Ordering properties of the smallest order statistics from generalized Birnbaum–Saunders models with associated random shocks

Let \(X_{1},\ldots , X_{n}\) be lifetimes of components with independent non-negative generalized Birnbaum–Saunders random variables with shape parameters \(\alpha _{i}\) and scale parameters \(\beta _{i},~ i=1,\ldots ,n\), and \(I_{p_{1}},\ldots , I_{p_{n}}\) be independent Bernoulli random variables, independent of \(X_{i}\)’s, with \(E(I_{p_{i}})=p_{i},~i=1,\ldots ,n\). These are associated with random shocks on \(X_{i}\)’s. Then, \(Y_{i}=I_{p_{i}}X_{i}, ~i=1,\ldots ,n,\) correspond to the lifetimes when the random shock does not impact the components and zero when it does. In this paper, we discuss stochastic comparisons of the smallest order statistic arising from such random variables \(Y_{i},~i=1,\ldots ,n\). When the matrix of parameters \((h({\varvec{p}}), {\varvec{\beta }}^{\frac{1}{\nu }})\) or \((h({\varvec{p}}), {\varvec{\frac{1}{\alpha }}})\) changes to another matrix of parameters in a certain mathematical sense, we study the usual stochastic order of the smallest order statistic in such a setup. Finally, we apply the established results to two special cases: classical Birnbaum–Saunders and logistic Birnbaum–Saunders distributions.     

On extremes of bivariate residual lifetimes from generalized Marshall–Olkin and time transformed exponential models

We study here extremes of residuals of the bivariate lifetime and the residual of extremes of the two lifetimes. In the case of generalized Marshall–Olkin model and the total time transformed exponential model, we first present some sufficient conditions for the extremes of residuals to be stochastically larger than the residual of the corresponding extremes, and then investigate the stochastic order of the residual of extremes of the two lifetimes based on the majorization of the age vector of the residuals.     

Dispersion of growth paths of macroeconomic models in thermodynamic limits: two-parameter Poisson–Dirichlet models

This paper discusses dispersion of growth patterns of macroeconomic models in thermodynamic limits. More specifically, the paper shows that the coefficients of variations of the total numbers of clusters and the numbers of clusters of specific sizes of one- and two-parameter Poisson–Dirichlet models behave qualitatively differently in the thermodynamic limits. The coefficients of variations of the numbers of clusters in the former class of distributions are all self-averaging, while the those in the latter class are all non-self averaging. In other words, dispersions or variations of growth rates about the means do not vanish in the two-parameter version of the model, while they do in the one-parameter version in the thermodynamic limits. The paper ends by pointing out other models, such as triangular urn models, may converge to Mittag–Leffler distributions which exhibit non-self-averaging behavior for certain parameter combinations. The author is grateful for many helps he received from H. Yoshikawa, and M. Sibuya.     

Second-best cost–benefit analysis in monopolistic competition models of urban agglomeration

This paper examines the agglomeration benefits of a transportation improvement in a city by modeling the microstructure of urban agglomeration based on monopolistic competition of differentiated intermediate products. Properly extended to include variety distortion in addition to price distortion, Harberger’s measure of excess burden yields the agglomeration benefits. The agglomeration benefits are positive if increasing the variety is procompetitive; however, in the anticompetitive case, we cannot exclude the possibility of negative additional benefits. If there are multiple cities, the net agglomeration benefits can be negative when other cities that experience a reduction in population have larger agglomeration economies.     

Symmetry and Bates’ rule in Ornstein–Uhlenbeck stochastic volatility models

We find necessary and sufficient conditions for the market symmetry property, introduced by Fajardo and Mordecki (Quant Finance 6(3):219–227, 2006), to hold in the Ornstein–Uhlenbeck stochastic volatility model, henceforth OU–SV. In particular, we address the non-Gaussian OU–SV model proposed by Barndorff-Nielsen and Shephard (J R Stat Soc B 63(Part 2):167–241, 2001). Also, we prove the Bates’ rule for these models.     

Random coefficient state-space model: Estimation and performance in M3–M4 competitions

The random coefficient state-space model was first introduced by McKenzie and Gardner (2010). This model is a stochastic combination of simple and double exponential smoothing, a desirable feature for time-series forecasting. This paper provides a simple method to estimate the random coefficient state-space model parameters by exploiting the link between the model’s autocovariance and the Kalman filter. A simulation exercise shows that the proposed estimator has good finite-sample properties. This paper also evaluates the model’s forecasting performance in large-scale empirical applications, which is remarkable. Indeed, this model outperforms all competing (not-combined) benchmarks when using the yearly data from the M3 competition dataset. Furthermore, employing the yearly data from the M4 competition, it continues to beat its competitors, with a performance comparable to that of the Theta method. The predictive performance is assessed using both the MASE/sMAPE metrics and the Model Confidence Set procedure.     

Mixed Causal–Noncausal Autoregressions: Bimodality Issues in Estimation and Unit Root Testing1

This paper stresses the bimodality of the likelihood function of the Mixed causal–noncausal AutoRegressions (MAR), and it is shown that the bimodality issue becomes more salient as the causal root approaches unity from below. The consequences are important as the roots of the local maxima are typically interchanged, attributing the noncausal component to the causal one and vice-versa. This severely changes the interpretation of the results, and the properties of unit root tests of the backward root are adversely affected. To circumvent the bimodality issue, this paper proposes an estimation strategy which (i) increases noticeably the probability of attaining the global MLE; and (ii) selects carefully the maximum used for the unit root test against a MAR stationary alternative.     

Stochastic leader–follower DEA models for two-stage systems

Data envelopment analysis (DEA) is a non-parametric approach for measuring the relative efficiencies of peer decision making units (DMUs). In recent years, it has been widely used to evaluate two-stage systems under different organization mechanisms. This study modifies the conventional leader–follower DEA models for two-stage systems by considering the uncertainty of data. The dual deterministic linear models are first constructed from the stochastic CCR models under the assumption that all components of inputs, outputs, and intermediate products are related only with some basic stochastic factors, which follow continuous and symmetric distributions with nonnegative compact supports. The stochastic leader–follower DEA models are then developed for measuring the efficiencies of the two stages. The stochastic efficiency of the whole system can be uniquely decomposed into the product of the efficiencies of the two stages. Relationships between stochastic efficiencies from stochastic CCR and stochastic leader–follower DEA models are also discussed. An example of the commercial banks in China is considered using the proposed models under different risk levels.     

To RAS or not to RAS? What is the difference in outcomes in multi-regional input–output models?

The global resource accounting model (GRAM), which is based on OECD input–output and bilateral trade data, is a multi-regional input–output model covering 53 countries and 2 regions. What differentiates GRAM from other state-of-the-art models in this field is that it does not use a matrix balancing technique, such as RAS, after the initial construction of the global intermediate coefficient and final demand matrices. Instead, it reproduces prescribed intermediate and final demand, and determines value added residually. This choice was made to alter the original data as little as possible and keep the calculations traceable. This simpler solution technique might, however, yield different results. This paper aims at identifying the difference between the current solution of GRAM and the solution of a RASed version of GRAM, thus contributing to the assessment of currently used methodologies in this research field. The short conclusion is that, even though some differences during the calculations are present, the calculated output (production) matrix does not differ substantially. The results show that larger differences are brought about by poor assumptions regarding missing or conflicting data rather than by applying or not applying a RAS procedure to the constructed global matrices.     

Verification results for age-structured models of economic–epidemics dynamics

In this paper we propose a macro-dynamic age-structured set-up for the analysis of epidemics/economic dynamics in continuous time.The resulting optimal control problem is reformulated in an infinite dimensional Hilbert space framework where we perform the basic steps of dynamic programming approach.Our main result is a verification theorem which allows to guess the feedback form of optimal strategies. This will be a departure point to discuss the behavior of the models of the family we introduce and their policy implications.     

Inference in dynamic models containing ‘surprise’ variables

Some new results on calculating moving average representation (MAR) coefficients and their limiting distribution from estimated vector ARMA processes are presented. The technique is applied to the problem of estimating the coefficients of unanticipated or ‘surprise’ variables in a single equation for a multi-period expectations horizon. The method naturally conditions the expectations on all past values of the process and avoids the necessity of using two-step regression procedures and adjusting the resulting standard errors.     

Lévy CARMA models for shocks in mortality

Decisions in Economics and Finance - Recent literature on mortality modeling suggests to include in the dynamics of mortality rates the effects of time, age, the interaction of these two and a term...     

A network approach for assembling and linking input–output models

Input–output (IO) models, describing trade between different sectors and regions, are widely used to study the environmental repercussions of human activities. A frequent challenge in assembling an IO model or linking several such models is the absence of flow data with the same level of detail for all components. Such problems can be addressed using proportional allocation, which is a form of algebraic transformations. In this paper, we propose a novel approach whereby the IO system is viewed as a network, the topology of which is transformed with the addition of virtual nodes so that available empirical flow data can be mapped directly to existing links, with no additional estimation required, and no impact on results. As IO systems become increasingly disaggregated, and coupled to adjacent databases and models, the adaptability of IO frameworks becomes increasingly important. We show that topological transformations also offer large advantages in terms of transparency, modularity and increasingly importantly for global IO models, efficiency. We illustrate the results in the context of trade linking, multi-scale integration and other applications.     

Non-structural and structural models in productivity analysis: study of the British Isles during the 2007–2009 financial crisis

Journal of Productivity Analysis - The paper compares unrestricted and restricted reduced-form estimates of productivity and efficiency performance constructed from non-structural stochastic...     

Estimation of technical change and price elasticities: a categorical time–varying coefficient approach

We propose a categorical time-varying coefficient translog cost function, where each coefficient is expressed as a nonparametric function of a categorical time variable, thereby allowing each time period to have its own set of coefficients. Our application to U.S. electricity firms reveals that this model offers two major advantages over the traditional time trend representation of technical change: (1) it is capable of producing estimates of productivity growth that closely track those obtained using the Törnqvist approximation to the Divisia index; and (2) it can solve a well-known problem commonly referred to as “the problem of trending elasticities”.     

Pricing basket spread options with default risk under Heston–Nandi GARCH models

In this paper, we investigate basket spread options under the Heston–Nandi GARCH model. Moreover, we adopt the reduced-form model to capture default risk, which is correlated with all underlying assets. Because of the nonexistence of the analytical fair values, we obtain a closed-form approximated pricing formula of basket spread options with default risk. Finally, we examine the accuracy of approximations and then use the proposed formulae to illustrate the effect of the number of the underlying assets and default risk as well.