I estimated the model of Smets and Wouters (2007) with Swiss data (1991-2019), accounting for the interest rate lower bound with Occbin. For this, I have built on @jpfeifer’s replication codes for the original paper.
The estimation results suggest that the Swiss economy was not at all constrained by the lower bound. Specifically, the smoothed notional interest rate (rnot) is identical to the smoothed nominal interest rate (r) over the whole sample period. The posterior parameter distributions are identical to those obtained from estimation without Occbin.
I am not sure whether my results are genuine. The Swiss policy rate was at -0.75% for five years between 2015 and 2019.
I am grafeful for feedback on my implementation of Occbin in the mod file and for further comments.
I am a bit confused by your implementation. You set the lower bound to r_lbch, which is -0.2. But the lowest interest rate in your data is -0.1875. Thus, the ZLB will never bind.
I set r_lbch to -0.2 because the Swiss Libor rate was repeatedly slightly below the -0.1875 threshold. I would argue that if you want to interpret r_lbch as a structural parameter of the economy (which is calibrated) the Libor rate falling below -0.1875 rules out this value as a choice for r_lbch. In other words, the fact that the Libor rate went below -0.1875 suggests that the policy rate (which is my observed interest rate) could also have gone a little bit lower.
Please let me know what you think of the above argument. Would you instead choose the value for r_lbch based on “practical and econometric” considerations? Specifically, would you suggest to simply set r_lbch equal to the lowest observed value of the interest rate? Could such a small change in r_lbch (-0.1875 vs. -0.2) lead to materially different results in the first place?
Does the fact that the ZLB is never binding imply that the ZLB constraint has no effect on the estimation results? Isn’t it the case that even though the ZLB is never binding the constraint still affects the computation of the time-varying decision rules in the Occbin algorithm?
For comparison I have in the meantime also estimated the model with r_lbch=-0.1875. The results are nearly identical. That is, the smoothed notional interest rate (rnot) still equals the smoothed nominal interest rate (r). I guess this should not come as a surprise given the very small change in r_lbch.
I am not sure I am following here. You are arguing that empirically the ZLB was never binding because the interest rate could have fallen even further. In that case, you don’t need OccBin.
Fundamentally, OccBin is a piecewise linear solution. It features certainty equivalence, i.e. there is no precautionary effect due to the constraint potentially binding in the future.
Thus, the way you constructed the problem, it is fully expected for the ZLB not have any effect.
Hi, I am not sure about that, but I cannot say I know the details of OccBin… Sure the model is solved under certainty equivalence, as it would be with extended path. But, with EP, even if at time t the nominal interest rate is not on the ZLB, it may be that the agents (deterministically) expect that the economy will hit the lower bound later (and this will affect their decisions). Is this not possible with OccBin?
Thank you @jpfeifer for your helpful response. I guess my misunderstanding was that I wanted to implement the interest lower bound in the same way as Gust et al. (2017, AER). They use a nonlinear approach to model the ZLB. Hence, with their approach the ZLB can have an effect even if the interest rate is slightly above 0.
The premise for my research is that the interest rate lower bound was binding for the U.S. in the aftermath of the Great Financial Crisis (I also look at Switzerland). I want to use Occbin to determine the extent to which monetary policy was constrained by the ZLB. I use the Federal Funds Rate to measure the observed policy rate. The Federal Funds rate has never exactly hit the ZLB (it was between 0.1-0.2% from 2009 to 2015).
What is the appropriate remedy here? I see two possibilities:
I set the observations of the Federal Funds rate to 0 for the 2009-2015 period?
I set the threshold value of the Occbin (ZLB) constraint to a value above 0, e.g., 0.2.
@stepan-a Yes, that is possible. But the setup here makes that unlikely to play an important role. As specified, the data informs us that the ZLB was never binding. Expectations of the ZLB binding would quickly be outed as incorrect and parameters draws that imply the ZLB binding should be rejected as unlikely. Indeed, that is what the reported estimation results reflect.
@sgersp The ZLB binding is not about the precise value the interest rate but rather whether it was constrained from reacting through the usual Taylor rule. For most practical purposes, the ZLB was binding at these low interest rates, as shown by the use of unconventional monetary policy measures.
I have a further question regarding the ZLB implementation with Occbin in Smets and Wouters (2007).
So far, I have always used (1) name ‘zlb’; bind robs <= - 1e-8; relax robs > + 1e-8;
However, Guerrieri and Iacoviello (2015) use in their online appendix the notional interest rate to check whether the economy has left the ZLB. Specifically, (2) name ‘zlb’; bind r < -conster - 1e-8; relax rnot > -conster + 1e-8;
When doing Monte Carlo simulations with (1) I noticed that it is possible to have rnot>r (see Figure 1). This happens in the first few periods after the economy has left the ZLB. When using (2) for the simulations it always holds that rnot<=r as desired (see Figure 2).
It is not possible to use model local variables (specifically, the variable conster) for the implementation of Occbin constraints. I suppose the solution is to substitute conster with ((1+constepinf/100)/((1/(1+constebeta/100))*(1+ctrend/100)^(-csigma))-1)*100 in the Occbin constraint? Is there an easier way to implement this?
More generally, do you think that the difference between (1) and (2) matters a lot in an estimation context?
You should always use (2) as that is the correct specification. That is particularly important for agents forming expectations about the future. Conceptually, you will leave the ZLB when the Taylor rule prescribes an interest rate above 0. It should not matter what robs is.
You cannot use model-local variables in the OccBin constraint. But you can define a rnot_level=rnot + conster in the model block and use relax rnot_level > 1e-8