Question About Conflicting IRFs with Different Taylor Rules

General DSGE Modeling Replication Attempts
1

Hello Dynare Community,

I am writing to ask for your help with a peculiar issue I encountered while simulating a basic New Keynesian model with habit consumption. I am analyzing the responses to technology, government spending, and interest rate shocks, but the IRFs for the interest rate shock seem unusual.

In my code, I have implemented two versions of the Taylor rule. Despite their similar structure, these two rules produce opposite IRFs when I apply an interest rate increase shock.

• With the first Taylor rule, R/\text{steady_state}(R) = (R(-1)/\text{steady_state}(R))^{(\text{RHO_r})}*((Pi)^{(\text{kappa_pi})}*(y/\text{steady_state}(y))^{\text{kappa_y}})^{(1-\text{RHO_r})}*exp(\text{eps_r} ), which is commonly used by many, the interest rate shock causes variables such as output, consumption, and investment to increase initially before returning to equilibrium. This seems counterintuitive, given the contractionary nature of an interest rate hike.

• With the second Taylor rule, R-\text{steady_state}(R) = \text{kappa_pi}*(Pi-1)+\text{kappa_y}*log(y/y(-1))+\text{eps_r};, the shock results in output, consumption, and investment decreasing initially (as expected) before returning to equilibrium. However, the behavior of the interest rate itself is puzzling: instead of increasing and then gradually declining, R decreases initially and then increases. This contradicts the expected dynamic of an interest rate shock, where R should rise first and then decline.

I am unsure why these two Taylor rules yield such conflicting IRFs. Could anyone explain why this is happening and suggest how to resolve the issue?

Thank you for your time and insights!

basic_NK.mod (2.3 KB)

2

Hi Bran_KY:
Since your model is nonlinear, so I think you should use the first taylor rule.
The second taylor rule is log-linear, so if your model is linear, you could use the second taylor rule.

3

Thank you for your response! I have one more question. When using the first Taylor rule, Dynare runs without any issues, but the responses to an interest rate shock appear counterintuitive. Specifically, despite an increase in the interest rate, output, consumption, and investment all rise, which goes against standard expectations.

I am curious why such results occur. Could it be because I have linked the interest rate in the Taylor rule to the return on capital (rk) in the Fisher equation? If that is the case, would introducing an additional component, such as government debt, and linking its return to the real interest rate (R) improve the results?

Thank you for your guidance!

4

From what I can see the counterintuitive results come from the endogenous feedback from output and inflation. If you use the proper linearization

    log(R)-log(steady_state(R)) = kappa_pi*log(Pi)+kappa_y*log(y/y(-1))+eps_r;

and set interest smoothing to zero, you get a similarly expansionary IRF.