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st: Linear mixed models and endogeneity
We have a panel containing the performance and several other attributes of more
than 100 mutual funds. The data is organized in a hierarchical way: The banks
(level 3) manage several mutual funds (level 2) over many periods (level 1).
If we estimate a random effect panel model (with Stata’s xtreg command) the
Hausman specification test rejects the null hypothesis of no endogeneity.
Therefore, we have to assume that the random intercepts are correlated with one
(or more) of the explanatory variables. Hence, the random effects model
(estimated with the GLS-estimator) seems to be misspecified and we should use
the fixed effects estimator in order to receive consistent parameter estimates.
However, several of our variables are constant over time and therefore the
fixed effects estimator is not adequate for our purposes.
Because our data is hierarchically organized we clearly prefer estimating a
linear mixed model compared to estimating a model with Hausman and Taylor’s
(1981) approach (command in Stata: xthtaylor). Unfortunately, we couldn’t find
any literature on whether there might be endogeneity (and with this
inconsistency) problems in linear random-coefficient models (other than
“simple” random intercept models) and how such problems might be mitigated.
Therefore, we would like to ask you, if it is possible to consistently estimate
linear mixed models even if the Hausman specification test rejects the null of
no model misspecification in the case of the GLS-estimator?
We thank you very much for looking into this matter in advance.
Daniel and Wolfgang
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