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t Test in a Structural Equation

结构方程中的 t 检验

Properties of t ratios associated with the LIML, TSLS, and OLS estimators in a structural form estimation are studied. The existence of moments of these t ratios including the LIML form is proved first. Second, Monte Carlo simulations are performed to find out real sizes of the t test and the likelihood ratio test. Third, asymptotic expansions of the distributions of t ratios are derived under the null hypothesis to find out deviations of real sizes from nominal sizes…

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Bayesian Inference in Econometric Models Using Monte Carlo Integration

利用蒙特卡洛积分进行计量经济模型的贝叶斯推断

Methods for the systematic application of Monte Carlo integration with importance sampling to Bayesian inference are developed. Conditions under which the numerical approximation converges almost surely to the true value with the number of Monte Carlo replications, and its numerical accuracy may be assessed reliably, are given. Importance sampling densities are derived from multivariate normal or student approximations to the posterior density. These densities are modified…

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Proper Posteriors from Improper Priors for an Unidentified Errors-in-Variables Model

未识别测量误差模型中由非正规先验得到正规后验

The problem considered is inference in a simple errors-in-variables model where consistent estimation is impossible without introducing additional exact prior information. The probabilistic prior information required for Bayesian analysis is found to be surprisingly light: despite the model's lack of identification, a proper posterior is guaranteed for any bounded prior density, including those representing improper priors. This result is illustrated with the improper…

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Sampling Performance of Some Joint One-Sided Preliminary Test Estimators under Squared Error Loss

平方误差损失下若干联合单侧预检验估计量的抽样表现

IN MANY AREAS OF SCIENCE, when drawing conclusions concerning a set of phenomena, individual or linear combinations of parameters are assumed to be nonnegative, nonpositive, or to lie between upper and lower bounds. Likewise, many functions are assumed to be monotonic, convex, or quasiconvex. Consequently, questions naturally arise as to the correctness of the assumptions and, within the context of statistical inference, how to evaluate the evidence against these assumptions…

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A Test of the Efficiency of a Given Portfolio

给定投资组合效率的检验

A test for the ex ante efficiency of a given portfolio of assets is analyzed. The relevant statistic has a tractable small sample distribution. Its power function is derived and used to study the sensitivity of the test to the portfolio choice and to the number of assets used to determine the ex post mean-variance efficient frontier. Several intuitive interpretations of the test are provided, including a simple mean-standard deviation geometric explanation. A univariate…

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Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications

条件约束异质过程的半非参数估计:资产定价应用

A. Ronald Gallant, George Tauchen, Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications, Econometrica, Vol. 57, No. 5 (Sep., 1989), pp. 1091-1120

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Power in Econometric Applications

计量经济应用中的检验功效

This paper is concerned with the use of power properties of tests in econometric applications. Inverse power functions are defined. These functions are designed to yield summary measures of power that facilitate the interpretation of test results in practice. Simple approximations are introduced for the inverse power functions of Wald, likelihood ratio, Lagrange multiplier, and Hausman tests. These approximations readily convey the general qualitative features of the power…

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Simulation and the Asymptotics of Optimization Estimators

模拟与优化估计量的渐近理论

A general central limit theorem is proved for estimators defined by minimization of the length of a vector-valued, random criterion function. No smoothness assumptions are imposed on the criterion function in order that the results might apply to a broad class of simulation estimators. Complete analyses of two simulation estimators, one introduced by A. Pakes (1986) and the other by D. McFadden (1989), illustrate the application of the general theorems. These examples…

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A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration

无需数值积分的离散响应模型模拟矩估计方法

This paper proposes a simple modification of a conventional generalized method of moments estimator for a discrete response model, replacing response probabilities that require numerical integration with estimators obtained by Monte Carlo simulation. This method of simulated moments does not require precise estimates of these probabilities, as the law of large numbers operating across observations controls simulation error, and, hence, can use simulations of practical size.…

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Econometric Analysis of Aggregation in the Context of Linear Prediction Models

线性预测模型中聚合问题的计量分析

This paper deals with the problem of aggregation where the focus of the analysis is whether to predict aggregate variables using macro or micro equations. The GrunfeldGriliches prediction criterion for choosing between aggregate and disaggregate equations is generalized to allow for contemporaneous covariances between the disturbances of micro equations and the possibility of different parametric restrictions on the equations of the disaggregate model. A new test is proposed…

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Learning Rational Expectations Under Computability Constraints

可计算性约束下的理性预期学习

In this paper, the author considers how boundedly rational agents learn rational expectations when all equilibrium price functions or forecasts of future equilibrium prices are required to be computable. The paper examines two learning environments. In the first, agents have perfect information about the state of nature. In this case, the theory of machine inference can be applied to show that there is a broad class of computable economies whose rational expectations…

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Estimation of Multi-Market Fix-Price Models: An Application of Pseudo Maximum Likelihood Methods

多市场固定价格模型的估计:伪最大似然方法的应用

The past decade has seen the econometric implementation of macroeconomic multimarket fix-price models for a number of European countries. The procedure in use, the full information maximum likelihood method, unfortunately becomes very cumbersome and seems out of reach when additional features are incorporated in the model (disaggregation into micro markets, opinion surveys ...). One purpose of the present work is to prove the fruitfulness of the following estimation…

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The Random Utility Hypothesis and Inference in Demand Systems

随机效用假说与需求系统中的推断

In this paper, the authors examine the consequences of adopting the random utility hypothesis as an approach for randomizing a system of demand equations. Random utility models are appealing since they allow the usual assumption of deterministic utility-maximizing behavior by each consumer to coexist with the apparent randomness across individuals that is exhibited by data. Their results show that the use of random utility models implies that the disturbances of the demand…

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Efficient Estimation Using Panel Data

利用面板数据进行有效估计

IN AN IMPORTANT RECENT PAPER, Hausman and Taylor (1981)-hereafter HT-considered the instrumental-variable estimation of a regression model using panel data, when the individual effects may be correlated with a subset of the explanatory variables. They provided a simple consistent estimator and an efficient estimator. More recently, Amemiya and MaCurdy (1986)-hereafter AM-have suggested an alternative estimator which is more efficient than the HT estimator, under certain…

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An Edgeworth Test Size Correction for the Linear Model with AR(1) Errors

AR(1) 误差线性模型的 Edgeworth 检验尺寸修正

T. J. Rothenberg's (1984) Edgeworth test size correction for the linear model with a nonscalar covariance matrix is applied to the special case of AR(1) errors. Simulations show that the correction reduces the overrejection that is commonly encountered in this model, although substantial overrejection remains when the original amount is large. When the regressors are autocorrelated and collinear (for example, two trended regressors) there is not nearly as much overrejection…

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Alternative Tests of the Error Components Model

误差分量模型的替代检验

The error Components regression model is now widely applied in econometics and statistics. Given the potentially high costs of incorrectly excluding the component from the model, an error components test should have high power. In addition, if a test is to gain acceptance from practitioners, the test should be computed easily. To obtain improved critical-value approximations, we introduce a standardized Lagrange multiplier (SLM) test statistic, which is centered and scaled…

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A Uniform Law of Large Numbers for Dependent and Heterogeneous Data Processes

依赖且异质数据过程的一致大数定律

Uniform laws of large numbers (ULLNs) consider sums of the form: n −1 Σ t n =1 [q t (z t , θ)-Eq t (z t , θ)], where (z t ) denotes a stochastic data generating process that takes its values in a space Z, θ is an element of the parameter space Θ, and q t : Z×Θ→R. ULLNs provide conditions under which the above sum converges to zero uniformly over the parameter space. The purpose of the present note is to introduce a new generic ULLN. It maintains a set of assumptions that is…

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On the Covariance Structure of Earnings and Hours Changes

劳动收入与工时变化的协方差结构

This paper presents an empirical analysis of individual earnings and hours data from three different longitudinal surveys. In the first part of the paper, the authors catalog the main features of the covariance structure of earnings and hours changes. In the second part of the paper, they offer an interpretation of this model in terms of a simple life-cycle, labor-supply model. On the assumption that they can identify individual productivity growth with the shared component…

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A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle

非平稳时间序列与经济周期分析的新方法

This paper models occasional, discrete shifts in the growth rate of a nonstationary series. Algorithms for inferring these unobserved shifts are presented, a byproduct of which permits estimation of parameters by maximum likelihood. An empirical application of this technique suggests that the periodic shift from a positive growth rate to a negative growth rate is a recurrent feature of the U.S. business cycle, and indeed could be used as an objective criterion for defining…

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Nonlinear Hypotheses, Inequality Restrictions, and Non-Nested Hypotheses: Exact Simultaneous Tests in Linear Regressions

线性回归中非线性假设、不等式约束与非嵌套假设的精确同时检验

In the classical linear model, comparison of two arbitrary hypotheses on the regression coefficients is considered. Problems involving nonlinear hypotheses, inequality restrictions, or non-nested hypotheses are included. Exact bounds on the null distribution of likelihood ratio statistics are derived (based on the central Fisher distribution). As a special case, a bounds test similar to the Durbin-Watson test is proposed. Multiple testing problems are studied: the bounds…

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Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses

模型选择与非嵌套假设的似然比检验

Using the Kullback-Leibler information criterion to measure the closeness of a model to the truth, the author proposes new likelihood-ratio-based statistics for testing the null hypothesis that the competing models are as close to the true data generating process against the alternative hypothesis that one model is closer. The tests are directional and are derived for the cases where the competing models are non-nested, overlapping, or nested and whether both, one, or…

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Implementation with Incomplete Information in Exchange Economies

交换经济中不完全信息下的实施

This paper studies the problem of implementation of allocation rules in economic environments when agents are incompletely informed about the environment. The concept of equilibrium used is that of Bayesian Nash equilibrium. The authors show that a condition called Bayesian monotonicity is necessary for implementation, as is an incentive compatibility condition. They also show that, when there are at least three agents, Bayesian monotonicity and a slightly stronger incentive…

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