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Dynamic model calibration of rate parameters

Economics Asked on May 16, 2021

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):

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

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.

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