1. Jan Brůha, Economic Research Division Czech National Bank
Discussion of the paper “Labour market institutions and business cycle dynamics, VAR analysis” by Petteri Juvonen
Jan Brůha, Economic Research Division
Czech National Bank
First Annual Workshop of ESCB Research Cluster 2,
Madrid, November 2017

2. Contribution of the paper
The paper proposes a hierarchical VAR model, whose coefficients depend on institutional parameters. Two extensions comparing existing models:
All coefficients (including entries of the variance matrix) can depend on institutional characteristics
The link between characteristics and coefficients is stochastic
A Gibbs sampler is proposed to estimate the model
The above mentioned hierarchical model is then applied to macroeconomic and labour market data on a set of advanced countries to investigate the link between labour market institutions and business cycle dynamics
Both contributions are important.
I cannot say much about the technical contribution (I can just admire it)
I will concentrate on the second contribution
The paper then proposes a Gibbs sampler to estimate the model
This is important contribution on its own.

3. Data and Data Transformation
The VAR model is applied on 3 time series, one of them is the unemployment rate in levels.
This implicitly assumes that the equilibrium level of unemployment is constant as the title of the paper contains the word “cyclical”.

4. Transformations matter

5. Transformation matters /2
I appreciate that there is a lot of controversy about data transformation in literature.
One camp: prefiltering data is evil
As it plagues results with “spurious” cycles
The other camp: we should NOT ignore low frequency movements / high frequency noise
The often-heard opinion that the use of statistical filters (e.g. the Hodrick-Prescott filter) always causes spurious cycles is misguided; see Pollock (2013) who demonstrates that “this idea is largely mistaken".
Ball, Leigh, Loungani (2013): “Okun’s Law: Fit at Fifty?” NBER WP “We think it is better to estimate Ut* and Yt* as accurately as possible than to assume the problem away.”
ANDRLE, BRUHA (2017): Trend Cyclical VARs.

6. 𝑠 𝑦 𝜔 = 𝑑𝑖𝑎𝑔((1− 𝑒 −𝑖𝜔 ) −1 ) 𝑠 ∆𝑦 𝜔 𝑑𝑖𝑎𝑔((1− 𝑒 −𝑖𝜔 ) −𝐻 )
A possible solution?
If one is shy to prefilter data using a statistical filter, possible solution can be as follows:
Estimates VAR on first differences (to make all series stationary), and from the estimated VAR the spectral density of the first-difference data can be derived 𝑠 ∆𝑦 (𝜔)
Application of the integration filter on this spectral density yields spectral density of series on levels (away from zero frequency)
𝑠 𝑦 𝜔 = 𝑑𝑖𝑎𝑔((1− 𝑒 −𝑖𝜔 ) −1 ) 𝑠 ∆𝑦 𝜔 𝑑𝑖𝑎𝑔((1− 𝑒 −𝑖𝜔 ) −𝐻 )
The frequency-specific correlations can be then easily derived
Γ 𝑙,𝑢 (𝑘)= 𝑙 𝑢 𝑒 𝑖𝑘𝜔 𝑠 𝑦 𝜔 d 𝜔

7. Is it VAR(2) sufficient for data transformed to yearly growth rates?
Other comments / 1
The model is complex and its estimation quite challenging. The reader may appreciate some evaluation:
E.g., in sample fit, comparison of model-implied moments with raw moments in data
Is it VAR(2) sufficient for data transformed to yearly growth rates?
Table 1, row on corr(y,u). COORD: -0.27, -0.29, and EPL: -0.16, -0.18, Is this consistent?
It would be interesting to look also at relative volatilities of labour market data, e.g. 𝑣𝑎𝑟(𝑢)/𝑣𝑎𝑟(𝑦)
The raw volatilities may be influenced by country specific shocks.

8. A similar comment applies also to impulse responses:
Other comments / 2
A similar comment applies also to impulse responses:
e.g. the Figure 2 in the paper implies no difference in IR from the US growth shock to unemployment between low and high COORD, but a significant difference in output response.
An interpretation?

9. Other comments /3
Impulse responses seem to imply that the maximum fall in unemployment lags the peak in output usually by 4 quarters.
This seems to me too long (I expect 1 or 2 quarters)
Is it caused by data transformation?
Source: Bruha, Polansky (2015)

10. Conclusions
The paper by Petteri is very interesting and at the same time important.
Two main contributions:
Technical (a hierarchical VAR model)
Insights on the effects of institutions on labour market
Three main comments:
Reconsider data transformations
Be more specific about units and quantitative implications of your results
Include some intuitive diagnostics of the hierarchical VAR model

11. Thank you for your attention
Jan Brůha
Economic Research Division
Monetary Department