# The difference between first and second order solution **URL:** \ **Category:** Stochastic simulations\ **Created:** [16 December 2018 07:03 UTC](https://forum.dynare.org/t/the-difference-between-first-and-second-order-solution/12967 "2018-12-16T07:03:18Z")\ **Posts on this page:** 4\ **Page:** 1
**Author:** ![xiongchen111](https://forum.dynare.org/letter_avatar_proxy/v4/letter/x/cdc98d/32.png) [@xiongchen111](https://forum.dynare.org/u/xiongchen111)\ **Post date:** [16 December 2018 07:03 UTC](https://forum.dynare.org/t/the-difference-between-first-and-second-order-solution/12967/1 "2018-12-16T07:03:18Z")
Dear all I have problem with quodratic tern in one equation of my mod file. The equation is as follows: mud=Omega\*((1-taustar)_R_( 1-tau\_adj\*( (Dstar-steady\_state(Dstar))^2)/ (1-tauB) )-ebar(+1)/ebar_Rstar); tau\_adj is a parameter, and Dstar is I found that when I set the solution order equals 1, there is no difference when I introduce the quadratic term: tau\_adj_( (Dstar-steady\_state(Dstar))^2) But when I set the solution order equals 2, the introduced quadratic term has an effect, i.e. , the result with tau\_adj\>0 is different with that of tau\_adj=0. Where is the problem? Thank you. ---
**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\ **Post date:** [16 December 2018 08:55 UTC](https://forum.dynare.org/t/the-difference-between-first-and-second-order-solution/12967/2 "2018-12-16T08:55:02Z")
I am not sure I understand the problem. You are introducing a term whose first order derivative evaluated at the steady state 2 \tau (\bar D^\*-\bar D^\*) is 0. The second derivative in contrast is 2 \tau \neq 0 Thus, it introduces a difference at second order. ---
**Author:** ![xiongchen111](https://forum.dynare.org/letter_avatar_proxy/v4/letter/x/cdc98d/32.png) [@xiongchen111](https://forum.dynare.org/u/xiongchen111)\ **Post date:** [16 December 2018 11:06 UTC](https://forum.dynare.org/t/the-difference-between-first-and-second-order-solution/12967/3 "2018-12-16T11:06:47Z")
Yes, I know this difference, but I mean, when order=1, the dynamics of the model has no difference between tau\_adj=0 and tau\_adj\>0. ---
**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\ **Post date:** [16 December 2018 11:31 UTC](https://forum.dynare.org/t/the-difference-between-first-and-second-order-solution/12967/4 "2018-12-16T11:31:37Z")
As I said, the first order derivative evaluated at the steady state is 0. If something is 0 at first order, it cannot play a role at first order.