Identifiability of mean‐reverting measurement error with instrumental variable

In the context where one main regressor is measured with error and at least one instrumental variable is available for the correction of measurement error, this paper provides, to the best of our knowledge, a first point‐identification result on the variance of measurement error, the variance of latent variable, and their covariance. We show that the parameters are identified if the regression model is not de facto linear. We illustrate the method in an application to identify mean‐reverting measurement error, a typical issue in reported income where the measurement error of income is negatively correlated with the true income.     

Spline regression for hazard rate estimation when data are censored and measured with error

In this paper, we study an estimation problem where the variables of interest are subject to both right censoring and measurement error. In this context, we propose a nonparametric estimation strategy of the hazard rate, based on a regression contrast minimized in a finite‐dimensional functional space generated by splines bases. We prove a risk bound of the estimator in terms of integrated mean square error and discuss the rate of convergence when the dimension of the projection space is adequately chosen. Then we define a data‐driven criterion of model selection and prove that the resulting estimator performs an adequate compromise. The method is illustrated via simulation experiments that show that the strategy is successful.     

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.     

THE ECONOMICS OF COUNTERTERRORISM: A SURVEY

We provide a review of theoretical and empirical contributions on the economic analysis of terrorism and counterterrorism. We argue that simple rational‐choice models of terrorist behavior – in the form of cost‐benefit models – already provide a well‐founded theoretical framework for the study of terrorism and counterterrorism. We also hint at their limitations which relate to the failure of accounting for the dynamics between terrorism and counterterrorism that may produce unintended second‐order effects as well as for the costs associated with counterterrorism and its international dimension. We reevaluate previously proposed counterterrorism strategies accordingly. Finally, in the light of our findings, we discuss interesting areas of future research.     

Estimation of Poverty Transition Matrices with Noisy Data

This paper investigates measurement error biases in estimated poverty transition matrices. We compare transition matrices based on survey expenditure data to transition matrices based on measurement‐error‐free simulated expenditure. The simulation model uses estimates that correct for measurement error in expenditure. We find that time‐varying measurement error in expenditure data magnifies economic mobility. Roughly 45% of households initially in poverty at time t ? 1 are found to be out of poverty at time t using data from the Korean Labor and Income Panel Study. When measurement error is removed, this drops to between 26 and 31% of households initially in poverty. Copyright © 2016 John Wiley & Sons, Ltd.     

Preliminary test estimators of the parameters of simple linear model with measurement error

In this paper, we discuss the properties of preliminary test estimators (PTE) of the parameters of simple linear model with measurement error (ME model) when the slope of the linear model is suspected to be zero. Expressions of the bias, MSE and efficiencies are obtained under conditional as well as unconditional situations with known reliability coefficient. Conditional model results are compared to the standard model without measurement error. We also provide the unconditional model analysis in finite samples. Asymptotic theory under local alternatives is developed when the variance of measurement error or the ratio of the variance of the model error relative to the variance of the measurement error is known. Asymptotic expressions of bias and MSE of the estimators along with their efficiencies are obtained. In every case, it is shown that the measurement error tend to increase the variability of the estimators compared to the estimators without measurement error. Graphs and tables are provided to see these results and to determine optimum level of significance for minimum guaranteed efficiency. Received October 2001 RID="*" ID="*"  A. K. Md. E. Saleh is a Distinguished Research Professor and H. M. Kim is a Ph.D. candidate in the School of Mathematics and Statistics, Carleton University, Ottawa. Acknowledgment. The authors gratefully acknowledge the constructive suggestion of the referees to improve the paper. The research is supported by NSERC grant A3088.     

Graphical Tools for Detecting Departures from Linear Mixed Model Assumptions and Some Remedial Measures

We review some results on the analysis of longitudinal data or, more generally, of repeated measures via linear mixed models starting with some exploratory statistical tools that may be employed to specify a tentative model. We follow with a summary of inferential procedures under a Gaussian set‐up and then discuss different diagnostic methods focusing on residual analysis but also addressing global and local influence. Based on the interpretation of diagnostic plots related to three types of residuals (marginal, conditional and predicted random effects) as well as on other tools, we proceed to identify remedial measures for possible violations of the proposed model assumptions, ranging from fine‐tuning of the model to the use of elliptically symmetric or skew‐elliptical linear mixed models as well as of robust estimation methods. We specify many results available in the literature in a unified notation and highlight those with greater practical appeal. In each case, we discuss the availability of model diagnostics as well as of software and give general guidelines for model selection. We conclude with analyses of three practical examples and suggest further directions for research.     

The relation between wealth and labour market transitions: an empirical study for the Netherlands

We study the relationship between wealth and labour market transitions. A lifecycle model, in which individuals are faced by uncertainty about the availability of jobs, serves as a basis for a reduced‐form specification for the probabilities of labour market transitions, which depend on wealth according to the model. Theory implies a negative effect of wealth on the probability of becoming or staying employed. This implication is tested for in a reduced‐from model of labour market transitions, in which we allow for random effects, initial conditions, and measurement error in wealth. Elasticities of transitions probabilities with respect to wealth are presented. Copyright © 2002 John Wiley & Sons, Ltd.     

Modelling Time Series of Counts in Epidemiology

We review generalized dynamic models for time series of count data. Usually temporal counts are modelled as following a Poisson distribution, and a transformation of the mean depends on parameters which evolve smoothly with time. We generalize the usual dynamic Poisson model by considering continuous mixtures of the Poisson distribution. We consider Poisson‐gamma and Poisson‐log‐normal mixture models. These models have a parameter for each time t which captures possible extra‐variation present in the data. If the time interval between observations is short, many observed zeros might result. We also propose zero inflated versions of the models mentioned above. In epidemiology, when a count is equal to zero, one does not know if the disease is present or not. Our model has a parameter which provides the probability of presence of the disease given no cases were observed. We rely on the Bayesian paradigm to obtain estimates of the parameters of interest, and discuss numerical methods to obtain samples from the resultant posterior distribution. We fit the proposed models to artificial data sets and also to a weekly time series of registered number of cases of dengue fever in a district of the city of Rio de Janeiro, Brazil, during 2001 and 2002.     

Partially varying coefficient instrumental variables models

In this article, we study a new class of semiparametric instrumental variables models, in which the structural function has a partially varying coefficient functional form. Under this specification, the model is linear in the endogenous/exogenous components with unknown constant or functional coefficients. As a result, the ill‐posed inverse problem in a general non‐parametric model with continuous endogenous variables can be avoided. We propose a three‐step estimation procedure for estimating both constant and functional coefficients and establish their asymptotic properties such as consistency and asymptotic normality. We develop consistent estimators for their error variances. We demonstrate that the constant coefficient estimators achieve the optimal ‐convergence rate, and the functional coefficient estimators are oracle. In addition, efficiency issue of the parameter estimation is discussed and a simple efficient estimator is proposed. The proposed procedure is illustrated via a Monte Carlo simulation and an application to returns to education.     

Stochastic error specification in primal and dual production systems

In this paper we derive both primal and dual‐cost systems in which the stochastic specifications arise from the model (random environment or measurement errors and optimization errors)—not tacked on at the end after the deterministic system is worked out. Derivation of the error structures is based on cost‐minimizing behavior on the firms. The primal systems constitute the production function and the first‐order conditions of cost minimization. We consider two dual‐cost systems. The first dual system is based on the cost function and cost share equations. The second dual system is based on a multiplicative general error production model that is an alternative to McElroy's additive general error production model. Our multiplicative general error model gives a clear and intuitive economic meaning to the error components. The resulting cost system is easy to estimate compared to the alternative cost systems. The error components in the multiplicative general error model can capture heterogeneity in the technology parameters even in a cross‐sectional model. Panel data are not necessary to estimate either the primal or dual systems. The models are estimated using data on 72 fossil fuel‐fired steam electric power generation plants (observed for the period 1986–1999) in the USA. Copyright © 2009 John Wiley & Sons, Ltd.     

BAYESIAN STATE SPACE MODELS IN MACROECONOMETRICS

State space models play an important role in macroeconometric analysis and the Bayesian approach has been shown to have many advantages. This paper outlines recent developments in state space modelling applied to macroeconomics using Bayesian methods. We outline the directions of recent research, specifically the problems being addressed and the solutions proposed. After presenting a general form for the linear Gaussian model, we discuss the interpretations and virtues of alternative estimation routines and their outputs. This discussion includes the Kalman filter and smoother, and precision-based algorithms. As the advantages of using large models have become better understood, a focus has developed on dimension reduction and computational advances to cope with high-dimensional parameter spaces. We give an overview of a number of recent advances in these directions. Many models suggested by economic theory are either non-linear or non-Gaussian, or both. We discuss work on the particle filtering approach to such models as well as other techniques that use various approximations – to either the time state and measurement equations or to the full posterior for the states – to obtain draws.     

Estimating the economic return to educational levels using data on twins

This paper relaxes some restrictions of previous twin‐based estimates of the effects of education on earnings. First, it estimates the earnings premiums associated with different educational levels. Second, it estimates a piecewise linear relationship between the natural logarithm of annual earnings and years of schooling. Third, the measurement error corrections are based on a less restrictive, ‘non‐classical’, measurement error model. The estimation strategy implies that ability bias can be investigated separately in different parts of the educational distribution. The linear relationship between the logarithm of annual earnings and years of schooling is rejected. Furthermore, the results in the sample of identical (MZ) twins indicated both that the ability bias could be of different signs and of different magnitudes in different parts of the educational distribution. The twin‐based estimates in the sample of fraternal (DZ) twins did not display any marked differences as compared to the cross‐sectional estimates. Finally, the results indicated that the error‐corrected twin‐based estimates of the average return to years of schooling that rely on a classical measurement error model are upwards biased by approximately 30%. Copyright © 2004 John Wiley & Sons, Ltd.     

ERRORS IN VARIABLES IN ECONOMETRICS: NEW DEVELOPMENTS AND RECURRENT THEMES*

The paper reviews some old and new approaches to the analysis of linear models with errors in variables. The emphasis is on the identification problems that usually arise in errors–in–variables models and on the various types of additional information that econometricians have invoked to be able to estimate parameters consistently. The approaches discussed include instrumental variables, grouping, simultaneous equations, multiple equations and bounds on measurement error variances.     

Network-centric business models for health,social care and wellbeing solutions in the internet of things

In this multiple case study we analyze solutions based on connected devices in the context of health, social care and wellbeing. Based on the consideration that a solution is a combination of services and products, we build on the notion that business models can be studied at a firm-level and also at a network-level. The network-level analysis is used to motivate the reasons why solutions emerging at the intersection of the healthcare and the ICT industries benefit from collaboration among different actors. We conclude that the firm- and the network-level development of business models provide alignment in the business network and are useful to establish the relation that technological component have with overall solutions. Our findings suggest that some component bring novelty in the final offer without affecting the ongoing operation, while other component aim at improving the internal working processes, with minimal effects on the final offer to end users. We discuss the benefits of a network-level perspective for each case.     

A SURVEY OF MEASUREMENT BIASES IN PRICE INDEXES

Abstract. This paper reviews the literature on measurement error in the major US price indexes—the Consumer Price Index (CPI), the Producer Price Index (RPI), and the Gross Domestic Product (GDP) deflators. We take as our point of departure Triplett's, 1975, survey and focus on the studies of measurement error that have appeared since then. We review the problems of substitution bias, quality bias, new goods bias, and outlet substitution bias that are generally considered to be the main sources of error in price indexes. The bulk of the paper is devoted to problems in the CPI and PPI, as the GDP deflators tend to be based mainly on the components of these series. We find that there has been surprisingly little work on the problem of overall measurement error in any of these price indexes, and we conclude that there is very little scientific basis for the commonly accepted notion that measured inflation at 2 to 3 percent a year is consistent with price stability.     

Modelling response error in school effectiveness research

Statistical modelling of school effectiveness in educational research is considered. Variance component models are generally accepted for the analysis of such studies. A shortcoming is that outcome variables are still treated as measured without an error. Unreliable variables produce biases in the estimates of the other model parameters. The variability of the relationships across schools and the effects of schools on students' outcomes differ substantially when taking the measurement error in the dependent variables of the variance component models into account. The random effects model can be extended to handle measurement error using a response model, leading to a random effects item response theory model. This extended random effects model is in particular suitable when subjects are measured repeatedly on the same outcome at several points in time.     

Small Area Estimation-New Developments and Directions

The purpose of this paper is to provide a critical review of the main advances in small area estimation (SAE) methods in recent years. We also discuss some of the earlier developments, which serve as a necessary background for the new studies. The review focuses on model dependent methods with special emphasis on point prediction of the target area quantities, and mean square error assessments. The new models considered are models used for discrete measurements, time series models and models that arise under informative sampling. The possible gains from modeling the correlations among small area random effects used to represent the unexplained variation of the small area target quantities are examined. For review and appraisal of the earlier methods used for SAE, see Ghosh & Rao (1994).     

Non‐Classical Measurement Error in Long‐Term Retrospective Recall Surveys*

Applied microeconomic researchers are beginning to use long‐term retrospective survey data in settings where conventional longitudinal survey data are unavailable. However, inaccurate long‐term recall could induce non‐classical measurement error, for which conventional statistical corrections are less effective. In this article, we use the unique Panel Study of Income Dynamics Validation Study to assess the accuracy of long‐term retrospective recall data. We find underreporting of transitory variation which creates a non‐classical measurement error problem.     

A Review on Dimension Reduction

Summarizing the effect of many covariates through a few linear combinations is an effective way of reducing covariate dimension and is the backbone of (sufficient) dimension reduction. Because the replacement of high‐dimensional covariates by low‐dimensional linear combinations is performed with a minimum assumption on the specific regression form, it enjoys attractive advantages as well as encounters unique challenges in comparison with the variable selection approach. We review the current literature of dimension reduction with an emphasis on the two most popular models, where the dimension reduction affects the conditional distribution and the conditional mean, respectively. We discuss various estimation and inference procedures in different levels of detail, with the intention of focusing on their underneath idea instead of technicalities. We also discuss some unsolved problems in this area for potential future research.