Semiparametric Efficiency Bounds and Efficient Estimation of Discrete Duration Models with Unspecified Hazard Rate
(With Sadat Reza)
Econometric Reviews , forthcoming.
Abstract: We consider semiparametric estimation of discrete duration models whose hazard rate can be characterized as an unknown transformation of a parametric index of the observable covariates and elapsed spell length. The information matrix is derived. In the case of separable duration dependence the information matrix for the parameters of the index is singular. In that situation, the information matrix for the regression component of the hazard function is derived. The information matrix is also singular when individual-specific/time-invariant unobserved errors are introduced. We develop ?N-consistent estimators for those instances when the information matrix is nonsingular. Less-than-?N-consistent estimators of the duration dependence component of the hazard rate of the separable model are developed. Simulations and an application to strike durations illustrate the viability of the approach.
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Saddlepoint Expansions for GEL Estimators
(With Gubhinder Khundi)
Statistical Methods and Applications , forthcoming
Abstract: A simple saddlepoint (SP) approximation for the distribution of generalized empirical likelihood (GEL) estimators is derived. Simulations compare the performance of the SP and other methods such as the Edgeworth and the bootstrap for special cases of GEL: continuous updating, empirical likelihood and exponential tilting estimators.
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A Simple Root-N-Consistent Semiparametric Estimator for Discrete Duration Models
(With Sadat Reza)
Statistics and Probability Letters , 94, 150-154.
Abstract: Incorrect specification of the hazard rate in duration analysis can produce inconsistent estimators of the parameters of the model. We propose a new estimator for discrete duration models in which the hazard rate is comprised of an inner index function of the covariates and time variable and an outer link function. The index function is specified up to a finite dimensional parameter, ? ₀ . ? ₀ is estimated using a least squares objective function. The link function is left unspecified and estimated by the method of kernels. We demonstrate the consistency and asymptotic normality of the estimator of ? ₀ . Simulations show the efficacy of the estimator.
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Edgeworth Expansions for GEL Estimators
(With Gubhinder Khundi)
Journal of Multivariate Analysis , 2012, 106, 118-146.
Abstract: Finite sample approximations for the distribution functions of Generalized Empirical Likelihood (GEL) are derived using Edgeworth expansions. The analytical results obtained are shown to apply to most of the common extremum estimators used in applied work in an i.i.d. sampling context. The GEL estimators considered include the Continuous Updating, Empirical Likelihood and Exponential Tilting estimators. These estimators are popular alternatives to Generalized Method of Moment (GMM) estimators and their finite sample properties are examined. In a Monte Carlo Experiment, higher order analytical corrections provided by Edgeworth approximations work well in comparison to first order approximations and improve inferences in finite samples.
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The Third Order Bias of Nonlinear Estimators
(With Gubhinder Khundi)
Communications in Statistics , 2008, 37(16), 2617-2633.
Abstract: The third-order bias of nonlinear estimators is derived and illustrated using a variety of estimators popular in applied econometrics. A simulation using the exponential regression model indicates that the third-order analytical correction reduces bias substantially compared to higher-order bootstrap and Jackknife corrections, particularly in very small samples
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Efficient Semiparametric Estimation of Duration Models with Unobserved Heterogeneity
(With Peter Bearse and Jose Canals)
Econometric Theory , 2007, 23(2), 281-308.
Abstract: This paper develops a new semiparametric approach for the estimation of hazard functions in the presence of unobserved heterogeneity. The hazard function is specified parametrically, whereas the distribution of the unobserved heterogeneity is indirectly estimated using the method of kernels. The semiparametric efficiency bounds are derived. The estimator obtains these bounds in large samples
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