Penalized estimation of panel vector autoregressive models: A panel LASSO approach

This paper proposes LASSO estimation specific for panel vector autoregressive (PVAR) models. The penalty term allows for shrinkage for different lags, for shrinkage towards homogeneous coefficients across panel units, for penalization of lags of variables belonging to another cross-sectional unit, and for varying penalization across equations. The penalty parameters therefore build on time series and cross-sectional properties that are commonly found in PVAR models. Simulation results point towards advantages of using the proposed LASSO for PVAR models over ordinary least squares in terms of forecast accuracy. An empirical forecasting application including 20 countries supports these findings.     

On bootstrapping panel factor series

This paper studies the asymptotic validity of sieve bootstrap for nonstationary panel factor series. Two main results are shown. Firstly, a bootstrap Invariance Principle is derived pointwise in i$i$, obtaining an upper bound for the order of truncation of the AR polynomial that depends on n$n$ and T$T$. Consistent estimation of the long run variances is also studied for (n,T)→∞$(n,T)\to \infty$. Secondly, joint bootstrap asymptotics is also studied, investigating the conditions under which the bootstrap is valid. In particular, the extent of cross sectional dependence which can be allowed for is investigated. Whilst we show that, for general forms of cross dependence, consistent estimation of the long run variance (and therefore validity of the bootstrap) is fraught with difficulties, however we show that “one-cross-sectional-unit-at-a-time” resampling schemes yield valid bootstrap based inference under weak forms of cross-sectional dependence.     

Estimates of technical inefficiency in stochastic frontier models with panel data: generalized panel jackknife estimation

Estimates of technical inefficiency based on fixed effects estimation of the stochastic frontier model with panel data are biased upward. Previous work has attempted to correct this bias using the bootstrap, but in simulations the bootstrap corrects only part of the bias. The usual panel jackknife is based on the assumption that the bias is of order T ⁻¹ and is similar to the bootstrap. We show that when there is a tie or a near tie for the best firm, the bias is of order T ^−1/2, not T ⁻¹, and this calls for a different form of the jackknife. The generalized panel jackknife is quite successful in removing the bias. However, the resulting estimates have a large variance.     

Multivariate regression models for panel data

The paper examines the relationship between heterogeneity bias and strict exogeneity in a distributed lag regression of y on x. The relationship is very strong when x is continuous, weaker when x is discrete, and non-existent as the order of the distributed lag becomes infinite. The individual specific random variables introduce nonlinearity and heteroskedasticity; so the paper provides an appropriate framework for the estimation of multivariate linear predictors. Restrictions are imposed using a minimum distance estimator. It is generally more efficient than the conventional estimators such as quasi-maximum likelihood. There are computationally simple generalizations of two- and three-stage least squares that achieve this efficiency gain. Some of these ideas are illustrated using the sample of Young Men in the National Longitudinal Survey. The paper reports regressions on the leads and lags of variables measuring union coverage, SMSA, and region. The results indicate that the leads and lags could have been generated just by a random intercept. This gives some support for analysis of covariance type estimates; these estimates indicate a substantial heterogeneity bias in the union, SMSA, and region coefficients.     

Errors in variables in panel data

Panel data based studies in econometrics use the analysis of covariance approach to control for various ‘individual effects’ by estimating coefficients from the ‘within’ dimension of the data. Often, however, the results are unsatisfactory, with ‘too low’ and insignificant coefficients. Errors of measurement in the independent variables whose relative importance gets magnified in the within dimension are then blamed for this outcome.Errors-in-variables models have not been used widely, in part because they seem to require extraneous information to be identified. We show how a variety of errors-in-variables models may be identifiable and estimable in panel data without the use of external instruments and apply it to a relatively simple but not uninteresting case: the estimation of ‘labor demand’ relationships, also known as the ‘short-run increasing returns to scale’ puzzle.     

Response for ILA worldviews panel papers

Leadership is about knowledge, skills, and abilities for transformation. It is also increasingly about worldviews or visions of life—beliefs, values, and principles. But worldviews are also ways of life, for beliefs direct us, values guide us, and principles motivate us to certain kinds of action and behavior. How, then, do worldviews have an impact on leadership for transformation? If worldviews are glasses or filters by which we view the world, mental models of the bigger picture, frameworks by which we make sense of the world, and narratives by which we orient our lives, then how do they influence human thoughts, ideas, and behaviors when it comes to transformative leadership? This was the subject matter of an International Leadership Association Conference panel discussion held in November 2009 in Prague, entitled Leadership for Transformation: The Impact of Worldviews. It is also the subject matter of this issue's symposium, in which we bring you the four papers and the response presented at the conference. Members of the panel were characterized by gender, disciplinary, religious, and global diversity. Nathan Harter, organizational leadership professor at Purdue University in the United States, begins the discussion with some preliminary remarks about worldviews. Ali Mohammed Mir, medical doctor and director of programs of Population Council, Pakistan, speaks of leadership from an Islamic perspective. Michael Jones, accomplished composer, pianist, and leadership educator, writer, and speaker from Orillia, Canada, reflects on how a “marriage of mythos and logos” can transform leadership today. Lisa Ncube, originally from Zimbabwe and currently assistant professor of organizational leadership at Purdue University, speaks about Ubuntu as an alternative leadership philosophy emerging from Africa. John Valk, associate professor of worldview studies at Renaissance College, University of New Brunswick, Canada, speaks of leadership for transformation from a Christian worldview perspective. Jonathan Reams, associate professor in the Department of Education at the Norwegian University of Science and Technology in Trondheim, responds to all of the papers and opens a venue for further discussion. We hope that you will find this symposium engaging. We hope it will give food for thought and that it might stimulate further thinking regarding the role worldviews play in leadership for transformation.     

Robust firm pricing with panel data

Firms often have imperfect information about demand for their products. We develop an integrated econometric and theoretical framework to model firm demand assessment and subsequent pricing decisions with limited information. We introduce a panel data discrete choice model whose realistic assumptions about consumer behavior deliver partially identified preferences and thus generate ambiguity in the firm pricing problem. We use the minimax-regret criterion as a decision-making rule for firms facing this ambiguity. We illustrate the framework’s benefits relative to the most common discrete choice analysis approach through simulations and empirical examples with field data.     

Nonresponse in dynamic panel data models

To verify whether data are missing at random (MAR) we need to observe the missing data. There are only two exceptions: when the relationship between the probability of responding and the missing variables is either imposed by introducing untestable assumptions or recovered using additional data sources. In this paper, we briefly review the estimation and test procedures for selectivity in panel data. Furthermore, by extending the MAR definition from a static setting to the case of dynamic panel data models, we prove that some tests for selectivity are not verifying the MAR condition.     

Indirect inference for dynamic panel models

Maximum likelihood (ML) estimation of the autoregressive parameter of a dynamic panel data model with fixed effects is inconsistent under fixed time series sample size and large cross section sample size asymptotics. This paper proposes a general, computationally inexpensive method of bias reduction that is based on indirect inference, shows unbiasedness and analyzes efficiency. Monte Carlo studies show that our procedure achieves substantial bias reductions with only mild increases in variance, thereby substantially reducing root mean square errors. The method is compared with certain consistent estimators and is shown to have superior finite sample properties to the generalized method of moment (GMM) and the bias-corrected ML estimator.     

Some strange properties of panel data estimators

We study the biases that are likely to arise in practice with panel data when parameters vary across individuals, but this is not allowed for in estimation. We consider both stationary and non-stationary regressors. We find that biases can be severe for relatively small parameter variation, and that this problem is hard to detect. We study in some detail by Monte-Carlo the performance of the Anderson-Hsiao estimator in the presence of this particular mis-specification.     

Beyond panel unit root tests: Using multiple testing to determine the nonstationarity properties of individual series in a panel

Most panel unit root tests are designed to test the joint null hypothesis of a unit root for each individual series in a panel. After a rejection, it will often be of interest to identify which series can be deemed to be stationary and which series can be deemed nonstationary. Researchers will sometimes carry out this classification on the basis of n$n$ individual (univariate) unit root tests based on some ad hoc significance level. In this paper, we suggest and demonstrate how to use the false discovery rate (FDR)$\left(FDR\right)$ in evaluating I(1)/I(0)$I\left(1\right)/I\left(0\right)$ classifications.     

First difference maximum likelihood and dynamic panel estimation

First difference maximum likelihood (FDML) seems an attractive estimation methodology in dynamic panel data modeling because differencing eliminates fixed effects and, in the case of a unit root, differencing transforms the data to stationarity, thereby addressing both incidental parameter problems and the possible effects of nonstationarity. This paper draws attention to certain pathologies that arise in the use of FDML that have gone unnoticed in the literature and that affect both finite sample performance and asymptotics. FDML uses the Gaussian likelihood function for first differenced data and parameter estimation is based on the whole domain over which the log-likelihood is defined. However, extending the domain of the likelihood beyond the stationary region has certain consequences that have a major effect on finite sample and asymptotic performance. First, the extended likelihood is not the true likelihood even in the Gaussian case and it has a finite upper bound of definition. Second, it is often bimodal, and one of its peaks can be so peculiar that numerical maximization of the extended likelihood frequently fails to locate the global maximum. As a result of these pathologies, the FDML estimator is a restricted estimator, numerical implementation is not straightforward and asymptotics are hard to derive in cases where the peculiarity occurs with non-negligible probabilities. The peculiarities in the likelihood are found to be particularly marked in time series with a unit root. In this case, the asymptotic distribution of the FDMLE has bounded support and its density is infinite at the upper bound when the time series sample size T→∞$T\to \infty$. As the panel width n→∞$n\to \infty$ the pathology is removed and the limit theory is normal. This result applies even for T$T$ fixed and we present an expression for the asymptotic distribution which does not depend on the time dimension. We also show how this limit theory depends on the form of the extended likelihood.     

Robust penalized quantile regression estimation for panel data

This paper investigates a class of penalized quantile regression estimators for panel data. The penalty serves to shrink a vector of individual specific effects toward a common value. The degree of this shrinkage is controlled by a tuning parameter λ$\lambda$. It is shown that the class of estimators is asymptotically unbiased and Gaussian, when the individual effects are drawn from a class of zero-median distribution functions. The tuning parameter, λ$\lambda$, can thus be selected to minimize estimated asymptotic variance. Monte Carlo evidence reveals that the estimator can significantly reduce the variability of the fixed-effect version of the estimator without introducing bias.     

A nonlinear panel data model of cross-sectional dependence

This paper proposes a nonlinear panel data model which can endogenously generate both ‘weak’ and ‘strong’ cross-sectional dependence. The model’s distinguishing characteristic is that a given agent’s behaviour is influenced by an aggregation of the views or actions of those around them. The model allows for considerable flexibility in terms of the genesis of this herding or clustering type behaviour. At an econometric level, the model is shown to nest various extant dynamic panel data models. These include panel AR models, spatial models, which accommodate weak dependence only, and panel models where cross-sectional averages or factors exogenously generate strong, but not weak, cross sectional dependence. An important implication is that the appropriate model for the aggregate series becomes intrinsically nonlinear, due to the clustering behaviour, and thus requires the disaggregates to be simultaneously considered with the aggregate. We provide the associated asymptotic theory for estimation and inference. This is supplemented with Monte Carlo studies and two empirical applications which indicate the utility of our proposed model as a vehicle to model different types of cross-sectional dependence.     

Wealth dynamics: reducing noise in panel data

Although the asset data from the Health and Retirement Study (HRS) is of very high quality, there is sufficient noise to frustrate attempts to study saving behaviour by examining wave‐to‐wave change in wealth. In this research, we attempt to reduce noise by means of reactive‐dependent interviewing in which respondents with large inexplicable changes in assets between 1998 and 2000 are called back by HRS interviewers, presented with their prior reports and asked to reconcile the data. We achieved reconciliation for 1255 households (2479 net‐worth components) and, as a result, the variance in measured change for the entire sample of 11,583 households with the same financial respondents in both waves was cut in half. The empirical validity of the data also appears to have been improved. The correlation of gross change in net worth and income, for instance, increased from an insignificant negative to a highly significant positive value. Although reconciliation of large asset changes marginally improves the goodness of fit of multivariate models, there remains sufficient noise in the asset‐change data to require analysts to employ additional methods to reduce the influence of outliers. Copyright © 2006 John Wiley & Sons, Ltd.     

Nonlinear continuous time modeling approaches in panel research

Stochastic differential equations (SDE) are used as dynamical models for cross-sectional discrete time measurements (panel data). Thus causal effects are formulated on a fundamental infinitesimal time scale. Cumulated causal effects over the measurement interval can be expressed in terms of fundamental effects which are independent of the chosen sampling intervals (e.g. weekly, monthly, annually). The nonlinear continuous–discrete filter is the key tool in deriving a recursive sequence of time and measurement updates. Several approximation methods including the extended Kalman filter (EKF), higher order nonlinear filters (HNF), the local linearization filter (LLF), the unscented Kalman filter (UKF), the Gauss–Hermite filter (GHF) and generalizations (GGHF), as well as simulated filters (functional integral filter FIF) are compared.     

Small sample considerations in estimation from panel data

Recent interest in statistical inference for panel data has focused on the problem of unobservable, individual-specific, random effects and the inconsistencies they introduce in estimation when they are correlated with other exogenous variables. Analysis of this problem has always assumed the variance components to be known. In this paper, we re-examine some of these questions in finite samples when the variance components must be estimated. In particular, when the effects are uncorrelated with other explanatory variables, we show that (i) the feasible Gauss-Markov estimator is more efficient than the within groups estimator for all but the fewest degrees of freedom and its variance is never more than 17% above the Cramer-Rao bound, (ii) the asymptotic approximation to the variance of the feasible Gauss-Markov estimator is similarly within 17% of the true variance but remains significantly smaller for moderately large samples sizes, and (iii) more efficient estimators for the variance components do not necessarily yield more efficient feasible Gauss-Markov estimators.