Nonparametric Engel Curves and Revealed Preference

This paper applies revealed preference theory to the nonparametric statistical analysis of consumer demand. Knowledge of expansion paths is shown to improve the power of nonparametric tests of revealed preference. The tightest bounds on indifference surfaces and welfare measures are derived using an algorithm for which revealed preference conditions are shown to guarantee convergence. Nonparametric Engel curves are used to estimate expansion paths and provide a stochastic structure within which to examine the consistency of household level data and revealed preference theory. An application is made to a long time series of repeated cross–sections from the Family Expenditure Survey for Britain. The consistency of these data with revealed preference theory is examined. For periods of consistency with revealed preference, tight bounds are placed on true cost of living indices.     

Up Then Down: Bid‐Price Trends in Revenue Management

In the classic revenue management (RM) problem of selling a fixed quantity of perishable inventories to price‐sensitive non‐strategic consumers over a finite horizon, the optimal pricing decision at any time depends on two important factors: consumer valuation and bid price. The former is determined exogenously by the demand side, while the latter is determined jointly by the inventory level on the supply side and the consumer valuations in the time remaining within the selling horizon. Because of the importance of bid prices in theory and practice of RM, this study aims to enhance the understanding of the intertemporal behavior of bid prices in dynamic RM environments. We provide a probabilistic characterization of the optimal policies from the perspective of bid‐price processes. We show that an optimal bid‐price process has an upward trend over time before the inventory level falls to one and then has a downward trend. This intertemporal up‐then‐down pattern of bid‐price processes is related to two fundamental static properties of the optimal bid prices: (i) At any given time, a lower inventory level yields a higher optimal bid price, which is referred to as the resource scarcity effect; (ii) Given any inventory level, the optimal bid price decreases with time; that is referred to as the resource perishability effect. The demonstrated upward trend implies that the optimal bid‐price process is mainly driven by the resource scarcity effect, while the downward trend implies that the bid‐price process is mainly driven by the resource perishability effect. We also demonstrate how optimal bid price and consumer valuation, as two competing forces, interact over time to drive the optimal‐price process. The results are also extended to the network RM problems.     

Intersection Bounds: Estimation and Inference

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or, equivalently, the value of a linear programming problem with a potentially infinite constraint set. We show that many bounds characterizations in econometrics, for instance bounds on parameters under conditional moment inequalities, can be formulated as intersection bounds. Our approach is especially convenient for models comprised of a continuum of inequalities that are separable in parameters, and also applies to models with inequalities that are nonseparable in parameters. Since analog estimators for intersection bounds can be severely biased in finite samples, routinely underestimating the size of the identified set, we also offer a median‐bias‐corrected estimator of such bounds as a by‐product of our inferential procedures. We develop theory for large sample inference based on the strong approximation of a sequence of series or kernel‐based empirical processes by a sequence of “penultimate” Gaussian processes. These penultimate processes are generally not weakly convergent, and thus are non‐Donsker. Our theoretical results establish that we can nonetheless perform asymptotically valid inference based on these processes. Our construction also provides new adaptive inequality/moment selection methods. We provide conditions for the use of nonparametric kernel and series estimators, including a novel result that establishes strong approximation for any general series estimator admitting linearization, which may be of independent interest.     

Individual Heterogeneity and Average Welfare

Individual heterogeneity is an important source of variation in demand. Allowing for general heterogeneity is needed for correct welfare comparisons. We consider general heterogeneous demand where preferences and linear budget sets are statistically independent. Only the marginal distribution of demand for each price and income is identified from cross‐section data where only one price and income is observed for each individual. Thus, objects that depend on varying price and/or income for an individual are not generally identified, including average exact consumer surplus. We use bounds on income effects to derive relatively simple bounds on the average surplus, including for discrete/continuous choice. We also sketch an approach to bounding surplus that does not use income effect bounds. We apply the results to gasoline demand. We find tight bounds for average surplus in this application, but wider bounds for average deadweight loss.     

考虑跨渠道退货的双渠道闭环供应链决策研究

双渠道闭环供应链存在制造商网络直销渠道和零售商实体店零售渠道。消费者会对购买不满意的产品进行退货，由于网上商店购买的产品缺乏现场体验故退货率较高。相比线下实体商店，线上退货流程更为复杂，这往往容易影响消费者购物体验。因此本文设计考虑跨渠道退货的双渠道闭环供应链结构，并分析跨渠道退货率以及渠道消费偏好对供应链的决策影响，基于Stackelberg博弈和Nash均衡博弈理论，从集中式决策与分散式决策两方面研究不同闭环供应链结构下的定价决策与利润分配，并结合数值算例进行分析。研究结果表明，跨渠道退货率以及消费者渠道偏好对闭环供应链的定价策略以及利润分配等决策具有显著影响。     

Asymptotically Efficient Estimation of Models Defined by Convex Moment Inequalities

This paper examines the efficient estimation of partially identified models defined by moment inequalities that are convex in the parameter of interest. In such a setting, the identified set is itself convex and hence fully characterized by its support function. We provide conditions under which, despite being an infinite dimensional parameter, the support function admits √n‐consistent regular estimators. A semiparametric efficiency bound is then derived for its estimation, and it is shown that any regular estimator attaining it must also minimize a wide class of asymptotic loss functions. In addition, we show that the “plug‐in” estimator is efficient, and devise a consistent bootstrap procedure for estimating its limiting distribution. The setting we examine is related to an incomplete linear model studied in Beresteanu and Molinari (2008) and Bontemps, Magnac, and Maurin (2012), which further enables us to establish the semiparametric efficiency of their proposed estimators for that problem.     

Bounds on Elasticities With Optimization Frictions: A Synthesis of Micro and Macro Evidence on Labor Supply

How can price elasticities be identified when agents face optimization frictions such as adjustment costs or inattention? I derive bounds on structural price elasticities that are a function of the observed effect of a price change on demand, the size of the price change, and the degree of frictions. The degree of frictions is measured by the utility losses agents tolerate to deviate from the frictionless optimum. The bounds imply that frictions affect intensive margin elasticities much more than extensive margin elasticities. I apply these bounds to the literature on labor supply. The utility costs of ignoring the tax changes used to identify intensive margin labor supply elasticities are typically less than 1% of earnings. As a result, small frictions can explain the differences between micro and macro elasticities, extensive and intensive margin elasticities, and other disparate findings. Pooling estimates from existing studies, I estimate a Hicksian labor supply elasticity of 0.33 on the intensive margin and 0.25 on the extensive margin after accounting for frictions.     

Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure

This paper is concerned with tests and confidence intervals for parameters that are not necessarily point identified and are defined by moment inequalities. In the literature, different test statistics, critical‐value methods, and implementation methods (i.e., the asymptotic distribution versus the bootstrap) have been proposed. In this paper, we compare these methods. We provide a recommended test statistic, moment selection critical value, and implementation method. We provide data‐dependent procedures for choosing the key moment selection tuning parameter κ and a size‐correction factor η.     

基于因素嵌入的非理性资产价格泡沫生成及膨胀演化研究

近几年,随着资产价格泡沫现象的频繁发生,实业家和学者开始重点关注泡沫生成、膨胀的演化过程。本文通过引入导致预期发生变化的三个影响因素(过度自信、资产缺乏弹性、流动性过剩),扩展了现有的噪声交易者(DSSW)模型,揭示由噪声交易者对资产价格预期发生变化而造成的非理性资产价格泡沫的生成及膨胀机理,分析得出:三个影响因素促使资产价格预期发生变化,进而导致非理性资产价格泡沫生成及膨胀;并利用MATLAB软件对非理性资产价格泡沫膨胀过程进行模拟,分析得出:噪声交易者占比、非知情噪声交易者占比、过度自信影响因子、资产缺乏弹性影响因子、流动性过剩影响因子越大,非理性资产价格泡沫的膨胀速度越快、波动幅度越大,这对防止泡沫膨胀速度过快、过大有一定的参考价值。     

产能约束下考虑消费者偏好的双渠道供应链决策与协调

制造商产能和消费者偏好均会对双渠道供应链成员决策产生影响。考虑消费者渠道和低碳双重偏好，研究产能约束下双渠道供应链成员决策与协调问题。构建集中决策和分散决策两种情形下的双渠道供应链成员决策模型，比较分析两种情形下产能约束、消费者渠道偏好和低碳偏好对供应链决策影响；设计改进的收益共享契约协调机制，证明了其有效性。研究结果表明：在集中决策和分散决策两种情形下消费者渠道偏好对供应链收益都起到促进作用，其中在集中决策下不考虑消费者渠道偏好时供应链收益最少；消费者低碳偏好程度的提高促使两渠道产品销售价格的提高，进而增加供应链收益；在分散决策下随着供应链产能的增大，网络直销渠道具有比传统零售渠道更大的销量增长幅度；设计的协调机制消除了供应链的"双重边际效应"，实现帕累托改进。最后通过算例验证以上研究结论。     

Measuring the Implications of Sales and Consumer Inventory Behavior

Temporary price reductions (sales) are common for many goods and naturally result in large increases in the quantity sold. Demand estimation based on temporary price reductions may mismeasure the long‐run responsiveness to prices. In this paper we quantify the extent of the problem and assess its economic implications. We structurally estimate a dynamic model of consumer choice using two years of scanner data on the purchasing behavior of a panel of households. The results suggest that static demand estimates, which neglect dynamics, (i) overestimate own‐price elasticities by 30 percent, (ii) underestimate cross‐price elasticities by up to a factor of 5, and (iii) overestimate the substitution to the no‐purchase or outside option by over 200 percent. This suggests that policy analysis based on static elasticity estimates will underestimate price–cost margins and underpredict the effects of mergers.     

具有网络外部性的双寡头市场的动态定价策略

本文通过将消费者对网络大小的预期引入消费者的效用函数,刻画了消费者预期如何影响市场潜量。然后,通过微分对策,分析了在垄断竞争的市场结构中的厂商如何在考虑到消费者对今后的预期时,如何动态的决定自己的价格和相应的策略。结果表明,随着消费者对网络增长预期的增大,将导致更大的网络规模和更低的初始价格。寡头的利润受消费者对其产量的预期的影响。     

FAIR PRICING

This paper explores the consequences of supposing that consumers see a firm as fair if they cannot reject the hypothesis that the firm is somewhat benevolent towards them. When consumers can reject this hypothesis, some become angry, which is costly to the firm. The desire to appear benevolent can lead firms to adopt third‐degree price discrimination based on the income of different consumer classes while foreswearing third‐degree price discrimination based on differences in the elasticity of demand. It can also explain why prices seem to be more responsive to changes in factor costs than to changes in demand that have the same effect on marginal cost. Lastly, if consumers experience regret or disappointment when faced by increased prices, the model can explain why prices can be more rigid in response to disasters that increase demand dramatically than they are when there is a less substantial increase in demand.     

A Competitive Model of Customization with Lead‐Time Effects

In this article, we study the competitive interactions between a firm producing standard products and a firm producing custom products. Consumers with heterogeneous preferences choose between n standard products, which may not meet their preferences exactly but are available immediately, and a custom product, available only after a certain lead time l. Standard products incur a variety cost that increases with n and custom products incur a lead time cost that is decreasing in the lead time l. We consider a two‐stage game wherein at stage 1, the standard product firm chooses the variety and the custom firm chooses the lead time and then both firms set prices simultaneously. We characterize the subgame‐perfect Nash equilibrium of the game. We find that both firms can coexist in equilibrium, either sharing the market as local monopolists or in a price‐competitive mode. The standard product firm may offer significant or minimal variety depending on the equilibrium outcome. We provide several interesting insights on the variety, lead time, and prices of the products offered and on the impact of problem parameters on the equilibrium outcomes. For instance, we show that the profit margin and price of the custom product are likely to be higher than that of standard products in equilibrium under certain conditions. Also, custom firms are more likely to survive and succeed in product markets with larger potential market sizes. Another interesting insight is that increased consumer sensitivity to product fit may result in lower lead time for the custom product.     

Nonparametric Welfare Analysis for Discrete Choice

We consider empirical measurement of equivalent variation (EV) and compensating variation (CV) resulting from price change of a discrete good using individual‐level data when there is unobserved heterogeneity in preferences. We show that for binary and unordered multinomial choice, the marginal distributions of EV and CV can be expressed as simple closed‐form functionals of conditional choice probabilities under essentially unrestricted preference distributions. These results hold even when the distribution and dimension of unobserved heterogeneity are neither known nor identified, and utilities are neither quasilinear nor parametrically specified. The welfare distributions take simple forms that are easy to compute in applications. In particular, average EV for a price rise equals the change in average Marshallian consumer surplus and is smaller than average CV for a normal good. These nonparametric point‐identification results fail for ordered choice if the unit price is identical for all alternatives, thereby providing a connection to Hausman–Newey's (2014) partial identification results for the limiting case of continuous choice.     

Push or Pull? Design of Content Delivery Systems

Advances in information technology, especially the expansion of cellular and WiFi networks, are dramatically changing how people consume digital content. These changes in user access behavior present a challenge of delivering content to a diversified consumer base. This article addresses this challenge by identifying the key factors for the design of content delivery systems (gross value of content, delivery delay, sensitivity to delivery delay, accessing cost, and processing cost) and explicitly modeling their interactions. We investigate two content delivery systems—push and pull systems, and solve for the content provider's optimal push frequency decision and consumers’ push versus pull decisions. We show that the content provider's selection of push frequency plays a critical role determining the segmentation of the consumer market into the push group and the pull group. Our findings suggest that firms should set a relatively high push frequency to cater to high‐type consumers, which leads to two consumer groups with low‐type consumers belonging to the pull group and high‐type consumers belonging to the push group.     

Estimation and Confidence Regions for Parameter Sets in Econometric Models1

This paper develops a framework for performing estimation and inference in econometric models with partial identification, focusing particularly on models characterized by moment inequalities and equalities. Applications of this framework include the analysis of game‐theoretic models, revealed preference restrictions, regressions with missing and corrupted data, auction models, structural quantile regressions, and asset pricing models. Specifically, we provide estimators and confidence regions for the set of minimizers Θ_I of an econometric criterion function Q(θ). In applications, the criterion function embodies testable restrictions on economic models. A parameter value θthat describes an economic model satisfies these restrictions if Q(θ) attains its minimum at this value. Interest therefore focuses on the set of minimizers, called the identified set. We use the inversion of the sample analog, Q_n(θ), of the population criterion, Q(θ), to construct estimators and confidence regions for the identified set, and develop consistency, rates of convergence, and inference results for these estimators and regions. To derive these results, we develop methods for analyzing the asymptotic properties of sample criterion functions under set identification.     

Identification and Inference in Ascending Auctions With Correlated Private Values

We introduce and apply a new nonparametric approach to identification and inference on data from ascending auctions. We exploit variation in the number of bidders across auctions to nonparametrically identify useful bounds on seller profit and bidder surplus using a general model of correlated private values that nests the standard independent private values (IPV) model. We also translate our identified bounds into closed form and asymptotically valid confidence intervals for several economic measures of interest. Applying our methods to much studied U.S. Forest Service timber auctions, we find evidence of correlation among values after controlling for a rich vector of relevant auction covariates; this correlation causes expected profit, the profit‐maximizing reserve price, and bidder surplus to be substantially lower than conventional (IPV) analysis of the data would suggest.     

Predicting the Incremental Benefits of Online Information Search for Heterogeneous Consumers

Consumer information search (CIS), the process by which a consumer browses and inspects a shopping environment for appropriate information to select a product or service from available options, has been a research focus in the context of online business. One of the key questions related to CIS is how to determine how much information to search (i.e., when to stop searching). Extensive literature on behavioral science has revealed that consumers often search either “too little” or “too much,” even with the help of existing consumer decision support systems (CDSSs). To address this issue, this article introduces a new method of CDSSs that provides effective estimation of incremental search benefits. The method, called the personalized distribution‐based prediction method (PDM), is developed from the perspective of machine learning and utilizes consumer preference information generated by collaborative filtering (CF) algorithms. In contrast to related methods that assume that all consumers follow the same distribution function in terms of product preference, the PDM method is designed to consider the diversified search behaviors of consumers through the incorporation of heterogeneous preference distribution functions. Experiments based on data provided by Netflix illustrate that the proposed method is effective and advantageous over existing applicable techniques. Theoretical analyses are also provided to explain the advantageous performance of PDM.     

产品责任、企业社会责任偏好与供应链中的质量-数量协调

在产品质量和产品数量（订货量）内生化的情形下，同时实现其质量和数量的协调将成为供应链管理的一个重要问题。进一步，在产品低质量对消费者造成伤害的情形下，制造商将面临着产品责任（表征制造商对消费者产品伤害的补偿），从而导致"产品责任如何影响供应链中的质量-数量协调"这一问题。最后，如果核心企业具有对消费者的企业社会责任（CSR）偏好，则这种CSR偏好又如何影响供应链中的质量-数量协调？针对这三个问题，首先，利用批发价合同构建了一个由上游制造商和下游零售商组成的两级供应链运作博弈模型；其次考察了制造商产品责任、CSR偏好程度和质量改进效率对其产品质量决策、批发价合同和相应的供应链节点企业利润的影响；最后，研究了供应链质量-数量协调问题。结果表明：（1）产品责任不影响产品质量、订货量、供应链节点企业经济利润和消费者剩余，但制造商批发价随产品责任的增加而增加；（2）随着CSR偏好程度的增加，产品质量、订货量、零售商经济利润、供应链系统经济利润和消费者剩余随之增加，而制造商经济利润随之减小；（3）质量改进效率的提高，有利于产品质量、订货量、零售商经济利润、供应链系统经济利润和消费者剩余的增加；（4）一个由数量折扣契约和质量改进成本分担契约共同构成的协调机制，可以有效的实现供应链系统的协调，其中，产品责任将促使数量折扣契约中产品批发价的增加和质量改进成本分担比例的减小，而CSR偏好程度的增加将促使数量折扣契约中产品批发价的减小，但不影响质量改进成本分担比例。