Hello, I am replicating a paper on search and matching with endogenous job separation. All value functions are included in equilibrium equations and there is integral with upper and lower limit in all value functions. Can anybody help me how to write these values functions with integral in dynare codes

The question is on what these integrals depend. If they depend on endogenous variables so that derivatives are required, then you may have to go for an external function. See e.g. Integration in Dynare 4

Thank you for your reply. I have 4 value functions which i have to write in my codes. Do i need external function of each of them or i can use one external function for all.

Thanking in anticipation

Without details, it is impossible to know. Often, you can define the whole object with the integral recursively as a separate variable so that integrals do not appear anywhere.

Hello,

Thank you for your reply. I am replicating paper of (Miyamoto et.al 2019) and following is the value function of filled job.

Jt=At*f*(kt*ht)-(wt*xt*ht)-rt*kt-xt+SDF*((1-rho^x*(integralunderline(x)^(xbar(t+1))*J(t+1)*(x(t+1)*Gamma(x(t+1)+(1-(1-rho^(x))*Gamma*xbar(t+1))*V(t+1))

Can you please explain how i can write it recursilvey?

best

Which paper exactly is it?

Have you asked the authors how they did this? It may be the easiest to linearize the equations by hand.