We investigate pairwise stochastic comparisons of stationary solutions to the linear recurrence 𝑋𝑡+1=𝐴𝑡𝑋𝑡+𝐵𝑡 , where 𝐴𝑡 and 𝐵𝑡 are non-negative random variables. We establish novel order-preserving properties, which enable us to obtain comparison theorems...

We document the extent to which major macroeconomic series, used to inform linear DSGE models, can be characterized by power laws whose indices we estimate via maximum likelihood. Assuming data follow a linear recursion with multiplicative noise, low estimated indices suggest fat tails. We then...