Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects

In this paper, we study the least squares (LS) estimator in a linear panel regression model with unknown number of factors appearing as interactive fixed effects. Assuming that the number of factors used in estimation is larger than the true number of factors in the data, we establish the limiting distribution of the LS estimator for the regression coefficients as the number of time periods and the number of cross‐sectional units jointly go to infinity. The main result of the paper is that under certain assumptions, the limiting distribution of the LS estimator is independent of the number of factors used in the estimation as long as this number is not underestimated. The important practical implication of this result is that for inference on the regression coefficients, one does not necessarily need to estimate the number of interactive fixed effects consistently.     

Retailer's Response to Alternate Manufacturer's Incentives Under a Single‐Period,Price‐Dependent,Stochastic‐Demand Framework*

This article considers the joint development of the optimal pricing and ordering policies of a profit‐maximizing retailer, faced with (i) a manufacturer trade incentive in the form of a price discount for itself or a rebate directly to the end customer; (ii) a stochastic consumer demand dependent upon the magnitude of the selling price and of the trade incentive, that is contrasted with a riskless demand, which is the expected value of the stochastic demand; and (iii) a single‐period newsvendor‐type framework. Additional analysis includes the development of equal profit policies in either form of trade incentive, an assessment of the conditions under which a one‐dollar discount is more profitable than a one‐dollar rebate, and an evaluation of the impact upon the retailer‐expected profits of changes in either incentive or in the degree of demand uncertainty. A numerical example highlights the main features of the model. The analytical and numerical results clearly show that, as compared to the results for the riskless demand, dealing with uncertainty through a stochastic demand leads to (i) (lower) higher retail prices if additive (multiplicative) error, (ii) lower (higher) pass throughs if additive (multiplicative) error, (iii) higher claw backs in both error structures wherever applicable, and (iv) higher rebates to achieve equivalent profits in both error structures.     

Early Sales of Seasonal Products with Weather‐Conditional Rebates

Some retailers of seasonal products adopt weather‐conditional rebate programs to induce early sales and increase profits. In such promotions, customers who buy the product in an advance preselling period are offered rebates if a pre‐specified weather condition is realized during the later normal selling season. We investigate the potential benefits of these programs for retailers. We show that the weather‐conditional rebate program can increase sales by price discriminating among a customer's post‐purchase states. Taking advantage of the early sales, it can also reduce the inventory holding cost and ordering cost, and hence can increase the retailer's expected profits. In addition, we numerically investigate the sensitivity of the rebate program's effectiveness to the model parameters and illustrate its advantages over an advance‐discount policy.     

基于变参数模型的流动性与上证综指收益率关系研究

研究了流动性与上证综合指数收益率之间的时间序列动态关系,并利用状态空间模型对流动性与上证综指收益率的动态关系进行了变参数分析。结论是:上证综指收益率对宏观流动性变动的时变弹性系数在近几年流动性过剩的背景下,呈现上升趋势。其中,能源、钢铁和金融行业时变弹性系数波动比较剧烈,而医药行业的时变弹性系数波动较小。证券市场(微观)流动性变动的时变弹性系数随着我国股票市场发展的逐步健全、完善而趋于平稳。     

Traffic‐Based Labor Planning in Retail Stores

Staffing decisions are crucial for retailers since staffing levels affect store performance and labor‐related expenses constitute one of the largest components of retailers’ operating costs. With the goal of improving staffing decisions and store performance, we develop a labor‐planning framework using proprietary data from an apparel retail chain. First, we propose a sales response function based on labor adequacy (the labor to traffic ratio) that exhibits variable elasticity of substitution between traffic and labor. When compared to a frequently used function with constant elasticity of substitution, our proposed function exploits information content from data more effectively and better predicts sales under extreme labor/traffic conditions. We use the validated sales response function to develop a data‐driven staffing heuristic that incorporates the prediction loss function and uses past traffic to predict optimal labor. In counterfactual experimentation, we show that profits achieved by our heuristic are within 0.5% of the optimal (attainable if perfect traffic information was available) under stable traffic conditions, and within 2.5% of the optimal under extreme traffic variability. We conclude by discussing implications of our findings for researchers and practitioners.     

公开或隐藏未来市场价格对新品预售的影响研究

预售是新产品上市前，商家允许消费者提前预定产品的一种销售手段。本文以新产品预售为背景，建立了商家同时销售新旧两代产品时的预售模型，先对消费者最优购买策略进行了分析，在此基础上，分两种情况，即商家在预售阶段公开或隐藏新品未来市场价格，研究了商家最优预售价格折扣和最优订购量。最后，通过数值仿真分析了影响新品预售策略和商家收益的一些因素。结果表明，商家在预售阶段公开新品未来市场价格可以获得更高期望收益。     

Estimation When a Parameter is on a Boundary

This paper establishes the asymptotic distribution of an extremum estimator when the true parameter lies on the boundary of the parameter space. The boundary may be linear, curved, and/or kinked. Typically the asymptotic distribution is a function of a multivariate normal distribution in models without stochastic trends and a function of a multivariate Brownian motion in models with stochastic trends. The results apply to a wide variety of estimators and models. Examples treated in the paper are: (i) quasi-ML estimation of a random coefficients regression model with some coefficient variances equal to zero and (ii) LS estimation of an augmented Dickey-Fuller regression with unit root and time trend parameters on the boundary of the parameter space.     

不同货架空间分配顺序下农产品供应链优化问题研究

货架是超市和生鲜便利店的重要资源，不仅具有储存和展示农产品的功能，同时货架空间大小对农产品的销量具有重要影响。针对产品需求受货架空间与零售价格共同影响的两级农产品供应链，在考虑供应商主导和零售商主导的情况下，分别对零售商在销售季节来临前和来临后分配货架空间四种分散式农产品供应链的最优决策与利润进行了分析，并与一体化供应链的最优决策进行了比较。研究发现，不论是在供应商主导还是在零售商主导的农产品供应链中，零售商在销售季节来临前分配货架空间，相比在销售季节来临后分配货架空间，农产品的批发价格与零售价格更高，分配的货架空间更小，供应商和零售商均获得更少的利润，相应的农产品供应链整体利润更少。因此，零售商在销售季节来临后分配货架空间对农产品供应链更有利。相比一体化供应链，分散式供应链的零售价格更高，分配的货架空间更小，供应链整体利润小于一体化供应链的最优利润，本文给出了基于利润共享与成本共担的合同对分散式供应链进行协调。最后，通过数值算例研究了参数变化对最优决策和供应链利润的影响。     

时间偏好不一致委托代理问题的优化与决策

现有讨论委托代理问题涉及将不同时点收益和成本折现时,几乎毫无例外的选择唯一能代表时间偏好一致的折现函数—指数折现.本文放松时间偏好一致这一假设,选择能反映时间偏好不一致的准双曲折现函数一ββδ作为代理人折现函数,分析收益由努力程度和外部因素共同作用,代理人的成本和收益发生在不同时点时,委托人如何制定激励合同使得代理人努力工作且委托人获得最大利润.研究发现,最优合同与代理人的现期偏好参数β和对未来现期偏好参数的认知β有关,委托人从时间偏好一致的代理人获取的利润高于时间偏好不一致的代理人,从悲观部分幼稚型获取利润小于成熟型,但从成熟型和乐观部分幼稚型获取的利润相同.     

员工动机对双元销售行为的影响研究:传统性的调节作用

营销人员经常面临现有产品销售和新产品销售之间的悖论，需要采用不同的方式来应对两种销售行为之间的冲突。本研究根据内外动机理论，探究不同动机影响下的销售行为，同时揭示国人的传统性对动机与产品销售两者关系的调节作用。本研究开发了中国情境下的双元销售行为量表，具有良好的信度（0.896）。实证结果表明：（1）内在动机与现有产品和新产品的双元销售行为之间呈现显著的正相关关系，外在动机与现有产品和新产品的双元销售行为呈不显著的正向关系。（2）中国传统性对营销人员的产品销售行为的直接影响作用非常显著，但传统性与内外动机的调节作用表现出多样性。（3）传统性与内在动机的交乘项对双元销售行为起不显著的负向调节作用。（4）传统性与外在动机的交乘项对现有产品销售起不显著的正向影响，对新产品销售起不显著的负向影响。     

不同双渠道结构下制造商的定价决策与渠道选择

根据网上渠道不同销售模式的特征将其划分为网上直销双渠道、网上分销双渠道和网上代销双渠道。分析在制造商主导的双渠道供应链中，三种不同双渠道结构下价格竞争系数、网上直销成本和佣金比例系数对其他经济变量的影响，以及制造商的最优定价决策与渠道选择问题。研究表明：制造商在保证一定网上直销单位成本和佣金比例系数条件下，网上代销双渠道和网上直销双渠道中获取的利润高于网上分销双渠道；在网络代销双渠道中，制造商利润随着佣金比例系数增加而减少，而传统零售商和网络零售商的利润会随着佣金比例系数增加而增加。     

Identification and Estimation of Average Partial Effects in “Irregular” Correlated Random Coefficient Panel Data Models

In this paper we study identification and estimation of a correlated random coefficients (CRC) panel data model. The outcome of interest varies linearly with a vector of endogenous regressors. The coefficients on these regressors are heterogenous across units and may covary with them. We consider the average partial effect (APE) of a small change in the regressor vector on the outcome (cf. Chamberlain (1984), Wooldridge (2005a)). Chamberlain (1992) calculated the semiparametric efficiency bound for the APE in our model and proposed a √N‐consistent estimator. Nonsingularity of the APE's information bound, and hence the appropriateness of Chamberlain's (1992) estimator, requires (i) the time dimension of the panel (T) to strictly exceed the number of random coefficients (p) and (ii) strong conditions on the time series properties of the regressor vector. We demonstrate irregular identification of the APE when T = p and for more persistent regressor processes. Our approach exploits the different identifying content of the subpopulations of stayers—or units whose regressor values change little across periods—and movers—or units whose regressor values change substantially across periods. We propose a feasible estimator based on our identification result and characterize its large sample properties. While irregularity precludes our estimator from attaining parametric rates of convergence, its limiting distribution is normal and inference is straightforward to conduct. Standard software may be used to compute point estimates and standard errors. We use our methods to estimate the average elasticity of calorie consumption with respect to total outlay for a sample of poor Nicaraguan households.     

Price,Rebate, and Returns Supply Contracts for Coordinating Supply Chains with Price‐Dependent Demands

Channel rebates and returns policies are common mechanisms for manufacturers to entice retailers to increase their order quantities and sales ultimately. However, when the underlying demand depends on the retail price, it has been known that channel coordination cannot be achieved if only one of these mechanisms is deployed. In this article, we show that a policy that combines the use of wholesale price, channel rebate, and returns can coordinate a channel with both additive and multiplicative price‐dependent demands. In addition to determining the sufficient conditions for the contract parameters associated with the equilibrium policy, we show that multiple equilibrium policies for channel coordination exist. We further explore how the equilibrium policy can be adjusted to achieve Pareto improvement. Other issues such as the maximum amount of expected profit that the manufacturer can share under the coordinated channel, the structural properties of the contracts under both the additive and multiplicative price‐dependent demand functions are also discussed.     

基于货架空间成本共担的不同权力供应链均衡分析

针对产品需求受货架空间与零售价格共同影响的两级供应链,通过比较供应商主导、零售商主导和权力均等三种不同权力结构供应链均衡结果,分析了供应商与零售商共同承担货架空间成本对供应链定价、货架空间分配和利润的影响。研究结果表明:供应商与零售商共同承担货架空间成本会减少供应商主导供应链的整体利润,但会使零售商主导和权力均等供应链通过分配更多的货架空间增加产品销量,在一定范围内使得供应链整体利润得到提高。由于三种不同权力结构供应链均未达到整体最优,提出了基于货架成本共担的收入共享合同,并给出了供应商和零售商均能接受的分配方案。     

Coordination in Games with Strategic Complementarities: An Experiment on Fixed vs. Random Matching

In this article, we study behavior in a series of two‐player supply chain game experiments. Each player simultaneously chooses a capacity before demand is realized, and sales are given by the minimum of realized demand and chosen capacities. We focus on the differences in behavior under fixed pairs and random rematching. Intuition suggests that long‐run relations should lead to more profitable outcomes. However, our results go against this intuition. While subjects' capacity choices are better aligned (i.e., closer together) under fixed pairs, average profits are more variable. Moreover, learning is slower under fixed pairs—so much so that over the last five periods, average profits are actually higher under random rematching. The underlying cause for this finding appears to be a “first‐impressions” bias, present only under fixed matching, in which the greater the misalignment in initial choices, the lower are average profits.     

Economic and Environmental Assessment of Remanufacturing Strategies for Product + Service Firms

This article provides a data‐driven assessment of economic and environmental aspects of remanufacturing for product + service firms. A critical component of such an assessment is the issue of demand cannibalization. We therefore present an analytical model and a behavioral study which together incorporate demand cannibalization from multiple customer segments across the firm's product line. We then perform a series of numerical simulations with realistic problem parameters obtained from both the literature and discussions with industry executives. Our findings show that remanufacturing frequently aligns firms' economic and environmental goals by increasing profits and decreasing the total environmental impact. We show that in some cases, an introduction of a remanufactured product leads to no changes in the new products' prices (positioning within the product line), implying a positive demand cannibalization and a decrease in the environmental impact; this provides support for a heuristic approach commonly used in practice. Yet in other cases, the firm can increase profits by decreasing the new product's prices and increasing sales—a negative effective cannibalization. With negative cannibalization the firm's total environmental impact often increases due to the growth in new production. However, we illustrate that this growth is nearly always sustainable, as the relative environmental impacts per unit and per dollar rarely increase.     

Competing for Shelf Space

In recent years, the competition for shelf space has intensified, as more products now compete for a retail space that has remained roughly constant. In this paper, we analyze the dynamics of this competition in a multi‐supplier retail point. Assuming that sales are shelf space dependent, we consider a retailer that optimizes its shelf space allocation among different products based on their sales level and profit margins. In this context, product manufacturers set their wholesale prices so as to obtain larger shelf space allocations but at the same time keep margins as high as possible. We analyze the equilibrium situation in the supply chain, and find that generally the retailer's and the suppliers' incentives are misaligned, resulting in suboptimal retail prices and shelf space allocations. We however find that the inefficiencies induced by suboptimal shelf space allocation decisions are small relative to those induced by suboptimal pricing decisions.     

供应链质量管理中抽样检验决策的非合作博弈分析

保证产品质量是建立与维护供应链企业间长期稳定合作关系的重要基础.本文提出一种供应链质量管理中抽样检验决策的非合作博弈模型,以分析供应链的下游制造商应如何根据供应商产品的质量水平确定其抽检方案.仿真结果表明,供应链背景下抽检方案不同于单个企业各自优化的制造商抽检方案.考虑供应链企业间互动关系的抽检方案与不考虑这种关系的独立抽检方案相比,能有效降低抽样成本,并使供应商和制造商获得更大的期望收益.     

Managerial Delegation under Alternative Unionization Structures

This paper studies the effects of managerial delegation in a duopoly game under alternative unionization structures. Introducing managerial delegation in a framework with centralized unionization leads to incentives for sales, lower profits and higher consumer surplus as well as overall welfare. In contrast, delegating output decisions to managers in the presence of decentralized unionization produces opposite results unless unions are strongly employment‐oriented. Moreover, managerial delegation makes unionization structure neutral in relation to consumer surplus and overall efficiency. Finally, the timing of moves in the three‐stage game proves to be important for obtaining the above qualitative results under decentralized unionization.     

Optimal Inspection of Imports to Prevent Invasive Pest Introduction

The United States imports more than 1 billion live plants annually—an important and growing pathway for introduction of damaging nonnative invertebrates and pathogens. Inspection of imports is one safeguard for reducing pest introductions, but capacity constraints limit inspection effort. We develop an optimal sampling strategy to minimize the costs of pest introductions from trade by posing inspection as an acceptance sampling problem that incorporates key features of the decision context, including (i) simultaneous inspection of many heterogeneous lots, (ii) a lot‐specific sampling effort, (iii) a budget constraint that limits total inspection effort, (iv) inspection error, and (v) an objective of minimizing cost from accepted defective units. We derive a formula for expected number of accepted infested units (expected slippage) given lot size, sample size, infestation rate, and detection rate, and we formulate and analyze the inspector's optimization problem of allocating a sampling budget among incoming lots to minimize the cost of slippage. We conduct an empirical analysis of live plant inspection, including estimation of plant infestation rates from historical data, and find that inspections optimally target the largest lots with the highest plant infestation rates, leaving some lots unsampled. We also consider that USDA‐APHIS, which administers inspections, may want to continue inspecting all lots at a baseline level; we find that allocating any additional capacity, beyond a comprehensive baseline inspection, to the largest lots with the highest infestation rates allows inspectors to meet the dual goals of minimizing the costs of slippage and maintaining baseline sampling without substantial compromise.