Hi all,

I am currently working on a New Keynesian model which includes the usual macro variables such as output, consumption, investment and inflation also some asset pricing related variables such as a bond, risk premium, bond price and the discount factor.

I would like to compute the second order approximation to get the precautionary savings motive. For now this motive is very small ( I can rarely/not see a difference in comparison to order 1). I was wondering if this is common and if so, is there a way to make this motive stronger (without deviating from a RANK model) ? for example including further assets or using EZW preferences.

For now I use CRRA preferences and habit formation for consumption and capital adjustment costs.

For me it would be essential to first (without proceeding with the actual analysis I want to do) show why second order approx. is important in a New Keynesian model for shock transmissions. I am wondering if there is any modeling trick I could add or if indeed in the NK model for usual technology shocks and so on (no uncertainty shocks) the second order approx. does not play a crucial role. Unfortunately, I could not find a paper writing about the explicit comparison for first and second order in a basic NK model and its implications for the irfs.

Thank you for your help!