Summary This paper is concerned with applications of mixture models in econometrics. Focused attention is given to semiparametric and nonparametric models that incorporate mixture distributions, where important issues about model specifications arise. For example, there is a significant difference between a finite mixture and a continuous mixture in terms of model identifiability. Likewise, the dimension of the latent mixing variables is a critical issue, in particular when a continuous mixture is used. We present applications of mixture models to address various problems in econometrics, such as unobserved heterogeneity and multiple equilibria. New nonparametric identification results are developed for finite mixture models with testable exclusion restrictions without relying on an identification‐at‐infinity assumption on covariates. The results apply to mixtures with both continuous and discrete covariates, delivering point identification under weak conditions.

We present a new class of methods for identification and inference in dynamic models with serially correlated unobservables, which typically imply that state variables are econometrically endogenous. In the context of Industrial Organization, these state variables often reflect econometrically endogenous market structure. We propose the use of Generalized Instrument Variables methods to identify those dynamic policy functions that are consistent with instrumental variable (IV) restrictions. Extending popular "two-step" methods, these policy functions then identify a set of structural parameters that are consistent with the dynamic model, the IV restrictions and the data. We provide computed illustrations to both single-agent and oligopoly examples. We also present a simple empirical analysis that, among other things, supports the counterfactual study of an environmental policy entailing an increase in sunk costs.

Demand estimates are essential for addressing a wide range of positive and normative questions in economics that are known to depend on the shape—and notably the curvature—of the true demand functions. The existing frontier approaches, while allowing flexible substitution patterns, typically require the researcher to commit to a parametric specification. An open question is whether these a priori restrictions are likely to significantly affect the results. To address this, I develop a nonparametric approach to estimation of demand for differentiated products, which I then apply to California supermarket data. While the approach subsumes workhorse models such as mixed logit, it allows consumer behaviors and preferences beyond standard discrete choice, including continuous choices, complementarities across goods, and consumer inattention. When considering a tax on one good, the nonparametric approach predicts a much lower pass‐through than a standard mixed logit model. However, when assessing the market power of a multiproduct firm relative to that of a single‐product firm, the models give similar results. I also illustrate how the nonparametric approach may be used to guide the choice among parametric specifications.

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This article reviews recent developments in the study of firm and industry dynamics, with a special emphasis on the econometric endogeneity of market structure. The endogeneity of market structure follows from the presence of serially correlated unobservable shocks to the profitability of firms’ [Formula: see text] dynamic decisions, a feature common to many empirical settings. Methods that ignore endogeneity can lead to misleading parameter estimates and misleading counterfactual results. We pay particular attention to extensions of standard two-step methods that leverage instrumental variables to address endogeneity in both single-agent and oligopoly models. A first step set-identifies dynamic policy functions together with serial correlation parameters, and a second step quickly solves for profit function parameters using an extension of existing forward-simulation methods. We discuss how these new methods provide a general solution to initial-conditions problems and how they can yield practical estimation strategies. Expected final online publication date for the Annual Review of Economics, Volume 13 is August 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.