arXiv subjects

Andres Santos

Publications and source records attributed to Andres Santos.

At least 19 recordsLinked to original sources

arXiv2026

Inference for Linear Systems with Unknown Coefficients

This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system of equations, including the slope coefficients, to be unknown. For this reason, we describe the linear system as having unknown (as opposed to known) coefficients. This hypothesis testing problem arises naturally when constructing confidence sets for possibly partially identified parameters in the analysis of nonparametric instrumental variables models, treatment effect models, and random coefficient models, among other settings. To rule out certain instances in which the testing problem is impossible, in the sense that the power of any test will be bounded by its size, we begin our analysis by characterizing the closure of the null hypothesis with respect to the total variation distance. We then use this characterization to develop novel testing procedures based on sample-splitting. We establish the validity of our testing procedures under weak and interpretable conditions on the linear system. An important feature of these conditions is that they permit the dimensionality of the problem to grow rapidly with the sample size. A further attractive property of our tests is that they do not require simulation to compute suitable critical values. We illustrate the practical relevance of our theoretical results in a simulation study.

econ.EM↗

arXiv2024

Inference for Treatment Effects Conditional on Generalized Principal Strata using Instrumental Variables

We propose a general approach for inference for a broad class of treatment effect parameters in a setting of a discrete valued treatment and instrument with a general outcome variable. The class of parameters considered are those that can be expressed as the expectation of a function of the response type conditional on a generalized principal stratum. Here, the response type refers to the vector of potential outcomes and potential treatments, and a generalized principal stratum is a set of possible values for the response type. In addition to instrument exogeneity, the main substantive restriction imposed rules out certain values for the response types in the sense that they are assumed to occur with probability zero. It is shown through a series of examples that this framework includes a wide variety of parameters and assumptions that have been considered in the previous literature. A key result in our analysis is a characterization of the identified set for such parameters under these assumptions in terms of existence of a non-negative solution to linear systems of equations with a special structure. We propose methods for inference exploiting this special structure and recent results in Fang et al. (2023).

econ.EM↗

arXiv2024

Overidentification in Shift-Share Designs

This paper studies the testability of identifying restrictions commonly employed to assign a causal interpretation to two stage least squares (TSLS) estimators based on Bartik instruments. For homogeneous effects models applied to short panels, our analysis yields testable implications previously noted in the literature for the two major available identification strategies. We propose overidentification tests for these restrictions that remain valid in high dimensional regimes and are robust to heteroskedasticity and clustering. We further show that homogeneous effect models in short panels, and their corresponding overidentification tests, are of central importance by establishing that: (i) In heterogenous effects models, interpreting TSLS as a positively weighted average of treatment effects can impose implausible assumptions on the distribution of the data; and (ii) Alternative identifying strategies relying on long panels can prove uninformative in short panel applications. We highlight the empirical relevance of our results by examining the viability of Bartik instruments for identifying the effect of rising Chinese import competition on US local labor markets.

econ.EM↗

arXiv2023

Identification and Estimation in a Class of Potential Outcomes Models

This paper develops a class of potential outcomes models characterized by three main features: (i) Unobserved heterogeneity can be represented by a vector of potential outcomes and a type describing the manner in which an instrument determines the choice of treatment; (ii) The availability of an instrumental variable that is conditionally independent of unobserved heterogeneity; and (iii) The imposition of convex restrictions on the distribution of unobserved heterogeneity. The proposed class of models encompasses multiple classical and novel research designs, yet possesses a common structure that permits a unifying analysis of identification and estimation. In particular, we establish that these models share a common necessary and sufficient condition for identifying certain causal parameters. Our identification results are constructive in that they yield estimating moment conditions for the parameters of interest. Focusing on a leading special case of our framework, we further show how these estimating moment conditions may be modified to be doubly robust. The corresponding double robust estimators are shown to be asymptotically normally distributed, bootstrap based inference is shown to be asymptotically valid, and the semi-parametric efficiency bound is derived for those parameters that are root-n estimable. We illustrate the usefulness of our results for developing, identifying, and estimating causal models through an empirical evaluation of the role of mental health as a mediating variable in the Moving To Opportunity experiment.

econ.EM↗

arXiv2023

Standard errors when a regressor is randomly assigned

We examine asymptotic properties of the OLS estimator when the values of the regressor of interest are assigned randomly and independently of other regressors. We find that the OLS variance formula in this case is often simplified, sometimes substantially. In particular, when the regressor of interest is independent not only of other regressors but also of the error term, the textbook homoskedastic variance formula is valid even if the error term and auxiliary regressors exhibit a general dependence structure. In the context of randomized controlled trials, this conclusion holds in completely randomized experiments with constant treatment effects. When the error term is heteroscedastic with respect to the regressor of interest, the variance formula has to be adjusted not only for heteroscedasticity but also for correlation structure of the error term. However, even in the latter case, some simplifications are possible as only a part of the correlation structure of the error term should be taken into account. In the context of randomized control trials, this implies that the textbook homoscedastic variance formula is typically not valid if treatment effects are heterogenous but heteroscedasticity-robust variance formulas are valid if treatment effects are independent across units, even if the error term exhibits a general dependence structure. In addition, we extend the results to the case when the regressor of interest is assigned randomly at a group level, such as in randomized control trials with treatment assignment determined at a group (e.g., school/village) level.

econ.EM↗

arXiv2022

Constrained Conditional Moment Restriction Models

Shape restrictions have played a central role in economics as both testable implications of theory and sufficient conditions for obtaining informative counterfactual predictions. In this paper we provide a general procedure for inference under shape restrictions in identified and partially identified models defined by conditional moment restrictions. Our test statistics and proposed inference methods are based on the minimum of the generalized method of moments (GMM) objective function with and without shape restrictions. Uniformly valid critical values are obtained through a bootstrap procedure that approximates a subset of the true local parameter space. In an empirical analysis of the effect of childbearing on female labor supply, we show that employing shape restrictions in linear instrumental variables (IV) models can lead to shorter confidence regions for both local and average treatment effects. Other applications we discuss include inference for the variability of quantile IV treatment effects and for bounds on average equivalent variation in a demand model with general heterogeneity. We find in Monte Carlo examples that the critical values are conservatively accurate and that tests about objects of interest have good power relative to unrestricted GMM.

math.ST↗

arXiv2021

Inference for Large-Scale Linear Systems with Known Coefficients

This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of settings, including random coefficient, treatment effect, and discrete choice models, as well as a class of linear programming problems. As a first contribution, we obtain a novel geometric characterization of the null hypothesis in terms of identified parameters satisfying an infinite set of inequality restrictions. Using this characterization, we devise a test that requires solving only linear programs for its implementation, and thus remains computationally feasible in the high-dimensional applications that motivate our analysis. The asymptotic size of the proposed test is shown to equal at most the nominal level uniformly over a large class of distributions that permits the number of linear equations to grow with the sample size.

econ.EM↗

arXiv2016

Inference on Directionally Differentiable Functions

This paper studies an asymptotic framework for conducting inference on parameters of the form $ϕ(θ_0)$, where $ϕ$ is a known directionally differentiable function and $θ_0$ is estimated by $\hat θ_n$. In these settings, the asymptotic distribution of the plug-in estimator $ϕ(\hat θ_n)$ can be readily derived employing existing extensions to the Delta method. We show, however, that the "standard" bootstrap is only consistent under overly stringent conditions -- in particular we establish that differentiability of $ϕ$ is a necessary and sufficient condition for bootstrap consistency whenever the limiting distribution of $\hat θ_n$ is Gaussian. An alternative resampling scheme is proposed which remains consistent when the bootstrap fails, and is shown to provide local size control under restrictions on the directional derivative of $ϕ$. We illustrate the utility of our results by developing a test of whether a Hilbert space valued parameter belongs to a convex set -- a setting that includes moment inequality problems and certain tests of shape restrictions as special cases.

math.ST↗

arXiv2014

MBIS: Multivariate Bayesian Image Segmentation Tool

We present MBIS (Multivariate Bayesian Image Segmentation tool), a clustering tool based on the mixture of multivariate normal distributions model. MBIS supports multi-channel bias field correction based on a B-spline model. A second methodological novelty is the inclusion of graph-cuts optimization for the stationary anisotropic hidden Markov random field model. Along with MBIS, we release an evaluation framework that contains three different experiments on multi-site data. We first validate the accuracy of segmentation and the estimated bias field for each channel. MBIS outperforms a widely used segmentation tool in a cross-comparison evaluation. The second experiment demonstrates the robustness of results on atlas-free segmentation of two image sets from scan-rescan protocols on 21 healthy subjects. Multivariate segmentation is more replicable than the monospectral counterpart on T1-weighted images. Finally, we provide a third experiment to illustrate how MBIS can be used in a large-scale study of tissue volume change with increasing age in 584 healthy subjects. This last result is meaningful as multivariate segmentation performs robustly without the need for prior knowledge

cs.CV↗

arXiv2011

The penetrable square-well model: extensive versus non-extensive phase

The phase diagram of the penetrable square-well fluid is investigated through Monte Carlo simulations of various nature. This model was proposed as the simplest possibility of combining bounded repulsions at short scale and short-range attractions. We prove that the model is thermodynamically stable for sufficiently low values of the penetrability parameter, and in this case the system behaves similarly to the square-well model. For larger penetration, there exists an intermediate region where the system is metastable, with well defined fluid-fluid and fluid-solid transitions, at finite size, but eventually becomes unstable in the thermodynamic limit. We characterize the unstable non-extensive phase appearing at high penetrability, where the system collapses into an isolated blob of a few clusters of many ovelapping particles each.

cond-mat.soft↗

arXiv2011

Phase diagram of the penetrable square well-model

We study a system formed by soft colloidal spheres attracting each other via a square-well potential, using extensive Monte Carlo simulations of various nature. The softness is implemented through a reduction of the infinite part of the repulsive potential to a finite one. For sufficiently low values of the penetrability parameter we find the system to be Ruelle stable with square-well like behavior. For high values of the penetrability the system is thermodynamically unstable and collapses into an isolated blob formed by a few clusters each containing many overlapping particles. For intermediate values of the penetrability the system has a rich phase diagram with a partial lack of thermodynamic consistency.

cond-mat.soft↗

arXiv2009

The second and third Sonine coefficients of a freely cooling granular gas revisited

In its simplest statistical-mechanical description, a granular fluid can be modeled as composed of smooth inelastic hard spheres (with a constant coefficient of normal restitution $α$) whose velocity distribution function obeys the Enskog-Boltzmann equation. The basic state of a granular fluid is the homogeneous cooling state, characterized by a homogeneous, isotropic, and stationary distribution of scaled velocities, $F(\mathbf{c})$. The behavior of $F(\mathbf{c})$ in the domain of thermal velocities ($c\sim 1$) can be characterized by the two first non-trivial coefficients ($a_2$ and $a_3$) of an expansion in Sonine polynomials. The main goals of this paper are to review some of the previous efforts made to estimate (and measure in computer simulations) the $α$-dependence of $a_2$ and $a_3$, to report new computer simulations results of $a_2$ and $a_3$ for two-dimensional systems, and to investigate the possibility of proposing theoretical estimates of $a_2$ and $a_3$ with an optimal compromise between simplicity and accuracy.

cond-mat.soft↗

arXiv2008

Longitudinal Viscous Flow in Granular Gases

The flow characterized by a linear longitudinal velocity field $u_x(x,t)=a(t)x$, where $a(t)={a_0}/({1+a_0t})$, a uniform density $n(t)\propto a(t)$, and a uniform temperature $T(t)$ is analyzed for dilute granular gases by means of a BGK-like model kinetic equation in $d$ dimensions. For a given value of the coefficient of normal restitution $α$, the relevant control parameter of the problem is the reduced deformation rate $a^*(t)=a(t)/ν(t)$ (which plays the role of the Knudsen number), where $ν(t)\propto n(t)\sqrt{T(t)}$ is an effective collision frequency. The relevant response parameter is a nonlinear viscosity function $η^*(a^*)$ defined from the difference between the normal stress $P_{xx}(t)$ and the hydrostatic pressure $p(t)=n(t)T(t)$. The main results of the paper are: (a) an exact first-order ordinary differential equation for $η^*(a^*)$ is derived from the kinetic model; (b) a recursion relation for the coefficients of the Chapman--Enskog expansion of $η^*(a^*)$ in powers of $a^*$ is obtained; (c) the Chapman--Enskog expansion is shown to diverge for elastic collisions ($α=1$) and converge for inelastic collisions ($α<1$), in the latter case with a radius of convergence that increases with inelasticity; (d) a simple approximate analytical solution for $η^*(a^*)$, hardly distinguishable from the numerical solution of the differential equation, is constructed.

cond-mat.soft↗

arXiv2008

Virial series for fluids of hard hyperspheres in odd dimensions

A recently derived method [R. D. Rohrmann and A. Santos, Phys. Rev. E. {\bf 76}, 051202 (2007)] to obtain the exact solution of the Percus-Yevick equation for a fluid of hard spheres in (odd) $d$ dimensions is used to investigate the convergence properties of the resulting virial series. This is done both for the virial and compressibility routes, in which the virial coefficients $B_j$ are expressed in terms of the solution of a set of $(d-1)/2$ coupled algebraic equations which become nonlinear for $d \geq 5$. Results have been derived up to $d=13$. A confirmation of the alternating character of the series for $d\geq 5$, due to the existence of a branch point on the negative real axis, is found and the radius of convergence is explicitly determined for each dimension. The resulting scaled density per dimension $2 η^{1/d}$, where $η$ is the packing fraction, is wholly consistent with the limiting value of 1 for $d \to \infty$. Finally, the values for $B_j$ predicted by the virial and compressibility routes in the Percus-Yevick approximation are compared with the known exact values [N. Clisby and B. M. McCoy, J. Stat. Phys. {\bf 122}, 15 (2006)]

cond-mat.soft↗

arXiv2008

Penetrable Square-Well fluids: Exact results in one dimension

We introduce a model of attractive penetrable spheres by adding a short range attractive square well outside a penetrable core, and we provide a detailed analysis of structural and thermodynamical properties in one dimension using the exact impenetrable counterpart as a starting point. The model is expected to describe star polymers in regimes of good and moderate solvent under dilute conditions. We derive the exact coefficients of a low density expansion up to second order for the radial distribution function and up to fourth order in the virial expansion. These exact results are used as a benchmark to test the reliability of approximate theories (Percus-Yevick and hypernetted chain). Notwithstanding the lack of an exact solution for arbitrary densities, our results are expected to be rather precise within a wide range of temperatures and densities. A detailed analysis of some limiting cases is carried out. In particular we provide a complete solution of the sticky penetrable-sphere model in one dimension up to the same order in density. The issue of Ruelle's thermodynamics stability is analyzed and the region of a well defined thermodynamic limit is identified.

cond-mat.soft↗

arXiv2008

Does the Chapman-Enskog expansion for viscous granular flows converge?

This paper deals with the convergence/divergence issue of the Chapman-Enskog series expansion of the shear and normal stresses for a granular gas of inelastic hard spheres. From the exact solution of a simple kinetic model in the uniform shear and longitudinal flows, it is shown that (except in the elastic limit) both series converge and their respective radii of convergence increase with inelasticity. This paradoxical result can be understood in terms of the time evolution of the Knudsen number and the existence of a nonequilibrium steady state.

cond-mat.soft↗

arXiv2008

Rheological properties of a granular impurity in the Couette flow

We discuss in this work the validity of the theoretical solution of the nonlinear Couette flow for a granular impurity obtained in a recent work [preprint arXiv:0802.0526], in the range of large inelasticity and shear rate. We show there is a good agreement between the theoretical solution and Monte Carlo simulation data, even under these extreme conditions. We also discuss an extended theoretical solution that would work for large inelasticities in ranges of shear rate $a$ not covered by our previous work (i.e., below the threshold value $a_{th}$ for which uniform shear flow may be obtained) and compare also with simulation data. Preliminary results in the simulations give useful insight in order to obtain an exact and general solution of the nonlinear Couette flow (both for $a\ge a_{th}$ and $a<a_{th}$).

cond-mat.soft↗

arXiv2008

Does the Chapman--Enskog expansion for sheared granular gases converge?

The fundamental question addressed in this paper is whether the partial Chapman--Enskog expansion $P_{xy}=-\sum_{k=0}^\infty η_k ({\partial u_x}/{\partial y})^{2k+1}$ of the shear stress converges or not for a gas of inelastic hard spheres. By using a simple kinetic model it is shown that, in contrast to the elastic case, the above series does converge, the radius of convergence increasing with inelasticity. It is argued that this paradoxical conclusion is not an artifact of the kinetic model and can be understood in terms of the time evolution of the scaled shear rate in the uniform shear flow.

cond-mat.soft↗