arXiv subjects

Matthew D. Webb

Publications and source records attributed to Matthew D. Webb.

12 recordsLinked to original sources

arXiv2026

Which Policy Works, and Where? Estimation and Inference for State-Level Treatment Effects in Difference-in-Differences

Policies with a common objective and implementation date may differ in details or context. We distinguish the aggregate average treatment effect on the treated (ATT) from sub-aggregate ATTs defined by implementation cohort, jurisdiction, period, or policy type. UN-DID and DID-INT, two DiD estimators that construct jurisdiction-by-time effects, estimate these ATTs under parallel-trends conditions matched to the aggregation. In CPS placebo-law simulations, randomization inference is generally well-sized, though some jurisdiction-specific tests are conservative. The jackknife can be undefined for sub-aggregate ATTs; when defined, it over-rejects with few treated or comparison jurisdictions. Estimands and inference methods should match the policy question and implementation setting.

econ.EM↗

arXiv2026

Good Guys With Guns? The Relationship Between Legal Firearm Ownership and Firearm Deaths and Crime in Canada

Civilian firearm ownership is politically contentious, yet most evidence linking guns to crime and death comes from the U.S. Canada offers a unique case: strict national regulations alongside widespread legal ownership. Using new administrative data from 2013-2019, we examine associations between gun prevalence and homicides, suicides, and firearms-related crime. During this period, we find that handgun ownership rose 50\% and restricted licenses by 70\%. Recent legislation proposes a handgun freeze and rifle buyback. We assess whether these measures are likely to improve safety or whether existing laws already strike a balance. We find little evidence of a strong relationship.

econ.GN↗

arXiv2026

Improved Inference for CSDID Using the Cluster Jackknife

Obtaining reliable inferences with traditional difference-in-differences (DiD) methods can be difficult. Problems can arise when both outcomes and errors are serially correlated, when there are few clusters or few treated clusters, when cluster sizes vary greatly, and in various other cases. In recent years, recognition of the ``staggered adoption'' problem has shifted the focus away from inference towards consistent estimation of treatment effects. One of the most popular new estimators is the CSDID procedure of Callaway and Sant'Anna (2021). We find that the issues of over-rejection with few clusters and/or few treated clusters are at least as severe for CSDID as for traditional DiD methods. We also propose using a cluster jackknife for inference with CSDID, which simulations suggest greatly improves inference. We provide software packages in Stata csdidjack and R didjack to calculate cluster-jackknife standard errors easily.

econ.EM↗

arXiv2024

Good Controls Gone Bad: Difference-in-Differences with Covariates

This paper introduces the two-way common causal covariates (CCC) assumption, which is necessary to get an unbiased estimate of the ATT when using time-varying covariates in existing Difference-in-Differences methods. The two-way CCC assumption implies that the effect of the covariates remain the same between groups and across time periods. This assumption has been implied in previous literature, but has not been explicitly addressed. Through theoretical proofs and a Monte Carlo simulation study, we show that the standard TWFE and the CS-DID estimators are biased when the two-way CCC assumption is violated. We propose a new estimator called the Intersection Difference-in-differences (DID-INT) which can provide an unbiased estimate of the ATT under two-way CCC violations. DID-INT can also identify the ATT under heterogeneous treatment effects and with staggered treatment rollout. The estimator relies on parallel trends of the residuals of the outcome variable, after appropriately adjusting for covariates. This covariate residualization can recover parallel trends that are hidden with conventional estimators.

econ.EM↗

arXiv2024

Jackknife inference with two-way clustering

For linear regression models with cross-section or panel data, it is natural to assume that the disturbances are clustered in two dimensions. However, the finite-sample properties of two-way cluster-robust tests and confidence intervals are often poor. We discuss several ways to improve inference with two-way clustering. Two of these are existing methods for avoiding, or at least ameliorating, the problem of undefined standard errors when a cluster-robust variance matrix estimator (CRVE) is not positive definite. One is a new method that always avoids the problem. More importantly, we propose a family of new two-way CRVEs based on the cluster jackknife and prove that they yield valid inferences asymptotically. Simulations for models with two-way fixed effects suggest that, in many cases, the cluster-jackknife CRVE combined with our new method yields surprisingly accurate inferences. We provide a software package, twowayjack for Stata, that implements our recommended variance estimator.

econ.EM↗

arXiv2024

Cluster-robust jackknife and bootstrap inference for logistic regression models

We study cluster-robust inference for logistic regression (logit) models. Inference based on the most commonly-used cluster-robust variance matrix estimator (CRVE) can be very unreliable. We study several alternatives. Conceptually the simplest of these, but also the most computationally demanding, involves jackknifing at the cluster level. We also propose a linearized version of the cluster-jackknife variance matrix estimator as well as linearized versions of the wild cluster bootstrap. The linearizations are based on empirical scores and are computationally efficient. Our results can readily be generalized to other binary response models. We also discuss a new Stata software package called logitjack which implements these procedures. Simulation results strongly favor the new methods, and two empirical examples suggest that it can be important to use them in practice.

econ.EM↗

arXiv2024

Using Images as Covariates: Measuring Curb Appeal with Deep Learning

This paper details an innovative methodology to integrate image data into traditional econometric models. Motivated by forecasting sales prices for residential real estate, we harness the power of deep learning to add "information" contained in images as covariates. Specifically, images of homes were categorized and encoded using an ensemble of image classifiers (ResNet-50, VGG16, MobileNet, and Inception V3). Unique features presented within each image were further encoded through panoptic segmentation. Forecasts from a neural network trained on the encoded data results in improved out-of-sample predictive power. We also combine these image-based forecasts with standard hedonic real estate property and location characteristics, resulting in a unified dataset. We show that image-based forecasts increase the accuracy of hedonic forecasts when encoded features are regarded as additional covariates. We also attempt to "explain" which covariates the image-based forecasts are most highly correlated with. The study exemplifies the benefits of interdisciplinary methodologies, merging machine learning and econometrics to harness untapped data sources for more accurate forecasting.

econ.GN↗

arXiv2024

Difference-in-Differences with Unpoolable Data

Difference-in-differences (DID) is commonly used to estimate treatment effects but is infeasible in settings where data are unpoolable due to privacy concerns or legal restrictions on data sharing, particularly across jurisdictions. In this study, we identify and relax the assumption of data poolability in DID estimation. We propose an innovative approach to estimate DID with unpoolable data (UN-DID) which can accommodate covariates, multiple groups, and staggered adoption. Through analytical proofs and Monte Carlo simulations, we show that UN-DID and conventional DID estimates of the average treatment effect and standard errors are equal and unbiased in settings without covariates. With covariates, both methods produce estimates that are unbiased, equivalent, and converge to the true value. The estimates differ slightly but the statistical inference and substantive conclusions remain the same. Two empirical examples with real-world data further underscore UN-DID's utility. The UN-DID method allows the estimation of cross-jurisdictional treatment effects with unpoolable data, enabling better counterfactuals to be used and new research questions to be answered.

econ.EM↗

arXiv2023

Leverage, Influence, and the Jackknife in Clustered Regression Models: Reliable Inference Using summclust

We introduce a new Stata package called summclust that summarizes the cluster structure of the dataset for linear regression models with clustered disturbances. The key unit of observation for such a model is the cluster. We therefore propose cluster-level measures of leverage, partial leverage, and influence and show how to compute them quickly in most cases. The measures of leverage and partial leverage can be used as diagnostic tools to identify datasets and regression designs in which cluster-robust inference is likely to be challenging. The measures of influence can provide valuable information about how the results depend on the data in the various clusters. We also show how to calculate two jackknife variance matrix estimators efficiently as a byproduct of our other computations. These estimators, which are already available in Stata, are generally more conservative than conventional variance matrix estimators. The summclust package computes all the quantities that we discuss.

econ.EM↗

arXiv2023

Testing for the appropriate level of clustering in linear regression models

The overwhelming majority of empirical research that uses cluster-robust inference assumes that the clustering structure is known, even though there are often several possible ways in which a dataset could be clustered. We propose two tests for the correct level of clustering in regression models. One test focuses on inference about a single coefficient, and the other on inference about two or more coefficients. We provide both asymptotic and wild bootstrap implementations. The proposed tests work for a null hypothesis of either no clustering or ``fine'' clustering against alternatives of ``coarser'' clustering. We also propose a sequential testing procedure to determine the appropriate level of clustering. Simulations suggest that the bootstrap tests perform very well under the null hypothesis and can have excellent power. An empirical example suggests that using the tests leads to sensible inferences.

econ.EM↗

arXiv2023

Fast and Reliable Jackknife and Bootstrap Methods for Cluster-Robust Inference

We provide computationally attractive methods to obtain jackknife-based cluster-robust variance matrix estimators (CRVEs) for linear regression models estimated by least squares. We also propose several new variants of the wild cluster bootstrap, which involve these CRVEs, jackknife-based bootstrap data-generating processes, or both. Extensive simulation experiments suggest that the new methods can provide much more reliable inferences than existing ones in cases where the latter are not trustworthy, such as when the number of clusters is small and/or cluster sizes vary substantially. Three empirical examples illustrate the new methods.

econ.EM↗

arXiv2022

Cluster-Robust Inference: A Guide to Empirical Practice

Methods for cluster-robust inference are routinely used in economics and many other disciplines. However, it is only recently that theoretical foundations for the use of these methods in many empirically relevant situations have been developed. In this paper, we use these theoretical results to provide a guide to empirical practice. We do not attempt to present a comprehensive survey of the (very large) literature. Instead, we bridge theory and practice by providing a thorough guide on what to do and why, based on recently available econometric theory and simulation evidence. To practice what we preach, we include an empirical analysis of the effects of the minimum wage on labor supply of teenagers using individual data.

econ.EM↗