Efficient estimation of factor models with time and cross‐sectional dependence

This paper studies the efficient estimation of large‐dimensional factor models with both time and cross‐sectional dependence assuming (N,T) separability of the covariance matrix. The asymptotic distribution of the estimator of the factor and factor‐loading space under factor stationarity is derived and compared to that of the principal component (PC) estimator. The paper also considers the case when factors exhibit a unit root. We provide feasible estimators and show in a simulation study that they are more efficient than the PC estimator in finite samples. In application, the estimation procedure is employed to estimate the Lee–Carter model and life expectancy is forecast. The Dutch gender gap is explored and the relationship between life expectancy and the level of economic development is examined in a cross‐country comparison.     

Diagnostic Tests of Cross‐section Independence for Limited Dependent Variable Panel Data Models*

This article considers the problem of testing for cross‐section independence in limited dependent variable panel data models. It derives a Lagrangian multiplier (LM) test and shows that in terms of generalized residuals of Gourieroux et al. (1987) it reduces to the LM test of Breusch and Pagan (1980) . Because of the tendency of the LM test to over‐reject in panels with large N (cross‐section dimension), we also consider the application of the cross‐section dependence test (CD) proposed by Pesaran (2004) . In Monte Carlo experiments it emerges that for most combinations of N and T the CD test is correctly sized, whereas the validity of the LM test requires T (time series dimension) to be quite large relative to N. We illustrate the cross‐sectional independence tests with an application to a probit panel data model of roll‐call votes in the US Congress and find that the votes display a significant degree of cross‐section dependence.     

SPATIAL LIMITED DEPENDENT VARIABLE MODELS: A REVIEW FOCUSED ON SPECIFICATION,ESTIMATION, AND HEALTH ECONOMICS APPLICATIONS

Modeling individual choices is one of the main aim in microeconometrics. Discrete choice models have been widely used to describe economic agents' utility functions and most of them play a paramount role in applied health economics. On the other hand, spatial econometrics collects a series of econometric tools, which are particularly useful when we deal with spatially distributed data sets. Accounting for spatial dependence can avoid inconsistency problems of the commonly used statistical estimators. However, the complex structure of spatial dependence in most of the nonlinear models still precludes a large diffusion of these spatial techniques. The purpose of this paper is then twofold. The former is to review the main methodological problems and their different solutions in spatial nonlinear modeling. The latter is to review their applications to health issues, especially those appeared in the last few years, by highlighting the main reasons why spatial discrete neighboring effects should be considered and suggesting possible future lines of development in this emerging field. Particular attention has been paid to cross‐sectional spatial discrete choice modeling. However, discussions on the main methodological advancements in other spatial limited dependent variable models and spatial panel data models are also included.     

Small‐sample bias in synthetic cohort models of labor supply

This paper investigates small‐sample biases in synthetic cohort models (repeated cross‐sectional data grouped at the cohort and year level) in the context of a female labor supply model. I use the Current Population Survey to compare estimates when group sizes are extremely large to those that arise from randomly drawing subsamples of observations from the large groups. I augment this approach with Monte Carlo analysis so as to precisely quantify biases and coverage rates. In this particular application, thousands of observations per group are required before small‐sample issues can be ignored in estimation and sampling error leads to large downward biases in the estimated income elasticity. Copyright © 2007 John Wiley & Sons, Ltd.     

Half‐panel jackknife fixed‐effects estimation of linear panels with weakly exogenous regressors

This paper considers estimation and inference in linear panel regression models with lagged dependent variables and/or other weakly exogenous regressors when N (the cross‐section dimension) is large relative to T (the time series dimension). It allows for fixed and time effects (FE‐TE) and derives a general formula for the bias of the FE‐TE estimator which generalizes the well‐known Nickell bias formula derived for the pure autoregressive dynamic panel data models. It shows that in the presence of weakly exogenous regressors inference based on the FE‐TE estimator will result in size distortions unless N/T is sufficiently small. To deal with the bias and size distortion of the FE‐TE estimator the use of a half‐panel jackknife FE‐TE estimator is considered and its asymptotic distribution is derived. It is shown that the bias of the half‐panel jackknife FE‐TE estimator is of order T^?2, and for valid inference it is only required that N/T³→0, as N,T→∞ jointly. Extension to unbalanced panel data models is also provided. The theoretical results are illustrated with Monte Carlo evidence. It is shown that the FE‐TE estimator can suffer from large size distortions when N>T, with the half‐panel jackknife FE‐TE estimator showing little size distortions. The use of half‐panel jackknife FE‐TE estimator is illustrated with two empirical applications from the literature.     

REALIZED BETA GARCH: A MULTIVARIATE GARCH MODEL WITH REALIZED MEASURES OF VOLATILITY

We introduce a multivariate generalized autoregressive conditional heteroskedasticity (GARCH) model that incorporates realized measures of variances and covariances. Realized measures extract information about the current levels of volatilities and correlations from high‐frequency data, which is particularly useful for modeling financial returns during periods of rapid changes in the underlying covariance structure. When applied to market returns in conjunction with returns on an individual asset, the model yields a dynamic model specification of the conditional regression coefficient that is known as the beta. We apply the model to a large set of assets and find the conditional betas to be far more variable than usually found with rolling‐window regressions based exclusively on daily returns. In the empirical part of the paper, we examine the cross‐sectional as well as the time variation of the conditional beta series during the financial crises. Copyright © 2014 John Wiley & Sons, Ltd.     

Weak and Strong Cross‐Sectional Dependence: A Panel Data Analysis of International Technology Diffusion

This paper provides an econometric examination of technological knowledge spillovers among countries by focusing on the issue of error cross‐sectional dependence, particularly on the different ways—weak and strong—that this dependence may affect model specification and estimation. A preliminary analysis based on estimation of the exponent of cross‐sectional dependence provides a clear result in favor of strong cross‐sectional dependence. This result has relevant implications in terms of econometric modeling and suggests that a factor structure is preferable to a spatial error model. The common correlated effects approach is then used because it remains valid in a variety of situations that are likely to occur, such as the presence of both forms of dependence or the existence of nonstationary factors. According to the estimation results, richer countries benefit more from domestic R&D and geographic spillovers than poorer countries, while smaller countries benefit more from spillovers originating from trade. The results also suggest that when the problem of (possibly many) correlated unobserved factors is addressed the quantity of education no longer has a significant effect. Finally, a comparison of the results with those obtained from a spatial model provides interesting insights into the bias that may arise when we allow only for weak dependence, despite the presence of strong dependence in the data. Copyright © 2016 John Wiley & Sons, Ltd.     

Common correlated effect cross‐sectional dependence corrections for nonlinear conditional mean panel models

This paper provides an approach to estimation and inference for nonlinear conditional mean panel data models, in the presence of cross‐sectional dependence. We modify Pesaran's (Econometrica, 2006, 74(4), 967–1012) common correlated effects correction to filter out the interactive unobserved multifactor structure. The estimation can be carried out using nonlinear least squares, by augmenting the set of explanatory variables with cross‐sectional averages of both linear and nonlinear terms. We propose pooled and mean group estimators, derive their asymptotic distributions, and show the consistency and asymptotic normality of the coefficients of the model. The features of the proposed estimators are investigated through extensive Monte Carlo experiments. We also present two empirical exercises. The first explores the nonlinear relationship between banks' capital ratios and riskiness. The second estimates the nonlinear effect of national savings on national investment in OECD countries depending on countries' openness.     

MULTIVARIATE METHODS FOR MONITORING STRUCTURAL CHANGE

Detection of structural change is a critical empirical activity, but continuous ‘monitoring’ for changes in real time raises well‐known econometric issues that have been explored in a single series context. If multiple series co‐break then it is possible that simultaneous examination of a set of series helps identify changes with higher probability or more rapidly than when series are examined on a case‐by‐case basis. Some asymptotic theory is developed for maximum and average CUSUM detection tests. Monte Carlo experiments suggest that these both provide an improvement in detection relative to a univariate detector over a wide range of experimental parameters, given a sufficiently large number of co‐breaking series. This is robust to a cross‐sectional correlation in the errors (a factor structure) and heterogeneity in the break dates. We apply the test to a panel of UK price indices. Copyright © 2011 John Wiley & Sons, Ltd.     

Spurious Fixed Effects Regression*

This article shows that spurious regression results can occur for a fixed effects model with weak time series variation in the regressor and/or strong time series variation in the regression errors when the first‐differenced and Within‐OLS estimators are used. Asymptotic properties of these estimators and the related t‐tests and model selection criteria are studied by sending the number of cross‐sectional observations to infinity. This article shows that the first‐differenced and Within‐OLS estimators diverge in probability, that the related t‐tests are inconsistent, that R²s converge to zero in probability and that AIC and BIC diverge to ?∞ in probability. The results of the article warn that one should not jump to the use of fixed effects regressions without considering the degree of time series variations in the data.     

Panel Unit‐root Tests for Cross‐sectionally Correlated Panels: A Monte Carlo Comparison*

This paper deals with the finite‐sample performance of a set of unit‐root tests for cross‐correlated panels. Most of the available macroeconomic time series cover short time periods. The lack of information, in terms of time observations, implies that univariate tests are not powerful enough to reject the null of a unit‐root while panel tests, by exploiting the large number of cross‐sectional units, have been shown to be a promising way of increasing the power of unit‐root tests. We investigate the finite sample properties of recently proposed panel unit‐root tests for cross‐sectionally correlated panels. Specifically, the size and power of Choi's [Econometric Theory and Practice: Frontiers of Analysis and Applied Research: Essays in Honor of Peter C. B. Phillips, Cambridge University Press, Cambridge (2001)], Bai and Ng's [Econometrica (2004), Vol. 72, p. 1127], Moon and Perron's [Journal of Econometrics (2004), Vol. 122, p. 81], and Phillips and Sul's [Econometrics Journal (2003), Vol. 6, p. 217] tests are analysed by a Monte Carlo simulation study. In synthesis, Moon and Perron's tests show good size and power for different values of T and N, and model specifications. Focusing on Bai and Ng's procedure, the simulation study highlights that the pooled Dickey–Fuller generalized least squares test provides higher power than the pooled augmented Dickey–Fuller test for the analysis of non‐stationary properties of the idiosyncratic components. Choi's tests are strongly oversized when the common factor influences the cross‐sectional units heterogeneously.     

CCE in fixed‐T panels

The presence of unobserved heterogeneity and its likely detrimental effect on inference has recently motivated the use of factor‐augmented panel regression models. The workhorse of this literature is based on first estimating the unknown factors using the cross‐section averages of the observables, and then applying ordinary least squares conditional on the first‐step factor estimates. This is the common correlated effects (CCE) approach, the existing asymptotic theory for which is based on the requirement that both the number of time series observations, T, and the number of cross‐section units, N, tend to infinity. The obvious implication of this theory for empirical work is that both N and T should be large, which means that CCE is impossible for the typical micro panel where only N is large. In the current paper, we put the existing CCE theory and its implications to a test. This is done by developing a new theory that enables T to be fixed. The results show that many of the previously derived large‐T results hold even if T is fixed. In particular, the pooled CCE estimator is still consistent and asymptotically normal, which means that CCE is more applicable than previously thought. In fact, not only do we allow T to be fixed, but the conditions placed on the time series properties of the factors and idiosyncratic errors are also much more general than those considered previously.     

Bootstrap inference for impulse response functions in factor‐augmented vector autoregressions

In this study, we consider residual‐based bootstrap methods to construct the confidence interval for structural impulse response functions in factor‐augmented vector autoregressions. In particular, we compare the bootstrap with factor estimation (Procedure A) with the bootstrap without factor estimation (Procedure B). Both procedures are asymptotically valid under the condition , where N and T are the cross‐sectional dimension and the time dimension, respectively. However, Procedure A is also valid even when with 0 ≤ c < ∞ because it accounts for the effect of the factor estimation errors on the impulse response function estimator. Our simulation results suggest that Procedure A achieves more accurate coverage rates than those of Procedure B, especially when N is much smaller than T. In the monetary policy analysis of Bernanke et al. (Quarterly Journal of Economics, 2005, 120(1), 387–422), the proposed methods can produce statistically different results.     

CROSS‐SECTIONAL DEPENDENCE AND SPILLOVERS IN SPACE AND TIME: WHERE SPATIAL ECONOMETRICS AND GLOBAL VAR MODELS MEET

To enhance the measurement of economic and financial spillovers, we bring together the spatial and global vector autoregressive (GVAR) classes of econometric models by providing a detailed methodological review where they meet in terms of structure, interpretation, and estimation. We discuss the structure of connectivity (weight) matrices used by these models and its implications for estimation. To anchor our work within the dynamic literature on spillovers, we define a general yet measurable concept of spillovers. We formalize it analytically through the indirect effects used in the spatial literature and impulse responses used in the GVAR literature. Finally, we propose a practical step‐by‐step approach for applied researchers who need to account for the existence and strength of cross‐sectional dependence in the data. This approach aims to support the selection of the appropriate modeling and estimation method and of choices that represent empirical spillovers in a clear and interpretable form.     

Jumps in cross‐sectional rank and expected returns: a mixture model

We propose a new nonlinear time series model of expected returns based on the dynamics of the cross‐sectional rank of realized returns. We model the joint dynamics of a sharp jump in the cross‐sectional rank and the asset return by analyzing (1) the marginal probability distribution of a jump in the cross‐sectional rank within the context of a duration model, and (2) the probability distribution of the asset return conditional on a jump, for which we specify different dynamics depending upon whether or not a jump has taken place. As a result, the expected returns are generated by a mixture of normal distributions weighted by the probability of jumping. The model is estimated for the weekly returns of the constituents of the SP500 index from 1990 to 2000, and its performance is assessed in an out‐of‐sample exercise from 2001 to 2005. Based on the one‐step‐ahead forecast of the mixture model we propose a trading rule, which is evaluated according to several forecast evaluation criteria and compared to 18 alternative trading rules. We find that the proposed trading strategy is the dominant rule by providing superior risk‐adjusted mean trading returns and accurate value‐at‐risk forecasts. Copyright © 2008 John Wiley & Sons, Ltd.     

L‐moments skewness and kurtosis as measures of regional convergence and cohesion

The paper deals with the statistical modeling of convergence and cohesion over time with the use of kurtosis, skewness and L‐moments. Changes in the shape of the distribution related to the spatial allocation of socio‐economic phenomena are considered as an evidence of global shift, divergence or convergence. Cross‐sectional time‐series statistical modeling of variables of interest is to overpass the minors of econometric theoretical models of convergence and cohesion determinants. L‐moments perform much more stable and interpretable than classical measures. Empirical evidence of panel data proves that one pure pattern (global shift, polarization or cohesion) rarely exists and joint analysis is required.     

Equilibrium Exchange Rates in Transition Economies: Taking Stock of the Issues*

Abstract. In this paper, we present an overview of a number of issues relating to the equilibrium exchange rates of transition economies of the former soviet bloc. In particular, we present a critical overview of the various methods available for calculating equilibrium exchange rates and discuss how useful they are likely to be for the transition economies. Amongst our findings is the result that the trend appreciation usually observed for the exchange rates of these economies is affected by factors other than the usual Balassa–Samuelson effect, such as the behaviour of the real exchange rate of the open sector and regulated prices. We then consider three main sources of uncertainty relating to the implementation of an equilibrium exchange rate model, namely: differences in the theoretical underpinnings, differences in the econometric estimation techniques, and differences relating to the time‐series and cross‐sectional dimensions of the data. The ensuing three‐dimensional space of real misalignments is probably a useful tool in determining the direction of a possible misalignment rather than its precise size.     

Optimal transformations for categorical autoregressive time series

This paper describes a method for finding optimal transformations for analyzing time series by autoregressive models. 'Optimal' implies that the agreement between the autoregressive model and the transformed data is maximal. Such transformations help 1) to increase the model fit, and 2) to analyze categorical time series. The method uses an alternating least squares algorithm that consists of two main steps: estimation and transformation. Nominal, ordinal and numerical data can be analyzed. Some alternative applications of the general idea are highlighted: intervention analysis, smoothing categorical time series, predictable components, spatial modeling and cross-sectional multivariate analysis. Limitations, modeling issues and possible extensions are briefly indicated.     

Combining Significance of Correlated Statistics with Application to Panel Data*

The inverse normal method, which is used to combine P‐values from a series of statistical tests, requires independence of single test statistics in order to obtain asymptotic normality of the joint test statistic. The paper discusses the modification by Hartung (1999, Biometrical Journal, Vol. 41, pp. 849–855) , which is designed to allow for a certain correlation matrix of the transformed P‐values. First, the modified inverse normal method is shown here to be valid with more general correlation matrices. Secondly, a necessary and sufficient condition for (asymptotic) normality is provided, using the copula approach. Thirdly, applications to panels of cross‐correlated time series, stationary as well as integrated, are considered. The behaviour of the modified inverse normal method is quantified by means of Monte Carlo experiments.     

Economic transition and growth

Some extensions of neoclassical growth models are discussed that allow for cross‐section heterogeneity among economies and evolution in rates of technological progress over time. The models offer a spectrum of transitional behavior among economies that includes convergence to a common steady‐state path as well as various forms of transitional divergence and convergence. Mechanisms for modeling such transitions, measuring them econometrically, assessing group behavior and selecting subgroups are developed in the paper. Some econometric issues with the commonly used augmented Solow regressions are pointed out, including problems of endogeneity and omitted variable bias which arise under conditions of transitional heterogeneity. Alternative regression methods for analyzing economic transition are given which lead to a new test of the convergence hypothesis and a new procedure for detecting club convergence clusters. Transition curves for individual economies and subgroups of economies are estimated in a series of empirical applications of the methods to regional US data, OECD data and Penn World Table data. Copyright © 2009 John Wiley & Sons, Ltd.