While not specifically addressing collinear categorical variables, Peter
Kennedy 's "Guide to Econometrics" presents two basic options to deal with
multicollinearity.
1. Do nothing.
2. Incorporate Additional Information.
a. Obtain more data
b. Formalize relationships among regressors and estimate in a simultaneous
approach.
c. Specify a relationship among some parameters. Theory may suggest that
two coefficients should be equal or sum to one, for example.
d. Drop a variable. However, omitting a relevant variables biases the
remaining coefficients unless they are uncorrelated with the omitted
variable. As noted by Dreze (1983) "setting a coefficient equal to zero
because it is estimated with poor precision amounts to elevating ignorance
to arrogance."
e. Incorporate estimates form other studies
f. Form a principal component.
g. Shrink the OLS estimates - a ridge or Stein estimator.
Hope this helps,
Scott
Dreze, J (1983). "Nonspecialist Teaching of Econometrics: A Personal Comment
and Personalistic Lament" Econometric Reviews 2, 291-9.
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