Term structure of interest rate and yield curve?

Steady state
1

Hi all,

I have a question regarding the computation of the yield curve or the term structure of interest rates using Dynare solution.

Typically, the interest rate of a one-period zero coupon bond can be computed as:

1/exp(r) = exp(m(+1));

where m is the stochastic discount factor. If we want to compute the interest rate of a two-period zero coupon bond, it can be computed as:

M2 = m(+1);
1/exp(r2*2) = exp(m(+1)+M2(+1));

However, this gives r2 = r, despite the model being solved using 3rd order in Dynare, which should result in a term structure of interest rates.

My question is: is it possible to compute the yield curve or the term structure of interest rates correctly in Dynare?

In addition, I am wondering if there are any differences between Dynare and Dynare++ for version 5.3. I have the impression that Dynare++ has been fully incorporated into Dynare, is that correct? Could the above issue be related to the differences between the two programs?

Thanks!

2
  1. Dynare 5 replaces Dynare++. You should get the same results.
  2. Are you sure the recursive formulation is correct? The first line implies there is only one period uncertainty in this model.
3

Thanks! How should one set up the term structure variables then?

My approach is as follows: given that m represents the SDF, the one-period bond yield can be calculated using the formula 1/exp(r) = exp(m(+1)).

For a two-period bond, M2 = m(+1) where M2 takes the SDF one period forward and r2 is the two-period yield. In this case, the formula for the two-period bond yield is 1/exp(r2*2) = exp(m(+1)+M2(+1)).

Does this seem like the correct approach?

4

But then M_2=E_t(m_{t+1}) such that 1/e^{2r_2} = E_t e^{m_{t+1}+E_{t+1}(m_{t+2})}. Is that what you want?

5

You are right, that’s not good.
What I want is

1/e^{2r_2} = E_t e^{m_{t+1} + m_{t+2}}

Would you suggest some references on how to do it correctly? Dynare does not seem to support m(+2), thanks!

6

Dynare should support m(+2).

7

Great to know that the updated version support m(+n), and m(-n), thank you!

8

Is there any paper or reference that I can learn how to do it correctly? i.e., any papers that have an upward-sloping or downward-sloping yield curve with dynare solution?

I am asking because I have implemented

1/e^{r_n} = E_t e^{m_{t+1}+m_{t+2}+...+m_{t+n}}

And then, I feed zero shocks to run the model simulation and obtain the yield curve. But I notice that the yield curve slope disappeared at period 3. That is

r_1 < r_2 \approx r_3=r_4= r_5=..

But in theory, it should be upward-sloping, it is because I solve the model with order 3? Or something I did run?

9

comes to mind