The aggregation of capital over vintages in a model of embodied technical progress

The paper considers how to measure capital in a model where technical progress is embodied in new units of capital. This embodiment model also assumes that once new units of capital are installed, it cannot be “unbolted” and sold on the second hand market. A significant difference between this Solow–Harper model and the traditional capital services model due to Jorgenson and his coworkers is that rising real wage rates will generally induce early retirement of assets; i.e., this model can provide an explanation for obsolescence. The paper studies how to aggregate over vintages and how to measure depreciation in the context of this embodiment model. These problems are more complicated than the corresponding problems in the traditional capital services model because the age of retirement of an asset is endogenous in the embodiment model. The paper uses duality theory to simplify the exposition.

Heterogeneous expectations and long-range correlation of the volatility of asset returns

Inspired by the recent literature on aggregation theory, we attempt to relate the long-range correlation of the stock return volatility to the heterogeneity of the investors' expectations concerning the level of the future volatility. Based on a semi-parametric model of investors' anticipations, we make the connection between the distributional properties of the heterogeneity parameters and the auto-covariance/auto-correlation functions of the realized volatility. We report different behaviors, or change of convention, the observation of which depends on the market phase under consideration. In particular, we report and justify the fact that the volatility exhibits significantly longer memory during phases of a speculative bubble than during the recovery phase following the collapse of a speculative bubble.     

Hierarchical structures in the aggregation of premium risk for insurance underwriting

In the valuation of the Solvency II capital requirement, the correct appraisal of risk dependencies acquires particular relevance. These dependencies refer to the recognition of risk diversification in the aggregation process and there are different levels of aggregation and hence different types of diversification. For instance, for a non-life company at the first level the risk components of each single line of business (e.g. premium, reserve, and CAT risks) need to be combined in the overall portfolio, the second level regards the aggregation of different kind of risks as, for example, market and underwriting risk, and finally various solo legal entities could be joined together in a group.

Solvency II allows companies to capture these diversification effects in capital requirement assessment, but the identification of a proper methodology can represent a delicate issue. Indeed, while internal models by simulation approaches permit usually to obtain the portfolio multivariate distribution only in the independence case, generally the use of copula functions can consent to have the multivariate distribution under dependence assumptions too.

However, the choice of the copula and the parameter estimation could be very problematic when only few data are available. So it could be useful to find a closed formula based on Internal Models independence results with the aim to obtain the capital requirement under dependence assumption.

A simple technique, to measure the diversification effect in capital requirement assessment, is the formula, proposed by Solvency II quantitative impact studies, focused on the aggregation of capital charges, the latter equal to percentile minus average of total claims amount distribution of single line of business (LoB), using a linear correlation matrix.

On the other hand, this formula produces the correct result only for a restricted class of distributions, while it may underestimate the diversification effect.

In this paper we present an alternative method, based on the idea to adjust that formula with proper calibration factors (proposed by Sandström (2007)) and appropriately extended with the aim to consider very skewed distribution too.

In the last part considering different non-life multi-line insurers, we compare the capital requirements obtained, for only premium risk, applying the aggregation formula to the results derived by elliptical copulas and hierarchical Archimedean copulas.     

Why the structure of capital and the useful lives of its components matter: A test based on a model of Austrian descent

This paper centers on the structure of capital and the useful lives of its components by considering an economy with two representative firms, one producing a necessity and another producing a luxury. This difference determines their reinvestment opportunities. Therefore, while the one applies replacement, the other adopts scrapping. However, as these capital policies lead to different service lives, the analysis confronts the issues raised by Miller (Review of Income and Wealth 29:284–296, 1982, Review of Income and Wealth 36:67–82, 1990) and deals with them by drawing on Haavelmo’s (A study in the theory of investment, Chicago: The University of Chicago Press, 1960) suggestions regarding the aggregation of capital. Among other findings, it turns out that the simulation results are highly robust, thus demonstrating that real-world implications may be even stronger than strictly suggested by the model.

Consumption dynamics under information processing constraints

This paper studies how “rational inattention” (RI)—a type of information processing constraint proposed by Sims [Sims, C.A., 2003. Implications of rational inattention, Journal of Monetary Economics 50 (3), 665–690]—affects the joint dynamics of consumption and income in a permanent income model with general income processes. Specifically, I propose an analytical approach to solve the multivariate permanent income model with RI and examine its implications for optimal consumption, saving, and welfare. It is shown that RI can affect the relative volatility of consumption and provide an endogenous propagation mechanism that disentangles the short-run and long-run responses of consumption to exogenous income shocks. I also explore how aggregation reduces the impact of the RI-induced endogenous noise on consumption and thus increases the smoothness of aggregate consumption. Finally, I compare RI with four alternative hypotheses (habit formation, signal extraction, robustness, and inattentiveness) by examining their implications for the joint behavior of consumption and income.     

计量模型中的加总偏误与内生性：一种数值模拟方法

理论文献已经证明了细分数据模型的内生性和加总过程产生的内生性是加总偏误的根本原因。但是由于内生性涉及误差项与回归量之间的相关性问题,试图通过实证方法审视这两类内生性对加总偏误的影响变得比较困难,而数值模拟却是一个较为理想的方法。在数值模拟中,我们通过控制随机变量的分布形式以及随机变量之间的相关程度,进而对两类内生性因素产生的加总偏误进行全面细致的考察。本文的研究将为加总偏误的内生性解释提供有力证据。     

Improving forecasting by estimating time series structural components across multiple frequencies

Identifying the most appropriate time series model to achieve a good forecasting accuracy is a challenging task. We propose a novel algorithm that aims to mitigate the importance of model selection, while increasing the accuracy. Multiple time series are constructed from the original time series, using temporal aggregation. These derivative series highlight different aspects of the original data, as temporal aggregation helps in strengthening or attenuating the signals of different time series components. In each series, the appropriate exponential smoothing method is fitted and its respective time series components are forecast. Subsequently, the time series components from each aggregation level are combined, then used to construct the final forecast. This approach achieves a better estimation of the different time series components, through temporal aggregation, and reduces the importance of model selection through forecast combination. An empirical evaluation of the proposed framework demonstrates significant improvements in forecasting accuracy, especially for long-term forecasts.     

EFFECTS OF SECTOR AGGREGATION ON CO2 MULTIPLIERS IN MULTIREGIONAL INPUT–OUTPUT ANALYSES

The past few years have seen the emergence of several global multiregional input–output (MRIO) databases. Due to the cost and complexity of developing such extensive tables, industry sectors are generally represented at a rather aggregate level. Currently, one of the most important applications of input–output analysis is environmental assessments, for which highly aggregate sectors may not be sufficient to yield accurate results. We experiment with four of the most important global MRIO systems available, analyzing the sensitivity of a set of aggregate CO₂ multipliers to aggregations in the MRIO tables used to calculate them. Across databases, we find (a) significant sensitivity to background system detail and (b) that sub-sectors contained within the same aggregate MRIO sector may exhibit highly different carbon multipliers. We conclude that the additional information provided by the extra sector detail may warrant the additional costs of compilation, due to the heterogeneous nature of economic sectors in terms of their environmental characteristics.     

Purchasing Power Parity and aggregation bias for a developing country: The case of Mexico

This paper investigates long-run Purchasing Power Parity (PPP) between the US and Mexico. We use a panel of disaggregated price data between the US and Mexico with a long time series to look at two types of aggregation bias. The first is examined in Imbs et al. — which we refer to as estimator aggregation bias — and the second is put forth by Broda and Weinstein — hereafter, data aggregation bias. The findings indicate substantial estimator aggregation bias and data aggregation bias. Although estimates using aggregate data and imposing homogeneous coefficients provide little evidence of PPP, findings with disaggregated data and heterogeneous coefficient estimators offer strong support. The results also suggest the presence of small-sample bias as examined in Chen and Engel, but with little effect on the qualitative results. Tradable goods and non-tradable goods show little distinction in convergence rates. Estimated half-lives are lower under flexible than fixed exchange rates and indicate rapid convergence during the Mexican peso crisis.     

Composite indicators of sustainable urban mobility: Estimating the rankings frequency distribution combining multiple methodologies

The contribution of this paper consists in applying several techniques to estimate a composite indicator of sustainable urban mobility for 116 Italian provincial towns, as proposed by Luzzati and Gucciardi (2015). The aim is to provide the decision-maker with a richer set of information on sustainable mobility, making explicit the impact of the techniques used on the values obtained. A set of 16 indicators with a nested structure has been selected and 33 combinations of normalization, weighting, and aggregation techniques are applied. The results are presented by city, by city groupings (size and location), and focusing on the ten largest Italian cities. It is found that small cities perform better in terms of sustainable mobility than medium or large cities. As expected, in some cases (e.g., Milan) the intervals of the results obtained are quite large, indicating that the techniques used to normalize, weight, and aggregate the indicators highly affect the performance indexes. In other cases (e.g., Rome) the results are stable across methodologies.