Hi,

I’m working on a model with money, in which I take the ‘money in utility’ form to construct my model. (U=…+gamma*log(M/P)+…)
It naturally gives a F.O.C. in the form of:
gamma/(M/P)=C^(-signa)*(i/(1+i))

Then during the process of log-linearization, the right side of the equation would be transformed into an expression with log(i/rho) (where rho is the steady-state interest rate).

(I define I=log((1+i)/(1+rho)) (in the traditional way), so approximately I=i-rho.)

Then using log-linearization, we can write down:

log(i/rho)=log((I+ rho)/rho)=log(1+I/rho)

We can fairly say that log(1+x)=x when x is small (|x|<0.1), but in this situation, I/rho would be in the interval [0,3] in the normal shock size, which absolutely does not suit for Taylor Approximation. (eg. log(1+3)=1.39<<3)

However, it seems that we have to use Taylor Approximation in Dynare, which would lead to bad accuracy. Even if you use higher order, it only makes the approximation worse, because using the Taylor Approximation

log(1+x)=x-x^2/2+x^3/3+…+(-x)^n/n+…

when |x|>1, this series just explodes…

I was wondering if you can help me solve this problem…