  We review the notion of a linearity-generating (LG) process introduced by
Gabaix (2007) and relate LG processes to linear-rational (LR) models studied by
Filipovic, Larsson, and Trolle (2017). We show that every LR model can be
represented as an LG process and vice versa. We find that LR models have two
basic properties which make them an important representation of LG processes.
First, LR models can be easily specified and made consistent with nonnegative
interest rates. Second, LR models go naturally with the long-term risk
factorization due to Alvarez and Jermann (2005), Hansen and Scheinkman (2009),
and Qin and Linetsky (2017). Every LG process under the long forward measure
can be represented as a lower dimensional LR model.
