具有三次代数曲线解的五次系统的极限环

本文利用Maple软件强大的符号计算能力,得到了以 y=ax~3+bx~2+cx+d 为解的平面五次多项式系统的特征,由此证明了该系统在奇点的邻域内可以存在极限环。     

“关系圈”稀释“受害者圈”：企业环境污染与村民大多数沉默的乡村逻辑—山东N村个案研究

基于山东N村手套加工厂及其环境影响的调查发现,村落内生企业的关系嵌入与乡村社会分化的叠加效应,是大多数村民面对环境危害而保持沉默的乡村逻辑。乡村作为兼具乡土底色与经济理性的生活共同体,被企业污染建构为具有统合性的整体受害者圈。“同住一个村”的共同体意识形塑大部分村民的环境沉默行为与少数积极分子环境抗争的自我克制,而企业生产建构的获利者群体进一步分化了受害者圈层,村落“双重圈层”互嵌式关系格局阻隔村民通过集体行动制止企业污染的底层路径。农村内生污染企业的嵌入属性加深了村落社会分化、侵蚀了农村环境治理的社会基础,更提醒关注农村污染企业的社区嵌入与村民环境行为选择的复杂性关联。     

Estimation for Partially Linear Single-index Instrumental Variables Models

In this article, we generalize the partially linear single-index models to the scenario with some endogenous covariates variables. It is well known that the estimators based on the existing methods are often inconsistent because of the endogeneity of covariates. To deal with the endogenous variables, we introduce some auxiliary instrumental variables. A three-stage estimation procedure is proposed for partially linear single-index instrumental variables models. The first stage is to obtain a linear projection of endogenous variables on a set of instrumental variables, the second stage is to estimate the link function by using local linear smoother for given constant parameters, and the last stage is to obtain the estimators of constant parameters based on the estimating equation. Asymptotic normality is established for the proposed estimators. Some simulation studies are undertaken to assess the finite sample performance of the proposed estimation procedure.     

New innovational outlier unit root test with a break at an unknown time

The Perron test which is based on a Dickey–Fuller test regression is a commonly employed approach to test for a unit root in the presence of a structural break of unknown timing. In the case of an innovational outlier (IO), the Perron test tends to exhibit spurious rejections in finite samples when the break occurs under the null hypothesis. In the present paper, a new Perron-type IO unit root test is developed. It is shown in Monte Carlo experiments that the new test does not over-reject the null hypothesis. Even for the case of a level and slope break for trending data, the empirical size is near its nominal level. The test distribution equals the case of a known break date. Furthermore, the test is able to identify the true break date very accurately even for small breaks. As an application serves the Nelson–Plosser data set.     

Pre‐procreative ages in population stability and cyclicity

Age‐specific models of population renewal (with and without feedback) which imply convergence to a stable state for some levels of fertility or feedback may imply the presence of long‐term cycling around a constant or exponentially changing equilibrium for other levels of fertility or feedback. The switch from one regime to the other is a “bifurcation.”; The conditions for bifurcation involve the roots of an analogue of Lotka's Equation.

Typically bifurcation is induced by raising the strength of feedback or the level of fertility. It has been known since the early 1980s, however, that this is sometimes impossible. It is sometimes impossible even with the linear renewal equation itself and with the most basic of non‐linear models, Lee's cohort feedback model.

Here it is proved that this typical route to bifurcation does not fail for these basic models in the presence of a condition which always holds for realistic applications with higher organisms: the existence of a span of ages before the onset of fertility.

Specifically, a strictly positive lower bound on ages of procreation is proved to be sufficient to guarantee the existence of a rescaling of Lotka's Equation for which the real part of some complex root vanishes. This result holds for absolutely Lebesgue‐integrable (signed) net maternity functions on the positive real line and for absolutely summable (signed) net maternities on the positive integers.

It follows that Coale's rescaling device for the analysis of approach to stability in stable population theory can be implemented for all realistic human net maternity schedules. It also follows that the many special cases of the cohort feedback model throughout population biology will all generate persistent cycling instead of stability if feedback is sufficiently strong.     

Instrumental variable based variable selection for generalized linear models with endogenous covariates

We study the variable selection problem for a class of generalized linear models with endogenous covariates. Based on the instrumental variable adjustment technology and the smooth-threshold estimating equation (SEE) method, we propose an instrumental variable based variable selection procedure. The proposed variable selection method can attenuate the effect of endogeneity in covariates, and is easy for application in practice. Some theoretical results are also derived such as the consistency of the proposed variable selection procedure and the convergence rate of the resulting estimator. Further, some simulation studies and a real data analysis are conducted to evaluate the performance of the proposed method, and simulation results show that the proposed method is workable.     

论经济周期波动的随机统计规律

从经济周期波动的特征出发，分析经济周期现象中考虑随机性的合理性和必要性，可看出经济周期运动的内在机制中蕴含着大量的不确定随机因素及对经济周期波动的影响，从随机周期现象入手，针对周期波动的研究历史和现状，就可得到新的启示和评价．     

Inference on Filtered and Smoothed Probabilities in Markov-Switching Autoregressive Models

ABSTRACT

We derive a statistical theory that provides useful asymptotic approximations to the distributions of the single inferences of filtered and smoothed probabilities, derived from time series characterized by Markov-switching dynamics. We show that the uncertainty in these probabilities diminishes when the states are separated, the variance of the shocks is low, and the time series or the regimes are persistent. As empirical illustrations of our approach, we analyze the U.S. GDP growth rates and the U.S. real interest rates. For both models, we illustrate the usefulness of the confidence intervals when identifying the business cycle phases and the interest rate regimes.     

Dynamic evolution of alliance portfolios

This research advances in the conceptualization and the operationalization of the factors or microdynamics that determine the choice of partners. Most of the literature in this area of research has centered on the individual alliance without taking into account the set of alliances that a firm makes. This research applies a holistic approach, analyzing the set of alliances as a whole and points to the factors related to alliance portfolios that affect the choice of partners. The authors propose a longitudinal model that allows us to analyze the evolution of interorganizational networks. A Simulation Investigation for Empirical Network Analysis (SIENA) has been applied to a sample of 229 firms, analyzing 10,556 strategic alliances established between them over a 12 year period. The results show that certain factors over which managers exercise a degree of control (deliberate endogenous microdynamics) exert significant influences on the choice of partners by the focal actor and thereby on the dynamic configuration of alliance portfolios.     

Sentiments

This paper develops a new theory of fluctuations—one that helps accommodate the notions of “animal spirits” and “market sentiment” in unique‐equilibrium, rational‐expectations, macroeconomic models. To this goal, we limit the communication that is embedded in a neoclassical economy by allowing trading to be random and decentralized. We then show that the business cycle may be driven by a certain type of extrinsic shocks which we call sentiments. These shocks formalize shifts in expectations of economic activity without shifts in the underlying preferences and technologies; they are akin to sunspots, but operate in unique‐equilibrium models. We further show how communication may help propagate these shocks in a way that resembles the spread of fads and rumors and that gives rise to boom‐and‐bust phenomena. We finally illustrate the quantitative potential of our insights within a variant of the RBC model.