Discrete Choice

Many of the decisions that economists care about are discrete: whether to work, which occupation to enter, whether a firm should enter or exit a market, whether to take up a welfare program. In this part of the course we develop the tools to model and estimate these decisions.

We begin with static discrete choice. Here we introduce the random utility framework and the generalized extreme value family of models, and derive some results about choice probabilities and expected utilities that we will use throughout this part. We then turn to models in which agents make a sequence of discrete choices, and in which today’s choice affects the options and payoffs available tomorrow. These dynamic models combine the static tools with the dynamic programming methods we used to solve our prototype models. After setting out the general framework, we put it to work in three prototype models: a model of market entry and exit from industrial organization, a life-cycle model of female labor force participation with human capital accumulation, and a model of labor supply and welfare participation under time limits. For each, we show how to solve the model, estimate it by maximum likelihood with a nested solution of the model, and use it to answer counterfactual questions.

Finally, we study an important class of estimators that exploit the fact that choice probabilities can be directly estimated from the data, which allows us to estimate structural parameters without repeatedly solving the model. These estimators are especially useful for dynamic games, where solving for equilibrium is costly and equilibria may not be unique.

Throughout, we will maintain the assumption that all persistent state variables are observed by the econometrician. The next part of the course relaxes this assumption.