Optimal fiscal/monetary policy - NK with consumption tax

[Andreas]

Hi everyone!

I’m new at DSGE modeling and Dynare and have run into a problem that I cannot find an answer to. I am trying to model fully optimal Ramsey policy in a standard New Keynesian log-linearized model with additional consumption taxes (so the policy instruments are nominal interest rate, labor income and consumption taxes). However, as soon as I implement the government budget constraint with both taxes, I get various error notifications ranging from Schur decomposition and Eigenvalues close to 0/0 to Blanchard Kahn conditions depending on how exactly I specify the model. I have read all posts I could find in this forum on each error message and I assume that some specification I am using is redundant – there is quite some collinearity when I run diagnostics. I also strongly believe that it is connected to the evolution of government debt but I just cannot figure out what is wrong with the model setup. Do I need to add any constraints to the GBC as it is now? I would greatly appreciate any specific help or suggestions what I might look into to figure things out.

Thanks in advance!
Andreas

[kyri82]

if you have colleniarities, then I would say that most likely you have an equation, a contraint, that is redundant. So, I would think you might need to remove equations instead of adding any. Make sure your model is well specified before you put it on Dynare.

[Andreas]

Thanks for the prompt reply! I was thinking that, too, but I cannot figure out where exactly this redundancy might occur. I assume it must be the government budget constraint. In a very stripped down version of the model with only lump-sum taxes financing exogenous government spending (i.e. no need for bonds), I get the same kind of error messages. Could there be an equation/constraint missing (possibly instead of the government budget constraint) that further specifies bonds or the fiscal instruments? Interestingly, when I take a small bond adjustment cost into the loss function (in the stripped down version), everything seems to go smoothly and the policymaker uses the lump-sum taxes instead of bonds, which is intuitive, only that now the model is specified without collinearity. Similarly, everything works with explicit rules for the policy instruments, which makes me think that I am overlooking some kind of additional condition/constraint either in addition to or instead of the GBC.
Any ideas whether something similar could be the root of my problem in the bigger model? More generally, is there anything to beware that I might have overlooked when modeling the government budget constraint and fiscal instruments?

Just for reference, the simple model:

[kyri82]

is it a closed or open economy model?

[Andreas]

It is a closed economy. The Ramsey planner can set nominal interest rates, consumption tax, and income tax. G is exogenous.

[kyri82]

I am not sure I can help you, but be careful on the ratio G/Y. If it is exogenous, make sure it is not too high. Remember that Y = C + I + G. Otherwise, I know that there are some determinacy issues that are solved with small adjustment costs in the contexts of Small open economy modes:
http://public.econ.duke.edu/~grohe/rese ... ng_jie.pdf

Good luck!

[Andreas]

Thanks for the suggestion! I incorporated portfolio adjustment costs as in SGU2003 in the linearized model but continue to receive the same error messages. Also, it still runs smoothly as soon as I add bonds to the loss function, which makes me believe that there continues to be a determinacy issue with 3 variables to be optimally chosen and bonds acting as a kind of residual in this case. I will next try to implement a nonlinear version and solve for the steady state but I am doubtful whether that would solve the underlying problem.

Does anyone have any other ideas? I am enormously grateful for any kind of help.