Trend Inflation in à la Christiano, Eichenbaum and Evans model

Hi everyone. I’m trying to implement a DSGE model à la Christiano, Eichenbaum and Evans 2005, and I want to augment it with the trend inflation features as proposed by Ascari 2014. I think I got most of the model right (you have the main equations here in the snippet):

model(linear);
  
// Eq 1. NK Philips Curve
pi = (lambda * y) + (b1*pi(+1)) + (k_appa*(phin*price_d)) + (b2*(y*(1-sigma) - phi(+1)));

// Eq dynamics of the auxiliary variable
phi = ((1-theta*beta*pi_bar^epsilon) * (phin *price_d + (phin + 1) *y)) + ((theta*beta*pi_bar^epsilon)*(phi(+1) + epsilon*pi(+1)));  

// Dynamics of price dispersion
price_d = (((epsilon*theta*pi_bar^(epsilon-1))/(1-theta*pi_bar^(epsilon-1)))*(pi_bar-1))*pi + (theta*pi_bar^epsilon)*price_d(-1);

// Eq 2. Wage equation
w = ((((1-beta*xi_w)*(1-xi_w))/((1 + beta) *(lam_w+1)*(xi_w)))*(phin*l - psi - w)) + ((beta/(1+beta))*w(+1)) + ((beta/(1+beta)) * pi(+1)) - (((beta*gamma_w+1)/(1+beta))*pi) + ((1/(1+beta)) * w(-1)) + ((gamma_w/(1+beta))*pi(-1));

// Eq 3. Euler Equation
psi = psi(+1) + r(+1) - pi(+1);

// Eq 4. Household's marginal utility of consumption 
psi = ((beta*b)/((1-(beta*b))*(1-b))*c(+1)) + ((b)/((1-(beta*b))*(1-b))*c(-1)) - ((1+(beta*b^2))/((1-(beta*b))*(1-b))*c);

// Eq 5. Capacity utilization definition
u = k - kbar;

// Eq 6. Return on capital (to add gamma)
rk = w + l - k;

// Eq 7. Aggregate resource constraint
y = (I_Y * i) + (C_Y * c) + (K_Y * rk);

// Eq 8. Capital Accumulation
kbar = (1-delt)*kbar(-1) + delt*i;

// Eq 9. Taylor rule
r = r(-1) * rho_r + ((rho_pi*pi) + (rho_y*y))*(1-rho_r) + eR;

// Eq 10. Investment decision equation
i - ((1/(kapa*(1+beta))) * p_ki) - ((1/(1+beta)) * i(-1)) - ((beta/(1+beta)) * i(+1)) = 0;

// Eq 11. Capital Euler Equation
pi(+1) + (beta*(1-delt)*p_ki(+1)) - p_ki = r(+1) - beta * (rk_bar * rk(+1));

// Eq 12. Capital utilization 
u = (1/sig_a)*rk;

// Eq 14. Marginal Cost
s = alph*rk + (1-alph)*(w);

// Eq 15. Production Function (to add gamma)
y = alph*k(-1) + (1-alph)*l - price_d; 

// Eq 16. Monetary policy shock (for persistence)
eR=rhor*eR(-1)+eps_m;
   
end;

However I’m puzzled by the wage equation, can I take it as it is in the CEE? Or is it affected in some way by the trend inflation?

Thanks in advance

Here you also have the full model file (a bit messy).
ProjectModel.mod (9.5 KB)

That is impossible to tell from the linearized equations.