Multifactor Error Structure Research Articles

Fixed T dynamic panel data estimators with multifactor errors

ABSTRACTThis article analyzes a growing group of fixed T dynamic panel data estimators with a multifactor error structure. We use a unified notational approach to describe these estimators and discuss their properties in terms of deviations from an underlying set of basic assumptions. Furthermore, we consider the extendability of these estimators to practical situations that may frequently arise, such as their ability to accommodate unbalanced panels and common observed factors. Using a large-scale simulation exercise, we consider scenarios that remain largely unexplored in the literature, albeit being of great empirical relevance. In particular, we examine (i) the effect of the presence of weakly exogenous covariates, (ii) the effect of changing the magnitude of the correlation between the factor loadings of the dependent variable and those of the covariates, (iii) the impact of the number of moment conditions on bias and size for GMM estimators, and finally (iv) the effect of sample size. We apply each of these estimators to a crime application using a panel data set of local government authorities in New South Wales, Australia; we find that the results bear substantially different policy implications relative to those potentially derived from standard dynamic panel GMM estimators. Thus, our study may serve as a useful guide to practitioners who wish to allow for multiplicative sources of unobserved heterogeneity in their model.

Heterogeneity in the Effect of Common Shocks on Healthcare Expenditure Growth.

Healthcare expenditure growth is affected by important unobserved common shocks such as technological innovation, changes in sociological factors, shifts in preferences, and the epidemiology of diseases. While common factors impact in principle all countries, their effect is likely to differ across countries. To allow for unobserved heterogeneity in the effects of common shocks, we estimate a panel data model of healthcare expenditure growth in 34 OECD countries over the years 1980 to 2012, where the usual fixed or random effects are replaced by a multifactor error structure. We address model uncertainty with Bayesian model averaging, to identify a small set of robust expenditure drivers from 43 potential candidates. We establish 16 significant drivers of healthcare expenditure growth, including growth in GDP per capita and in insurance premiums, changes in financing arrangements and some institutional characteristics, expenditures on pharmaceuticals, population ageing, costs of health administration, and inpatient care. Our approach allows us to provide robust evidence to policy makers on the drivers that were most strongly associated with the growth in healthcare expenditures over the past 32years. Copyright © 2016 John Wiley & Sons, Ltd.

Estimation of heterogeneous panels with structural breaks

This paper extends Pesaran’s (2006) work on common correlated effects (CCE) estimators for large heterogeneous panels with a general multifactor error structure by allowing for unknown common structural breaks. Structural breaks due to new policy implementation or major technological shocks, are more likely to occur over a longer time span. Consequently, ignoring structural breaks may lead to inconsistent estimation and invalid inference. We propose a general framework that includes heterogeneous panel data models and structural break models as special cases. The least squares method proposed by Bai (1997a, 2010) is applied to estimate the common change points, and the consistency of the estimated change points is established. We find that the CCE estimator have the same asymptotic distribution as if the true change points were known. Additionally, Monte Carlo simulations are used to verify the main results of this paper.

Panicca: Panic on Cross‐Section Averages

SummaryThe cross‐section average (CA) augmentation approach of Pesaran (A simple panel unit root test in presence of cross‐section dependence. Journal of Applied Econometrics 2007; 22: 265–312) and Pesaran et al. (Panel unit root test in the presence of a multifactor error structure. Journal of Econometrics 2013; 175: 94–115), and the principal components‐based panel analysis of non‐stationarity in idiosyncratic and common components (PANIC) of Bai and Ng (A PANIC attack on unit roots and cointegration. Econometrica 2004; 72: 1127–1177; Panel unit root tests with cross‐section dependence: a further investigation. Econometric Theory 2010; 26: 1088–1114) are among the most popular ‘second‐generation’ approaches for cross‐section correlated panels. One feature of these approaches is that they have different strengths and weaknesses. The purpose of the current paper is to develop PANICCA, a combined approach that exploits the strengths of both CA and PANIC. Copyright © 2015 John Wiley & Sons, Ltd.

A Simple Panel Unit‐Root Test with Smooth Breaks in the Presence of a Multifactor Error Structure

AbstractThis paper extends the cross‐sectionally augmented panel unit‐root test (CIPS) developed by Pesaran et al. (2013, Journal of Econometrics, Vol. 175, pp. 94–115) to allow for smoothing structural changes in deterministic terms modelled by a Fourier function. The proposed statistic is called the break augmented CIPS (BCIPS) statistic. We show that the non‐standard limiting distribution of the (truncated) BCIPS statistic exists and tabulate its critical values. Monte‐Carlo experiments point out that the sizes and powers of the BCIPS statistic are generally satisfactory as long as the number of time periods, T, is not less than fifty. The BCIPS test is then applied to examine the validity of long‐run purchasing power parity.

IV estimation of panels with factor residuals

This paper proposes a new instrumental variables approach for consistent and asymptotically efficient estimation of panel data models with weakly exogenous or endogenous regressors and residuals generated by a multi-factor error structure. In this case, the standard dynamic panel estimators fail to provide consistent estimates of the parameters. The novelty of our approach is that we introduce new parameters to represent the unobserved covariances between the instruments and the factor component of the residual; these parameters are estimable when N is large. Some important estimation and identification issues are studied in detail. The finite sample performance of the proposed estimators is investigated using simulated data. The results show that the method produces reliable estimates of the parameters over several parameterisations.

Varying Responses to Common Shocks and Complex Cross-Sectional Dependence: Dynamic Multilevel Modeling with Multifactor Error Structures for Time-Series Cross-Sectional Data

Multifactor error structures utilize factor analysis to deal with complex cross-sectional dependence in Time-Series Cross-Sectional data caused by cross-level interactions. The multifactor error structure specification is a generalization of the fixed-effects model. This article extends the existing multifactor error models from panel econometrics to multilevel modeling, from linear setups to generalized linear models with the probit and logistic links, and from assuming serial independence to modeling the error dynamics with an autoregressive process. I develop Markov Chain Monte Carlo algorithms mixed with a rejection sampling scheme to estimate the multilevel multifactor error structure model with apth-order autoregressive process in linear, probit, and logistic specifications. I conduct several Monte Carlo studies to compare the performance of alternative specifications and approaches with varying degrees of data complication and different sample sizes. The Monte Carlo studies provide guidance on when and how to apply the proposed model. An empirical application sovereign default demonstrates how the proposed approach can accommodate a complex pattern of cross-sectional dependence and helps answer research questions related to units' sensitivity or vulnerability to systemic shocks.

Drugs and Violence in Afghanistan: A Panel Var With Unobserved Common Factor Analysis

This paper addresses the relationship between the level of violence and the opium market in Afghanistan’s provinces. We first provide an overview of the nature and extent of the Afghan drug trafficking. This is followed by a vector autoregressive analysis of the nexus opium-insurgency activities using monthly time-series data on opium prices and the number of security incidents for 15 Afghan provinces over the period 2004–2009. We use a multifactor error structure, the common correlated effect, to include unobservable common factors; Impulse Response functions to describe the time path of the dependent variables in response to shocks; and the mean group estimator to summarize our results across the provinces. Results suggest a conflict-induced reduction in opium prices, while the reverse opium-violence mechanism is mostly negligible. Moreover, unobservable common factors are the main drivers of opium prices and violence.

A Simple Panel Unit-Root Test with Smooth Breaks in the Presence of a Multifactor Error Structure

This paper proposes a new simple panel unit-root test by extending the cross-sectionally augmented panel unit-root test (CIPS) developed by Pesaran et al. (2013) to allow for smoothing structural changes in deterministic terms, approximated by a Fourier series. The proposed statistic is the simple average of the individual statistics constructed from the breaks and cross-sectional dependence augmented Dickey-Fuller (BCADF) regression and is called the BCIPS statistic. We initially develop the tests by assuming that the number of factors in the model is known and show that the limiting distribution of the BCADF statistic is free of nuisance parameters. The nonstandard limiting distribution of the (truncated) BCIPS statistic is also shown to exist and its critical values are tabulated. Monte-Carlo experiments point out that the sizes and powers of the BCIPS statistic are generally satisfactory as long as T is greater than or equal to fifty and a hundred, respectively. By using two different methods to determine the number of factors, both the BCIPS and CIPS tests are applied to examine the validity of long-run purchasing power parity. The proposed test complements the panel unit-root tests with breaks using dummy variables.

On the estimation and inference in factor-augmented panel regressions with correlated loadings

In an influential paper, Pesaran [Pesaran, M.H. (2006). Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica 74, 967–1012] proposes a very simple estimator of factor-augmented regressions that has since then become very popular. In this note we demonstrate how the presence of correlated factor loadings can render this estimator inconsistent.

Panel unit root tests in the presence of a multifactor error structure

This paper extends the cross-sectionally augmented panel unit root test (CIPS) proposed by Pesaran (2007) to the case of a multifactor error structure, and proposes a new panel unit root test based on a simple average of cross-sectionally augmented Sargan–Bhargava statistics (CSB). The basic idea is to exploit information regarding the m unobserved factors that are shared by k observed time series in addition to the series under consideration. Initially, we develop the tests assuming that m0, the true number of factors, is known and show that the limit distribution of the tests does not depend on any nuisance parameters, so long as k≥m0−1. Small sample properties of the tests are investigated by Monte Carlo experiments and are shown to be satisfactory. Particularly, the proposed CIPS and CSB tests have the correct size for all combinations of the cross section (N) and time series (T) dimensions considered. The power of both tests rises with N and T, although the CSB test performs better than the CIPS test for smaller sample sizes. The various testing procedures are illustrated with empirical applications to real interest rates and real equity prices across countries.

Least squares estimation of a panel data model with multifactor error structure and endogenous covariates

We propose a method for estimating the slope parameter in an interactive effects panel data model with endogenous loadings and factors, and endogenous regressors.

Large panels with common factors and spatial correlation

This paper considers methods for estimating the slope coefficients in large panel data models that are robust to the presence of various forms of error cross-section dependence. It introduces a general framework where error cross-section dependence may arise because of unobserved common effects and/or error spill-over effects due to spatial or other forms of local dependencies. Initially, this paper focuses on a panel regression model where the idiosyncratic errors are spatially dependent and possibly serially correlated, and derives the asymptotic distributions of the mean group and pooled estimators under heterogeneous and homogeneous slope coefficients, and for these estimators proposes non-parametric variance matrix estimators. The paper then considers the more general case of a panel data model with a multifactor error structure and spatial error correlations. Under this framework, the Common Correlated Effects (CCE) estimator, recently advanced by Pesaran (2006), continues to yield estimates of the slope coefficients that are consistent and asymptotically normal. Small sample properties of the estimators under various patterns of cross-section dependence, including spatial forms, are investigated by Monte Carlo experiments. Results show that the CCE approach works well in the presence of weak and/or strong cross-sectionally correlated errors.

Panels with non-stationary multifactor error structures

The presence of cross-sectionally correlated error terms invalidates much inferential theory of panel data models. Recently, work by Pesaran (2006) has suggested a method which makes use of cross-sectional averages to provide valid inference in the case of stationary panel regressions with a multifactor error structure. This paper extends this work and examines the important case where the unobservable common factors follow unit root processes. The extension to I ( 1 ) processes is remarkable on two counts. First, it is of great interest to note that while intermediate results needed for deriving the asymptotic distribution of the panel estimators differ between the I ( 1 ) and I ( 0 ) cases, the final results are surprisingly similar. This is in direct contrast to the standard distributional results for I ( 1 ) processes that radically differ from those for I ( 0 ) processes. Second, it is worth noting the significant extra technical demands required to prove the new results. The theoretical findings are further supported for small samples via an extensive Monte Carlo study. In particular, the results of the Monte Carlo study suggest that the cross-sectional-average-based method is robust to a wide variety of data generation processes and has lower biases than the alternative estimation methods considered in the paper.

Panel Unit Root Tests in the Presence of a Multifactor Error Structure

This paper extends the cross sectionally augmented panel unit root test proposed by Pesaran (2007) to the case of a multifactor error structure. The basic idea is to exploit information regarding the unobserved factors that are shared by other time series in addition to the variable under consideration. Importantly, our test procedure only requires specification of the maximum number of factors, in contrast to other panel unit root tests based on principal components that require in addition the estimation of the number of factors as well as the factors themselves. Small sample properties of the proposed test are investigated by Monte Carlo experiments, which suggest that it controls well for size in almost all cases, especially in the presence of serial correlation in the error term, contrary to alternative test statistics. Empirical applications to Fisher's inflation parity and real equity prices across different markets illustrate how the proposed test works in practice.

Panel Unit Root Tests in the Presence of a Multifactor Error Structure

Panel Unit Root Tests in the Presence of a Multifactor Error Structure

Real options — delay vs. pre-emption: Do industrial characteristics matter?

This paper presents an empirical study of the channels of influence from uncertainty to fixed investment suggested by real options theory. Using panel data from the Confederation of British Industry (CBI) Industrial Trends Survey, we report OLS estimates of the impact of uncertainty on investment where the regressors are augmented by cross-sectional averages of the dependent variable and of the individual specific regressors, as recently suggested by Pesaran [Pesaran, M.H., 2006. Estimation and Inference in large heterogeneous panels with a multifactor error structure. Econometrica 74, 967–1012]. The cross-industry pattern of results is checked for consistency with the pattern predicted by real options theory, using a specially constructed data set of industrial characteristics. We find that irreversibility is able to predict the pattern detected, but only when combined with a measure of the information advantage of delay. There is also evidence for expansion options effects; industries with high R&D and advertising intensities tend to have positive uncertainty effects.

Large Panels with Common Factors and Spatial Correlations

This paper considers the statistical analysis of large panel data sets where even after conditioning on common observed effects the cross section units might remain dependently distributed. This could arise when the cross section units are subject to unobserved common effects and/or if there are spill over effects due to spatial or other forms of local dependencies. The paper provides an overview of the literature on cross section dependence, introduces the concepts of time-specific weak and strong cross section dependence and shows that the commonly used spatial models are examples of weak cross section dependence. It is then established that the Common Correlated Effects (CCE) estimator of panel data model with a multifactor error structure, recently advanced by Pesaran (2006), continues to provide consistent estimates of the slope coefficient, even in the presence of spatial error processes. Small sample properties of the CCE estimator under various patterns of cross section dependence, including spatial forms, are investigated by Monte Carlo experiments. Results show that the CCE approach works well in the presence of weak and/or strong cross sectionally correlated errors. We also explore the role of certain characteristics of spatial processes in determining the performance of CCE estimators, such as the form and intensity of spatial dependence, and the sparseness of the spatial weight matrix.

Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure

This paper presents a new approach to estimation and inference in panel data models with a general multifactor error structure. The unobserved factors and the individual-specific errors are allowed to follow arbitrary stationary processes, and the number of unobserved factors need not be estimated. The basic idea is to filter the individual-specific regressors by means of cross-section averages such that asymptotically as the cross-section dimension (N) tends to infinity, the differential effects of unobserved common factors are eliminated. The estimation procedure has the advantage that it can be computed by least squares applied to auxiliary regressions where the observed regressors are augmented with cross-sectional averages of the dependent variable and the individual-specific regressors. A number of estimators (referred to as common correlated effects (CCE) estimators) are proposed and their asymptotic distributions are derived. The small sample properties of mean group and pooled CCE estimators are investigated by Monte Carlo experiments, showing that the CCE estimators have satisfactory small sample properties even under a substantial degree of heterogeneity and dynamics, and for relatively small values of N and T.

Panels with Nonstationary Multifactor Error Structures

The presence of cross-sectionally correlated error terms invalidates much inferential theory of panel data models. Recently work by Pesaran (2006) has suggested a method which makes use of cross-sectional averages to provide valid inference for stationary panel regressions with multifactor error structure. This paper extends this work and examines the important case where the unobserved common factors follow unit root processes and could be cointegrated. It is found that the presence of unit roots does not affect most theoretical results, which continue to hold irrespective of the integration and the cointegration properties of the unobserved factors. This finding is further supported for small samples via an extensive Monte Carlo study. In particular, the results of the Monte Carlo study suggest that the cross-sectional average based method is robust to a wide variety of data generation processes and has lower biases than all of the alternative estimation methods considered in the paper.