How Do Right-to-Carry Laws Affect Crime Rates? Coping with Ambiguity Using Bounded-Variation Assumptions

Manski, Charles F.; Pepper, John V.

doi:10.1162/rest_a_00689

Cited by 108 publications

(35 citation statements)

References 22 publications

(23 reference statements)

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“…In that case, taking account of the causal nature of the estimand is important, because a descriptive perspective would suggest the standard errors should be zero. This covers the case discussed in Manski and Pepper (2018).…”

Section: The Asymptotic Distribution Of the Least Squares Estimatormentioning

confidence: 90%

“…the sample) with X i = x. Units could be U.S. states and the binary regressor X i could be an indicator for a state regulation, say the state having a right-to-carry law (RTC), as in Manski and Pepper (2018) and Donohue, Aneja, and Weber (2019). We view the regressor X i not as a fixed attribute or characteristic of each unit, but as a cause or policy variable whose value could have been different from the observed value.…”

Section: A Simple Examplementioning

confidence: 99%

“…In many other settings, however, this sampling perspective is less appropriate. For example, Manski and Pepper (2018) wrote, "Random sampling assumptions, however, are not natural when considering states or counties as units of observation." In this article, we provide an alternative framework for the interpretation of uncertainty in regression analysis regardless of whether a substantial fraction of the population or even the entire population is included in the sample.…”

Section: Introductionmentioning

confidence: 99%

“…More importantly in our view, our results are relevant in empirical settings where it is not natural to think of the data as a random sample from a well-defined population. Instead, the researcher may have the entire population, for example, states or counties as in the Manski and Pepper (2018) quote, or the set of all visits to a website, or the researcher may have a convenience sample. In that case, our design-based approach to uncertainty provides a coherent interpretation for sampling-based standard errors.…”

Section: Introductionmentioning

confidence: 99%

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Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis

Abadie

Athey

Imbens

et al. 2020

ECTA

228

138

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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.

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Section: The Asymptotic Distribution Of the Least Squares Estimatormentioning

confidence: 90%

Section: A Simple Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis

Abadie

Athey

Imbens

et al. 2020

ECTA

228

138

View full text Add to dashboard Cite

show abstract

“…(2013), who proposed doing inference on a breakdown point. Finally, our focus on multidimensional frontiers builds on the graphical sensitivity analysis of Imbens (2003) and the multidimensional sensitivity analysis of Manski and Pepper (2018). We discuss these papers and others in detail in Appendix A.…”

Section: Introductionmentioning

confidence: 99%

Inference on breakdown frontiers

Masten

Poirier

2020

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Given a set of baseline assumptions, a breakdown frontier is the boundary between the set of assumptions which lead to a specific conclusion and those which do not. In a potential outcomes model with a binary treatment, we consider two conclusions: First, that ATE is at least a specific value (e.g., nonnegative) and second that the proportion of units who benefit from treatment is at least a specific value (e.g., at least 50%). For these conclusions, we derive the breakdown frontier for two kinds of assumptions: one which indexes relaxations of the baseline random assignment of treatment assumption, and one which indexes relaxations of the baseline rank invariance assumption. These classes of assumptions nest both the point identifying assumptions of random assignment and rank invariance and the opposite end of no constraints on treatment selection or the dependence structure between potential outcomes. This frontier provides a quantitative measure of the robustness of conclusions to relaxations of the baseline point identifying assumptions. We derive √ N-consistent sample analog estimators for these frontiers. We then provide two asymptotically valid bootstrap procedures for constructing lower uniform confidence bands for the breakdown frontier. As a measure of robustness, estimated breakdown frontiers and their corresponding confidence bands can be presented alongside traditional point estimates and confidence intervals obtained under point identifying assumptions. We illustrate this approach in an empirical application to the effect of child soldiering on wages. We find that sufficiently weak conclusions are robust to simultaneous failures of rank invariance and random assignment, while some stronger conclusions are fairly robust to failures of rank invariance but not necessarily to relaxations of random assignment.

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Difference-in-Differences for Policy Evaluation

Callaway

2022

Handbook of Labor, Human Resources and Population Economics

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How Do Right-to-Carry Laws Affect Crime Rates? Coping with Ambiguity Using Bounded-Variation Assumptions

Cited by 108 publications

References 22 publications

Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis

Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis

Inference on breakdown frontiers

Difference-in-Differences for Policy Evaluation

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