Poisson Regression for Clustered Data

We compare five methods for parameter estimation of a Poisson regression model for clustered data: (1) ordinary (naive) Poisson regression (OP), which ignores intracluster correlation, (2) Poisson regression with fixed cluster‐specific intercepts (FI), (3) a generalized estimating equations (GEE) approach with an equi‐correlation matrix, (4) an exact generalized estimating equations (EGEE) approach with an exact covariance matrix, and (5) maximum likelihood (ML). Special attention is given to the simplest case of the Poisson regression with a cluster‐specific intercept random when the asymptotic covariance matrix is obtained in closed form. We prove that methods 1–5, except GEE, produce the same estimates of slope coefficients for balanced data (an equal number of observations in each cluster and the same vectors of covariates). All five methods lead to consistent estimates of slopes but have different efficiency for unbalanced data design. It is shown that the FI approach can be derived as a limiting case of maximum likelihood when the cluster variance increases to infinity. Exact asymptotic covariance matrices are derived for each method. In terms of asymptotic efficiency, the methods split into two groups: OP & GEE and EGEE & FI & ML. Thus, contrary to the existing practice, there is no advantage in using GEE because it is substantially outperformed by EGEE and FI. In particular, EGEE does not require integration and is easy to compute with the asymptotic variances of the slope estimates close to those of the ML.     

非线性延迟系统Runge-Kutta方法的稳定性探讨

针对时间依赖型的非线性多变延迟系统,采用变步长的Runge-Kutta方法求解,证明了匹配一定插值方法的代数稳定的Runge-Kutta方法是VR稳定的。     

贸易摩擦对中国钢铁产品出口影响的实证研究

随着中国钢铁产业快速的发展和世界经济环境的变化,涉华钢铁产品贸易摩擦日趋激烈。文章分析了中国钢铁产品出口贸易摩擦的概况,运用理论分析与实证分析相结合的方法,详细分析贸易摩擦对中国钢铁产品出口规模、出口市场结构以及国际竞争力的影响,对贸易摩擦的影响进行了总结:负面影响主要是出口规模的萎缩、限制相关企业的发展和提高出口贸易的成本,正面影响主要是促进贸易地理方向的多元化、产生优胜劣汰效应和促进技术创新。     

Can good marketing carry a bad product? Evidence from the motion picture industry

We examine the relative roles of marketing actions and product quality in determining commercial success. Using the motion picture context, in which product quality is difficult for consumers to anticipate and information on product success is available for different points in time, we model the effects of studio actions and movie quality on a movie’s sales during different phases of its theatrical run. For a sample of 331 recent motion pictures, structural equation modeling demonstrates that studio actions primarily influence early box office results, whereas movie quality influences both short- and long-term theatrical outcomes. The core results are robust across moderating conditions. We identify two data segments with follow-up latent class regressions and explore the degree of studio actions needed to “save” movies of varying quality. We finally offer some implications for research and management.     

PROPERTIES OF OPTION PRICES IN MODELS WITH JUMPS

We study convexity and monotonicity properties of option prices in a model with jumps using the fact that these prices satisfy certain parabolic integro–differential equations. Conditions are provided under which preservation of convexity holds, i.e., under which the value, calculated under a chosen martingale measure, of an option with a convex contract function is convex as a function of the underlying stock price. The preservation of convexity is then used to derive monotonicity properties of the option value with respect to the different parameters of the model, such as the volatility, the jump size, and the jump intensity.     

Repeated Dichotomous Choice Formats for Elicitation of Willingness to Pay: Simultaneous Estimation and Anchoring Effect

Repeated dichotomous choice contingent valuation data are generated from responses to a succession of binary questions regarding alternative prices for an environmental good. In this paper we propose a simultaneous equation model that allows for endogeneity and error correlation across the responses at each stage of the bidding process. The model allows us to study the evolution of anchoring effects after the second dichotomous choice question. Estimation involves the Bayesian techniques of Gibbs sampling and data augmentation, and the application focuses on the preservation value of a natural area. The results for a data set involving up to four successive dichotomous choice questions show that restricted multiple-bounded models are rejected by the data with the general model. In addition, willingness to pay tends to stabilize after the second stage in the elicitation process for the general unrestricted model. When taking anchoring effects into consideration, it is revealed that individuals’ responses in the latter stages are influenced by the sequence of bid prices offered in earlier questions. Nevertheless, they do not have a significant effect on welfare estimates.      

PARTIAL HEDGING IN A STOCHASTIC VOLATILITY ENVIRONMENT

We consider the problem of partial hedging of derivative risk in a stochastic volatility environment. It is related to state-dependent utility maximization problems in classical economics. We derive the dual problem from the Legendre transform of the associated Bellman equation and interpret the optimal strategy as the perfect hedging strategy for a modified claim. Under the assumption that volatility is fast mean-reverting and using a singular perturbation analysis, we derive approximate value functions and strategies that are easy to implement and study. The analysis identifies the usual mean historical volatility and the harmonically averaged long-run volatility as important statistics for such optimization problems without further specification of a stochastic volatility model. The approximation can be improved by specifying a model and can be calibrated for the leverage effect from the implied volatility skew. We study the effectiveness of these strategies using simulated stock paths.     

Asymptotically optimal estimation of smooth functionals for interval censoring, part 2

Estimation in the interval censoring model is considered. A class of smooth functionals is introduced, of which the mean is an example. We consider case 2, with two observation times for each unobservable event time, in the situation that the observation times cannot become arbitrarily close to each other. It is proved that the nonparametric maximum likelihood estimator of the functional asymptotically reaches the information lower bound.     

Processes with volatility-induced stationarity: an application for interest rates

In this paper we propose a refinement of the existing definition of volatility-induced stationarity that allows us to distinguish between processes with drift and diffusion induced stationarity and processes with pure volatility-induced stationarity. We also propose a classification of stationary processes with volatility-induced stationarity according to the volatility that is needed to inject stationarity. Processes with volatility-induced stationarity are potentially applicable to interest rate time-series since, as has been acknowledged, mean-reversion effects occur mainly in periods of high volatility. As such, we provide evidence that the logarithm of the Fed funds rate can be modelled as a local martingale with volatility-induced stationarity.