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Latent Tastes, Incomplete Stratification, and the Plausibility of Vertical Sorting Models

Environmental and Resource Economics volume 66, pages 339–361 (2017)Cite this article

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Abstract

This paper uses the 2011 Phoenix Area Social Survey to evaluate the plausibility of the assumptions made with pure characteristics sorting models to rationalize incomplete stratification of households across local communities by income. The analysis with the New Ecological Paradigm, a well-recognized index of environmental attitudes, confirms the correlations in equilibrium outcomes implied by these models. As a result, it provides the first empirical support for the role of differences in the tastes for public goods as one explanation that provides the rationale for the commonly observed sorting outcomes.

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Fig. 1
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Notes

  1. See Kuminoff et al. (2013) for a review of the sorting literature and Parmeter and Pope (2013) for a comparable overview of the quasi-experimental method along with discussion of some applications relevant to urban, public and environmental policies.

  2. Grimm and Redman (2004) describe the detailed process for the first survey conducted in 2006. The second survey that provides the basis for this analysis was completed in 2011–2012, and used the same definitions as described later in the paper.

  3. Google Scholar accessed 6/28/15 records 13,708 citations to Tiebout and 7093 to Samuelson. Of course, this is only one gauge. The ideas developed in classic papers became embedded in the “language” and background context for a field through its textbooks and the original papers are often not cited because the concept is taken as established.

  4. See Kuminoff et al. (2013) for a more complete discussion of the features of the two modeling strategies.

  5. See Sieg et al. (2004) or Walsh (2007) as examples.

  6. Sieg et al. (2004), Walsh (2007) and Klaiber and Smith (2012) all found negative correlations in their estimates of pure characteristics sorting models. They were \(-0.29\) to \(-0.19\) for the first study, \(-0.02\) for Walsh, and \(-0.28\) for Klaiber and Smith.

  7. The single crossing condition assures the income elasticity of the virtual price of the public good will exceed the income elasticity of housing (the weak complement in vertical sorting models). This result is a natural extension to Palmquist (2005). For the specific CES specification used in all the vertical models, the income elasticity for the virtual price is the sum of the income elasticity of demand for housing plus a non-negative term.

  8. Seven sites of the sixteen visited were eliminated because the residents were not close to the plot used for monitoring.

  9. Urban core neighborhoods are within 5 miles of downtown Phoenix or within 1.5 miles of the other 7 large city downtowns. The exact distances somewhat based on historical development patterns.

  10. Urban fringe areas are defined as having a moderate amount of undeveloped land within a mile of the neighborhood as of 2005.

  11. In some applications an exponential transformation has been used to rescale the indexes. By definition they are estimated relative to one of the neighborhoods. See Sieg et al. (2002).

  12. The original NEP scale had 12 items (8 pro-trait and 4 con-trait) and was based on a four point Likert scale using test identifiers of strongly agree and strongly disagree for the anchors. The new items expanded the scope based on comments and is based on 15 questions with a 5 point Likert scale.

  13. The data appendix for Smith et al. (2015) includes copies of the mailers.

  14. The minimum response rate is the number of complete interviews divided by the number of interviews (complete plus partial) plus the number of non-interviews (refusal and break-off plus non-contacts plus others) plus all cases of unknown eligibility.

  15. We also investigated the effects of reducing the sample sale dates to 2007, due to the housing downturn in Phoenix and this did not affect our conclusions.

  16. Thanks are due Allen Klaiber for his assistance in developing these data as part of research reported in Klaiber and Smith (2012).

  17. The key requirement is the consistent spatial resolution for measures of attitudes, household income and prices as the aggregator reflecting local public goods. A partial regression coefficient between any two variables measures the correlation between those two variables after the linear effect of other variables have been removed. Our test should focus on the partial correlation between average NEP and average income after the effects of local public goods have been removed. By the Frisch–Waugh–Lovell theorem the coefficient on income in a regression model for NEP that includes the price along with income provides this information.

  18. We could reverse this logic and regress income on NEP and the price index. We have also estimated the model in this form and the results parallel those in Table 4. Income and NEP are not significantly related until the price index is included and the estimated parameter for NEP is negative and statistically significant. This should not be surprising given the link to between the regression model Frisch-Waugh-Lovell theorem noted in footnote #11, and our focus on the conditional correlation.

  19. The \(\hbox {R}^{2}\) estimates are not comparable to the OLS results from (1) and (2). FGLS was implemented by transforming the dependent and independent variables. So the \(\hbox {R}^{2}\) is in terms of the re-weighted NEP and not comparable.

  20. The coefficient of skewness for income, \(s^{k}\), is defined in terms of the second \(\left( {m_2 } \right) \) and third moments \(\left( {m_3 } \right) \) about the mean income as:

    $$\begin{aligned} s^{k}=\frac{m_3 }{m_2^{3/2} } \end{aligned}$$

    Skewness measure the extent of asymmetry in a distribution. See Kendall and Stuart (1969, Vol. I, pp. 85–86), for discussion of this index. This includes a comparison to measures based on the mean and mode of each distribution.

  21. See footnote 6 for examples.

  22. This correlation was computed using the residuals from a regression of NEP on the price index and mean income at the neighborhood level. Using median income the correlation is \(-0.23\).

  23. See Carbone and Smith (2008, 2013) for discussion.

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Authors and Affiliations

  1. Department of Economics, Arizona State University, Tempe, AZ, USA

    Jacob Fishman & V. Kerry Smith

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  1. Jacob Fishman
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  2. V. Kerry Smith
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Correspondence to V. Kerry Smith.

Additional information

This material is based upon research supported by the National Science Foundation under Grants BCS-1026865 and DEB-0423704 CAP LTER. Thanks are due to Jon Krosnick and the Stanford Political Psychology Research Group for comments on this research; to Shauna Mortensen for assistance in preparing this manuscript; to Sharon Harlan, Michael McLaen, Marcia Nation, and Carlos Valcarcel for assistance with the PASS survey data; and to Michael Kaminsky and Carlos Silva for assistance with the test score data for our education quality measure and air pollution measure respectively.

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Fishman, J., Smith, V.K. Latent Tastes, Incomplete Stratification, and the Plausibility of Vertical Sorting Models. Environ Resource Econ 66, 339–361 (2017). https://doi.org/10.1007/s10640-015-9952-7

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Keywords

  • Equilibrium sorting models
  • Local public goods
  • New Ecological Paradigm

JEL Classification

  • D58
  • H4
  • Q51