MockMarket and Usual Expectations syncing on Lucas Expectations

[sbenthall]

A test case where:

• The HARK agents are ex ante homogeneous on $\beta$ and $\rho$, and zero variance income shocks.
• The MockMarket is calibrated to Lucas pricing given:
  • Population ex ante $\beta$ and $\rho$
  • Dividend process statistics
• HARK agents have USUAL expectations calibrated the same way as the MockMarket

Test for:

• Results being identical to the analytical Lucas results.

Note that in this case, the agents have no market power. This is pre-established harmony between the market and the agents.

(It may be of interest how the ex post heterogeneity of the agents is affected?)

[sbenthall]

@alanlujan91 let's work on this together

[sbenthall]

Need to pass in $\rho$ and $\beta$ as command line arguments, then pass these to a Lucas population generator, as well as to the formulae for price dividend ration and usual expectations.

[sbenthall]

If $C$ is the price to dividend ratio, $G$ is the dividend growth rate, and $Z$ is the lognormal mean 1 shock to the dividend each period, then the random variable that characterizes the returns on the risky asset is:

$\frac{C + 1}{C} G Z$

with mean $\frac{C + 1}{C}G$ (RiskyAvg) and standard deviation is $\frac{C + 1}{C}G\sigma_Z$.

We can compute this with the formula for $C$ given $\rho$ and $\beta$.

[sbenthall]

Solution to this merged but needs https://github.com/sbenthall/SHARKFin/issues/193 to show it's done...