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Regression analysis with independent variables in shares: a guide and an empirical example

Author

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  • Ulrich B. Morawetz

    (University of Natural Resources and Life Sciences Vienna)

  • H. Allen Klaiber

    (The Ohio State University)

Abstract

The use of shares or percentages as independent variables in regressions is a popular modeling technique for aggregated data but can be particularly challenging when it comes to model specification and interpretation. Reviewing theory and providing an empirical application to building height in Vienna, Austria, we discuss aggregation bias and show how to appropriately identify and interpret share coefficients. We further distinguish interpretation for constant and non-constant share sums and extend our analysis to the case of two stage least squares. Finally, we suggest a test for the conditional correlation of an instrument with shares which is needed for exogeneity if only one instrument is available.

Suggested Citation

  • Ulrich B. Morawetz & H. Allen Klaiber, 2025. "Regression analysis with independent variables in shares: a guide and an empirical example," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 52(1), pages 63-98, February.
    • Handle: RePEc:kap:empiri:v:52:y:2025:i:1:d:10.1007_s10663-024-09635-x
    DOI: 10.1007/s10663-024-09635-x
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    1. Caselli, Francesco & Wilson, Daniel J., 2004. "Importing technology," Journal of Monetary Economics, Elsevier, vol. 51(1), pages 1-32, January.
    2. Briant, A. & Combes, P.-P. & Lafourcade, M., 2010. "Dots to boxes: Do the size and shape of spatial units jeopardize economic geography estimations?," Journal of Urban Economics, Elsevier, vol. 67(3), pages 287-302, May.
    3. Deepankar Basu, 2020. "Bias of OLS Estimators due to Exclusion of Relevant Variables and Inclusion of Irrelevant Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(1), pages 209-234, February.
    4. Abdul Quddoos & Klaus Salhofer & Ulrich B. Morawetz, 2023. "Utilising farm‐level panel data to estimate climate change impacts and adaptation potentials," Journal of Agricultural Economics, Wiley Blackwell, vol. 74(1), pages 75-99, February.
    5. Breitung, Jörg & Salish, Nazarii, 2021. "Estimation of heterogeneous panels with systematic slope variations," Journal of Econometrics, Elsevier, vol. 220(2), pages 399-415.
    6. Hilber, Christian A.L. & Palmer, Charles & Pinchbeck, Edward W., 2019. "The energy costs of historic preservation," Journal of Urban Economics, Elsevier, vol. 114(C).
    7. Welsch, Heinz & Biermann, Philipp, 2014. "Electricity supply preferences in Europe: Evidence from subjective well-being data," Resource and Energy Economics, Elsevier, vol. 38(C), pages 38-60.
    8. Kirill Borusyak & Peter Hull & Xavier Jaravel, 2025. "Design-based identification with formula instruments: a review," The Econometrics Journal, Royal Economic Society, vol. 28(1), pages 83-108.
    9. Cornago, Elisabetta & Dressler, Luisa, 2020. "Incentives to (not) disclose energy performance information in the housing market," Resource and Energy Economics, Elsevier, vol. 61(C).
    10. Otto, Alkis Henri & Steinhardt, Max Friedrich, 2014. "Immigration and election outcomes — Evidence from city districts in Hamburg," Regional Science and Urban Economics, Elsevier, vol. 45(C), pages 67-79.
    11. Carlo Fezzi & Ian Bateman, 2015. "The Impact of Climate Change on Agriculture: Nonlinear Effects and Aggregation Bias in Ricardian Models of Farmland Values," Journal of the Association of Environmental and Resource Economists, University of Chicago Press, vol. 2(1), pages 57-92.
    12. Sunding, David L. & Swoboda, Aaron M., 2010. "Hedonic analysis with locally weighted regression: An application to the shadow cost of housing regulation in Southern California," Regional Science and Urban Economics, Elsevier, vol. 40(6), pages 550-573, November.
    13. Murillo Campello & Antonio F. Galvao & Ted Juhl, 2019. "Testing for Slope Heterogeneity Bias in Panel Data Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(4), pages 749-760, October.
    14. Timothy J. Bartik, 1991. "Who Benefits from State and Local Economic Development Policies?," Books from Upjohn Press, W.E. Upjohn Institute for Employment Research, number wbsle.
    15. Richard A. Kronmal, 1993. "Spurious Correlation and the Fallacy of the Ratio Standard Revisited," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 156(3), pages 379-392, May.
    16. Ernesto Calvo & Marcelo Escolar, 2003. "The Local Voter: A Geographically Weighted Approach to Ecological Inference," American Journal of Political Science, John Wiley & Sons, vol. 47(1), pages 189-204, January.
    17. repec:hal:journl:hal-04246943 is not listed on IDEAS
    18. Brueckner, Jan K., 2011. "Lectures on Urban Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262016362, December.
    19. Ulrich B. Morawetz & H. Allen Klaiber, 2022. "Does housing policy impact income sorting near urban amenities? Evidence from Vienna, Austria," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 69(2), pages 411-454, October.
    20. Shively, W. Phillips, 1969. "“Ecological” Inference: The Use of Aggregate Data to Study Individuals," American Political Science Review, Cambridge University Press, vol. 63(4), pages 1183-1196, December.
    21. J. L. Scealy & A. H. Welsh, 2011. "Regression for compositional data by using distributions defined on the hypersphere," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(3), pages 351-375, June.
    22. Schöniger, Franziska & Morawetz, Ulrich B., 2022. "What comes down must go up: Why fluctuating renewable energy does not necessarily increase electricity spot price variance in Europe," Energy Economics, Elsevier, vol. 111(C).
    23. Mustafa U. Karakaplan & Levent Kutlu, 2019. "School district consolidation policies: endogenous cost inefficiency and saving reversals," Empirical Economics, Springer, vol. 56(5), pages 1729-1768, May.
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    More about this item

    Keywords

    Compositional data; Shares; Regression; Aggregation bias; Ecological inference; Instrumental variables; Spatial fixed effects;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • R14 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Land Use Patterns

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