The authors measure the time-series property of catastrophic medical costs facing the elderly using information on medical deductions from a panel of tax returns. During the period of analysis, 1968-73, taxpayers could deduct medical expenses above 3 percent of income. They correct for the resulting censoring bias using multivariate tobit estimated with a variant of the smoothed simulated maximum likelihood method. The estimated coefficients imply a $1.00 increase in out-of-pocket medical spending is associated with $2.65 in future out-of-pocket spending. Copyright 1994 by MIT Press.