Remainder Disturbances Research Articles

Forecasting with unbalanced panel data

AbstractThis paper derives the best linear unbiased prediction (BLUP) for an unbalanced panel data model. Starting with a simple error component regression model with unbalanced panel data and random effects, it generalizes the BLUP derived by Taub (Journal of Econometrics, 1979, 10, 103–108) to unbalanced panels. Next it derives the BLUP for an unequally spaced panel data model with serial correlation of the AR(1) type in the remainder disturbances considered by Baltagi and Wu (Econometric Theory, 1999, 15, 814–823). This in turn extends the BLUP for a panel data model with AR(1) type remainder disturbances derived by Baltagi and Li (Journal of Forecasting, 1992, 11, 561–567) from the balanced to the unequally spaced panel data case. The derivations are easily implemented and reduce to tractable expressions using an extension of the Fuller and Battese (Journal of Econometrics, 1974, 2, 67–78) transformation from the balanced to the unbalanced panel data case.

Driving factors of material consumption in European countries – spatial panel data analysis

ABSTRACT The aim of this study is to identify the main drivers of material consumption measured by DMC per capita. Due to data availability, the study is limited to European countries in 2000–2016. We analyse panel data compiled from the Eurostat database. At first, we estimated the fixed-effects model with robust standard errors [Arellano, Manuel. 2003. Panel Data Econometrics. Oxford: Oxford University Press]. Then we applied the method proposed by Baltagi and Wu [1999. “Unequally Spaced Panel Data Regressions with AR(1) Disturbances.” Econometric Theory 15: 814–823] for unequally spaced panel data regression models with AR(1) remainder disturbances (implemented in Stata – xtregar). Finally, we estimated the spatial autocorrelation model (SAR) to account for spatial dependencies in the data (Stata – xsmle). Results show the strong coupling of material consumption and GDP per capita. Another strongly significant factors are final energy consumption per capita and the share of the construction sector in GDP. We received mixed results on the impact of investments and R&D expenditures depending on model specification.

Generalized spatial autocorrelation in a panel-probit model with an application to exporting in China

This paper proposes a generalized spatial panel-data probit model with spatial autocorrelation of the dependent variable, the time-invariant individual shocks, and the remainder disturbances. It proposes its estimation with a Bayesian Markov chain Monte Carlo procedure. Simulation results show that the proposed estimation method performs well in small- to medium-sized samples. This method is then applied to the analysis of export-market participation of 1451 Chinese firms between 2002 and 2006 in the prefecture-level city of Wenzhou in the province of Zhejiang. Empirical results show that two of the three forms of the hypothesized spatial autocorrelation are significant, namely the spatial lag for the dependent variable and the time-invariant firm-specific shocks, but not the time-variant shocks. Ignoring any of these significant spatial effects would lead to misspecification.

Disturbance-Observer-Based Global Sliding Mode Controller for Electro-Hydraulic System

In order to improve the system performance affected by the model uncertainties and loading moments, a robust tracking controller is proposed for electro-hydraulic servo system. Considering the conventional disturbance observer (DOB) lacks the enough ability in estimating the whole disturbances in electro-hydraulic servo system, one global sliding mode controller (GSMC) is proposed based on the inner-loop DOB. The GSMC not only suppresses the remainder disturbances which cannot be observed by DOB, but also realizes the position tracking of electro-hydraulic servo system. Simulation results present that, compared with other traditional control schemes, the proposed robust control scheme can ensure electro-hydraulic servo system possess higher tracking precision. Moreover, there is no obvious high-frequency chattering at control input, therefore it also possesses higher application value.

Detection of Outliers in Panel Data of Intervention Effects Model Based on Variance of Remainder Disturbance

The presence of outliers can result in seriously biased parameter estimates. In order to detect outliers in panel data models, this paper presents a modeling method to assess the intervention effects based on the variance of remainder disturbance using an arbitrary strictly positive twice continuously differentiable function. This paper also provides a Lagrange Multiplier (LM) approach to detect and identify a general type of outlier. Furthermore, fixed effects models and random effects models are discussed to identify outliers and the corresponding LM test statistics are given. The LM test statistics for an individual-based model to detect outliers are given as a particular case. Finally, this paper performs an application using panel data and explains the advantages of the proposed method.

Estimation and prediction in the random effects model with AR() remainder disturbances

Abstract This paper considers the problem of estimation and forecasting in a panel data model with random individual effects and AR( p ) remainder disturbances. It utilizes a simple exact transformation for the AR( p ) time series process derived by Baltagi and Li (1994) and obtains the generalized least squares estimator for this panel model as a least squares regression. This exact transformation is also used in conjunction with Goldberger’s (1962) result to derive an analytic expression for the best linear unbiased predictor. The performance of this predictor is investigated using Monte Carlo experiments and illustrated using an empirical example.

The Hausman–Taylor panel data model with serial correlation

This paper modifies the Hausman and Taylor (1981) panel data estimator to allow for serial correlation in the remainder disturbances. It demonstrates the gains in efficiency of this estimator versus the standard panel data estimators that ignore serial correlation using Monte Carlo experiments.

Testing for Cross-Sectional Dependence in a RandomEffects Model

This paper extends and generalizes the works of [1,2] to allow for cross-sectional dependence in the context of a two-way error components model and consequently develops LM test. The cross-sectional dependence follows the first order spatial autoregressive error (SAE) process and is imposed on the remainder disturbances. It is important to note that this paper does not consider alternative forms of spatial lag dependence other than SAE. It also does not allow for endogeneity of the regressors and requires the normality assumption to derive the LM test.

Prediction in the Random Effects Model with MA (q) Remainder Disturbances

This paper considers the problem of forecasting in a panel data model with random individual effects and MA (q) remainder disturbances. It utilizes a recursive transformation for the MA (q) process derived by Baltagi and Li (Econometric Theory 1994; 10: 396–408) which yields a simple generalized least-squares estimator for this model. This recursive transformation is used in conjunction with Goldberger's result (Journal of the American Statistical Association 1962; 57: 369–375) to derive an analytic expression for the best linear unbiased predictor, for the ith cross-sectional unit, s periods ahead. Copyright © 2011 John Wiley & Sons, Ltd.

Forecasting with spatial panel data

Various forecasts using panel data with spatial error correlation are compared using Monte Carlo experiments. The true data generating process is assumed to be a simple error component regression model with spatial remainder disturbances of the autoregressive or moving average type. The best linear unbiased predictor is compared with other forecasts ignoring spatial correlation, or ignoring heterogeneity due to the individual effects. In addition, the root mean squared error performance of these forecasts is examined under misspecification of the spatial error process, various spatial weight matrices, and heterogeneous rather than homogeneous panel data models.

Forecasting with Spatial Panel Data

This paper compares various forecasts using panel data with spatial error correlation. The true data generating process is assumed to be a simple error component regression model with spatial remainder disturbances of the autoregressive or moving average type. The best linear unbiased predictor is compared with other forecasts ignoring spatial correlation, or ignoring heterogeneity due to the individual effects, using Monte Carlo experiments. In addition, we check the performance of these forecasts under misspecification of the spatial error process, various spatial weight matrices, and heterogeneous rather than homogeneous panel data models.

Asymptotic properties of estimators for the linear panel regression model with random individual effects and serially correlated errors: the case of stationary and non-stationary regressors and residuals

Summary This paper studies the asymptotic properties of standard panel data estimators in a simple panel regression model with random error component disturbances. Both the regressor and the remainder disturbance term are assumed to be autoregressive and possibly non-stationary. Asymptotic distributions are derived for the standard panel data estimators including ordinary least squares (OLS), fixed effects (FE), first-difference (FD) and generalized least squares (GLS) estimators when both T and n are large. We show that all the estimators have asymptotic normal distributions and have different convergence rates dependent on the non-stationarity of the regressors and the remainder disturbances. We show using Monte Carlo experiments that the loss in efficiency of the OLS, FE and FD estimators relative to true GLS can be substantial.

Detecting and identifying interventions with the Whittle spectral approach in a long memory panel data model

This article provides a procedure for the detection and identification of outliers in the spectral domain where the Whittle maximum likelihood estimator of the panel data model proposed by Chen [W.D. Chen, Testing for spurious regression in a panel data model with the individual number and time length growing, J. Appl. Stat. 33(88) (2006b), pp. 759–772] is implemented. We extend the approach of Chang and co-workers [I. Chang, G.C. Tiao, and C. Chen, Estimation of time series parameters in the presence of outliers, Technometrics 30 (2) (1988), pp. 193–204] to the spectral domain and through the Whittle approach we can quickly detect and identify the type of outliers. A fixed effects panel data model is used, in which the remainder disturbance is assumed to be a fractional autoregressive integrated moving-average (ARFIMA) process and the likelihood ratio criterion is obtained directly through the modified inverse Fourier transform. This saves much time, especially when the estimated model implements a huge data-set. Through Monte Carlo experiments, the consistency of the estimator is examined by growing the individual number N and time length T, in which the long memory remainder disturbances are contaminated with two types of outliers: additive outlier and innovation outlier. From the power tests, we see that the estimators are quite successful and powerful. In the empirical study, we apply the model on Taiwan's computer motherboard industry. Weekly data from 1 January 2000 to 31 October 2006 of nine familiar companies are used. The proposed model has a smaller mean square error and shows more distinctive aggressive properties than the raw data model does.

Asymptotic Properties of Estimators for the Linear Panel Regression Model with Individual Effects and Serially Correlated Errors: The Case of Stationary and Non-Stationary Regressors and Residuals

This paper studies the asymptotic properties of standard panel data estimators in a simple panel regression model with error component disturbances. Both the regressor and the remainder disturbance term are assumed to be autoregressive and possibly non-stationary. Asymptotic distributions are derived for the standard panel data estimators including ordinary least squares, fixed effects, first-difference, and generalized least squares (GLS) estimators when both T and n are large. We show that all the estimators have asymptotic normal distributions and have different convergence rates dependent on the non-stationarity of the regressors and the remainder disturbances. We show using Monte Carlo experiments that the loss in efficiency of the OLS, FE and FD estimators relative to true GLS can be substantial.

Testing for spurious regression in a panel data model with the individual number and time length growing

This article shows a test for the spurious regression problem in a panel data model with a growing individual number and time series length. In the estimation, tapers are used and the integrated order for the remainder disturbance is extended to a real number; at the same time, the spurious regression problem can be detected without prior knowledge. Through Monte Carlo experiments, we examine the consistent estimators by various sizes of time length and individual number, in which the remainder disturbance is assumed to be either stationary or non-stationary. In addition, the asymptotic normality properties are discussed with a quasi log-likelihood function. From the power tests we can see that the estimators are quite successful and powerful.

An approximate likelihood function for panel data with a mixed ARMA(p, q) remainder disturbance model

Abstract. An approximate likelihood function for panel data with an autoregressive moving‐average (ARMA)(p, q) model remainder disturbance is presented and Whittle's approximate maximum likelihood estimator (MLE) is used to yield an asymptotic estimator. Although an asymptotic approach, the power test is quite successful for estimating and testing. In this approach, we do not need to calculate the transformation matrix in exact form. Through the Riemann sum approach, we can construct a simple approximate concentrated likelihood function. In addition, the model is also extended to the restricted maximum likelihood (REML) function, in which the package of Gilmour, Thompson and Cullis [Biometrics (1995) Vol. 51, pp. 1440–1450] is applied without difficulty. In the case study, we implement the model on the characteristic line for the investment analysis of Taiwanese computer motherboard makers.

BLUP in the panel regression model with spatially and serially correlated error components

This paper considers a panel data regression model with spatial and serial correlation. We derive the best linear unbiased predictors for a spatial error component model including remainder disturbances that follow an AR(1) process, an AR(2) process, a special AR(4) process for quarterly data or an MA(1) process.

Monte Carlo Results on Pure and Pretest Estimators of an Error Component Model with Autocorrelated Disturbances

A Monte Carlo study is used to compare the finite sample relative efficiency of a number of pure and pre-test estimators for an error component model with first-order autocorrelated remainder disturbances.

Estimating Error Component Models With General MA(q) Disturbances

This paper provides a simple estimation method for an error component regression model with general MA(q) remainder disturbances. The estimation method utilizes the transformation derived by Baltagi and Li [3] for an error component model with autoregressive remainder disturbances, and a standard orthogonalizing algorithm for the general MA(q) model. This estimation method is computationally simple utilizing only least-squares regressions. This is important for panel data regressions where brute force GLS is in many cases not feasible.This estimation method performs well relative to true GLS in Monte-Carlo experiments.

Prediction in the one‐way error component model with serial correlation

AbstractThis paper derives the best linear unbiased predictor for a one‐way error component model with serial correlation. A transformation derived by Baltagi and Li (1991) is used to show how the forecast can be easily computed from the GLS estimates and residuals. This result is useful for panel data applications which utilize the error component specification and exhibit serial correlation in the remainder disturbance term. Analytical expressions for this predictor are given when the remainder disturbances follow (1) an AR(1) process, (2) an AR(2) process, (3) a special AR(4) process for quarterly data, and (4) an MA(1) process.