Calibration, the practice of choosing the parameters of a structural model to match certain empirical moments, can be viewed as minimum distance estimation. Existing standard error formulas for such estimators require a consistent estimate of the correlation structure of the empirical moments, which is often unavailable in practice. Instead, the variances of the individual empirical moments are usually readily estimable. Using only these variances, we derive conservative standard errors and confidence intervals for the structural parameters that are valid even under the worst-case correlation structure. In the over-identified case, we show that the moment weighting scheme that minimizes the worst-case estimator variance amounts to a moment selection problem with a simple solution. Finally, we develop tests of over-identifying or parameter restrictions. We apply our methods empirically to a model of menu cost pricing for multi-product firms and to a heterogeneous agent New Keynesian model.

We study partially linear models when the outcome of interest and some of the covariates are observed in two different datasets that cannot be linked. This type of data combination problem arises very frequently in empirical microeconomics. Using recent tools from optimal transport theory, we derive a constructive characterization of the sharp identified set. We then build on this result and develop a novel inference method that exploits the specific geometric properties of the identified set. Our method exhibits good performances in finite samples, while remaining very tractable. We apply our approach to study intergenerational income mobility over the period 1850–1930 in the U.S. Our method allows us to relax the exclusion restrictions used in earlier work, while delivering confidence regions that are informative.

We consider a procurement auction for the provision of a basic service to which an add-on must later be appended. Potential providers are symmetric, have private information on their cost for the basic service and the winning firm must also implement the add-on. To finance value-enhancing activities related to the add-on, this firm may need extra funding by outside financiers. Nonverifiable effort related to these activities creates a moral hazard problem which makes the firm’s payoff function for the second period concave in returns over the relevant range. Concavity has two effects. First, it makes it more attractive to backload payments to facilitate information revelation. Second, uncertainty on the cost of the add-on introduces a background risk which requires a risk premium. In this context, we characterize the optimal intertemporal structure of payments to the winning firm, equilibrium bidding behaviour and reserve prices for a first-price auction.