Theoretical Questions Related to Bayesian Estimation


If your model has a policy reaction function, you will observe that the variables on the right-hand side change, while the left-hand side is constant. The only way to square this is to estimate big monetary policy shocks. For that reason, people often use a shadow rate estimate.


In other words, are you saying that because the short-term rate still affects the economy through expectations for the length of the zero lower bound for instance, this would be captured by the error term in the policy rule and that model would not be able to account for forward guidance for instance. In short, is that a reason why people may not want to estimate the model using the actual fed funds rate as an observable?

To give you context, I have a model with financial frictions and for the purposes of simulations, a financial shock is of key interest. Obviously, it is a sticky price economy hence why I have monetary policy. As you said, I can consider a shadow rate, but what if I am willing to ignore the precise impact of monetary policy during the ZLB without considering monetary policy. I know that this would affect the coefficient estimates, but I am wondering how much this may be a subjective choice based on the question of study versus an actual bias that must be remedied.


That is hard to tell. Without properly accounting for the ZLB, the ZLB period will be associated with big implied estimated monetary policy shocks. In order for estimation to not assign too large shocks, it will consider other shocks as having happened as also quite likely. That is the general problem with the ZLB.

An additional complication/measurement error comes from unconventional monetary policy. This is not reflected in the nominal interest rate. So if you abstract from this, you will think monetary policy was more contractionary than it actually was. At the same time, having unconventional monetary policy implies that the ZLB was less binding, meaning that problem 1 was less severe.That is why I suggested to use the shadow rate as it (partially) gets around both problems.


That was a very clear explanation. Thank you.


I had asked a couple of questions on this post, which I had deleted since I figured out my issues. Instead, in this post I would post a solution to the common issue of how does one go about in finding the mode of the prior distribution (which is what my initial questions were related to).

I had struggled with this issue for a few days and I am posting what worked for me.

First, I recommend that you use the estimated_params_init block. Hence, for each parameter you do the following:

parameter 1, initial value;
parameter 2, initial values;
…(and so on for all your estimated parameters (and shocks))
Note, initially you have no prior knowledge on what the standard deviations of the shock should be. Do not restrict them to any values. Keep the standard deviations of the shocks to inf.

Set the initial values to your calibrated parameters in the beginning of the mod file (or the mean of your prior distribution).
Next, use mode_compute=6. It is a monte-carlo computation and is a global mode optimizer. The output of that optimizer will (most likely) not find the optimal local maximum for each parameter. However it will proceed with the estimation. At this point, you can stop the estimation, since it is pointless to continue. (Your results will never converge).
However, use the mode estimates from this optimization and update your initial parameter values in the estimated_params_init block. After you update all values, switch to mode_compute=4. Hopefully, absent any additional problems, this optimizer should find the local maximum for each parameter and it would proceed with the estimation.


I am wondering if my definition for hours and the wage is correct. I am first differencing my trending variables while keeping the mean (I have a trend in the model). However, for hours I take the growth rate (LN(hours_t)-LN(hours_t-1)*100 and then demean it. Is this a correct way of specifying hours? My model labor variable is a standard one (between 0 and 1).

On a separate note, when and why would one want to have more shocks than observables in the estimation. What are the pros/cons with that?


Hi Johannes,

If you can spare a few minutes if your time, can you please look at my mod file and tell me if you think something seems off? I think something is wrong in the model, but I cannot identify it. The model runs under mode_compute=4, and I have also attached the prior and posterior plots, but I don’t think some of my estimates make sense. The calvo wage parameter theta_w for instance is getting estimated at zero. b and L are levels of public and private debt, whereas R_L is a bond yield. The other observables are as in smets and wouters (2007) (258.1 KB)