# Elasticity calculation on real data

I have data set on several SKU (within one Brand, which were divided by 3 groups) daily demand and prices during one month. Prices were fixed in this period. After this period we begin to increase prices in Group 1 by 1% (on weekdays), stay constant in group 2, and decrease in Group 3 by 1% (on weekdays). We also have demand and price data during test period. How should I analyze price elasticity of brand demand? Which model perfect fit for this data? All analysis should be understandable and can be done using Excel. Thanks in advance.

• I can calculate elasticity for all SKUs separately and all of them will be different. Also I can make it for Group 1 and Group 3. But how can I calculate Brand elasticity? – Василий Лукин Jun 4 '15 at 13:00

Personally, I wouldn't go down the Box-Jenkins road. Transfer functions are really pretty limited in the number of predictors and a large amount of time series data is required just to initialize the models.

Pooled time series approaches (aka event modeling in the social sciences or mix modeling in marketing) are quite flexible and conservative wrt the amount of information required. One reference providing a good, general overview is free and downloadable from Lee Cooper's UCLA website and titled Market Share Analysis. Cooper's framework is marketing but price elasticities are given explicit consideration, the prescriptions are generalizable to any discipline and he provides specific examples of applied data structures based on supermarket scanner data to leverage in answering the questions you've posed.

Another, more academically technical reference is Wooldridge's Econometric Analysis of Cross Section and Panel Data. Wooldridge has much less to say about pricing than Cooper, whose recommendations regarding price elasticities are extensive.

• Transfer Function modelling is not limited by the number of predictors and identification does not require large amounts of data. Identification is based upon the relative importance of lags and is quite easy when the signal is clear. After accounting for omitted deterministic structure like pulses/level shifts/local time trends, identification is often straightforward. I have been able to automatically identify structures and suggest that you review AUTOBOX which I have helped develop. – IrishStat Jun 3 '15 at 17:37
• @IrishStat With all due respect, that sounds like a sales snowjob to me. If the lags are to account for calendar seasonality, then 2 years of information are required at a minimum. Moreover, for short amounts of information, e.g., newly launched products with sparse amounts of available data, where the signal is not clear B-J methods are virtually useless. All of your prescriptions regarding "pulses/level shifts/local time trends, identification" are straightforward only to an expert. – Mike Hunter Jun 3 '15 at 19:37
• Very interesting discussion. I am a little bit surprised that there are no one accepted method to calculate elasticity. I want to ask you several clarifying questions: 1) if we calculate brand elasticity, that mean that for all this SKU elasticities the same? 2) How to use data from base period? 3) Should I aggregate demand by groups or I have to make regression on each SKU? – Василий Лукин Jun 4 '15 at 10:18

I would myself use ARIMAX or transfer function modeling where aggregated demand series is explained via price index.

You could form an price index which is normalized to 100 for each individual group in the base period and then chained by the daily change. Aggregated Laspeyres type on price index is obtained via weighting individual index series by the value shares of groups inside the Brand in the base period.

• How can I calculate price elasticity of demand? Form log-log model on test period price index and demand data? How should I use base period data on price and demand in this case? – Василий Лукин Jun 3 '15 at 17:02

Transfer Function modeling is not limited by the number of predictors and identification does not require large amounts of data. Identification is based upon the relative importance of lags and is quite easy when the signal is clear. After accounting for omitted deterministic structure like pulses/level shifts/local time trends, identification is often straightforward. I have been able to automatically identify structures and suggest that you review AUTOBOX which I have helped develop. @Analyst is quite correct in his suggestion. Please see http://www.autobox.com/cms/index.php/blog/entry/elasticities-for-all for efficient elasticity computation strategies.

• I agree that if we have big data sets we should use AUTOBOX. But If I have only 30 days and several SKUs can I perform elasticity calculation using Excel? – Василий Лукин Jun 3 '15 at 19:08
• Yes ....for each SKU include price as a predictor variable. Set the price for the next data point using the price at the most recent data point. Store the forecast as f1 . Now set price as 1.01 times the most recent price and obtain a forecast called f2. Compute (f2-f1)/f1 and that will be the elasticity of price. – IrishStat Jun 3 '15 at 19:41
• I have data on demand and prices in test period and on base period. I need to calculate brand elasticity. – Василий Лукин Jun 3 '15 at 22:04