Hi, I implemented a Bayesian estimation of a DSGE model and obtained posterior estimates.
However, what is strange is the estimated magnitude of a shock.
In fact, I think two equations are matter.
According to my program,
// model ;
ac - ac(-1) = dFX + de - pi ;
dFX = beta_fx*de + eps_fx ;
stderr eps_fx, , 1E-10, , INV_GAMMA_PDF,0.5,inf;
varobs PI_US y_st R_US PI_AUS de R_AUS y ds dFX;
The problematic estimates of the shock is the standard deviation of “eps_fx” which is huge. (8.1748 in this case.)
In fact, “ac” is defined as real bond holdings to steady state GDP (like the government debt as a share of GDP), so that it is already a ratio.
And the data for “dFX” is expressed as percentage change.
Since the steady state value of “ac” is assumed to be zero in this case,
its percentage change is simply the change in the variable.
Now, ac - ac(-1) is nothing but its percentage change.
However, it is not equal to the sum of the percentage change in the three variables (de, pi, y-y(-1)).
Because if FX changes 10%, that is, dFX = 10, AC just changes in 1%.
For example, suppose a consumption output ratio(C/Y) = 10% (C=100/Y=1000)
If C changes 50%, C=150 / Y=1000, the percentage change in C/Y is 5%. ((150*100)/1000)
Therefore, I think (2) have to be changed as
ac - ac(-1) = 0.1*(dFX + de - pi) ;
because all of my data is expressed as percentage change.
How do you think?