The Markets of Green Cars of Three Countries: Analysis Using Lotka–Volterra and Bertalanffy–Pütter Models

Abstract

Did the diesel scandal of 2015 affect the market for cars? We consider this question in relation to Germany, Austria, and Switzerland. Starting with historical registration data of cars with different drivetrain technologies, we considered each technology in isolation and fitted a five-parameter Bertalanffy–Pütter (BP) growth model to the stocks of cars. We used this model as it generalizes several well-known three-parameter models, which are distinguished by their exponent pair, e.g., Brody model BP (0, 1), West model BP (0.75, 1), and logistic growth BP (1, 2). We then used these models to derive a Lotka–Volterra (LV) model for the co-evolution of the (annual) market shares of the different drivetrain technologies. We augmented this model by a consideration of model uncertainty and found that initially all technologies were in a state of competition, except for Austria, which changed in 2015 to a predator–prey situation with diesel as the sole prey. This analysis of model uncertainty compared the best-fitting growth curve with the growth trajectories of other likely (Akaike weight 5% or higher) models of BP type. We conclude with remarks about open innovation.