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.     

粮食主产区农村居民食物消费行为的计量分析

“民以食为天”,食物消费是人类生存和发展首要的物质基础。农村居民的食物消费水平是决定农村居民身体健康的物质基础,是农村居民生活水平的重要标志。研究和掌握食物消费结构特征,有利于农业产业结构调整和制定正确的农业产业政策,从而促进农民增收,实现农业的可持续发展。粮食主产区的粮食产量占全国粮食总产量的60%以上,对中国的粮食供给和安全具有举足轻重的作用,增加主产区农民收入有利于提高农民种粮食积极性,保证中国的粮食供给和粮食安全。为此,借助几乎理想的需求系统模型(Almost Ideal Demand System,简称AIDS),建立联立方程…     

Censored Quantile Instrumental Variable Estimates of the Price Elasticity of Expenditure on Medical Care

Efforts to control medical care costs depend critically on how individuals respond to prices. I estimate the price elasticity of expenditure on medical care using a censored quantile instrumental variable (CQIV) estimator. CQIV allows estimates to vary across the conditional expenditure distribution, relaxes traditional censored model assumptions, and addresses endogeneity with an instrumental variable. My instrumental variable strategy uses a family member’s injury to induce variation in an individual’s own price. Across the conditional deciles of the expenditure distribution, I find elasticities that vary from ?0.76 to ?1.49, which are an order of magnitude larger than previous estimates. Supplementary materials for this article are available online.     

Reduced-Form Versus Structural Models of Water Demand Under Nonlinear Prices

Increasing-block prices are common in markets for water, cellular phone service, and retail electricity. This study estimates demand models under block prices and conducts a Monte Carlo experiment to test the small-sample bias of structural and instrumental variables (IV) estimators. We estimate the price and income elasticity of water demand under increasing-block prices using a structural discrete/continuous choice (DCC) model, as well as random effects and IV. Elasticity estimates are sensitive to the modeling framework. The Monte Carlo experiment suggests that IV and DCC models estimate both price and income elasticity with bias, with no clear best choice among estimators.     

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.     

Systematic Effects of Capital Service Price Definition on Perceptions of Input Substitution

Earlier attempts at reconciling disparate substitution elasticity estimates examined differences in separability hypotheses, data bases, and estimation techniques, as well as methods employed to construct capital service prices. Although these studies showed that differences in elasticity estimates between two or three studies may be attributable to the aforementioned features of the econometric models, they have been unable to demonstrate this link statistically and establish the existence of systematic relationships between features of the econometric models and the perception of production technologies generated by those models. Using sectoral data covering the entire production side of the U.S. economy, we estimate 34 production models for alternative definitions of the capital service price. We employ substitution elasticities calculated from these models as dependent variables in the statistical search for systematic relationships between features of the econometric models and perceptions of the sectoral technology as characterized by the elasticities. Statistically significant systematic effects are found between the monotonicity and concavity properties of the cost functions and service price–technical change specifications as well as between substitution elasticities.     

A Dynamic Model of Investment in the U.S. Beef-Cattle Industry

Reproduction constraints lead to some a priori information that may prove valuable in econo- metrically modeling inventory dynamics within the U.S. cattle herd. The distributed-lag models estimated for animal inventories suggest an implicit incorporation of the age distribution of the herd that is crucial to understanding the retention/culling (investment) decisions. The estimated equations are validated using post-sample observations that were withheld prior to estimation. The final-form dynamic equations have complex roots and protracted price and investment effects. The parameter estimates are used to calculate intermediate and long-run elasticities at the means of relevant variables.     

Comment

This article tests the hypothesis of perfect competition in the consumer nondurables sector of the U.K. economy. First, it uses household-level data to estimate time-varying price elasticities of demand for disaggregated commodity groups. U.S. product prices are used as instruments for U.K. prices in the demand equation. Then it matches the product definitions to the Standard Industry Classification and uses firm-level data, combined with the estimated elasticities, to estimate a price model of firms operating in different industries. Household characteristics are used as instruments for the demand effects in the firms' supply equation. The results reject perfect competition and appear to be consistent with the argument that less competition increases profits through collusion.     

Interest-Rate Arbitrage in Currency Baskets: Forecasting Weights and Measuring Risk

This article addresses the problem of the bias of income and expenditure elasticities estimated on pseudopanel data caused by measurement error and unobserved heterogeneity. We gauge these biases empirically by comparing cross-sectional, pseudo-panel, and true panel data from both Polish and U.S. expenditure surveys. Our results suggest that unobserved heterogeneity imparts a downward bias to cross-section estimates of income elasticities of at-home food expenditures and an upward bias to estimates of income elasticities of away-from-home food expenditures. “Within” and first-difference estimators suffer less bias, but only if the effects of measurement error are accounted for with instrumental variables.     

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.     

EM Algorithm Estimation of Simultaneous Equation Model with Limited Variables: An Example of Cigarette Consumption

The two-part model and Heckman's sample selection model are often used in economic studies which involve analyzing the demand for limited variables. This study proposed a simultaneous equation model (SEM) and used the expectation-maximization algorithm to obtain the maximum likelihood estimate. We then constructed a simulation to compare the performance of estimates of price elasticity using SEM with those estimates from the two-part model and the sample selection model. The simulation shows that the estimates of price elasticity by SEM are more precise than those by the sample selection model and the two-part model when the model includes limited independent variables. Finally, we analyzed a real example of cigarette consumption as an application. We found an increase in cigarette price associated with a decrease in both the propensity to consume cigarettes and the amount actually consumed.     

Standard Errors for Elasticities: A Comparison of Bootstrap and Asymptotic Standard Errors

This article compares two methods of deriving standard errors for elasticities in a linear expenditure demand system with first-order autoregressive errors. The first is the ordinary Taylor series method and the second is Efron's bootstrap. In an example problem, these two methods yielded similar values for the standard errors, with the exception of the income elasticity standard errors, for which the asymptotic standard errors were apparently too large by a factor of two.     

The Demand for Lotto: The Role of Conscious Selection

This article presents estimates of the elasticity of demand for lottery tickets using time series data in which there is variation in the expected value of a lottery ticket induced by rollovers. An important feature of our data is that there are far more rollovers than expected given the lottery design. We find strong evidence that individuals do not choose their lottery numbers uniformly from a uniform distribution—that is, conscious selection. We use our estimates to derive the inverse supply function for the industry, and this enables us to identify the demand elasticity. We find the price elasticity to be close to unity, which implies that the operator is revenue maximizing—which is the regulator's objective.     

Time-of-Day Electricity Consumption Response to Temperature and the Ownership of Air Conditioning Appliances

This article is concerned with the endogeneity of air conditioning appliance ownership in the consumption of electricity by time of day (TOD). Both TOD consumption and air conditioning appliance ownership depend on temperature level and on household responsiveness to temperature variation, as well as on other measured household characteristics. The article presents an appropriate econometric methodology and applies it to obtain estimates and perform tests based on data from Southern California Edison's Residential TOD Pricing Experiment. The authors emphasize the implications for estimated consumption price elasticities.     

Problems in estimating non-linear Engel parameters in the absence of appropriate grouped means and average elasticity of variable elasticity Engel functions

Household Expenditure Survey (HES) data are widely reported in grouped form for a number of reasons. Only within-group arithmetic means (AMs) of the household expenditures on various consumption items, total expenditure, income . and other variables are reported in the tabular form. However, the use of such within-group AMs introduces biases when the parameters of various commonly used non-linear Engel functions are estimated by the Aitken's generalized least squares (GLS) method. This is because the within-group geometric means (GMs)/harmonic means (HMs) are needed in order to estimate unbiased parameters of those non-linear Engel functions. Kakwani (1977) estimated the within-group GMs/HMs from the Kakwani-Podder (1976) Lorenz curve for Indonesian data. We have extended his method to estimate within-group GMs/HMs to a set of variables, based on a general type of concentration curve. It is shown that our estimated within-group GMs/HMs based on concentration curves are not entirely suitable for the Australian HES data. However, these GMs/HMs are then used to estimate Engel parameters for various non-linear Engel functions and it is seen that these elasticities are different for some items of certain non-linear Engel functions than those when the reported within-group AMs are used as proxies for within-group GMs/HMs in order to estimate those non-linear Engel functions. The concept of the average elasticity of a variable elasticity Engel function is discussed and computed for various Australian household consumption items. It is empirically demonstrated that the average elasticities are more meaningful than the traditional elasticity estimates computed at some representative values for certain functions.     

Energy Use in Institutional Buildings: Estimates From State Energy-Audit Surveys

This article examines the determinants of energy demand for nearly 9,000 institutional buildings in the United States. The data were collected, as part of the federal Institutional Conservation Program, by state energy offices using mail surveys. The article presents energy demand estimates adjusted for differences in state surveys as well as for nonresponse bias, as functions of energy prices, building characteristics, and fuel-type variables for approximations of the installed heating ventilation and air-conditioning equipment. Energy price elasticities are found to vary from ?.28 for schools to ?1.05 for hospitals.     

非线性定价有效吗

非线性定价存在于日常生活的方方面面,如阶梯电、水、气价格以及累进税率、通话套餐等。然而,价格信号的复杂性,使得消费者常常并未基于边际价格做出经济决策,关于非线性定价对于需求是否存在抑制的争论亦是此起彼伏。有鉴于此,本文基于Ito（2014）所提模型,利用广东省2010-2013年间各城市阶梯水价在时间维度和横截面维度的变异性以及微观住户月度用水消费数据,对消费者认知价格进行了甄别,并指出既往研究存在的识别问题。实证结果显示,住户当月消费基本是对上月平均价格而非边际价格或者期望边际价格做出反应,弹性约为-0.24。这说明,阶梯水价并未如设计初衷那样,通过跳跃性的价格激励机制降低住户用水需求,而是通过提高平均价格实现了对于住户用水的抑制。本文对于税率设计以及其他能源价格、通信套餐定价也有一定启发意义。     

Nonresponse Assessment of a Consumer Price Index

A household budget survey often suffers from a high nonresponse rate and a selective response. The bias that may be introduced in the estimation of budget shares because of this nonresponse can affect the estimate of a consumer price index, which is a weighted sum of partial price index numbers (weighted with the estimated budget shares). The bias is especially important when related to the standard error of the estimate. Because of the impossibility of subsampling nonrespondents to the budget survey, no exact information on the bias can be obtained. To evaluate the nonresponse bias, bounds for this bias are calculated using linear programming methods for several assumptions. The impact on a price index of a high nonresponse rate among people with a high income can also be assessed by using the elasticity with respect to total expenditure. Attention is also given to the possible nonresponse bias in a time series of price index numbers. The possible nonresponse bias is much larger than the standard error of the estimate.     

Age,Trend, and Cohort Effects in a Macro Model of Canadian Expenditure Patterns

A quadratic almost ideal demand system allowing for age, cohort, and trend effects is developed at the macro level. The model is estimated by maximum likelihood, using a three-tier iterative/search method applied to pooled 1961–1992 time series for five regions of Canada and six categories of expenditure. Hypothesis tests indicate support for the model specification. Elasticities are compared with those reported in other studies, with special attention to food. Effects of demographic and trend variables on elasticities and expenditure shares are investigated. An overall conclusion is that such effects can be very important in a macro demand system.     

Measuring Substitution in Monetary-Asset Demand Systems

The Allen elasticity of substitution (AES) is widely used to study monetary-asset substitution and structural demand stability. Blackorby and Russell showed that the AES is uninformative and that the Morishima elasticity of substitution (MES) is the appropriate measure, a point overlooked in the monetary literature. Use of improper measures can lead to incorrect inferences. This article considers five alternative measures of substitution—the AES, the MES, the Hicksian and Marshallian elasticities of demand, and Mundlak's unencountered, but appealing, constant-cost elasticity of substitution. Selection of the substitution measure appropriate to respective research questions is addressed.