I’ve been in a headache for this problem for quite a while, which i couldn’t find out the solution by any means.
I’m now writing an article about housing market,using DSGE models.
I found it necessary to devide firms into two distinct sectors :comsumer goods and residential goods ,so there is an equation,Y=YC+YH.Here YC stands for output from consumer goods sector,and YH stands for output from residential goods sector.
After log-linearasation,it transformed into this:Ybary=Ybaryc+Ybaryh.
So how can i put this equation into dynare?
Should I write the code as:
Ybary=YCbaryc+YHbaryh ?
if i write the code as above,how can i give the initial value of Ybar,YCbar and YHbar which are the values of steady date,and which i have no idea at all ?
I’m looking forward for your help,thanks a lot!!
Indeed the log-linearised form is: Ybary=YCbaryc+YHbar*yh ^(note that the first time you write it in your question you write it wrong!). Note that this is equivalent to:
y=(YCbar/Ybar)*yc+(YHbar/Ybar)*yh
so that total GDP is some weighted average of the output in the two sectors (since by definition at steady-state we have Ybar = YCbar + YHbar) with the weights being the shares of each sector to output (YCbar/Ybar and YHbar/Ybar). From your model, you should have an idea what these ratios are so you could give initial conditions accordingly. However, as it is explained in the manual, initial conditions are tricky and there is not really a “rule” as to what makes a “good” initial condition. Its basically “trial and error” and luck.
Personally, I prefer to solve the steady-state by hand and put the log-linearised model into Dynare. That gives you more control and you don’t have to worry about initial conditions since by definition all variables are zero at steady-state (since they are expressed in deviation from the steady state).
Hope that helps.
Kyriacos
dear Kyriacos,
Thank you so much!! I really appreciate your help!
You are right ,maybe the best solution is to solve the steady-state by hand,but right now i’m just not that skilled.So maybe i should come up with an intial value .But here comes another question ,what if the innitial value is far from the steady-state solved by dynare ?and what if they’re close?
Besides,the equation i put in my question was a simple one ,there is another type of equation i don’t know how to deal with:
Cbarc+qbarhbar*(q+h(+1))-qbarhbar(1-delta)(q+h)+rbarbbar（r(-1)+b(-1)-pi)=bbarb+wbarlbar*(w+l)
this loglinearized equation comes from the eqution below:
c+q*(h(+1)-(1-delta)*h)+r(-1)b(-1)/pi=b+wl
this is the constraints of household department.c stands for consumption,q stands for the real price of residential goods,h stands for the quantity of houses owned by household department.,r stands for intrest rate of a loan,b stands for a loan ,pi stands for the inflation rate ,w stands for salary,l stands for labor.
Could you please give me a hand? i’m really grateful for your help!!
Looking forward for your reply!!