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Semiparametric Estimation of Regression Models for Panel Data

面板数据回归模型的半参数估计

Linear models with error components are widely used to analyse panel data. Some applications of these models require knowledge of the probability densities of the error components. Existing methods handle this requirement by assuming that the densities belong to known parametric families of distributions (typically the normal distribution). This paper shows how to carry out nonparametric estimation of the densities of the error components, thereby avoiding the assumption…

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Quadratic ARCH Models

二次ARCH模型

We introduce a new model for time-varying conditional variances as the most general quadratic version possible within the ARCH class. Hence, it encompasses all the existing restricted quadratic variance functions. Its properties are very similar to those of GARCH models, but avoids some of their criticisms. In univariate applications to daily U.S. and monthly U.K. stock market returns, QARCH adequately represents volatility and risk premia. QARCH is easy to incorporate in…

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Nonlinear Econometric Models with Deterministically Trending Variables

含确定性趋势变量的非线性计量模型

This paper considers an alternative asymptotic framework to standard sequential asymptotics for nonlinear models with deterministically trending variables. The asymptotic distributions of generalized method of moments estimators and corresponding test statistics are derived using this framework. The asymptotic distributions are shown to be the same with deterministically trending variables as with non-trending variables. That is, the distributions are normal and chi-squared…

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The Efficiency Bound of the Mixed Proportional Hazard Model

混合比例风险模型的效率界

The semiparametric efficiency bound of the mixed proportional hazard model is derived. The density of the model factors in such a way that there exists a complete sufficient statistic for the individual heterogeneity. The efficient score is shown to be the difference between the score in the parametric direction and its conditional expectation given the sufficient statistic. Applying this result to the single-spell Weibull mixed proportional hazard model, it is shown that…

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Semiparametric Specification Testing of Non-nested Econometric Models

非嵌套计量模型的半参数设定检验

We propose a specification test of a parametrically specified nonlinear model against a weakly specified non-nested alternative. We estimate the alternative model by using nonparametric regression (nearest neighbours). The test is based on the t-statistic of an artificial regression. Monte-Carlo simulations suggest that the test has good power and size characteristics.

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A Simulation Estimator for Dynamic Models of Discrete Choice

动态离散选择模型的模拟估计量

This paper analyses a new estimator for the structural parameters of dynamic models of discrete choice. Based on an inversion theorem due to Hotz and Miller (1993), which establishes the existence of a one-to-one mapping between the conditional valuation functions for the dynamic problem and their associated conditional choice probabilities, we exploit simulation techniques to estimate models which do not possess terminal states. In this way our Conditional Choice Simulation…

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Shadow Wages and Peasant Family Labour Supply: An Econometric Application to the Peruvian Sierra

影子工资与农户家庭劳动供给:秘鲁山区的计量应用

This paper develops a methodology for estimating structural time-allocation models for self-employed households and applies it to peasant family labour supply behaviour in the Peruvian Sierra. The opportunity costs of time, or shadow wages, of household workers are explicitly estimated from an agricultural production function. Using an instrumental variables procedure, the household's structural labour supply parameters are recovered from variation in these shadow wages. The…

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Conditional Choice Probabilities and the Estimation of Dynamic Models

This paper develops a new method for estimating the structural parameters of (discrete choice) dynamic programming problems. The method reduces the computational burden of estimating such models. We show the valuation functions characterizing the expected future utility associated with the choices often can be represented as an easily computed function of the state variables, structural parameters, and the probabilities of choosing alternative actions for states which are…

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Aggregation with Log-Linear Models

对数线性模型的加总

When economic theory suggests a log-linear specification for individual agents, e.g., Cobb-Douglas production, it is common to estimate the same log-linear model with aggregate data, invoking a representative agent assumption and thereby assuming away aggregation errors. This paper gives necessary and sufficient restrictions on the distribution of agents in an economy for log-linear agent models to aggregate into log-linear macro models, and discusses the aggregation bias…

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Estimation and Testing of the Union Wage Effect Using Panel Data

利用面板数据估计与检验工会工资效应

We present estimates of the union wage effect controlling for unmeasured individual effects, and subject the conventional fixed-effects model to specification tests. For PSID men the union wage effect is 5-8% after controlling for person effects, as opposed to 20% in cross-section. Omnibus tests based on an unrestricted reduced form and instrumental variables tests based on differencing are consistent with conventional models. Tests based on comparing those who enter and…

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Identification and Estimation of Dichotomous Latent Variables Models Using Panel Data

利用面板数据识别和估计二元潜变量模型

Identification conditions for binary choice errors-in-variables models are explored. Conditions for the consistency and asymptotic normality of the maximum likelihood estimators of binary choice models with unbounded explanatory variables are given. Two- or three-step estimators to simplify computation are also suggested.

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Some Theory of Statistical Inference for Nonlinear Science

非线性科学统计推断的若干理论

This article shows how standard errors can be estimated for a measure of the number of excited degrees of freedom (the correlation dimension), and a measure of the rate of information creation (a proxy for the Kolmogorov entropy), and a measure of instability. These measures are motivated by nonlinear science and chaos theory. The main analytical method is central limit theory of U-statistics for mixing processes. The paper takes a step toward formal hypothesis testing in…

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Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations

This paper presents specification tests that are applicable after estimating a dynamic model from panel data by the generalized method of moments (GMM), and studies the practical performance of these procedures using both generated and real data. Our GMM estimator optimally exploits all the linear moment restrictions that follow from the assumption of no serial correlation in the errors, in an equation which contains individual effects, lagged dependent variables and no…

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Identification and Panel Data Models with Endogenous Regressors

含内生解释变量的面板数据模型识别

This paper provides sufficient conditions for the identification of both static and dynamic models containing endogenous regressors from panel data by utilizing the restrictions across time periods on the parameters. It is shown that identification is achieved under quite weak conditions even in the presence of a general pattern of correlation between the errors and the time-varying variables. Efficient estimation procedures for the models considered and some specification…

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Imhof Approximations to Econometric Estimators

计量经济估计量的Imhof分布近似

The article develops new approximations to the distribution function of a general econometric estimator or test statistic from a linear model. The method relies heavily on the general arguments for the validity of Edgeworth approximations, and produces formulae of a similar type, except that, instead of using the cumulative normal distribution, an Imhof distribution is used derived from the exact distribution of a linear combination of the sample data second moments. On…

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Statistical Inference in Instrumental Variables Regression with I(1) Processes

This paper studies the asymptotic properties of instrumental variable (IV) estimates of multivariate cointegrating regressions and allows for deterministic and stochastic regressors as well as quite general deterministic processes in the data-generating mechanism. It is found that IV regressions are consistent even when the instruments are stochastically independent of the regressors. This phenomenon, which contrasts with traditional theory for stationary time series, is a…

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Hypothesis Testing in Semiparametric and Nonparametric Models for Econometric Time Series

计量时间序列半参数与非参数模型的假设检验

A restriction on a semiparametric or nonparametric econometric time series model determines the value of a finite-dimensional functional τ of an infinite-dimensional nuisance function. The estimate of τ and its estimated covariance matrix use nonparametric probability and spectral density estimation. A consequent test of the restriction is given approximate large sample justification under absolute regularity on the time series and other conditions. The methodology relates…

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Identification and Estimation of Equivalence Scales under Weak Separability

弱可分性下等价尺度的识别与估计

This paper shows that most methods of incorporating demographic variation into separable models can be represented in a form that is identical to Barten equivalence scales, except that the scales themselves depend on the exact mix of goods that comprise each group, as well as on demographic variables. This generalization of Barten scales is shown to be more plausible than ordinary scales, can be used to increase the efficiency of demand system estimation, and can overcome…

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Inference in Nonlinear Econometric Models with Structural Change

存在结构变化的非线性计量模型推断

This paper extends the classical test for structural change in linear regression models (see Chow (1960)) to a wide variety of nonlinear models, estimated by a variety of different procedures. Wald, Lagrange multiplier-like, and likelihood ratio-like test statistics are introduced. The results allow for heterogeneity and temporal dependence of the observations. In the process of developing the above tests, the paper also provides a compact presentation of general unifying…

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Probit with Dependent Observations

观测相关情形下的Probit估计

Estimation of limited dependent variable models with dependent observations has received relatively little attention due to the computational complexity of the maximum likelihood estimator. We develop a computationally attractive and relatively efficient estimator for this case that utilises the orthogonality conditions. The resulting Generalized Conditional Moment (GCM) estimators can be applied with a known or an unknown disturbance covariance matrix. Although the paper…

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Alternative Asymptotically Optimal Tests and Their Application to Dynamic Specification

替代性渐近最优检验及其在动态设定中的应用

A method is presented for generating test statistics which share the same first order asymptotic optimality properties of the classical statistics. Generalizing Neyman's (1959) work, the linearised classical statistic tests restrictions in implicit function form using a parameter estimator which is consistent and asymptotically normally distributed under the alternative hypothesis. By judicious choice of estimator and form of restrictions at which to evaluate the statistic,…

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Post-simulation Analysis of Monte Carlo Experiments: Interpreting Pesaran's (1974) Study of Non-nested Hypothesis Test Statistics

蒙特卡洛实验的模拟后分析:解读Pesaran的非嵌套假设检验研究

"Monte Carlo experimentation in econometrics helps ‘solve’ deterministic problems by simulating stochastic analogues in which the analytical unknowns are reformulated as parameters to be estimated." (Hendry (1980)) With that in mind, Monte Carlo studies may be divided operationally into three phases: design, simulation, and post-simulation analysis. This paper provides a guide to the last of those three, post-simulation analysis, given the design and simulation of a Monte…

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Two Stage and Related Estimators and Their Applications

两阶段及相关估计量与其应用

This paper aims to provide a unified treatment of the properties of two stage estimators. General conditions are set forth for consistency, efficiency and correct inferences. Applications of the general theorems are made to models with expectations and diagnostic tests. The general approach frequently enables much simpler derivation of existing results, and provides a number of new ones.

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Hypothesis Testing in Unidentified Models

未识别模型中的假设检验

An identified model is not necessary for statistical inference, but ambiguities can arise. This paper examines some simple examples and proposes a framework that distinguishes between the "refutation" and "confirmation" aspects of testing in an unidentified model. One particular problem is the interpretation given to overidentifying restrictions: a common view is that these are somehow not properly testable.

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