Essays in Nonparametric Econometrics.
详细信息
- 作者：Christensen ; Timothy.
- 学历：Ph.D.
- 年：2014
- 毕业院校：Yale University
- ISBN：9781321048162
- CBH：3580652
- Country：USA
- 语种：English
- FileSize：8065632
- Pages：200
文摘
This dissertation consists of four chapters which study nonparametric identification and estimation of models which have been the subject of much recent research in economic and econometric theory. The first three chapters study nonparametric identification and nonparametric sieve estimation of positive eigenfunction problems in economics,with particular application to dynamic asset pricing models. The fourth chapter,which is jointly authored with Xiaohong Chen,studies optimal uniform convergence rates for nonparametric instrumental variables models. The first chapter introduces new econometric techniques for studying the long-run implications of dynamic asset pricing models. The long-run implications of a model are jointly determined by the functional form of the stochastic discount factor SDF) and the dynamic behavior of the variables in the model. The estimators introduced in this chapter treat the dynamics as an unknown nuisance parameter. Nonparametric sieve estimators of the positive eigenfunction and eigenvalue used to decompose the SDF into its permanent and transitory components are proposed,together with estimators of the long-term yield and entropy of the permanent component of the SDF. The estimators are particularly simple to implement,and may be used to numerically compute the long-run implications of fully specified models for which analytical solutions are unavailable. Nonparametric identification conditions are presented. Consistency and convergence rates of the estimators are established. An approach for conducting asymptotic inference on the eigenvalue,long-term yield,and entropy of the permanent component of the SDF is provided. The semiparametric efficiency bounds for these parameters are derived and their estimators are shown to be efficient. The long-run implications of the consumption CAPM are investigated using these methods. This investigation reveals a long-run version of the equity premium puzzle which is robust to certain augmentations of the representative agents utility function. The estimators,identification conditions,and large sample theory presented in this chapter have broader application in economics including,for example,the nonparametric estimation of marginal utilities of consumption in representative agent models. In the second chapter,the nonparametric identification conditions presented in Chapter ?? are both weakened and extended to more general function spaces. High-level conditions for consistency and convergence rates for nonparametric sieve estimators of the positive eigenfunctions of a collection of nonselfadjoint operators and their adjoints are also presented,along with useful results on the convergence of random matrices. The third chapter further investigates the conditions under which the positive eigenfunction of an operator is nonparametrically identified. Identification is achieved if the operator satisfies two mild positivity conditions and a power compactness condition. Both existence and identification are achieved under an additional non-degeneracy condition. The identification conditions are presented for the general case of positive operators on Banach lattices. The general identification conditions presented in this chapter are applied to obtain new identification conditions for the positive eigenfunctions which are used to extract the long-run implications of dynamic asset pricing models. The identification conditions have other applications in economics. For example,the conditions may be applied to obtain new primitive nonparametric identification conditions for marginal utilities in heterogeneous-agent and representative-agent consumption-based asset pricing models,and to facilitate future nonparametric estimation of these models. The fourth chapter is joint work with Xiaohong Chen. This chapter establishes optimality properties of sieve estimators of nonparametric regression models with endogeneity. Nonparametric regression with an endogenous regressor is an important nonparametric instrumental variables NPIV) regression in econometrics and a difficult ill-posed inverse problem with unknown operator in statistics. This chapter establishes new uniform sup-norm) convergence rates for sieve NPIV estimators,which are a nonparametric version of two-stage least squares estimators. The literature on NPIV estimation has so far only studied mean-square convergence rates. This chapter derives the best possible i.e. minimax optimal) uniform convergence rates for estimators of NPIV models,and provides conditions under which sieve NPIV estimators attain their best possible rates. As an indication of the sharpness of the convergence rates obtained,it is shown that spline or wavelet nonparametric series regression estimators attain their well-known best possible rates even with weakly dependent data and heavy-tailed error terms.