I’m currently working on a paper focusing on Exchange Rate Disconnect in a General Equilibrium framework. I’ve developed a model for a small open economy, but I’ve encountered an issue when loglinearizing by hand. After introducing both the nonlinear and linear models in Dynare, I’ve noticed a discrepancy in the correlations.

Specifically, the correlation between the current account and GDP shows a negative sign in the nonlinear model, but it turns positive in the linear (loglinearized) model. This difference is concerning, and I’m unsure how to proceed.

Could anyone offer insights or advice on why this might be happening and how to resolve it?

You need to check your linearization and make sure that your are comparing the correct objects. If your model is loglinearized, you need to compare the IRFs of the logged nonlinear variables to the ones of the loglinearized model.

Why are you linearizing by hand? That is often not a good idea. For example, in your linearized Euler equation inflation does not show up.

Thank you for your response, Professor Pfeifer. I am linearizing the equations by hand because I need the linearized forms to derive specific properties for the paper I am currently writing. In my model, CPI is normalized to 1 (i.e., pp=1), resulting in zero inflation. However, I’m uncertain about which results to proceed with. I’ve already checked the log-linearized equations, not a big problem with that because they are standard. Would you recommend using the results from the linearized model or the nonlinear model?

Thank you a lot for your time! I have another question related to the timing of capital used in the production function. I found a mod from you that says:

This file implements a simple RBC model with a time t shock to the capital stock.

Basically, the capital stock used in time t is not completey predetemined anymore.

While the model conforms to Dynare’s end of period stock notation, the production

function uses k instead of k(-1), because the effective capital stock used at time t

for production can change at time to due to a shock.

My model presents a financial shock that alters capital returns through the asset pricing equations and ultimately transmits to investment decisions. Even though this is not a time t shock to the capital stock, is it still correct that I can write 𝑦=𝑘 rather than 𝑦=𝑘(-1)?

You as the model builder are the only one who can answer that question. But it sounds as if k(-1) is still the correct timing. You are altering the return to investment, not the value of capital itself and there is still one period time to build.

To be more specific, the model i ve written has the following capital-related equations:

[name=‘3. Euler investment’] \kappa (kk-kk(-1)) + \gamma cc(+1) - \gamma cc = (1-\beta (1-\delta)) r^k + \kappa (k(+1)-kk); (instead of r^k(+1))
[name=‘4. Investment’] kk = zz + (1-\delta)kk(-1);
[name=‘10. Production function’] yy = aa + \vartheta kk + (1-\vartheta) hh (instead of kk(-1))

Is my timing correct with this approach? I am using this timing because I apply a shock to the nominal interest rate of bonds, and I want to link it directly to the return on capital.