Estimating Censored Price Elasticities Using SAS/ETS®: Frequentist and Bayesian Approaches


The number of rooms rented by a hotel, spending by “loyalty card” customers, automobile purchases by households—these are just a few examples of variables that can best be described as “limited” variables. When limited (censored or truncated) variables are chosen as dependent variables, certain necessary assumptions of linear regression are violated. This paper discusses the use of SAS/ETS® tools to analyze data in which the dependent variable is limited. It presents several examples that use the classical approach and the Bayesian approach that was recently added to the QLIM procedure, emphasizing the advantages and disadvantages that each approach provides. INTRODUCTION Economic theory suggests that as the price of a product or service rises, the demand for it falls, if all other factors are equal. This theory is often applied in the field of revenue management. As part of a company’s optimization strategy, revenue management analysts are often asked to build models that allow prices to influence the number of units sold and therefore affect the company’s revenue. A necessary component of this effort is the development of price elasticities. Price elasticity measures how quantities respond to changes in price. The analyst usually uses a data set that contains past prices and quantities, along with additional explanatory variables, and applies regression techniques to estimate this historical relationship. Price elasticities are used in many revenue management applications. Sophisticated revenue management systems for clothing retailers, hotels, and airline and sports ticket agencies incorporate price elasticities into their optimization routines. Analysts must give special consideration to the statistical or, more precisely, the econometric methods that they use to estimate these elasticities. Neglecting certain aspects of the data and the model can severely bias the elasticity estimate and lead to nonoptimal policy recommendations. Among the important considerations is awareness of the possible values that the data might realize. This paper focuses on hotel data. The maximum number of hotel rooms that can be occupied on a given day is limited by the capacity of the hotel. This capacity is fixed over any reasonable period of time. Therefore, the maximum number of rooms that can be booked for any given day must be less than or equal to the capacity of the hotel. This type of data is commonly referred to as censored data (Maddala 1983). In the case of censored data, analysts must use special considerations to estimate price elasticities. This paper presents a classic case of censoring and the econometric concerns that arise from ignoring censoring. It then presents a real-life example of censoring in the hotel industry. Finally, the paper shows how to estimate the model by using the newest Bayesian estimation techniques that are available in SAS/ETS 12.1. ELASTICITY ESTIMATION Suppose a management analyst is charged with estimating the price elasticity p for a product or service. More formally, the price elasticity of demand is p D Quantity.Price/=Quantity.Price/ Price=Price where Quantity(Price) is the dependent variable in the regression of quantity on price of the product and Price is the price of the product. Based on this regression model, ordinary least squares (OLS) or some other 1 Statistics and Data Analysis SAS Global Forum 2013

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@inproceedings{Macaro2013EstimatingCP, title={Estimating Censored Price Elasticities Using SAS/ETS®: Frequentist and Bayesian Approaches}, author={Christian Macaro and Jan Chvosta and Kenneth Sanford and James Michael Lemieux}, year={2013} }