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

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.