arXiv subjects

Adam M. Rosen

Publications and source records attributed to Adam M. Rosen.

5 recordsLinked to original sources

arXiv2026

The Projection Solution to the Incidental Parameter Problem

This paper introduces a new approach to econometric analysis of nonlinear panel data models when the number of observations per observational unit is small. In such models the presence of variables that are constant within, while varying across, units results in an incidental parameter problem. The approach taken in this paper removes these incidental parameters via projection, which produces a correspondence specifying all combinations of observed variables and within-unit-varying unobserved heterogeneity that are achievable by choice of some value of the unit-specific incidental parameters. With unit-specific variables removed, there is no need for assumptions concerning their joint distribution with other variables. The result is an incomplete model which is typically partially identifying. Identified sets are characterized via moment inequalities using tools of random set theory. Examples of application to static and dynamic models with discrete or continuous outcomes using distribution-free restrictions on within-unit-varying unobserved heterogeneity are presented.

econ.EM↗

arXiv2025

Policy Learning with Confidence

This paper introduces a rule for policy selection in the presence of estimation uncertainty, explicitly accounting for estimation risk. The rule belongs to the class of risk-aware rules on the efficient decision frontier, characterized as policies offering maximal estimated welfare for a given level of estimation risk. Among this class, the proposed rule is chosen to provide a reporting guarantee, ensuring that the welfare delivered exceeds a threshold with a pre-specified confidence level. We apply this approach to the allocation of a limited budget among social programs using estimates of their marginal value of public funds and associated standard errors.

econ.EM↗

arXiv2024

Robust Analysis of Short Panels

Many structural econometric models include latent variables on whose probability distributions one may wish to place minimal restrictions. Leading examples in panel data models are individual-specific variables sometimes treated as "fixed effects" and, in dynamic models, initial conditions. This paper presents a generally applicable method for characterizing sharp identified sets when models place no restrictions on the probability distribution of certain latent variables and no restrictions on their covariation with other variables. In our analysis latent variables on which restrictions are undesirable are removed, leading to econometric analysis robust to misspecification of restrictions on their distributions which are commonplace in the applied panel data literature. Endogenous explanatory variables are easily accommodated. Examples of application to some static and dynamic binary, ordered and multiple discrete choice and censored panel data models are presented.

econ.EM↗

arXiv2020

Finite Sample Inference for the Maximum Score Estimand

We provide a finite sample inference method for the structural parameters of a semiparametric binary response model under a conditional median restriction originally studied by Manski (1975, 1985). Our inference method is valid for any sample size and irrespective of whether the structural parameters are point identified or partially identified, for example due to the lack of a continuously distributed covariate with large support. Our inference approach exploits distributional properties of observable outcomes conditional on the observed sequence of exogenous variables. Moment inequalities conditional on this size n sequence of exogenous covariates are constructed, and the test statistic is a monotone function of violations of sample moment inequalities. The critical value used for inference is provided by the appropriate quantile of a known function of n independent Rademacher random variables. We investigate power properties of the underlying test and provide simulation studies to support the theoretical findings.

econ.EM↗

arXiv2013

Intersection Bounds: Estimation and Inference

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with a potentially infinite constraint set. We show that many bounds characterizations in econometrics, for instance bounds on parameters under conditional moment inequalities, can be formulated as intersection bounds. Our approach is especially convenient for models comprised of a continuum of inequalities that are separable in parameters, and also applies to models with inequalities that are non-separable in parameters. Since analog estimators for intersection bounds can be severely biased in finite samples, routinely underestimating the size of the identified set, we also offer a median-bias-corrected estimator of such bounds as a by-product of our inferential procedures. We develop theory for large sample inference based on the strong approximation of a sequence of series or kernel-based empirical processes by a sequence of "penultimate" Gaussian processes. These penultimate processes are generally not weakly convergent, and thus non-Donsker. Our theoretical results establish that we can nonetheless perform asymptotically valid inference based on these processes. Our construction also provides new adaptive inequality/moment selection methods. We provide conditions for the use of nonparametric kernel and series estimators, including a novel result that establishes strong approximation for any general series estimator admitting linearization, which may be of independent interest.

math.ST↗