Structural budget balance in DSGE model

Dear Dynare users,

I’m working on a DSGE model of Adolfson et al. (2008), where I want to derive the structural budget balance. My derivations are in attachment. Is this correct? Any suggestions?

Best regards, J
SBB.pdf (185 KB)

I gave it a quick skim and it looks ok (I did not check all computations). Note that you suddenly change the timing of some of the variables when you go from (15) to (16).

Dear prof. Pfeifer,

first of all, thank you for your answer.

In Adolfson et al. (2008) the real aggregate net foreign position of the domestic economy is defined as:

a_t= B_t+1_asterisk/P_t z_t.

Similarly, I defined the domestic bond holdings as : b_t-1 = B_t/P_t-1 z_t-1. Is this wrong?

Another question: to get the structural budget balance I simply substracted the deviations of tax revenues, i.e. t (and transfers, i.e. ben) from the actual budget balance. But we know that changes in G (referred to as discretionary changes) affects GDP (Y = C+G), which has further impact on tax revenues (T = tau*Y). Taking this into account, I would actually need structural revenues?

PS: Note also that when simulating the model, I do not assume any specific process for G. It adjusts endogenously.

  1. That depends on the notation. If B_t+1 was a predetermined variable (stock at the beginning of period notation) then you are fine. Otherwise, you are potentially introducing a timing error.
  2. This all depends on your concept of “structural budget balance”. Without knowing what you are after, this is hard to tell.
  1. Yes, B_t+1 is defined at the beginning of period.
  2. The following paper (see page 13) … af49f80540 was used to derive the structural budget balance.

In their paper, they construct a fiscal rule for debt. They do not start with the actual government budget constraint.
Their rule, equation (16), can be implemented in an ad-hoc way when you set or estimate the phi. Because instead of computing the phi implied by the model when you set a given tau, they simply start from the phi and forget about tau. In that case, you don’t need to worry about properly taking into account the feedback.

Ok, my Dynare code currently contains:

  1. Actual government budget constraint equation, i.e. equation (16) from SBB.pdf
  2. Structural budget balance equation, i.e. equation (18) from SBB.pdf
  3. Debt rule, i.e. equation (19) from SBB.pdf
  4. No specific process for gov. consumption G which means that it adjusts endogenously

Is this ok or should I make any changes?