Analysis of the Substitution between the Production

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Analysisof the Substitution betweenthe Production Factors and Intermediate Inputsin the lightof KLEMS Growth Accounting for PolandDariusz Kotlewski - Warsaw School of Economics and Statistics Poland

and

Mirosław Błażej – Statistics Poland

Sixth World KLEMS Conference March 9-10; 16-17,

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Structure of the presentation:

Part I Introduction

Part II The adopted methodology

Part III Discussion of the results

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Part IIntroduction

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Part I Introduction

Although, in various releases of EU KLEMS database Poland is present no decomposition of GVA or GO growth is availablethere (with the exception of 2007 EU KLEMS release).

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Part I Introduction

The reason is that:no sufficient data are being sent to Eurostat on the one handsome data need to be imputed innovatively because they are

not straightforwardly available on the other hand

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Part I Introduction

For over 5 years a GVA decomposition is performed by Statistics Poland thanks to some developments lastlypresented in:

Kotlewski D. and Błażej M. (2020), KLEMS GrowthAccounting Implemented in Poland, Statistics in Transition 3/2020

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Part I Introduction

Lastly, some new input data resource concerning the intermediate inputs in different prices became available. This turn has made possible to perform a gross output

decomposition into the contributions of intermediate inputs, labor services, capital services and MFP.

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Part I Introduction

Having that in mind, it is now possible to compare the two kinds of MFP:gross-output-basedgross-value-added-based

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Part I Introduction

When comparing the two kinds of MFPs, it was assumed that they are both valuable analytical tools

Therefore, the analysis of the substitution phenomenonbetween primary production factors and intermediate inputsis sensible and informative

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Part IIThe adopted methodology

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The methodology is based on the well-known KLEMS type GO growthdecomposition:

∆ 𝑙𝑙𝑙𝑙 𝑌𝑌𝑗𝑗𝑗𝑗 = �̅�𝑣𝑗𝑗𝑗𝑗𝑋𝑋∆ 𝑙𝑙𝑙𝑙 𝑋𝑋𝑗𝑗𝑗𝑗 + �̅�𝑣𝑗𝑗𝑗𝑗𝐾𝐾 ∆ 𝑙𝑙𝑙𝑙 𝐾𝐾𝑗𝑗𝑗𝑗 + �̅�𝑣𝑗𝑗𝑗𝑗𝐿𝐿 ∆ 𝑙𝑙𝑙𝑙 𝐿𝐿𝑗𝑗𝑗𝑗 +∆ 𝑙𝑙𝑙𝑙 𝐴𝐴𝑗𝑗𝑗𝑗𝑌𝑌 (1)

and the well-known KLEMS type GVA growth decomposition:

∆ 𝑙𝑙𝑙𝑙 𝑉𝑉𝑗𝑗𝑗𝑗 = �𝑤𝑤𝑗𝑗𝑗𝑗𝐾𝐾∆ 𝑙𝑙𝑙𝑙 𝐾𝐾𝑗𝑗𝑗𝑗 + �𝑤𝑤𝑗𝑗𝑗𝑗𝐿𝐿∆ 𝑙𝑙𝑙𝑙 𝐿𝐿𝑗𝑗𝑗𝑗 +∆ 𝑙𝑙𝑙𝑙 𝐴𝐴𝑗𝑗𝑗𝑗𝑉𝑉 (2)

However, the decomposition (2) is the one that is usually performed because ofdata availability issues!

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It is best the calculations to remain consistent between (1) and (2). Some

mathematical tool discrepancies will then be reduced. To do so, some values from

(2) have to be transposed into (1) as following:

∆ 𝑙𝑙𝑙𝑙 𝑌𝑌𝑗𝑗𝑗𝑗 = �̅�𝑣𝑗𝑗𝑗𝑗𝑋𝑋∆ 𝑙𝑙𝑙𝑙 𝑋𝑋𝑗𝑗𝑗𝑗 +𝑉𝑉𝑗𝑗𝑗𝑗𝑌𝑌𝑗𝑗𝑗𝑗

�𝑤𝑤𝑗𝑗𝑗𝑗𝐾𝐾 ∆ 𝑙𝑙𝑙𝑙 𝐾𝐾𝑗𝑗𝑗𝑗 +𝑉𝑉𝑗𝑗𝑗𝑗𝑌𝑌𝑗𝑗𝑗𝑗

�𝑤𝑤𝑗𝑗𝑗𝑗𝐿𝐿∆ 𝑙𝑙𝑙𝑙 𝐿𝐿𝑗𝑗𝑗𝑗 +∆ 𝑙𝑙𝑙𝑙 𝐴𝐴𝑗𝑗𝑗𝑗𝑌𝑌 (3)

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∆ 𝑙𝑙𝑙𝑙 𝑌𝑌𝑗𝑗𝑗𝑗 = �̅�𝑣𝑗𝑗𝑗𝑗𝑋𝑋∆ 𝑙𝑙𝑙𝑙 𝑋𝑋𝑗𝑗𝑗𝑗 +𝑉𝑉𝑗𝑗𝑗𝑗𝑌𝑌𝑗𝑗𝑗𝑗

�𝑤𝑤𝑗𝑗𝑗𝑗𝐾𝐾 ∆ 𝑙𝑙𝑙𝑙 𝐾𝐾𝑗𝑗𝑗𝑗 +𝑉𝑉𝑗𝑗𝑗𝑗𝑌𝑌𝑗𝑗𝑗𝑗

�𝑤𝑤𝑗𝑗𝑗𝑗𝐿𝐿∆ 𝑙𝑙𝑙𝑙 𝐿𝐿𝑗𝑗𝑗𝑗 +∆ 𝑙𝑙𝑙𝑙 𝐴𝐴𝑗𝑗𝑗𝑗𝑌𝑌 (3)

As can be seen in (3) the components from (2) have to be multiplied by the ratios between

GVA and GO at the industry j level. Moreover, they should be averages for two discrete

time periods t-1 and t, which are calculated by linear interpolation in a similar way as the

shares in the previous formulae (1) and (2).

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The contributions of production factors services from (3) should therefore be

further decomposed as following:

𝑉𝑉𝑗𝑗𝑗𝑗𝑌𝑌𝑗𝑗𝑗𝑗

�𝑤𝑤𝑗𝑗𝑗𝑗𝐾𝐾∆ 𝑙𝑙𝑙𝑙 𝐾𝐾𝑗𝑗𝑗𝑗 = 𝑉𝑉𝑗𝑗𝑗𝑗𝑌𝑌𝑗𝑗𝑗𝑗

�𝑤𝑤𝑗𝑗𝑗𝑗𝐾𝐾𝐾𝐾𝐾𝐾∆ 𝑙𝑙𝑙𝑙 𝐾𝐾𝐾𝐾𝐾𝐾𝑗𝑗𝑗𝑗 + 𝑉𝑉𝑗𝑗𝑗𝑗𝑌𝑌𝑗𝑗𝑗𝑗

�𝑤𝑤𝑗𝑗𝑗𝑗𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝐾∆ 𝑙𝑙𝑙𝑙 𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝑗𝑗𝑗𝑗 (4)

𝑉𝑉𝑗𝑗𝑗𝑗𝑌𝑌𝑗𝑗𝑗𝑗

�𝑤𝑤𝑗𝑗𝑗𝑗𝐿𝐿 ∆ 𝑙𝑙𝑙𝑙 𝐿𝐿𝑗𝑗𝑗𝑗 = 𝑉𝑉𝑗𝑗𝑗𝑗𝑌𝑌𝑗𝑗𝑗𝑗

�𝑤𝑤𝑗𝑗𝑗𝑗𝐿𝐿∆ 𝑙𝑙𝑙𝑙 𝐻𝐻𝑗𝑗𝑗𝑗 + 𝑉𝑉𝑗𝑗𝑗𝑗𝑌𝑌𝑗𝑗𝑗𝑗

�𝑤𝑤𝑗𝑗𝑗𝑗𝐿𝐿∆ 𝑙𝑙𝑙𝑙 𝐿𝐿𝐿𝐿𝑗𝑗𝑗𝑗 (5)

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The contribution of gross-output-based MFP from (1) and (3) can be made comparable to

the contribution of gross-value-added-based MFP from formula (2), if it is multiplied by the

inverse ratio between GVA and GO at industry j level taken from formula (3):

∆ 𝑙𝑙𝑙𝑙 𝐴𝐴𝑗𝑗𝑗𝑗𝑉𝑉∗ =𝑌𝑌𝑗𝑗𝑗𝑗𝑉𝑉𝑗𝑗𝑗𝑗

∆ 𝑙𝑙𝑙𝑙 𝐴𝐴𝑗𝑗𝑗𝑗𝑌𝑌 (6)

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∆ 𝑙𝑙𝑙𝑙 𝐴𝐴𝑗𝑗𝑗𝑗𝑉𝑉∗ = 𝑌𝑌𝑗𝑗𝑗𝑗𝑉𝑉𝑗𝑗𝑗𝑗

∆ 𝑙𝑙𝑙𝑙 𝐴𝐴𝑗𝑗𝑗𝑗𝑌𝑌 (6)

The asterisk indicates that the value from the left-hand side of (6) is derived from

the gross-output-based MFP, that can be equal to gross-value-added-based MFP,

on the condition that there is no substitution between the production factors

services and intermediate consumption:

∆ 𝑙𝑙𝑙𝑙 𝐴𝐴𝑗𝑗𝑗𝑗𝑉𝑉∗ ≈ ∆ 𝑙𝑙𝑙𝑙 𝐴𝐴𝑗𝑗𝑗𝑗𝑉𝑉 (7)

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If it is not so, then the phenomenon of substitution between primary production

factors and the intermediate consumption is to be considered as substantial!

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Part IIIDiscussion of the results

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Having calculated MFP both ways we can now make the comparison and try to interpret the difference


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MFP contribution to GO growth adjusted to GVA growthagainst MFP contribution to GVA growth straightforward

MFP contribution to GO growth adjustedto GVA growth

MFP contribution to GVA growthstraightforward

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After 2011 changes related to factor substitution by intermediate inputs have ceased

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…i.e. outsourcing growth (and additionallychanges in some capital being treated as intermediate consumption) has ceased

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During the onslaught of the financial crisis thischanges were also temporarily contained

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A sectoral analysis can be also performed in order to establishwhere in the economy these changes mostly take place!


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pp NACE section A MFP contribution to GO growth adjusted to GVA growthMFP contribution to GVA growth straightforward

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It is the manufacturing that contributes the most to the observed phenomenon of substitution

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This is because it accounts for about a quarter of the Polish economy and also because the vertical axis is steep

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pp NACE sections M-N One important feature is that in the ICT industriesthese changes seam to speed up

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pp NACE sections M-N … but because this NACE section is of much lower weight in the economy in comparison with manufacturing this is not

conspicuous at the aggregate level

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Access to data: https://stat.gov.pl/en/experimental-statistics/klems-economic-productivity-accounts

https://stat.gov.pl/en/experimental-statistics/klems-economic-productivity-accounts

Documents

Analysis of the Substitution between the Production