ECONOMETRICS IN ACTION Vince Daly Kingston University October

ECONOMETRICS IN ACTION © Vince Daly & Kingston University, October 2009 This work is licenced under a Creative Commons Licence. Forecasting the rate of adoption of new products S-CURVES & MARKET DIFFUSION

THE CLASSIC STAGES OF MARKET PENETRATION FOR A NEW PRODUCT The S-curve shape reflects the stages of market development. 100 Market Penetration 90 80 70 60 50 40 30 20 10 0 2002 Early adopter s 2004 2006 Take off 2008 2010 Mass adoptio n 2012 2014 Slow down 2016 2018 2020

TRANSFORMING TO A LINEAR MODEL The S-curve has a complicated formula but a change of variables produces a simple linear equivalent. The non-linear Scurve Can be changed by ‘logistic’ transformation to Its linear transformation S: market saturation level (i. e. max possible sales) = 100 in this example Pt: penetration of market at time t

MOBILE TELEPHONES IN EUROPE - AN EXAMPLE OF FITTING & EXTRAPOLATING S-CURVES MSc student T. Vrionis gathered the OECD data for % penetration of this market DATA: 5. 0 EXCEL’s TREND function can be used to fit a linear trend to the transformed data by the OLS method, and also to extrapolate this trend 3. 0 1. 0 -3. 0 -5. 0 1990 100. 0 The logistic transformation can then be reversed for a graph that shows observed and extrapolated market penetration. ln(P/(100 -P)) 1995 P 2000 forecast 2005 2010 80. 0 60. 0 40. 0 20. 0 1990 1995 2000 2005 2010

COMMERCIAL APPLICATION ADVENTIS PLC have used S-Curve calculations as a basis forecasting development of various M-commerce markets Saturation Levels Vary By Segment © Adventis PLC, 2001 Extract from presentation to IBC conference Forecasting the Telecoms Market , London 2001