RDP 2016-08: The Slowdown in US Productivity Growth: Breaks and Beliefs Appendix D: Can Our Estimation Recover Date Breaks?

In this appendix, we show that our estimation can identify the timing and magnitude of changes in steady-state productivity growth.

We simulate the model for 201 quarters, with all parameter values set to the posterior means recorded in Justiniano et al (2013). We impose a break in the steady-state growth rate of productivity in quarter 50 that lowers the value of this parameter by 0.4 percentage points, from 0.49 to 0.09. We set the date at which agents' beliefs about steady-state productivity growth adjust to quarter 125. We then estimate our model on the simulated data, using the methodology and priors described in Section 3.

Table D1 shows the estimation results for the parameters of the productivity process and the timing of the structural breaks. The estimation successfully recovers the steady-state productivity growth rates in the initial and final regimes as well as the timing of the break in productivity growth. It also comes very close to matching the persistence of the AR(1) growth process and the standard deviation of productivity shocks. The estimate of the timing of the break in beliefs is slightly less precisely estimated and contains some mass at dates before the actual break. However, the mode and the median of the distribution are both close to the actual break date. Overall, these results give us confidence that the estimation can accurately recover the timing and size of breaks in steady-state productivity growth.