14/n So, the greatest benefit of writing and solving HA models is to figure out what to do when a BIG crisis hits. We are already well-equipped to deal with average recessions! So, new methods are only useful to the extent that they can solve complex models accurately for BIG shocks. - ThreadSky

fatihguvenen.bsky.social • 15 days ago

14/n So, the greatest benefit of writing and solving HA models is to figure out what to do when a BIG crisis hits.
We are already well-equipped to deal with average recessions!

So, new methods are only useful to the extent that they can solve complex models accurately for BIG shocks.

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patricksecon.bsky.social•15 days ago

💯

fatihguvenen.bsky.social•15 days ago

15/n Are linearization-based methods accurate for such large deviations? Note that even Krusell-Smith is a "local" solution method, valid only near the steady state (inside the ergodic set).
How big are the discrepancies of linearized solutions from the “true” solution? I’d love to see the answer.

fatihguvenen.bsky.social•15 days ago

16/n A partial answer is provided by Terry (JMCB, 2017) who compares KS to Reiter for varying degrees of counter-cyclicality of firm-level shocks (see figure):

For larger values, the linearized solution is both quantitatively AND qualitatively moving in opposite direction of the true solution.

fatihguvenen.bsky.social•15 days ago

17/n Problem is that 3 to 5 sigma shocks are so rare under Gaussian shocks that most solution algorithms effectively ignore them (they are rarely realized in ergodic set solutions).
But in reality, they occur much more frequently because aggregate shocks in data have a longer tail.

fatihguvenen.bsky.social•15 days ago

18/n Suppose we keep developing more and more methods based on linearization that get so complex that we can never solve those models through more accurate methods. We may never know how accurate or inaccurate our solutions are since we will have no benchmark to compare them to.

fatihguvenen.bsky.social•15 days ago

19/n I know that some colleagues are working to introduce second-order terms into these models but I don’t know if any of them has answered the questions raised above about accuracy for large shocks.

fatihguvenen.bsky.social•15 days ago

20/n Famously, the 2010 JEDC special issue on post Krusell-Smith models included one method that took less than 1 second to obtain a solution compared more 7 to 300 minute for other solutions. But it was so inaccurate that it looked nothing like the true solution (Den Haan (JEDC, 2010))

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