财务危机预警文献,仅供学习研究
Shumway (2001) advocates the use of discrete-time hazard model for bankruptcy prediction. The concept of discrete-time hazard model originates from survival model that is widely used in biological medication field. It was not until recent years that social science researchers started using it for analyzing variables’ effect upon survival (e.g., Lancaster 1990). Cox and Oakes (1984) calculate hazard rate to estimate the likelihood of survival and survival time.
Shumway (2001) defines firm age,T∈{1,2,3,...,t}, as the period that starts from the inception date of a firm to the date of bankruptcy filing or the end of sample period. The probability mass function of bankruptcy isf(t,x; θ), which x represents
the vector of explained variable and θ represents the vector of parameter. Equations (3) and (4) represent respectively the two most important functions of hazard model, survival function and hazard function.
Survival function: S(t,x;θ)=1 ∑f(j,x;θ) (3)
j<t
Equation (3) represents the probability of survival up to time t. Hazard function: φ(t,x;θ)=
f(t,x;θ)
(4)
S(t,x;θ)
Equation (4) represents the probability of bankruptcy at time t conditional on surviving to t.
The likelihood function of the hazard model is expressed as:
L=∏φ(ti, xi; θ)yiS(ti, xi; θ), (5)
i=1n
