자동차 시장 내 최적의 리베이트 수준 결정을 위한 계층 베이즈 분산구성 모형 (Hierarchical Bayes Variance Components Model for Developing Optimal Rebate Program in the Automotive Industry)

서지정보

· 발행기관 : 한국마케팅학회
· 수록지 정보 : 마케팅연구 / 25권 / 3호 / 119 ~ 135페이지
· 저자명 : 장광필

초록

이 연구의 목적은 포장 소비재 시장에서의 A.C. Nielsen 패널 자료와 유사한 수준의 개별적 자동차 거래 자료(disaggregate transaction data)를 사용하여 마케팅 관리적 차원에서 지역별로 축적된 자료의 구조에 적합한 모형화 방식을 통해 최적의 리베이트 수준을 결정하는 방법론을 제시하는 것이다. 기존의 계층 베이즈 모형의 적용은 1단계에서 최소의 분석단위인 소비자의 브랜드 선택을 로짓(logit)이나 프로빗(probit)모형의 선택확률로 모형화하고 2단계에서 소비자별 모수의 선험분포(prior)를 의 다변량 정규분포로 가정하고 3단계에서 선험분포의 모수 와 의 초 선험분포 (hyper prior)를 각 각 다변량 정규분포와 Wishart분포로 가정하는 방식이었다. 이러한 3단계 모형화 방식으로 추정된 소비자별 모수를 의사결정의 근거로 사용하였다. 이 논문에서는 기존의 3단계 베이즈 모형을 자동차 시장에 응용하고 확장하여 1단계에서 최소의 분석단위를 zip code로 가정하여 zip code별 소비자의 자동차 모델선택을 로짓모형의 선택확률로 모형화하고, 2단계에서 zip code별 모수 의 분포를 지역(regional) 평균을 중심으로 분포된다는 가정 하에 의 다변량 정규분포로 가정하고, 3단계에서 지역평균 의 분포를 전국(national) 평균을 중심으로 분포된다는 가정 하에 의 다변량 정규분포로 가정하고, 4단계에서 과 의 초 선험분포를 각 각 다변량 정규분포와 Whishart분포로 가정하였다. 제안된 4단계 계층 베이즈 모형은 분산구성 모형 (Variance Components Model)으로서 zip code별 모수의 이질성을 지역내 이질성과 지역간 이질성으로 분해하여 반영함으로써 실증분석 결과 모형적합도와 예측타당성 측면에서 기존의 3단계 모형에 비해 우월한 것으로 나타났다. 실증분석 대상은 미국 내 미니 밴 시장으로 하였고 다양한 프로모션 수단 중에 가장 빈번히 사용되는 리베이트를 중심으로 zip code별로 서로 다른 리베이트 모수를 추정하여 최적의 리베이트 수준을 추정하였다. 시뮬레이션을 통해 관행적으로 집행되어온 일률적인 리베이트(uniform blanket rebate)보다 서로 다른 zip code별로 차별적 리베이트를 제공했을 때 수익성이 높다는 것을 실증적으로 보였으며, 3단계 모형보다 4단계의 분산구성 모형에 근거한 의사결정이 보다 높은 수익을 제공하는 것으로 나타났다.

영어초록

The current study attempts to design optimal rebate program for manufacturers in the automobile industry, who have to determine the combinations of incentives to be used (e.g., consumer rebates and dealer incentives) in a wide variety of automobile makes, models and regional markets. Allocating promotional budget to regional offices is further complicated by the need to evaluate and react to the conflicting information provided by different district managers, each pushing for a greater slice of the promotional budget.
This study develops an approach to capture zip code-level response to the marketing mix that is based on a Hierarchical Bayes multinomial logit model (random coefficient model) of automobile choice and show how it can be used for developing optimal rebate program in the automobile market. The approach requires us to hierarchically structure the data according to geographical proximity, e.g., zip codes under a particular region (e.g., DMA: Designated Marketing Area) to account for similarities within a region and differences across regions. In contrast to scanner panel data, the long inter-purchase times in this category provide only one observation per buyer in the sample, which makes it difficult to directly apply previously developed methods to account for consumer heterogeneity. We overcome this limitation by treating the transactions from a particular zip code as a “purchase string” and estimating choice model parameters at a zip code level using the MCMC method. This permits us to implement a micro approach to the development of the marketing mix such that responses to the marketing mix reflect differences in consumer price and promotion sensitivities across geographical areas.
In this approach the zip code level parameters in a region are distributed according to a normal distribution that is centered on a region-specific mean, with each regional mean, in turn, being distributed around a national mean, which is drawn from the distribution specified by the hyper-parameters. The priors for the variance covariance matrices of the parameters also follow the same hierarchical, set-up. We label this set up as the NRZ (National-Regional-Zip code) model. In this model, the first stage of the hierarchical structure, is a multinomial logit choice model. In the second stage we specify the multivariate normal distribution for the zip code-level parameters in the region r. In the third stage we specify the multivariate normal distribution for region-specific means, and the Wishart distribution for . In the final (fourth) stage we specify the hyper prior distribution for and . This four-stage approach results in the Variance Components model that accounts for both between-region () and within-region heterogeneity ().
The data for this study come from Power Information Network (PIN), an affiliate of J.D. Power and Associates. PIN collects sales transaction data from a sample of dealerships in the major metropolitan areas in the U.S. These are retail transactions, i.e., sales or leases to final consumers, excluding fleet sales. Each observation in the PIN database contains the transaction date, the manufacturer, model year, make, model, trim and other car information, the transaction price, consumer rebates, the interest rate, term, amount financed (when the vehicle is financed or leased), etc. We use data for 2000 model-year minivans for the period October 1999–September 2000 (52 weeks). Fifteen models are included in the study: Chevrolet Astro, Dodge Caravan, Dodge Grand Caravan, Chrysler Grand Voyager, Pontiac Montana, Honda Odyssey, Nissan Quest, GMC Safari, Toyota Sienna, Oldsmobile Silhouette, Chrysler Town&Country, Chevrolet Venture, Mercury Villager, Chrysler Voyager and Ford Windstar. These models in the study account for 96% of category (i.e., minivan segment) unit sales.
Empirical results show that the proposed four-stage model (NRZ) outperformed a typical three-stage model (NZ) that accounts for only within-region heterogeneity (by assuming that all zip codes belong to one big nation) in terms of model fit in both calibration and holdout samples. The superiority of the NRZ model can be attributable to more thorough corrections of heterogeneity which is due to between- and within-differences in responses to the marketing mix. The managerial setting that we study provides some natural ways to structure the prior distribution of the zip code level parameters to accommodate their differences and similarities. Comparing the empirical performance of competing models based on different prior distributions provides insights into the best ways to borrow information across the different zip codes.
The approach permits managers the flexibility to use different promotional instruments in different ways. Thus, a general promotional incentive, such as manufacturer cash-back promotion, can be constrained to be equal across different zip codes in the same region to address antitrust concerns, while a targeted coupon mailing could be customized for a particular zip code.
We examine a realistic (but hypothetical) problem faced by one particular manufacturer, which involves setting the optimal rebate levels to be offered in various markets. First, we determine the optimal rebate level according to each model assumption (i.e., homogeneous MNL model, NRZ model assumptions). Given the model-specific optimal rebate level, we calculate expected profits by using the NRZ model parameters since in terms of model fit, the NRZ model is the best and most likely to describe market responses close to reality. We show how the model parameters can be used to determine these rebate levels and demonstrate that the profits obtained with the NRZ model assumption are significantly higher than those with the uniform blanket rebate program.

참고자료

· 없음