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The Bartik instrument is formed by interacting local industry shares and national industry growth rates. We show that the typical use of a Bartik instrument assumes a pooled exposure research design, where the shares measure differential exposure to common shocks, and identification is based on exogeneity of the shares. Next, we show how the Bartik instrument weights each of the exposure designs. Finally, we discuss how to assess the plausibility of the research design. We illustrate our results through two applications: estimating the elasticity of labor supply, and estimating the elasticity of substitution between immigrants and natives.

Consider a researcher estimating the parameters of a regression function based on data for all 50 states in the United States or on data for all visits to a website. What is the interpretation of the estimated parameters and the standard errors? In practice, researchers typically assume that the sample is randomly drawn from a large population of interest and report standard errors that are designed to capture sampling variation. This is common even in applications where it is difficult to articulate what that population of interest is, and how it differs from the sample. In this article, we explore an alternative approach to inference, which is partly design-based. In a design-based setting, the values of some of the regressors can be manipulated, perhaps through a policy intervention. Design-based uncertainty emanates from lack of knowledge about the values that the regression outcome would have taken under alternative interventions. We derive standard errors that account for design-based uncertainty instead of, or in addition to, sampling-based uncertainty. We show that our standard errors in general are smaller than the usual infinite-population sampling-based standard errors and provide conditions under which they coincide.

We study regression discontinuity designs when covariates are included in the estimation. We examine local polynomial estimators that include discrete or continuous covariates in an additive separable way, but without imposing any parametric restrictions on the underlying population regression functions. We recommend a covariate-adjustment approach that retains consistency under intuitive conditions and characterize the potential for estimation and inference improvements. We also present new covariateadjusted mean-squared error expansions and robust bias-corrected inference procedures, with heteroskedasticity-consistent and cluster-robust standard errors. We provide an empirical illustration and an extensive simulation study. All methods are implemented in R and Stata software packages.

When countries change most favored nation (MFN) tariffs, partners that trade on MFN terms experience plausibly exogenous tariff changes. Using this variation, we estimate the trade elasticity at short and long horizons with local projections. We find that the elasticity of tariff-exclusive trade flows is −0.76 in the short run, and approximately −2 in the long run. Our long-run estimates are smaller than typical in the literature, and it takes 7 to10 years to converge to the long run, implying that (i) the welfare gains from trade are high and (ii) there are substantial convexities in the costs of adjusting exports.

We consider inference in regression discontinuity designs when the running variable only takes a moderate number of distinct values. In particular, we study the common practice of using confidence intervals (CIs) based on standard errors that are clustered by the running variable as a means to make inference robust to model misspecification (Lee and Card 2008). We derive theoretical results and present simulation and empirical evidence showing that these CIs do not guard against model misspecification, and that they have poor coverage properties. We therefore recommend against using these CIs in practice. We instead propose two alternative CIs with guaranteed coverage properties under easily interpretable restrictions on the conditional expectation function.

We use LASSO methods to shrink, select, and estimate the high-dimensional network linking the publicly traded subset of the world’s top 150 banks, 2003–2014. We characterize static network connectedness using full-sample estimation and dynamic network connectedness using rolling-window estimation. Statically, we find that global bank equity connectedness has a strong geographic component, whereas country sovereign bond connectedness does not. Dynamically, we find that equity connectedness increases during crises, with clear peaks during the Great Financial Crisis and each wave of the subsequent European Debt Crisis, and with movements coming mostly from changes in cross-country as opposed to within-country bank linkages.

Priors are important for achieving proper posteriors with physically meaningful covariance structures for Gaussian random fields (GRFs) since the likelihood typically only provides limited information about the covariance structure under in-fill asymptotics. We extend the recent penalized complexity prior framework and develop a principled joint prior for the range and the marginal variance of one-dimensional, two-dimensional, and three-dimensional Matérn GRFs with fixed smoothness. The prior is weakly informative and penalizes complexity by shrinking the range toward infinity and the marginal variance toward zero. We propose guidelines for selecting the hyperparameters, and a simulation study shows that the new prior provides a principled alternative to reference priors that can leverage prior knowledge to achieve shorter credible intervals while maintaining good coverage. We extend the prior to a nonstationary GRF parameterized through local ranges and marginal standard deviations, and introduce a scheme for selecting the hyperparameters based on the coverage of the parameters when fitting simulated stationary data. The approach is applied to a dataset of annual precipitation in southern Norway and the scheme for selecting the hyperparameters leads to conservative estimates of nonstationarity and improved predictive performance over the stationary model. Supplementary materials for this article are available online.

Random-effects meta-analyses of observational studies can produce biased estimates if the synthesized studies are subject to unmeasured confounding. We propose sensitivity analyses quantifying the extent to which unmeasured confounding of specified magnitude could reduce to below a certain threshold the proportion of true effect sizes that are scientifically meaningful. We also develop converse methods to estimate the strength of confounding capable of reducing the proportion of scientifically meaningful true effects to below a chosen threshold. These methods apply when a \"bias factor\" is assumed to be normally distributed across studies or is assessed across a range of fixed values. Our estimators are derived using recently proposed sharp bounds on confounding bias within a single study that do not make assumptions regarding the unmeasured confounders themselves or the functional form of their relationships with the exposure and outcome of interest. We provide an R package, EValue, and a free website that compute point estimates and inference and produce plots for conducting such sensitivity analyses. These methods facilitate principled use of random-effects meta-analyses of observational studies to assess the strength of causal evidence for a hypothesis. Supplementary materials for this article are available online.

This paper examines the approaches accounting researchers adopt to draw causal inferences using observational (or nonexperimental) data. The vast majority of accounting research papers draw causal inferences notwithstanding the well-known difficulties in doing so. While some recent papers seek to use quasi-experimental methods to improve causal inferences, these methods also make strong assumptions that are not always fully appreciated. We believe that accounting research would benefit from more in-depth descriptive research, including a greater focus on the study of causal mechanisms (or causal pathways) and increased emphasis on the structural modeling of the phenomena of interest. We argue these changes offer a practical path forward for rigorous accounting research.

We combine data on trade, production, and input use to document changes in the value-added content of trade between 1970 and 2009. The ratio of value-added to gross exports fell by roughly 10 percentage points worldwide. The ratio declined 20 percentage points in manufacturing, but rose in nonmanufacturing sectors. Declines also differ across countries and trade partners: they are larger for fast-growing countries, for nearby trade partners, and among partners that adopt regional trade agreements. Using a multisector structural gravity model with input-output linkages, we show that changes in trade frictions play a dominant role in explaining all these facts.