This paper considers two models for analyzing the dynamics of firm behavior that allow for idiosyncratic (or firm-specific) sources of uncertainty, and discrete outcomes (exit and/or entry). Models with these characteristics are needed for the structural econometric analysis of several economic phenomena, including the behavior of capital markets when there are significant failure probabilities, and the analysis of productivity movements in industries with large amounts of entry and exit. In addition, these models provide a means of correcting for the self-selection induced by liquidation decisions in empirical studies of firms responses to alternative policy and environmental changes. It is shown that both models have nonparametric implications - implications that depend only on basic behavioral assumptions and mild regularity conditions on the functional forms of interest - that can be taken directly to data. This circumvents the need for the computationally difficult, and functional-form specific, estimation algorithms that have been needed for analyzing stochastic control models with discrete outcomes in the past. One difference between the two models corresponds to the distinction between heterogeneity and an ergodic form of state-dependence (a form in which the effect of being in a state in a particular period erodes away as time from that period lapses). So we develop a test for this difference based on~mixing conditions. The paper concludes by checking for the implications of the two models on an eight-year panel of Wisconsin firms. We find one model to be consistent with the data for manufacturing, and the other to be consistent with the data for retail trade.