Estimation of Poverty Transition Matrices with Noisy Data

This paper investigates measurement error biases in estimated poverty transition matrices. We compare transition matrices based on survey expenditure data to transition matrices based on measurement‐error‐free simulated expenditure. The simulation model uses estimates that correct for measurement error in expenditure. We find that time‐varying measurement error in expenditure data magnifies economic mobility. Roughly 45% of households initially in poverty at time t ? 1 are found to be out of poverty at time t using data from the Korean Labor and Income Panel Study. When measurement error is removed, this drops to between 26 and 31% of households initially in poverty. Copyright © 2016 John Wiley & Sons, Ltd.     

Phase transition in the S&P stock market

We analyze the returns of stocks contained in the Standard & Poor’s 500 index from 1987 until 2011. We use covariance matrices of the firms’ returns determined in a time windows of several years. We find that the eigenvector belonging to the leading eigenvalue (the market) exhibits a phase transition. The market is in an ordered state from 1995 to 2005 and in a disordered state after 2005. We can relate this transition to an order parameter derived from the stocks’ beta and the trading volume. This order parameter can also be interpreted within an agent-based model.     

Reinforced urn processes for credit risk models

We propose a Bayesian nonparametric model to estimate rating migration matrices and default probabilities using the reinforced urn processes (RUP) introduced in Muliere et al. (2000). The estimated default probability becomes our prior information in a parametric model for the prediction of the number of bankruptcies, with the only assumption of exchangeability within rating classes. The Polya urn construction of the transition matrix justifies a Beta distributed de Finetti measure. Dependence among the processes is introduced through the dependence among the default probabilities, with the Bivariate Beta Distribution proposed in Olkin and Liu (2003) and its multivariate generalization.     

Intergenerational Earnings Mobility Among Daughters and Sons: Evidence from Sweden and a Comparison with the United States

This article adopts Chadwick and Solon's (2002 ) model by using family earnings in the study of intergenerational earnings mobility with a highlight on the role of assortative mating. I analyze mean and quantile regression coefficients as well as transition matrices to investigate family earnings mobility between parents and daughters and parents and sons from Swedish register data. My findings indicate that Sweden has a higher degree of mobility compared to the United States, and that assortative mating also plays an important role as a channel through which income status is transmitted across generations in Sweden. However, the difference in intergenerational mobility patterns between the two countries does not, inherently, depend on factors that affect the marriage match. Swedish daughters and sons exhibit a rather similar scheme of intergenerational earnings transmission. Daughters tend to be slightly more mobile than sons, and the difference between their elasticity estimates is small but statistically significant. The quantile regression approach reveals that parents' family earnings are less important as an explanatory variable at the upper end of the children's earnings distribution than they are at the bottom, while transition matrices show substantial earnings persistence in the top earnings class.     

A Markov Switching Factor‐Augmented VAR Model for Analyzing US Business Cycles and Monetary Policy

This paper develops a Markov switching factor‐augmented vector autoregression to investigate the transmission mechanisms of monetary policy for distinct stages of the US business cycle. We assume that autoregressive parameters and covariance matrices of the error terms are regime dependent, driven by an unobserved Markov indicator. Endogenously determined transition probabilities are governed by an underlying probit model that features a large set of possible predictors. The empirical findings provide evidence for differences in the transmission of monetary policy shocks that mainly stem from heterogeneity in the responses of financial market quantities.     

Development of environmentally extended social accounting matrices for policy analysis in Alberta

This paper outlines the development of inputs to an integrated land use and transportation model based on a series of environmentally extended social accounting matrices (SAMs) for the Canadian province of Alberta. A novel form of industry disaggregation is employed, based on aggregate iterative proportion and a unique formulation of location quotients. Social accounts are extended via the inclusion of detailed household consumption broken down by income quintiles. The SAMs are developed from supply-use matrices. Physical flow accounts are framed as derived demands, acting as necessary inputs to the production of downstream goods and services. Applications to regional economic modeling are considered, as planning authorities increasingly seek to model the environmental impacts of policy. The SAMs are then applied to the assessment of two technology change scenarios: a shift in the provincial electricity generation mix and a transition to a fully electric private automobile fleet.     

Decomposing economic mobility transition matrices

We present a decomposition method for transition matrices to identify forces driving the persistence of economic status across generations. The method decomposes differences between an estimated transition matrix and a benchmark transition matrix into portions attributable to differences in characteristics between individuals from different households (a composition effect) and portions attributable to differing returns to these characteristics (a structure effect). A detailed decomposition based on copula theory further decomposes the composition effect into portions attributable to specific characteristics and their interactions. To examine potential drivers of economic persistence in the USA, we apply the method to white males from the 1979 US National Longitudinal Survey of Youth. Depending on the transition matrix entry of interest, differing characteristics between sons from different households explain between 40% and 70% of observed income persistence, with differing returns for these characteristics explaining the remaining gap. Further, detailed decompositions reveal significant heterogeneity in the role played by specific characteristics (e.g., education) across the income distribution.     

Interconnections Between Eurozone and US Booms and Busts Using a Bayesian Panel Markov‐Switching VAR Model

The proposed panel Markov‐switching VAR model accommodates changes in low and high data frequencies and incorporates endogenous time‐varying transition matrices of country‐specific Markov chains, allowing for interconnections. An efficient multi‐move sampling algorithm draws time‐varying Markov‐switching chains. Using industrial production growth and credit spread data, several important data features are obtained. Three regimes appear, with slow growth becoming persistent in the eurozone. Turning point analysis indicates the USA leading the eurozone cycle. Amplification effects influence recession probabilities for Eurozone countries. A credit shock results in temporary negative industrial production growth in Germany, Spain and the USA. Core and peripheral countries exist in the eurozone. Copyright © 2016 John Wiley & Sons, Ltd.     

Productivity Dynamics: U.S. Manufacturing Plants, 1972–1986

This paper presents an analysis of the dynamics of total factor productivity measures for large plants in SICs 35, 36 and 38. Several TFP measures, derived from production functions and Solow type residuals, are computed and their behavior over time is compared, using non-parametric tools. Aggregate TFP, which has grown substantially over the time period, is compared with average plant level TFP, which has declined or remained flat. Using transition matrices, the persistence of plant productivity is examined, and it is shown how the transition probabilities vary by industry, plant age, and other characteristics.     

On equalities of estimations of parametric functions under a general linear model and its restricted models

Estimations of parametric functions under a general linear model and its restricted models involve some complicated operations of matrices and their generalized inverses. In the past several years, a powerful tool—the matrix rank method was utilized to manipulate various complicated matrix expressions that involve generalized inverses of matrices. In this paper, we use this method to derive necessary and sufficient conditions for six equalities of the ordinary least-squares estimators and the best linear unbiased estimators of parametric functions to equal under a general linear model and its corresponding restricted model.     

A new method for automatic synthesis of tolerances for complex assemblies based on polychromatic sets

In computer-aided tolerance design (CAT), integrated design of dimensional and geometric tolerances is still one of the research hotspots. Polychromatic sets theory (PST) is a new mathematic tool, which is especially suitable for formal hierarchical structure models. Based on PST, in this article, a new hierarchical representation model for tolerance synthesis is presented to realise integrated design of dimensional and geometric tolerances. According to the inference relations between unified and individual colours of PST, the synthesis matrices of variational geometric constraints (VGC) are established in the VGC tier of the model, and the synthesis matrices of tolerance types are established in the tolerance type tier of the model. On this basis, the synthesis processes from the feature tier to the VGC tier and from the VGC tier to the tolerance type tier can be realised. VGCs, which are achieved by the synthesis matrices of VGCs, can be combined together to establish a well-constrained VGC network (VGCN). Tolerance types, which are achieved by the synthesis matrices of tolerance types, can be added to the well-constrained VGCN to construct a well-constrained tolerance network. An application example is given in the article to illustrate the synthesis steps.     

The conditional autoregressive Wishart model for multivariate stock market volatility

We propose a Conditional Autoregressive Wishart (CAW) model for the analysis of realized covariance matrices of asset returns. Our model assumes an autoregressive moving average structure for the scale matrix of the Wishart distribution. It accounts for positive definiteness of covariance matrices without imposing parametric restrictions, and can be estimated by Maximum Likelihood. We also propose extensions of the CAW model obtained by including a Mixed Data Sampling (MIDAS) component and Heterogeneous Autoregressive (HAR) dynamics for long-run fluctuations. The CAW models are applied to realized variances and covariances for five New York Stock Exchange stocks.     

Testing for financial spillovers in calm and turbulent periods

In this paper, we investigate financial spillovers between stock markets during calm and turbulent periods. We explicitly define financial spillovers and financial contagion in accordance with the literature and construct statistical models corresponding to these definitions in a Markov switching framework. Applying the new testing methodology based on transition matrices, we find that spillovers from the US stock market to the UK, Japanese and German markets are more frequent when the latter markets are in a crisis regime. However, we reject the hypothesis of strong financial contagion from the US to the other markets.     

Sectoral Rates of Profit and Productive Structure

This paper analyzes an economic system in which rates of profit are not uniform but differ from one sector to another, and discusses the acceptable intervals of variation of the rates of profit compatible with non-negative prices. The investigation is conducted in a Leontief price model with fixed capital. The limits of variation of the rates of profit are ascertained using a mathematical algorithm based on the properties of Z matrices and dominant-diagonal matrices.     

The Wishart Autoregressive process of multivariate stochastic volatility

The Wishart Autoregressive (WAR) process is a dynamic model for time series of multivariate stochastic volatility. The WAR naturally accommodates the positivity and symmetry of volatility matrices and provides closed-form non-linear forecasts. The estimation of the WAR is straighforward, as it relies on standard methods such as the Method of Moments and Maximum Likelihood. For illustration, the WAR is applied to a sequence of intraday realized volatility–covolatility matrices from the Toronto Stock Market (TSX).     

On MLEs in an extended multivariate linear growth curve model

In this paper the extended growth curve model is considered. The literature comprises two versions of the model. These models can be connected by one-to-one reparameterizations but since estimators are non-linear it is not obvious how to transmit properties of estimators from one model to another. Since it is only for one of the models where detailed knowledge concerning estimators is available (Kollo and von Rosen, Advanced multivariate statistics with matrices. Springer, Dordrecht, 2005) the object in this paper is therefore to present uniqueness properties and moment relations for the estimators of the second model. One aim of the paper is also to complete the results for the model presented in Kollo and von Rosen (Advanced multivariate statistics with matrices. Springer, Dordrecht, 2005). The presented proofs of uniqueness for linear combinations of estimators are valid for both models and are simplifications of proofs given in Kollo and von Rosen (Advanced multivariate statistics with matrices. Springer, Dordrecht, 2005).     

A new test for fourth-order autoregressive disturbances

This paper proposes a new test for simple fourth-order autoregressive disturbances in the linear regression model. The test is shown to be most powerful invariant in a given neighourhood of the alternative hypothesis for all design matrices. An empirical power comparison suggests that the test is generally more powerful than the Wallis test, the difference in power probably being slight for most economic applications, although for certain design matrices, the power advantage of the new test is very real. Selected bounds for the test's significance points are tabulated.     

Structural Models of Factor Demands and Technological Change: An Empirical Assessment of Dynamic Adjustment Specifications for Sectors of the Dutch Economy

In this paper, we combine a translog cost functional form with an adjustment process according to the error correction mechanism to explain the simultaneous determination of factor demands and technological change. To save degrees of freedom in the estimation procedure, we also consider the imposition of restrictions on the matrices of lag parameters and/or the covariance matrix of the disturbances. Using a model selection strategy based on a combination of economic-theoretical considerations and a formal model selection criterion, a model is selected for each of 17 sectors of the Dutch economy. It turns out that, for 14 of the 17 sectors under consideration, a model is chosen that allows the imposition of restrictions with respect to the matrices of lag parameters. A comparison of the present results with those obtained by Lesuis and de Boer reveals that the application of more general dynamic structures leads to results that are more in accordance with economic theory.     

On variable ordination of modified Cholesky decomposition for estimating time-varying covariance matrices

Estimating time-varying covariance matrices of the vector of interest is challenging both computationally and statistically due to a large number of constrained parameters. In this work, we consider an order-averaged Cholesky-log-GARCH (OA-CLGARCH) model for estimating time-varying covariance matrices through the orthogonal transformations of the vector based on the modified Cholesky decomposition. The proposed method is to transform the vector at each time as a linear transformation of uncorrelated latent variables and then to use simple univariate GARCH models to model them separately. But the modified Cholesky decomposition relies on a given order of variables, which is often not available, to sequentially orthogonalize the variables. The proposed method develops an order-averaged strategy for the Cholesky-GARCH method to alleviate the effect of order of variables. The merits of the proposed method are illustrated through simulations and real-data studies.     

Information Matrices for Non Full Rank Subsystems

Consider the standard linear model Y=X θ + ε. If the parameter of interest is a full rank subsystem K′θ of mean parameters, the associated information matrix can be defined via an extremal representation. For rank deficient subsystems, Pukelsheim (1993) introduced the notion of generalized information matrices that inherit many properties of the information matrices. However, this notion is not a direct extension of the full rank case in the sense that the definition of the generalized information matrix applied to full rank subsystems does not lead to the usual information matrix. In this paper, we propose a definition of the information matrix via an extremal representation that encompasses the full rank and the non-full rank cases. We also study its properties and show its links with the generalized information matrices.