Nonresponse in panel data: The impact on estimates of a life cycle consumption function

If missing observations in a panel data set are not missing at random, many widely applied estimators may be inconsistent. In this paper we examine empirically several ways to reveal the nature and severity of the selectivity problem due to nonresponse, as well as a number of methods to estimate the resulting models. Using a life cycle consumption function and data from the Expenditure Index Panel from the Netherlands, we discuss simple procedures that can be used to assess whether observations are missing at random, and we consider more complicated estimation procedures that can be used to obtain consistent or efficient estimates in case of selectivity of attrition bias. Finally, some attention is paid to the differences in identification, consistency, and efficiency between inferences from a single wave of the panel, a balanced sub-panel, and an unbalanced panel.     

Missing Data: A Unified Taxonomy Guided by Conditional Independence

Recent work (Seaman et al., 2013 ; Mealli & Rubin, 2015 ) attempts to clarify the not always well‐understood difference between realised and everywhere definitions of missing at random (MAR) and missing completely at random. Another branch of the literature (Mohan et al., 2013 ; Pearl & Mohan, 2013 ) exploits always‐observed covariates to give variable‐based definitions of MAR and missing completely at random. In this paper, we develop a unified taxonomy encompassing all approaches. In this taxonomy, the new concept of ‘complementary MAR’ is introduced, and its relationship with the concept of data observed at random is discussed. All relationships among these definitions are analysed and represented graphically. Conditional independence, both at the random variable and at the event level, is the formal language we adopt to connect all these definitions. Our paper covers both the univariate and the multivariate case, where attention is paid to monotone missingness and to the concept of sequential MAR. Specifically, for monotone missingness, we propose a sequential MAR definition that might be more appropriate than both everywhere and variable‐based MAR to model dropout in certain contexts.     

Monotone missing data and pattern-mixture models

It is shown that the classical taxonomy of missing data models, namely missing completely at random, missing at random and informative missingness, which has been developed almost exclusively within a selection modelling framework, can also be applied to pattern-mixture models. In particular, intuitively appealing identifying restrictions are proposed for a pattern-mixture MAR mechanism.     

Externalities and Industrial Development

Using panel data for five capital goods industries, this paper estimates dynamic externalities. In contrast to previous studies, panel data allow separation of externalities from fixed effects and identification of a lag structure. I find strong evidence of Marshall–Arrow–Romer (MAR) (own industry, or localization) externalities. For Jacobs (urbanization) externalities effects are smaller. In terms of lag structure, for MAR externalities the biggest effects are typically from several years ago, but die out after six years. For urbanization phenomena, effects persist to the end of the time horizon of the data–eight or nine years back.     

Inference in panel data models under attrition caused by unobservables

This paper concerns identification and estimation of a finite-dimensional parameter in a panel data-model under nonignorable sample attrition. Attrition can depend on second period variables which are unobserved for the attritors but an independent refreshment sample from the marginal distribution of the second period values is available. This paper shows that under a quasi-separability assumption, the model implies a set of conditional moment restrictions where the moments contain the attrition function as an unknown parameter. This formulation leads to (i) a simple proof of identification under strictly weaker conditions than those in the existing literature and, more importantly, (ii) a sieve-based root-n$n$ consistent estimate of the finite-dimensional parameter of interest. These methods are applicable to both linear and nonlinear panel data models with endogenous attrition and analogous methods are applicable to situations of endogenously missing data in a single cross-section. The theory is illustrated with a simulation exercise, using Current Population Survey data where a panel structure is introduced by the rotation group feature of the sampling process.     

The development of delinquency during adolescence: a comparison of missing data techniques

Conclusions on the development of delinquent behaviour during the life-course can only be made with longitudinal data, which is regularly gained by repeated interviews of the same respondents. Missing data are a problem for the analysis of delinquent behaviour during the life-course shown with data from an adolescents’ four-wave panel. In this article two alternative techniques to cope with missing data are used: full information maximum likelihood estimation and multiple imputation. Both methods allow one to consider all available data (including adolescents with missing information on some variables) in order to estimate the development of delinquency. We demonstrate that self-reported delinquency is systematically underestimated with listwise deletion (LD) of missing data. Further, LD results in false conclusions on gender and school specific differences of the age–crime relationship. In the final discussion some hints are given for further methods to deal with bias in panel data affected by the missing process.     

Testing for Seasonal Unit Roots in Monthly Panels of Time Series*

We consider the problem of testing for seasonal unit roots in monthly panel data. To this aim, we generalize the quarterly cross‐sectionally augmented Hylleberg–Engle–Granger–Yoo (CHEGY) test to the monthly case. This parametric test is contrasted with a new non‐parametric test, which is the panel counterpart to the univariate record unit–root seasonal (RURS) test that relies on counting extrema in time series. All methods are applied to an empirical data set on tourism in Austrian provinces. The power properties of the tests are evaluated in simulation experiments that are tuned to the tourism data.     

Cointegration Testing in Panels with Common Factors*

Panel unit‐root and no‐cointegration tests that rely on cross‐sectional independence of the panel unit experience severe size distortions when this assumption is violated, as has, for example, been shown by Banerjee, Marcellino and Osbat [Econometrics Journal (2004), Vol. 7, pp. 322–340; Empirical Economics (2005), Vol. 30, pp. 77–91] via Monte Carlo simulations. Several studies have recently addressed this issue for panel unit‐root tests using a common factor structure to model the cross‐sectional dependence, but not much work has been done yet for panel no‐cointegration tests. This paper proposes a model for panel no‐cointegration using an unobserved common factor structure, following the study by Bai and Ng [Econometrica (2004), Vol. 72, pp. 1127–1177] for panel unit roots. We distinguish two important cases: (i) the case when the non‐stationarity in the data is driven by a reduced number of common stochastic trends, and (ii) the case where we have common and idiosyncratic stochastic trends present in the data. We discuss the homogeneity restrictions on the cointegrating vectors resulting from the presence of common factor cointegration. Furthermore, we study the asymptotic behaviour of some existing residual‐based panel no‐cointegration tests, as suggested by Kao [Journal of Econometrics (1999), Vol. 90, pp. 1–44] and Pedroni [Econometric Theory (2004a), Vol. 20, pp. 597–625]. Under the data‐generating processes (DGP) used, the test statistics are no longer asymptotically normal, and convergence occurs at rate T rather than as for independent panels. We then examine the possibilities of testing for various forms of no‐cointegration by extracting the common factors and individual components from the observed data directly and then testing for no‐cointegration using residual‐based panel tests applied to the defactored data.     

Testing for Multicointegration in Panel Data with Common Factors*

This paper addresses the concept of multicointegration in a panel data framework and builds upon the panel data cointegration procedures developed in Pedroni [Econometric Theory (2004), Vol. 20, pp. 597–625]. When individuals are either cross‐section independent, or cross‐section dependence can be removed by cross‐section demeaning, our approach can be applied to the wider framework of mixed I(2) and I(1) stochastic processes. The paper also deals with the issue of cross‐section dependence using approximate common‐factor models. Finite sample performance is investigated through Monte Carlo simulations. Finally, we illustrate the use of the procedure investigating an inventories, sales and production relationship for a panel of US industries.     

DATA GAPS,DATA INCOMPARABILITY,AND DATA IMPUTATION: A REVIEW OF POVERTY MEASUREMENT METHODS FOR DATA‐SCARCE ENVIRONMENTS

Questions that often come up in contexts where household consumption data are unavailable or missing include: what are the best existing methods to obtain poverty estimates at a single snapshot in time? and over time? and what are the best available methods to study poverty dynamics? A variety of different techniques have been developed to tackle these questions, but unfortunately, they are presented in different forms and lack unified terminology. We offer a review of poverty imputation methods that address contexts ranging from completely missing and partially missing consumption data in cross‐sectional household surveys, to missing panel household data. We present the various existing methods under a common framework, with pedagogical discussion on their intuition. Empirical illustrations are provided using several rounds of household survey data from Vietnam. Furthermore, we also offer a practical guide with detailed instructions on computer programs that can be used to implement the reviewed techniques.     

Testing for Error Correction in Panel Data*

This paper proposes new error correction‐based cointegration tests for panel data. The limiting distributions of the tests are derived and critical values provided. Our simulation results suggest that the tests have good small‐sample properties with small size distortions and high power relative to other popular residual‐based panel cointegration tests. In our empirical application, we present evidence suggesting that international healthcare expenditures and GDP are cointegrated once the possibility of an invalid common factor restriction has been accounted for.     

A Simple Panel‐CADF Test for Unit Roots*

In this paper, we propose a simple extension to the panel case of the covariate‐augmented Dickey–Fuller (CADF) test for unit roots developed in Hansen (1995) . The panel test we propose is based on a P values combination approach that takes into account cross‐section dependence. We show that the test has good size properties and gives power gains with respect to other popular panel approaches. An empirical application is carried out for illustration purposes on international data to test the purchasing power parity (PPP) hypothesis.     

Measuring the impact of nonignorability in panel data with non‐monotone nonresponse

The analysis of panel data with non‐monotone nonresponse often relies on the critical and untestable assumption of ignorable missingness. It is important to assess the consequences of departures from the ignorability assumption. Non‐monotone nonresponse, however, can often make such sensitivity analysis infeasible because the likelihood functions for alternative models involve high‐dimensional and difficult‐to‐evaluate integrals with respect to missing outcomes. We develop an extension of the local sensitivity method that overcomes computational difficulty and completely avoids fitting alternative models and evaluating these high‐dimensional integrals. The proposed method is applicable to a wide range of panel outcomes. We apply the method to a Smoking Trend dataset where we relax the standard ignorability assumption and evaluate how smoking‐trend estimates in different groups of US young adults are affected by alternative assumptions about the missing‐data mechanism. The main finding is that the standard estimate in the black male group is sensitive to nonignorable missingness but those in other groups are reasonably robust. Copyright © 2010 John Wiley & Sons, Ltd.     

An algorithm for panel ANOVA with grouped data

In this paper, we present an algorithm suitable for analysing the variance of panel data when some observations are either given in grouped form or are missed. The analysis is carried out from the perspective of ANOVA panel data models with general errors. The classification intervals of the grouped observations may vary from one to another, thus the missing observations are in fact a particular case of grouping. The proposed Algorithm (1) estimates the parameters of the panel data models; (2) evaluates the covariance matrices of the asymptotic distribution of the time-dependent parameters assuming that the number of time periods, T, is fixed and the number of individuals, N, tends to infinity and similarly, of the individual parameters when T → ∞ and N is fixed; and, finally, (3) uses these asymptotic covariance matrix estimations to analyse the variance of the panel data.     

Likelihood-based estimation in a panel setting: Robustness,redundancy and validity of copulas

This paper considers the estimation of likelihood-based models in a panel setting. That is, we have panel data, and for each time period separately we have a correctly specified model that could be estimated by MLE. We want to allow non-independence over time. This paper shows how to improve on the QMLE. It then considers MLE based on joint distributions constructed using copulas. It discusses the efficiency gain from using the true copula, and shows that knowledge of the true copula is redundant only if the variance matrix of the relevant set of moment conditions is singular. It also discusses the question of robustness against misspecification of the copula, and proposes a test of the validity of the copula. GMM methods are argued to be useful analytically, and also for reasons of efficiency if the copula is robust but not correct.     

Minimax-regret treatment choice with missing outcome data

I use the minimax-regret criterion to study choice between two treatments when some outcomes in the study population are unobservable and the distribution of missing data is unknown. I first assume that observable features of the study population are known and derive the treatment rule that minimizes maximum regret over all possible distributions of missing data. When no treatment is dominant, this rule allocates positive fractions of persons to both treatments. I then assume that the data are a random sample of the study population and show that in some instances, treatment rules that estimate certain point-identified population means by sample averages are finite-sample minimax regret.     

Sieve estimation of panel data models with cross section dependence

In this paper we consider the problem of estimating semiparametric panel data models with cross section dependence, where the individual-specific regressors enter the model nonparametrically whereas the common factors enter the model linearly. We consider both heterogeneous and homogeneous regression relationships when both the time and cross-section dimensions are large. We propose sieve estimators for the nonparametric regression functions by extending Pesaran’s (2006) common correlated effect (CCE) estimator to our semiparametric framework. Asymptotic normal distributions for the proposed estimators are derived and asymptotic variance estimators are provided. Monte Carlo simulations indicate that our estimators perform well in finite samples.     

Lock-in and unobserved preferences in server operating systems: A case of Linux vs. Windows

This paper investigates to what extent the persistence of Microsoft Windows in the market for server operating systems is due to lock-in or unobserved preferences. While the hypothesis of lock-in plays an important role in the antitrust policy debate for the operating systems market, it has not been extensively documented empirically. To account for unobserved preferences, we use a panel data identification approach based on time-variant group fixed effects, and estimate the dynamic discrete choice panel data model developed by Arellano and Carrasco (2003). Using detailed establishment-level data, we find that once we account for unobserved preferences, the estimated magnitudes of lock-in are considerably smaller than those from the conventional approaches, suggesting that unobserved preferences play a major role in the persistence of Windows. Further robustness checks are consistent with our findings.     

Quantile regression for dynamic panel data with fixed effects

This paper studies a quantile regression dynamic panel model with fixed effects. Panel data fixed effects estimators are typically biased in the presence of lagged dependent variables as regressors. To reduce the dynamic bias, we suggest the use of the instrumental variables quantile regression method of Chernozhukov and Hansen (2006) along with lagged regressors as instruments. In addition, we describe how to employ the estimated models for prediction. Monte Carlo simulations show evidence that the instrumental variables approach sharply reduces the dynamic bias, and the empirical levels for prediction intervals are very close to nominal levels. Finally, we illustrate the procedures with an application to forecasting output growth rates for 18 OECD countries.     

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.