First references for 2nd order approximations

Hello everyone,

i am working on a model in which i would like to account for the effect of changes in the interest rate on the households debt services. As i assume a zero debt steady state, changes in the interest rate unfortunately drop out in a first-order approximation of the households budget.

The only solution i can imagine is to take a second order approximation which comprises cross-terms of the deviations. So i am wondering if anyone has a hint concerning first references for this problem? Is it possible to take a second-order approximation of the budget only, leaving the remaining equations in first order approximation?

Many many thanks in advance for any advice!