The micro-foundations of intertemporal price discrimination

Summary. This paper investigates the optimality of intertemporal price discrimination for a durable-good monopoly in a model where infinitely-lived households face an intertemporal budget constraint, and consume both durable goods and non-durable goods. We prove that the optimal price of the durable good is not constant, and may decrease or increase over time. Some households may choose to purchase the durable good at a later date, and pay lower or higher prices, since the gain in discounted utility of consuming more of the non-durable good more than compensates for the loss in utility from delaying the consumption of the durable good.Received: 12 March 2004, Revised: 7 January 2005, JEL Classification Numbers: D40, D42, D91.I would like to thank C.D. Aliprantis, the Editor, and an anonymous referee for their generous advice, and constructive comments and suggestions. I have also enjoyed discussions with John Quah on the subject. Research support from the Wharton-SMU Research Centre, Singapore Management University, is gratefully acknowledged.     

Intertemporal price discrimination and consumer demand

Under a particular class of utility functions, intertemporal price discrimination (IPD) is not feasible. That is, customers cannot be made to pay different prices for a durable good at different points in time. Other factors such as falling costs, and differing discount rates between buyers and sellers have been found to make intertemporal pricing schemes feasible, or even profitable. None of these factors, however, were fundamental demand differences which give rise to static price discriminations. In this paper we argue that IPD is indeed feasible and sometimes profitable, if only we allow for a nondurable good in the utility function. A simple additively separable utility is examined first, which is then extended to a nonseparable utility function which allows richer substitution/complementary relations between the durable and the nondurable goods. This may help us to better understand the similarities between static and intertemporal price discriminations.     

Intertemporal elasticity of substitution and risk aversion: are they related empirically?

This article examines the relationship between two types of preference: preference of intertemporal choices and preference towards risk. In the simplest form of the constant relative risk aversion utility function, the intertemporal elasticity of substitution (IES) and risk aversion have an inverse relationship. However, there is no empirical evidence that suggests this inverse relationship holds. We examine the relationship between risk aversion and IES using household consumption data from the Consumer Expenditure Survey during 1996–2010. Multiple risk domains are selected to represent risk preference, and for each domain, we consider some households to be more risk averse than others. We separately estimate IES for the more risk-averse and less risk-averse households. We find that the IES estimates are generally smaller for the more risk-averse households than for the less risk-averse households and that the difference is statistically significant in the majority of the financial domains. This finding supports the inverse relationship between the two parameters, although considerable heterogeneity is found across domains.     

The welfare costs of unreliable water service

Throughout the developing world, many water distribution systems are unreliable. As a result, it becomes necessary for each household to store its own water as a hedge against this uncertainty. Since arrivals of water are not synchronized across households, serious distributional inefficiencies arise. We develop a model describing the optimal intertemporal depletion of each household's private water storage if it is uncertain when water will next arrive to replenish supplies. The model is calibrated using survey data from Mexico City, a city where many households store water in sealed rooftop tanks known as tinacos. The calibrated model is used to evaluate the potential welfare gains that would occur if alternative modes of water provision were implemented. We estimate that most of the potential distributional inefficiencies can be eliminated simply by making the frequency of deliveries the same across households which now face haphazard deliveries. This would require neither costly investments in infrastructure nor price increases.     

Durability in a Monopoly With a Small Number of Buyers

This paper shows that the number of buyers is a crucial demand characteristic for a monopolist's choice of durability. When he sells to a few large buyers, he offers a more durable good than when selling to many small buyers. By increasing durability of the good sold to large buyers, the monopolist encourages current purchasing and can thus engage in greater intertemporal price discrimination and make more profit. Therefore Bulow's proposition of minimal durability does not survive in the case of few buyers. This has not been pointed out thus far.     

Regulated price reforms and unregulated substitutes: the case of residential piped gas in Argentina

This paper examines the impact of regulated piped gas price changes on connection decisions and households’ welfare. The analysis explicitly considers bottled gas as a substitute for piped gas and therefore uses a simple utility maximization model that yields both a gas-type choice model and a demand specification whose parameterization allows examining households’ responses to regulated price changes. The results show that relative gas prices and household features explain households’ piped gas usage. They also provide insights on the distribution of welfare changes. The findings illustrate the impact of tariff rebalancing and unregulated substitutes on further access to regulated network services.     

What explains consumption in the very short-run? Evidence from checking account data

This paper investigates consumption behavior within an intertemporal optimization model of the representative household. Our dataset consists of deposits and withdrawals from individual household checking accounts that received paychecks by direct deposit. We construct samples of panel data for households with weekly, biweekly, and semi-monthly pay-periods and form two different measures of consumption for each sample. GMM estimates of structural parameters provide mixed evidence for habit formation or durability and limited support for the permanent income hypothesis. The results instead point to “rule of thumb” consumption under liquidity constraints, where the household consumes its current disposable income each pay-period with possible debt servicing. These findings are uniform with regard to estimation of sub-samples split according to age or household income.     

A SIMPLIFIED MODEL FOR SOCIAL WELFARE ANALYSIS: AN APPLICATION TO SPAIN, 1973–74 TO 1980–81

Most of the literature on income distribution has concentrated on inequality. In this paper we introduce a concern for efficiency in a social welfare model. We propose a simple but useful specification which combines three features: (i) the selection of measurement instruments in the relative and the absolute case on the grounds of their properties for applied work; (ii) a procedure to make welfare comparisons across households with different needs, in a model in which equivalence scales depend only on house-hold size; and (iii) the use of household specific statistical price indices to make intertemporal comparisons in real terms. The methodology is applied to the study of the role of prices and demographic effects in the evolution of the standard of living in Spain from 1973–74 to 1980–81.     

INCOME UNCERTAINTY,CONSUMER DURABLES INVESTMENTS,AND HOME PRODUCTION: EVIDENCE FROM CHINA

We investigate the effect of uncertainty on home durable purchase decisions, and empirically evaluate the efficacy of consumer durable policies under uncertainty. A model of lumpy home capital adjustment shows that elevated uncertainty leads households to adopt a cautionary perspective and postpone their capital adjustment. We test this prediction using microevidence from China where both uncertainty and home production are substantial. We exploit a wide‐scale rebate program funded by the Chinese government as a natural experiment, and examine the impact on household investment. We find strong, significant, and robust evidence that greater income uncertainty inhibits durable adjustment. Our findings highlight the impediment that income uncertainty poses to investment in home durables, which are often considered as “engines of liberation” in emerging economies. (JEL E21, E64, J22, O16, O23, D91)     

A micro-analytic threshold model for the timing of first purchases of durable goods

A micro-analytic threshold model to describe the timing of household purchases of consumer durable goods is developed and tested. The model incorporates unobserved heterogeneity via a generalized gamma distribution and accounts for time varying covariates. Further, we employ estimation methods applicable or purchase data observed at periodic intervals of time. The model outperforms other competing models for predicting the timing of purchase of durable goods in terms of fit and predictive ability. In particular, this model outperforms the logit model and the diffusion model. The generalized gamma timing model predicts well the time to purchase the durable good; we show how it can be employed for micro-segmentation of households. Several research directions and applications are described.     

Organic labelling,private label,and U.S. household demand for fluid milk

The U.S. fluid milk market has been experiencing two trends in the recent decade: the fast growth of private label milk and organic milk. Using the data from Nielsen Homescan Panel, we estimate a censored demand system to study the demand relations among types of milk differentiated by brand types and organic status. We find that sociodemographic factors still play important roles in household choice of milk types, and fluid milk, as a whole, is an inferior good. Moreover, as income increases, households are more likely to shift from buying conventional milk to organic milk and from private label conventional milk to branded conventional milk, as indicated by the asymmetric cross price elasticities. Corresponding implications for milk producers and marketers are discussed.     

Equivalence Scales in an Intertemporal Setting with an Application to the Former West Germany

Equivalence scales provide answers to questions like how much a household with two children needs to spend compared to a couple to attain the same welfare level. These are important questions for child allowances, social benefits and to assess the cost of children over the life-cycle for example. We discuss equivalence scales in an intertemporal setting with uncertainty. To estimate equivalence scales we use a panel from German households (GSOEP) containing subjective data on satisfaction with life and satisfaction with income to represent the welfare level. Because satisfaction is measured on a discrete scale we use limited dependent variable models for panel data in estimation. Using satisfaction with life data we find that larger households do not need any additional income to be as satisfied as a couple. Using satisfaction with income, however, yields equivalence scales that increase with household size.     

经济转轨与城镇化进程中的居民消费行为特征——对1396户城镇家庭的实证分析

基于中国9个省1396户城镇家庭的面板数据,运用系统广义矩估计法对一个包括习惯形成和不确定性的欧拉方程进行估计以考察家庭消费是否跨时演进,研究结果表明,偏好的设定偏误是传统的生命周期——持久收入模型不能很好地诠释中国城镇家庭消费决策的一个原因,在解释消费决策的影响因素时假定偏好的跨时可分性会得出错误的结论,城镇居民消费偏好的跨时不可分性以及由收入和支出不确定性引发的预防性储蓄动机是导致居民消费倾向持续偏低的重要原因。     

Liquidity constraints and housing prices: Theory and evidence from the VA Mortgage Program

This paper employs a simple intertemporal model to show that presence of liquidity constraints can depress the price of a durable good below its net present rental value, regardless of the overall supply elasticity. The existence of price effects implies that the relaxation of liquidity constraints is not Pareto improving, and may in fact be regressive. Historical evidence, which exploits the fact that a clearly identifiable group, war veterans, enjoyed the most favored access to mortgage credit after World War II, supports the model. The results suggest that more recent mortgage market innovations have served primarily to increase prices rather than home ownership rates, and that such innovations have the potential to exacerbate socioeconomic disparities in ownership rates.     

中国住房改革对家庭耐用品消费的影响

中国的住房改革对许多城市家庭形成正的财富冲击。利用CHNS数据,我们发现:同理论预期一致,受益于住房改革的家庭消费了更多的耐用品。特别是,在住房改革的随后几年,其影响更为显著。我们还发现,住房改革对耐用品消费的次序具有影响,经历住房改革的家庭倾向于首先消费生活最必需的耐用品,然后再消费其他耐用品。通过增加家庭的耐用品消费,住房改革对扩大内需和走出当时的通货紧缩产生了积极影响。     

Household Intertemporal Behaviour: A Collective Characterization and a Test of Commitment

In this paper, a formal test of intra-household commitment is derived and performed. To that end, two models of household intertemporal behaviour are developed. In both models, household members are characterized by individual preferences. In the first formulation, household decisions are always on the ex ante Pareto frontier. In the second model, the assumption of intra-household commitment required by ex ante efficiency is relaxed. It is shown that the full-efficiency household Euler equations are nested in the no-commitment Euler equations. Using this result, the hypothesis that household members can commit to future allocations of resources is tested using the Consumer Expenditure Survey. I strongly reject this hypothesis. It is also shown that the standard unitary framework is a special case of the full-efficiency model. However, if household members are not able to commit, household intertemporal behaviour cannot be characterized using the standard life-cycle model. These findings have two main implications. First, policy makers can change household behaviour by modifying the decision power of individual household members. Second, to evaluate programmes designed to improve the welfare of household members, it would be beneficial to replace the standard unitary model with a characterization of household behaviour that allows for lack of commitment.     

Household Finances and Social Interaction: Bayesian Analysis of Household Panel Data

We investigate the relationship between social interaction and household finances using the British Household Panel Survey. We explore the relationship between a wide range of aspects of household finances and social interaction, rather than focusing on one particular facet of household finances, such as the holding of stocks and shares. We develop a Bayesian statistical framework to simultaneously explore both sides of the household balance sheet—liabilities and assets. Additionally, we allow the influence of social interaction on household finances to be time dependent, enabling us to model the effects of social interaction from a dynamic perspective. We also develop a two‐part model to jointly investigate the influence of social interaction on the amount of different types of debt and financial assets held conditional on holding the different types of debt and assets. Our analysis suggests that social interaction is associated with households holding larger amounts of debt and assets.     

Entry deterrence and innovation in durable-goods monopoly

This paper investigates the efficiency of innovation investments in a durable-goods monopoly when a potential entrant threatens to innovate as well. We show that the durability of the good endows the monopolist with the power to discourage rival innovation since current sales alter the demand for a new generation of the good. The equilibrium is therefore determined not only by the incentive for intertemporal price discrimination in durable-goods monopoly, but also by the incumbent's concern for maintaining the technological leadership. We demonstrate that entry deterrence followed by no innovation always implies underinvestment in innovation.     

Price Stability in Open Economies

This paper studies the theoretical conditions under which price stability is the optimal policy in a two-country open-economy model with imperfect competition and price stickiness. Special conditions on the levels of country-specific distortionary taxation and the intratemporal and intertemporal elasticities of substitution need to be satisfied. These restrictions apply to both cooperative and non-cooperative settings. Importantly, we show that cooperative and non-cooperative solutions do not coincide despite market completeness and producer currency pricing. We study the conditions under which quadratic approximations of single countries' welfare can be correctly evaluated by relying only on log-linear approximations of the equilibrium conditions.     

Reproductive behaviour in peasant societies: a theoretical and empirical analysis

In spite of the concern and repeated attempts to promote population control programs, a coherent and unified theory of peasant reproductive behavior has not emerged. The author attempts to extend the microeconomic foundations of reproductive behavior by considering a dynamic intertemporal model of household production emphasizing survival uncertainty and age specific differences in productive ability. An optimal policy is derived in a single sex model in which decisions are made sequentially based on new information. It is shown that households will follow a stopping rule; the household will continue to reproduce until an optimal number of living children is reached. As a consequence of the stopping rule households will appear to be replacing infant and child deaths if these occurred early in the program. After presenting the model, empirical applications of the theory are explored and the model is estimated using sample survey data collected in Bangladesh in 1977. Issues raised in the analysis are discussed.