Price/demand elasticity model from the Bayesian approach: The case of a Chilean retail company
Keywords:
elasticity, detail, frequentist, inference, normal-gamma-inverseAbstract
This project presents data from a Chilean retail firm to model elasticity from a Bayesian perspective. Elasticity measures the behavior of products based on price and demand. It can be obtained through linear regressions of the logarithm of prices and units sold. The problem arises with discounts, special days, etc. This temporal relationship causes biases in the estimates that the company compensates for by performing a chain of regressions. Bayesian statistics fixes a distribution for the parameters, and then, with plausibility, uses Bayes ’ rule to obtain a posteriori distribution. The project uses an a priori Normal-Gamma-Inverse to specify the linear regression model. For the application, we obtain the line level elasticities through the classical model and the product elasticities with the Bayesian model, incorporating the line information. Through a t-test we conclude that the average of the chain elasticities does not differ from those obtained by the Bayesian model. Therefore, by complementing the two points of view, we obtain good results that can be used in trade.
References
Agresti, A. (2015). Foundations of linear and generalized linear models. John Wiley & Sons.
View in Google Scholar
Fahrmeir, L., Kneib, T., Lang, S., & Marx, B. (2013). Regression: Models, methods and appli-cations. Springer-Verlag. https://doi.org/10.1007/978-3-642-34333-9
View in Google Scholar
Hoff, P. D. (2009). A first course in Bayesian statistical methods. Springer Science + Business Media.
View in Google Scholar
Kim, S., & Kim, H. (2016). A new metric of absolute percentage error for intermittent demand forecasts. International Journal of Forecasting, 32(3), 669–679. https://doi.org/10.1016/j.ijforecast.2015.12.003
View in Google Scholar
Laurinec, P. (2018). TSrepr R package: Time series representations. The Journal of Open Source Software, 3(23), 577. https://doi.org/10.21105/joss.00577
View in Google Scholar
Marrero, F., Font, E., & Lazcano, C. (2015). Reflexiones sobre el concepto de elasticidad y su interpretación matemática y económica. Revista de Ciencia, Tecnología e Innovación, 2(2), 105–115.
View in Google Scholar
Ruxton, G. D. (2006). The unequal variance t-test is an underused alternative to Student’s t-test and the Mann-Whitney U test. Behavioral Ecology, 17(4), 688–690. https://doi.org/10.1093/beheco/ark016
View in Google Scholar
Schauberger, P., & Walker, A. (2020). openxlsx: Read, Write and Edit xlsx files. https://CRAN.R-project.org/package=openxlsx
View in Google Scholar
Wickham, H., Averick, M., Bryan, J., Chang, W., McGowan, L.D., François, R., Grolemund, G., Hayes, A., Henry, L., Hester, J., Kuhn, M., Pedersen, T. L., Miller, E., Bache, S. M., Müller, K., Ooms, J., Robinson, D., Seidel, D. P., Spinu, V., ..., Yutani, H. (2019). Welcome to the tidyverse. The Journal of Open Source Software, 4(43), 1686. https://doi.org/10.21105/joss.01686
View in Google Scholar
Willmott, C., & Matsuura, M. (2005). Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance. Climate Research, 30, 79–82. https://www.int-res.com/articles/cr2005/30/c030p079.pdf
View in Google Scholar
Yan, Y. (2016). MLmetrics: Machine learning evaluation metrics. https://CRAN.R-project.org/package=MLmetrics
View in Google Scholar
Downloads
Published
Issue
Section
License
Copyright (c) 2023 Poznań University of Economics and Business
This work is licensed under a Creative Commons Attribution 4.0 International License.
