Dear All,

I was wondering if it is possible using dynare to construct an IRF for one firm from the continuum? Suppose we have a model with Calvo frictions, where all firms are subject to idiosyncratic price rigidities. While we tend to aggregate the model, then find a solution and construct IRFs, is it possible to see how **one** firm behaves (its profit or labor decision) when assuming its future history of idiosyncratic shocks (t=0 cannot change prices, t=1 can change price, t=2 cannot)?

Could you refer where I can read more about this?

Thanks a lot

Hi burgerino,

what is done in representative agent NK-DSGE models is to, in the end, always think about representative agents and not a continuum of them, be it households or firms. Hence, for the “normal” model set-up this is not possible.

You could have a look into the heterogeneous firm literature maybe this would work better for your use-case. I am not an expert in this field and cannot really help you there but what I know is that solving these kinds of models is much more involved and not done in Dynare.

Thanks for the answer. I understand that I rely on a “representative” case, as Calvo allows for an easy aggregation, as well as I understand that models with proper heterogeneous firms is beyond dynare. However, I am still unsure if what I am asking cannot be answered using dynare in a simple setting.

Could I introduce an auxiliary block of two firms and play with stochastic simulation? Suppose one firm can always change prices but expects that it may not get to change it next period, the other firm cannot change price, which stays at some predetermined level, but still expects that it could change next period. Now if there are not any other idiosyncratic firm-level state variable (e.g. capital), could I simulate stochastic simulation for both and just combine when I assume that there was a switch from state of switching prices to a non-switching one? This should be allowed because firm’s problem does not rely on any firm state variable.

Does it make sense? What am I missing? One could also think of a simpler situation of just two representative firms which differ in their price adjustment costs ala Rotemberg. Then I guess one can use the solution to simulate the path if firm is switching state.

Thanks!

I guess that is doable. After all, the hard part in DSGE modeling is solving for the general equilibrium, which is required for firm choices. The choice of an individual is governed by its FOCs, which you can use to compute firm behavior given the rest of the model.

I attempt using a simplified case.

Suppose there are two representative firms in the economy that are contain of a continuum of firms. Shares of firm A or firm B do change over time. Firms differ in demand elasticities but also face an exogenous probability p_t and q_t to switch from type A to type B.

Firm optimal valuation can be written in the following way (the reminder of the model can be anything):

Q_{A,t} = \frac{mc_t}{1-\eta_a}Y_t + E_t sdf_{t,t+1} (p_t Q_{A,t+1} + (1-p_t) Q_{B,t+1})

Q_{B,t} = \frac{mc_t }{1-\eta_b}Y_t + E_t sdf_{t,t+1} (q_t Q_{A,t+1} + (1-q_t) Q_{B,t+1})

So these are the equations that dynare will solve for me, prepare policy functions and, including other equations, give me aggregate dynamics for other variables as well. In order to obtain a specific simulated path for one firm, can I just add an auxiliary equations?

Q_{switch,t}=e_{switch,t} Q_{A,t} + (1-e_{switch,t})Q_{B,t}

And then I could assume some path of e_{switch,t}, that takes a value of zero or one, to simulate a path for one firm, Q_{switch,t}. Does that make sense? There is not any firm specific state variable, only idiosyncratic exogenous risk to switch from one type to the other.

I appreciate your help.