# BK conditions and Walras law

Hi,

relying on Walras law, I imposed only n-1 market clearing equations in my mod file for solving my model with Dynare, because the n-th market clearing condition is implied by the others n-1 market clearing conditions.

However, I found out that when I do not impose market clearing on the bonds market in my model, but impose all other market clearing conditions, the Blanchard Kahn conditions are no longer satisfied, whereas they are satisfied when I do not impose any of the other market clearing conditions. I find this really weird, because the market clearing condition on the bonds market in my model should be satisfied even though I don’t explicitly impose this condition in the mod file, and the Blanchard Kahn conditions should be either never satisfied, either always satisfied, whatever the market clearing condition that I don’t include in the Dynare file.

So I am wondering if this weird result reveals something wrong about my model ? In the cases when the Blanchard Kahn conditions are satisfied, everything seems right, and I used the model_diagnostics command in both cases, and nothing wrong is detected. So I really don’t understand what’s going on.

Thank you very much for any help with that

Hard to tell without the model.

1. For government bonds, the problem can be the distinction between lump sum taxes and bonds, which is not unique when Ricardian equivalence holds. The market clearing condition may then impose an unspecified assumption about the split between taxes and bonds.
2. For private bonds, it may be that the aggregate market clearing conditions do not actually imply anything about the distribution of bonds between individual private agents. In that case stating that bonds are in 0 net supply may be necessary.

In my model, bonds are private bonds. Bond supply is provided by patient households, and both impatient households and firms buy bonds.
Therefore, the market clearing condition on the bonds market is :

B_t= B_{t,I}+ B_{t,F} where B is bond supply, B_I is bond holdings by impatient households and B_F is bond holdings by firms.

Stating that bonds are in zero net supply is an issue in my model, because bonds’ supply is endogenous and debt dynamics is one of the thing I aim at replicating. Iacoviello (2015) has a similar setting and he does not assume that bonds are in zero net supply.

Does the fact that the Blanchard Kahn conditions are not satisfied when I do not include the debt market clearing condition means that the model’s simulations results when including the debt market clearing conditions (with the Blanchard Kahn conditions then satisfied) are irrelevant ? The market condition which is not included is satisfied in the simulations, which suggests that the Walras’ law applies in this case.

Thank you for any help

Or maybe setting

B - B_I - B_F = 0

is what you call setting bonds in zero net supply ? I didn’t pay attention to the “net” in the first place

Yes, that is what I meant with 0 net supply. How did you stationarize bond holdings? I.e. what makes sure that bonds return back to steady state instead of agents just consuming the annuity out of their additional savings?

Bonds are one-period bonds, providing payment to the lenders only in the next period, and borrowers can only borrow up to a limit defined by collateralized borrowing constraints.

That is no answer to my question. In e.g. small-open economy models you need something to assure stationarity of debt positions as well. I infer that in your case that seems to be the multiplier on the borrowing constraint that goes up and provides an incentive for moving back?

Are you sure that

is implied by the other market clearing conditions? Because this seems to be a condition saying that there is no access to international bond markets so that borrowing can only work between agents.

Thank you. I indeed think that this is the increase in the Lagrange multiplier that provides incentives for debt returning back to steady state. When I look at the response of debt positions following shocks in my model, they ultimately go back to the steady state.

My model features a closed-economy with no international borrowing. However, when I aggregate all flow of funds constraints and impose all market clearing conditions except that on the debt market, I indeed don’t find back the market clearing condition B_t= B_{t,I} + B_{t,F} but rather :

` B_t- B_{t,I} - B_{t,F}= R_{t-1} ( B_{t-1}- B_{t-1,I} - B_{t-1,F} ) `.

This might explain why when I include the debt market clearing condition in Dynare, all works fine, but when I don’t, it doesn’t work out, because the debt market clearing condition is not implied by the others (except in the deterministic steady state).

Does this imply that I have to be careful when choosing the market clearing condition that I don’t include in Dynare (this shouldn’t be the debt market clearing condition, as in this case, the Walras’ law does not apply), or does this mean something more, like I need to make additional assumptions in the model ?

Thanks a lot

It means that indeed this market clearing condition is not implied by the equations you entered, because it imposes a different assumption: that bonds are in zero net supply. Of course you need to be careful to not leave this condition out, because you will be losing this additional assumption.