Firm survival and time aggregation bias

Abstract

This note provides some evidence of the sensitivity of firm survival duration dependence to time aggregation, when durations are Weibull distributed. The results indicate that estimates of duration dependence are always positively biased: This bias increases with the width of time aggregation window and decreases with the length of expected durations. On the other hand, time aggregation does not seem to have drastic effect on the regression parameter estimates. These results are unaffected by the time aggregation mechanism.

Notes

¹See Hensler et al. (1998)

²Buehler et al. (2006)

³Mata et al. (1995). They used the unrestricted Cox model

⁴The results for the exponential are not reported since by definition σ = 1

⁵The variance of aggregated duration is given by Var(T) = β²(Γ(1 + 2/α) − (Γ(1 + 1/α²))²). For monthly data β = 42 and β = 3.05 for annual data.