Class-size effects in school systems around the world: Evidence from between-grade variation in TIMSS

We estimate the effect of class size on student performance in 11 countries, combining school fixed effects and instrumental variables to identify random class-size variation between two adjacent grades within individual schools. Conventional estimates of class-size effects are shown to be severely biased by the non-random placement of students between and within schools. While we find sizable beneficial effects of smaller classes in Greece and Iceland, we reject the possibility of even small effects in four countries and of large beneficial effects in an additional four countries. Noteworthy class-size effects are observed only in countries with relatively low teacher salaries.     

Semi‐analytic Approaches to Collateralized Debt Obligation Modelling

Collateralized debt obligations (CDOs) constitute an important class of asset‐backed securities. Most major banks use CDOs as portfolio management tools for achieving regulatory capital relief, economic risk transfer and funding. On the other side, banks and other financial institutions invest in CDO tranches with a risk/return profile matching their risk appetite and investment policies. For both sides (risk selling and risk buying) of a CDO transaction, sound mathematical tools are required for an evaluation of the deal. In this paper, we investigate some techniques for CDO modelling, paying special attention to approaches based on semi‐analytic approximations.     

Specifying Human Capital

A review of the measures of the stock of human capital used in empirical growth research – including adult literacy rates, school enrollment ratios, and average years of schooling of the working‐age population – reveals that human capital is mostly poorly proxied. The simple use of the most common proxy, average years of schooling, misspecifies the relationship between education and the stock of human capital. Based on human capital theory, the specification of human capital is extended to allow for decreasing returns to education and for differences in the quality of a year of education. The different specifications give rise to hugely differing measures of the stock of human capital across countries, and development‐accounting results show that misspecified human capital measures can lead to severe underestimation of the development effect of human capital.     

Copula dynamics in CDOs

Values of tranche spreads of collateralized debt obligations (CDOs) are driven by the joint default performance of the assets in the collateral pool. The dependence between the entities in the portfolio mainly depends on current economic conditions. Therefore, a correlation implied from tranches can be seen as a measure of the general situation of the credit market. We analyse the European market of standardized CDOs using tranches of the iTraxx index in the periods before and during the global financial crisis. We investigate the evolution of the correlations using different copula models: the standard Gaussian, the NIG, the double-t, and the Gumbel copula model. After calibration of these models, one obtains a time varying vector of parameters. We analyse the dynamic pattern of these coefficients. That enables us to forecast future parameters and consequently calculate Value-at-Risk measures for iTraxx Europe tranches.     

On optimal portfolio diversification with respect to extreme risks

Extreme losses of portfolios with heavy-tailed components are studied in the framework of multivariate regular variation. Asymptotic distributions of extreme portfolio losses are characterized by a functional γ _ξ =γ _ξ (α,Ψ) of the tail index α, the spectral measure Ψ, and the vector ξ of portfolio weights. Existence, uniqueness, and location of the optimal portfolio are analysed and applied to the minimization of risk measures. It is shown that diversification effects are positive for α>1 and negative for α<1. Strong consistency and asymptotic normality are established for a semiparametric estimator of the mapping ξ ↦ γ _ξ . Strong consistency is also established for the estimated optimal portfolio.     

Model uncertainty and VaR aggregation

Despite well-known shortcomings as a risk measure, Value-at-Risk (VaR) is still the industry and regulatory standard for the calculation of risk capital in banking and insurance. This paper is concerned with the numerical estimation of the VaR for a portfolio position as a function of different dependence scenarios on the factors of the portfolio. Besides summarizing the most relevant analytical bounds, including a discussion of their sharpness, we introduce a numerical algorithm which allows for the computation of reliable (sharp) bounds for the VaR of high-dimensional portfolios with dimensions d possibly in the several hundreds. We show that additional positive dependence information will typically not improve the upper bound substantially. In contrast higher order marginal information on the model, when available, may lead to strongly improved bounds. Several examples of practical relevance show how explicit VaR bounds can be obtained. These bounds can be interpreted as a measure of model uncertainty induced by possible dependence scenarios.     

Expenditure Reform in Industrialised Countries: A Case‐Study Approach*

This study examines reforms of public expenditure in industrialised countries over the past two decades. We distinguish ambitious and timid reformers and analyse in detail reform experiences in eight case studies of ambitious reform episodes. We find that ambitious reform countries reduce spending on transfers, subsidies and public consumption. Such expenditure retrenchment is also typically part of a comprehensive reform package that includes improvements in fiscal institutions as well as structural and other macroeconomic reforms. The study finds that ambitious expenditure retrenchment and reform coincides with large improvements in fiscal and economic growth indicators.     

Risk bounds for factor models

Recent literature has investigated the risk aggregation of a portfolio \(X=(X_{i})_{1\leq i\leq n}\) under the sole assumption that the marginal distributions of the risks \(X_{i} \) are specified, but not their dependence structure. There exists a range of possible values for any risk measure of \(S=\sum_{i=1}^{n}X_{i}\), and the dependence uncertainty spread, as measured by the difference between the upper and the lower bound on these values, is typically very wide. Obtaining bounds that are more practically useful requires additional information on dependence.Here, we study a partially specified factor model in which each risk \(X_{i}\) has a known joint distribution with the common risk factor \(Z\), but we dispense with the conditional independence assumption that is typically made in fully specified factor models. We derive easy-to-compute bounds on risk measures such as Value-at-Risk (\(\mathrm{VaR}\)) and law-invariant convex risk measures (e.g. Tail Value-at-Risk (\(\mathrm{TVaR}\))) and demonstrate their asymptotic sharpness. We show that the dependence uncertainty spread is typically reduced substantially and that, contrary to the case in which only marginal information is used, it is not necessarily larger for \(\mathrm{VaR}\) than for \(\mathrm{TVaR}\).     

Reduction of Value-at-Risk bounds via independence and variance information

We derive lower and upper bounds for the Value-at-Risk of a portfolio of losses when the marginal distributions are known and independence among (some) subgroups of the marginal components is assumed. We provide several actuarial examples showing that the newly proposed bounds strongly improve those available in the literature that are based on the sole knowledge of the marginal distributions. When the variance of the joint portfolio loss is small enough, further improvements can be obtained.