Fixed and Random Effects in Classical and Bayesian Regression*

This paper proposes a common and tractable framework for analyzing fixed and random effects models, in particular constant‐slope variable‐intercept designs. It is shown that, regardless of whether effects (i) are treated as parameters or as an error term, (ii) are estimated in different stages of a hierarchical model, or whether (iii) correlation between effects and regressors is allowed, when the same prior information on idiosyncratic parameters is introduced into all estimation methods, the resulting common slope estimator is also the same across methods. These results are illustrated using the Grünfeld investment data with different prior distributions. Random effects estimates are shown to be more efficient than fixed effects estimates. This efficiency gain, however, comes at the cost of neglecting information obtained in the computation of the prior unknown variance of idiosyncratic parameters.     

A Pairwise Difference Estimator for Partially Linear Spatial Autoregressive Models

Abstract

We propose a pairwise difference estimator for partially linear spatial autoregressive models with heteroscedastic or/and spatially correlated error terms. In comparison with other competing estimators, e.g. the profile QMLE (Su & Jin, 2010) and the semiparametric GMM estimator (Su, 2012), our estimator has the advantage of computational simplicity particularly when one is interested in estimating the finite dimensional parameters in the model. Large sample properties of the estimator are formally established and a consistent estimate of the asymptotic CV matrix is provided. We then use the method to robustly estimate the effect of strategic interaction in deciding local school spending.

RÉSUMÉ nous proposons un estimateur de différence par paire pour des modèles autorégressifs spatiaux partiellement linéaires, avec conditions d'erreurs à corrélation hétéroscédastique et/ou spatiale. Par rapport à d'autres estimateurs possibles, p.ex. le QMLE de profil (Su & Jin, 2010), et l'estimateur GMM semi-paramétrique (Su, 2012), notre estimateur présente l'avantage de la simplicité du calcul, notamment lorsque l'on s'intéresse à l'estimation des paramètres dimensionnels finis dans le modèle. Les propriétés de grand échantillon de l'estimateur sont établies officiellement, et une estimation homogène de la matrice CV asymptotique est fournie. Nous utilisons ensuite la méthode d'estimation consistante de l'effet de l'interaction stratégique dans les décisions sur les dépenses des écoles locales.

EXTRACTO Proponemos un estimador de diferencias por pares para modelos autorregresivos espaciales parcialmente lineales con términos de error heteroscedásticos o/y espacialmente correlacionados. En comparación con otros estimadores competidores, p. ej., QMLE (Su & Jin, 2010) y el estimador GMM semiparamétrico (Su, 2012), nuestro estimador tiene la ventaja de la simplicidad computacional, particularmente cuando uno está interesado en estimar los parámetros dimensionales finitos en el modelo. Las propiedades de muestras grandes del estimador se establecen formalmente y se proporciona una estimación constante de la matriz CV asimptótica. Seguidamente, utilizamos el método para estimar contundentemente el efecto de la interacción estratégica para decidir el gasto de escuelas locales.

摘要 : 我们对部分线性空间自回归模型提出了–种成对差异估计量, 采用异方差或/和空间相关误差项。与其他估计量, 例如包络准最大似然估计 (Su & Jin, 2010) 和半参量 GMM 估计 (Su, 2012) 相比, 我们的估计量具有计算复杂度低的优势, 尤其是用于估计模型中的有限维度参数时。我们已经建立了这种估计方法的大采样样本, 还提供对渐近线 CV 矩阵的–致估计。接着, 使用这种方法, 我们透彻分析了政策对本地学校支出的影响。     

A Generalized Method of Moments Estimator for a Spatial Panel Model with an Endogenous Spatial Lag and Spatial Moving Average Errors

Abstract

This paper proposes a new generalized method of moments (GMM) estimator for spatial panel models with spatial moving average errors combined with a spatially autoregressive dependent variable. Monte Carlo results are given suggesting that the GMM estimator is consistent. The estimator is applied to English real estate price data.     

A combined random effect and fixed effect forecast for panel data models

When some of the regressors in a panel data model are correlated with the random individual effects, the random effect (RE) estimator becomes inconsistent while the fixed effect (FE) estimator is consistent. Depending on the various degree of such correlation, we can combine the RE estimator and FE estimator to form a combined estimator which can be better than each of the FE and RE estimators. In this paper, we are interested in whether the combined estimator may be used to form a combined forecast to improve upon the RE forecast (forecast made using the RE estimator) and the FE forecast (forecast using the FE estimator) in out-of-sample forecasting. Our simulation experiment shows that the combined forecast does dominate the FE forecast for all degrees of endogeneity in terms of mean squared forecast errors (MSFE), demonstrating that the theoretical results of the risk dominance for the in-sample estimation carry over to the out-of-sample forecasting. It also shows that the combined forecast can reduce MSFE relative to the RE forecast for moderate to large degrees of endogeneity and for large degrees of heterogeneity in individual effects.     

Estimating and Forecasting with a Dynamic Spatial Panel Data Model*

This study focuses on the estimation and predictive performance of several estimators for the dynamic and autoregressive spatial lag panel data model with spatially correlated disturbances. In the spirit of Arellano and Bond (1991) and Mutl (2006) , a dynamic spatial generalized method of moments (GMM) estimator is proposed based on Kapoor, Kelejian and Prucha (2007) for the spatial autoregressive (SAR) error model. The main idea is to mix non‐spatial and spatial instruments to obtain consistent estimates of the parameters. Then, a linear predictor of this spatial dynamic model is derived. Using Monte Carlo simulations, we compare the performance of the GMM spatial estimator to that of spatial and non‐spatial estimators and illustrate our approach with an application to new economic geography.     

Small-sample Properties of Panel Spatial Autoregressive Models: Comparison of the Bayesian and Maximum Likelihood Methods

Abstract

This article considers autoregressive (SAR) models. We method to estimate the parameters of likelihood (ML) method. Our Bayesian by the Monte Carlo studies. We found the efficient as the ML estimators.     

带未知异方差广义空间模型的有效估计

空间单元大小以及其它的经济特征上的差异,常常会导致空间异方差问题。本文给出了广义空间模型异方差问题的三种不同估计方法。第一种方法是将异方差形式参数化,来克服自由度的不足,使用ML估计进行实现。而针对异方差形式未知时,分别采用了基于2SLS的迭代GMM估计和更加直接的MCMC抽样方法加以解决,特别是MCMC方法表现得更加优美。蒙特卡罗模拟表明,给定异方差形式条件下, ML估计通过异方差参数化的方法依然可以获得较好的估计效果。而异方差形式未知的情况下,另外两种方法随着样本数的增大时也可以与ML的估计结果趋于一致。     

Technical efficiency and firm heterogeneity in stochastic frontier models: application to smallholder maize farms in Ethiopia

This study estimates the technical efficiency measures of maize producing farm households in Ethiopia using stochastic frontier (SF) panel models that take different approaches to model firm heterogeneity. The efficiency measures are found to vary depending on how the estimation model treats both unobserved and observed firm heterogeneity. Estimates from the ‘true’ random effects (TRE) models that treat firm effects as heterogeneity are found to be identical to those from pooled SF models. Those results differ from the ones generated from the basic random effects (RE) models that treat firm effects as part of overall technical inefficiency. The more flexible generalised ‘true’ random effects (GTRE) model that splits the error term into firm effects, persistent inefficiency, transient inefficiency, and a random noise component indicates the presence of higher levels of persistent inefficiency than transient inefficiency. The basic truncated-normal RE model and heteroscedastic RE model yields similar efficiency estimates. The GTRE model predict persistent efficiency measures similar to those from the basic RE and flexible RE model with environmental variables incorporated in the variance function as well as in the deterministic production frontier. These results imply that the RE and GTRE panel models provide reliable efficiency estimates for our data compared to the TRE models. All the estimated SF models generate comparable production function parameters in terms of magnitude and sign. Overall, the results underscore the importance of scrutinising stochastic frontier models for their reliability of analytical results before drawing policy inferences.

     

On parameter estimation of partly observed bilinear discrete-time stochastic systems

The parameter estimation problem of a partly observed nonlinear discrete-time stochastic system is considered. The unobserved component of the system is a q-dimensional stable autoregressive process of the pth order with random parameters, observed in the presence of multiplicative and additive noises. The distributions of all the noises of the system are supposed to be unknown. The problem is to estimate the mean of the drifting parameters of the object and variances of the additive noises of the system. Asymptotic correlation estimators of all these parameters are investigated and sequential estimators with given mean square accuracy of the mean of the drifting autoregressive parameters are obtained.     

Second order longitudinal dynamic models with covariates: estimation and forecasting

In this paper, we propose an extension to the first-order branching process with immigration in the presence of fixed covariates and unobservable random effects. The extension permits the possibility that individuals from the second generation of the process may contribute to the total number of offsprings at time \(t\) by producing offsprings of their own. We will study the basic properties of the second order process and discuss a generalized quasilikelihood (GQL) estimation of the mean and variance parameters and the generalized method of moments estimation of the correlation parameters. We will discuss the asymptotic distribution of the GQL estimator by first deriving the influence curve of the estimator. For the fixed effects model we shall derive a forecasting function and the variance of the forecast error. The performance of the proposed estimators and forecasts will be examined through a simulation study.     

Ordinal-response GARCH models for transaction data: A forecasting exercise

We use numerous high-frequency transaction data sets to evaluate the forecasting performances of several dynamic ordinal-response time series models with generalized autoregressive conditional heteroscedasticity (GARCH). The specifications account for three components: leverage effects, in-mean effects and moving average error terms. We estimate the model parameters by developing Markov chain Monte Carlo algorithms. Our empirical analysis shows that the proposed ordinal-response GARCH models achieve better point and density forecasts than standard benchmarks.     

Space-varying Coefficient Simultaneous Autoregressive Models for the Structural Analysis of Residential Water Demand

Abstract

This study develops two space-varying coefficient simultaneous autoregressive (SVC-SAR) models for areal data and applies them to the discrete/continuous choice model, which is an econometric model based on the consumer's utility maximization problem. The space-varying coefficient model is a statistical model in which the coefficients vary depending on their location. This study introduces the simultaneous autoregressive model for the underlying spatial dependence across coefficients, where the coefficients for one observation are affected by the sum of those for the other observations. This model is named the SVC-SAR model. Because of its flexibility, we use the Bayesian approach and construct its estimation method based on the Markov chain Monte Carlo simulation. The proposed models are applied to estimate the Japanese residential water demand function, which is an example of the discrete/continuous choice model.     

Incorporating Transportation Network Structure in Spatial Econometric Models of Commodity Flows

Abstract

We use a spatial econometric extension of the traditional regression-based gravity model to model commodity flows, focusing on a formal methodology for incorporating information regarding the highway network into the spatial connectivity structure of the spatial autoregressive econometric model. We show that our simple approach to incorporating this information in the model produces improved model fit and higher likelihood function values. Empirical estimates of the relative importance of the different types of origin–destination connectivity between regions indicates that the strongest spatial autoregressive effects arise when both origin and destination regions have neighbouring regions located on the highway network.     

Optimal Control of Heteroscedastic Macroeconomic Models

This paper analyses the implications of heteroscedasticity for optimal macroeconomic policy and welfare. We find that changes in the variance structure driven by exogenous processes like generalized autoregressive conditional heteroscedasticity (GARCH) affect welfare but not the optimal feedback rule. However, changes in the variance structure driven by state‐dependent processes affect both. We also derive certainty‐equivalent transformations of state‐dependent volatility models that allow standard quadratic dynamic programming algorithms to be employed to study optimal policy. These results are illustrated numerically using a reduced‐form model of the US economy in which changes in volatility are driven by a GARCH process and the rate of inflation. Copyright © 2015 John Wiley & Sons, Ltd.     

基于双自适应Lasso惩罚的随机效应分位回归模型研究

研究目标：解决随机效应分位回归模型中固定效应和随机效应系数同时估计和选择问题。研究方法：对固定效应和随机效应系数同时实施自适应Lasso惩罚,并为参数估计设计交替迭代算法。研究发现：新方法不仅对随机误差分布具有较强的稳健性,而且在不同稀疏度模型下均有着良好的表现,尤其是在高维情形时。研究创新：本文提出的方法在对模型中重要自变量进行选择的同时能够充分考虑随机效应的影响;交替迭代算法不仅有效解决了需要选择两个惩罚参数的困境,而且收敛速度快。研究价值：为实际工作者对面板数据和纵向数据的分析提供了有效的建模方法。     

Heteroskedasticity-robust semi-parametric GMM estimation of a spatial model with space-varying coefficients

Heteroskedasticity-robust semi-parametric GMM estimation of a spatial model with space-varying coefficients. Spatial Economic Analysis. The spatial model with space-varying coefficients proposed by Sun et al. in 2014 has proved to be useful in detecting the location effects of the impacts of covariates as well as spatial interaction in empirical analysis. However, Sun et al.’s estimator is inconsistent when heteroskedasticity is present – a circumstance that is more realistic in certain applications. In this study, we propose a kind of semi-parametric generalized method of moments (GMM) estimator that is not only heteroskedasticity robust but also takes a closed form written explicitly in terms of observed data. We derive the asymptotic distributions of our estimators. Moreover, the results of Monte Carlo experiments show that the proposed estimators perform well in finite samples.     

On exact D-optimal designs with 2 two-level factors and n autocorrelated observations

In this paper we consider the exact D-optimal designs for estimation of the unknown parameters in the two factors, each at only two-level, main effects model with autocorrelated errors. The vector of the n random errors in the observed responses is assumed to follow a first-order autoregressive model (AR(1)). The exact D-optimal designs seek the optimal combinations of the design levels as well as the optimal run orders, so that the determinant of the information matrix of BLUEs for the unknown parameters is maximized. Bora-Senta and Moyssiadis (1999) gave some conjectures about the exact D-optimal designs based on their experience of several exhaustive searches. In this paper their conjectures are partially proved to be true.Received: January 2003 / Accepted: October 2003Partially supported by the National Science Council of Taiwan, R.O.C. under grant NSC 91-2115-M-008-013.Supported in part by the National Science Council of Taiwan, R.O.C. under grant NSC 89-2118-M-110-003.     

Hedonic Housing Prices in Paris: An Unbalanced Spatial Lag Pseudo‐Panel Model with Nested Random Effects

This paper estimates a hedonic housing model based on flats sold in the city of Paris over the period 1990–2003. This is done using maximum likelihood estimation, taking into account the nested structure of the data. Paris is historically divided into 20 arrondissements, each divided into four quartiers (quarters), which in turn contain between 15 and 169 blocks (îlot, in French) per quartier. This is an unbalanced pseudo?panel data containing 156,896 transactions. Despite the richness of the data, many neighborhood characteristics are not observed, and we attempt to capture these neighborhood spillover effects using a spatial lag model. Using likelihood ratio tests, we find significant spatial lag effects as well as significant nested random error effects. The empirical results show that the hedonic housing estimates and the corresponding marginal effects are affected by taking into account the nested aspects of the Paris housing data as well as the spatial neighborhood effects.Copyright © 2014 John Wiley & Sons, Ltd.     

Spatial Vector Autoregressions

Abstract

A spatial vector autoregressive model (SpVAR) is defined as a VAR which includes spatial as well as temporal lags among a vector of stationary state variables. SpVARs may contain disturbances that are spatially as well as temporally correlated. Although the structural parameters are not fully identified in SpVARs, contemporaneous spatial lag coefficients may be identified by weakly exogenous state variables. Dynamic spatial panel data econometrics is used to estimate SpVARs. The incidental parameter problem is handled by bias correction rather than more popular alternatives such as generalised methods of moments (GMM). The interaction between temporal and spatial stationarity is discussed. The impulse responses for SpVARs are derived, which naturally depend upon the temporal and spatial dynamics of the model. We provide an empirical illustration using annual spatial panel data for Israel. The estimated SpVAR is used to calculate impulse responses between variables, over time, and across space. Finally, weakly exogenous instrumental variables are used to identify contemporaneous spatial lag coefficients.