arXiv subjects

Konrad Menzel

Publications and source records attributed to Konrad Menzel.

8 recordsLinked to original sources

arXiv2026

Model Selection in Panel Data Models: A Generalization of the Vuong Test

This paper generalizes the classical Vuong (1989) test to panel data models by employing modified profile likelihoods and the Kullback-Leibler information criterion. Unlike the standard likelihood function, the profile likelihood lacks certain regular properties, making modification necessary. We adopt a generalized panel data framework that incorporates group fixed effects for time and individual pairs, rather than traditional individual fixed effects. Applications of our approach include linear models with non-nested specifications of individual-time effects.

econ.EM↗

arXiv2025

Fixed-Population Causal Inference for Models of Equilibrium

In contrast to problems of interference in (exogenous) treatments, models of interference in unit-specific (endogenous) outcomes do not usually produce a reduced-form representation where outcomes depend on other units' treatment status only at a short network distance, or only through a known exposure mapping. This remains true if the structural mechanism depends on outcomes of peers only at a short network distance, or through a known exposure mapping. In this paper, we first define causal estimands that are identified and estimable from a single experiment on the network under minimal assumptions on the structure of interference, and which represent average partial causal responses which generally vary with other global features of the realized assignment. Under a fixed-population, design-based approach, we show unbiasedness and consistency for inverse-probability weighting (IPW) estimators for those causal parameters from a randomized experiment on a single network. We also analyze more closely the case of marginal interventions in a model of equilibrium with smooth response functions where we can recover LATE-type weighted averages of derivatives of those response functions. Under additional structural assumptions, these ``agnostic" causal estimands can be combined to recover model parameters, but also retain their less restrictive causal interpretation.

econ.EM↗

arXiv2023

Transfer Estimates for Causal Effects across Heterogeneous Sites

We consider the problem of extrapolating treatment effects across heterogeneous populations (``sites"/``contexts"). We consider an idealized scenario in which the researcher observes cross-sectional data for a large number of units across several ``experimental" sites in which an intervention has already been implemented to a new ``target" site for which a baseline survey of unit-specific, pre-treatment outcomes and relevant attributes is available. Our approach treats the baseline as functional data, and this choice is motivated by the observation that unobserved site-specific confounders manifest themselves not only in average levels of outcomes, but also how these interact with observed unit-specific attributes. We consider the problem of determining the optimal finite-dimensional feature space in which to solve that prediction problem. Our approach is design-based in the sense that the performance of the predictor is evaluated given the specific, finite selection of experimental and target sites. Our approach is nonparametric, and our formal results concern the construction of an optimal basis of predictors as well as convergence rates for the estimated conditional average treatment effect relative to the constrained-optimal population predictor for the target site. We quantify the potential gains from adapting experimental estimates to a target location in an application to conditional cash transfer (CCT) programs using a combined data set from five multi-site randomized controlled trials.

econ.EM↗

arXiv2022

Structural Sieves

This paper explores the use of deep neural networks for semiparametric estimation of economic models of maximizing behavior in production or discrete choice. We argue that certain deep networks are particularly well suited as a nonparametric sieve to approximate regression functions that result from nonlinear latent variable models of continuous or discrete optimization. Multi-stage models of this type will typically generate rich interaction effects between regressors ("inputs") in the regression function so that there may be no plausible separability restrictions on the "reduced-form" mapping form inputs to outputs to alleviate the curse of dimensionality. Rather, economic shape, sparsity, or separability restrictions either at a global level or intermediate stages are usually stated in terms of the latent variable model. We show that restrictions of this kind are imposed in a more straightforward manner if a sufficiently flexible version of the latent variable model is in fact used to approximate the unknown regression function.

econ.EM↗

arXiv2021

Central Limit Theory for Models of Strategic Network Formation

We provide asymptotic approximations to the distribution of statistics that are obtained from network data for limiting sequences that let the number of nodes (agents) in the network grow large. Network formation is permitted to be strategic in that agents' incentives for link formation may depend on the ego and alter's positions in that endogenous network. Our framework does not limit the strength of these interaction effects, but assumes that the network is sparse. We show that the model can be approximated by a sampling experiment in which subnetworks are generated independently from a common equilibrium distribution, and any dependence across subnetworks is captured by state variables at the level of the entire network. Under many-player asymptotics, the leading term of the approximation error to the limiting model established in Menzel (2015b) is shown to be Gaussian, with an asymptotic bias and variance that can be estimated consistently from a single network.

econ.GN↗

arXiv2019

A Causal Bootstrap

The bootstrap, introduced by Efron (1982), has become a very popular method for estimating variances and constructing confidence intervals. A key insight is that one can approximate the properties of estimators by using the empirical distribution function of the sample as an approximation for the true distribution function. This approach views the uncertainty in the estimator as coming exclusively from sampling uncertainty. We argue that for causal estimands the uncertainty arises entirely, or partially, from a different source, corresponding to the stochastic nature of the treatment received. We develop a bootstrap procedure that accounts for this uncertainty, and compare its properties to that of the classical bootstrap.

stat.ME↗

arXiv2017

Bootstrap with Clustering in Two or More Dimensions

We propose a bootstrap procedure for data that may exhibit clustering in two or more dimensions. We use insights from the theory of generalized U-statistics to analyze the large-sample properties of statistics that are sample averages from the observations pooled across clusters. The asymptotic distribution of these statistics may be non-standard if there is no clustering in means. We show that the proposed bootstrap procedure is (a) point-wise consistent for any fixed data-generating process (DGP), (b) uniformly consistent if we exclude the case of clustering without clustering in means, and (c) provides refinements for any DGP such that the limiting distribution is Gaussian.

stat.ME↗

arXiv2012

Inference on Sets in Finance

In this paper we consider the problem of inference on a class of sets describing a collection of admissible models as solutions to a single smooth inequality. Classical and recent examples include, among others, the Hansen-Jagannathan (HJ) sets of admissible stochastic discount factors, Markowitz-Fama (MF) sets of mean-variances for asset portfolio returns, and the set of structural elasticities in Chetty (2012)'s analysis of demand with optimization frictions. We show that the econometric structure of the problem allows us to construct convenient and powerful confidence regions based upon the weighted likelihood ratio and weighted Wald (directed weighted Hausdorff) statistics. The statistics we formulate differ (in part) from existing statistics in that they enforce either exact or first order equivariance to transformations of parameters, making them especially appealing in the target applications. Moreover, the resulting inference procedures are also more powerful than the structured projection methods, which rely upon building confidence sets for the frontier-determining sufficient parameters (e.g. frontier-spanning portfolios), and then projecting them to obtain confidence sets for HJ sets or MF sets. Lastly, the framework we put forward is also useful for analyzing intersection bounds, namely sets defined as solutions to multiple smooth inequalities, since multiple inequalities can be conservatively approximated by a single smooth inequality. We present two empirical examples that show how the new econometric methods are able to generate sharp economic conclusions.

stat.AP↗