OLS with Heterogeneous Coefficients

Nikolas Mittag ()
Additional contact information
Nikolas Mittag: CERGE-EI

No 17856, IZA Discussion Papers from Institute of Labor Economics (IZA)

Abstract: Regressors often have heterogeneous effects in the social sciences, implying unit-specific slopes. OLS is frequently applied to these correlated coefficient models. I first show that without restrictions on the relation between slopes and regressors, OLS estimates can take any value including being negative even though all individual slopes are positive. I derive a simple formula for the bias in the OLS estimates, which depends on the covariance of the slopes with the squared regressor. While instrumental variable methods still allow estimation of (local) average effects under the additional assumptions that the instrument is independent of the coefficients in the first stage and reduced form equations, the results here imply complicated biases when these assumptions fail. Taken together, these results imply that heterogeneous effects systematically affect estimates beyond the well-known case of local average effects and provides researchers with a simple approach to assess how heterogeneity alters their estimates and conclusions.

Keywords: correlated coefficient model; heterogeneous effects (search for similar items in EconPapers)
JEL-codes: C21 C26 (search for similar items in EconPapers)
Date: 2025-04
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://docs.iza.org/dp17856.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:iza:izadps:dp17856

Ordering information: This working paper can be ordered from
IZA, Margard Ody, P.O. Box 7240, D-53072 Bonn, Germany

Access Statistics for this paper

More papers in IZA Discussion Papers from Institute of Labor Economics (IZA) IZA, P.O. Box 7240, D-53072 Bonn, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Holger Hinte ().