### 1. 文章基本信息

 - **文章标题**：Structural models in marketing

 - **作者**：Pradeep K. Chintagunta

 - **发表情况**：《Handbook of Marketing Analytics》相关章节，2018年

 - **文章主旨**：介绍营销领域的结构模型，包括其定义、关键要素、示例，阐述其在营销研究中的必要性，并探讨其发展趋势及未来研究方向。

• Main Idea of the Article: To introduce the structural models in the field of marketing, including its definition, key elements, examples, explain its necessity in marketing research, and explore its development trends and future research directions.

### 2. 结构模型的定义与关键要素

 - **定义**：结构模型是一种基于理论（通常是经济理论，但也可涵盖其他学科理论）的实证模型，它通过理论预测经济主体（消费者、企业等）的行为，从而建立解释变量与结果变量之间的关系。

• Structural models are empirical models based on theory (usually economic theory, but also other disciplinary theories), which predict the behavior of economic agents (such as consumers and firms) through theory and establish the relationship between explanatory variables and outcome variables.

 - **关键要素**

    - **经济主体**：如消费者或企业。

    - **行为性质**：如优化、满意等行为。

    - **变量关系**：解释变量与结果变量之间的关系由主体行为决定。

• Economic Agents: Such as consumers or firms.

• Nature of Behavior: Such as optimizing or satisficing behavior.

• Relationship between Variables: The relationship between explanatory variables and outcome variables is determined by the behavior of agents.

 - **不可观测因素（Unobservables）**

    - **结构误差项**：经济模型中解释变量集合的一部分，但研究者无法观测，如货架空间和位置对品牌市场份额的影响。

    - **未观测到的异质性**：解释不同主体之间解释变量与结果变量关系的差异，如不同消费者对品牌的价格敏感度不同。

    - **主体对模型参数的不确定性**：主体对特定参数不确定，通过接收信号逐渐学习更新信念，研究者通常无法观测这些信号。

    - **测量误差**：如研究消费者接收的广告水平与购买行为之间的关系时，可能使用广告支出或特定人群平均暴露水平作为代理变量，存在测量误差。

• Structural Error Terms: They are part of the explanatory variables in the economic model but are not observed by researchers, such as shelf space and location.

• Unobserved Heterogeneity: They help explain the differences in the relationship between explanatory and outcome variables across different agents, such as different consumers' price sensitivities.

• Agent Uncertainty about Model Parameters: Agents are uncertain about specific parameters in the model and learn about them over time through signals, and these signals are usually not observed by researchers.

• Measurement Errors: There are errors in measuring variables, such as using proxies for advertising exposure.

### 3. 结构模型示例：品牌选择模型

 - **基本模型**

    - 基于消费者效用最大化模型，消费者在预算约束下从J个品牌中选择，选择品牌j的条件由式

    - 通过对数变换和假设误差项服从独立同分布的极值分布，得到消费者i在购买时刻t选择品牌j的概率公式。

    - 模型参数通常通过消费者层面的选择数据随时间进行估计，如通过最大似然估计法。

• based on the consumer utility maximization model, consumers choose from J brands under the budget constraint. The selection condition is given by the formula 

  , where  represents quality and  represents price.

• Through logarithmic transformation and assuming that the error term follows the independent and identically distributed extreme value distribution, the probability that consumer i chooses brand j at purchase time t is obtained as 

  .

• The model parameters  are usually estimated from consumer-level choice data over time using maximum likelihood estimation.

 - **引入异质性的模型**

    - 考虑消费者在偏好和对营销活动的反应上存在异质性，即，消费者i选择品牌j的概率变为

    - 当服从多元正态分布时，模型参数的识别需要面板数据，通过构建似然函数进行估计。

• Model with Heterogeneity

• Considering the heterogeneity of consumers in preferences and responses to marketing activities, that is, , the probability that consumer i chooses brand j becomes 

  .

• When  follows the multivariate normal distribution, the identification of model parameters requires panel data, and the estimation is performed by constructing the likelihood function.

### 4. 结构模型在营销研究中的必要性

 - **量化营销干预效果**

    - 通过估计结构模型的潜在参数，量化各种营销干预的效果。例如在Sriram等人的研究中，结构模型可量化消费者对质量的敏感度和风险厌恶程度，帮助管理者了解影响终止行为的因素。

 - **评估模型要素变化的后果**

    - 使用估计的模型参数评估改变模型中一个要素的后果。如Misra和Nair的研究，通过构建销售团队补偿的动态结构模型，进行反事实分析，评估不同补偿方案对公司利润的影响，并实施新方案使公司收入提高了9%。

• Quantifying Marketing Intervention Effects

• By estimating the potential parameters of structural models, we can quantify the effects of various marketing interventions. For example, in the study of Sriram et al., the structural model can quantify the consumers' sensitivity to quality and risk aversion, helping managers understand the factors that affect termination behavior.

• Assessing the Consequences of Changing Model Elements

• Using the estimated model parameters to assess the consequences of changing one element of the model. For example, in the study of Misra and Nair, by building a dynamic structural model of agent behavior, they conduct counterfactual analysis to evaluate the impact of different compensation schemes on the firm's profits and implement a new compensation scheme, resulting in a 9% improvement in overall revenues.

### 5. 结构模型的分类

 - **需求与供给模型**

    - 这类模型在经济学文献中有悠久历史，包括基于消费者效用行为的需求规格和企业行为的供给模型，涉及价格、广告等营销组合决策。例如Berry等人的研究。

 - **动态结构模型**

    - 需求侧的动态性可由多种原因产生，如产品的可储存性、耐用性和体验性等。例如Erdem等人和Sun的研究涉及可储存性和耐用性商品的动态需求，体验商品的动态需求可通过学习模型描述。

 - **涉及不确定性的模型（搜索模型）**

    - 消费者可能不完全了解市场上产品的价格，需要进行搜索以获取信息，或者搜索最符合自己偏好的产品。例如Mehta等人和Kim等人的研究。

• Demand and Supply Models

• These models have a long history in the economics literature, including the demand specification based on consumers' utility behavior and the supply model of firms' behavior, involving marketing mix decisions such as prices and advertising. For example, the studies of Berry et al.

• Dynamic Structural Models

• The dynamics on the demand side can be caused by several reasons, such as the storability, durability, and experience goods of products. For example, the studies of Erdem et al. and Sun involve the dynamic demand for durable and experience goods.

• Models Involving Uncertainty (Search Models)

• Consumers may not be fully informed about the price of a product in the market and need to search for information, or search for a product that best matches their preferences. For example, the studies of Mehta et al. and Kim et al.

### 6. 结构模型的发展趋势及未来研究方向

 - **结合多数据源**

    - 随着结构模型变得更复杂，对数据的要求增加，研究者可利用多种数据源（市场结果数据、消费者调查数据、实验室实验数据等）提高估计的可信度，放松模型假设。例如Dube等人的研究展示了如何结合联合分析的输入来更好地估计动态结构模型。

 - **结合多种方法**

    - 当识别关键依赖于数据的某些变化时，可先通过其他方法（如差异分析）确定这种变化是否存在，再构建复杂的结构模型。例如Rossi和Chintagunta的研究，先通过价格标志引入前后价格变化确定价格确实改变，再从结构模型中识别顾客的搜索成本。

 - **使用实地实验验证和实施基于反事实的建议**

    - 随着基于结构模型建议的实地实施变得更广泛，结构模型辅助决策的能力将更加清晰。但实地实施有成本，不能替代精心构建的结构模型。例如Misra和Nair的研究实施了新的销售团队补偿方案，结果验证了结构模型的有效性。

• Combining Multiple Data Sources

• As structural models become more complex, the requirements for data increase. Researchers can use multiple data sources (market outcome data, consumer survey data, laboratory experiment data, etc.) to improve the credibility of estimates and relax the assumptions of the model. For example, the study of Dube et al. shows how to combine the inputs of conjoint analysis to better estimate the dynamic structural model.

• Combining Multiple Methods

• When the identification depends critically on some variations in the data, it may make sense to first establish the existence of such variations before constructing a complicated structural model. For example, in the study of Rossi and Chintagunta, they first determine whether the price changes with the introduction of price signs through a different approach, and then identify the search costs from the structural model.

• Using Field Experiments to Validate and Implement Recommendations based on Counterfactuals

• With the wider implementation of recommendations based on structural models in the field, the ability of structural models to assist decision-making will become more clear. However, the field implementation has costs and cannot replace the carefully constructed structural models. For example, the study of Misra and Nair implemented a new compensation scheme for the firm's employees, and the results verified the effectiveness of the structural model.