I would like to analyse the impact of Fund Size on Mutual Fund Performance by using quintiles (based on fund size). My approach is to look at the effect within each quintile to conclude uniformity of the potential effect among all size groups. My initial thought was to use a dummy regression (quintiles=dummies) with interaction terms (dummy*Lagged Fund Size). However, I would like to include a quadratic effect of the Lagged Fund Size as well and use interaction terms. In other words, analysing both the linear and quadratic effect in each quintile by using interaction terms. To avoid multicollinearity, I have to omit one of the quintiles (i.e. dummies) (since excluding the constant term instead results in the omission of one of the interaction terms in both Stata and SPSS).
My questions are the following:
- How can I interpret the constant term as it includes both the linear and quadratic effect for the omitted dummy? Is it even statistically correct?
- Ideally I would like to include all dummies hence excluding the constant term to better visualise the effect within each quintile. Is it possible to do this (by for example omitting the general (non-interaction) effect, i.e. either the dummies or the Fund Size effect in the regression)?
- Are there any other models/regression forms that could avoid this hindrance and analyse the linear and quadratic effect in one regression?