Identification and Counterfactuals in Dynamic Models of Market Entry and Exit

This paper deals with a fundamental identification problem in the structural estimation of dynamic oligopoly models of market entry and exit. Using the standard datasets in existing empirical applications, there are three key components of a firm's profit function that are not separately identified: the fixed cost of an incumbent firm, the entry cost of a new entrant, and the scrap-value of an exiting firm. We study the implications of this result on the power of this class of models to identify the effects of comparative static exercises or public policies involving changes in these structural functions. First, we derive a closed-form relationship between the three unknown structural functions and two functions that are identified from the data. We use this relationship to provide the correct interpretation of the estimated objects that are obtained under the 'normalization assumptions' considered in most applications. Second, we characterize a class of counterfactual experiments that are identified using the estimated model, despite the non-separate identification of the three primitives. Third, we show that there is a general class of counterfactual experiments of economic relevance that are not identified. We present numerical examples that illustrate how ignoring the non-identification of these counterfactuals (i.e., making a 'normalization assumption' on some of the three primitives) generates sizable biases that can modify even the sign of the estimated effects. Finally, we discuss possible solutions to deal with these identification problems