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.     

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.     

k‐Nearest neighbors local linear regression for functional and missing data at random

We combine the k‐Nearest Neighbors (kNN) method to the local linear estimation (LLE) approach to construct a new estimator (LLE‐kNN) of the regression operator when the regressor is of functional type and the response variable is a scalar but observed with some missing at random (MAR) observations. The resulting estimator inherits many of the advantages of both approaches (kNN and LLE methods). This is confirmed by the established asymptotic results, in terms of the pointwise and uniform almost complete consistencies, and the precise convergence rates. In addition, a numerical study (i) on simulated data, then (ii) on a real dataset concerning the sugar quality using fluorescence data, were conducted. This practical study clearly shows the feasibility and the superiority of the LLE‐kNN estimator compared to competitive estimators.     

GMM with Multiple Missing Variables

We consider efficient estimation in moment conditions models with non‐monotonically missing‐at‐random (MAR) variables. A version of MAR point‐identifies the parameters of interest and gives a closed‐form efficient influence function that can be used directly to obtain efficient semi‐parametric generalized method of moments (GMM) estimators under standard regularity conditions. A small‐scale Monte Carlo experiment with MAR instrumental variables demonstrates that the asymptotic superiority of these estimators over the standard methods carries over to finite samples. An illustrative empirical study of the relationship between a child's years of schooling and number of siblings indicates that these GMM estimators can generate results with substantive differences from standard methods. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Bartlett correction to the likelihood ratio test for MCAR with two‐step monotone sample

Assuming that two‐step monotone missing data is drawn from a multivariate normal population, this paper derives the Bartlett‐type correction to the likelihood ratio test for missing completely at random (MCAR), which plays an important role in the statistical analysis of incomplete datasets. The advantages of our approach are confirmed in Monte Carlo simulations. Our correction drastically improved the accuracy of the type I error in Little's (1988, Journal of the American Statistical Association, 83 , 1198–1202) test for MCAR and performed well even on moderate sample sizes.     

ESTIMATION OF CENSORED PANEL‐DATA MODELS WITH SLOPE HETEROGENEITY

This paper considers estimation of censored panel‐data models with individual‐specific slope heterogeneity. The slope heterogeneity may be random (random slopes model) or related to covariates (correlated random slopes model). Maximum likelihood and censored least‐absolute deviations estimators are proposed for both models. The estimators are simple to implement and, in the case of maximum likelihood, lead to straightforward estimation of partial effects. The rescaled bootstrap suggested by Andrews (Econometrica 2000; 68 : 399–405) is used to deal with the possibility of variance parameters being equal to zero. The methodology is applied to an empirical study of Dutch household portfolio choice, where the outcome variable (portfolio share in safe assets) has corner solutions at zero and one. As predicted by economic theory, there is strong evidence of correlated random slopes for the age profiles, indicating a heterogeneous age profile of portfolio adjustment that varies significantly with other household characteristics. Copyright © 2013 John Wiley & Sons, Ltd.     

ECONOMIC PROGRESS AND CLIMATE CHANGE ISSUES: A DISSENTING VIEWPOINT

The attached text formed the basis for my opening contribution, and also some later remarks, at the discussion that followed the 2008 Clare Distinguished Lecture in Economics and Public Policy, given in Cambridge, England, on 14 May 2008. The lecturer was Professor Mohan Munasinghe, a Vice‐Chair of the Intergovernmental Panel on Climate Change, and his subject was ‘A Policy Framework for Climate Change and Sustainable Development: Economic Analysis and Beyond’. I have made a few small changes to take account of some more recent developments.     

A Random Effects Transition Model For Longitudinal Binary Data With Informative Missingness

Understanding the transitions between disease states is often the goal in studying chronic disease. These studies, however, are typically subject to a large amount of missingness either due to patient dropout or intermittent missed visits. The missing data is often informative since missingness and dropout are usually related to either an individual's underlying disease process or the actual value of the missed observation. Our motivating example is a study of opiate addiction that examined the effect of a new treatment on thrice-weekly binary urine tests to assess opiate use over follow-up. The interest in this opiate addiction clinical trial was to characterize the transition pattern of opiate use (in each treatment arm) as well as to compare both the marginal probability of a positive urine test over follow-up and the time until the first positive urine test between the treatment arms. We develop a shared random effects model that links together the propensity of transition between states and the probability of either an intermittent missed observation or dropout. This approach allows for heterogeneous transition and missing data patterns between individuals as well as incorporating informative intermittent missing data and dropout. We compare this new approach with other approaches proposed for the analysis of longitudinal binary data with informative missingness.     

Business Strategy and Firm Reorganization: Role of Changing Environmental Standards,Sustainable Business Initiatives and Global Market Conditions

My study is framed against the backdrop of increasingly stringent environmental demands on the pulp and paper industry to reduce water and air pollution, and the changing global market conditions. I first present an observation‐based analysis conducted by visiting selected paper mills in Finland, the US, Germany and Sweden. Interesting differences and similarities emerge. Some of the observed differences lie in their focus on achieving incremental efficiency gains from better management of production processes, inventories, supply‐chain, product distribution and timing of modernization investments such as information technology. In the second part of the paper I present evidence on firms' productivity paths and the heterogeneity in productivity among relatively similar firms, and selected evidence of firms' investments in specific areas and how these affected productivity. My findings have implications for organizational behavior and business strategies employed by firms to improve their performance and productivity under changing environmental standards and market conditions. Copyright © 2013 John Wiley & Sons, Ltd and ERP Environment     

Evaluating a sequential tree-based procedure for multivariate imputation of complex missing data structures

Item nonresponse in survey data can pose significant problems for social scientists carrying out statistical modeling using a large number of explanatory variables. A number of imputation methods exist but many only deal with univariate imputation, or relatively simple cases of multivariate imputation, often assuming a monotone pattern of missingness. In this paper we evaluate a tree-based approach for multivariate imputation using real data from the 1970 British Cohort Study, known for its complex pattern of nonresponse. The performance of this tree-based approach is compared to mode imputation and a sequential regression based approach within a simulation study.     

Smooth estimation of a monotone hazard and a monotone density under random censoring

We consider kernel smoothed Grenander‐type estimators for a monotone hazard rate and a monotone density in the presence of randomly right censored data. We show that they converge at rate n^2/5 and that the limit distribution at a fixed point is Gaussian with explicitly given mean and variance. It is well known that standard kernel smoothing leads to inconsistency problems at the boundary points. It turns out that, also by using a boundary correction, we can only establish uniform consistency on intervals that stay away from the end point of the support (although we can go arbitrarily close to the right boundary).     

Replicating the Results in ‘A New Model of Trend Inflation’ Using Particle Markov Chain Monte Carlo

An article by Chan et al. ( 2013 ) published in the Journal of Business and Economic Statistics introduces a new model for trend inflation. They allow the trend inflation to evolve according to a bounded random walk. In order to draw the latent states from their respective conditional posteriors, they use accept–reject Metropolis–Hastings procedures. We reproduce their results using particle Markov chain Monte Carlo (PMCMC), which approaches drawing the latent states from a different technical point of view by relying on combining Markov chain Monte Carlo and sequential Monte Carlo methods. To conclude: we are able to reproduce the results of Chan et al. ( 2013 ). Copyright © 2015 John Wiley & Sons, Ltd.     

Non‐parametric bounds on quantiles under monotonicity assumptions: with an application to the Italian education returns

Within the inferential context of predicting a distribution of potential outcomes P[y(t)] under a uniform treatment assignment t ∈ T, this paper deals with partial identification of the α‐quantile of the distribution of interest Q_α[y(t)] under relatively weak and credible monotonicity‐type assumptions on the individual response functions and the population selection process. On the theoretical side, the paper adds to the existing results on non‐parametric bounds on quantiles with no prior information and under monotone treatment response (MTR) by introducing and studying the identifying properties of α‐quantile monotone treatment selection (α‐QMTS), α‐quantile monotone instrumental variables (α‐QMIV) and their combinations. The main result parallels that for the mean; MTR and α‐QMTS aid identification in a complementary fashion, so that combining them greatly increases identification power. The theoretical results are illustrated through an empirical application on the Italian returns to educational qualifications. Bounds on several quantiles of ln(wage) under different qualifications and on quantile treatments effects (QTE) are estimated and compared with parametric quantile regression (α‐QR) and α‐IVQR estimates from the same sample. Remarkably, the α‐QMTS & MTR upper bounds on the α‐QTE of a college degree versus elementary education imply smaller year‐by‐year returns than the corresponding α‐IVQR point estimates. Copyright © 2010 John Wiley & Sons, Ltd.     

The Living Arrangements of Single Mothers with Dependent Children

Abstract . Despite the rapid increase in families headed by single mothers, sufficient attention has not been paid to the living arrangements of these families. Most prior research has generally relied on Bureau of the Census definitions as household head and subfamily head to categorize single mothers' living arrangements. This two part grouping, however, obscures the actual diversity of living arrangements undertaken, including cohabitation with unrelated males. This paper moves beyond the standard two part grouping of single mothers and instead provides a detailed taxonomy of single mothers' living arrangements using data from the Current Population Survey. Among the findings, the economic status of families headed by single mothers varies tremendously by living arrangement, a fact which has been entirely overlooked in earlier research.     

Party loyalty as habit formation

In most democracies, at least two out of any three individuals vote for the same party in sequential elections. This paper presents a model in which vote‐persistence is partly due to the dependence of the utility on the previous voting decision. This dependence is termed ‘habit formation’. The model and its implications are supported by individual‐level panel data on the presidential elections in the USA in 1972 and 1976. For example, it is found that the voting probability is a function of the lagged choice variable, even when the endogeneity of the lagged variable is accounted for, and that the tendency to vote for different parties in sequential elections decreased with the age of the voter. Furthermore, using structural estimation the effect of habit is estimated, while allowing unobserved differences among respondents. The structural habit parameter implies that the effect of previous votes on the current decision is quite strong. The habit model fits the data better than the traditional ‘party identification’ model. Copyright © 2003 John Wiley & Sons, Ltd.     

Discrimination of Observations into One of Two Elliptic Populations based on Monotone Training Samples

In this paper we deal with the problem of classifying a p-dimensional random vector into one of two elliptically contoured populations with unknown and distinct mean vectors and a common, but unknown, scale matrix. The classification procedure is based on two-step monotone training samples, one from each population, with the same monotone pattern. Our aim is to extend the classification procedure, which proposed recently by Chung and Han (Ann Ins Stat Math 52:544–556, 2000). This procedure is a linear combination of two discriminant functions, one based on the complete samples and the other on the incomplete samples. The performance of the proposed classification rule is compared with the plug-in method, this means with the classification rule which arises if the unknown parameters are substituted, into the usual classification rule, by their estimators. In order to apply the plug-in method, the MLE of the location parameters and of the common scale matrix of g ≥ 2 elliptically contoured populations are analytically obtained on the basis of two-step monotone training samples.     

Greenwashing Revisited: In Search of a Typology and Accusation‐Based Definition Incorporating Legitimacy Strategies

Is greenwashing a concept describing companies using misleading communication or is it co‐constructed in the eye of the beholder? By discussing the literature, we find that existing definitions of greenwashing overemphasize the strategic intention to mislead and do not incorporate unjust allegations. Then, by combining signaling theory with legitimacy theory, we frame the communication process of the greenwashing accusation and the emergence of a negative narrative caused by the accusation and its effect on legitimacy. Hence, in this paper we argue that greenwashing epistemologically is constituted in the eye of the beholder , depending on an external accusation. Following this view, the greenwashing accusation is understood as a distortion factor altering the signal reliability of green messages. Based on our conceptual analysis, we provide a conceptual framework introducing a new typology of case‐based greenwashing (greenwashing , false greenwashing , potential greenwashing and no greenwashing ) and the effects of these types on corporate legitimacy. Finally, we propose a revised definition of greenwashing as co‐creation of an external accusation toward an organization with regard to presenting a misleading green message. Copyright © 2015 John Wiley & Sons, Ltd and ERP Environment     

Confidence Intervals for the Area Under the Receiver Operating Characteristic Curve in the Presence of Ignorable Missing Data

Receiver operating characteristic curves are widely used as a measure of accuracy of diagnostic tests and can be summarised using the area under the receiver operating characteristic curve (AUC). Often, it is useful to construct a confidence interval for the AUC; however, because there are a number of different proposed methods to measure variance of the AUC, there are thus many different resulting methods for constructing these intervals. In this article, we compare different methods of constructing Wald‐type confidence interval in the presence of missing data where the missingness mechanism is ignorable. We find that constructing confidence intervals using multiple imputation based on logistic regression gives the most robust coverage probability and the choice of confidence interval method is less important. However, when missingness rate is less severe (e.g. less than 70%), we recommend using Newcombe's Wald method for constructing confidence intervals along with multiple imputation using predictive mean matching.     

Standardization of Variables and Collinearity Diagnostic in Ridge Regression

Ridge estimation (RE) is an alternative method to ordinary least squares when there exists a collinearity problem in a linear regression model. The variance inflator factor (VIF) is applied to test if the problem exists in the original model and is also necessary after applying the ridge estimate to check if the chosen value for parameter k has mitigated the collinearity problem. This paper shows that the application of the original data when working with the ridge estimate leads to non‐monotone VIF values. García et al. (2014) showed some problems with the traditional VIF used in RE. We propose an augmented VIF, VIF_R(j,k), associated with RE, which is obtained by standardizing the data before augmenting the model. The VIF_R(j,k) will coincide with the VIF associated with the ordinary least squares estimator when k = 0. The augmented VIF has the very desirable properties of being continuous, monotone in the ridge parameter and higher than one.