Estimating and driving the DSGE model

We know that DSGE is a Euler equilibrium system that sets the Euler exponents based on regressions between the aggregate data and the model. The causes of variance in the model is simply that agents do not operate with Euler's number, but instead operate with an approximation of it.  We can specify the approximation error by the polynomial order of the agents estimation, as I have done on the right. And we can see that DSGE is useful, a bit, when the estimation order is above four.

How do agents estimate euler's number? Well it is mostly done in metropolitan districts where most of the economy occurs and where exchanges and trade is most stable. The typical case is the USA where DSGE is an aggregate model of the government and central banking function in DC, while the consumer is assumed to be an economy wide model. But the actual data generated is really the outcome of citywide trade.

Now the estimation order is about 3-4 for metropolitian districts, I know because Richard Florida does good work and his bubble chart has a very good distribution of cities that maps my estimation of geography.  He really has about 3-4 bubbles sizes in that chart, and that is likely a good entropy based grouping of city economic function.

I am putting his chart up again because I am starting to really like his work.

 And you can see that taking the top four bubble sizes will really capture the stable portion of the economy.

So, how do these cities adapt to the foibles of state and federal government?  They most survive and send the state and federal governments into debt. They do this by changing their estimation of euler, to a lower numbers in sensible acts of nullification. So federal and state politicians end up making really unsound assumptions about the elasticity of the agents.

We can see how to fix the DSGE model. Make it a bit simpler, then derive the Euler exponents.  Then replace Euler with the approximation, using the Lucas polynomial value of x works because the cities are likely a Lucas sequence, they are internally connects and optimally adapted in real time.

The California example.

In California this adaptation system is very advanced.  As soon as the legislature appears, anywhere near public sector labor unions, the cities slow down their hiring. The California legislature gets the idea real quick.  Our cities learned this technique with No Child Left Behind. They set up the virtual lunacy buffer and they activate it as soon as some bonehead program arrives from DC. And we  can see that the public sector suffered about a 8% swing in employment during the recession. That would be the fourth order estimation of Euler plus the lunacy buffer.

A quick summary of the logic used here.

The cities are self adapting, they maintain their own stability. The are the bulk of the economy. So we can assume they are minimally redundant and spread their precision among their connected components fairly.  So, with their bubble size being probability of transaction, in the chart above, they will obey the -iLog(i) law in groups. The connected group seems to be  fourth order. So, all these put together we can estimate that their elasticity, flexibility, is a fourth order power series. That power series will be a compact representation, and by duality, therefore, it will match any other copact representation of elasticity. E Euler is a fixed point estimate of elasticity and its compact polynomial is:
1.0 = n*(e^(1/n)-1), which we can get from a number of derivations.

It is really as simple as that, and its going to work.