misspecified model

[gazzani.andrea]

Hello everyone,
I am trying to solve a model with borrowers, savers and enodogenous collateral constraint but it is not working.
Does anybody has any ideas about why this model is not well specified? I keep getting indeterminacy and it seems that I am missing one eigenvalue bigger than one and that this fact does not depend on the parametrization.
These are anyway the parameter I am using at the moment:

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theta = 0;
beta_d = 0.9925;
beta_b = 0.988;
rho = 0.9;
m = 0.7;
delta = 0.1;
j = 0.12;
sig_ez = 0.01;
mi = 0.5;
epsilon_d = 0.66;
epsilon_b = 0.97;

Thank you very much

[jpfeifer]

Often, it's about the timing of variables. Why does the stochastic discount factor definition feature a (-1)? Moreover, do all stocks follow the end of period notation?

[gazzani.andrea]

Thank you for your reply

If I am not mistaken Lamba = beta*lambda(+1)/lambda written Lamba = beta*lambda(+1)*lambda^(-1)

I guess I am using the right notation but of course there might be errors I am not able to spot. Anyway there is no time to build so it should not be to hard to make it right.

I spotted some typos and made some modification but the problem with eigenvalues is the same nonetheless..

I am posting it toghether with the parametrization..

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theta = 0.75;
beta_d = 0.9925;
beta_b = 0.988;
rho = 0.9;
m = 0.925;
delta = 0.1/4;
j = 0.01;
sig_ez = 0.01;
mi = 0.5;
epsilon_d = 0.97;
epsilon_b = 0.66;
sigma = 6;
phi = 1.5;


save parametervalues j sigma phi theta beta_b beta_d rho m epsilon_d epsilon_b mi theta delta sig_ez

[jpfeifer]

Sorry, I did not spot the ^. So the stochastic discount factor is correct. However, your timing is not always correct. I think

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H = h_d + h_b;


should be

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H = h_d(-1) + h_b(-1);


as this would be the housing stock available at time t

[gazzani.andrea]

For what I have understood the timing should be given by the period in which the variable is determined. Without time to build housing (h) is determined at time t so it should not have any lag..Am I correct?

[jpfeifer]

What do you mean with time to build? In Kydland/Prescott's paper it refers to a lag larger than one period.

Usually, you have a law of motion and a production function

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k=(1-delta)*k(-1)+i;
y=k(-1)^alpha*l^(1-alpha);

In this case, capital is predetermined. It gets the timing when it is determined by investment. However, production takes place using the capital determined in last period.

In your code, you have something like

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h_b - (1-delta)*h_b(-1)

suggesting housing is predetermined. However, if you have two housing stocks that are predetermined (a law of motion for each) and you define an aggregate housing stock H to be able to plot it, H is just a definition and thus gets a contemporaneous timing. At time t it is the sum of the the two predetermined stocks.

Note also that it is different, if you only assume one capital stock that can be divided into two within the period: http://www.dynare.org/phpBB3/viewtopic.php?f=1&t=3564

[gazzani.andrea]

I agree with you. What I meant is that housing (both individual and aggregate) is decided at time t and it is operative at time t..so I guess that

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H = h_d + h_b;

is correct..