I have been trying to replicate the following paper for quite some time but I haven’t been able to get past the steady state computation.

Firstly I tried to solve the exact model, with household heterogeneity, but I failed miserably, thus I tried to simplify things and revert to a simpler model with a representative household which maintains the core characteristics of the initial specification. That is, I consider every household a Ricardian one and I drop the aggregation equations.

My approach in solving for the steady state was using the first order conditions and solve for ratios with regards to H (labour) because I set steady state hours equal to 0.3, as they already do in the paper. I also set An=1 (non-energy firms’ technological factor), Pe=1 (relative energy price) and I also normalize the energy sector’s output Ye=1. I get meaningful steady state values but the model cannot close as I have a residual in the budget constraint of 0.01 which is suspiciously the same as the steady state value of the fiscal instruments (The, Tne and se). I also get some strange results, that is when I solve for the relative price Pe, based on the other steady state values I have computed, I get Pe < 1 and not unity as I had initially set (P_e_ss_test in the steady state file).

I am literally stuck and whatever combinations I have tried seem not to work. I would be really grateful if anyone could provide me with a pointer or tell me if I’m missing something really obvious as this is a very important paper for my PhD.

P.S. The authors refer to Dr. Michel Juillard in thanking him for helpful discussions so I don’t know if there is a level of computational complexity in the model that I’m unaware of. energy6_simple_new.mod (8.5 KB) steady_energy5_new.m (3.1 KB)

This very much sounds like a conceptual problem where potentially the model equations still have a mistake. Alternatively, the normalizations do not work as intended, i.e. you are not correctly setting the necessary parameters to achieve the desired values.

Thank you very much for your response. New day, new problems. I’ve set the model in such a way that it “closes” in the steady state file, as I’m having a nearly 0 residual in the budget constraint test I ran. However, when I tried to simulate the model I’m having indeterminacy problems due to collinearity and/or unit root.

It seems that nearly every equation in the model is collinear, even the AR(1) equations that determine the shock processes. I think I’ve exhausted all the model’s equations in order to swap around and find the one causing problems. Even if I simplify things I have no other equations to turn to. Do you think this is an inherent model problem or these issues could be also parameter based?

I’ve tried to contact the authors on multiple occasions to address potential typos and errors, with no luck unfortunately.

You can’t use the steady state operator for the autoregressive equations. You need to calibrate these steady states.
You can only use the steady state operator if there are other restrictions that define the steady state. This is not the case here.

Dr. Juillard and Dr. Pfeifer thank you so much for your responses.

I am not entirely sure I understand what I have to do. The model is calibrated using pre-determined steady state values for the shocks i.e., I have already chosen the values of the non-energy sector technology shock (A_n_ss = 1 in the .mod file), and the household, firm and investment endowments (T_h_e_ss = T_n_e_ss = s_e_ss = 0.01 in the .mod file). The energy sector’s technology shock is calibrated, per se, but based on my normalization of the steady state energy sector output (Y_e_ss = 1 in the .mod file).

These variables are endogenously determined in the model but it was my assumption that they were driven by an AR(1) process (the authors say nothing about this in the paper) because somehow they have to be simultaneously shocked, following a negative energy sector technology shock.

How can I calibrate these variables in the steady state if I have already calibrated the model based on these particular steady state values in the first place?