Payoff Element Types |
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It is now possible to mix calibration and policy elements in optimization payoff files. This makes it possible to do things like adding penalty terms to calibration payoffs that account for priors on model parameters or enforce complex constraints.
There are also several additional subtypes that make payoffs logarithmic, restrict the timing of payoff computation, and use non-Gaussian calibration error assumptions.
The new payoff keywords modify the existing *C (calibration) and *P (policy) options, and can be mixed.
For example:
Note that the extended payoff options are generally not meaningful for Kalman filtering, which assumes Gaussian errors, and will generally be treated like type *C.
Examples
See the examples in OptSensi .
Calibration Payoffs For calibration payoffs, the *C keyword may be followed by a Transform modifier L, and a Distribution modifier, G, K, O, R, or Y. The Transform and Distribution modifiers may be combined, e.g. *CRL computes a robust error metric on log-transformed model and data.
Transform
Logarithmic
Like policy payoffs, calibration payoffs may now use the ‘L’ modifier to take logarithms of the model and data values before computing payoff contributions. Thus a *CL payoff with the default (Normal) distribution computes:
((LN(model)-LN(data))*weight)^2
This provides lognormal errors, rather than the standard normal assumption. The logarithm requires positive values for model and data variables; nonpositive values will be skipped with a warning message.
The log transform should not be used with Kalman filtering.
Distribution
The treatment of the distribution option depends on whether Kalman filtering is active. The filter implementation assumes Normally distributed (Gaussian) errors, and therefore other options like Robust are not appropriate and generally will be ignored. When the Kalman filter is active, the scale or weight parameter is always interpreted as a variance.
Policy Payoffs
For policy payoffs, the *P keyword may be followed by a Transform modifier L, and a Timing modifier, I or F. The Transform and Timing modifiers may be combined, e.g. *PFL contributes weight*LN(variable), only at final time.
Transform
Timing
These options are equivalent to adding a model variable with a timing switch, like:
payoff elm = IF THEN ELSE(Time > FINAL TIME-TIME STEP/2,model var,0)
Note that if you are combining initial or final values with other values, you may need to adjust the weights to compensate for the fact that ordinary values are integrated over the course of the simulation. |