# Simulating a model with zero spread

I am trying to simulate a model which features a spread between lending rate and deposit rate. I define the equation for spread as

where `rlhat` is lending rate and `rdhat` is deposit rate. I want to simulate a version of the model in which `spread` is 0. I wonder how to do it? I am not sure I am getting the right results if I just set

rlhat-rdhat =0

because in that case, there is no variable `spread` and how do I plot `spread`, in this case?

I am not sure what you mean. You know that `spread=0` for all periods. It should be easy to plot a zero line.

I apologize, I was perhaps not clear enough. I am simulating a model with deep habits in lending in which case the spread moves significantly (compared to no-deep habits case) in response to a shock, for example, a TFP shock. I want to simulate a version of the model that resembles perfect competition in banking which will mean the spread will be zero. I am confused regarding how to simulate this version of the model.

is the only equation in which the variable `spread` appears. I need to set it to zero and then simulate the model. If I comment out the previous equation and instead set

it will probably be not correct because in that case, I am just setting it equal to 0 and am not telling that model that it is `rlhat - rdhat` that is equal to 0. So I am trying to simulate the model where I can both define `spread = rlhat - rdhat` and then I can subsequently set this `spread` to 0. Please let me know if I make sense.

What I am saying is: if `spread only appears in that one equation, then that equation is essentially the definition of `spread`. If you put in the restriction `spread=0`, this should make your model overdetermined.

Thanks @jpfeifer. As you said, putting both the definition of `spread` and then setting it to zero makes the model overdetermined. Instead, when I remove `spread` from the variables and just set `0 = rlhat - rdhat`, it makes the model underdetermined (more equations than variables). I wonder how I can do it correctly.

You need to approach this from an economic perspective, not a technical one. Which economic feature will set the spread to 0?

I am working with a model with deep habits in lending. When I simulate the model with deep habits on (with parameters governing deep habits different from zero), the spread between lending and deposit rate moves after a shock, for example, a TFP shock. I want to see what happens in this model when banking sector is perfectly competitive. In this environment, it will mean that the spread between lending and deposit rate becomes zero. It is this scenario that I am trying to simulate by figuring out how I can set the spread to zero, leave rest of the model unchanged and then see how other variables in the model behave.

From what you describe, there is something preventing the competitive solution when deep habits are still on.

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