Local Linear GMM Estimation of Functional Coefficient IV Models With an Application to Estimating the Rate of Return to Schooling

Su, Liangjun; Murtazashvili, Irina; Ullah, Aman

doi:10.1080/07350015.2012.754314

Cited by 35 publications

(14 citation statements)

References 56 publications

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“…There is also an important case for which β( z ) = β for all z (where β is q × 1 vector of constants) which is not covered by the above theorems. It is of course perfectly natural to test for the constancy of the functional coefficients; see the recent work by Su et al (2011) by way of example. When β( z ) is a constant vector, this corresponds to the case where all components of Z are irrelevant covariates, i.e.…”

Section: Semiparametric Kernel Estimation Of Varying‐coefficient Mmentioning

confidence: 99%

Categorical semiparametric varying‐coefficient models

Ouyang

Racine

2011

J of Applied Econometrics

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SUMMARYSemiparametric varying‐coefficient models have become a common fixture in applied data analysis. Existing approaches, however, presume that those variables affecting the coefficients are continuous in nature (or that there exists at least one such continuous variable) which is often not the case. Furthermore, when all variables affecting the coefficients are categorical/discrete, theoretical underpinnings cannot be obtained as a special case of existing approaches and, as such, requires a separate treatment. In this paper we use kernel‐based methods that place minimal structure on the underlying mechanism governing parameter variation across categorical variables while providing a consistent and efficient approach that may be of interest to practitioners. One area where such models could be particularly useful is in settings where interactions among the categorical and real‐valued predictors consume many (or even exhaust) degrees of freedom for fully parametric models (which is frequently the case in applied settings). Furthermore, we demonstrate that our approach behaves optimally when in fact there is no variation in a model's coefficients across one or more of the categorical variables (i.e. the approach pools over such variables with a high probability). An illustrative application demonstrates potential benefits for applied researchers. Copyright © 2011 John Wiley & Sons, Ltd.

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Section: Semiparametric Kernel Estimation Of Varying‐coefficient Mmentioning

confidence: 99%

Categorical semiparametric varying‐coefficient models

Ouyang

Racine

2011

J of Applied Econometrics

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“…The idea of local maximum likelihood (and local generalized method of moments) estimation has a long history, including Fan, Farmen and Gijbels (1998), Newey (1994a), Staniswalis (1989), Stone (1977), Tibshirani and Hastie (1987) and Lewbel (2007). In economics, popular applications of these techniques include multinomial choice modeling in a panel data setting (e.g., Honoré and Kyriazidou, 2000) and instrumental variables regression (e.g., Su, Murtazashvili and Ullah, 2013). The core idea is that when estimating parameters at a particular value of covariates, a kernel weighting function is used to place more weight on nearby observations in the covariate space.…”

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confidence: 99%

Generalized random forests

Athey¹,

Tibshirani²,

Wager³

2019

Ann. Statist.

1,158

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We propose generalized random forests, a method for nonparametric statistical estimation based on random forests (Breiman, 2001) that can be used to fit any quantity of interest identified as the solution to a set of local moment equations. Following the literature on local maximum likelihood estimation, our method considers a weighted set of nearby training examples; however, instead of using classical kernel weighting functions that are prone to a strong curse of dimensionality, we use an adaptive weighting function derived from a forest designed to express heterogeneity in the specified quantity of interest. We propose a flexible, computationally efficient algorithm for growing generalized random forests, develop a large sample theory for our method showing that our estimates are consistent and asymptotically Gaussian, and provide an estimator for their asymptotic variance that enables valid confidence intervals. We use our approach to develop new methods for three statistical tasks: non-parametric quantile regression, conditional average partial effect estimation, and heterogeneous treatment effect estimation via instrumental variables. A software implementation, grf for R and C++, is available from CRAN. imsart-aos ver.

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“…Pagan and Ullah, 1999 [10]; Ullah 1988[11]; Su, Ullah and Wang, 2013 [12]; Su, Murtazashvili, and Ullah, 2013 [13]. Our Monte Carlo simulation considers p = 1 and p = 2.)…”

Section: Estimationmentioning

confidence: 99%

Combined estimation of semiparametric panel data models

Bai

Lee

Ullah

2020

Econometrics and Statistics

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The combined estimation for the semiparametric panel data models is proposed. The properties of estimators for the semiparametric panel data models with random effects (RE) and fixed effects (FE) are examined. When the RE estimator suffers from endogeneity due to the individual effects correlated with the regressors, the semiparametric RE and FE estimators may be adaptively combined, with the combining weights depending on the degree of endogeneity. The asymptotic distributions of these three estimators (RE, FE, and combined estimators) for the semiparametric panel data models are derived using a local asymptotic framework. These three estimators are then compared in asymptotic risk. The semiparametric combined estimator has strictly smaller asymptotic risk than the semiparametric fixed effect estimator. The Monte Carlo study shows that the semiparametric combined estimator outperforms semiparametric FE and RE estimators except when the degrees of endogeneity and heterogeneity of the individual effects are very small. Also presented is an empirical application where the effect of public sector capital in the private economy production function is examined using the US state level panel data.

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Local Linear GMM Estimation of Functional Coefficient IV Models With an Application to Estimating the Rate of Return to Schooling

Cited by 35 publications

References 56 publications

Categorical semiparametric varying‐coefficient models

Categorical semiparametric varying‐coefficient models

Generalized random forests

Combined estimation of semiparametric panel data models

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