Journal of Real Estate Finance and Economics, 20:3, 275±293, 2000
# 2000 Kluwer Academic Publishers. Manufactured in The Netherlands.
The Hazard Rates of First and Second Defaults
BRENT W. AMBROSE
Center for Real Estate Studies, University of Kentucky, Lexington, KY 40506, (606) 257-7726,
CHARLES A. CAPONE
Congressional Budget Of®ce, Ford House Building, Room 489A, Washington, DC 20515, (202) 226-2649,
This article examines hazards of repeated mortgage default, conditional on reinstating out of an initial default
episode. Results indicate that subsequent default risk for reinstated borrowers is signi®cantly greater than the risk
of ®rst default, especially during the ®rst two years after a default episode. In addition, economic factors helpful in
predicting ®rst defaults are not helpful in predicting subsequent default episodes. This has important implications
for mortgage investors and servicers as industry foreclosure avoidance efforts intensify.
Key Words: mortgage default, foreclosure, hazard rates, competing risks
The dynamics of borrower default and the conditions that result in foreclosure are gaining
importance as mortgage lenders and services realize that foreclosure avoiding loss
mitigation efforts can pay signi®cant dividends by reducing the incidence of foreclosure.
Lenders, responding to growing pressure from mortgage insurers and secondary market
agencies, are actively engaging in foreclosure forbearance programs in an effort to reduce
mortgage credit losses. One key issue not yet addressed in the mortgage default literature
is the relative post default payment performance of mortgages that have avoided
foreclosure on an initial default. Understanding the propensity of these mortgages to
default again is of critical importance to mortgage servicers and investors and is ultimately
necessary to determine the success of any foreclosure forbearance program. Thus, this
article presents a model of the hazard of second default, given that a borrower has
reinstated out of a ®rst default, and compares it to the hazard rates of default for mortgages
of the same age that have not defaulted previously. It is the ®rst known effort at analyzing
the risk pro®le of these borrowers.
Statistical models suited for this type of analysis include failure time or duration
Duration analysis studies the length of time that elapses from the beginning of
some event to its end or else the waiting time before an event occurs. In the present case,
we estimate the time from loan origination to either prepayment or default, and the time
from reinstatement out of a ®rst default to a second default, in a competing risks
In the next section, we de®ne default events for this study, and we discuss the