News Shock in Deterministic NK model with a ZLB

[Ned]

Hello everyone.

I am currently working on an NK model under the effects of a zero lower bound, trying to see the effects of fiscal policy on the multiplier. In the benchmark version the government spending shock is an AR(1) process taking the form

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g_t = rho_g * g_t(-1) + epsilon_g

I have assumed that the ZLB binds for 12 periods and so does the fiscal shock. If I want to model this shock as an anticipated news shock (4 periods before the actual shock) of government expenditure I will have to set it like

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g_t = rho_g * g_t(-1) + epsilon_g(-4)

This gives me an initial increase in output and an expected second one which is really mild and as a result I get a lower multiplier than in the case of the unexpected shock. The news shock dampens the effect of the multiplier or am I missing something? Furthermore, how can I make the news shock and another surprise shock have an impact on output? I was thinking something like below but I get the same results as if I only had one unexpected shock at time t=0.

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model;
g_t = rho_g * g_t(-1) + epsilon_g(-4);
s_t = rho_s * s_t + epsilon_s;
end;

shock;
var epsilon_g;
periods 1:12;
values 0.1;

var epsilon_s;
periods 1:12;
values 0.1;

var epsilon_e, epsilon_s=0.05;
end;


Also, I arbitrarily set the 0.05 relationship of the second shock. Am I supposed to do that or is a more refined way?

Thank you all in advance for your answers. I am also providing my .mod file.

[jpfeifer]

I am not sure I understand what you are trying to do. Your code in the forum post seems to be using a weird mixture of stochastic and deterministic syntax (in contrast to the attached mod-file). It is rather complicated to implement "news shock" in deterministic perfect foresight simulations of the type you are conducting. The reason is that all shocks are perfectly anticipated. If you set a shock to happen in period 4, this shock will be perfectly anticipated for four periods.

Note also that

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    var epsilon_g;
    periods 1:12;
    values 0.1;


will give a sequence of news shocks for epsilon_g, the first shock of 0.1 happens in the first period and is not anticipated. Then there is a new shock happening in period 2, which is anticipated for 1 period and so on. Thus, there is a new shock in every period. I don't know if this was intended. More common would be to specify g_t as an exogenous variable and let this change jump one and stay at this new level for a longer period of time.

[Ned]

Dear Johannes,

thank you so much for your prompt reply. The main goal of the code was to monitor the fiscal multiplier under interest rates governed by a Taylor rule (dummy_mp=0) and under the ZLB (dummy_mp=1). I wanted to set a predefined period of the ZLB, in my case 12 periods, to explore the effects of government expenditure under different timings. That's why I modeled the government shock having an effect for 12 periods, or at least I was planning to do that. I had in mind a really aggressive fiscal expansion taking place for the full duration of the ZLB. I do not know if it is modeled correctly though.

Furthermore, I wanted to check if the multiplier would alter and by how much if we had a news shock of an expansive fiscal policy mixture in the future. I understand that this would be difficult in a deterministic setting but would Matlab give me a measurable output of...output in a stochastic setting so as to define the multiplier (I am saying so because the way I measured the multiplier in the deterministic model was by taking the series of output over the series of the actual shock in the oo_ file) ?

When I run the stochastic version of the model I get IRFS which make sense but everything changes when I try to do the following things:


1)Firstly, when I try to model the AR(1) government spending shock as a "news" shock, such as

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g_t = rho_g * g_t(-1) + epsilon_g(-4)

I get an IRF showing that output falls under zero at time t-4, ascending up until t-1 and then decreasing at time t=0. Is it plausible? Does it have to do again with the perfect foresight of the agents?

2) When I try to model the Taylor rule as:

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i_t = rho + e_t

wanting to impose the ZLB I get

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There are 3 eigenvalue(s) larger than 1 in modulus
for 4 forward-looking variable(s)

The rank condition ISN'T verified!

3) When I try to set the dummy variable equal to 1, I get the same IRFs plus one figure which only accounts for the dummy shock. How am I supposed to impose zero interest rates for a given amount of periods in a stochastic version of the model?

4) When I try to change the stochastic simulation to a deterministic one, I get strange results.

Forgive my large reply and my amateur approach in general. I am fairly new to MatLab. Please find attached the stochastic version of the NK model I'm working on.