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Large Sample Sieve Estimation of SemiNonparametric Models
 Handbook of Econometrics
, 2007
"... Often researchers find parametric models restrictive and sensitive to deviations from the parametric specifications; seminonparametric models are more flexible and robust, but lead to other complications such as introducing infinite dimensional parameter spaces that may not be compact. The method o ..."
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Cited by 185 (19 self)
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Often researchers find parametric models restrictive and sensitive to deviations from the parametric specifications; seminonparametric models are more flexible and robust, but lead to other complications such as introducing infinite dimensional parameter spaces that may not be compact. The method of sieves provides one way to tackle such complexities by optimizing an empirical criterion function over a sequence of approximating parameter spaces, called sieves, which are significantly less complex than the original parameter space. With different choices of criteria and sieves, the method of sieves is very flexible in estimating complicated econometric models. For example, it can simultaneously estimate the parametric and nonparametric components in seminonparametric models with or without constraints. It can easily incorporate prior information, often derived from economic theory, such as monotonicity, convexity, additivity, multiplicity, exclusion and nonnegativity. This chapter describes estimation of seminonparametric econometric models via the method of sieves. We present some general results on the large sample properties of the sieve estimates, including consistency of the sieve extremum estimates, convergence rates of the sieve Mestimates, pointwise normality of series estimates of regression functions, rootn asymptotic normality and efficiency of sieve estimates of smooth functionals of infinite dimensional parameters. Examples are used to illustrate the general results.
Mobility and the return to education: Testing a Roy Model with multiple markets
 ECONOMETRICA
, 2002
"... Selfselected migration presents one potential explanation for why observed returns to a college education in local labor markets vary widely even though U.S. workers are highly mobile. To assess the impact of selfselection on estimated returns, this paper first develops a Roy model of mobility and ..."
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Cited by 184 (0 self)
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Selfselected migration presents one potential explanation for why observed returns to a college education in local labor markets vary widely even though U.S. workers are highly mobile. To assess the impact of selfselection on estimated returns, this paper first develops a Roy model of mobility and earnings where workers choose in which of the 50 states (plus the District of Columbia) to live and work. Available estimation methods are either infeasible for a selection model with so many alternatives or place potentially severe restrictions on earnings and the selection process. This paper develops an alternative econometric methodology which combines Lee's (1983) parametric maximum order statistic approach to reduce the dimensionality of the error terms with more recent work on semiparametric estimation of selection models (e.g., Ahn and Powell, 1993). The resulting semiparametric correction is easy to implement and can be adapted to a variety of other polychotomous choice problems. The empirical work, which uses 1990 U.S. Census data, confirms the role of comparative advantage in mobility decisions. The results suggest that selfselection of higher educated individuals to states with higher returns to education generally leads to upward biases in OLS estimates of the returns to education in statespecific labor markets. While the estimated returns to a college education are significantly biased, correcting for the bias does not narrow the range of returns across states. Consistent with the finding that the corrected return to a college education differs across the U.S., the relative statetostate migration flows of college versus high schooleducated individuals respond strongly to differences in the return to education and amenities across states.
Understanding Instrumental Variables in Models with Essential Heterogeneity
 The Review of Economics and Statistics
, 2006
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Higher order properties of GMM and generalized empirical likelihood estimators
 ECONOMETRICA
, 2003
"... In an effort to improve the small sample properties of generalized method of moments (GMM) estimators, a number of alternative estimators have been suggested. These include empirical likelihood (EL), continuous updating, and exponential tilting estimators. We show that these estimators share a comm ..."
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Cited by 146 (6 self)
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In an effort to improve the small sample properties of generalized method of moments (GMM) estimators, a number of alternative estimators have been suggested. These include empirical likelihood (EL), continuous updating, and exponential tilting estimators. We show that these estimators share a common structure, being members of a class of generalized empirical likelihood (GEL) estimators. We use this structure to compare their higher order asymptotic properties. We find that GEL has no asymptotic bias due to correlation of the moment functions with their Jacobian, eliminating an important source of bias for GMM in models with endogeneity. We also find that EL has no asymptotic bias from estimating the optimal weight matrix, eliminating a further important source of bias for GMM in panel data models. We give bias corrected GMM and GEL estimators. We also show that bias corrected EL inherits the higher order property of maximum likelihood, that it is higher order asymptotically efficient relative to the other bias corrected estimators.
Endogeneity in Nonparametric and Semiparametric Regression Models
, 2000
"... This paper considers the nonparametric and semiparametric methods for estimating regression models with continuous endogenous regressors. We list a number of different generalizations of the linear structural equation model, and discuss how three common estimation approaches for linear equations — t ..."
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Cited by 130 (19 self)
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This paper considers the nonparametric and semiparametric methods for estimating regression models with continuous endogenous regressors. We list a number of different generalizations of the linear structural equation model, and discuss how three common estimation approaches for linear equations — the “instrumental variables, ” “fitted value, ” and “control function ” approaches — may or may not be applicable to nonparametric generalizations of the linear model and to their semiparametric variants. The discussion then turns to a particular semiparametric model, the binary response model with linear index function and nonparametric error distribution, and describes in detail how estimation of the parameters of interest can be constructed using the “control function ” approach. This estimator is then applied to an empirical problem of the relation of labor force participation to nonlabor income, viewed as an endogenous regressor.
Efficient semiparametric estimation of quantile treatment effects
, 2003
"... This paper presents calculations of semiparametric efficiency bounds for quantile treatment effects parameters when selection to treatment is based on observable characteristics. The paper also presents three estimation procedures for these parameters, all of which have two steps: a nonparametric e ..."
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Cited by 121 (5 self)
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This paper presents calculations of semiparametric efficiency bounds for quantile treatment effects parameters when selection to treatment is based on observable characteristics. The paper also presents three estimation procedures for these parameters, all of which have two steps: a nonparametric estimation and a computation of the difference between the solutions of two distinct minimization problems. RootN consistency, asymptotic normality, and the achievement of the semiparametric efficiency bound is shown for one of the three estimators. In the final part of the paper, an empirical application to a job training program reveals the importance of heterogeneous treatment effects, showing that for this program the effects are concentrated in the upper quantiles of the earnings distribution.
Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity
, 2002
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Two Step Series Estimation of Sample Selection Models," mimeo, MIT (revised version
, 1988
"... working paper ..."
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2010): “Sparse Models and Methods for Optimal Instruments with an Application to Eminent Domain,” Arxiv Working Paper
"... Abstract. We develop results for the use of Lasso and PostLasso methods to form firststage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p. Our results apply even when p is much larger than the sample size, n. We show that the IV e ..."
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Cited by 55 (19 self)
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Abstract. We develop results for the use of Lasso and PostLasso methods to form firststage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p. Our results apply even when p is much larger than the sample size, n. We show that the IV estimator based on using Lasso or PostLasso in the first stage is rootn consistent and asymptotically normal when the firststage is approximately sparse; i.e. when the conditional expectation of the endogenous variables given the instruments can be wellapproximated by a relatively small set of variables whose identities may be unknown. We also show the estimator is semiparametrically efficient when the structural error is homoscedastic. Notably our results allow for imperfect model selection, and do not rely upon the unrealistic ”betamin ” conditions that are widely used to establish validity of inference following model selection. In simulation experiments, the Lassobased IV estimator with a datadriven penalty performs well compared to recently advocated manyinstrumentrobust procedures. In an empirical example dealing with the effect of judicial eminent domain decisions on economic outcomes, the Lassobased IV estimator outperforms an intuitive benchmark. Optimal instruments are conditional expectations. In developing the IV results, we estab