Abstract
School quality indicators such as student test scores have been shown to be capitalized into the value of local homes. The presence of households with different preferences for education implies that the implicit price of improvements in school quality might vary even within a region. In this paper, we employ a finite mixture model (FMM) to capture unobserved heterogeneity in household preferences. Using school quality and residential property sales data from Pitt County, North Carolina, we find evidence of two subpopulations of houses, where the prices for one group are virtually invariant to school quality. Consistent with recent research by Davis et al. (2017) these results indicate that heterogeneous valuation of educational quality by households with different socio-economic backgrounds should be taken into consideration when devising policies targeted at the local level.
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Notes
United States Census Bureau (n.d.-a, n.d.-b). Census 2000 Summary File. American FactFinder. Retrieved 18 June, 2017, from www.factfinder.census.gov.
As mentioned in Cameron et al. (1988), it is useful to parameterize the grouping probabilities using, for instance, a logit function: πg = exp(γg)/(1 + ∑ exp(γg)) to help ensure 0 ≤ πg ≤ 1, where γg may be further parameterized in terms of observable covariates.
With the usual conditions\( \sum \limits_g{\pi}_{g,i}\left(\cdotp \right)=1 \), 0 ≤ πg, i(·) ≤ 1, and \( {\pi}_{g,i}\left({y}_i;\hat{\Phi}\right)={\hat{\pi}}_g{f}_g\left({y}_i;{\hat{\varphi}}_g\right)/\sum \limits_h{\hat{\pi}}_h{f}_h\left({y}_i;{\hat{\varphi}}_h\right) \) (McLachlan and Peel 2004).
Greenville is its largest and most populated city. As of the census of 2000, there are 133,798 people, 52,539 households, and 32,258 families residing in the county.
Pitt County Management Information Systems published the school zone map for the whole county as of February 2005, and no major change in the school zone was made between 2001 and 2005.
All information from test scores to hazard code violations are accessible at http://www.ncpublicschools.org/src/.
Following Coulson (2008), polynomials (up to the second power) of the variable age are included in attempt to capture the nonlinearities in the age effects, such as depreciation effects, survival effects, and vintage effects.
All school quality measures enter the regression in natural log forms for easier interpretation.
Indicators of each unique city-year pairs make up our city-year fixed effects.
The relative entropy index ε is a scaled version of the entropy of fuzzy classification\( EN=\sum \limits_{i=1}^n\sum \limits_{g=1}^G-{\pi}_{ig}\ln \left({\pi}_{ig}\right) \), where EN ∈ [0, ∞). As mentioned by Celeux and Soromenho (1996), EN cannot be used directly to assess the number of components. The authors suggested a normalized entropy criterion but found some limitations in its applicability. The Wedel and Kamakura (2000) relative measure has seen wider acceptance for use in latent class studies (Morey et al. 2006; Dias and Vermunt 2008).
We do not report the information criteria for a four-component model as it failed to converge. One reason for non-convergence may be due to the four-component model being a misspecification. In multilevel analysis, convergence issues arise from trying to estimate too many random components (variance) that are near or equal to zero where the solution is a simplification of the model by excluding some random components (Hox 2010). Thus, the difficulty in obtaining convergence of the four-component model may be indicative of it being overly parameterized. In addition, the entrophy value decreases significantly when we break up the sample into three groups as opposed to two groups, suggesting lack of distinctiveness across a larger number of groups. It is likely that the cross-group distinctiveness as measured by the entrophy value would be even lower for a four-component model.
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Hwang, J.W., Kuang, C. & Bin, O. Are all Homeowners Willing to Pay for Better Schools? ─ Evidence from a Finite Mixture Model Approach. J Real Estate Finan Econ 58, 638–655 (2019). https://doi.org/10.1007/s11146-018-9658-z
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DOI: https://doi.org/10.1007/s11146-018-9658-z