Is Completeness Necessary? Penalized Estimation in Non Identified Linear Models

Babii, Andrii; Florens, Jean‐Pierre

doi:10.2139/ssrn.3035393

Cited by 13 publications

(16 citation statements)

References 52 publications

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“…It is well known in the literature on inverse problems, see, e.g. Carrasco and Florens (2011), Horowitz (2011), Centorrino et al (2017), Florens and Sokullu (2017), Babii and Florens (2020), that estimating h −1 1 , h −1 2 and β by naively inverting the sample analogues of ( 18) and ( 19) as in ( 20) and ( 21) is a statistically ill-posed problem, in the sense that the naive estimators are not stable with respect to estimation error. We then use regularization to smooth out discontinuities due to inversion.…”

Section: Estimationmentioning

confidence: 99%

Time-varying linear transformation models with fixed effects and endogeneity for short panels

2022

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This paper considers a class of fixed-T nonlinear panel models with timevarying link function, fixed effects, and endogenous regressors. We establish sufficient conditions for the identification of the regression coefficients, the time-varying link function, the distribution of counterfactual outcomes, and certain (time-varying) average partial effects. We propose estimators for these objects and study their asymptotic properties. We show the relevance of our model by estimating the effect of teaching practices on student attainment as measured by test scores on standardized tests in mathematics and science. We use data from the Trends in International Mathematics and Science Study, and show that both traditional and modern teaching practices have positive effects of similar magnitudes on the performance of U.S. students on standardized tests in math and science.* We would like to thank Stéphane Bonhomme, Xavier D'Haultfoeuille, Jean-Pierre Florens, Laura Liu, Thierry Magnac for comments and suggestions, and participants at various conferences and seminars. We would also like to thank Jan Bietenbeck for sharing the data.

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Section: Estimationmentioning

confidence: 99%

Time-varying linear transformation models with fixed effects and endogeneity for short panels

2022

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“…Some additional results about completeness that rely on stronger restrictions on the DGP are provided in D'Haultfoeuille [25]. When completeness fails, Babii and Florens [4] and Florens et al [32] show that the estimator may still converge to the minimal norm solution.…”

Section: Case 1: U Is Mean Independent Of Wmentioning

confidence: 99%

“…If ϕ † is identified under the mean independence condition, this solution is a consistent estimator, and we conjecture that imposing the independence restriction should improve the properties of this estimator. If ϕ † is under-identified this estimation gives an approximation [see4,32]. Finally, one could use a linear or nonlinear parametric instrumental variable estimator.• At each iteration k ≥ 0, we compute the estimated centered residuals Ûki…”

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confidence: 99%

Nonparametric estimation of accelerated failure-time models with unobservable confounders and random censoring

Centorrino

Florens

2021

Electron. J. Statist.

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We consider nonparametric estimation of an accelerated failure-time model when the response variable is randomly censored on the right, and regressors are not mean independent of the error component. This dependence can arise, for instance, because of measurement error. We achieve identification and conduct estimation using a vector of instrumental variables. Censoring is independent of the response variable given the instruments. We consider settings in which regressors are continuously distributed. However, the instruments may or may not be continuous, and we show how various independence restrictions allow us to identify and estimate the unknown function of interest depending on the nature of instruments. We provide rates of convergence of our estimator and showcase its finite sample properties in simulations.

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“…Lastly, Assumption (v) is a completeness condition, Newey and Powell (2003). In case of its failure, the estimator is still well-defined and converge to the best approximation to function in the orthogonal complement of the null space of the operator , see Babii and Florens (2016).…”

Section: Nonparametric IVmentioning

confidence: 99%

Honest Confidence Sets in Nonparametric Iv Regression and Other Ill-Posed Models

Babii

2020

Econom. Theory

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This paper provides novel methods for inference in a very general class of ill-posed models in econometrics, encompassing the nonparametric instrumental regression, different functional regressions, and the deconvolution. I focus on uniform confidence sets for the parameter of interest estimated with Tikhonov regularization, as in Darolles, Fan, Florens, and Renault (2011). I first show that it is not possible to develop inferential methods directly based on the uniform central limit theorem. To circumvent this difficulty I develop two approaches that lead to valid confidence sets. I characterize expected diameters and coverage errors uniformly over a large class of models (i.e. constructed confidence sets are honest). Finally, I illustrate that introduced confidence sets have reasonable width and coverage properties in samples commonly used in applications with Monte Carlo simulations and considering application to Engel curves. ′ 1, . On the other hand, the process 2, is assumed not to change with . Since stochastic processes ′ 1, and 2, may be not readily available, we denote by^′ 1, and^2 , their respective consistent estimators and by^1 = max 1≤ ≤ ‖^′ 1, ‖ and^2 = max 1≤ ≤ ‖^2 , ‖ ∞ the corresponding estimators of their envelops. Finally, for some i.i.d. sequence of Rademacher random variables ( ) =1 , independent 7 The rigorous study of bootstrap properties is beyond the scope of this paper and is left for future research.

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Is Completeness Necessary? Penalized Estimation in Non Identified Linear Models

Cited by 13 publications

References 52 publications

Time-varying linear transformation models with fixed effects and endogeneity for short panels

Time-varying linear transformation models with fixed effects and endogeneity for short panels

Nonparametric estimation of accelerated failure-time models with unobservable confounders and random censoring

Honest Confidence Sets in Nonparametric Iv Regression and Other Ill-Posed Models

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