What is the difference between identification, calibration and estimation? In fitting theoretical models to data, what is the difference between identification, calibration and estimation?
Identification and estimation are often used interchangeably (at least that’s my observation from attending conferences and reading papers) but according to econometric literature there is a subtle difference.
For example, in the John Stachurski &quot;A Primer in Econometric Theory&quot; the identification is a process of finding out if the parameters are identifiable and identifiability is defined as

“Identifiability means that the parameter vector associated with the unknown distribution can eventually be distinguished from the data.”

I will omit all the other formalism that follows but in essence we can say that parameter is identified if the map from the parameter space to the space of probability distributions of observables can be inverted.
The estimation is actually the process of calculating what the actual parameter $\hat{\beta}$ is.
When it comes to calibration in forecasting it is the comparison of model estimates to actual data with an aim to improve the model fit.
In macroeconomics it is a strategy for finding numerical values for the parameters of artificial economic worlds. A model is calibrated when its parameters are quantified from casual empiricism or unrelated economic studies or are chosen to guarantee that the model mimics some particular feature of the historical data. In other fields it might have different uses as well.