Hi.

In many DSGE models we use quarterly time series but some information of the model for calibration are in annual rates.For example depreciation rate or average annual steady-state interest rate.

I want to know how we can convert annual interest rate to quarterly rates ?

For example suppose that in the calculation of discount factor \beta average annual steady state growth rate is 5 percent. How we can convert this rare to quarterly interest rate ?

Can we employ the following formula?

1.05=(1+r)^4

1.05^{0.25}=1+r

Then we can calculate discount factor.

\beta=\frac{1}{1+r}=\frac{1}{1.05^{0.25}}

Another problem is calculation of quarterly depreciation rate with annual depreciation rate.

Suppose that annual depreciation rate is 10 percent. How we can calculate quarterly depreciation rate ?

Can we use the following formula?

1.1=(1+\delta)^4

1.1^{\frac{1}{4}} -1 = \delta

and \delta is quarterly depreciation rate.