arXiv subjects

Leonard Goff

Publications and source records attributed to Leonard Goff.

9 recordsLinked to original sources

arXiv2025

Identification of Causal Effects with a Bunching Design

We show that causal effects can be identified when there is bunching in the distribution of a continuous treatment variable, without imposing any parametric assumptions. This yields a new nonparametric method for overcoming selection bias in the absence of instrumental variables, panel data, or other popular research designs for causal inference. The method leverages the change of variables theorem from integration theory, relating the selection bias to the ratio of the density of the treatment and the density of the part of the outcome that varies with confounders. At the bunching point, the treatment level is constant, so the variation in the outcomes is due entirely to unobservables, allowing us to identify the denominator. Our main result identifies the average causal response to the treatment among individuals who marginally select into the bunching point. We further show that under additional smoothness assumptions on the selection bias, treatment effects away from the bunching point may also be identified. We propose estimators based on standard software packages and apply the method to estimate the effect of maternal smoking during pregnancy on birth weight.

econ.EM↗

arXiv2025

Testing the Solvability of Systems of Linear Inequalities

This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in partially identified models can be formulated as hypotheses of this form. Our approach exploits an alternative characterization of the hypothesis based on whether the value of a certain linear program is equal to zero. Building on this characterization, we develop bootstrap-based testing procedures and establish their uniform validity over large classes of data-generating processes. Simulation results demonstrate good finite-sample performance, even for moderate sample sizes. We illustrate the usefulness of the approach in two empirical applications.

econ.EM↗

arXiv2024

Testing Identifying Assumptions in Parametric Separable Models: A Conditional Moment Inequality Approach

In this paper, we propose a simple method for testing identifying assumptions in parametric separable models, namely treatment exogeneity, instrument validity, and/or homoskedasticity. We show that the testable implications can be written in the intersection bounds framework, which is easy to implement using the inference method proposed in Chernozhukov, Lee, and Rosen (2013), and the Stata package of Chernozhukov et al. (2015). Monte Carlo simulations confirm that our test is consistent and controls size. We use our proposed method to test the validity of some commonly used instrumental variables, such as the average price in other markets in Nevo and Rosen (2012), the Bartik instrument in Card (2009), and the test rejects both instrumental variable models. When the identifying assumptions are rejected, we discuss solutions that allow researchers to identify some causal parameters of interest after relaxing functional form assumptions. We show that the IV model is nontestable if no functional form assumption is made on the outcome equation, when there exists a one-to-one mapping between the continuous treatment variable, the instrument, and the first-stage unobserved heterogeneity.

econ.EM↗

arXiv2024

When does IV identification not restrict outcomes?

Many identification results in instrumental variables (IV) models hold without requiring any restrictions on the distribution of potential outcomes, or how those outcomes are correlated with selection behavior. This enables IV models to allow for arbitrary heterogeneity in treatment effects and the possibility of selection on gains in the outcome. I provide a necessary and sufficient condition for treatment effects to be point identified in a manner that does not restrict outcomes, when the instruments take a finite number of values. The condition generalizes the well-known LATE monotonicity assumption, and unifies a wide variety of other known IV identification results. The result also yields a brute-force approach to reveal all selection models that allow for point identification of treatment effects without restricting outcomes, and then enumerate all of the identified parameters within each such selection model. The search uncovers new selection models that yield identification, provides impossibility results for others, and offers opportunities to relax assumptions on selection used in existing literature. An application considers the identification of complementarities between two cross-randomized treatments, obtaining a necessary and sufficient condition on selection for local average complementarities among compliers to be identified in a manner that does not restrict outcomes. I use this result to revisit two empirical settings, one in which the data are incompatible with this restriction on selection, and another in which the data are compatible with the restriction.

econ.EM↗

arXiv2022

Identifying causal effects with subjective ordinal outcomes

Survey questions often ask respondents to select from ordered scales where the meanings of the categories are subjective, leaving each individual free to apply their own definitions in answering. This paper studies the use of these responses as an outcome variable in causal inference, accounting for variation in interpretation of the categories across individuals. I find that when a continuous treatment variable is statistically independent of both i) potential outcomes; and ii) heterogeneity in reporting styles, a nonparametric regression of response category number on that treatment variable recovers a quantity proportional to an average causal effect among individuals who are on the margin between successive response categories. The magnitude of a given regression coefficient is not meaningful on its own, but the ratio of local regression derivatives with respect to two such treatment variables identifies the relative magnitudes of convex averages of their effects. These results can be seen as limiting cases of analogous results for binary treatment variables, though comparisons of magnitude involving discrete treatments are not as readily interpretable outside of the limit. I obtain a partial identification result for comparisons involving discrete treatments under further assumptions. An empirical application illustrates the results by revisiting the effects of income comparisons on subjective well-being, without assuming cardinality or interpersonal comparability of responses.

econ.EM↗

arXiv2022

Partial Identification from Bunching at Kinks and Notches

This paper proposes a partial identification approach to using choices around a kink or notch as a means to overcome endogeneity in a general nonparametric choice model. I show that observed choices are informative about the joint distribution of two counterfactual choices, which leads naturally to analyzing bunching using tools from causal inference. I define as the parameter of interest an average treatment effect among bunchers, which nests the traditional elasticity parameter while allowing for heterogeneity in responsiveness. Identification of the buncher ATE (and hence the elasticity) requires the researcher to extrapolate the distribution of each counterfactual choice beyond where it is observed. I introduce a flexible family of nonparametric shape restrictions to obtain partial identification, and propose a method for empirical validation of this approach using changes in the location of the kink/notch or using the distribution from another comparison group. I find that a log-concavity version of the distributional assumption is widely---though not universally---supported across the empirical literature, and leads to informative bounds in a canonical tax kink application. The approach accommodates diffuse bunching, at the expense of wider bounds.

econ.EM↗

arXiv2020

A Vector Monotonicity Assumption for Multiple Instruments

When a researcher combines multiple instrumental variables for a single binary treatment, the monotonicity assumption of the local average treatment effects (LATE) framework can become restrictive: it requires that all units share a common direction of response even when separate instruments are shifted in opposing directions. What I call vector monotonicity, by contrast, simply assumes treatment uptake to be monotonic in all instruments. I characterize the class of causal parameters that are point identified under vector monotonicity, when the instruments are binary. This class includes, for example, the average treatment effect among units that are in any way responsive to the collection of instruments, or those that are responsive to a given subset of them. The identification results are constructive and yield a simple estimator for the identified treatment effect parameters. An empirical application revisits the labor market returns to college.

econ.EM↗

arXiv2012

Classical simulation of measurement-based quantum computation on higher-genus surface-code states

We consider the efficiency of classically simulating measurement-based quantum computation on surface-code states. We devise a method for calculating the elements of the probability distribution for the classical output of the quantum computation. The operational cost of this method is polynomial in the size of the surface-code state, but in the worst case scales as $2^{2g}$ in the genus $g$ of the surface embedding the code. However, there are states in the code space for which the simulation becomes efficient. In general, the simulation cost is exponential in the entanglement contained in a certain effective state, capturing the encoded state, the encoding and the local post-measurement states. The same efficiencies hold, with additional assumptions on the temporal order of measurements and on the tessellations of the code surfaces, for the harder task of sampling from the distribution of the computational output.

quant-ph↗

arXiv2008

Particle motion during the compaction of granular matter

We track particle motions in a granular material subjected to compaction using a laser scattering based imaging method where compaction is achieved through thermal cycling. Particle displacements in this jammed fluid correlate strongly with rearrangments of the Voronoi cells defining the local spatial partitioning about the particles, similar to previous observations of Rahman on cooled liquids. Our observations provide further evidence of commonalities between particle dynamics in granular matter close to jamming and supercooled liquids.

cond-mat.soft↗