Applied Welfare Analysis for Discrete Choice with Interval-Data on Income

Lee, Ying‐Ying; Bhattacharya, Debopam

doi:10.2139/ssrn.3167071

Cited by 5 publications

(4 citation statements)

References 51 publications

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“…and Lee and Bhattacharya (2015) among others. We hope these are just the first applications of this framework, which should be of use to theorists and empirical researchers alike in determining statistical properties such as asymptotic distributions, bootstrap validity, and ability of tests to locally control size.…”

Section: Discussionmentioning

confidence: 96%

“…For instance, Seo (2014) and Beare and Shi (2015) have used our framework to develop tests of stochastic monotonicity and of density ratio ordering respectively. Other applications of our results also include Hansen (2015) who studied the asymptotic properties of regression kink models, Jha and Wolak (2015) who estimated transaction costs in energy future markets, and Lee and Bhattacharya (2015) who proposed methods for estimation welfare changes in partially identified discrete choice models. Finally, in a highly complementary paper, Hong and Li (2015) have built on our results and established that a consistent estimator of φ n for the directional derivative φ θ 0 can often be obtained through numerical differentiation of φ at θn (under appropriate conditions on the step size).…”

Section: Introductionmentioning

confidence: 84%

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Inference on Directionally Differentiable Functions

Fang

Santos

2018

The Review of Economic Studies

189

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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 byθ n . In these settings, the asymptotic distribution of the plug-in estimator φ(θ n ) can be readily derived employing existing extensions to the Delta method. We show, however, that (full) differentiability of φ is a necessary and sufficient condition for bootstrap consistency whenever the limiting distribution ofθ 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 seta setting that includes moment inequality problems, tests of random utility models, and certain tests of shape restrictions as special cases (e.g. tests of monotonicity of the pricing kernel or of parametric conditional quantile model specifications).

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Section: Discussionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 84%

Inference on Directionally Differentiable Functions

Fang

Santos

2018

The Review of Economic Studies

189

View full text Add to dashboard Cite

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“…We then use the numerical bootstrap of and to construct our confidence bands. For other applications of Hadamard directional differentiability, see Lee and Bhattacharya (2016), Kaido (2016), andHansen (2017).…”

Section: A Related Literaturementioning

confidence: 99%

Inference on Breakdown Frontiers

Masten

Poirier

2017

SSRN Journal

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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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“…We then use the numerical bootstrap of Hong and Li (2015) to construct our confidence bands. Also see Lee and Bhattacharya (2016) and Hansen (2017) for other applications of these methods.…”

Section: Related Literaturementioning

confidence: 99%

Inference on breakdown frontiers

Masten¹,

Poirier²

2017

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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 deviations from random assignment of treatment, and one which indexes deviations from rank invariance. 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 robustness of conclusions to deviations in the point identifying assumptions. We derive √ N -consistent sample analog estimators for these frontiers. We then provide an asymptotically valid bootstrap procedure for constructing lower uniform confidence bands for the breakdown frontier. As a measure of robustness, this confidence band 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 conclusions are fairly robust to failure of rank invariance, when random assignment holds, but conclusions are much more sensitive to both assumptions for small deviations from random assignment.JEL classification: C14; C18; C21; C25; C51

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Applied Welfare Analysis for Discrete Choice with Interval-Data on Income

Cited by 5 publications

References 51 publications

Inference on Directionally Differentiable Functions

Inference on Directionally Differentiable Functions

Inference on Breakdown Frontiers

Inference on breakdown frontiers

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