A correlation sensitivity analysis of non-life underwriting risk in solvency capital requirement estimation

This paper analyses the impact of using different correlation assumptions between lines of business when estimating the risk-based capital reserve, the Solvency Capital Requirement (SCR), under Solvency II regulations. A case study is presented and the SCR is calculated according to the Standard Model approach. Alternatively, the requirement is then calculated using an Internal Model based on a Monte Carlo simulation of the net underwriting result at a one-year horizon, with copulas being used to model the dependence between lines of business. To address the impact of these model assumptions on the SCR we conduct a sensitivity analysis. We examine changes in the correlation matrix between lines of business and address the choice of copulas. Drawing on aggregate historical data from the Spanish non-life insurance market between 2000 and 2009, we conclude that modifications of the correlation and dependence assumptions have a significant impact on SCR estimation.

A correlation sensitivity analysis of non-life underwriting risk in solvency capital requirement estimation

This paper analyses the impact of using different correlation assumptions between lines of business when estimating the risk-based capital reserve, the Solvency Capital Requirement -SCR-, under Solvency II regulations. A case study is presented and the SCR is calculated according to the Standard Model approach. Alternatively, the requirement is then calculated using an Internal Model based on a Monte Carlo simulation of the net underwriting result at a one-year horizon, with copulas being used to model the dependence between lines of business. To address the impact of these model assumptions on the SCR we conduct a sensitivity analysis. We examine changes in the correlation matrix between lines of business and address the choice of copulas. Drawing on aggregate historical data from the Spanish non-life insurance market between 2000 and 2009, we conclude that modifications of the correlation and dependence assumptions have a significant impact on SCR estimation.

Dynamic graphics of parametrically linked multivariate methods used in compositional data analysis

Many multivariate methods that are apparently distinct can be linked by introducing oneor more parameters in their definition. Methods that can be linked in this way arecorrespondence analysis, unweighted or weighted logratio analysis (the latter alsoknown as "spectral mapping"), nonsymmetric correspondence analysis, principalcomponent analysis (with and without logarithmic transformation of the data) andmultidimensional scaling. In this presentation I will show how several of thesemethods, which are frequently used in compositional data analysis, may be linkedthrough parametrizations such as power transformations, linear transformations andconvex linear combinations. Since the methods of interest here all lead to visual mapsof data, a "movie" can be made where where the linking parameter is allowed to vary insmall steps: the results are recalculated "frame by frame" and one can see the smoothchange from one method to another. Several of these "movies" will be shown, giving adeeper insight into the similarities and differences between these methods

Modelling structural zeros in compositional data

This analysis was stimulated by the real data analysis problem of householdexpenditure data. The full dataset contains expenditure data for a sample of 1224 households. The expenditure is broken down at 2 hierarchical levels: 9 major levels (e.g. housing, food, utilities etc.) and 92 minor levels. There are also 5 factors and 5 covariates at the household level. Not surprisingly, there are a small number of zeros at the major level, but many zeros at the minor level. The question is how best to model the zeros. Clearly, models that tryto add a small amount to the zero terms are not appropriate in general as at least some of the zeros are clearly structural, e.g. alcohol/tobacco for households that are teetotal. The key question then is how to build suitable conditional models. For example, is the sub-composition of spendingexcluding alcohol/tobacco similar for teetotal and non-teetotal households?In other words, we are looking for sub-compositional independence. Also, what determines whether a household is teetotal? Can we assume that it is independent of the composition? In general, whether teetotal will clearly depend on the household level variables, so we need to be able to model this dependence. The other tricky question is that with zeros on more than onecomponent, we need to be able to model dependence and independence of zeros on the different components. Lastly, while some zeros are structural, others may not be, for example, for expenditure on durables, it may be chance as to whether a particular household spends money on durableswithin the sample period. This would clearly be distinguishable if we had longitudinal data, but may still be distinguishable by looking at the distribution, on the assumption that random zeros will usually be for situations where any non-zero expenditure is not small.While this analysis is based on around economic data, the ideas carry over tomany other situations, including geological data, where minerals may be missing for structural reasons (similar to alcohol), or missing because they occur only in random regions which may be missed in a sample (similar to the durables)

Bayesian tools for zero counts in compositional data

The log-ratio methodology makes available powerful tools for analyzing compositionaldata. Nevertheless, the use of this methodology is only possible for those data setswithout null values. Consequently, in those data sets where the zeros are present, aprevious treatment becomes necessary. Last advances in the treatment of compositionalzeros have been centered especially in the zeros of structural nature and in the roundedzeros. These tools do not contemplate the particular case of count compositional datasets with null values. In this work we deal with \count zeros" and we introduce atreatment based on a mixed Bayesian-multiplicative estimation. We use the Dirichletprobability distribution as a prior and we estimate the posterior probabilities. Then weapply a multiplicative modi¯cation for the non-zero values. We present a case studywhere this new methodology is applied.Key words: count data, multiplicative replacement, composition, log-ratio analysis

Possible solution of some essential zero problems in compositional data analysis

One of the tantalising remaining problems in compositional data analysis lies in how to deal with data sets in which there are components which are essential zeros. By anessential zero we mean a component which is truly zero, not something recorded as zero simply because the experimental design or the measuring instrument has not been sufficiently sensitive to detect a trace of the part. Such essential zeros occur inmany compositional situations, such as household budget patterns, time budgets,palaeontological zonation studies, ecological abundance studies. Devices such as nonzero replacement and amalgamation are almost invariably ad hoc and unsuccessful insuch situations. From consideration of such examples it seems sensible to build up amodel in two stages, the first determining where the zeros will occur and the secondhow the unit available is distributed among the non-zero parts. In this paper we suggest two such models, an independent binomial conditional logistic normal model and a hierarchical dependent binomial conditional logistic normal model. The compositional data in such modelling consist of an incidence matrix and a conditional compositional matrix. Interesting statistical problems arise, such as the question of estimability of parameters, the nature of the computational process for the estimation of both the incidence and compositional parameters caused by the complexity of the subcompositional structure, the formation of meaningful hypotheses, and the devising of suitable testing methodology within a lattice of such essential zero-compositional hypotheses. The methodology is illustrated by application to both simulated and real compositional data

Dynamic graphics of parametrically linked multivariate methods used in compositional data analysis

Many multivariate methods that are apparently distinct can be linked by introducing oneor more parameters in their definition. Methods that can be linked in this way arecorrespondence analysis, unweighted or weighted logratio analysis (the latter alsoknown as "spectral mapping"), nonsymmetric correspondence analysis, principalcomponent analysis (with and without logarithmic transformation of the data) andmultidimensional scaling. In this presentation I will show how several of thesemethods, which are frequently used in compositional data analysis, may be linkedthrough parametrizations such as power transformations, linear transformations andconvex linear combinations. Since the methods of interest here all lead to visual mapsof data, a "movie" can be made where where the linking parameter is allowed to vary insmall steps: the results are recalculated "frame by frame" and one can see the smoothchange from one method to another. Several of these "movies" will be shown, giving adeeper insight into the similarities and differences between these methods.

Convergence in panel data: Evidence from the skipping estimation

This paper demonstrates that, unlike what the conventional wisdom says, measurement error biases in panel data estimation of convergence using OLS with fixed effects are huge, not trivial. It does so by way of the "skipping estimation"': taking data from every m years of the sample (where m is an integer greater than or equal to 2), as opposed to every single year. It is shown that the estimated speed of convergence from the OLS with fixed effects is biased upwards by as much as 7 to 15%.

Testing for multicointegration in panel data with common factors

The paper addresses the concept of multicointegration in panel data frame- work. The proposal builds upon the panel data cointegration procedures developed in Pedroni (2004), for which we compute the moments of the parametric statistics. When individuals are either cross-section independent or cross-section dependence can be re- moved by cross-section demeaning, our approach can be applied to the wider framework of mixed I(2) and I(1) stochastic processes analysis. 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 inventories, sales and production relationship for a panel of US industries.

Testing for multicointegration in panel data with common factors

The paper addresses the concept of multicointegration in panel data frame- work. The proposal builds upon the panel data cointegration procedures developed in Pedroni (2004), for which we compute the moments of the parametric statistics. When individuals are either cross-section independent or cross-section dependence can be re- moved by cross-section demeaning, our approach can be applied to the wider framework of mixed I(2) and I(1) stochastic processes analysis. 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 inventories, sales and production relationship for a panel of US industries.

Fluctuations in domain growth: Ginzburg-Landau equations with multiplicative noise

Ginzburg-Landau equations with multiplicative noise are considered, to study the effects of fluctuations in domain growth. The equations are derived from a coarse-grained methodology and expressions for the resulting concentration-dependent diffusion coefficients are proposed. The multiplicative noise gives contributions to the Cahn-Hilliard linear-stability analysis. In particular, it introduces a delay in the domain-growth dynamics.

Mining and exploiting domain-specific corpora in the PANACEA platform

The objective of the PANACEA ICT-2007.2.2 EU project is to build a platform that automates the stages involved in the acquisition,production, updating and maintenance of the large language resources required by, among others, MT systems. The development of a Corpus Acquisition Component (CAC) for extracting monolingual and bilingual data from the web is one of the most innovative building blocks of PANACEA. The CAC, which is the first stage in the PANACEA pipeline for building Language Resources, adopts an efficient and distributed methodology to crawl for web documents with rich textual content in specific languages and predefined domains. The CAC includes modules that can acquire parallel data from sites with in-domain content available in more than one language. In order to extrinsically evaluate the CAC methodology, we have conducted several experiments that used crawled parallel corpora for the identification and extraction of parallel sentences using sentence alignment. The corpora were then successfully used for domain adaptation of Machine Translation Systems.

Human capital in growth regressions: how much difference does data quality make? An update and further results

We construct estimates of educational attainment for a sample of OECD countries using previously unexploited sources. We follow a heuristic approach to obtain plausible time profiles for attainment levels by removing sharp breaks in the data that seem to reflect changes in classification criteria. We then construct indicators of the information content of our series and a number of previously available data sets and examine their performance in several growth specifications. We find a clear positive correlation between data quality and the size and significance of human capital coefficients in growth regressions. Using an extension of the classical errors in variables model, we construct a set of meta-estimates of the coefficient of years of schooling in an aggregate Cobb-Douglas production function. Our results suggest that, after correcting for measurement error bias, the value of this parameter is well above 0.50.

Distributional equivalence and subcompositional coherence in the analysis of contingency tables, ratio-scale measurements and compositional data

We consider two fundamental properties in the analysis of two-way tables of positive data: the principle of distributional equivalence, one of the cornerstones of correspondence analysis of contingency tables, and the principle of subcompositional coherence, which forms the basis of compositional data analysis. For an analysis to be subcompositionally coherent, it suffices to analyse the ratios of the data values. The usual approach to dimension reduction in compositional data analysis is to perform principal component analysis on the logarithms of ratios, but this method does not obey the principle of distributional equivalence. We show that by introducing weights for the rows and columns, the method achieves this desirable property. This weighted log-ratio analysis is theoretically equivalent to spectral mapping , a multivariate method developed almost 30 years ago for displaying ratio-scale data from biological activity spectra. The close relationship between spectral mapping and correspondence analysis is also explained, as well as their connection with association modelling. The weighted log-ratio methodology is applied here to frequency data in linguistics and to chemical compositional data in archaeology.

Level shifts in a panel data based unit root test : an application to the rate of unemployment

Several unit root tests in panel data have recently been proposed. The test developed by Harris and Tzavalis (1999 JoE) performs particularly well when the time dimension is moderate in relation to the cross-section dimension. However, in common with the traditional tests designed for the unidimensional case, it was found to perform poorly when there is a structural break in the time series under the alternative. Here we derive the asymptotic distribution of the test allowing for a shift in the mean, and assess the small sample performance. We apply this new test to show how the hypothesis of (perfect) hysteresis in Spanish unemployment is rejected in favour of the alternative of the natural unemployment rate, when the possibility of a change in the latter is considered.