Dear Dynare’s users,

I would like to ask for your support in helping me to solve an odd welfare ranking result, if possible, please. Check column C of the “Table.png” file (click here).

As you see in the former Table, the Strict Domestic Inflation (-41.754) delivers higher welfare than the one attained under the Ramsey policy (-41.773). Clearly, this goes against theoretical intuition, and consequently, I wonder what could be wrong or explain such an outcome.

“Conditional welfare” numbers are the representative agent’s utility function values at the steady state. Note that the competitive equilibrium steady state is imposed on all the regimes (including that of the recursive Ramsey planner). [The odd welfare ranking outcome does not change if the recursive Ramsey planner regime is imposed on all the regimes instead.]

The model is solved by relying on a second-order perturbation approximation. Therefore, welfare steady states are equal at first-order (-41.507; see column D) but differ in second-order (column E), as expected. In that regard, one would hope that the recursive Ramsey planner optimizes welfare and minimizes uncertainty (at the stochastic steady state) as much as possible. That is to say, the second-order uncertainty term of welfare at the steady state should be the least among all the regimes. However, it turns out that the second-order term of welfare at the steady state under the strict domestic inflation regime (-0.247) is more desirable than the uncertainty constant term reported under the Ramsey planner (-0.266). So, I wonder how could I explain and/or solve this issue.

[Although this recursive Ramsey approach penalizes for any past/present commitment deviation/s, I still believe welfare should be optimal --and not suboptimal, as it’s the case–. Moreover, the planner under this regime yields the best stabilization policy for the economy (i.e., all real macro variables allocations are optimally assigned and have lower volatilities). Even welfare volatility is the lowest under this regime. So, it is curious why the uncertainty constant term is higher under the Ramsey policy].

Conditional welfare is calculated as briefly detailed in image “Welfare.png” file (click here)

In terms of codes, I calculate the respective steady states as

weo = M_.params(strmatch(‘weSS’,M_.param_names,‘exact’))+0.5*oo_.dr.ghs2(oo_.dr.inv_order_var(strmatch(‘we’,M_.endo_names,‘exact’))) % Welfare level under this specific monetary policy regime.

The value for the parameter \beta = 0.99163. But even if I try to multiply the uncertainty constant term by the parameter \beta, I still cannot get a higher value for welfare under the Ramsey planner (in comparison to the rest of the regimes).

Note that this Recursive Ramsey approach (á la Marcet and Marimon, Recursive Contracts | The Econometric Society) is different from the one attained under the Timeless Perspective Approach (à la Woodford).

The *.mod file can be found in this folder (click here).

Any help on this issue is more than welcome.