Confusion over estimation & a paper's Measurement Equations

Estimation
1

I am trying to run an estimation with UK data using the model of Gertler, Sala and Trigari (2008) [https://onlinelibrary.wiley.com/doi/epdf/10.1111/j.1538-4616.2008.00180.x] and their estimation is also similar to Smet and Wouters (2007). However my mode checks are really off and I’m not sure how to get it right to get the estimation working.

On page 49 of the above link you can see the measurement equations used (which are also very similar to SW2007). In my mod file (I am not using data on hours yet) I set:

dy = 100*(gammaz-1) + y_hat - y_hat(-1);
dc = 100*(gammaz-1) + c_hat - c_hat(-1);
dinve = 100*(gammaz-1) + i_hat - i_hat(-1);
pinfobs = pi_hat;
robs = r_hat;
dw = 100*(gammaz-1) + w_hat - w_hat(-1);

But say gammaz (steady state growth) equals its prior mean (see page 22 and table 2), 1.25, given dy is just the quarterly percentage growth, the measurement equation seems way off? I.e. 100*(1.25-1)=25… so how is this sensible? (However when I’ve played around with the measurement equations I get basically no improvement).

In my mod file I also include:

steady_state_model;
dy=100*(gammaz-1);
dc=100*(gammaz-1);
dinve=100*(gammaz-1);
pinfobs=0;
robs=0;
dw=100*(gammaz-1);
end;

since 100*(gammaz-1) is “the common quarterly trend growth rate to real GDP, consumption, investment…” (SW2007) we expect this along the steady state right? And then I’ve followed GST 2008’s measurement equations in setting pinfobs and robs to 0 since they demean the observable inflation and interest rates. Am I right in this? (Although when the above block isn’t included in the mod file the output doesn’t change).

If so I’m really unsure why my mode check plot of the rhos and sigmas are so off (“the hessian matrix at the “mode” is not positive definite!”) as I’ve read issues are very often related to the measurement equations.

I’ve attached my data and mod file. The way I construct my dataset mimics SW2007 but with UK data.

(Also, on page 22 table 3 I don’t understand why the authors set the distribution of the AR rho parameters’ standard deviations to 2 when the rhos have to be between 0 and 1? When I initially put their standard deviations as 2 I got an error saying they must be less than 0.5 so I changed them to 0.2).

Thanks for any insight, it’d be really appreciated.

GSTest.mod (9.8 KB)
ukfullh1.xlsx (66.5 KB)

2
  1. Where do you get the number 1.25 from? \gamma_z is 1.004 or about 1.6 percent per year in Table 2.
  2. The reported standard deviation of 2 in the beta distribution must be a typo. The reference of Smets/Wouters uses 0.2.
  3. You are not handling parameter dependence correctly. Please refer to Pfeifer(2013): “A Guide to Specifying Observation Equations for the Estimation of DSGE Models”
3

Hi, thanks for the reply.

1.25 is the prior mean of that parameter (it was set as Uniform(1, 1.5). Also If I hold everything else constant and change γz to a smaller value the simulation breaks down but struggle to see why.

About parameter dependence, isn’t that only relevant when I’m estimating parameters that are functions of other parameters? Because of this issue, I was wanting to first just estimate the shock parameters on their own so I’m not concerned about parameter dependence right? Also on that topic, estimating a deep parameter like the bargaining parameter eta wouldn’t be concerned about parameter dependence. Is my thinking right here?

Thank you

4
  1. With a uniform distribution, all values are equally likely. So the prior mean is not really important here. What do you mean with

?
2. In the scenario you describe, the parameter dependence is not an issue, because all other parameters and steady state values are independent of the shock processes. Nevertheless, it is bad practice to write a mod-file this way, because estimation cannot be easily extended to other parameters.