Extending the simultaneous equations approach to jointly determined discrete outcomes has proved to be challenging. One has to impose the so-called coherency condition to guarantee the existence of a unique reduced form. These conditions effectively convert a model where the endogenous variables are jointly determined into a model that is triangular or recursive. In the spirit of a suggestion by Lewbel (2007), I propose using panel data to decide how the coherency condition will hold without restricting error supports or imposing triangularity. Furthermore, incidental parameter biases are avoided and time-invariant unobserved heterogeneity can now be thought of as an indicator of the direction of causality between the discrete outcomes. Finally, I apply the proposal and revisit the model of employment conditions and borrowing constraints estimated by Hajivassiliou and Ioannides (2007).