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Unit root tests for panel data with AR(1) errors and small T

具有AR(1)误差和短时间维度的面板单位根检验

We propose unit root tests for panel data with a small number of time periods, T, and increments that follow an AR(1) process under the null. The model is a fixed‐effect panel version of the augmented Dickey–Fuller regression of order 1. Individual‐specific linear trends may also be included. The test statistics are t‐type statistics based on least‐squares estimates from which the Nickell bias is removed. Their limiting distributions (for an increasing number of independent…

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Testing for common trends in semi‐parametric panel data models with fixed effects

固定效应半参数面板模型的共同趋势检验

This paper proposes a non‐parametric test for common trends in semi‐parametric panel data models with fixed effects based on a measure of non‐parametric goodness‐of‐fit (R2). We first estimate the model under the null hypothesis of common trends by the method of profile least squares, and obtain the augmented residual which consistently estimates the sum of the fixed effect and the disturbance under the null. Then we run a local linear regression of the augmented residuals…

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Break point estimators for a slope shift: levels versus first differences

斜率变化的断点估计:水平模型与一阶差分模型

This paper analyses two break point estimators: one for a univariate slope‐shift model under unit root errors, the other for its first difference (a mean shift model). The asymptotic theory is developed for the estimators under a specific Pitman drift, assuming the break magnitude is within a T−1/2 neighbourhood of zero. Compared to the existing asymptotics assuming a fixed break magnitude or a shrinking one converging at a slower rate than T1/2, the limiting distributions…

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Statistical inference in the presence of heavy tails

重尾情形下的统计推断

Income distributions are usually characterized by a heavy right‐hand tail. Apart from any ethical considerations raised by the presence among us of the very rich, statistical inference is complicated by the need to consider distributions of which the moments may not exist. In extreme cases, no valid inference about expectations is possible until restrictions are imposed on the class of distributions admitted by econometric models. It is therefore important to determine the…

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On the problem of inference for inequality measures for heavy‐tailed distributions

重尾分布下不平等指标的推断问题

We consider the class of heavy‐tailed income distributions and show that the shape of the income distribution has a strong effect on inference for inequality measures. In particular, we demonstrate how the severity of the inference problem responds to the exact nature of the right tail of the income distribution. It is shown that the density of the studentized inequality measure is heavily skewed to the left, and that the excessive coverage failures of the usual confidence…

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Identification of treatment response with social interactions

存在社会互动时处理响应的识别

This paper develops a formal language for study of treatment response with social interactions, and uses it to obtain new findings on identification of potential outcome distributions. Defining a person's treatment response to be a function of the entire vector of treatments received by the population, I study identification when shape restrictions and distributional assumptions are placed on response functions. An early key result is that the traditional assumption of…

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Breakdown point theory for implied probability bootstrap

隐含概率自助法的崩溃点理论

This paper studies robustness of bootstrap inference methods under moment conditions. In particular, we compare the uniform weight and implied probability bootstraps by analysing behaviours of the bootstrap quantiles when outliers take arbitrarily large values, and derive the breakdown points for those bootstrap quantiles. The breakdown point properties characterize the situation where the implied probability bootstrap is more robust against outliers than the uniform weight…

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Testing for common trends in semiparametric panel data models with fixed effects

固定效应半参数面板模型的共同趋势检验

This paper proposes a non‐parametric test for common trends in semi‐parametric panel data models with fixed effects based on a measure of non‐parametric goodness‐of‐fit (R2). We first estimate the model under the null hypothesis of common trends by the method of profile least squares, and obtain the augmented residual which consistently estimates the sum of the fixed effect and the disturbance under the null. Then we run a local linear regression of the augmented residuals…

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Generalised empirical likelihood testing in semiparametric conditional moment restrictions models

半参数条件矩限制模型中的广义经验似然检验

This paper shows how generalized empirical likelihood can be used to obtain specification tests in semiparametric conditional moment restrictions models. The resulting test statistics are similar in spirit to classical Kolmogorov–Smirnov and Cramer von Mises goodness‐of‐fit statistics and are based on an integrated version of the original moment restrictions. The results are applied to test the correct specification of an instrumental variable smooth varying coefficient…

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Statistical inference in the presence of heavy tails

厚尾情形下的统计推断

Income distributions are usually characterized by a heavy right‐hand tail. Apart from any ethical considerations raised by the presence among us of the very rich, statistical inference is complicated by the need to consider distributions of which the moments may not exist. In extreme cases, no valid inference about expectations is possible until restrictions are imposed on the class of distributions admitted by econometric models. It is therefore important to determine the…

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Rank estimation of partially linear index models

部分线性指标模型的秩估计

Summary We consider a generalized regression model with a partially linear index. The index contains an additive non-parametric component in addition to the standard linear component, and the model is characterized by an unknown monotone link function. We propose weighted rank estimation procedures for estimating (a) the coefficients for the linear component, (b) the non-parametric component (and its derivative) and (c) the average derivative for the non-parametric…

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Non‐parametric regression under location shifts

位置移动下的非参数回归

Recent work by Wang and Phillips (2009b, 2011) has shown that ill‐posed inverse problems do not arise in non‐stationary non‐parametric regression and there is no need for non‐parametric instrumental variable estimation. Instead, simple Nadaraya–Watson non‐parametric estimation of a cointegrating regression equation is consistent irrespective of the endogeneity in the regressor. The present paper shows that some closely related results apply in the case of structural…

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Non‐parametric models in binary choice fixed effects panel data

二元选择固定效应面板中的非参数模型

In this paper we extend the fixed effects approach to deal with non‐linear panel data with non‐parametric components. Specifically, we propose a non‐parametric procedure that generalizes the conditional logit approach. We develop an estimator based on non‐linear stochastic integral equations and provide the asymptotic property of the estimator and an iterative algorithm to implement the estimator. We analyse the small sample behaviour of the estimator through a Monte Carlo…

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Dealing with endogeneity in a time‐varying parameter model: joint estimation and two‐step estimation procedures

时变参数模型中的内生性:联合估计与两步估计

In dealing with the problem of endogeneity in a time‐varying parameter model, we develop the joint and two‐step estimation procedures based on the control function approach. We show that a key to the success of the joint estimation procedure is in an appropriate state‐space representation of the model. On the other hand, a correct treatment of the problem of generated regressors plays an important role in our two‐step estimation procedure. Monte Carlo experiments confirm…

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Non‐parametric time‐varying coefficient panel data models with fixed effects

带固定效应的非参数时变系数面板数据模型

This paper is concerned with developing a non‐parametric time‐varying coefficient model with fixed effects to characterize non‐stationarity and trending phenomenon in a non‐linear panel data model. We develop two methods to estimate the trend function and the coefficient function without taking the first difference to eliminate the fixed effects. The first one eliminates the fixed effects by taking cross‐sectional averages, and then uses a non‐parametric local linear method…

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A simple approach to quantile regression for panel data

This paper provides a set of sufficient conditions that point identify a quantile regression model with fixed effects. It also proposes a simple transformation of the data that gets rid of the fixed effects under the assumption that these effects are location shifters. The new estimator is consistent and asymptotically normal as both n and T grow.

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Test statistics for prospect and Markowitz stochastic dominances with applications

前景随机占优与马科维茨随机占优的检验统计量及应用

Levy and Levy (2002, 2004) extend the stochastic dominance (SD) theory for risk averters and risk seekers by developing the prospect SD (PSD) and Markowitz SD (MSD) theory for investors with S‐shaped and reverse S‐shaped (RS‐shaped) utility functions, respectively. Davidson and Duclos (2000) develop SD tests for risk averters whereas Sriboonchitra et al. (2009) modify their statistics to obtain SD tests for risk seekers. In this paper, we extend their work by developing new…

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On the efficiency of a semi‐parametric GARCH model

半参数GARCH模型的估计效率

Financial time series exhibit time‐varying volatilities and non‐Gaussian distributions. There has been considerable research on the GARCH models for dealing with these issues related to financial data. Since in practice the true error distribution is unknown, various quasi maximum likelihood methods based on different assumptions on the error distribution have been studied in the literature. However, the specification of the distribution family or in particular the shape…

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An I(2) cointegration model with piecewise linear trends

含分段线性趋势的I(2)协整模型

This paper presents likelihood analysis of the I(2) cointegrated vector autoregression which allows for piecewise linear deterministic terms. Limiting behaviour of the maximum likelihood estimators are derived, which is used to further derive the limiting distribution of the likelihood ratio statistic for the cointegration ranks, extending Nielsen and Rahbek. The provided asymptotic theory extends also the results in Johansen et al. where asymptotic inference is discussed in…

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Non‐parametric identification of the mixed proportional hazards model with interval‐censored durations

区间删失持续期数据下混合比例风险模型的非参数识别

This note presents identification results for the mixed proportional hazards model when duration data are interval‐censored. Earlier positive results on identification under interval‐censoring require both parametric specification on how covariates enter the hazard functions and assumptions of unbounded support for covariates. New results provided here show how one can dispense with both of these assumptions. The mixed proportional hazards model is non‐parametrically…

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Quasi‐maximum likelihood estimation of discretely observed diffusions

离散观测扩散过程的拟极大似然估计

This paper introduces a quasi‐maximum likelihood estimator for discretely observed diffusions when a closed‐form transition density is unavailable. Higher‐order Wagner–Platen strong approximation is used to derive the first two conditional moments and a normal density function is used in estimation. Simulation study shows that the proposed estimator has high numerical precision and good numerical robustness. This method is applicable to a large class of diffusions.

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Testing for sphericity in a fixed effects panel data model

固定效应面板模型的球形性检验

This paper proposes a test for sphericity in a fixed effects panel data model. It uses the Random Matrix Theory based approach of Ledoit and Wolf (2002) to test for sphericity of the error terms in a fixed effects panel model with a large number of cross-sectional units and time series observations. Since the errors are unobservable, the residuals from the fixed effects regression are used. The limiting distribution of the proposed test statistic is derived. Additionally,…

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Weak and strong cross‐section dependence and estimation of large panels

弱与强横截面依赖及大面板估计

This paper introduces the concepts of time‐specific weak and strong cross‐section dependence, and investigates how these notions are related to the concepts of weak, strong and semi‐strong common factors, frequently used for modelling residual cross‐section correlations in panel data models. It then focuses on the problems of estimating slope coefficients in large panels, where cross‐section units are subject to possibly a large number of unobserved common factors. It is…

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Short‐term forecasts of euro area GDP growth

欧元区GDP增长的短期预测

This paper evaluates models that exploit timely monthly releases to compute early estimates of current quarter GDP (now‐casting) in the euro area. We compare traditional methods used at institutions with a new method proposed by Giannone et al. The method consists in bridging quarterly GDP with monthly data via a regression on factors extracted from a large panel of monthly series with different publication lags. We show that bridging via factors produces more accurate…

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