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I propose a point-identifying restriction and estimation procedure for a linear panel data quantile regression model with a fixed time dimension.
These moment conditions are functions of the model parameters and the data, such that their expectation is zero at the true values of the parameters.
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Before we can make a statement about the asymptotic distribution of the GMM estimator, we need to define two auxiliary matrices: So far we have said nothing about the choice of matrix W, except that it must be positive semi-definite.
In fact any such matrix will produce a consistent and asymptotically normal GMM estimator, the only difference will be in the asymptotic variance of that estimator.