This paper presents a general specification for dynamic equilibrium models where nonnegative variables follow the autoregressive gamma process in Jasiak and Gourieroux (2006). The model solution implies linear dynamics for endogenous variables, and provides conditional and unconditional moments in closed-form. Finding the solution is computationally inexpensive, requiring only to solve linear and quadratic equations. The specification can be applied to a wide variety of models in finance and economics. Two applications are presented. First, a time-varying volatility premium in a long-run risks asset pricing model. Second, time-varying volatility in policy shocks in a simple New Keynesian model. Accuracy in these models’ solutions is high and not significantly affected by time-varying volatility.