tag:blogger.com,1999:blog-5908830827135060852.post6997352052350404069..comments2021-12-08T08:42:26.348-05:00Comments on Bond Economics: Empirical Testing Of Macro ModelsBrian Romanchukhttp://www.blogger.com/profile/02699198289421951151noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-5908830827135060852.post-32960175560355315332020-10-20T16:34:21.708-04:002020-10-20T16:34:21.708-04:00differential inequalities, wow, never heard of tha...differential inequalities, wow, never heard of that. I did a bit of optimization, linear programming, basic interior point stuff, etc.<br /><br />In general I don't see much point of statistical regressions in macroeconomics, because by my assessment it only finds very simple relationships between variables. But that seems like all mainstream ever does.Derekhttps://www.blogger.com/profile/11265404998402355578noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-44942793276129769302020-10-20T07:34:48.016-04:002020-10-20T07:34:48.016-04:00You want a solution? The standard practice is to j...You want a solution? The standard practice is to just assume its existence.<br /><br />If we go back 15 years ago, the nonlinear models were largely a red herring; they only dealt with the linearisations. They allegedly have the ability to solve the models numerically, but I’ve not looked that carefully into how this was supposedly being done. My academic work was in nonlinear partial differential inequalities, and yes, they were all intractable. There were a few ways around this, but not entirely satisfying.Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-31938173127232806342020-10-20T03:26:57.931-04:002020-10-20T03:26:57.931-04:00Okay, so I've been trying to dig through how e...Okay, so I've been trying to dig through how exactly DSGE models are constructed, but before we get there, I'm trying to recall everything from my computer science "theory of computation" class, I took years ago, as well as similar courses. I recall specifically, the halting problem(essentially, that you can't determine, in the general case, whether a program will terminate without actually running it), as well as reductions, where you reduce something like 3SAT to another NP complete problem, etc.<br /><br />The point of reductions, If I recall correctly, was not necessarily to solve a problem by mapping it to another domain, although that is possible, but rather to demonstrate, that it is "at least as hard" as another problem, so that you don't expect an overly simplistic answer, as any polynomial solution to an NP problem would demonstrate P=NP. It seems like economists <br /><br />Also, I do recall from my differential equations class that "most" diff eq's lack a closed form solution, about halfway through the course I quickly realized they were giving us essentially all the easy problems.<br /><br />On top of all that, chaos theory dictates unpredictability even for deterministic systems based on a high degree of sensitivity to initial conditions, so any measurement error means that long run outcomes are not really <br /><br />Also, from diff eq, I recall certain problems like the "3 body problem" not having any kind of stable solution.<br /><br />As for some more approachable "simulations", I have played around with cellular automata a great deal, and while conway's game of life may be the most famous, wolfram's 8-bit rules are very simple and very instructive, of the great diversity of structure, that is possible even under simple rules.<br /><br />On top of all that, I would expect society, and not only individuals within society, to function as a "learning system" such that groups and people adapt on the fly to solve problems in new and innovative ways all the time. This perspective would mean that we should not limit our agent behavior to a stable set of rules.<br /><br />Even still, agent simulations, could be instructive for understanding a broad range of possible emergent behaviors, even if it was not compelling as a realistic simulation. Just like one can learn a lot by observing all the possible interactions in Wolfram's 255 cellular automata rules(google rule 30, rule 110, etc), one could gain insights on possible economic phenomenon by observing <br /><br />But this whole notion of performing "statistical fitting" on such models, seems misplaced. The whole purpose of "deep neural networks", for example, is to learn complex relational structure, which is difficult to model statistically, and really does not lend its self to statistical analysis.<br /><br />This whole endeavor seems deeply flawed. One of the most insightful parts of our "theory of computation" class, was it showed us all sorts of unproductive problems we could try to solve, and gave us a taste at the sheer mathematical difficulty of some very hard problems(NP computational classes and beyond). For example, in a compiler, you don't want to try to bake in too much static analysis, because you could easily inadvertently end up trying to solve the "halting problem", in which case your solution would either be likely to run a long time or be outright incorrect.<br /><br />I just don't really expect that economists trying to get mileage out of DSGE's have much sophisticated understanding of theory of computation, tractability and stability issues in dynamical systems, etc. I don't really see the point. Computer scientists don't try to simulate computer systems for a very good reason, they run them and they debug them, at most creating sandboxed tests based on the real thing.Derekhttps://www.blogger.com/profile/11265404998402355578noreply@blogger.com