Unobserved Heterogeneity

Every model we have estimated so far has assumed that, once we condition on observables, the remaining unobservables are either fixed across individuals (and hence parameters) or independent across time (like the payoff shocks in our dynamic discrete choice models). In reality, people, firms, and markets differ in ways that persist over time and that we cannot measure. Some workers are more productive than others; some markets are more profitable; some families find welfare participation more stigmatizing.

Ignoring this unobserved heterogeneity can be a serious problem. In dynamic models in particular, persistent unobservables generate dynamic selection: the individuals who find themselves in a given state are not a random sample of the population, because their past choices (which determined their current state) were influenced by their unobserved type. This is the classic problem of distinguishing state dependence from heterogeneity (Heckman 1981).

In this part of the course we will:

1. Introduce finite mixture models and the Expectation-Maximization (EM) algorithm for estimating them, including its combination with the CCP estimators from the previous part (Arcidiacono and Miller 2011).
2. Extend these methods to unobservables that evolve over time using hidden Markov models and the forward-backward algorithm.
3. Study an alternative approach that discretizes heterogeneity with clustering methods (Bonhomme and Manresa 2015; Bonhomme, Lamadon, and Manresa 2022).
4. Discuss when and how models with unobserved heterogeneity are identified, focusing on the role of panel data and instruments.

Arcidiacono, Peter, and Robert A Miller. 2011. “Conditional Choice Probability Estimation of Dynamic Discrete Choice Models with Unobserved Heterogeneity.” Econometrica 79 (6): 1823–67.

Bonhomme, Stéphane, Thibaut Lamadon, and Elena Manresa. 2022. “Discretizing Unobserved Heterogeneity.” Econometrica 90 (2): 625–43.

Bonhomme, Stéphane, and Elena Manresa. 2015. “Grouped Patterns of Heterogeneity in Panel Data.” Econometrica 83.

Heckman, James J. 1981. “Heterogeneity and State Dependence.” In Studies in Labor Markets, edited by Sherwin Rosen, 91–140. University of Chicago Press.