Regression by clustering using Metropolis Hastings

High quality risk adjustment in health insurance markets weakens insurer incentives to engage in inefficient behavior to attract lower-cost enrollees. We propose a novel methodology based on Markov Chain Monte Carlo methods to improve risk adjustment by clustering diagnostic codes into risk groups optimal for health expenditure prediction. We test the performance of our methodology against common alternatives using panel data from 3.5 million enrollees of the Colombian Healthcare System. Results show that our methodology outperforms common alternatives and suggest that it has potential to improve access to quality healthcare for the chronically ill.