Hi,
I would like to compare the unconditional welfare between two different models where model A has an extra sector compared to model B. Contrary to optimal policy studies, in this case the two steady states cannot be harmonized, so I guess looking at consumption equivalent between the welfare (defined as recursive utility) in model A compared to model B is not correct. At the same time, simply comparing oo_.mean(W) between the models seems wrong, because model A has a higher SS consumption by construction.
Any ideas on how to do this?
Many thanks
There is no general answer. What exactly do you want to compare, i.e., what is the economic logic that you want to analyze?
I am comparing an economy B where borrowers can get financing from banks with an economy A where they can get financing from both banks and non-banks. More SS credit in economy A leads to more SS investment, output, consumption and welfare as a consequence. But the structure of the model does not allow to come up with shortcuts to make the two steady states to coincide.
That does not answer my question. Are you analyzing the effect of introducing banks? In that case the shift in the steady state is part of the economic effect and should be reflected.
Yes, I am analizing the effect of introducing non-banks. I agree that the shift in the steady state is part of the economic effect, but I am looking for an alternative measure to quantify this effect, since I guess consumption equivalent cannot be the solution here.
Consumption equivalent is just a different way of expressing welfare differences. That approach would still be valid here. You can compute how much of the steady state consumption in the regime with banks agents would be willing to give up to obtain the same unconditional welfare level as without banks. That number will incorporate both the steady state effects as well as the stochastic effect.
Thanks, I see your point. Could it be that there are errors in my .m file that calculates welfare? It seemed to me to be correct, but the results in CE are clearly wrong.
model_nosb_test.mod (8.5 KB)
model_nosb_test_steadystate.m (3.5 KB)
model_test.mod (9.6 KB)
welfare_test.m (1.0 KB)
model_test_steadystate.m (4.2 KB)
Your welfare levels have huge differences. That will of course be reflected in the consumption equivalent. It don’t think the computation itself is wrong. I would also recommend to use theoretical instead of simulated moments:
model_test.mod (9.6 KB)
model_nosb_test.mod (8.5 KB)
Many thanks. However, shouldn’t be consumption equivalent variations bounded at 100%? Getting 2.7130e+04 would still make me think that there is a mistake in the computation.
My guess is that the formula
CEP_gain = (exp((1-betap)*(valp_con - valp_nosb_con))-1)*100
is wrong. How did you derive it? Shouldn’t there by logs somewhere?
This would be my derivation. Does it make sense?
welfare_test.m (1 KB)
The way you set it up with \lambda giving the additional consumption required in regime B to get to the welfare in regime A, the regime A with the higher welfare should be first in the difference. You will obtain
CEE_gain=1+lambda=429.8231
which means that you need 4.3 times the consumption of regime B to be indifferent to living in regime A.
Yes, I guess that Wa-Wb needs to be negative so that the exponential function of a negative number is bounded between zero and one, while exp^(Wa-Wb) explodes if Wa-Wb is positive and large. But even doing that as you said the welfare differences are so huge that you would get -99.99% most of the times.
