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Nonparametric Inference in Dynamic Network Formation: Comments on “Homophily and Transitivity in Dynamic Network Formation”

动态网络形成的非参数推断:对“动态网络形成中的同质性与传递性”的评论

1 IntroductionDano et al. (2026) develop a novel conditional logit approach to identify the structural parameters of a model of dynamic network formation. They propose a conditional maximum likelih...

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Nuclear norm regularized estimation of panel regression models

面板回归模型的核范数正则化估计

In this paper we investigate panel regression models with interactive fixed effects. We propose two new estimation methods that are based on minimizing convex objective functions. The first method minimizes the sum of squared residuals with a nuclear (trace) norm regularization. The second method minimizes the nuclear norm of the residuals. We establish the consistency of the two resulting estimators. Those estimators have a very important computational advantage compared to…

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Test of neglected heterogeneity in dyadic models

双边关系模型中遗漏异质性的检验

We develop a Lagrange Multiplier (LM) test of neglected heterogeneity in dyadic models. The test statistic is derived by modifying Breusch and Pagan (1980)’s test. We establish the asymptotic distribution of the test statistic under the null using a novel martingale construction. We also consider the power of the LM test in generic panel models. Even though the test is motivated by random effects, we show that it has a power for detecting fixed effects as well. Finally, we…

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SEQUENTIALLY ESTIMATING THE STRUCTURAL EQUATION BY POWER TRANSFORMATION

通过幂变换序贯估计结构方程

This study provides an econometric methodology to test a linear structural relationship among economic variables. We propose the so-called distance-difference (DD) test and show that it has omnibus power against arbitrary nonlinear structural relationships. If the DD-test rejects the linear model hypothesis, a sequential testing procedure assisted by the DD-test can consistently estimate the degree of a polynomial function that arbitrarily approximates the nonlinear…

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Forecasting with a panel Tobit model

面板 Tobit 模型预测

We use a dynamic panel Tobit model with heteroskedasticity to generate forecasts for a large cross‐section of short time series of censored observations. Our fully Bayesian approach allows us to flexibly estimate the cross‐sectional distribution of heterogeneous coefficients and then implicitly use this distribution as prior to construct Bayes forecasts for the individual time series. In addition to density forecasts, we construct set forecasts that explicitly target the…

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A UNIFORM BOUND ON THE OPERATOR NORM OF SUB-GAUSSIAN RANDOM MATRICES AND ITS APPLICATIONS

次高斯随机矩阵算子范数的一致界及其应用

For an $N \times T$ random matrix $X(\beta )$ with weakly dependent uniformly sub-Gaussian entries $x_{it}(\beta )$ that may depend on a possibly infinite-dimensional parameter $\beta \in \mathbf {B}$ , we obtain a uniform bound on its operator norm of the form $\mathbb {E} \sup _{\beta \in \mathbf {B}} ||X(\beta )|| \leq CK \left (\sqrt {\max (N,T)} + \gamma _2(\mathbf {B},d_{\mathbf {B}})\right )$ , where C is an absolute constant, K controls the tail behavior of (the…

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Estimation of Peer Effects in Endogenous Social Networks: Control Function Approach

内生社会网络中同伴效应的控制函数估计

Abstract We propose methods of estimating the linear-in-means model of peer effects in which the peer group, defined by a social network, is endogenous in the outcome equation for peer effects. Endogeneity is due to unobservable individual characteristics that influence both link formation in the network and the outcome of interest. We propose two estimators of the peer effect equation that control for the endogeneity of the social connections using a control function…

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Panel forecasts of country-level Covid-19 infections

国家层面新冠活跃感染人数的面板预测

We use a dynamic panel data model to generate density forecasts for daily active Covid-19 infections for a panel of countries/regions. Our specification that assumes the growth rate of active infections can be represented by autoregressive fluctuations around a downward sloping deterministic trend function with a break. Our fully Bayesian approach allows us to flexibly estimate the cross-sectional distribution of slopes and then implicitly use this distribution as prior to…

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Forecasting With Dynamic Panel Data Models

This paper considers the problem of forecasting a collection of short time series using cross‐sectional information in panel data. We construct point predictors using Tweedie's formula for the posterior mean of heterogeneous coefficients under a correlated random effects distribution. This formula utilizes cross‐sectional information to transform the unit‐specific (quasi) maximum likelihood estimator into an approximation of the posterior mean under a prior distribution that…

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Estimation of graphical models using the L1,2 norm

使用 L1,2 范数估计图模型

Gaussian graphical models are recently used in economics to obtain networks of dependence among agents. A widely used estimator is the graphical least absolute shrinkage and selection operator (GLASSO), which amounts to a maximum likelihood estimation regularized using the L1,1 matrix norm on the precision matrix Ω. The L1,1 norm is a LASSO penalty that controls for sparsity, or the number of zeros in Ω. We propose a new estimator called structured GLASSO (SGLASSO) that uses…

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Estimation of random coefficients logit demand models with interactive fixed effects

具有交互固定效应的随机系数 Logit 需求模型估计

We extend the Berry, Levinsohn and Pakes (BLP, 1995) random coefficients discrete-choice demand model, which underlies much recent empirical work in IO. We add interactive fixed effects in the form of a factor structure on the unobserved product characteristics. The interactive fixed effects can be arbitrarily correlated with the observed product characteristics (including price), which accommodate endogeneity and, at the same time, capture strong persistence in market…

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Inference for VARs identified with sign restrictions

符号限制识别的 VAR 模型推断

There is a fast growing literature that set‐identifies structural vector autoregressions (SVARs) by imposing sign restrictions on the responses of a subset of the endogenous variables to a particular structural shock (sign‐restricted SVARs). Most methods that have been used to construct pointwise coverage bands for impulse responses of sign‐restricted SVARs are justified only from a Bayesian perspective. This paper demonstrates how to formulate the inference problem for…

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Many IVs estimation of dynamic panel regression models with measurement error

含测量误差动态面板回归的多工具变量估计

In this paper, we investigate a dynamic linear panel regression model with measurement error. We consider the panel data estimation whose time dimension (T) is not small and comparable to the cross sectional dimension (N). First, we show that the 2SLS estimator suffers from the bias problem due to many instrumental variables. Using the alternative asymptotics where T3N goes to a constant as N,T→∞, we characterize its asymptotic bias due to many IVs. As a bias reduction…

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LM Test of Neglected Correlated Random Effects and Its Application

遗漏相关随机效应的 LM 检验及其应用

This article aims at achieving two distinct goals. The first is to extend the existing LM test of overdispersion to the situation where the alternative hypothesis is characterized by the correlated random effects model. We obtain a result that the test against the random effects model has a certain max-min type optimality property. We will call such a test the LM test of overdispersion. The second goal of the article is to draw a connection between panel data analysis and…

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DYNAMIC LINEAR PANEL REGRESSION MODELS WITH INTERACTIVE FIXED EFFECTS

具有交互固定效应的动态线性面板回归

We analyze linear panel regression models with interactive fixed effects and predetermined regressors, for example lagged-dependent variables. The first-order asymptotic theory of the least squares (LS) estimator of the regression coefficients is worked out in the limit where both the cross-sectional dimension and the number of time periods become large. We find two sources of asymptotic bias of the LS estimator: bias due to correlation or heteroscedasticity of the…

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Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects

因子数未知时含交互固定效应的线性面板回归

In this paper we study the least squares (LS) estimator in a linear panel regression model with unknown number of factors appearing as interactive fixed effects. Assuming that the number of factors used in estimation is larger than the true number of factors in the data, we establish the limiting distribution of the LS estimator for the regression coefficients as the number of time periods and the number of cross-sectional units jointly go to infinity. The main result of the…

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Point-optimal panel unit root tests with serially correlated errors

误差序列相关下的点最优面板单位根检验

Generalizations of the point‐optimal panel unit root tests of Moon, Perron and Phillips (MPP) are developed to cover cases of serially correlated errors. The resulting statistics involve two modifications relative to those of MPP: (a) the error variance is replaced by the long‐run variance; (b) centring of the statistic is adjusted to correct for second‐order bias effects induced by the correlation between the error and lagged dependent variable.

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A predictability test for a small number of nested models

针对少量嵌套模型的预测能力检验

We introduce quasi-likelihood ratio tests for one sided multivariate hypotheses to evaluate the null that a parsimonious model performs equally well as a small number of models which nest the benchmark. The limiting distributions of the test statistics are non-standard. For critical values we consider: (i) bootstrapping and (ii) simulations assuming normality of the mean square prediction error difference. The proposed tests have good size and power properties compared with…

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PETER C.B. PHILLIPS’S CONTRIBUTIONS TO PANEL DATA METHODS

Peter C. B. Phillips 对面板数据方法的贡献

This paper discusses Peter Phillips’s contributions to panel data methods. These include contributions in the areas of seemingly unrelated regressions, nonstationary panel data, dynamic panels, and the development of multiple index asymptotic theory. We also discuss his empirical contributions in the area of economic growth and convergence that use macro panel data.

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The Hausman test and weak instruments

Hausman 检验与弱工具变量

We consider the following problem. There is a structural equation of interest that contains an explanatory variable that theory predicts is endogenous. There are one or more instrumental variables that credibly are exogenous with regard to this structural equation, but which have limited explanatory power for the endogenous variable. Further, there is one or more potentially 'strong' instruments, which has much more explanatory power but which may not be exogenous. Hausman…

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PANEL DATA MODELS WITH FINITE NUMBER OF MULTIPLE EQUILIBRIA

具有有限个多重均衡的面板数据模型

We study a nonlinear panel data model in which the fixed effects are assumed to have finite support. The fixed effects estimator is known to have the incidental parameters problem. We contribute to the literature by making a qualitative observation that the incidental parameters problem in this model may not be not as severe as in the conventional case. Because fixed effects have finite support, the probability of correctly identifying the fixed effect converges to one even…

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Estimation with overidentifying inequality moment conditions

具有过度识别矩不等式条件的估计

This paper derives limit distributions of empirical likelihood estimators for models in which inequality moment conditions provide overidentifying information. We show that the use of this information leads to a reduction of the asymptotic mean-squared estimation error and propose asymptotically uniformly valid tests and confidence sets for the parameters of interest. While inequality moment conditions arise in many important economic models, we use a dynamic macroeconomic…

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Asymptotic local power of pooled t-ratio tests for unit roots in panels with fixed effects

含固定效应面板中混合 t 比率单位根检验的渐近局部功效

. This latter test is equivalent to the well-known pooled t test proposed by Levin et al. (2002, Journal of Econometrics 108, 1--24), and its power depends only on the mean of the local-to-unity parameters. This implies that it has the same power against homogeneous and heterogeneous alternatives with the same mean autoregressive parameter. We then compare these tests to a panel version of the Sargan-Bhargava (1983, Econometrica 51, 153--74) statistic for a unit root and the…

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