How to select parameters for estimation?

There is no hard rule. But it’s quite common to calibrate parameters that i) are not well-identified from the data and ii) where we have a good idea what the parameter value is. An example are the discount factor and the depreciation rate. They are often not well identified from cyclical moments but can often be set to to sensible values based on long-run averages for the investment to capital ratio and the long-run interest rate. The risk aversion parameter is another example. There is good micro evidence to set its value.

In contrast, we have no good idea how the TFP process looks like. That’s a good reason to estimate it.

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