Moment Inequalities in Econometric Modeling
Summary
Moment inequalities form a core component of modern econometric analysis, allowing researchers to derive bounds on parameters when full identification is infeasible. Rather than relying on exact equality constraints, models impose one-sided restrictions on expected values of functions of data and parameters. These inequalities arise naturally in contexts with incomplete or weak assumptions, such as entry games, auction bidding, random-coefficients frameworks and models with endogenous regressors. By characterising an identified set—that is, the collection of parameter values consistent with the imposed inequalities—econometricians can conduct inference that is robust to model misspecification and partial observability. Advances in computation and theory have led to tractable algorithms for constructing confidence regions, evaluating least-favourable critical values and harnessing conditional structures to improve power. Applications span industrial organisation, labour economics, finance and policy evaluation, where researchers seek credible inference under limited data richness or adversarial sampling conditions.
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Moment Inequalities in Econometric Modeling publication trend
The graph below shows the total number of articles in moment inequalities in econometric modeling across all publications each year (not limited to Nature Index journals).
Technical terms
Moment inequalities: Restrictions that impose one-sided bounds on the expected values of specified functions of data and parameters, replacing exact equality conditions.
Partial identification: A situation in which model assumptions and data yield a set of feasible parameter values rather than a unique solution.
Conditional moment inequalities: Inequalities on expectations conditional upon covariates or instruments, exploiting additional structure to sharpen inference.
Identified set: The collection of all parameter values that satisfy the imposed moment inequalities given the observed data.
Least-favourable critical value: A threshold ensuring valid inference by guarding against the worst-case binding of all inequality constraints.
References
- Recent Developments in Partial Identification. Annual Review of Economics (2023).
- Inference for Linear Conditional Moment Inequalities. The Review of Economic Studies (2023).
- An instrumental variable random‐coefficients model for binary outcomes. Econometrics Journal (2014).
- IV models of ordered choice. Journal of Econometrics (2012).
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