Ramsey policy with constrained agents

Dear users,
I’m trying to figure out ramsey optimal policy using three instruments (monetary policy, sterilization and capital controls) in the context of SOE with constrained households. In the case of unconstrained households, ramsey_policy runs without any problem. however, under constrained households either I get this message: "warning matrix singular to machine precision ", or the command window closes suddenly .
Could any one help me please to undesrtand better the source of this problem?

I would need to see the mod-file. Where exactly does the message come from?

Hi jpfeifer,
I found the problem thank you very much for your response.

However, I have an other question about lmccp, I dont know how to get IRF using this command.

Thank you for your precious help

lmccp is a perfect foresight option. Here, the concept of an IRF is not that well-defined. You would need to construct something like this by running a simulation with a shock and substract the steady state.

Ok thank you for your replay. I’m trying to reproduce the same analysis using the same model as in Uribé paper using dynare macroprudential.pdf (253.9 KB)
I have learned that to deal with collatéral constraint we can study two different environments in which the constraint binds eternally or not at all, is it right ? and so I make two diferent versions of the model uribe_2017.mod (1.3 KB)
uribe_2017_nc.mod (1.2 KB)
the most surprising thing is that the STD. DEV. of the one with collateral constraint are smaller than those of the model without it.
I’m not sure that this procedure is right what do you think about it ? do you have any idea how to solve this kind of model in dynare ?

Thank you alot again :slight_smile:

I am not too familiar with that paper, so I cannot really help you. I only saw that they do not solve the model using perturbation techniques.

Thank you very much dear professor

Dear professor @jpfeifer,

I’m always dealing with the same model and I need your help to understand what’s wrong with my dynare code. I’m using ramsey policy command and I get this
THEORETICAL MOMENTS
VARIABLE MEAN STD. DEV. VARIANCE
ct 0.9601 NaN NaN
yt 1.0000 0.0002 0.0000
R 1.0400 0.0002 0.0000
c 0.9874 NaN NaN
pn 2.1192 NaN NaN
mu 0.0536 NaN NaN
lambda -1.0968 0.0006 0.0000
d 1.0381 0.0003 0.0000
Rf 1.0101 0.0002 0.0000
tb 0.0399 NaN NaN
tho 0.0000 NaN NaN
I’m sure that my steady states are corrects, when I run model_diagnostics(M_,options_,oo_)
I get
MODEL_DIAGNOSTICS: The Jacobian of the static model is singular
MODEL_DIAGNOSTICS: there is 4 colinear relationships between the variables and the equations

I can not identify where the collinearity comes from

ramsey_uribe_2017.mod (1.4 KB)

Thank you alot in advance

You do not use a proper conditional steady state file. If your instrument takes any value different from 0, it does not work anymore.

Thank you very much for your response. I found another way to implement my optimal policy.
However, I wonder if it is correct to assume that collateral constraint binds eternally and to use perturbation methods to resolve the model ? if yes which approximation order is more adequat ?
I’m really sorry to ask a lot questions about that, this is my first time working on such models ( I mean SOE models).
Thank you again and agaaiin !

That question cannot generally be answered. Many papers assume the an occasionally binding constraint is always binding. But whether that assumption is justified is hard to tell and in principle needs to be checked.

Regarding approximation order: that depends on what you are trying to do.

Good morning Professor,
I want to show that there is a welfare loss ( or gain) when the constraint is binding so I have to use the second approximation order according to the existing literature. am I right ?

Have a nice day!

Yes, welfare evaluations generally require a second order approximation.

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Thank you Professor

Just to share the outcomes of my research. For occasionally binding constraint of the form of Schmitt-Grohe and Uribé 2017 and Bianchi 2011, perturbation methods are not useful because of full nonlinearities, global method works perfectly but it’s costly in time and money :smile: because it needs a powerful laptop. I worked on an other model with occasionally binding constraint using Occbin toolkit, it works also, all what you need to do is to apply step by step what is explained in the technical paper. The only thing to be aware about when using Occbin (I believe) is to consider a small wedge between the discount factor and interest rate’s steady state, elsewhere it doesn’t work.
Best

Global methods will be fully stochastic while Occbin in its usual version assumes perfect foresight.

Yes thank you for precising