Uniform inference for value functions

Firpo, Sérgio; Galvao, Antônio F.; Parker, Thomas M.

doi:10.1016/j.jeconom.2022.11.009

Cited by 4 publications

(12 citation statements)

References 42 publications

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“…This confidence set does not require the uniqueness of the infimum and supremum in the Makarov bounds. As pointed out by Firpo et al (2021), however, this confidence set is likely to be conservative.…”

Section: Estimation and Bootstrap Proceduresmentioning

confidence: 99%

“…The main challenge to constructing uniform confidence bands, however, is that the mappings ϕ L and ϕ U are not Hadamard differentiable. To overcome this difficulty, we use Theorem 3.2 in Firpo et al (2021) that shows that these functionals are Hadamard directionally differentiable. Based on this result, we employ the inference method of Fang and Santos (2019) to establish the asymptotic theory.…”

Section: Inference Under the Unconfoundedness Assumptionmentioning

confidence: 99%

“…It is worth pointing out that the development of weak convergence of the estimated bounds does not rely on some pointwise asymptotic theory when establishing the asymptotic theory for the estimated Makarov bounds. Instead, we first derive the weak convergence of the standard kernel estimators for a fixed conditioning value and consider the double-supremum as an operator to establish the weak convergence of the estimated bounds, as in Firpo et al (2021). In doing so, we can avoid imposing the uniqueness of argsup and arginf that is needed for pointwise inference.…”

Section: Inference Under the Unconfoundedness Assumptionmentioning

confidence: 99%

“…Theorem 3.1 of Fang & Santos, 2019). To resolve this problem, we utilize the result of bootstrap validity that was proposed by Firpo et al (2021). The next assumption imposes conditions on the bootstrap weight B: Assumption 4.6.…”

Section: Inference Under the Unconfoundedness Assumptionmentioning

confidence: 99%

“…They are useful for comparing bounds between two subpopulations defined in terms of different values of observable characteristics. 4 We adapt the results on uniform inference for value functions that were developed recently by Firpo et al (2021) and provide a set of conditions under which the estimated bounds are consistent for the true bounds. We propose a bootstrap procedure to mimic the asymptotic distributions of the estimated bounds and show its validity.…”

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confidence: 99%

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Partial identification and inference for conditional distributions of treatment effects

Lee

2023

J of Applied Econometrics

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SummaryThis paper considers identification and inference for the distribution of treatment effects conditional on observable covariates. Since the conditional distribution of treatment effects is not point identified without strong assumptions, we obtain bounds on the conditional distribution of treatment effects by using the Makarov bounds. We also consider the case where the treatment is endogenous and propose two stochastic dominance assumptions to tighten the bounds. We develop a nonparametric framework to estimate the bounds and establish the asymptotic theory that is uniformly valid over the support of treatment effects. An empirical example illustrates the usefulness of the methods.

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Section: Estimation and Bootstrap Proceduresmentioning

confidence: 99%

Section: Inference Under the Unconfoundedness Assumptionmentioning

confidence: 99%

Section: Inference Under the Unconfoundedness Assumptionmentioning

confidence: 99%

Section: Inference Under the Unconfoundedness Assumptionmentioning

confidence: 99%

mentioning

confidence: 99%

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Partial identification and inference for conditional distributions of treatment effects

Lee

2023

J of Applied Econometrics

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Loss aversion and the welfare ranking of policy interventions

Firpo,

Galvao,

Kobus

et al. 2023

Journal of Econometrics

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Partially Linear Models under Data Combination

D’Haultfœuille,

Gaillac,

Maurel

2024

Review of Economic Studies

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We study partially linear models when the outcome of interest and some of the covariates are observed in two different datasets that cannot be linked. This type of data combination problem arises very frequently in empirical microeconomics. Using recent tools from optimal transport theory, we derive a constructive characterization of the sharp identified set. We then build on this result and develop a novel inference method that exploits the specific geometric properties of the identified set. Our method exhibits good performances in finite samples, while remaining very tractable. We apply our approach to study intergenerational income mobility over the period 1850-1930 in the United States. Our method allows us to relax the exclusion restrictions used in earlier work, while delivering confidence regions that are informative.

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Uniform inference for value functions

Cited by 4 publications

References 42 publications

Partial identification and inference for conditional distributions of treatment effects

Partial identification and inference for conditional distributions of treatment effects

Loss aversion and the welfare ranking of policy interventions

Partially Linear Models under Data Combination

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