I have been tasked with a long-run analysis of the Japanese and Brazilian economies, and as part of this, I have decomposed GDP growth into the contributions from capital, labour and TFP (following the standard Solow model and using Penn World Table's data). My method is fairly standard: the capital contribution to GDP growth is the growth in the capital stock growth times 'alpha', and the labour contribution to GDP growth is employment growth to the power of 'beta', with 'beta' being the labour share of income and 'alpha' being the capital share of income'. The TFP contribution to GDP growth is then the residual, GDP growth minus the capital contribution minus the labour contribution.

However, this approach means that all the short-run business cycles and other noise from real GDP is included in the TFP contribution to the GDP growth. I feel that this is unhelpful for long-run analysis and that, by using the HP Filter to smooth real GDP across the business cycle, this would give a better picture of the long run. For instance, the first chart below shows my results for Brazil without smoothing GDP using the HP Filter, and the second chart shows the results for Brazil after smoothing GDP with the HP Filter.

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Thank you in advance!

  • 1
    $\begingroup$ It would be helpful if you could post your formal growth decomposition. $\endgroup$
    – BrsG
    Jan 30, 2023 at 16:09
  • $\begingroup$ Thank you for your reply, I have added two charts which show the growth decomposition before and after using the HP filter. Thanks! $\endgroup$
    – Cola
    Jan 30, 2023 at 18:26
  • $\begingroup$ "Why You Should Never Use the Hodrick-Prescott Filter" by Jim Hamilton (ReStat, 1300+ citations) econweb.ucsd.edu/~jhamilto/hp.pdf $\endgroup$
    – BKay
    Jan 30, 2023 at 18:39
  • $\begingroup$ @Cola: the charts are nice, but I was really after a formula for each of the components. I am asking partly because in your description you say you use the capital stock and labor growth at the same time which seems an odd combination. Also where do you get data for the capital stock? $\endgroup$
    – BrsG
    Jan 30, 2023 at 18:52
  • $\begingroup$ @BrsG Sorry about that, I believe I have described them well enough in writing? 'capital stock' should have been 'capital stock growth', apologies for that typo - I have fixed this in the original post. For capital stock, I have used the variable 'rnna' from the Penn World Tables. $\endgroup$
    – Cola
    Jan 31, 2023 at 18:11


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