Health care expenditure growth is affected by important unobserved common shocks such as technological innovation, changes in sociological factors, shifts in preferences and the epidemiology of diseases. While common factors impact in principle all countries, their effect is likely to differ across countries. To allow for unobserved heterogeneity in the effects of common shocks, we estimate a panel data model of health care expenditure growth in 34 OECD countries over the years 1980 to 2012 where the usual fixed or random effects are replaced by a multifactor error structure. We address model uncertainty with Bayesian Model Averaging, to identify a small set of important expenditure drivers from 43 potential candidates. We establish 16 significant drivers of healthcare expenditure growth, including growth in GDP per capita and in insurance premiums, changes in financing arrangements and some institutional characteristics, expenditures on pharmaceuticals, population aging, costs of health administration, and inpatient care. Our approach allows us to derive estimates that are less subject to bias than in previous analyses, and provide robust evidence to policy makers on the drivers that were most strongly associated with the growth in health care expenditures over the past 32 years.