Calibration (α, β, γ, δ, ...)

I found many values for DSGE parameters in many DSGE books, like (α, β, γ, δ, …) how to get these values, on other hand how to calculate them, I need an example pls


The steady state is a mapping between endogenous variables and the parameters of the model. To calibrate a model, we somehow revert this mapping, expressing parameters as function of steady state ratios. For instance, in the Solow model, we have the law of motion for the physical capital stock:

K_{t+1} = (1-\delta)K_{t} + I_t

at the steady state we must have:

K^{\ast} = (1-\delta) K^{\ast} + I^{\ast}
\Leftrightarrow K^{\ast} = (1-\delta) K^{\ast} + I^{\ast}
\Leftrightarrow \delta K^{\ast} = I^{\ast}

hence we know that the depreciation rate must be such that:

\delta = \frac{I^{\ast}}{K^{\ast}}

If you have long time series on physical capital and investment you can then calibrate the depreciation rate with average of the investment/capital ratio. Not all the parameters can be deduced from steady state considerations, since not all parameters will affect the steady state (rigidity parameters for instance). In this case you will have to consider other moments to calibrate these parameters.


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Thank you so much Stéphane

So, for example I can get or calibrate the depreciation from local time series data, and the same for others parameters based on economic theory. For instance Consumption Function

C = a + by

but the question is if there is no way to calibrate the parameters, what should I do.

I can suggest and values based on other researches, but the most important thing is how to calculate this values by myself.

Thanks again Stéphane

By the way How can I type the equations like in your reply