorting model
Decennial Census -- restricted version (1990)
– Filled out by 15% of households
– Individual Level Data: race, age, education attainment, income of each household member,
type of residence: owned, rented, property tax payment, number of rooms, number of
bedroom, types of structure, age of building, house location, workplace location
– Neighborhood level data: race, education, income composition, also add data on crime, land
use, topography, local schools
– matched with county level transactions data, matched with HMDA data
Relevant Study Sites: Area: Bay Area: Alameda, Contr Costa, Marin, San Mateo, San Francisco, Santa
to get 60% of home sales and neighborhood variables for 85%
small area, ppl don’t typically commute out of area
lots of data:
1,100 census tracts, 4,000 census block groups, 39500 census
full sample 650k people, 242.1k households
School quality measure: avg. 4th grade math and reading score
– Advantage: easily observable to both teachers and parents
Summary Statistics
Home value $300,000
Rent $750/month,
60% homes owned,
68% black, 8% white,
44% head of households college degree,
avg. block income $55,000
Implementing BDD
• Each census block assigned to closest school
attendance zone boundary
• Each block paired with a “twin” census block
– Closest block on opposite side of boundary
• For each pair, block with lowest average test
score designated “low” side of boundary, the
other “high” side
• Boundary Cutoff: census blocks ≤ 0.2 miles from
nearest (SAZ)
– Have power to restrict even further to ≤ 0.1 m
BBD Continuous Observations
• Housing Characteristics that are continuous
across the boundary:
– Number of rooms
– Construction date
– Ownership status: owner occupied/rented
– Size: lot size, square footage
Construction Date and Size
BBD Discontinuous Observations
• Housing Characteristics that are discontinuous
across the boundary:
– House Price (by $18,719 , i.e. 7%-8% of mean value)
• Neighborhood Characteristics that are
discontinuous across the boundary:
Test Scores (by 74 pts)
Percentage Black (by 3%)
Percentage with College Degree (by 5%)
Mean Income (by $2,861, i.e.6%-7%)
Education, Income & Race
Conceptual Take Away
– Quality of physical housing stock same across
– prices different
– socio-demographics
– and test scores different
– Inference: households on the “high” side of the
boundary paying for higher quality schools and
sorting into the SAZ with better schools
Hedonic Price Regression
• Accounting for Boundary Fixed Effects
Reduces hedonic valuation of good schools
– Consistent with Black (1999)
• Controlling for Neighborhood Sociodemographics reduces it further
• Households racial preferences for neighbors
not capitalized in housing prices
– Coefficient on percent black drops from -$100 to
almost zero with Boundary fixed effects
Robustness Checks
• School level socio-demographics
– Race, language ability, teacher education, student income
– estimate on preference for school test score in baseline:
17.3 (5.9)
– with addition control estimate: 22.6 (8.5)
• Inclusion of Block-level socio-demographics
• Dropped Top Coded Houses in Census Data (with values greater than
• Use housing prices from transactions data
• Using Only owner occupied units
• Take-away: results robust to those in base-line specification w/o these
detailed measures
Discrete Choice Sorting Model
• Model
– Each household (i) decides which house (h) to
– Random Utility Model (McFadden)
• House characteristics (Xh)
– size, age, type)
– Type (owned/rented)
– Neighborhood and School characteristics
Distance from house to work (d ih)
Boundary fixed effects (Θbh)
Price (ph)
Unobserved housing quality (ξh)
Individual specific error term (εih)
Maximization Problem
• Objective:
• Allow for agents valuation of housing
characteristics to depend on individual
Estimation Strategy
• Two step process
– Separate utility function into part that captures mean
preferences and part that captures preference
– Step #1: Use MLE to estimate heterogeneous
parameters and mean utility
– Step #2: Separate mean utility in components that are
observable and unobservable
• Utilize assumption that Individual specific error term (εih)
follows extreme value distribution
• Use characteristics of houses > 3miles away as price
instrument to obtain causal estimates
• Preferences for better schools similar across
hedonic BDD estimates and discrete choice
• Preferences for black neighbors highly
negative in discrete choice model estimate
– Different from hedonic estimation for race
– Idea: self-segregation by race can arise through
sorting that does not affect equilibrium prices
Robustness Checks