Variance Estimation for Price Indexes From a Two-Stage Sample With Rotating Panels

Estimation of price indexes in the United States is generally based on complex rotating panel surveys. The sample for the Consumer Price Index, for example, is selected in three stages—geographic areas, establishments, and individual items—with 20% of the sample being replaced by rotation each year. At each period, a time series of data is available for use in estimation. This article examines how to best combine data for estimation of long-term and short-term changes and how to estimate the variances of the index estimators in the context of two-stage sampling. I extend the class of estimators, introduced by Valliant and Miller, of Laspeyres indexes formed using sample data collected from the current period back to a previous base period. Linearization estimators of variance for indexes of long-term and short-term change are derived. The theory is supported by an empirical simulation study using two-stage sampling of establishments and items from a population derived from U.S. Bureau of Labor Statistics data.     

Estimation of Laspeyres Price Indexes Using the Prediction Approach for Finite Population Sampling

Estimators of chain and fixed-base Laspeyres price indexes are studied using the prediction approach to finite population sampling. The estimators include some that are based on those used in several U.S. government index programs and others derived from prediction models. Biases and variances of the estimators are studied for a case in which the reference period index weights are unknown for nonsample items. Under a model for a one-period price change in which items have common within-stratum means, unbiased estimators can be constructed, but under a more general regression model, special sample balance conditions are needed for unbiasedness of those estimators. The theory for the estimators of fixed-base indexes is illustrated in an empirical study using a population of items priced for the U.S. Consumer Price Index.     

Using Scanner Data to Construct CP1 Basic Component Indexes

This article considers how scanner data could be used in constructing component indexes for the U.S. Consumer Price Index. One product, coffee, in two cities generates over 1.8 million observations in just over two years, so coping with the sheer volume of data would be a challenge. Some other findings are (1) some aggregation of prices into “unit-value” averages is necessary for practical reasons and to avoid bias, (2) chained Laspeyres indexes are very high, (3) “modified” Laspeyres indexes have some upward bias but much less than a true Laspeyres index, (4) Fisher ideal or modified Edgeworth indexes perform well, and (5) aggregating prices across outlets to form city-level unit values reduces the discrepancies between index-number formulas.     

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.     

The Sensitivity of the True Cost of Living to Price-Induced and Income-Induced Changes in Aggregate Consumers' Tastes

This article examines the sensitivity of the cost of living to some aspects of price changes and income changes that cannot be detected by Laspeyres indexes like the CPI-U or CPI-W. Effects of price-induced and income-induced changes in consumers tastes on the cost of living in the United States from 1947 to 1981 are estimated and found to be generally substantial.     

Standard errors for the Laspeyres index number with autocorrelated error models

This paper deals with the stochastic approach to Laspeyres price index number with the assumption of serial correlation of orders 1 and 2. The first round of estimation provides the estimates of Laspeyres index numbers in the presence of serial correlation assuming that variance is independent of time. In the second round of estimation, we use the weighted least square approach to derive the standard errors of Laspeyres index number assuming variance is dependent on time. These standard errors are linked to the variability of relative prices and are simple to evaluate. It shows that the larger index numbers are expected to estimate with less degree of precision. The results are illustrated with price data of Pakistan.     

Measuring price-induced changes in standard of living in least developed countries: economic validity of laspeyres price indices and some further suggestions

Usually, also in developing countries, price-induced changes in standard of living are measured by means of Laspeyres price indices. Looking at the special economic situation characterizing least developed countries, the economic validit of such indices is doubtful. The main theoretical results of this paper are derived on the basis of a special utility concept which may be considered typical for least developed countries. It is shown that, under certain conditions, a Laspeyres price index over- or underestimates respectively changes in standard of living. Furthermore, it does not sufficiently evaluate households’ supply positions. These theoretical results are motivated and illustrated by a special least developed country, the Republic of Niger. The paper closes with some further suggestions for measuring changes in standard of living in developing countries.     

Scanner Data and the Treatment of Quality Change in Nonrevisable Price Indexes

The recently developed rolling year GEKS procedure makes maximum use of all matches in the data to construct nonrevisable price indexes that are approximately free from chain drift. A potential weakness is that unmatched items are ignored. In this article we use imputation Törnqvist price indexes as inputs into the rolling year GEKS procedure. These indexes account for quality changes by imputing the “missing prices” associated with new and disappearing items. Three imputation methods are discussed. The first method makes explicit imputations using a hedonic regression model which is estimated for each time period. The other two methods make implicit imputations; they are based on time dummy hedonic and time-product dummy regression models and are estimated on bilateral pooled data. We present empirical evidence for New Zealand from scanner data on eight consumer electronics products and find that accounting for quality change can make a substantial difference.     

Construction of confidence intervals for the Laspeyres price index

In the paper, we present and discuss several methods of the construction of confidence intervals for the Laspeyres price index. We assume that prices of commodities are normally distributed and we consider both independent and dependent prices. Using Monte Carlo simulation, the paper compares the confidence interval computed from a simple econometric model with those obtained based on the Laspeyres density function. Our conclusions can be generalized to other price index formulas.     

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。     

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.     

The True Cost-of-Living Index With Changing Preferences

This article investigates the theoretical and empirical properties of a true cost-of-living index under conditions of changing preferences. A family of true indexes is defined based on the notion of the current utility function. A particular index, based on the previous period's utility level, is then defined. Given this definition, a true cost-of-living index is computed based on a quadratic expenditure system estimated with quarterly data from 1960–1981. For empirical purposes, changes in preferences are represented by the linear habit formation hypothesis. This index is then compared with Paasche and Laspeyres indexes. The true cost-of-living index grows somewhat faster than either the Paasche or Laspeyres index. It also displays considerably more variability.     

中国股指期货与股票市场波动性关系的实证分析

使用修正的EGARCH模型与VaR方法检验股指期货的推出对中国股票市场波动性所产生的影响。采用的数据为沪深300指数,样本数据分为股指期货推出前,股指期货推出后的短期、中期和长期与样本数据全体五个时间段。研究表明,从股指期货推出的短期与中期来看,市场对信息的反应比较混乱。从长期来看,股指期货的推出加速了信息的传递速度并且弱化了非对称效应,并没有加大股市的波动性。VaR方法检验表明,股指期货的推出有效降低了股市风险,使A股市场更加成熟和完善。     

消费者偏好与真实生活成本

本文在消费者偏好结构可变的假设下,探讨了1998-2012年我国消费者真实生活成本。研究表明忽视消费者偏好结构的变化通常会高估消费者真实生活成本水平和增长幅度,而这种替代偏误的程度取决于基期的选择。基于这种研究发现,政府有关部门在使用消费者物价指数制定相关政策（尤其是福利政策）时,本文研究的非参数型真实生活成本指数 可能比一般的拉氏物价指数更为合适。因此,建议统计部门在使用拉氏价格指数统计消费者物价水平的同时,应该定期编制和公布 指数。     

Inference Tests for Gini-Based Tax Progressivity Indexes

Distribution-free statistical inference procedures for changes in Lorenz- and Gini-based indexes of tax progressivity are developed and applied. Related but distinct tests for the Reynolds–Smolensky index of residual progression and the Kakwani index of liability progression are provided. The inference procedures are illustrated by applying them to Luxembourg Income Study microdata for Sweden, the United Kingdom, and the United States before and after periods of tax reform. In each country a finding of significant change depends on the choice among progressivity indexes. No single index exhibits a consistent pattern of significant change in all countries across time.     

Nonparametric regression estimation of conditional tails: the random covariate case

We present families of nonparametric estimators for the conditional tail index of a Pareto-type distribution in the presence of random covariates. These families are constructed from locally weighted sums of power transformations of excesses over a high threshold. The asymptotic properties of the proposed estimators are derived under some assumptions on the conditional response distribution, the weight function and the density function of the covariates. We also introduce bias-corrected versions of the estimators for the conditional tail index, and propose in this context a consistent estimator for the second-order tail parameter. The finite sample performance of some specific examples from our classes of estimators is illustrated with a small simulation experiment.     

A location-invariant non-positive moment-type estimator of the extreme value index

This paper investigates a class of location invariant non-positive moment-type estimators of extreme value index, which is highly flexible due to the tuning parameter involved. Its asymptotic expansions and its optimal sample fraction in terms of minimal asymptotic mean square error are derived. A small scale Monte Carlo simulation turns out that the new estimators, with a suitable choice of the tuning parameter driven by the data itself, perform well compared to the known ones. Finally, the proposed estimators with a bootstrap optimal sample fraction are applied to an environmental data set.     

PORT Hill and Moment Estimators for Heavy-Tailed Models

In this article, we use the peaks over random threshold (PORT)-methodology, and consider Hill and moment PORT-classes of extreme value index estimators. These classes of estimators are invariant not only to changes in scale, like the classical Hill and moment estimators, but also to changes in location. They are based on the sample of excesses over a random threshold, the order statistic X _[np]+1:n , 0 ≤ p < 1, being p a tuning parameter, which makes them highly flexible. Under convenient restrictions on the underlying model, these classes of estimators are consistent and asymptotically normal for adequate values of k, the number of top order statistics used in the semi-parametric estimation of the extreme value index γ. In practice, there may however appear a stability around a value distant from the target γ when the minimum is chosen for the random threshold, and attention is drawn for the danger of transforming the original data through the subtraction of the minimum. A new bias-corrected moment estimator is also introduced. The exact performance of the new extreme value index PORT-estimators is compared, through a large-scale Monte-Carlo simulation study, with the original Hill and moment estimators, the bias-corrected moment estimator, and one of the minimum-variance reduced-bias (MVRB) extreme value index estimators recently introduced in the literature. As an empirical example we estimate the tail index associated to a set of real data from the field of finance.     

中国居民消费价格指数间的关系与选择

居民消费价格是宏观经济监测的重要内容之一,其指数间的关系与选择具有重要意义。通过与国外发达国家的比较,从我国目前价格指数编制和选择使用的现状及存在的问题出发,研究环比、同比和定基价格指数以及环比“折年率”之间的相互转化情况和它们各自在经济监测中的特征。重点研究了基于X-12-ARIMA模型的环比价格指数的季节调整和同比价格指数相对环比价格指数对物价监测的时滞性。同时验证了研究中同比向定基指数转化的合理性。由此对我国居民价格实时监测的指数选择提供政策建议,也为我国价格指数的编制提出建议。     

我国股指期货价格发现功能研究

本文基于沪深300股指期货5分钟高频数据,利用协整检验、误差修正模型和脉冲响应函数研究了我国股指期货长短期的价格发现机制,并用信息共享模型、共因子模型研究了我国股指期货市场的价格发现贡献程度,在此基础上,引入分位数回归,探讨不同涨跌幅度的期现关系。实证结果表明：我国指数期货和现货价格存在相互引导关系,而现阶段现货市场能更快反应全部市场的冲击,且现货市场在价格发现功能中的作用相对较大;随着涨跌幅度的变化,现货对期货的影响呈U型走势,而期货对现货的影响呈单边上升走势。