Using Dynamic Linear Models with Changepoints to Understand Trends in the Auto Insurance Industry

Industry-wide auto insurance losses can be difficult to model but are very important for companies to understand. Loss trends can be used to help with ratemaking, on-leveling, and risk management of future losses. We develop a new dynamic linear model with seasonality, regression on congestion, and a linear trend with a changepoint. The changepoint allows us to model structural shifts in the industry, regardless of why they occur (e.g., regulatory, economic, or social changes). We find that the changepoint improves the model fit and will likely lead to improved predictions of future losses; urban congestion best describes the loss process; frequency has generally decreased; and severity has generally increased. Loss cost has increased overall, but it decreased in a significant number of states at the beginning of our time window. We look forward to this model being better able to forecast loss trends in the industry going forward.