A comment on
Olivier Blanchard, Eugenio Cerutti, and Lawrence Summers: Inflation and Activity–Two Explorations and their Monetary Policy Implications:
update: Anne in comments said it was impossible to understand what, if anything, I concluded. My conclusion
is was that Blanchard, Cerutti and Summers have found striking evidence of hysteresis. They reject the null hypothesis that GDP is a stationary AR(2) around a quadratic trend. It is true that I came up with the null (they don’t do formal hypothesis testing) based on what I guessed they had in mind. In any case, I personally am reassured that they are on to something.
Major update: I have been playing with the program. I find that the proportion of simulated recessions followed by lower output (as defined by BCS) is very sensitive to assumptions about trends and persistence of shocks. I no longer draw any particular conclusion from my effort.
While I really like the non-parametric approach of ” we look at 122 recessions over the past 50 years in 23 countries. We find that a high proportion of them have been followed by lower
output or even lower growth. ” I worry that this might happen even without hysteresis.BCS do not consider the distribution of their statistic under the no hysteresis null. This isn’t hard to do — just simulate data with a trend stationary process and do the calculations.
This also isn’t very useful. Without details, it is possible to make a large fraction of recessions be followed by lower output as defined by BCS by playing with assumptions about the trend stationary process. I am deleting my first effort to do this (there was a bug in the program) and just reporting that (as usual) if one makes arbitrary assumptions, one can get arbitrary results.
I don’t think this worries BCS, because they know
that GDP is very far from a trend stationary AR(1) with coefficient 0.5. how common the pattern is given standard models with standard parameters.
I did a more serious effort to check the distribution of their statistic under their null. I model log GDP as an AR(2) around a quadratic trend. Coefficients estimated with US data
AR coeffs rho1 = 1.328043 ; rho2 = -0.3781878; trend tr=.0105446 per quarter ;
-0.000009077 per (quarter -1947) squared. SE of disturbance to get roughly the right number of recessions.
update 3: new simulations here too
update 6: newer simulations.
27,700 pseudo recessions of which 15,172 = 54.8 % are followed by low output. For the reasonable null hypothesis with parameters based on data, the fraction with low output as defined by BCS is
about very roughly what they would hope (to be cautious they round down their estimated trends by one standard deviation).
the Gauss file which I used for the simulations [was] after the jump (yes I still use Gauss)
update 4: jmg points out that the Gauss code was messed up. It seems that wordpress assumed it was html code and rendered it. I won’t try to post the Gauss code.