Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/319125 
Authors: 
Year of Publication: 
2025
Series/Report no.: 
IZA Discussion Papers No. 17856
Publisher: 
Institute of Labor Economics (IZA), Bonn
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.
Subjects: 
correlated coefficient model
heterogeneous effects
JEL: 
C21
C26
Document Type: 
Working Paper

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