Dear Professor Pfeifer,
I read that sometimes a parameter is added in households’ untility function as a scaling fator of consumption, such as GAMMA_C in
Any reply will be appreciated. Thank you so much.
Hi Issp1,
In this specification of preferences, \Gamma_c=(1-\varepsilon) is a shift term which normalizes the consumption term in the utility function to ensure that in the steady state the marginal utility of consumption does not depend on the habit stock.
Habits in consumption are a standard form of real rigidities, just like, for instance, capital adjustment costs, and it is sensible to devise them such that they are switched off in the steady state and kick in only in the dynamics, so as to avoid unnecessary distortions in the steady state but obtain some desirable degree of sluggishness in the business cycle.
The \Gamma_c term serves precisely such purpose.
For this reason, I would suggest against eliminating it, unless you have some specific economic rationale for distorted consumption in steady state
Apart from the reason @cmarch mentions, you sometimes need parameters like this to govern the relative weight of consumption and leisure (and housing) in utility. If you leave it out, you are imposing equal weight (which may not be desirable to match steady state targets)
Dear Mr. Marchesini,
Thank you so much for your nicely reply. I really appreciate your kindness.
Dear Professor Pfeifer,
Thank you so much for your supplement. It is very kind of you.
