T HE M ICRO F OUNDATIONS OF M ACRO S ORTING M ODELS Timothy L. - PowerPoint PPT Presentation

T HE M ICRO F OUNDATIONS OF M ACRO S ORTING M ODELS Timothy L. Hamilton University of Richmond Daniel J. Phaneuf University of Wisconsin October 22, 2012

I NTRODUCTION – S ORTING M ODELS FOR N ON -M ARKET V ALUATION Households sort a la Tiebout to optimal residential location:  Choice reveals tradeoffs between prices and attributes of locations  Use to quantify preferences for local public goods Examples:  Bayer et al. (2009) – particulate matter pollution  Klaiber and Phaneuf (2010) – open space  Tra et al. (2012) – school quality  Tra (2012) – ozone pollution Many apparent advantages vis-à- vis first stage hedonic modeling…

A SSUMPTION H EAVY M ODELING E NVIRONMENT Need assertions on:  Spatial extent of analysis → “macro” choice level vs. “micro” choice level → Bayer et al. ‘macro’ – country-wide choice → Klaiber and Phaneuf ‘micro’ – city-wide choice  Definition of a choice element  Functional form for utility and error distributions  Nature/form of equilibrium conditions Important element of research agenda is examining extent to which advantages are assumption-driven …

C HOICE E LEMENTS AND S PATIAL S CALE Seems that most location choices are two- tiered…  Choose region/city based on labor market, regional amenities, family roots…  Choose neighborhoo d based on local amenities, schools, commute patterns… Choices are distinct – but interrelated?  Complement/substitute relationship between regional and local public goods? e.g. does regional air quality have higher value if local landscape provides more outdoor opportunities?

R ESEARCH Q UESTIONS How do estimates of the non-market value of air quality depend on the interconnectedness between macro and micro sorting margins? → revisit Bayer et al. (2009) macro -sorting application to regionally varying air pollution → examine more general model that nests their specification while adding micro margin How can we tractably model the multiple sorting decision margins? → examine ‘two stage budgeting’ assumptions as applied to ‘two stage sorting’ → develop sequential estimation approach to accommodating both margins

F INDINGS /C ONTRIBUTIONS Consideration of micro sorting margin matters empirically:  Elasticity of WTP with respect to air quality 0.31 (macro only) vs. 0.48 (macro/micro)  Marginal WTP for air quality $232 vs. $371 Difference due to an implicit omitted variable in macro only model Operationalize sequential estimation of two stage budgeting/two stage sorting model  Micro-level choices aggregated to a “quality adjusted price index” summarizing neighborhood level choice sets  Connect practical use of nested logit model to two stage budgeting concept

O UTLINE OF T ALK 1) Introduction 2) Conceptual Basis 3) Empirical Basis 4) Application and Data 5) Estimation/Results 6) Conclusions We are working on finalizing paper for submission – what is still needed? Where should it go? Contribution well-framed?

C ONCEPTUAL B ASIS            max exp( ) U C Y H X C Y H X ijm m jm jm m ijm (1) , C H   . . s t C p H I jm im C : numeraire consumption H : consumption of ‘housing services’ Y m ,  m : regionally (MSA) varying public goods X jm ,  jm : neighborhood public goods (deviations from MSA averages) I im : income in MSA m  ijm : idiosyncratic preference shock p jm : price of housing unit in neighborhood j , MSA m ln p jm = ln  m + ln  jm ↔ p jm =  m ×  jm

Conditional indirect utility for person i , neighborhood j , MSA m :              ln ln ln ln ln ln V I Y X ijm I im Y m X jm H m jm (2)         , 1,..., 1,..., j J m M jm m ijm m Note:   I =  C +  H  Literature-standard additively separable form   jm =1, X jm =1, J m =1,  jm =0 → collapses to Bayer et al. model

T WO S TAGE B UDGETING A restriction on preferences implying:  Consumer first determines expenditures on commodity groups – e.g. food, housing, clothing – conditional on income and commodity group price indices  Consumer subsequently allocates commodity group expenditures among individual products – e.g. food expenditures spent on steak, beer, pizza, … Empirically convenient restriction often used in demand system estimation

P ROPOSITION  ‘Macro’ stage sorting involves income allocation to broad non- housing ( C ) and housing ( Q ) consumption groups  ‘Micro’ stage sorting involve s allocation of Q expenditures to house structure ( H ) and local public goods ( X )  Utility function (1) satisfies conditions for this division Proof in paper – relies on establishing ‘price aggregation’ and ‘decentralisability’ (Blackorby and Russell, 1997)

T WO S TAGE S ORTING M ODEL Consistency of (1) with two-stage budgeting allows us to write (2) as:               i ln ln ln ln , 1,..., V I Y j M im I im Y m H m m m im where            i max{ ln ln } X | m H jm X jm jm i j m  j J m      | ijm im ij m  is a quality-adjust price ( or utility ) index for the second stage of i m sorting

E MPIRICAL B ASIS Start with                    k k ln ln ln ln ln ln V I Y X ijm I im Y m X jm H m jm jm m ijm   1,..., 1,..., j J m M m Assume GEV distribution for            ,..., ,..., ,...,  . 11 1, 21 2 1 ,..., i i iJ i iJ i M iJ M 1 2 M ‘Nested Logit’ s pecification:  There are M ‘nests’ corresponding to MSAs  There are J m alternatives in each nest corresponding to neighborhood within the MSA  Household type specific heterogeneity ( k =1,…, K )

P ROPERTIES OF N ESTED L OGIT M ODEL Probability of observing ( m , j ) = Pr ijm =Pr ij | m × Pr im :             k k exp ln ln ln I Y IV  I im Y m H m m m Pr    im M           k k exp ln ln ln I Y IV  I in Y n H n n n 1 n                k k k k exp ln / X exp    H jm X jm jm  jm Pr ,       | ij m J   J          k k k k m m exp ln / exp X     H jl X lm l m lm 1 1 l l J    m     k k i ln exp ( ) I V E m jm m  1 j               k k k max{ ln ln } E X | H jm X jm jm ij m m  j J m

T WO S TAGE B UDGETING /T WO -S TAGE SORTING /N ESTED LOGIT PUNCH L INE  Literature-standard functional form provides useful structure for sequential estimation  Use micro-sorting data to estimate inclusive value for lower nest ↔ (expectation of) price index in first stage budget allocation  Estimate ‘dissimilarity’ coefficient  k via macro-choice conditional logit model ↔ reflects degree of importance of micro-choice set in macro decisions Links upper and lower levels of nested logit to stages of budgeting (though two stage budgeting holds for any error distribution)

A PPLICATION AND D ATA Empirical objective follows Bayer et al (2009):  Measure marginal WTP for regionally-varying air pollution (PM 10 )  Estimate a macro sorting model across 226 MSAs in continental US Data needs:  Neighborhood level residential locations – Census Data Research Center (confidential)  MSA level residential location – IPUMS (public use census micro data)  PM 10 emissions – EPA National Emissions Inventory (converted to concentrations using source/receptor matrix)  Other MSA level variables – various sources

C ENSUS D ATA Confidential micro data:  8.5 million people 1990 and 7.6 million 2000  Observe 23 to 40 year olds locating in 40,416 census tracts  Divide out by household types Public use micro data (IPUMS):  39,058 1990 and 37,165 2000  23 – 40 year olds sorting across 226 MSAs  Observe income, education, household makeup, etc. Use IPUMS data to predict MSA-level housing prices and (potential) household income at all M locations

H OUSEHOLD T YPES Type Definition (presence of children and education) Type 1 No children in household, No high school degree Type 2 No children in household, High school degree or some college Type 3 No children in household, Bachelor's degree Type 4 No children in household, Graduate or professional degree Type 5 Children in household, No high school degree Type 6 Children in household, High school degree or some college Type 7 Children in household, Bachelor's degree Type 8 Children in household, Graduate or professional degree