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Difference-in-differences with Economic Factors and the Case of Housing Returns


Huang, Jiyuan; Östberg, Per (2023). Difference-in-differences with Economic Factors and the Case of Housing Returns. Swiss Finance Institute Research Paper 23-55, University of Zurich.

Abstract

This paper studies how to incorporate observable factors in difference-in-differences and document their empirical relevance. We show that even under random assignment directly adding factors with unit-specific loadings into the difference-in-differences estimation results in biased estimates. This bias, which we term the “bad time control problem” arises when the treatment effect covaries with the factor variation. Researchers often control for factor structures by using: (i) unit time trends, (ii) pre-treatment covariates interacted with a time trend and (iii) group-time dummies. We show that all these methods suffer from the bad time control problem and/or omitted factor bias. We propose two solutions to the bad time control problem. To evaluate the relevance of the factor structure we study US housing returns. Adding macroeconomic factors shows that factors have additional explanatory power and estimated factor loadings differ systematically across geographic areas. This results in substantially altered treatment effects.

Abstract

This paper studies how to incorporate observable factors in difference-in-differences and document their empirical relevance. We show that even under random assignment directly adding factors with unit-specific loadings into the difference-in-differences estimation results in biased estimates. This bias, which we term the “bad time control problem” arises when the treatment effect covaries with the factor variation. Researchers often control for factor structures by using: (i) unit time trends, (ii) pre-treatment covariates interacted with a time trend and (iii) group-time dummies. We show that all these methods suffer from the bad time control problem and/or omitted factor bias. We propose two solutions to the bad time control problem. To evaluate the relevance of the factor structure we study US housing returns. Adding macroeconomic factors shows that factors have additional explanatory power and estimated factor loadings differ systematically across geographic areas. This results in substantially altered treatment effects.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
JEL Classification:C22, C54, G28, R30
Uncontrolled Keywords:Difference-in-differences, Factor models, House prices
Scope:Discipline-based scholarship (basic research)
Language:English
Date:30 June 2023
Deposited On:25 Jan 2024 14:27
Last Modified:06 Mar 2024 14:41
Series Name:Swiss Finance Institute Research Paper
Number of Pages:67
ISSN:1556-5068
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.2139/ssrn.4495214
Other Identification Number:merlin-id:24298
  • Content: Published Version
  • Language: English