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When market structure is complete, factor demands by households will be independent of their characteristics, and households will take their production decisions as if they were profit-maximizing firms. This observation constitutes the basis for one of the most popular empirical tests for complete markets, commonly known as the “separation” hypothesis. In this article, we show that most existing tests for separation using panel data are potentially biased towards rejecting the null-hypothesis of complete markets, because of the failure to adequately control for unobservable household-specific effects. Since the variables on which the test for separation is based cannot be identifed in most panel datasets following the usual covariance transformations, and are likely to be correlated with the household-specific effect, neither the within nor the variance-components procedures are able to solve the problem. We show that the Hausman-Taylor 1981 estimator, in which the impact of covariates that are invariant along one dimension of a panel can be identifed through the use of covariance transformations of other included variables that are orthogonal to the household-specific effects as instruments, provides a simple solution. Our approach is applied to a rich Tunisian dataset in which separation –and thus the null of complete markets– is strongly rejected using the standard approach, but is not rejected once correlated unobservable household-specific effects are controlled for using the Hausman-Taylor instrument set.