The Multilevel Approach to Repeated Measures for Complete and Incomplete Data

Repeated measurements often are analyzed by multivariate analysis of variance (MANOVA). An alternative approach is provided by multilevel analysis, also called the hierarchical linear model (HLM), which makes use of random coefficient models. This paper is a tutorial which indicates that the HLM can be specified in many different ways, corresponding to different sets of assumptions about the covariance matrix of the repeated measurements. The possible assumptions range from the very restrictive compound symmetry model to the unrestricted multivariate model. Thus, the HLM can be used to steer a useful middle road between the two traditional methods for analyzing repeated measurements. Another important advantage of the multilevel approach to analyzing repeated measures is the fact that it can be easily used also if the data are incomplete. Thus it provides a way to achieve a fully multivariate analysis of repeated measures with incomplete data. This revised version was published online in June 2006 with corrections to the Cover Date.     

Robustness issues in multilevel regression analysis

A multilevel problem concerns a population with a hierarchical structure. A sample from such a population can be described as a multistage sample. First, a sample of higher level units is drawn (e.g. schools or organizations), and next a sample of the sub‐units from the available units (e.g. pupils in schools or employees in organizations). In such samples, the individual observations are in general not completely independent. Multilevel analysis software accounts for this dependence and in recent years these programs have been widely accepted. Two problems that occur in the practice of multilevel modeling will be discussed. The first problem is the choice of the sample sizes at the different levels. What are sufficient sample sizes for accurate estimation? The second problem is the normality assumption of the level‐2 error distribution. When one wants to conduct tests of significance, the errors need to be normally distributed. What happens when this is not the case? In this paper, simulation studies are used to answer both questions. With respect to the first question, the results show that a small sample size at level two (meaning a sample of 50 or less) leads to biased estimates of the second‐level standard errors. The answer to the second question is that only the standard errors for the random effects at the second level are highly inaccurate if the distributional assumptions concerning the level‐2 errors are not fulfilled. Robust standard errors turn out to be more reliable than the asymptotic standard errors based on maximum likelihood.     

A model of the Dutch labour market (AMO-K)

Summary So far, the labour market has not received any special attention from macro-econometric model builders. In this article an attempt has been made to describe the labour market in detail, paying attention to such important phenomena as the friction between labour supply and demand, the heterogeneity of labour, the dependence of labour supply on the labour-market situation, the Phillips mechanism and the impact of real wages on labour demand. To make it suitable for policy simulations, the model has been extended to a complete macro-econometric model, taking account of the fact that both labour and capital limit the production possibilities.This paper summarises an extensive Dutch report on the construction of a model for the Netherlands labour market. The title of the original report is AMO-K: Een arbeidsmarktmodel met twee categorieën arbeid; (AMO-K, A labour-market model with two categories of labour) ; it was published by the Netherlands Economic Institute (NEI) in Rotterdam in the so-called Olive Series, 1982-2, pp. 403ff. Some details of the model presented in that report were changed after its publication; see G. den Broeder, AMO-K 81-12, Tussenrapport betreffende de verdere ontwikkeling van het arbeidsmarktmodel (Interim report on the further development of the labourmarket model), Rotterdam, September 1983. Since then, only minor changes have been carried through. The model reproduced in this paper is the modified version. The model was developed within the National Programme of Labour-Market Research (NPAO) (now defunct), the NPAO organisation having granted a commission to the NEI in Rotterdam.     

Multivariate volatility forecasts for stock market indices

Volatility forecasts aim to measure future risk and they are key inputs for financial analysis. In this study, we forecast the realized variance as an observable measure of volatility for several major international stock market indices and accounted for the different predictive information present in jump, continuous, and option-implied variance components. We allowed for volatility spillovers in different stock markets by using a multivariate modeling approach. We used heterogeneous autoregressive (HAR)-type models to obtain the forecasts. Based an out-of-sample forecast study, we show that: (i) including option-implied variances in the HAR model substantially improves the forecast accuracy, (ii) lasso-based lag selection methods do not outperform the parsimonious day-week-month lag structure of the HAR model, and (iii) cross-market spillover effects embedded in the multivariate HAR model have long-term forecasting power.     

How Proper Is Sequential Equilibrium?

A strategy profile of a normal form game is proper if and only if it is quasi-perfect in every extensive form (with that normal form). Thus, properness requires optimality along a sequence of supporting trembles, while sequentiality only requires optimality in the limit. A decision-theoretic implementation of sequential rationality, strategic independence respecting equilibrium (SIRE), is defined and compared to proper equilibrium, using lexicographic probability systems. Finally, we give tremble-based characterizations, which do not involve structural features of the game, of the rankings of strategies that underlie proper equilibrium and SIRE.Journal of Economic LiteratureClassification Numbers: C70, C72.     

Structural Decomposition Analysis of Physical Flows in the Economy

Many environmental problems can be attributedto the extraction and emissions of physicalsubstances. Increasing our understanding of theeconomic and technological driving forcesbehind these physical flows can contribute tosolving the environmental problems related tothem. The input-output framework is a usefulsetting in which to integrate detailedinformation about economic structure andphysical flows. In this article a specificmethod in input-output analysis is reviewed,namely Structural Decomposition Analysis (SDA).It is based on comparative static analysis,which decomposes historical changes of a policyvariable into determinant effects. SDA has beenapplied, for example, to analyze the demand andtechnological driving forces of energy use,CO₂-emissions and various other pollutantsand resources. This article examines thetheoretical aspects of structuraldecomposition, in particular those concerningphysical flows and environmental issues.Furthermore, the article includes an extensivesurvey of empirical studies.     

Evolution of harvesting strategies: replicator and resource dynamics

Abstract. Economic theories of managing renewable resources, such as fisheries and forestry, traditionally assume that individual harvesters are perfectly rational and thus able to compute the harvesting strategy that maximizes their discounted profits. The current paper presents an alternative approach based on bounded rationality and evolutionary mechanisms. It is assumed that individual harvesters face a choice between two harvesting strategies. The evolution of the distribution of strategies in the population is modeled through a replicator dynamics equation. The latter captures the idea that strategies yielding above average profits are demanded more than strategies yielding below average profits, so that the first type ends up accounting for a larger part in the population. From a mathematical perspective, the combination of resource and evolutionary processes leads to complex dynamics. The paper presents the existence and stability conditions for each steady-state of the system and analyzes dynamic paths to the equilibrium. In addition, effects of changes in prices are analyzed. A main result of the paper is that under certain conditions both strategies can survive in the long-run. Correspondence to: J. Noailly     

Towards a kernel theory of external knowledge integration for high-tech firms: Exploring a failed theory test

Designing information systems (ISs) requires a thorough understanding of the organizational knowledge processes in which these systems are used. Although much is known about internal organizational knowledge processes, the understanding of external knowledge processes is less developed. Hence, this paper reflects an attempt to operationalize and test a model of the process of external knowledge integration (EKI), consisting of an identification, acquisition, and utilization stage. We utilize high-technology based firms from a variety of high-tech categories including nanotechnology based firms since these firms have critical knowledge integration needs. The results of an international survey, with responses of 317 high-tech companies, suggest that not these three EKI-stages, but four organizational effectiveness functions (goal attainment, pattern maintenance, adaptation, and integration) account for most variation in responses. These findings seem to imply that ISs that are to support the EKI-process should be designed according to organizational effectiveness functions rather than to EKI-stages. It is proposed that each organizational effectiveness function imposes different requirements on ISs because users interact differently with IS in each function.     

Evolutionary stability and lexicographic preferences

We explore the interaction between evolutionary stability and lexicographic preferences. To do so, we define a limit Nash equilibrium for a lexicographic game as the limit of Nash equilibria of nearby games with continuous preferences. Nash equilibria of lexicographic games are limit Nash equilibria, but not conversely. Modified evolutionarily stable strategies (Binmore and Samuelson, 1992. J. Econ. Theory 57, 278–305) are limit Nash equilibria. Modified evolutionary stability differs from “lexicographic evolutionarily stability” (defined by extending the common characterization of evolutionary stability to lexicographic preferences) in the order in which limits in the payoff space and the space of invasion barriers are taken.     

A way out of the credibility crisis of models used in integrated environmental assessment

Integrated Assessment Models (IAMs) have been widely used in environmental policy making because they simulate natural and socio-economic systems by integrating knowledge derived from a wide range of disciplines. The current IAMs have been found to be limited due to their inability to display both the value-laden nature of the assumptions that underlie the model and the uncertainties in their outputs. A Post-Normal Science approach is required for dealing with these issues, involving participation of ‘extended peer communities’ providing their ‘extended facts’.