<p>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.</p>
<p>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.</p>
<p><a href="https://i.sstatic.net/uZdBe.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/uZdBe.png" alt="enter image description here" /></a>
<a href="https://i.sstatic.net/5Pk13.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/5Pk13.png" alt="enter image description here" /></a></p>
<p>Thank you in advance!</p>

CC BY-SA 4.0
2023-01-30T16:09:29.983Z
It would be helpful if you could post your formal growth decomposition.
BrsG
CC BY-SA 4.0
2023-01-30T18:26:08.333Z
Thank you for your reply, I have added two charts which show the growth decomposition before and after using the HP filter. Thanks!
Cola
CC BY-SA 4.0
2023-01-30T18:39:19.757Z
"Why You Should Never Use the Hodrick-Prescott Filter" by Jim Hamilton (ReStat, 1300+ citations)
https://econweb.ucsd.edu/~jhamilto/hp.pdf
BKay
CC BY-SA 4.0
2023-01-30T18:52:17.720Z
@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?
BrsG
CC BY-SA 4.0
2023-01-31T18:11:53.250Z
@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.
Cola
CC BY-SA 4.0
2023-01-31T18:23:09.560Z
@BKay I have seen this article but I feel that the criticisms aren't relevant - I am using the HP Filter simply to reduce the 'noise' from short-term fluctuations in order to paint a clearer picture of TFP's contribution to GDP growth over time. The TFP is calculated as the difference between capital and labour's estimated contributions to growth, and the total economic growth, so all the volatility from economic growth ends up in my estimate of TFP's contribution. That said, I am only a 2nd year student of a BSc Economics degree, so if you feel I have missed something, criticisms are welcome!
Cola
CC BY-SA 4.0
2023-01-31T19:56:51.113Z
@Cola: well then I'll give it a pass, especially as it's still not clear where capital stock comes from.
BrsG
CC BY-SA 4.0
2023-02-01T01:24:08.610Z
@BrsG https://www.rug.nl/ggdc/productivity/pwt/?lang=en
Cola
<economic-growth><business-cycles>
Should business cycles be included in a growth accounting exercise that is focused on the long run?
Cola
# Should business cycles be included in a growth accounting exercise that is focused on the long run?

(Asked by: username_0 on 2023-01-30)

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.

[![enter image description here](https://i.sstatic.net/uZdBe.png)](https://i.sstatic.net/uZdBe.png)
[![enter image description here](https://i.sstatic.net/5Pk13.png)](https://i.sstatic.net/5Pk13.png)

Thank you in advance!

**Tags:** economic-growth, business-cycles

> **Comments:**
> **username_1**: It would be helpful if you could post your formal growth decomposition.  
> **username_0**: Thank you for your reply, I have added two charts which show the growth decomposition before and after using the HP filter. Thanks!  
> **username_2**: "Why You Should Never Use the Hodrick-Prescott Filter" by Jim Hamilton (ReStat, 1300+ citations) https://econweb.ucsd.edu/~jhamilto/hp.pdf  
> **username_1**: @username_0: 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?  
> **username_0**: @username_1  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.  
> **username_0**: @username_2 I have seen this article but I feel that the criticisms aren't relevant - I am using the HP Filter simply to reduce the 'noise' from short-term fluctuations in order to paint a clearer picture of TFP's contribution to GDP growth over time. The TFP is calculated as the difference between capital and labour's estimated contributions to growth, and the total economic growth, so all the volatility from economic growth ends up in my estimate of TFP's contribution. That said, I am only a 2nd year student of a BSc Economics degree, so if you feel I have missed something, criticisms are welcome!  
> **username_1**: @username_0: well then I'll give it a pass, especially as it's still not clear where capital stock comes from.  
> **username_0**: @username_1 https://www.rug.nl/ggdc/productivity/pwt/?lang=en  

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