Testing a Theory of Exact Aggregation

This article analyzes the importance of exact aggregation restrictions and the modeling of demographic effects in Jorgenson, Lau, and Stoker's (1982) model of aggregate consumer behavior. These issues are examined at the household level, using Canadian cross-sectional microdata. Exact aggregation restrictions and some implicit restrictions on household demographic effects are strongly rejected by our data. These results do not preclude pooling aggregate time series data with cross-sectional microdata to estimate a model of aggregate consumer behavior. They do suggest, however, an alternative basis for the aggregate model.     

Estimating consumer acceptance limits

A methodology is developed for estimating consumer acceptance limits on a sensory attribute of a manufactured product. In concept these limits are analogous to engineering tolerances. The method is based on a generalization of Stevens' Power Law. This generalized law is expressed as a nonlinear statistical model. Instead of restricting the analysis to this particular case, a strategy is discussed for evaluating nonlinear models in general since scientific models are frequently of nonlinear form. The strategy focuses on understanding the geometrical contrasts between linear and nonlinear model estimation and assessing the bias in estimation and the departures from a Gaussian sampling distribution. Computer simulation is employed to examine the behavior of nonlinear least squares estimation. In addition to the usual Gaussian assumption, a bootstrap sample reuse procedure and a general triangular distribution are introduced for evaluating the effects of a non-Gaussian or asymmetrical error structure. Recommendations are given for further model analysis based on the simulation results. In the case of a model for which estimation bias is not a serious issue, estimating functions of the model are considered. Application of these functions to the generalization of Stevens’ Power Law leads to a means for defining and estimating consumer acceptance limits, The statistical form of the law and the model evaluation strategy are applied to consumer research data. Estimation of consumer acceptance limits is illustrated and discussed.     

Comparing Two-Stage Segmentation Methods for Choice Data with a One-Stage Latent Class Choice Analysis

Market segmentation is a key concept in marketing research. Identification of consumer segments helps in setting up and improving a marketing strategy. Hence, the need is to improve existing methods and to develop new segmentation methods. We introduce two new consumer indicators that can be used as segmentation basis in two-stage methods, the forces and the dfbetas. Both bases express a subject’s effect on the aggregate estimates of the parameters in a conditional logit model. Further, individual-level estimates, obtained by either estimating a conditional logit model for each individual separately with maximum likelihood or by hierarchical Bayes (HB) estimation of a mixed logit choice model, and the respondents’ raw choices are also used as segmentation basis. In the second stage of the methods the bases are classified into segments with cluster analysis or latent class models. All methods are applied to choice data because of the increasing popularity of choice experiments to analyze choice behavior. To verify whether two-stage segmentation methods can compete with a one-stage approach, a latent class choice model is estimated as well. A simulation study reveals the superiority of the two-stage method that clusters the HB estimates and the one-stage latent class choice model. Additionally, very good results are obtained for two-stage latent class cluster analysis of the choices as well as for the two-stage methods clustering the forces, the dfbetas and the choices.     

Estimating the Structure of Agricultural Investment: A Stochastic- Coefficients Approach

Two approaches, a flexibie-accelerator model and a stochastic-coefficients alternative, are used to estimate the structure of aggregate agricultural investment. Structural estimates of the adjustment rates for each model differ. The stochastic-coefficients model, however, performs better in out-of-sample forecasting.     

A Discussion on Nonlinear Models for Price Decisions in Rating-Based Product Preference Models

The purpose of this article is to discuss the application of nonlinear models to price decisions in the framework of rating-based product preference models. As revealed by a comparative simulation study, when a nonlinear model is the true model, the traditional linear model fails to properly describe the true pattern. It appears to be unsatisfactory in comparison with nonlinear models, such as logistic and natural spline, which offer some advantages, the most important being the ability to take into account more than just linear and/or monotonic effects. Consequently, when we model the product preference with a nonlinear model, we are potentially able to detect its ‘best’ price level, i.e., the price at which consumer preference towards a given attribute is at its maximum. From an application point of view, this approach is very flexible in price decisions and may produce original managerial suggestions which might not be revealed by traditional methods.     

ARCH and Bilinear Time Series Models: Comparison and Combination

Two extensions to the ARMA model, bilinearity and ARCH errors are compared, and their combination is considered. Starting with the ARMA model, tests for each extension are discussed, along with various least squares and maximum likelihood estimates of the parameters and tests of the estimated models based on these. The effects each may have on the identification, estimation, and testing of the other are given, and it is seen that to distinguish between the two properly, it is necessary to combine them into a bilinear model with ARCH errors. Some consequences of the misspecification caused by considering only the ARMA model are noted, and the methods are applied to two real time series.     

Two-Stage Budgeting and Exact Aggregation

This paper presents an econometric model of demand for energy based on two-stage budgeting. The model provides own-price and cross-price elasticities of demand for energy and nonenergy commodities for the United States. These elasticities are estimated separately for households classified by family size, age of head, region, race, and urban versus rural residence. Price elasticities are presented conditional on total energy expenditure and total expenditure on all commodities. The model combines individual cross-section data with aggregate time series data and is based on exact aggregation over individual demand functions.     

Intertemporal consumer behaviour under structural changes in income

In this paper we analyze models of forward looking consumer behaviour and give empirical evidence for aggregate quarterly data for the Netherlands, 1967-1984. Special attention is devoted to the implications of unanticipated structural changes in the income process, which because of replanning, will have an impact on the consumption decision. We start with the life cycle hypothesis. Since the fall in aggregate consumption in the Netherlands in the eighties can not be explained by the life cycle model, the theory is reformulated by assuming that the planning horizon of the consumers moves ahead as time goes on. As a result, an error correction mechanism has to be introduced in the consumption function.The modified model is found to be in agreement with the data.     

一类扩展的投入产出模型

 内容提要：基于居民部门封闭的投入产出模型进行扩展,并将政府部门从最终需求列中转移出来,纳入到生产部门,列入投入产出表的第Ⅰ象限,政府部门所在的行是以货币形式表现的各部门（包括居民部门）的税收支付,政府部门所在的列是政府对各个部门的各种消费品和劳务的消费额,得到了扩展的局部闭投入产出模型,并在此模型的基础上得到了各种乘数。进一步将投资考虑进去得到动态投入产出扩展模型,使得国民经济各个生产部门、居民部门、政府部门成为一个完整的投入产出平衡体。     

The Effects of Price Aggregation Bias in Systems of Demand Equations

This article illustrates the importance of maintaining consistent levels of aggregation between prices and quantities when estimating consumer demand functions. The impact of violating this condition is quantified by using summary performance measures and estimates of demand elasticity biases. Results derived from an application of 1972–1973 Consumer Expenditure Survey data and supported with a quasi-Monte Carlo experiment consistently indicate that the point estimates of demand elasticities are significantly biased. Thus the study indicates the importance of developing and maintaining price indexes disaggregated to the same level as the expenditure data in consumer expenditure and budget surveys.     

Search With Learning for Differentiated Products: Evidence from E-Commerce

This article provides a method to estimate search costs in a differentiated product environment in which consumers are uncertain about the utility distribution. Consumers learn about the utility distribution by Bayesian updating their Dirichlet process prior beliefs. The model provides expressions for bounds on the search costs that can rationalize observed search and purchasing behavior. Using individual-specific data on web browsing and purchasing behavior for MP3 players sold online we show how to use these bounds to estimate search costs as well as the parameters of the utility distribution. Our estimates indicate that search costs are sizable. We show that ignoring consumer learning while searching can lead to severely biased search cost and elasticity estimates.     

中国核心通货膨胀的指数测算、分类特征与冲击传导

为了测算和分析我国核心通货膨胀指数，本文在动态因子模型分析框架下引入了时变因子载荷系数、随机扰动和异常值调整，构建了基于我国城市环比CPI的UCSVO模型和基于八大类城市环比CPI及消费支出权重的MUCSVO模型。研究发现：①UCSVO模型识别出的CPI异常变动时间点符合经济现实，由其测算得出的核心通货膨胀指数适用于我国通货膨胀的实时监测；②MUCSVO模型中共同的趋势成份因子及其载荷系数能体现宏观冲击与价格粘性的现实经济含义，价格粘性的差异是各大类核心通货膨胀指数对宏观冲击产生异质性响应的重要原因；③MUCSVO模型所测算的核心通货膨胀指数的分类权重与消费支出成正比、与波动性成反比，在测算分类以及总体核心通货膨胀指数的同时，还能准确反映各大类CPI的变化特征。     

基于局部闭模型与乘数分析的投资对消费影响研究——以北京市42部门投入产出分析为例

基于北京市42部门的投入产出表,利用投入产出局部闭模型、完全经济联系乘数和结构化凯恩斯乘数等方法,研究北京市分部门投资对消费的拉动关系,考察不同部门的投资变化对于消费的影响,结果表明:劳动报酬系数比影响力系数对消费的拉动效应要大,投资对消费的拉动系数主要决定于劳动报酬系数;公共管理和社会组织、教育、研究与试验发展业等基础性服务行业的投资对消费拉动系数较大。在一定投资的情况下,应该加大这些行业的投资以平衡消费与投资的关系。     

Understanding the Risk-Return Relation: The Aggregate Wealth Proxy Actually Matters

ABSTRACT

The ICAPM implies that the market’s conditional expected return is proportional to its conditional variance and that the reward-to-risk ratio equals the representative investor’s coefficient of relative risk aversion. Prior studies examine this relation using the stock market to proxy for aggregate wealth and find mixed results. We show, however, that stock-based tests suffer from low power and lead to biased estimates of the risk-return tradeoff when stocks are an imperfect market proxy. Tests designed to mitigate this bias by incorporating a more comprehensive measure of aggregate wealth produce large, positive estimates of the risk-aversion coefficient around seven to nine. Supplementary materials for this article are available online.     

What Level of Statistical Model Should We Use in Small Area Estimation?

If unit‐level data are available, small area estimation (SAE) is usually based on models formulated at the unit level, but they are ultimately used to produce estimates at the area level and thus involve area‐level inferences. This paper investigates the circumstances under which using an area‐level model may be more effective. Linear mixed models (LMMs) fitted using different levels of data are applied in SAE to calculate synthetic estimators and empirical best linear unbiased predictors (EBLUPs). The performance of area‐level models is compared with unit‐level models when both individual and aggregate data are available. A key factor is whether there are substantial contextual effects. Ignoring these effects in unit‐level working models can cause biased estimates of regression parameters. The contextual effects can be automatically accounted for in the area‐level models. Using synthetic and EBLUP techniques, small area estimates based on different levels of LMMs are investigated in this paper by means of a simulation study.     

Search With Dirichlet Priors: Estimation and Implications for Consumer Demand

This article is an empirical application of the search model with an unknown distribution, as introduced by Rothschild in 1974. For searchers who hold Dirichlet priors, we develop a novel characterization of optimal search behavior. Our solution delivers easily computable formulas for the ex-ante purchase probabilities as outcomes of search, as required by discrete-choice-based estimation. Using our method, we investigate the consequences of consumer learning on the properties of search-generated demand. Holding search costs constant, the search model from a known distribution predicts larger price elasticities, mainly for the lower-priced products. We estimate a search model with Dirichlet priors, on a dataset of prices and market shares of S&P 500 mutual funds. We find that the assumption of no uncertainty in consumer priors leads to substantial biases in search cost estimates.     

The Bias in Price Elasticity Estimates Under Homothetic Separability: Implications for Analysis of Peak-Load Electricity Pricing

This article demonstrates that the assumption of a homothetically separable utility function places a priori restrictions on the parameters of the demand system. If these restrictions are unwarranted, an open question if they are not explicitly tested, they will lead to biased price elasticity estimates. In particular, we show that the uncompensated own-price elasticities must be smaller than the negative of the expenditure shares; that is, the price elasticity of peak electricity demand must be less than the negative of the share of expenditure devoted to peak electricity. This finding is probably not new to economists familiar with consumer demand analysis. Nevertheless, many recent studies of consumer demand for electricity under time-of-day rates explicitly impose this restriction. The resulting price elasticity estimates are usually quite large in absolute value (.5 to .8); but they are the product of restrictive a priori assumptions as well as information embodied in the sample data. The results of two analyses of time-of-day experiments, where the researchers imposed the untested assumption of homothetic separability, are examined more closely. We find that the reported price elasticities are strongly influenced by that a priori assumption. A Monte Carlo experiment demonstrates that using this model will lead to the reported price elasticities even if the consumption data are perfectly random with respect to price.     

The Estimation of Short-Run Household Electricity Demand Using Pooled Aggregate Data

Short-run household electricity demand has been estimated with conditional demand models by a variety of authors using both aggregate data and disaggregate data. Disaggregate data are most desirable for estimating these models. However, in many cases, available disaggregate data may be inappropriate. Furthermore, disaggregate data may be unavailable altogether. In these cases, readily available aggregate data may be more appropriate. This article develops and evaluates an econometric technique to generate unbiased estimates of household electricity demand using such aggregate data.     

Selection of the Ridge Parameter Using Mathematical Programming

Ridge regression solves multicollinearity problems by introducing a biasing parameter that is called ridge parameter; it shrinks the estimates and their standard errors in order to reach acceptable results. Selection of the ridge parameter was done using several subjective and objective techniques that are concerned with certain criteria. In this study, selection of the ridge parameter depends on other important statistical measures to reach a better value of the ridge parameter. The proposed ridge parameter selection technique depends on a mathematical programming model and the results are evaluated using a simulation study. The performance of the proposed method is good when the error variance is greater than or equal to one; the sample consists of 20 observations, the number of explanatory variables in the model is 2, and there is a very strong correlation between the two explanatory variables.     

The Performance of Robust Two-Stage Estimator in Nonlinear Regression with Autocorrelated Error

Some statistics practitioners often ignore the underlying assumptions when analyzing a real data and employ the Nonlinear Least Squares (NLLS) method to estimate the parameters of a nonlinear model. In order to make reliable inferences about the parameters of a model, require that the underlying assumptions, especially the assumption that the errors are independent, are satisfied. However, in a real situation, we may encounter dependent error terms which prone to produce autocorrelated errors. A two-stage estimator (CTS) has been developed to remedy this problem. Nevertheless, it is now evident that the presence of outliers have an unduly effect on the least squares estimates. We expect that the CTS is also easily affected by outliers since it is based on the least squares estimator, which is not robust. In this article, we propose a Robust Two-Stage (RTS) procedure for the estimation of the nonlinear regression parameters in the situation where autocorrelated errors come together with the existence of outliers. The numerical example and simulation study signify that the RTS is more efficient than the NLLS and the CTS methods.