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Time-varying instrumental variable estimation

时变工具变量估计

We develop non-parametric instrumental variable estimation and inferential theory for econometric models with possibly endogenous regressors whose coefficients can vary over time either deterministically or stochastically, and the time-varying and uniform versions of the standard Hausman exogeneity test. After deriving the asymptotic properties of the proposed procedures, we assess their finite sample performance by means of a set of Monte Carlo experiments, and illustrate…

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Robust nonlinear regression estimation in null recurrent time series

零常返时间序列中的稳健非线性回归估计

In this article, we study parametric robust estimation in nonlinear regression models with regressors generated by a class of non-stationary and null recurrent Markov processes. The nonlinear regression functions can be either integrable or asymptotically homogeneous, covering many commonly-used functional forms in parametric nonlinear regression. Under regularity conditions, we derive both the consistency and limit distribution results for the developed general robust…

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Diagnostic tests for homoskedasticity in spatial cross-sectional or panel models

空间横截面与面板模型的同方差诊断检验

We propose an Adjusted Quasi-Score (AQS) method for constructing tests for homoskedasticity in spatial econometric models. We first obtain an AQS function by adjusting the score-type function from the given model to achieve unbiasedness, and then develop an Outer-Product-of-Martingale-Difference (OPMD) estimate of its variance. In standard problems where a genuine (quasi) score vector is available, the AQS–OPMD method leads to finite sample improved tests over the usual…

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Robust estimation with exponentially tilted Hellinger distance

基于指数倾斜 Hellinger 距离的稳健估计

This paper is concerned with estimation of parameters defined by moment equalities. We introduce the exponentially tilted Hellinger distance (ETHD) estimator which is efficient under correct specification, and robust to both global and local misspecification. In the spirit of Schennach (2007), ETHD combines the Hellinger distance and the Kullback–Leibler information criterion. We show that it achieves optimal minimax robust properties under local deviations from the model…

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Bias in the effective bid-ask spread

有效买卖价差的测量偏误

The effective bid-ask spread measured relative to the spread midpoint overstates the true effective bid-ask spread in markets with discrete prices and elastic liquidity demand. The average bias is 13%–18% for S&P 500 stocks in general, depending on the estimator used as benchmark, and up to 97% for low-priced stocks. Cross-sectional bias variation across stocks, trading venues, and investor groups can influence research inference. The use of the midpoint also undermines…

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A NONPARAMETRIC TEST OF SIGNIFICANT VARIABLES IN GRADIENTS

回归梯度中显著变量的非参数检验

We propose a nonparametric test of significant variables in the partial derivative of a regression mean function. The derivative is estimated by local polynomial estimation and the test statistic is constructed through a variation-based measure of the derivative in the direction of variables of interest. We establish the asymptotic null distribution of the test statistic and demonstrate that it is consistent. Motivated by the null distribution, we propose a wild bootstrap…

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AVERAGE DERIVATIVE ESTIMATION UNDER MEASUREMENT ERROR

测量误差下的平均导数估计

In this paper, we derive the asymptotic properties of the density-weighted average derivative estimator when a regressor is contaminated with classical measurement error and the density of this error must be estimated. Average derivatives of conditional mean functions are used extensively in economics and statistics, most notably in semiparametric index models. As well as ordinary smooth measurement error, we provide results for supersmooth error distributions. This is a…

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LIMIT THEOREMS FOR FACTOR MODELS

因子模型的极限定理

This paper establishes central limit theorems (CLTs) and proposes how to perform valid inference in factor models. We consider a setting where many counties/regions/assets are observed for many time periods, and when estimation of a global parameter includes aggregation of a cross-section of heterogeneous microparameters estimated separately for each entity. The CLT applies for quantities involving both cross-sectional and time series aggregation, as well as for quadratic…

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NONSTATIONARY LINEAR PROCESSES WITH INFINITE VARIANCE GARCH ERRORS

具有无限方差 GARCH 误差的非平稳线性过程

Recently, Cavaliere, Georgiev, and Taylor (2018, Econometric Theory 34, 302–348) (CGT) considered the augmented Dickey–Fuller (ADF) test for a unit-root model with linear noise driven by i.i.d. infinite variance innovations and showed that ordinary least squares (OLS)-based ADF statistics have the same distribution as in Chan and Tran (1989, Econometric Theory 5, 354–362) for i.i.d. infinite variance noise. They also proposed an interesting question to extend their results…

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ESTIMATION OF VOLATILITY FUNCTIONS IN JUMP DIFFUSIONS USING TRUNCATED BIPOWER INCREMENTS

利用截断双幂增量估计跳跃扩散的波动率函数

In this article, we introduce and analyze a new methodology to estimate the volatility functions of jump diffusion models. Our methodology relies on the standard kernel estimation technique using truncated bipower increments. The relevant asymptotics are fully developed, allowing for the time span to increase as well as the sampling interval to decrease, and accommodate both stationary and nonstationary recurrent processes. We evaluate the performance of our estimators by…

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NONPARAMETRIC EULER EQUATION IDENTIFICATION AND ESTIMATION

欧拉方程的非参数识别与估计

We consider nonparametric identification and estimation of pricing kernels, or equivalently of marginal utility functions up to scale, in consumption-based asset pricing Euler equations. Ours is the first paper to prove nonparametric identification of Euler equations under low level conditions (without imposing functional restrictions or just assuming completeness). We also propose a novel nonparametric estimator based on our identification analysis, which combines standard…

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Exact computation of maximum rank correlation estimator

最大秩相关估计量的精确计算

Summary In this paper we provide a computation algorithm to get a global solution for the maximum rank correlation estimator using the mixed integer programming (MIP) approach. We construct a new constrained optimization problem by transforming all indicator functions into binary parameters to be estimated and show that it is equivalent to the original problem. We also consider an application of the best subset rank prediction and show that the original optimization problem…

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Sparse covariance estimation in logit mixture models

混合 Logit 模型的稀疏协方差估计

Summary This paper introduces a new data-driven methodology for estimating sparse covariance matrices of the random coefficients in logit mixture models. Researchers typically specify covariance matrices in logit mixture models under one of two extreme assumptions: either an unrestricted full covariance matrix (allowing correlations between all random coefficients), or a restricted diagonal matrix (allowing no correlations at all). Our objective is to find optimal subsets of…

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Unifying inference for semiparametric regression

半参数回归的统一推断

Summary In the literature, a discrepancy in the limiting distributions of least square estimators between the stationary and nonstationary cases exists in various regression models with different persistence level regressors. This hinders further statistical inference since one has to decide which distribution should be used next. In this paper, we develop a semiparametric partially linear regression model with stationary and nonstationary regressors to attenuate this…

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Partial effects in non-linear panel data models with correlated random effects

相关随机效应非线性面板模型中的偏效应

Summary Nonlinearity and heterogeneity are known to cause difficulties in estimating and interpreting partial effects. This paper provides a systematic characterization of the various partial effects in nonlinear panel data models that might be of interest to empirical researchers. The interpretation of the partial effects depends upon (i) whether the distribution of unobserved heterogeneity is treated as fixed or allowed to vary with covariates, and (ii) whether one is…

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Instrument-based estimation with binarised treatments: issues and tests for the exclusion restriction

处理变量二值化后的工具变量估计:排除限制问题与检验

Summary When estimating local average and marginal treatment effects using instrumental variables (IVs), multivalued endogenous treatments are frequently converted to binary measures, supposedly to improve interpretability or policy relevance. Such binarisation introduces a violation of the IV exclusion if (a) the IV affects the multivalued treatment within support areas below and/or above the threshold and (b) such IV-induced changes in the multivalued treatment affect the…

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Identification without assuming mean stationarity: quasi–maximum likelihood estimation of dynamic panel models with endogenous regressors

无需均值平稳假设的识别:含内生解释变量动态面板模型的拟极大似然估计

Summary Linear generalised method of moments (GMM) estimators for dynamic panel models with predetermined or endogenous regressors suffer from a weak instruments problem when the data are highly persistent. In this paper, we propose new random- and fixed-effects limited-information quasi–maximum likelihood estimators (LIQMLEs) for such models. We also discuss LIQMLEs for models that contain time-varying individual effects. Unlike system GMM estimators, the LIQMLEs do not…

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Panel kink threshold regression model with a covariate-dependent threshold

阈值依赖协变量的面板折点阈值回归模型

Summary This article extends the kink threshold regression model with a constant threshold to a panel data framework with a covariate-dependent threshold, where the threshold is modeled as a function of informative covariates. We suggest an estimator based on the within-group transformation and propose test statistics for kink threshold effect and threshold constancy. We establish the asymptotic joint normality of the slope and threshold estimators and derive the limiting…

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Approximate Laplace Approximations for Scalable Model Selection

用于可扩展模型选择的近似拉普拉斯近似

Abstract We propose the approximate Laplace approximation (ALA) to evaluate integrated likelihoods, a bottleneck in Bayesian model selection. The Laplace approximation (LA) is a popular tool that speeds up such computation and equips strong model selection properties. However, when the sample size is large or one considers many models the cost of the required optimizations becomes impractical. ALA reduces the cost to that of solving a least-squares problem for each model.…

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Joint Quantile Regression for Spatial Data

空间数据的联合分位数回归

Abstract Linear quantile regression is a powerful tool to investigate how predictors may affect a response heterogeneously across different quantile levels. Unfortunately, existing approaches find it extremely difficult to adjust for any dependency between observation units, largely because such methods are not based upon a fully generative model of the data. For analysing spatially indexed data, we address this difficulty by generalizing the joint quantile regression model…

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Spatial Birth–Death–Move Processes: Basic Properties and Estimation of their Intensity Functions

空间出生—死亡—移动过程:基本性质与强度函数估计

Abstract Many spatiotemporal data record the time of birth and death of individuals, along with their spatial trajectories during their lifetime, whether through continuous-time observations or discrete-time observations. Natural applications include epidemiology, individual-based modelling in ecology, spatiotemporal dynamics observed in bioimaging and computer vision. The aim of this article is to estimate in this context the birth and death intensity functions that depend…

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The Confidence Interval Method for Selecting Valid Instrumental Variables

选择有效工具变量的置信区间方法

Abstract We propose a new method, the confidence interval (CI) method, to select valid instruments from a larger set of potential instruments for instrumental variable (IV) estimation of the causal effect of an exposure on an outcome. Invalid instruments are such that they fail the exclusion conditions and enter the model as explanatory variables. The CI method is based on the CIs of the per instrument causal effects estimates and selects the largest group with all CIs…

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Leveraging the Fisher Randomization Test using Confidence Distributions: Inference, Combination and Fusion Learning

借助置信分布拓展Fisher随机化检验:推断、组合与融合学习

Abstract The flexibility and wide applicability of the Fisher randomization test (FRT) make it an attractive tool for assessment of causal effects of interventions from modern-day randomized experiments that are increasing in size and complexity. This paper provides a theoretical inferential framework for FRT by establishing its connection with confidence distributions. Such a connection leads to development’s of (i) an unambiguous procedure for inversion of FRTs to generate…

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Optimal Statistical Inference for Individualized Treatment Effects in High-Dimensional Models

高维模型中个体化处理效应的最优统计推断

Abstract The ability to predict individualized treatment effects (ITEs) based on a given patient's profile is essential for personalized medicine. We propose a hypothesis testing approach to choosing between two potential treatments for a given individual in the framework of high-dimensional linear models. The methodological novelty lies in the construction of a debiased estimator of the ITE and establishment of its asymptotic normality uniformly for an arbitrary future…

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