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  • 1
    UID:
    (DE-602)gbv_1831646994
    ISBN: 9780444887665
    Content: Asymptotic distribution theory is the primary method used to examine the properties of econometric estimators and tests. We present conditions for obtaining cosistency and asymptotic normality of a very general class of estimators (extremum estimators). Consistent asymptotic variance estimators are given to enable approximation of the asymptotic distribution. Asymptotic efficiency is another desirable property then considered. Throughout the chapter, the general results are also specialized to common econometric estimators (e.g. MLE and GMM), and in specific examples we work through the conditions for the various results in detail. The results are also extended to two-step estimators (with finite-dimensional parameter estimation in the first step), estimators derived from nonsmooth objective functions, and semiparametric two-step estimators (with nonparametric estimation of an infinite-dimensional parameter in the first step). Finally, the trinity of test statistics is considered within the quite general setting of GMM estimation, and numerous examples are given.
    In: Handbook of econometrics, Amsterdam [u.a.] : Elsevier, 1986, (1994), Seite 2111-2245, 9780444887665
    In: 0444887660
    In: year:1994
    In: pages:2111-2245
    Language: English
    URL: Volltext  (Deutschlandweit zugänglich)
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  • 2
    UID:
    (DE-602)gbv_1831646986
    ISBN: 9780444887665
    Content: This paper provides an introduction to the use of empirical process methods in econometrics. These methods can be used to establish the large sample properties of econometric estimators and test statistics. In the first part of the paper, key terminology and results are introduced and discussed heuristically. Applications in the econometrics literature are briefly reviewed. A select set of three classes of applications is discussed in more detail. The second part of the paper shows how one can verify a key property called stochastic equicontinuity. The paper takes several stochastic equicontinuity results from the probability literature, which rely on entropy conditions of one sort or another, and provides primitive sufficient conditions under which the entropy conditions hold. This yields stochastic equicontinuity results that are readily applicable in a variety of contexts. Examples are provided.
    In: Handbook of econometrics, Amsterdam [u.a.] : Elsevier, 1986, (1994), Seite 2247-2294, 9780444887665
    In: 0444887660
    In: year:1994
    In: pages:2247-2294
    Language: English
    URL: Volltext  (Deutschlandweit zugänglich)
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  • 3
    UID:
    (DE-602)gbv_1831646978
    ISBN: 9780444887665
    Content: We review different approaches to nonparametric density and regression estimation. Kernel estimators are motivated from local averaging and solving ill-posed problems. Kernel estimators are compared to k-NN estimators, orthogonal series and splines. Pointwise and uniform confidence bands are described, and the choice of smoothing parameter is discussed. Finally, the method is applied to nonparametric prediction of time series and to semiparametric estimation.
    In: Handbook of econometrics, Amsterdam [u.a.] : Elsevier, 1986, (1994), Seite 2295-2339, 9780444887665
    In: 0444887660
    In: year:1994
    In: pages:2295-2339
    Language: English
    URL: Volltext  (Deutschlandweit zugänglich)
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  • 4
    UID:
    (DE-602)gbv_183164696X
    ISBN: 9780444887665
    Content: A brief account is given of the methodology and theory for the bootstrap. Methodology is developed in the context of the “equation” approach, which allows attention to be focussed on specific criteria for excellence, such as coverage error of a confidence interval or expected value of a bias-corrected estimator. This approach utilizes a definition of the bootstrap in which the key component is replacing a true distribution function by its empirical estimator. Our theory is Edgeworth expansion based, and is aimed specifically at elucidating properties of different methods for constructing bootstrap confidence intervals in a variety of settings. The reader interested in more detail than can be provided here is referred to the recent monograph of Hall (1992) .
    In: Handbook of econometrics, Amsterdam [u.a.] : Elsevier, 1986, (1994), Seite 2341-2381, 9780444887665
    In: 0444887660
    In: year:1994
    In: pages:2341-2381
    Language: English
    URL: Volltext  (Deutschlandweit zugänglich)
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  • 5
    UID:
    (DE-602)gbv_1831646951
    ISBN: 9780444887665
    Content: This chapter discusses classical estimation methods for limited dependent variable (LDV) models that employ Monte Carlo simulation techniques to overcome computational problems in such models. These difficulties take the form of high-dimensional integrals that need to be calculated repeatedly. In the past, investigators were forced to restrict attention to special classes of LDV models that are computationally manageable. The simulation estimation methods we discuss here make it possible to estimate LDV models that are computationally intractable using classical estimation methods. The chapter first reviews the ways in which LDV models arise, describing the differences and similarities in censored and truncated data generating processes. Censoring and truncation give rise to the troublesome multivariate integrals. Following the LDV models, we described various simulation methods for evaluating such integrals. Naturally, censoring and truncation play roles in simulation as well. Finally, estimation methods that rely on simulation are described. The chapter also reviews three general approaches that combine estimation of LDV models and simulation: simulation of the log-likelihood function (MSL), simulation of moment functions (MSM), and simulation of the score (MSS). The MSS is a combination of ideas from MSL and MSM, treating the efficient score of the log-likelihood function as a moment function.
    In: Handbook of econometrics, Amsterdam [u.a.] : Elsevier, 1986, (1994), Seite 2383-2441, 9780444887665
    In: 0444887660
    In: year:1994
    In: pages:2383-2441
    Language: English
    URL: Volltext  (Deutschlandweit zugänglich)
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  • 6
    UID:
    (DE-602)gbv_1831646943
    ISBN: 9780444887665
    Content: A semiparametric model for observational data combines a parametric form for some component of the data generating process (usually the behavioral relation between the dependent and explanatory variables) with weak nonparametric restrictions on the remainder of the model (usually the distribution of the unobservable errors). This chapter surveys some of the recent literature on semiparametric methods, emphasizing microeconometric applications using limited dependent variable models. An introductory section defines semiparametric models more precisely and reviews the techniques used to derive the large-sample properties of the corresponding estimation methods. The next section describes a number of weak restrictions on error distributions — conditional mean, conditional quantile, conditional symmetry, independence, and index restrictions — and show how they can be used to derive identifying restrictions on the distributions of observables. This general discussion is followed by a survey of a number of specific estimators proposed for particular econometric models, and the chapter concludes with a brief account of applications of these methods in practice.
    In: Handbook of econometrics, Amsterdam [u.a.] : Elsevier, 1986, (1994), Seite 2443-2521, 9780444887665
    In: 0444887660
    In: year:1994
    In: pages:2443-2521
    Language: English
    URL: Volltext  (Deutschlandweit zugänglich)
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  • 7
    UID:
    (DE-602)gbv_1831646935
    ISBN: 9780444887665
    Content: This chapter describes several nonparametric estimation and testing methods for econometric models. Instead of using parametric assumptions on the functions and distributions in an economic model, the methods use the restrictions that can be derived from the model. Examples of such restrictions are the concavity and monotonicity of functions, equality conditions, and exclusion restrictions. The chapter shows, first, how economic restrictions can guarantee the identification of nonparametric functions in several structural models. It then describes how shape restrictions can be used to estimate nonparametric functions using popular methods for nonparametric estimation. Finally, the chapter describes how to test nonparametrically the hypothesis that an economic model is correct and the hypothesis that a nonparametric function satisfies some specified shape properties.
    In: Handbook of econometrics, Amsterdam [u.a.] : Elsevier, 1986, (1994), Seite 2523-2558, 9780444887665
    In: 0444887660
    In: year:1994
    In: pages:2523-2558
    Language: English
    URL: Volltext  (Deutschlandweit zugänglich)
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  • 8
    UID:
    (DE-602)gbv_1831646927
    ISBN: 9780444887665
    Content: Suppose that one wants to estimate a parameter characterizing some feature of a specified population. One has some prior information about the population and a random sample of observations. A widely applicable approach is to estimate the parameter by a sample analog; that is, by a statistic having the same properties in the sample as the parameter does in the population. If there is no such statistic, then one may choose an estimate that, in some well-defined sense, makes the known properties of the population hold as closely as possible in the sample. These are analog estimation methods. This chapter surveys some uses of analog methods to estimate two classes of econometric models, the separable and the response models.
    In: Handbook of econometrics, Amsterdam [u.a.] : Elsevier, 1986, (1994), Seite 2559-2582, 9780444887665
    In: 0444887660
    In: year:1994
    In: pages:2559-2582
    Language: English
    URL: Volltext  (Deutschlandweit zugänglich)
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  • 9
    UID:
    (DE-602)gbv_1831646919
    ISBN: 9780444887665
    Content: The comparison of different hypotheses, i.e. of competing models, is the basis of model specification. It may be performed along two main lines. The first one consists in associating with each model a loss function and in retaining the specification implying the smallest (estimated) loss. In practice, the loss function is defined either by updating some a priori knowledge on the models given the available observations (the Bayesian point of view), or by introducing some criterion taking into account the trade-off between the goodness of fit and the complexity of the model. The second approach is hypothesis testing theory. However, the determination of the decision rule is not done on the same basis as model choice. The basis of hypothesis testing theory is to introduce the probability of errors. This chapter focuses on the case where none of the hypotheses is a particular case of another one.
    In: Handbook of econometrics, Amsterdam [u.a.] : Elsevier, 1986, (1994), Seite 2583-2637, 9780444887665
    In: 0444887660
    In: year:1994
    In: pages:2583-2637
    Language: English
    URL: Volltext  (Deutschlandweit zugänglich)
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  • 10
    UID:
    (DE-602)gbv_1831646900
    ISBN: 9780444887665
    Content: This chapter provides an overview of asymptotic results available for parametric estimators in dynamic models. Three cases are treated: stationary (or essentially stationary) weakly dependent data, weakly dependent data containing deterministic trends, and nonergodic data (or data with stochastic trends). Estimation of asymptotic covariance matrices and computation of the major test statistics are covered. Examples include multivariate least squares estimation of a dynamic conditional mean, quasi-maximum likelihood estimation of a jointly parameterized conditional mean and conditional variance, and generalized method of moments estimation of orthogonality conditions. Some results for linear models with integrated variables are provided, as are some abstract limiting distribution results for nonlinear models with trending data.
    In: Handbook of econometrics, Amsterdam [u.a.] : Elsevier, 1986, (1994), Seite 2639-2738, 9780444887665
    In: 0444887660
    In: year:1994
    In: pages:2639-2738
    Language: English
    URL: Volltext  (Deutschlandweit zugänglich)
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