Centres Científics i Tecnològics UB



Car sales follow Gibrat's law

Dr. Jose Ramón Seoane Trigo, the Director of the Scientific and Technological Centers of the University of Barcelona (CCiTUB), has participated in the article "Maximum Entropy Principle underlying the dynamics of automobile sales". This article explains, from a mathematical point of view, the act of buying cars, when the choice of a particular model not only responds to rational and emotional reasons, but also has a clear social component.

The CCiTUB together with the team of SThAR and SEAT's Department of Data Science have analyzed the evolution of car sales over the last ten years using mathematical models such as the principle of maximum entropy, Langevin equation, etc. The set has taken into account more than 6500 models of cars and all of the 10 million cars sold between January 2007 and January 2017. The analysis’ result has been public in the cited article.

The purchase of a car or other has relation to the popularity of the chosen model and, this decision has relation to the purchases made during the last five years (memory of decay). These data help to conclude also that we can predict what types of cars will be the ones that will triumph in the sales of the next 5 years bearing in mind that today's sales are already marking this trend.

According to the article, the sale of cars follows Gibrat's law or proportional growth: the more cars of a type we see today in the street, the more we will see tomorrow and so on until people who are prone to buy this car already have it. Then a more modern model would come on the market and the cycle would start again.


"We analyze an exhaustive data-set of new-cars monthly sales. The set refers to 10 years of Spanish sales of more than 6500 dierent car model congurations and a total of 10M sold cars, from January 2007 to January 2017. We nd that for those model congurations with a monthly market-share higher than 0.1% the sales become scalable obeying Gibrat's law of proportional growth under logistic dynamics. Remarkably, the distribution of total sales follows the predictions of the Maximum Entropy Principle for systems subject to proportional growth in dynamical equilibrium. We also encounter that the associated dynamics are non-Markovian, i.e., the system has a decaying memory or inertia of about 5 years. Thus, car sales are predictable within a certain time-period. We show that the main characteristics of the dynamics can be described via a construct based upon the Langevin equation. This construct encompasses the fundamental principles that any predictive model on car sales should obey."