On Hypothesis about the Second Eigenvalue of the Leontief Matrix

If an arbitrarily positive eigenvector is repeatedly premultiplied by a positive matrix, then the result tends towards a unique, positive (Frobenius) eigenvector. Brady has demonstrated that the expected absolute magnitude of the estimate of the second largest eigenvalue of a positive random matrix (with identically and independently distributed entries) declines monotonically with the increasing size of the matrix. Hence, the larger the system is, the faster is the convergence. Molnár and Simonovits examined Brady's conjecture in the case where entries of a stochastic matrix are close to 1/n. We prove this hypothesis for any stochastic and positive matrix.     

The Spectrum of Random Matrices

The Frobenius eigenvector of a positive square matrix is obtained by iterating the multiplication of an arbitrary positive vector by the matrix. Bródy (1997) noticed that, when the entries of the matrix are independently and identically distributed, the speed of convergence increases statistically with the dimension of the matrix. As the speed depends on the ratio between the subdominant and the dominant eigenvalues, Bródy's conjecture amounts to stating that this ratio tends to zero when the dimension tends to infinity. The paper provides a simple proof of the result. Some mathematical and economic aspects of the problem are discussed.     

The Subdominant Eigenvalue of a Large Stochastic Matrix

Using intuition and computer experimentation, Brady conjectured that the ratio of the subdominant eigenvalue to the dominant eigenvalue of a positive random matrix (with identically and independently distributed entries) converges to zero when the number of the sectors tends to infinity. In this paper, we discuss the deterministic case and, among other things, prove the following version of this conjecture: if each entry of the matrix deviates from 1/n by at most θ/n^1+е, then the modulus of the subdominant root is at most θ/n^е where θ and ε are arbitrary positive real parameters.     

Is there convergence amongst shadow economies? International evidence

This paper examines convergence among cross-country shadow economies. Using the Phillips-Sul (2007, 2009) club convergence approach and data for over 150 countries from 1991 to 2017, the results show evidence against absolute convergence for all shadow economies; however, we find evidence of multiple convergence clubs. In particular, we find evidence for seven distinct convergence clubs and six divergent shadow economies. Each club is characterised by an increasingly larger shadow economy with the countries in club 1 having the largest shadow economy and those in club 7 having the smallest shadow economy. Using a two-way fixed effects approach, we also find that the determinants of the shadow economy are somewhat conditional on the convergence club. The existence of multiple equilibria suggests that policy makers in their attempt to combat the shadow economy would benefit by considering the different transitional paths associated with the different convergence clubs.     

一类与工程设计相关的Jacobi矩阵逆特征值问题

Jacobi矩阵逆特征值问题,在振动工程、结构设计、工程设计应用和系数参数识别等领域有重要应用,文章考虑了由混合型特征对构造一个Jacobi矩阵的问题,给出了问题有唯一解的充分必要条件。     

On the asymptotic normality of Fourier flexible form estimates

Rates of increase in the number of parameters of a Fourier factor demand system that imply asymptotically normal elasticity estimates are characterized. This is the multivariate analog of work by Andrews (1991). Our proof strategy is new and consists of relating the minimum eigenvalue of the sample sum of squares and cross-products matrix to the minimum eigenvalue of the population matrix via a uniform strong law with rate that is established using results from the empirical processes literature. In its customary form, the minimum eigenvalue of the Fourier sum of squares and cross-products matrix, considered as a function of the number of parameters, decreases faster than any polynomial. The consequence is that the rate at which parameters may increase is slower than any fractional power of the sample size. In this case, we get the same rate as Andrews. When our results are applied to multivariate regressions with a minimum eigenvalue that is bounded or declines at a polynomial rate, the rate on the parameters is a fractional power of the sample size. In this case, our method of proof gives faster rates than Andrews. Andrews' results cover the heteroskedastic case, ours do not.     

Inflationary bias in middle to late transition Czech Republic

A series of studies has now confirmed the Filer and Hanousek’s [Economic Systems 24 (2000) 285] suggestion that inflation mismeasurement during the transition is a serious problem of the same relative magnitude (and greater absolute magnitude), as in advanced market economies. During the 1990s in the Czech Republic, inflation was overstated by more than four percentage points a year. The largest portion of this bias is due to uncaptured quality changes. In effect, Czech consumers are living considerably better after the fall of communism, but this increase in living standards is manifested through better quality, rather than greater quantities of goods consumed.     

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.     

浅谈跨河桥梁改造工程的施工

跨河桥梁的改造涉及新、旧结构的可靠合理衔接,使新旧结构协同工作,最大可能的发挥作用,确保工程快速、有序的进行。     

Largest shareholder and dividend policy around the world

This paper examines the interaction between the largest shareholder and dividend policy in a sample of 8,279 listed firms drawn from 37 countries. We find that firms are more likely to pay dividends when profitability is high, debt is low, investment opportunities are limited or when the largest shareholder is not an insider. Further, the magnitude of dividend payout tends to be smaller when the largest shareholder is either an insider or a financial institution. It is also apparent that largest shareholding and dividend payout are related and that, consistent with the extant literature, legal system does matter in dividend policy decisions.     

东江特大桥主桥二次张拉低回缩钢绞线竖向预应力设计与施工

东江特大桥是博深高速公路最大的一座特大桥,北接博罗苏村,南接惠州潼湖,跨越广东东江,全长2675.43m,其中东江特大桥属于博深高速公路第一合同,主桥采用连续刚构方案,并采用竖向预应力二次张拉设计与施工,本文介绍主桥竖向预应力设计与施工关键技术,希望对类似桥型的设计与施工起到借鉴与参考作用。     

On non-linear extensions of the Perron-Frobenius theorem

The note provides bounds for eigenvalues of non-negative, homogeneous mappings, which need not be linear. It also gives a simple proof of the result, that repeated iterations of a primitive mapping take any semipositive vector to the positive eigenvector.     

中国经济双循环耦合协调度分布动态、空间差异及收敛性研究

研究目标:测算1999～2019年中国经济“内循环”与“外循环”耦合协调度的实际水平并分析其分布动态、空间差异及收敛性。研究方法:耦合协调度模型、Kernel密度估计、Dagum基尼系数及其分解法和β收敛模型。研究发现:考察期内,中国经济“内循环”与“外循环”之间的耦合协调度呈现稳定的上升趋势,但总体水平仍然较低,地区异质性、时间阶段性特征明显;空间差异持续扩大,主要来源是区域间差异;正空间相关关系持续而稳定;全国及四大地区经济双循环耦合协调度存在显著的绝对β收敛和条件β收敛过程,不同地区耦合协调度收敛位置的影响因素各不相同。研究创新:测算了中国经济双循环耦合协调度水平并分析其时空演进规律与收敛性。研究价值:对于总体把握我国经济双循环发展规律,因地制宜,精准施策,加快构建双循环新发展格局具有积极的现实意义。     

Mispricing and trader positions in the S&P 500 index futures market

This study examines the effect of traders’ net positions on mispricing in the S&P 500 index futures market. We find that while positive mispricing is associated with hedgers’ net short and speculators’ net long positions, negative mispricing is related to hedgers’ net long and speculators’ net short positions. This relationship is stable for speculators across the pre- and post-2004 periods; however, it is dominant for hedgers particularly during the pre-2004 period. Contrary to the popular belief, our analysis finds no evidence that speculators are responsible for irrational movements in futures prices by enlarging the size of mispricing. Furthermore, a high magnitude of hedgers’ net positions signals the convergence of mispricing. We also found that according to a recent new disaggregation for trader positions, asset managers tend to delay the convergence of mispricing and hedge funds help shrink the size of mispricing. However, these relationships are not stronger than those implies by the hedger/speculator classification. These findings support the view that speculators’ positions are informative about the direction of index futures mispricing, while hedgers’ positions determine the convergence of mispricing.     

Kernel estimation for disequilibrium models for floorspace efficiency in retailing

Conclusions In this paper we have proposed new techniques for simplifying the estimation of disequilibrium models by avoiding constrained maximum likelihood methods (which cannot avoid numerous theoretical and practical difficulties mentioned above) including an unrealistic assumption of the independence of errors in demand and supply system of equations. In the proposed first stage, one estimates the relative magnitude of the residuals from the demand and supply equations nonparametrically, even though they suffer from omitted variables bias, because the coefficient of the omitted variable is known to be the same in both equations. The reason for using nonparametric methods is that they do not depend on parametric functional forms of biased (bent inward) demand and supply equations. The first stage compares the absolute values of residuals from conditional expectations in order to classify the data points as belonging to the demand or the supply curve. We estimate the economically meaningful scale elasticity and distribution parameters at the second stage from classified (separated) data.We extend nonparametric kernel estimation to the r = 4 case to improve the speed of convergence, as predicted by Singh's [1981] theory. In the first stage, r = 4 results give generally improved R² and ¦t¦ values in our study of the Dutch data—used by many authors concerned with the estimation of floorspace productivity. We find that one can obtain reasonable results by our approximate but simpler two stage methods. Detailed results are reported for four types of Dutch retail establishments. More research is needed to gain further experience and to extend the methodology to other disequilibrium models and other productivity estimation problems.This paper was processed by W. Eichhorn.     

The First Two Eigenvalues of Large Random Matrices and Brody's Hypothesis on the Stability of Large Input–Output Systems

Bródy (1997) notices that for large random Leontief matrices, namely non-negative square matrices with all entries i.i.d., the ratio between the subdominant eigenvalue (in modulus) and the dominant eigenvalue declines generically to zero at a speed of the square root of the size of the matrix as the matrix size goes to infinity. Since then, several studies have been published in this journal in attempting to rigorously verify Bródy's conjecture. This short article, drawing upon some theorems obtained in recent years in the literature on empirical spectral distribution of random matrices, offers a short proof of Bródy's conjecture, and discusses briefly some related issues.     

Testing the convergence hypothesis: a longitudinal and cross-sectional analysis of the world trade web through social network and statistical analyses

Different theoretical perspectives support opposite views on convergence: although the dominant view is that convergence is the inevitable outcome of globalization, divergentists (that is, world-system economists and, potentially, also evolutionary geographic ones) argue that convergence forces could be annihilated by the need to keep power relationships within the international division of labor. Even when limiting the convergence issue to international trade, the debate has so far been inconclusive, because various studies have dealt with different and/or short time series or selected too small and different sets of countries. Moreover, none of these studies have analyzed trade patterns and have instead been limited to the aggregate value. Here, through a social network analysis, we examine the world trade patterns from 1980 to 2016 (1980–1992, 1993–2007 and 2008–2016) of at least 164 countries, which have been divided into import and export patterns and into four groups of countries: from core countries to far periphery ones. We test the convergence hypothesis in two directions: the level and trend of convergence, and its possible determination by means of structural or economic globalization, measured in terms of exchanges density and economic values, respectively. We have found that the convergence hypothesis only seems to be confirmed when considering the pure structural aspect and core countries. Conversely, economic convergence—which also includes the structural dimension—has been found to be high for core countries and to increase over time. Moreover, our analysis shows that economic globalization influences convergence, albeit in a strongly negative way. Therefore, our findings seem to support divergentists and the convergence hypothesis should be rejected.

     

超控制权私人收益及其非货币性收益的度量

股权分置改革以后,大股东与中小股东的利益趋于一致,但是关于大股东利用控制权来侵占中小股东利益的问题还是没有解决,特别是大股东控制权私人的非货币性收益的计量仍然缺乏相关的理论研究。本文把控制性大股东的超控制权私人收益分为可以货币化的和不能货币化的收益,并着重说明非货币化的收益如何进行度量,最后提出抑制超控制权私人收益的相关措施。     

Truncation and Spectrum of the Dynamic Inverse

The possibility of negative elements and perplexing computational problems hinder the widespread and universal use of this powerful instrument. A different solution for the truncation is proposed here that remedies some of the ills. It is also shown that— exploiting the skew-symmetric form, first suggested by Goodwin—we may obtain an interesting and important spectral decomposition of the system matrix. This decomposition, existing already for the simplest, one sector, totally aggregated model, describes those cycles that may disturb the path of a growing economy.     

Some sampling properties of minimum expected loss (MELO) estimators of structural coefficients

Some sampling properties of Zellner's (1978) MELO estimates of structural coefficients of linear simultaneous equation models are examined by a series of sampling experiments. The MELO estimates appear to have more pronounced biases in estimating structural coefficients than the 2SLS estimates. However, MELO is found to outperform 2SLS according to several criteria, including MSE and MAE in a wide range of situations generated by varying structural coefficients, the variance-covariance matrix of structural disturbances, and the sample size. The magnitude of absolute sampling errors, the estimation of the variance of structural disturbances, and the large-sample standard errors are also compared among OLS, 2SLS, and MELO.