arXiv subjects

Patrik Guggenberger

Publications and source records attributed to Patrik Guggenberger.

4 recordsLinked to original sources

arXiv2026

Minimax regret treatment rules with finite samples when a quantile is the object of interest

Consider a setup in which a decision maker is informed about the population by a finite sample and based on that sample has to decide whether or not to apply a certain treatment. We work out finite sample minimax regret treatment rules under various sampling schemes when outcomes are restricted onto the unit interval. In contrast to Stoye (2009) where the focus is on maximization of expected utility the focus here is instead on a particular quantile of the outcome distribution. We find that in the case where the sample consists of a fixed number of untreated and a fixed number of treated units, any treatment rule is minimax regret optimal. The same is true in the case of random treatment assignment in the sample with any assignment probability and in the case of testing an innovation when the known quantile of the untreated population equals 1/2. However if the known quantile exceeds 1/2 then never treating is the unique optimal rule and if it is smaller than 1/2 always treating is optimal. We also consider the case where a covariate is included.

econ.EM↗

arXiv2025

On the numerical approximation of minimax regret rules via fictitious play

Finding numerical approximations to minimax regret treatment rules is of key interest. To do so when potential outcomes are in {0,1} we discretize the action space of nature and apply a variant of Robinson's (1951) algorithm for iterative solutions for finite two-person zero sum games. Our approach avoids the need to evaluate regret of each treatment rule in each iteration. When potential outcomes are in [0,1] we apply the so-called coarsening approach. We consider a policymaker choosing between two treatments after observing data with unequal sample sizes per treatment and the case of testing several innovations against the status quo.

econ.EM↗

arXiv2022

A Powerful Subvector Anderson Rubin Test in Linear Instrumental Variables Regression with Conditional Heteroskedasticity

We introduce a new test for a two-sided hypothesis involving a subset of the structural parameter vector in the linear instrumental variables (IVs) model. Guggenberger et al. (2019), GKM19 from now on, introduce a subvector Anderson-Rubin (AR) test with data-dependent critical values that has asymptotic size equal to nominal size for a parameter space that allows for arbitrary strength or weakness of the IVs and has uniformly nonsmaller power than the projected AR test studied in Guggenberger et al. (2012). However, GKM19 imposes the restrictive assumption of conditional homoskedasticity. The main contribution here is to robustify the procedure in GKM19 to arbitrary forms of conditional heteroskedasticity. We first adapt the method in GKM19 to a setup where a certain covariance matrix has an approximate Kronecker product (AKP) structure which nests conditional homoskedasticity. The new test equals this adaption when the data is consistent with AKP structure as decided by a model selection procedure. Otherwise the test equals the AR/AR test in Andrews (2017) that is fully robust to conditional heteroskedasticity but less powerful than the adapted method. We show theoretically that the new test has asymptotic size bounded by the nominal size and document improved power relative to the AR/AR test in a wide array of Monte Carlo simulations when the covariance matrix is not too far from AKP.

econ.EM↗

arXiv2022

A Test for Kronecker Product Structure Covariance Matrix

We propose a test for a covariance matrix to have Kronecker Product Structure (KPS). KPS implies a reduced rank restriction on a certain transformation of the covariance matrix and the new procedure is an adaptation of the Kleibergen and Paap (2006) reduced rank test. To derive the limiting distribution of the Wald type test statistic proves challenging partly because of the singularity of the covariance matrix estimator that appears in the weighting matrix. We show that the test statistic has a chi square limiting null distribution with degrees of freedom equal to the number of restrictions tested. Local asymptotic power results are derived. Monte Carlo simulations reveal good size and power properties of the test. Re-examining fifteen highly cited papers conducting instrumental variable regressions, we find that KPS is not rejected in 56 out of 118 specifications at the 5% nominal size.

econ.EM↗