Originally posted by telerion I'd have to look at their specific model, but dimension itself doesn't have to be the limiting problem if the policy function can be well-approximated by only a few grid points in any dimension. After all if everything is linear even 2^20 is peanuts on a computer.
My job market paper had quite a few dimensions in the value function and policy rules: t ...[text shortened]... oximate well (where as personal wealth needed something like 500 smartly chosen gridpoints).
I'm pretty sure that with two wealth dimensions, that problem will tend to arise very quickly. Add retirement and there's another very non-linear moment, etc.
Anyway, that's all well and good, but it actually goes to my point that computational issues shouldn't be THAT important when the amounts involved in healthcare reform are gigantic.
Originally posted by Palynka I'm pretty sure that with two wealth dimensions, that problem will tend to arise very quickly. Add retirement and there's another very non-linear moment, etc.
Anyway, that's all well and good, but it actually goes to my point that computational issues shouldn't be THAT important when the amounts involved in healthcare reform are gigantic.
I don't understand. The amounts involved in growth models are huge too, but computational problems arise. In the end we both know that the models that are produced any time in the near future are going to have to restrict themselves to certain aspects of health reform if they hope to a micro-founded model that is sufficiently detailed in terms of decisions.
Are you saying that things probably aggregate up well so maybe a stylized representative agent model could do a sufficiently good job (in which case I agree that computation likely isn't too hard)?
Originally posted by telerion I don't understand. The amounts involved in growth models are huge too, but computational problems arise. In the end we both know that the models that are produced any time in the near future are going to have to restrict themselves to certain aspects of health reform if they hope to a micro-founded model that is sufficiently detailed in terms of decision ...[text shortened]... uld do a sufficiently good job (in which case I agree that computation likely isn't too hard)?
Of course not, what the heck made you think I believe things aggregate nicely?
By amounts, I mean real funding. How much does a government value a better understanding of health care reform? The cost of a few uses of a good supercomputer are almost negligible. How many dimensions of heterogeneity are that relevant? Most of the non-standard in KS-type models would not even be in a continuum, and more standard KS-type models can easily be ran in laptops these days.
Anyway, this is not relevant for this topic.
Edit - And to be clear, my original point is that I don't think the limitation is computing power, but the lack of a convincing theoretical model of healthcare, that could be built upon.
Originally posted by Palynka Of course not, what the heck made you think I believe things aggregate nicely?
By amounts, I mean real funding. How much does a government value a better understanding of health care reform? The cost of a few uses of a good supercomputer are almost negligible. How many dimensions of heterogeneity are that relevant? Most of the non-standard in KS-type mod ...[text shortened]... power, but the lack of a convincing theoretical model of healthcare, that could be built upon.
One problem -- suppose we could somehow come up with a strong enough computer, and a computer program that would be able to accurately assess all of the many variables that any plan for healthcare reform would involve. I fear that you'd end up with "butterfly effect". A very small variation in your inputs would probably lead rapidly to widely diverging results.
Originally posted by Melanerpes One problem -- suppose we could somehow come up with a strong enough computer, and a computer program that would be able to accurately assess all of the many variables that any plan for healthcare reform would involve. I fear that you'd end up with "butterfly effect". A very small variation in your inputs would probably lead rapidly to widely diverging results.
It's very possible. Just depends upon the stability of the system within the relevant region. Without having any idea what the model might contain, it is entirely possible that the whole system is sink-stable so that every combination of input leads to the same long run outcome. We can only speculate.
Originally posted by Melanerpes One problem -- suppose we could somehow come up with a strong enough computer, and a computer program that would be able to accurately assess all of the many variables that any plan for healthcare reform would involve. I fear that you'd end up with "butterfly effect". A very small variation in your inputs would probably lead rapidly to widely diverging results.
To add to telerion's remark, this can be also be an issue because a system with too many parameters to estimate may provide unstable estimators. If the degrees of freedom are very large then it's easy to have a model that fits the sample very well but that forecasts very poorly (and so was mistaking goodness of fit with correct model specification).
Will the real Paul Krugman please stand up?
04 Sep '09 18:53
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