# Scale of a data

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 ;

//(1)
ac - ac(-1) = dFX + de - pi ;
//(2)
dFX = beta_fx*de + eps_fx ;
end;

estimated_params;

stderr eps_fx, , 1E-10, , INV_GAMMA_PDF,0.5,inf;
end;

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?

Thank you

Jerry

You need to approach this more systematically.

1. The loglinearization of an equation is independent of the measurement of the variables. It is the purpose of the observation equation/measurement equation to link the data to the model equation

2. The part

makes no sense. Are you trying to say that `ac` is already in percent, so you are doing a linearization instead of a log-linearization to get a variable measured in percentage points?

In fact, ac is a ratio between foreign bond holdings and nominal gdp and I did linearization.

Ok, but then why do you think you need to adjust the (hopefully) properly linearized equation by a different scaling factor?