Forecasting the Distribution of Economic Variables in a Data-Rich Environment

This article investigates the relevance of considering a large number of macroeconomic indicators to forecast the complete distribution of a variable. The baseline time series model is a semiparametric specification based on the quantile autoregressive (QAR) model that assumes that the quantiles depend on the lagged values of the variable. We then augment the time series model with macroeconomic information from a large dataset by including principal components or a subset of variables selected by LASSO. We forecast the distribution of the h-month growth rate for four economic variables from 1975 to 2011 and evaluate the forecast accuracy relative to a stochastic volatility model using the quantile score. The results for the output and employment measures indicate that the multivariate models outperform the time series forecasts, in particular at long horizons and in tails of the distribution, while for the inflation variables the improved performance occurs mostly at the 6-month horizon. We also illustrate the practical relevance of predicting the distribution by considering forecasts at three dates during the last recession.     

Unbiased Estimation of the Distribution Function of an Exponential Population Using Order Statistics with Application in Ranked Set Sampling

In this paper we consider the problem of unbiased estimation of the distribution function of an exponential population using order statistics based on a random sample. We present a (unique) unbiased estimator based on a single, say ith, order statistic and study some properties of the estimator for i = 2. We also indicate how this estimator can be utilized to obtain unbiased estimators when a few selected order statistics are available as well as when the sample is selected following an alternative sampling procedure known as ranked set sampling. It is further proved that for a ranked set sample of size two, the proposed estimator is uniformly better than the conventional nonparametric unbiased estimator, further, for a general sample size, a modified ranked set sampling procedure provides an unbiased estimator uniformly better than the conventional nonparametric unbiased estimator based on the usual ranked set sampling procedure.     

A Proposal for a New Bound for Discrete Distributions

In this work we re-examine some classical bounds for non negative integer-valued random variables by means of information theoretic or maxentropic techniques using fractional moments as constraints. The proposed new bound, no more analytically expressible in terms of moments or moment generating function (mgf), is built by mixing classical bounds and the Maximum Entropy (ME) approximant of the underlying distribution; such a new bound is able to exploit optimally all the information content provided by the sequence of given moments or by the mgf. Particular care will be devoted to obtain fractional moments from the available information given in terms of integer moments and/or moment generating function. Numerical examples show clearly that the bound improvement involving the ME approximant based on fractional moments is not trivial.     

Approximation of distributions by using the Anderson Darling statistic

ABSTRACT

In practice, it is often not possible to find an appropriate family of distributions which can be used for fitting the sample distribution with high precision. In these cases, it seems to be opportune to search for the best approximation by a family of distributions instead of an exact fit. In this paper, we consider the Anderson–Darling statistic with plugged-in minimum distance estimator for the parameter vector. We prove asymptotic normality of the Anderson–Darling statistic which is used for a test of goodness of approximation. Moreover, we introduce a measure of discrepancy between the sample distribution and the model class.     

The distribution of the product of two independent generalized trapezoidal random variables

ABSTRACT

In this article, we derive the probability density function (pdf) of the product of two independent generalized trapezoidal random variables having different supports, in closed form, by considering all possible cases. We also show that the results for the product of two triangular and uniform random variables follow as special cases of our main result. As an illustration, we obtain pdf of product for a suitably constrained set of parameters and plot some graphs using MATLAB, which express variation in pdf with change in different parameters of the generalized trapezoidal distribution.     

Some bivariate uniform distributions

Bivariate uniform distributions with dependent components are readily derived by distribution function transformations of the components of non-uniform dependent continuous bivariate random variables (X,Y). Contour plots of joint density functions show the various, and varying, forms of dependence which can arise from different distributional forms for (X,Y) and aids the choice of bivariate uniform distributions as empirical models.     

混合指数几何分布

本文讨论元件的寿命分布服从双参数混合指数分布,元件个数服从几何分布的情形下,定义了混合指数几何分布,并研究了该分布的各种性质,讨论了参数的极大似然估计,并使用EM算法得到参数的近似估计. 最后,本文给出了参数的渐近方差、协方差、置信区间.     

国有企业双层分配关系的公平与效率研究

本文实证考察上市公司许继电气、格力电气和四川长虹的双层分配关系的公平和效率问题。从公平性来看,许继电气在2003年之前存在资本偏向分配,之后存在劳动偏向分配;格力电器一直存在资本偏向分配;四川长虹主要表现为劳动偏向分配。在管理层和职工之间,许继电气和格力电器存在管理层偏向分配,而四川长虹在2008年之前存在管理层偏向分配,其后存在职工偏向的分配。从收入分配关系影响来看,资劳收入比对企业效率没有显著影响,而高管员工差距对企业效率的存在负面影响。从经验数据来看,当兼顾公平与效率时,许继电气、格力电器和四川长虹综合指数最高年份分别是2004、2003和2006年。鉴于上述情形,企业应当根据现实情况从治理机制上进行改进,实现较好的分配关系。     

增值税“扩围”对我国城镇居民收入的分配效应

本文提出了一个新的增值税收入分配效应的分解方法,并运用2007-2011年我国城镇分组家庭的消费支出数据,分析了增值税“扩围”对居民收入分配的影响。实证结论表明,增值税“扩围”后不同收入等级的增值税税负随着收入的增加而降低,增值税对食品、居住、家庭设备用品及服务等领域具有不均等效应,而对衣着、医疗保健、交通和通信、教育文化与娱乐服务等领域具有均等效应。我国增值税总体上呈现不均等效应,但不均等效应逐步减弱,其中平均税率和消费支出差异的分配效应是决定因素。