Soft Power, World System Dynamics, and Democratization: A Bass Model of Democracy Diffusion 1800-2000

This article uses Polity IV data to probe system dynamics for studies of the global diffusion of democracy from 1800 to 2000. By analogy with the Bass model of diffusion of innovations, as translated into system dynamics by Sterman, the dynamic explanation proposed focuses on transitions to democracy, soft power, and communication rates on a global level. The analysis suggests that the transition from democratic experiences (\'the soft power of democracy\') can be estimated from the systems dynamics simulation of an extended Bass model. Soft power, fueled by the growth in communications worldwide, is today the major force behind the diffusion of democracy. Our findings indicate the applicability of system dynamics simulation tools for the analysis of political change over time in the world system of polities.Democracy, Bass, Communication, System Dynamics, Power, Diffusion

The Product Life Cycle of Durable Goods

A dynamic model of the product lifecycle of (nearly) homogeneous durables in polypoly markets is established. It describes the concurrent evolution of the unit sales and price of durable goods. The theory is based on the idea that the sales dynamics is determined by a meeting process of demanded with supplied product units. Taking advantage from the Bass model for first purchase and a logistic model for repurchase the entire product lifecycle of a durable can be established. For the case of a fast growing supply the model suggests that the mean price of the good decreases according to a logistic law. Both, the established unit sales and price evolution are in agreement with the empirical data studied in this paper. The presented approach discusses further the interference of the diffusion process with the supply dynamics. The model predicts the occurrence of lost sales in the initial stages of the lifecycle due to supply constraints. They are the origin for a retarded market penetration. The theory suggests that the imitation rate B indicating social contagion in the Bass model has its maximum magnitude for the case of a large amount of available units at introduction and a fast output increase. The empirical data of the investigated samples are in qualitative agreement with this prediction

Forecasting in marketing

With the advent of advanced data collection techniques, there is an increased interest in using econometric models to support decisions in marketing. Due to the sometimes specific nature of variables in marketing, the discipline uses econometric models that are rarely, if ever, used elsewhere. This chapter deals with techniques to derive forecasts from these models. Due to the intrinsic non-linear nature of these models, these techniques draw heavliy on simulation techniques.marketing;forecasting;unobserved heterogeneity;Koyck model;attraction model;Bass model

Forecasting Sales

This chapter deals with forecasting sales (in units or money), where an explicit distinction is made between sales of durable goods (computers, cars, books) and sales of utilitarian products (SKU level in supermarkets). Invariably, sales forecasting amounts to a combination of statistical modeling and an expert’s touch. Models for durable goods sales are usually based on (variants of) the Bass model, while SKU sales forecasts are typically based on simple extrapolation methods. Forecast evaluation is not standard due to the interaction of model and expert.diffusion;SKU-level sales;durable goods;human judgment;sales forecasting

Modelling Of Eco-innovation Diffusion: The EU Eco-label

The aim of this article is to carry out a theoretical and empirical analysis of the process of eco-label diffusion. Eco-labels allow consumers to identify products and services that have a reduced environmental impact during their life cycle. Thus, they are aimed at diminishing the information gap between sellers and buyers. The results of the estimation using the Bass model indicate that the diffusion of the EU eco-label has been most dynamic in countries such as Hungary, Poland, Denmark, Germany and France. In turn, the scope of diffusion (absolute saturation level) reached the highest value for companies in France and Italy. In addition, the results of the study confirm the stimulating impact of the scope of eco-label diffusion on consumer awareness of environmental issues. This finding points to the need for environmental education among consumers, which could in turn encourage firms to undertake pro-environmental actions

Compartmental limit of discrete Bass models on networks

We introduce a new method for proving the convergence and the rate of convergence of discrete Bass models on various networks to their respective compartmental Bass models, as the population size $M$ becomes infinite. In this method, the full set of master equations is reduced to a smaller system of equations, which is closed and exact. The reduced finite system is embedded into an infinite system, and the convergence of that system to the infinite limit system is proved using standard ODE estimates. Finally, an ansatz provides an exact closure of the infinite limit system, which reduces that system to the compartmental model. Using this method, we show that when the network is complete and homogeneous, the discrete Bass model converges to the original 1969 compartmental Bass model, at the rate of $1/M$. When the network is circular, however, the compartmental limit is different, and the rate of convergence is exponential in $M$. In the case of a heterogeneous network that consists of $K$ homogeneous groups, the limit is given by a heterogeneous compartmental Bass model, and the rate of convergence is $1/M$. Using this compartmental model, we show that when the heterogeneity in the external and internal influence parameters among the $K$ groups is positively monotonically related, heterogeneity slows down the diffusion.Comment: 28 pages, 5 figure