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A common stochastic restriction in econometric models separable in the latent variables is the assumption of stochastic independence between the unobserved and observed exogenous variables. Both simple and composite tests of this assumption are derived from properties of independence empirical processes and the consistency of these tests is established. As an application, we simulate estimation of a random quasilinear utility function, where we apply our tests of independence.
Brown, Donald J.; Deb, Rahul; and Wegkamp, Marten H., "Tests of Independence in Separable Econometric Models: Theory and Application" (2003). Cowles Foundation Discussion Papers. 1661.