Proposition of a General Formula for Price Indices

In this article, we propose a general formula for aggregative price indices that satisfies most postulates coming from the axiomatic price index theory. We show that the ideal Fisher index, Laspeyres and Paasche formulas, and a lot of other indices are particular cases of the proposed formula. Moreover, using the general formula we can easily define new indices, that would satisfy given postulates. We also present an interesting result for the proposed formula.     

Approximation of the Fisher price index by using the Lloyd–Moulton index: Simulation study

The Lloyd–Moulton price index does not make use of current-period expenditure data and, as it is commonly known, it allows us to approximate superlative indices, in particular the Fisher price index. This is a very important property for the inflation measurement and the Consumer Price Index bias calculations. In this article, we verify the utility of the Lloyd–Moulton price index in the Fisher price index approximation. We propose a simple modification of that index which reduces the variation of the estimator of an unknown parameter in this index formula. We also examine the influence of the price volatility on the quality of estimation of the parameter from the Lloyd–Moulton formula.     

Comparison of elementary price indices

Abstract

Most countries use the Dutot, Jevons or Carli index for the calculation of their Consumer Price Index (CPI) at the lowest (elementary) level of aggregation. The choice of the elementary formula for inflation measurement does matter and the effect of the change of the index formula was estimated by the Bureau of Labor Statistics. It has been shown that difference between elementary indices can be explained in terms of changes in price dispersion. In this article, we extend these results comparing both population and sample elementary indices. We assume that prices from two compared time moments are log-normally distributed and correlated. Under the above-mentioned assumption, we provide formulas for biases and mean-squared errors of main elementary indices.     

Approximation of the Fisher price index by using Lowe,Young, and AG Mean indices

The Consumer Price Index (CPI) approximates changes in the costs of household consumption assuming the constant utility (COLI, Cost of Living Index). In practice, the Laspeyres price index is used to measure the CPI despite the fact that many economists consider the superlative indices to be the best approximation of COLI. The Fisher index is one of the superlative indices and additionally it satisfies most of tests from the axiomatic price index theory. Nevertheless, the Fisher price index makes use of current-period expenditure data and its usefulness in CPI measurement is limited. In this article, we verify the utility of using the Lowe, Young, and AG Mean indices for Fisher price index approximation. We confirm this utility in a simulation study and we provide an empirical proof.     

特有冲击、共同冲击与通货膨胀持续性

中国分类价格指数的通货膨胀持续性有何特征？如何理解分类价格指数和加总价格指数通货膨胀持续性之间的关系？我们对2001年1月至2011年12月的数据进行实证分析,结果表明分类价格指数比较明显的表现出行业间异质的通货膨胀波动性和通货膨胀持续性,而与加总价格指数相比,它的通货膨胀波动性更大而通货膨胀持续性更低。通货膨胀持续性的这些现象可以从特有冲击和共同冲击的角度加以理解。共同冲击的相对重要性存在差异解释了分类价格指数的通货膨胀持续性呈现行业间异质性;特有冲击的重要性在数据加总时被削弱,解释了分类价格指数具有比加总价格指数更低的通货膨胀持续性。     

Volatility estimation from short time series of stock prices

We consider estimation of the historical volatility of stock prices. It is assumed that the stock prices are represented as time series formed as samples of the solution of a stochastic differential equation with random and time-varying parameters; these parameters are not observable directly and have unknown evolution law. The price samples are available with limited frequency only. In this setting, the estimation has to be based on short time series, and the estimation error can be significant. We suggest some supplements to the existing nonparametric methods of volatility estimation. Two modifications of the standard summation formula for the volatility are derived. In addition, a linear transformation eliminating the appreciation rate and preserving the volatility is suggested.     

关于多维指标抽样调查中删除指标的均值估计

针对多维度指标抽样调查情况,运用多变量幂函数逼近理论,对多指标中删除的指标构造出一类依赖于保留指标的估计量,通过对其性质的讨论,得出了该估计量的抽样误差与样本量的倒数同阶的结论。在抽样调查的实际应用中,可以根据给定的抽样误差,对部分指标进行调查,未被调查指标的均值通过调查指标值的估计去实现,从而达到了解全部指标信息的目的。     

Reliability of global sensitivity indices

Uncertainty and sensitivity analysis is an essential ingredient of model development and applications. For many uncertainty and sensitivity analysis techniques, sensitivity indices are calculated based on a relatively large sample to measure the importance of parameters in their contributions to uncertainties in model outputs. To statistically compare their importance, it is necessary that uncertainty and sensitivity analysis techniques provide standard errors of estimated sensitivity indices. In this paper, a delta method is used to analytically approximate standard errors of estimated sensitivity indices for a popular sensitivity analysis method, the Fourier amplitude sensitivity test (FAST). Standard errors estimated based on the delta method were compared with those estimated based on 20 sample replicates. We found that the delta method can provide a good approximation for the standard errors of both first-order and higher-order sensitivity indices. Finally, based on the standard error approximation, we also proposed a method to determine a minimum sample size to achieve the desired estimation precision for a specified sensitivity index. The standard error estimation method presented in this paper can make the FAST analysis computationally much more efficient for complex models.     

铁路运价指数编制方法的探讨

一、编制铁路运价指数的必要性铁路运价是国家价格体系的重要组成部分 ,对铁路发展至关重要 ,对国民经济和社会发展也有广泛影响。长期以来 ,我国铁路运价由于长期在计划经济体制下运作 ,运价方面的基础数据、统计资料和指标不系统、不完整 ,国家价格统计和铁路统计均缺乏反映铁路运价水平变化幅度的指标 ,在研究铁路运价水平变化幅度时常用平均收入率来代替。由于收入率包含非价格因素对铁路运输收入的影响 ,因此收入率指数不能真正反映铁路客货运价水平及其价格变化情况 ,这种状况不能满足运价结构调整的需要 ,也不能适应运输市场供求关系…     

Relatioinships between economic and statistical price indices

In the following, the economic counterparts of Eichhorn's and Voeller's tests for statistical price indices will be studied. We will see that replacing the statistical Commensurability Axiom in the economic price index theory by a property which is only concerned with price changes leads to similar relationships between this one and several other tests as in the statistical price index theory.     

A general class of capability indices in the case of asymmetric tolerances

Vannman has earlier studied a class of capability indices, containing the indices C _p , C _pk , C _pm and C _pmk , when the tolerances are symmetric. We study the properties of this class when the tolerances are asymmetric and suggest a new enlargened class of indices. Under the assumption of normality an explicit form of the distribution of the new class of the estimated indices is provided. Numerical investigations are made to explore the behavior of the estimators of the indices for different values of the parameters. Based on the estimator a decision rule that can be used to determine whether the process can be considered capable or not is provided and suitable criteria for choosing an index from the family are suggested.     

Bootstrapping a hedonic price index: experience from used cars data

Every hedonic price index is an estimate of an unknown economic parameter. It depends, in practice, on one or more random samples of prices and characteristics of a certain good. Bootstrap resampling methods provide a tool for quantifying sampling errors. Following some general reflections on hedonic elementary price indices, this paper proposes a case-based, a model-based, and a wild bootstrap approach for estimating confidence intervals for hedonic price indices. Empirical results are obtained for a data set on used cars in Switzerland. A simple and an enhanced adaptive semi-logarithmic model are fit to monthly samples, and bootstrap confidence intervals are estimated for Jevons-type hedonic elementary price indices.     

关于物价综合指数性质的探析

通过对拉氏和帕氏物价指数的讨论，明确了物价综合指数之间的相互关系和物价综合指数的数学性质，找到了物价综合指数的变化特点。在保持原有指数特性的前提下，提出了新的综合指数改进方案，并对其进行了检验。检验表明，新的综合指数方案计算简便，能够准确地反映物量和价格的变化，并且误差较小。     

中国城乡居民信息消费的半参数估计分析#

以中国1993-2008年30个省份的面板数据为研究对象,通过构建中国城镇和农村居民信息消费的半参数模型,对信息消费的恩格尔曲线、总消费支出和价格指数对信息消费支出份额的边际影响进行了非参数估计,并在此基础上分析比较中国城乡居民信息消费的差异性。实证结果表明：地区经济发展水平仅对农村信息消费支出有显著影响,而居民受教育水平、居民总消费支出以及价格水平均对城乡居民信息消费支出有显著影响;居民总消费支出和价格水平变量对城乡居民信息消费支出的边际影响均存在一个极大值水平;价格水平对农村居民信息消费支出的负效应要大于总消费支出对信息消费支出的正效用,而城镇居民信息消费中没有表现出这一特征。通过控制价格水平、增加农村居民收入、增加农村基础设施投入等方式,可以缩小城乡居民信息消费的差异。     

An empirical investigation of the box-cox model and a nonlinear least squares alternative

In this paper we present a generalized functional form estimator, recently developed by jeffrey Wooldridge; and then we compare it empirically to the popular Box-Cox (BC) estimator using three data sets. We begin by briefly reviewing the drawbacks of the BC estimator. We Then introduce the nonlinear lest squares (NLS) alternative of Wooldridge which retains the desirable qualities of the BC estimator without the associated theoretical problems. We continue by applying both the BC and the NLS models to data from three classic hedonic regression studies and then compare the estimation resuts-point estimates, inferences and fitted values. The estimations include a wage rate equation, and two computer hedonic regression equations, one using data from a classic study by Gregory Chow and the other using an IBM data set that formed the basis of the new official BLS computer price index.     

对GDP缩减指数中“负权数”的研究——兼与徐强同志商榷

 摘　　要:把GDP缩减指数中出现的减号称之为“负权数”是不妥的，因为这个减号在GDP缩减指数公式中的分子与分母中都有出现，它只是计算GDP的理论定义公式中规定要出现的一个计算符号，说明的只是“GDP=总产出-中间消耗（或GDP=最终消费＋资本形成总额＋出口-进口）”这样一种逻辑计算关系。它并不能说明中间消耗价格（或进口价格）的变化与GDP价格的变化是反向关系，也不能权衡中间消耗价格（或进口价格）变化对GDP价格变化的影响轻重作用。它不是GDP缩减指数扭曲真实价格变动的根源。     

An empirical investigation of the box-cox model and a nonlinear least squares alternative

In this paper we present a generalized functional form estimator, recently developed by jeffrey Wooldridge; and then we compare it empirically to the popular Box-Cox (BC) estimator using three data sets. We begin by briefly reviewing the drawbacks of the BC estimator. We Then introduce the nonlinear lest squares (NLS) alternative of Wooldridge which retains the desirable qualities of the BC estimator without the associated theoretical problems. We continue by applying both the BC and the NLS models to data from three classic hedonic regression studies and then compare the estimation resuts-point estimates, inferences and fitted values. The estimations include a wage rate equation, and two computer hedonic regression equations, one using data from a classic study by Gregory Chow and the other using an IBM data set that formed the basis of the new official BLS computer price index.     

The gini-simpson index of diversity: estimation in the stratified sampling

In previous papers the problem of estimating the Gini-Simpson index of diversity for large populations has been considered by using random samplings with and without replacement, Nevertheless, the populations to which this estimation is usually applied (e.g., anthropoiogicai, ecological, linguistic and sociological populations) often arise naturally stratified.

In this paper we first construct unbiased estimators of the Gini-Simpson index from a sample drawn according to a stratified sampling with proportional allocation and independently in different strata. Then, we determine the standard error of such estimators. The advantages of the stratification in estimating diversity are later confirmed by means of a practical example. We finally suggest complementary studies that could be additionally developed.     

对我国消费价格指数编制方法的一点看法

对我国消费价格指数编制方法的一点看法谢安ＡＢＳＴＲＡＣＴＴｈｅａｕｔｈｏｒｄｉｓｃｕｓｓｅｄｔｈｅｓｈｏｒｔｃｏｍｉｎｇｓｅｘｉｓｔｅｄｉｎｔｈｅｃｏｍｐｉｌａｔｉｏｎｏｆＣｏｎｓｕｍｅｒｓｐｒｉｃｅｉｎｄｅｘ．Ｔｈｅｍａｉｎｐｒｏｂｌｅｍｉｓｔｈａ...