# 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?