Example of estimation vs. calibration

Question

What's a good example to demonstrate the difference between estimation and calibration?

Edit: I'm looking for something that has the same definition of "calibration" and "estimation" that Krugman uses here (i.e. that they are in some way substitutes):

“calibration” — which basically means tweaking the parameters of your model until it fits some aspects of the data, rather than flat-out estimating the model

Answer 1

Model estimation is the process of picking the best (according to some metric) kind and structure of model. Estimation may include calibration.

Calibration is the process of finding the coefficients that enable a model (the kind and structure of which is already determined) to most closely (according to some metric) reflect a particular known dataset.

So: estimation will set kind, structure and coefficients. Calibration will tweak coefficients, holding kind and structure constant.

Newton's model of motion is fine for most purposes. By calibrating the gravitational coefficient in it, we can make estimates of the mass of the Earth. But it won't work as a model of relativistic motion - that needs the estimation of a different model: there is no recalibration of Newton's model that works for relativistic motion - no coeffecient will work, because the model itself is simply the wrong kind and structure. It omits mechanisms and responses that are absolutely crucial, if the model is to be useful.

Similarly with economic models, Paul Krugman's point is that freshwater economists are saying that their model structures are fine, just the coefficients need tweaking. The problem with that is that if their structures are wrong, no amount of tweaking will make the models useful. Only by going back to basics, and re-estimating the whole model, would they incorporate the crucial mechanisms and responses. He argues that they won't do that, because that would require them to recognise that their existing paradigm is inadequate.

Answer 2

As the edit changed the meaning of the question a little:

What Krugman described is the following process:

1. One wants to model something, like the monetary policy
2. One creates a model and estimates something out of it
3. The results are for some reason not satisfactory, for example, they counter some widely accepted theory
4. Not believing that what was estimated is a correct model, one "calibrates" it (tweaking some variables, assumptions, etc.) until the estimations conform to what one believes is the proper answer

For example, one creates a model to estimate sales of a product in a store at a given day of the year. The forecast for most of the year look plausible, but the estimation looks wrong for Christmas season (for example, the sales are on the similar level as in November, but they should be bigger). One then calibrates the model, perhaps changing or adding some new variables, so the forecast for December will be bigger than the ones previously received.

Answer 3

Calibration is comparing between two measurements - one of known magnitude or correctness, and one we want to be as close to the first one as possible. For example, if we have data on how much given merchandise a shop did sell on a given day, and we want to calibrate a model that will predict the sales, we give past data to the model and compare the given output to the real value (and possibly alter the model to accurately predict the data).

Estimation is approximation of the results, even if we don't have all the data. In the same example, estimation would be asking the model what will the sales be in the future (as we don't yet know what all the variables that will occur from now until the date of estimation).

So in short, you calibrate the model until it works as correctly as you want it, and then you use it for estimating of what will happen in the future.