Estimation and inference with a (nearly) singular Jacobian

Han, Sukjin; McCloskey, Adam

doi:10.3982/qe989

Cited by 23 publications

(12 citation statements)

References 47 publications

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“…Robust inference methods in scenarios where the source of weak identification is known includes Andrews and Cheng (), Cox (), and Han and McCloskey ().…”

Section: Discussion Of the Related Literaturementioning

confidence: 99%

Identification‐ and singularity‐robust inference for moment condition models

Andrews¹,

Guggenberger

2019

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This paper introduces a new identification‐ and singularity‐robust conditional quasi‐likelihood ratio (SR‐CQLR) test and a new identification‐ and singularity‐robust Anderson and Rubin (1949) (SR‐AR) test for linear and nonlinear moment condition models. Both tests are very fast to compute. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For example, in i.i.d. scenarios, all that is required is that the moment functions and their derivatives have 2 + γ bounded moments for some γ > 0. No conditions are placed on the expected Jacobian of the moment functions, on the eigenvalues of the variance matrix of the moment functions, or on the eigenvalues of the expected outer product of the (vectorized) orthogonalized sample Jacobian of the moment functions. The SR‐CQLR test is shown to be asymptotically efficient in a GMM sense under strong and semi‐strong identification (for all k ≥ p, where k and p are the numbers of moment conditions and parameters, respectively). The SR‐CQLR test reduces asymptotically to Moreira's CLR test when p = 1 in the homoskedastic linear IV model. The same is true for p ≥ 2 in most, but not all, identification scenarios. We also introduce versions of the SR‐CQLR and SR‐AR tests for subvector hypotheses and show that they have correct asymptotic size under the assumption that the parameters not under test are strongly identified. The subvector SR‐CQLR test is shown to be asymptotically efficient in a GMM sense under strong and semi‐strong identification.

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“…Robust inference methods in scenarios where the source of weak identification is known includes Andrews and Cheng (), Cox (), and Han and McCloskey ().…”

Section: Discussion Of the Related Literaturementioning

confidence: 99%

Identification‐ and singularity‐robust inference for moment condition models

Andrews¹,

Guggenberger

2019

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“…shares would be unreliable. If it were the case in the limit, then inference is polluted by weak identification problems (see Han and McCloskey 2019). Consequently, it is valuable to have a test of identification to tell us whether or not these methods will work at all.…”

Section: A Linear Test Of Model Identificationmentioning

confidence: 99%

OLS estimation of the intra-household distribution of expenditure

Lechêne¹,

Pendakur²,

Wolf³

2021

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We provide a method to estimate resource shares-the fraction of total household expenditure allocated to each household member-using OLS estimation of Engel curves.The method is a linear reframing of the nonlinear model of Dunbar, Lewbel and Pendakur (2013), extended to allow single-parent and other complex households, scale economies in assignable goods and complementarities between non assignable goods, and supplemented with a linear identification test.We apply the model to data from 12 countries, and investigate resource shares, gender gaps, and poverty at the individual level. We reject equal sharing, and find large gender gaps in resource shares, and consequently in poverty rates, in some countries.

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“…22 The F-statistic in the first-stage linear regression may not be the best indicator for detecting weak instruments in nonlinear models. Han and McCloskey (2019) developed inference methods that were robust to weak identification for a class of nonlinear models, and considered bivariate probit models as one of the leading examples. Note.…”

Section: Empirical Examplementioning

confidence: 99%

Estimation in a generalization of bivariate probit models with dummy endogenous regressors

Han

Lee

2019

J of Applied Econometrics

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Summary The purpose of this paper is to provide guidelines for empirical researchers who use a class of bivariate threshold crossing models with dummy endogenous variables. A common practice employed by the researchers is the specification of the joint distribution of unobservables as a bivariate normal distribution, which results in a bivariate probit model. To address the problem of misspecification in this practice, we propose an easy‐to‐implement semiparametric estimation framework with parametric copula and nonparametric marginal distributions. We establish asymptotic theory, including root‐n normality, for the sieve maximum likelihood estimators that can be used to conduct inference on the individual structural parameters and the average treatment effect (ATE). In order to show the practical relevance of the proposed framework, we conduct a sensitivity analysis via extensive Monte Carlo simulation exercises. The results suggest that estimates of the parameters, especially the ATE, are sensitive to parametric specification, while semiparametric estimation exhibits robustness to underlying data‐generating processes. We then provide an empirical illustration where we estimate the effect of health insurance on doctor visits. In this paper, we also show that the absence of excluded instruments may result in identification failure, in contrast to what some practitioners believe.

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Estimation and inference with a (nearly) singular Jacobian

Cited by 23 publications

References 47 publications

Identification‐ and singularity‐robust inference for moment condition models

Identification‐ and singularity‐robust inference for moment condition models

OLS estimation of the intra-household distribution of expenditure

Estimation in a generalization of bivariate probit models with dummy endogenous regressors

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