Defining shocks in Steady-states

Stochastic simulations
1

Hi all,
It is much appreciated if someone could help me in sorting out the following problem about shocks.

I see some shocks are defined as AR(1) and some as VAR(1).
I want to know,

  1. how to determine which type of the above two types should be selected?
  2. what is P (capital P) in the VAR(1) equation?
  3. in VAR(1) type how to determine the steady state values?
    For AR(1): zf = RHOO_zfzf(-1)+epszf; RHOO_zf=0.9
    and in ss, zf=0
    likewise,
    how to define VAR(1): log(p)=(1-RHOO_p)P+RHOO_p    log(p(-1))+epsp;

Thank you!!!

2

Sorry, but you need to provide more context for your question. Are we supposed to understand your notation?

3

Thank you very much for the reply!!!
I do not understand why some shocks are represented as AR(1) process while others are defined as VAR(1).
For example, technology shock, has been defined as AR(1): zf = RHOO_zf*zf(-1)+epszf. total factor productivity = exp(zf)
in this case, I know zf=0 in steady state.

However, some other shocks, such as tax shock, has been defined as VAR(1):
log(p)=(1-RHOO_p)P+RHOO_p log(p(-1))+epsp; p is a tax variable, RHOO_p=0.9
and average tax rate is 25%.
I do not understand this VAR(1) process and how to define it in the steady state.

4

Where do these processes come from? What is P supposed to be? It looks like a constant term fixed during calibration. That does not make it a VAR.

6

image

I got this from Prof. Eric Sims’s documents.
I want to solve the equation for the steady state.
I know that the first term in this equation tauk,without t (or capital P in my equation) is non-stochastic. i got average tax rate in steady state as 25%.
In steady state,
log(p)=(1-RHOO_p)P+RHOO_plog(p(-1))+epsp
log(p)=(1-RHOO_p)P+RHOO_plog(p)+0
(1-RHOO_p)* log(p) = (1-RHOO_p)*P
log(p) = P , if p=0.25
SS is solved.

But I get an error;
Prior distribution for parameter RHOO_p has unbounded density!

Prior for RHOO_p is as follows;
RHOO_p, beta_pdf,0.9,0.1;

Thanks

7

But that is a different issue, see Unbounded density