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The effect of amenities on local wage distributions

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Abstract

This paper predicts that local wage distributions will contract with an improvement in amenities by imposing structure on the standard model of amenity capitalization with multiple worker types (Roback in Econ Inq 26(1):23–41, 1988). The added structure is Ellickson’s (Am Econ Rev 61(2):334–339, 1971) single-crossing condition, which assumes that the willingness to accept higher housing prices for better amenities increases with income. The model predicts that under empirically plausible conditions, workers at the upper end of the wage distribution will earn less in locations with better amenities while those at the lower end will actually earn more.

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Notes

  1. When using the “traditional hedonic model”, Bayer et al. (2009) estimate a positive relationship between amenities (lack of air pollution) and wages using an OLS regression and an insignificant positive relationship using instrumental variables. Gyourko and Tracy (1991) estimate a negative wage differential for the disamenity student/teacher ratio.

  2. However, given the nature of the specific productive amenity in Moretti (2004), it is most likely that the correct separation for that study is in fact education group.

  3. It is assumed that the utility function of the workers is such that a positive amount of land l is always purchased.

  4. A utility function that satsfies this condition is provided in Ellickson (1971) as the nested CES function \(U(x,l;\varPhi )=\{[a_{1}\varPhi ]^{\frac{1}{\rho }}+[(a_{3}X)^{\frac{1}{\omega }}+(a_{2}l)^{\frac{1}{\omega }}]^{\frac{\omega }{\rho }}\}^{\rho }\) where the a’s, \(\rho \), and \(\omega \) are constants, \(\rho =\frac{\sigma }{\sigma -1}\), and \(\sigma <1\).

  5. Roy’s identity is used here to convert preference ratios into land consumption \(-V_{l}^{k}/V_{w}^{k}=l_{k}\).

  6. Recall the unit cost of x is equal to one.

  7. This is because the firm pays \(\theta _{r}\) of each unit of revenue to land and \(\theta _{w}^{k}\) to worker k, who spends \(s_{l}^{k}\) of \(\theta _{w}^{k}\) on land.

  8. This assumption is commonly employed in sorting models to achieve stratification of households by income. See Epple et al. (1984) and (1993), Epple and Sieg (1999), Walsh (2007), and Banzhaf and Walsh (2008) for examples.

  9. Too see this, apply the implicit function theorem to \(V(r_j,w_{j}^{k};\varPhi _{j})={\overline{V}}^{k}\) and note that \(V_{\varPhi }>0\) and \(V_{r}<0\).

  10. See appendix for proof.

  11. Note that the magnitude of this difference is decreasing in \(\varDelta \), the percentage of revenue from x production that accrues to land. A similar theoretical prediction in Black et al. (2009) states that the more amenities are capitalized into rents, the less the return to education will be.

  12. See Kerr (2011) for a theoretical treatment of the remaining two cases.

  13. The value of \({\tilde{\eta }}_{w}^{B}=0\) is arbitrarily chosen for convenience of the graph’s readability. Under single-crossing, \({\tilde{\eta }}_{w}^{B}\gtrless 0\) is also possible. All other thresholds (\({\tilde{\eta }}_{w}^{A}\), \({\tilde{\eta }}_{r}\), and \({\tilde{\eta }}\)) are guaranteed to be the sign they are shown to be in Fig. 2 and \({\tilde{\eta }}_{w}^{A}<{\tilde{\eta }}_{w}^{B}<{\tilde{\eta }}_{r}\) always holds.

  14. See appendix for proof.

  15. See Mayo (1981) for a review of early studies and Hansen et al. (1998) for evidence from Lorenz curve approach as well as the traditional approach. The general conclusion from this line of research is that income elasticities of housing is less than unity, even when elasticities are allowed to vary by income.

References

  • Albouy, D.: Are big cities bad places to live? Estimating quality of life across metropolitan areas. Technical Report, National Bureau of Economic Research (2008)

  • Albouy, D.: What are cities worth? Land rents, local productivity, and the capitalization of amenity values. Technical Report, National Bureau of Economic Research (2009)

  • Banzhaf, S., Walsh, R.: Do people vote with their feet? An empirical test of Tiebout’s mechanism. Am. Econ. Rev. 98(3), 843–863 (2008)

    Article  Google Scholar 

  • Baum-Snow, N., Pavan, R.: Inequality and city size. Rev. Econ. Stat. 95(5), 1535–1548 (2013)

    Article  Google Scholar 

  • Bayer, P., Keohane, N., Timmins, C.: Migration and hedonic valuation: the case of air quality. J. Environ. Econ. Manag. 58(1), 1–14 (2009)

    Article  Google Scholar 

  • Beeson, P.: Amenities and regional differences in returns to worker characteristics. J. Urban Econ. 30(2), 224–241 (1991)

    Article  Google Scholar 

  • Beeson, P.E.: Eberts. R.W.: Identifying productivity and amenity effects in interurban wage differentials. Rev. Econ. Stat. 71(3), 443–452 (1989)

    Article  Google Scholar 

  • Black, D., Kolesnikova, N., Taylor, L.: Earnings functions when wages and prices vary by location. J. Labor Econ. 27(1), 21–47 (2009)

    Article  Google Scholar 

  • Blomquist, G.C., Berger, M.C., Hoehn, J.P.: New estimates of quality of life in urban areas. Am. Econ. Rev. 78(1), 89–107 (1988)

    Google Scholar 

  • Chen, Y., Rosenthal, S.: Local amenities and life-cycle migration: Do people move for jobs or fun? J. Urban Econ. 64(3), 519–537 (2008)

    Article  Google Scholar 

  • Ellickson, B.: Jurisdictional fragmentation and residential choice. Am. Econ. Rev. 61(2), 334–339 (1971)

    Google Scholar 

  • Epple, D., Sieg, H.: Estimating equilibrium models of local jurisdictions. J. Polit. Econ. 107(4), 645–681 (1999)

    Article  Google Scholar 

  • Epple, D., Filimon, R., Romer, T.: Equilibrium among local jurisdictions: toward an integrated approach of voting and residential choice. J. Public Econ. 24(3), 281–308 (1984)

    Article  Google Scholar 

  • Epple, D., Filimon, R., Romer, T.: Existence of voting and housing equilibrium in a system of com-existence of voting and housing equilibrium in a system of com- munities with property taxes. Reg. Sci. Urban Econ. 23(5), 585–610 (1993)

    Article  Google Scholar 

  • Fuerst, F., Shimizu, C.: Green luxury goods? The economics of eco-labels in the Japanese housing market. J. Jpn. Int. Econ. 39(1), 108–122 (2016)

    Article  Google Scholar 

  • Gyourko, J., Tracy, J.: The structure of local public finance and the quality of life. J. Polit. Econ. 99(4), 774–806 (1991)

    Article  Google Scholar 

  • Hansen, J.L., Formby, J.P., Smith, W.J.: Estimating the income elasticity of demand for housing: a comparison of traditional and lorenz-concentration curve methodologies. J. Hous. Econ. 7(4), 328–342 (1998)

    Article  Google Scholar 

  • Jaramillo, F., Kempf, H., Moizeau, F.: Inequality and club formation. J. Public Econ. 87(5), 931–955 (2003)

    Article  Google Scholar 

  • Kerr, C.: The effects of amenities on wage distributions and migratory responses to racial wage disparity. PhD thesis, University of Colorado (2011)

  • Lee, S.: Ability sorting and consumer city. J. Urban Econ. 68(1), 20–33 (2010)

    Article  Google Scholar 

  • Mayo, S.K.: Theory and estimation in the economics of housing demand. J. Urban Econ. 10(1), 95–116 (1981)

    Article  Google Scholar 

  • Moretti, E.: Estimating the social return to higher education: evidence from longitudinal and repeated cross-sectional data. J. Econom. 121(1–2), 175–212 (2004)

    Article  Google Scholar 

  • Moretti, E.: Real wage inequality. Am. Econ. J. Appl. Econ. 5(1), 65–103 (2013)

    Article  Google Scholar 

  • Peiser, R.B., Smith, L.B.: Homeownership returns, tenure choice and inflation. Real Estate Econ. 13(4), 343–360 (1985)

    Article  Google Scholar 

  • Roback, J.: Wages, rents, and the quality of life. J. Polit. Econ. 90(6), 1257–1278 (1982)

    Article  Google Scholar 

  • Roback, J.: Wages, rents, and amenities: differences among workers and regions. Econ. Inq. 26(1), 23–41 (1988)

    Article  Google Scholar 

  • Walsh, R.: Endogenous open space amenities in a locational equilibrium. J. Urban Econ. 61(2), 319–344 (2007)

    Article  Google Scholar 

  • Wood, R.: Suburbia. Houghton Mifflin Company, Boston (1958)

    Google Scholar 

Download references

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Appendix

Appendix

Proof that \({\tilde{\eta }}_{w}^{A}<{\tilde{\eta }}_{w}^{B}<{\tilde{\eta }}_{r}\)

$$\begin{aligned} {\tilde{\eta }}_{w}^{A}<{\tilde{\eta }}_{w}^{B} \end{aligned}$$
(15)

when

$$\begin{aligned} 0<\left( \theta _{r}+\theta _{w}^{A}s_{l}^{A}+\theta _{w}^{B}s_{l}^{B}\right) \left[ \left( s_{\varPhi }^{A}/s_{l}^{A}\right) -\left( s_{\varPhi }^{B}/s_{l}^{B}\right) \right] . \end{aligned}$$
(16)

The single-crossing assumption guarantees that the right hand side is positive. Likewise,

$$\begin{aligned} {\tilde{\eta }}_{w}^{B}<{\tilde{\eta }}_{r} \end{aligned}$$
(17)

when

$$\begin{aligned} 0<\left( s_{\varPhi }^{B}/s_{l}^{B}\right) \left( s_{l}^{B}\theta _{w}^{A}+s_{l}^{A}\theta _{w}^{B}+\theta _{r}\right) , \end{aligned}$$
(18)

where all terms on the ride hand side are positive. By transitivity, the proof is complete.

Proof that \(({\hat{w}}^{A}/{\hat{\varPhi }})-({\hat{w}}^{B}/{\hat{\varPhi }})<0\) when \(s_{l}^{A}<s_{l}^{B}\), \(s_{\varPhi }^{B}<s_{\varPhi }^{A}\) and \(\eta <{\tilde{\eta }}_{r}\)

Signing Equation 14 requires solving for

$$\begin{aligned} -\theta _{r}\left( s_{\varPhi }^{A}-s_{\varPhi }^{B}\right) -(1-\theta _{r})s_{l}^{B}s_{l}^{A}\left[ \left( s_{\varPhi }^{A}/s_{l}^{A}\right) -\left( s_{\varPhi }^{B}/s_{l}^{B}\right) \right] +\left( s_{l}^{B}-s_{l}^{A}\right) \eta \lesseqgtr 0\nonumber \\ \end{aligned}$$
(19)

or

$$\begin{aligned} {\tilde{\eta }}\equiv \frac{\theta _{r}\left( s_{\varPhi }^{A}-s_{\varPhi }^{B}\right) +(1-\theta _{r})\left( s_{\varPhi }^{A}s_{l}^{B}-s_{\varPhi }^{B}s_{l}^{A}\right) }{s_{l}^{B}-s_{l}^{A}}\gtreqless \eta \end{aligned}$$
(20)

Therefore, \({\tilde{\eta }}\) is the value of \(\eta \) for which \(({\hat{w}}^{A}/{\hat{\varPhi }})=({\hat{w}}^{B}/{\hat{\varPhi }})\). What remains is to show is that this value is greater than \(\eta _{r}\) as shown in Figs. 2 and 3. In this case, we will have \(\eta<{\tilde{\eta }}_{r}<{\tilde{\eta }}\) rendering Eq. 19 negative.

The assumptions \(s_{\varPhi }^{A}>s_{\varPhi }^{B}\) and \(s_{l}^{A}<s_{l}^{B}\) imply that \({\tilde{\eta }}_{r}<{\tilde{\eta }}\). To see this, note that the latter inequality holds when

$$\begin{aligned} s_{\varPhi }^{A}\theta _{w}^{A}+s_{\varPhi }^{B}\theta _{w}^{B}<\frac{\theta _{r}\left( s_{\varPhi }^{A}-s_{\varPhi }^{B}\right) +(1-\theta _{r})\left( s_{\varPhi }^{A}s_{l}^{B}-s_{\varPhi }^{B}s_{l}^{A}\right) }{s_{l}^{B}-s_{l}^{A}}, \end{aligned}$$
(21)

which can be rearranged as

$$\begin{aligned} 0<\varDelta \left( s_{\varPhi }^{A}-s_{\varPhi }^{B}\right) \end{aligned}$$
(22)

where \(\varDelta \equiv \theta _{r}+s_{l}^{A}\theta _{w}^{A}+s_{l}^{B}\theta _{w}^{B}>0\) as before. Clearly, this holds when \(s_{\varPhi }^{A}>s_{\varPhi }^{B}\). The assumption \(s_{l}^{A}<s_{l}^{B}\) dictates the direction of the inequality since simplification of Eq. 21– 22 requires multiplying both sides by \((s_{l}^{B}-s_{l}^{A})\). Thus, under the assumptions \(s_{l}^{A}<s_{l}^{B}\) and \(s_{\varPhi }^{B}<s_{\varPhi }^{A}\), \(({\hat{w}}^{A}/{\hat{\varPhi }})-({\hat{w}}^{B}/{\hat{\varPhi }})<0\) whenever \(\eta <{\tilde{\eta }}_{r}\).

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Kerr, C. The effect of amenities on local wage distributions. Lett Spat Resour Sci 10, 215–228 (2017). https://doi.org/10.1007/s12076-017-0183-0

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