Regular Variation and the Identification of Generalized Accelerated Failure-Time Models

Abstract

Ridder (1990) provides an identification result for the Generalized AcceleratedFailure-Time (GAFT) model. We point out that Ridder's proof of this result is incomplete, and provide an amended proof with an additional necessary and sufficient condition that requires that a function varies regularly at 0 and ∞. We also give more readily interpretable sufficient conditions on the tails of the error distribution or the asymptotic behavior of the transformation of the dependent variable. The sufficient conditions are shown to encompass all previous results on the identification of the Mixed Proportional Hazards (MPH) model. Thus, this paper not only clarifies, but also unifies the literature on the non-parametric identification of the GAFT and MPH models.

Identification of Models of the Labor Market

“…20 The econometrician can observe whether the worker 19 Key papers include Elbers and Ridder (1982), Heckman and Singer (1984a,b), Ridder (1990), Honoré (1993), and Abbring and Ridder (2009). 20 We do not need to make use of exclusion restrictions here so we do not distinguish between observables that may enter differently.…”

Mixed Hitting-Time Models

“…First, our proof makes explicit use of the assumption that both MHT triplets have a regularly varying tail. Ridder's Theorem 1 implicitly requires a similar regularity condition (Abbring and Ridder, 2009). Second, we allow for defective duration distributions, which naturally arise in the context of an MHT model.…”

“…In the MPH literature, this is invariably achieved by not only requiring regular variation of one of their tails, but also fixing the corresponding exponent of regular variation (Ridder, 1990;Abbring and Ridder, 2009). First, consider tail assumptions on L. Elbers and Ridder (1982) have proved identifiability of the two-sample MPH model, up to scale, under the assumption that the unobserved factor has a finite mean.…”