# Dynamic model calibration of rate parameters

Let's say I have this dynamic model where $$\delta$$ is the depreciation rate of capital $$K_t$$:

$$K_{t+1}=sY_t+(1-\delta)K_t$$

Now, if I'm going to make some analysis where I state time $$t$$ as being in years, and I decide to calibrate my model with some bibliographical reference that propose that the value of depreciation rate is, say $$0.01$$ monthly. Given that I structured my model as being in annual periodicity, I could use financial mathematics formulas of rate conversion to get this rate from monthly to annual (given that this is a compounded rate):

$$\delta_{annual}=(1+\delta_{monthly})^{12}-1\implies \delta_{annual}=(1+0.01)^{12}-1\approx 0.1268$$

Then, I might use $$0.1268...$$ as my model's depreciation rate for capital in annual periodicity. Is this right and keeps the necessary rigorousness of economic analysis standards or is there another way it should be done?

PD: I'm conscious that the exponent of the formula really depends on the month we're at (say January should be really 31/365, if this year is not leap, etc.), but since overall any given year always have 12 months in our current calendar system, I assume the power of 12 to be a good approximation.

• Hi: given the model and, if you have data for $K_t$ and $Y_t$, you can estimate $\delta$ if you wish. ( I can show how to do that in an answer if you want ? ) Otherwise, if you want to use the number given by the authors. your approximation regardlng leap years etc should be okay. – mark leeds Jan 30 at 17:20