Multifactor Error Structure Research Articles

Short T dynamic panel data models with individual, time and interactive effects

SummaryThis paper proposes a transformed quasi‐maximum likelihood (TQML) estimator for short dynamic fixed effects panel data models allowing for interactive effects through a multifactor error structure. The proposed estimator is robust to the heterogeneity of the initial values and common unobserved effects, while at the same time allowing for standard fixed and time effects. It is applicable to both stationary and unit root cases. The order condition for identification of the number of interactive effects is established, and conditions are derived under which the parameters are locally identified. It is shown that global identification in the presence of the lagged dependent variable cannot be guaranteed. The TQML estimator is proven to be consistent and asymptotically normally distributed. A sequential multiple testing likelihood ratio procedure is also proposed for estimation of the number of factors which is shown to be consistent. Finite sample results obtained from Monte Carlo simulations show that the proposed procedure for determining the number of factors performs very well, and the TQML estimator has small bias and root mean square error (RMSE) and correct empirical size in most settings. The practical use of the TQML approach is demonstrated by means of two empirical illustrations from the literature on cross county crime rates and cross country growth regressions.

Nowcasting from cross‐sectionally dependent panels

SummaryThis paper builds a mixed‐frequency panel data model for nowcasting economic variables across many countries. The model extends the mixed‐frequency panel vector autoregression (MF‐PVAR) to allow for heterogeneous coefficients and a multifactor error structure to model cross‐sectional dependence. We propose a modified common correlated effects (CCE) estimation technique which performs well in simulations. The model is applied in two distinct settings: nowcasting gross domestic product (GDP) growth for a pool of advanced and emerging economies and nowcasting inflation across many European countries. Our method is capable of beating standard benchmark models and can produce updated nowcasts whenever data releases occur in any country in the panel.

Economic, social, and political determinants of environmental sustainability: Panel data evidence from NEXT eleven economies

This paper aims to investigate the impact of social, economic, and political variables on per capita ecological footprint consumption in the NEXT Eleven economies over the period 1984- 2018. The study utilized the dynamic heterogeneous panel estimators of Cross-Sectionally Augmented Auto-regressive Distributive Lag (CS-ARDL) along with the estimator with a multifactor error structure. The study also estimated the cross-Sectionally augmented distributed lag (CS-DL) model while for robustness check the augmented mean group (AMG) and cross-Sectionally augmented error correction method (CS-ECM) is also considered. The study finding maintains that the impact of GDP per capita, multifaceted phenomena of financial development, and military expenditure is positive and significant suggesting that a unit increase in these variables deteriorates the environment in the NEXT Eleven economies. In contrast, higher life expectancy and government stability improve the environment in the long run. The findings of the study suggest that eco-friendly technologies to be used in the production process, as well as projects using outdated technologies, should be discouraged along with the assurance of government stability and reduction of military expenditure in the NEXT Eleven economies.

Do the components of government expenditure affect the long-run dynamics of private investments? A heterogeneous panel analysis with a multifactor error structure

ABSTRACT Using data on 30 OECD countries over 1993–2019, this paper examines the ties between the components of government expenditure and the supply side of the private sector. We employ an ECM version of the novel dynamic common correlated effects estimator (DCCE) in order to account for nonstationarity, country-heterogeneity, and cross-sectional dependence. The estimates suggest that allocating public resources toward general public services and health positively affects the long-run dynamics of private investments. Conversely, rises in the expenditure on housing and social protection are associated with significant crowding-out effects.

The Impact of Climate Change on Economic Growth in Africa: An Econometric Analysis

African economics are characterized by strong economic dependency on sectors highly vulnerable to climate change that may make it more susceptible to climate change. This study aims to investigate the effect of climate change on both short and long-run economic growth in Africa using a panel of 34 selected African countries for the period of 1971–2019. The study relies on a dynamic panel model with a multifactor error structure; we estimate the model through the cross-sectionally augmented autoregressive distributed lag (CS-ARDL) and the cross-sectionally augmented distributed lag (CS-DL) approaches. We find clear evidence that climate change is negatively associated with economic growth in both the short and long-run. We establish that a rise in the mean temperature change with one degree would significantly reduce the real GDP per capita in Africa by 1.68% (2.45%) in the short-run (long-run), respectively

Testing Unemployment Hysteresis with Multi-Factor Panel Unit Root: Evidence from OECD Countries

Hysteresis is a dominant feature of unemployment in numerous countries. According to the hysteresis hypothesis, it is a well-known fact that high unemployment may persist and remain an economic threat in the long run if policy measures are not taken. In this study, it is tested whether the unemployment rates for 10 selected countries of the Organisation for Economic Co-operation and Development (OECD) (Belgium, Canada, Czech Republic, Estonia, France, Japan, Netherlands, Spain, Britain and the USA) contain unit root or not, in other words, whether the hysteresis effect is valid for these countries. For this purpose, this study utilises the concept of the multi-factor panel unit root test proposed by Pesaran, Smith and Yamagata. This method measures cross-section dependence through factors. The test analyses whether the unit root is valid or not, using information about a sufficient number of additional explanatory variables. The characteristic of these additional variables is that they must share a common factor with the variable whose stationarity is tested. It is accepted that this common factor causes cross-sectional dependence. We have taken tax wedge, trade union density and minimum wage as factors that cause cross-sectional dependency and affect unemployment hysteresis. In this test developed by the authors, in the case of a multi-factor error structure, the test procedure is completed by using the information contained in 3 additional variables. The study explores not only the validity of unemployment hysteresis but also the factors that affect the rigidity of the unemployment rate. However, the research was unable to encompass the entire OECD countries and all times because of the lack of data. The results showed that the hysteresis is valid for 10 selected OECD countries.

Interactive R&D spillovers: An estimation strategy based on forecasting-driven model selection

This paper proposes an estimation strategy that exploits recent non-parametric panel data methods that allow for a multifactor error structure and extends a recently proposed data-driven model-selection procedure, which has its roots in cross validation and aims to test whether two competing approximate models are equivalent in terms of their expected true error. We extend this procedure to a large panel data framework by using moving block bootstrap resampling techniques in order to preserve cross-sectional dependence in the bootstrapped samples. Such an estimation strategy is illustrated by revisiting an analysis of international technology diffusion. Model selection procedures clearly conclude in the superiority of a fully non-parametric (non-additive) specification over parametric and even semi-parametric (additive) specifications. This work also refines previous results by showing threshold effects, non-linearities, and interactions that are obscured in parametric specifications and which have relevant implications for policy.

Estimation and inference in heterogeneous spatial panels with a multifactor error structure

We develop a unifying econometric framework for the analysis of heterogeneous panel data models that can account for both spatial dependence and common factors. To tackle the challenging issues of endogeneity due to the spatial lagged term and the correlation between the regressors and factors, we propose the CCEX-IV estimation procedure that approximates factors by the cross-section averages of regressors and deals with the spatial endogeneity using the internal instrumental variables. We develop the individual and Mean Group estimators, and establish their consistency and asymptotic normality. By contrast, the Pooled estimator is shown to be inconsistent in the presence of parameter heterogeneity. Monte Carlo simulations confirm that the finite sample performance of the proposed estimators is quite satisfactory. We demonstrate the usefulness of our approach with an application to the house price growth for Local Authority Districts in the UK over 1997Q1–2016Q4.

Instrumental variable estimation of dynamic linear panel data models with defactored regressors and a multifactor error structure

This paper develops two instrumental variable (IV) estimators for dynamic panel data models with exogenous covariates and a multifactor error structure when both the cross-sectional and time series dimensions, N and T respectively, are large. The main idea is to project out the common factors from the exogenous covariates of the model, and to construct instruments based on defactored covariates. For models with homogeneous slope coefficients, we propose a two-step IV estimator. In the first step, the model is estimated consistently by employing defactored covariates as instruments. In the second step, the entire model is defactored based on estimated factors extracted from the residuals of the first-step estimation, after which an IV regression is implemented using the same instruments as in step one. For models with heterogeneous slope coefficients, we propose a mean-group-type estimator, which involves the averaging of first-step IV estimates of cross-section-specific slopes. The proposed estimators do not need to seek for instrumental variables outside the model. Furthermore, these estimators are linear, and therefore computationally robust and inexpensive. Notably, they require no bias correction. We investigate the finite sample performances of the proposed estimators and associated statistical tests, and the results show that the estimators and the tests perform well even for small N and T.

Estimation and inference for multi-dimensional heterogeneous panel datasets with hierarchical multi-factor error structure

Given the growing availability of large datasets and following recent research trends on multi-dimensional modelling, we develop three dimensional (3D) panel data models with hierarchical error components that allow for strong cross-section dependence through unobserved heterogeneous global and local factors. We propose consistent estimation procedures by extending the common correlated effects (CCE) estimation approach proposed by Pesaran (2006). The standard CCE approach needs to be modified in order to account for the hierarchical factor structure in 3D panels. Further, we provide asymptotic theory, including new nonparametric variance estimators. The validity of the proposed approach is confirmed by Monte Carlo simulation studies. We demonstrate the empirical usefulness of the proposed framework through an application to a 3D panel gravity model of bilateral export flows.

Short T Dynamic Panel Data Models with Individual and Interactive Time Effects

This paper proposes a transformed quasi maximum likelihood (TQML) estimator for short T dynamic fixed effects panel data models allowing for interactive effects through a multi-factor error structure. The proposed estimator is robust to the heterogeneity of the initial values and common unobserved effects, whilst at the same time allowing for standard fixed and time effects. It is applicable to both stationary and unit root cases. The order condition for identification of the number of interactive effects is established, and conditions are derived under which the parameters are almost surely locally identified. It is shown that global identification in the presence of the lagged dependent variable cannot be guaranteed. The TQML estimator is proven to be consistent and asymptotically normally distributed. A sequential multiple testing likelihood ratio procedure is also proposed for estimation of the number of factors which is shown to be consistent. Finite sample results obtained from Monte Carlo simulations show that the proposed procedure for determining the number of factors performs very well and the TQML estimator has small bias and RMSE, and correct empirical size in most settings. The practical use of the TQML approach is demonstrated by means of two empirical illustrations from the literature on cross county crime rates and cross country growth regressions.

Econometric Analysis of Panel Data Models with Multifactor Error Structures

Economic panel data often exhibit cross-sectional dependence, even after conditioning on appropriate explanatory variables. Two approaches to modeling cross-sectional dependence in economic panel data are often used: the spatial dependence approach, which explains cross-sectional dependence in terms of distance among units, and the residual multifactor approach, which explains cross-sectional dependence by common factors that affect individuals to a different extent. This article reviews the theory on estimation and statistical inference for stationary and nonstationary panel data with cross-sectional dependence, particularly for models with a multifactor error structure. Tests and diagnostics for testing for unit roots, slope homogeneity, cointegration, and the number of factors are provided. We discuss issues such as estimating common factors, dealing with parameter plethora in practice, testing for structural stability and nonlinearity, and dealing with model and parameter uncertainty. Finally, we address issues related to the use of these economic panel models.

Focused Information Criterion and Model Averaging for Large Panels With a Multifactor Error Structure

This article considers model selection and model averaging in panel data models with a multifactor error structure. We investigate the limiting distribution of the common correlated effects estimator in a local asymptotic framework and show that the trade-off between bias and variance remains in asymptotic theory. We then propose a focused information criterion and a plug-in averaging estimator for large heterogeneous panels and examine their theoretical properties. The novel feature of the proposed method is that it aims to minimize the sample analog of the asymptotic mean squared error and can be applied to cases irrespective of whether the rank condition holds or not. Monte Carlo simulations show that both proposed selection and averaging methods generally achieve lower mean squared error than other methods. The proposed methods are applied to examine possible causes that lead to the increasing wage inequality between high-skilled and low-skilled workers in the U.S. manufacturing industries.

Estimation and Inference for Multi-dimensional Heterogeneous Panel Datasets with Hierarchical Multi-factor Error Structure

Given the growing availability of large datasets and following recent research trends on multi-dimensional modelling, we develop three dimensional (3D) panel data models with hierarchical error components that allow for strong cross-sectional dependence through unobserved heterogeneous global and local factors. We propose consistent estimation procedures by extending the common correlated effects (CCE) estimation approach proposed by Pesaran (2006). The standard CCE approach needs to be modified in order to account for the hierarchical factor structure in 3D panels. Further, we provide the associated asymptotic theory, including new nonparametric variance estimators. The validity of the proposed approach is confirmed by Monte Carlo simulation studies. We also demonstrate the empirical usefulness of the proposed approach through an application to a 3D panel gravity model of bilateral export flows.

CCE estimation of factor‐augmented regression models with more factors than observables

SummaryThis paper considers estimation of factor‐augmented panel data regression models. One of the most popular approaches towards this end is the common correlated effects (CCE) estimator of Pesaran (Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica, 2006, 74, 967–1012, 2006). For the pooled version of this estimator to be consistent, either the number of observables must be larger than the number of unobserved common factors, or the factor loadings must be distributed independently of each other. This is a problem in the typical application involving only a small number of regressors and/or correlated loadings. The current paper proposes a simple extension to the CCE procedure by which both requirements can be relaxed. The CCE approach is based on taking the cross‐section average of the observables as an estimator of the common factors. The idea put forth in the current paper is to consider not only the average but also other cross‐section combinations. Asymptotic properties of the resulting combination‐augmented CCE (C3E) estimator are provided and tested in small samples using both simulated and real data.

Instrumental Variable Estimation of Dynamic Linear Panel Data Models with Defactored Regressors and a Multifactor Error Structure

This paper develops two instrumental variable (IV) estimators for dynamic panel data models with exogenous covariates and a multifactor error structure when both crosssectional and time series dimensions, N and T respectively, are large. Our approach initially projects out the common factors from the exogenous covariates of the model, and constructs instruments based on this defactored covariates. For models with homogeneous slope coe_cients, we propose a two-step IV estimator: the _rst step IV estimator is obtained using the defactored covariates as instruments. In the second step, the entire model is defactored by the extracted factors from the residuals of the _rst step estimation and subsequently obtain the _nal IV estimator. For models with heterogeneous slope coe _cients, we propose a mean-group type estimator, which is the cross-sectional average of _rst-step IV estimators of cross-section speci_c slopes. It is noteworthy that our estimators do not require us to seek for instrumental variables outside the model. Furthermore, our estimators are linear hence computationally robust and inexpensive. Moreover, they require no bias correction, and they are not subject to the small sample bias of least squares type estimators. The _nite sample performances of the proposed estimators and associated statistical tests are investigated, and the results show that the estimators and the tests perform well even for small N and T.

A two-stage estimator for heterogeneous panel models with common factors

The estimation in a stationary heterogeneous panel model where unknown common factors are present is considered. A two-stage estimator is proposed and compared to existing alternative methods for the estimation of slope parameters in panels with a multifactor error structure. The asymptotic properties of this estimator are provided alongside the comparison of its finite-sample properties with those of a range of estimators by means of Monte Carlo experiments. The two-stage estimator affords a greater computational simplicity with respect to existing iterative estimators that fail to achieve convergence in a relevant number of cases considered. The proposed estimator is employed in the analysis of the determinants of Euro-denominated bonds in a framework of a heterogeneous panel data model with multifactor error structure.

Testing slope homogeneity in panel data models with a multifactor error structure

Based on the common correlated effects (CCE) method and the Lagrange multiplier (LM) principle, this paper proposes a slope homogeneity test in a panel data model with a multifactor error structure that allows unobserved factors to be correlated with explanatory variables. The CCE method is first used to transform the regression equation to control for the unobserved common factors. Then, we adopt the idea of an LM-type test to conduct a homogeneity test. Our asymptotic analysis indicates that the test statistic is asymptotically normally distributed under the null hypothesis of homogeneity, regardless of the errors’ normality or homoskedasticity, as both N and T go to infinity, with \(T^{2/3}N^{-1}\rightarrow 0\) and \(T^{2}N^{-1}\rightarrow \infty \). It is also proved that the test is asymptotically powerful under a sequence of Pitman local alternatives. Monte Carlo simulations indicate that the test has good finite sample properties for all combinations of N and T, with the exception of a large N / T. The simulation results also suggest that the proposed test is robust to the errors’ non-normality and conditional heteroskedasticity.

Focused Information Criterion and Model Averaging for Large Panels with a Multifactor Error Structure

This paper considers model selection and model averaging in panel data models with a multifactor error structure. We investigate the limiting distribution of the common correlated effects estimator (Pesaran, 2006) in a local asymptotic framework and show that the trade-off between bias and variance remains in the asymptotic theory. We then propose a focused information criterion and a plug-in averaging estimator for large heterogeneous panels and examine their theoretical properties. The novel feature of the proposed method is that it aims to minimize the sample analog of the asymptotic mean squared error and can be applied to cases irrespective of whether the rank condition holds or not. Monte Carlo simulations show that both proposed selection and averaging methods generally achieve lower expected squared error than other methods. The proposed methods are applied to analyze the consumer response to gasoline taxes.

FDI and Economic Growth in European Transition Economies: Panel Data Analysis

The main purpose of this paper is to investigate relationship between foreign direct investment and economic growth based on 14 European Transition Economies for the period 1995 to 2014. Empirical model includes GDP per capita growth (% annual), foreign direct investment, net inflows (% GDP) and composite index of control variables which developed with PCA. Firstly homogeneity and cross sectional dependence among units are examined with Delta and tests and it is found that all series have heterogeneity and cross sectional dependency. For that reason, second generation Multifactor error structure (Pesaran et al, 2013) panel unit root test is used and it is also taken into account effect of unobserved common factors as a prerequisite of CCE Model just after proving the co-integration relationship and causality between variables via of Durbin-Hausmann (Westerlund, 2008) co-integration and Dumetriscu-Hurlin (2012) causality tests. Obtained results strongly support one-way causality from foreign direct investments and composite index to economic growth. Unfortunately, there is no causality between foreign direct investments and composite index of control variables. Our findings indicate that foreign direct investments contribute negatively to economic growth in contrast to theory points out but control variables contribute positively at European transition countries.