Productivity in Ireland 2021

Detailed Methodology

Methodology

All calculations used in this publication follow the methodology outlined by the OECD in their Measuring Productivity manual unless otherwise stated.

Sector Classifications

Sectors in this publication are classified using the Statistical Classification of Economic Activities in the European Community, also known as NACE classifications.

Foreign and Domestic Sectors of the Economy

This publication separates the economy into two distinct sectors: Foreign and Domestic. Foreign-owned Multinational Enterprise (MNE) dominated sectors are sectors where MNE turnover on average exceeds 85% of the sector total. Redomiciled PLCs (also known as corporate inversions) are also classified as foreign-owned MNEs. All other sectors are categorised as Domestic sectors.

The sectors classified as Foreign MNE-dominated in this publication are:

• Reproduction of Recorded Media (NACE 18.2)
• Chemicals & Chemical Products (NACE 20)
• Basic Pharmaceutical Products & Pharmaceutical Preparations (NACE 21)
• Computer, Electronic & Optical Products (NACE 26)
• Manufacture of Electrical Equipment (NACE 27)
• Manufacture of Medical and Dental Instruments and Supplies (NACE 32.5)
• Information & Communications (NACE 58-63)

The Manufacturing sector (NACE 10-33) therefore consists of both foreign and domestic subsectors. In order to present a more detailed view of the domestic economy, the Manufacturing sector is split into its foreign and domestic components in this publication.

Gross Value Added

Gross Value Added (GVA) is the typical measure of goods and services produced when analysing productivity. GVA is the difference between total output and intermediate consumption in the economy. In other words, it is the difference between the value of goods and services produced and the cost of raw materials and other inputs that are used up in the production process. Data on GVA is sourced from the both the Annual National Accounts and the Quarterly National Accounts publications.

Current Prices and Chain-Linked Volumes

While GVA is often reported in current prices, this is not an appropriate measure for calculating the growth of output in the economy over time, as it includes inflation. In order to best measure the change in the actual volume of goods and services produced, GVA is instead measured in chain-linked volumes, which removes the effect of changes in prices from year-to-year.

Hours Worked

Hours worked are the unit of labour input in this publication, following OECD methodology. Total hours worked are considered to be a more precise measure of labour input than employment as it captures differences in hours worked in different jobs due to factors such as leave, part-time working arrangements and time unemployed during the year. Hours worked in this publication includes both employees and the self-employed, and measures hours actually worked, rather than paid hours worked. Data on hours worked is sourced from the Labour Force Survey (LFS), which is published by the CSO on a quarterly basis.

Labour Productivity

Labour productivity (LP) measures output in the economy relative to labour input. It is calculated as Gross Value Added in chain-linked volumes (GVA^CL) divided by total hours worked (HW) in the economy.

LPt	=	GVAtCL
		HWt

Growth Rates and Log Growth Rates

All growth rates presented in this publication are log growth rates. A log growth rate is a logarithmic transformation of an ordinary growth rate. As many of the indices used in productivity analysis are related multiplicatively, using a log transformation allows for the relationships between these variables to be shown additively.

For example, labour productivity growth (γ^LP) can be described using the relationship between GVA and hours worked as follows:

1	+	γtLP	=	(	GVAtCL	)
					GVAt-1CL
				(	HWt	)
					HWt-1

However, by using a log transformation, using the natural logarithm, the log growth rate of labour productivity can be expressed as:

ln(1+γtLP)	=	ln	(	GVAtCL	)	-	ln	(	HWt	)
				GVAt-1CL					HWt-1

Additionally, the ratios of GVA and hours worked can also be rewritten as log growth rates giving:

ln(1+γtLP)

=

ln(1+γtGVA)

-

ln(1+γtHW)

This expression shows that the log growth rate of labour productivity can be expressed as the difference between the log growth rates of GVA and hours worked. A similar formula is used for calculating Multifactor Productivity (MFP) growth. By using log growth rates, these relationships can also be easily visualised using stacked bar charts, unlike ordinary growth rates.

It should be noted that while log growth rates are approximately equal to ordinary growth rates when growth rates are small (, this relationship breaks down for larger growth rates. In cases where the growth rate is both negative and large in magnitude, the log growth rate will be greater than the ordinary growth rate. If the growth rate is both large and positive, the log growth rate will be less than the ordinary growth rate.

Converting Log Growth Rates to Ordinary Growth Rates

As log growth rates are logarithmic transformations of ordinary growth rates, they can be easily transformed back to ordinary growth rates using an exponential transformation. For example, the log growth rate of Labour Productivity (β_LPt) can be transformed to the ordinary growth rate of Labour Productivity (y_LPt) using:

γLPt

=

exp(βLPt)

-

1

Labour and Capital Shares

The labour share is defined as the proportion of GVA attributed to labour. The labour share reflects the proportion of national income received by workers in the form of wages and salaries as well as self-employed income. Likewise, the capital share reflects the proportion of national income received by companies in the form of profits. The labour share and capital shares are calculated using the methodology outlined by the OECD. In order to calculate the labour and capital shares, labour and capital compensation must first be estimated.

Calculating Labour and Capital Compensation

Labour Compensation (COMP^L) measures the value of GVA attributed to labour in current prices. It consists of Compensation of Employees (COE) and the labour shares of both Gross Mixed Income (GMI^L) and Net Taxes less Subsidies on Production (NTS^L):

COMPtL

=

COEt+GMItL+NTStL

Capital Compensation (COMP^K) consists of Gross Operating Surplus (GOS) and the capital shares of both Gross Mixed Income (GMI^K) and Net Taxes less Subsidies on Production (NTS^K):

COMPtK

=

GOSt+GMItK+NTStK

All of the calculations related to labour and capital compensation are calculated at the sector level. Higher aggregates such as the total economy level are calculated as the sum of the sector components, rather than repeating the calculation at aggregate level.

Calculating the Labour and Capital Components of Gross Mixed Income

The labour component of Gross Mixed Income (GMI^L) is defined as the portion of GMI that is attributable to labour. It is measured by assuming that self-employed workers earn the same hourly wage as employees in the sector. In the case that this figure would exceed total GMI, it is set equal to GMI as follows:

GMItL =

{

HWtSELF

x

(

COEt

),

HWtSELF

x

(

COEt

)

≤ GMIt

HWtEMP

HWtEMP

GMIt

,

HWtSELF

x

(

COEt

)

> GMIt

HWtEMP

The capital component of Gross Mixed Income (GMI_K) is then calculated as the remainder of total GMI:

GMItK

=

GMIt

-

GMItL

Calculating the Labour and Capital Components of Net Taxes less Subsidies on Production

The labour component of Net Taxes less Subsidies on Production (NTS^L) is defined as the portion of net taxes less subsidies on production that is attributable to labour. It is calculated using the ratio of the sum of COE and the labour component of GMI to the sum of COE, GMI and GOS. In some rare cases, this ratio can be greater than one, which occurs only when GOS is negative. In such cases, the labour component of net taxes less subsidies on production is set equal to total net taxes less subsidies as follows:

NTStL

=

{

NTSt

X

(

COEt + GMItL

)

,

(

COEt + GMItL

)

< 1

COEt + GOSt + GMIt

COEt + GOSt + GMIt

NTSt

,

(

COEt + GMItL

)

≥ 1

COEt + GOSt + GMIt

The capital component of Net Taxes less Subsidies on Production (NTS^L) is then calculated as the remainder of total net taxes less subsidies on production:

NTStK

=

NTSt

-

NTStL

Calculating the Labour and Capital Shares

Having calculated labour compensation (COMP^L) and capital compensation (COMP^K), the labour share (s^L) is calculated as the ratio of labour compensation to the sum of labour compensation and capital compensation. In some rare cases, this ratio is greater than one, which only occurs when capital compensation is negative. In such cases, the labour share is set to one as follows:

stL	=	{	COMPtL	,	COMPtL	< 1
			COMPtL + COMPtK		COMPtL + COMPtK
			1	,	COMPtL	≥ 1
					COMPtL + COMPtK

The capital share (s^K) is then calculated as one minus the labour share:

stK

=

1 - stL

Capital Services

Capital services are the measure of capital input (equivalent to hours worked for labour) used for productivity analysis following the OECD methodology. They are distinct from capital stocks in that they measure the flow of services from the assets rather than level of the capital stock. For this reason, they are the measure of capital used to calculate multifactor productivity (MFP).

Capital services are provided by produced fixed assets, which are assets that result from human effort. They exclude financial assets and natural assets such as land and mineral deposits.

There are six categories of produced fixed assets used in this publication:

• Dwellings
• Buildings and Structures excluding Dwellings
• Transport Assets
• Machinery and Equipment excluding Transport Equipment
• Cultivated Assets
• Intangible Assets

Data on capital stocks is taken from the Estimates of the Capital Stock of Fixed Assets publication.

Calculating Capital Services

Capital services are calculated at the asset-specific sector level for each year. In order to calculate capital services for a particular asset type in a given sector in a given year, there are several input variables required:

• The value of the asset type in both current prices (CAP^CP) and chain-linked volumes (CAP^CL)
• The deflator (q) used to convert the asset value from current prices to chain-linked volumes
• The depreciation rate (d) of the asset type
• The capital compensation (COMP^K) of the sector

Using these variables, an endogenous rate of return for each sector can be calculated, which is then used to calculate the user cost for each asset and ultimately, the value of the capital services provided by each asset type.

Calculating the Rate of Return

The rate of return (r) for each asset type is the rate of return on capital within each sector. As capital compensation cannot be specifically allocated to a particular asset type within a sector, a common rate of return is calculated at the sector level and assumed to be the same for each asset type within each sector.

For a sector i with asset types j = 1,...,J, the rate of return (r_i) is given by:

ri,t	=	COMPi,tK + ∑j[CAPi,j,tCL X (qi,j,t - qi,j,t-1)] - ∑j[CAPi,j,tCL x qi,j,t  x di,j,t]
		∑j[CAPi,j,tCL X qi,j,t]

The rate of return for a sector is therefore calculated as the sum of capital compensation (COMP_i,t^K) and capital gains/losses (∑_j[CAPi,j,t^CL X (q_i,j,t - q_i,j,t-1)] less depreciation (∑_j[CAPi,j,t^CL X (q_i,j,t X  d_i,j,t]) divided by the total capital stock for the sector (∑_j[CAPi,j,t^CL x q_i,j,t]).

Calculating the User Costs

The user cost (μ) of an asset type measures the implied rental price of one unit of that particular asset type. It is calculated at the asset level for each sector as follows:

μi,j,t

=

qi,j,t

X

[

ri,t + di,j,t

]

-

[

(qi,j,t - qi,j,t)

]

The user cost of an asset is therefore calculated as the difference between the cost of financing the asset (q_i,j,t x [r_i,t + d_i,j,t]) and the capital gains/losses on the asset.

Calculating Capital Services

Having calculated the user cost (μ_i,j) of asset type j for sector i, the value of the capital services (CS_i,j) provided by that asset type is given by: 

CSi,j,t

=

μi,j,t

X

CAPi,j,tCL

The value of capital services provided by an asset type is therefore measured as the net capital stock of the asset type in chain-linked volumes multiplied by its user cost.

Finally, the capital services used by a sector i is measured as the sum of the capital services provided by each asset-type j = 1, ..., J as follows:

CSi,t

=

∑j CSi,j,t

Calculating the Capital Services Index

In order to calculate the contribution of capital to GVA growth, a capital services index must be constructed. The OECD manual recommends using a Tornqvist quantity index of aggregate capital services for this purpose. The key benefits of this choice of index are that it allows for each of the asset types to be weighted by their user costs, while also allowing for flexible weights over time, rather than using the fixed weights of a particular base period. By using user costs as the weights for the index, higher weights are given to assets which depreciate more quickly, while lower weights are given to asset types with longer service lives.

The user cost capital services weights (s_i,j^CS) for sector (i) with asset types j = 1, ..., J is given by:

si,j,tCS	=	CSi,j,t
		∑jCSi,j,t

Having calculated the user cost capital services weights, the Tornqvist quantity index of aggregate capital services (CSI_i) for sector (i) with asset types j = 1, ..., J is given by:

CSIi,t	=	πj	[		]	(	si,j,tCS+si,j,t-1CS	)
				CAPi,j,tCL			2
				CAPi,j,t-1CL

For higher level aggregates with i = 1, ..., I subsectors, such as the Total Economy, the aggregate capital services index CSI_t is given by:

CSIt	=	πi,j	[		]	(	si,j,tCS + si,j,t-1CS	)
				CAPi,j,tCL			2
				CAPi,j,t-1CL

Log Transformation of the Capital Services Index

Applying a log transformation to the capital services index facilitates the decomposition of the index into the contributions of each asset type (or sector for higher level aggregates). The log capital services index (ln(CSI_i)) for sector i with asset types j = 1, ..., J is given by:

ln(CSIi,t)	=	∑j	(	si,j,tCS+si,j,t-1CS	)	ln	(	CAPi,j,tCL	)
				2				CAPi,j,t-1CL

Multifactor Productivity (MFP)

Multifactor productivity (MFP) reflects the overall efficiency with which labour and capital inputs are used in the production process. It is a more detailed measure of productivity than labour productivity as it explicitly considers the influence of capital in overall productivity. Changes in MFP are indicative of changes in organisational behaviour and management practices, economies of scale and all factors other than the level of labour and capital. Unlike labour productivity, MFP is not directly observable, and so changes in MFP have to be calculated as a residual measure. This means that changes in MFP also include measurement error, however this is also the case for all other measures of productivity.

Multifactor Productivity Growth

As stated above, while the level of MFP is not directly observable, changes in the level of MFP can be calculated by residual. This is achieved by constructing a combined index of labour and capital. The OECD methodology recommends the use of a Tornqvist index for this purpose, using the labour and capital shares as the weights with which the combine the labour and capital indices.

Gross Value Added, Labour and Capital Indices

The GVA index (Y) of a sector  is given by:

Yi,t	=	GVAi,tCL
		GVAi,tCL

The labour input index (L) of a sector i is given by:

Li,t	=	HWi,t
		HWi,t-1

The capital input index (K) of a sector i is given by:

								(	si,j,tCS + si,t-1CS	)
Ki,t		CSIi,t	=	πj	[	CAPi,j,tCL	]		2
						CAPi,j,t-1CL

Calculating MFP Growth

Having constructed the GVA index (Y), the labour index (L) and capital index (K), as well as the labour share (s^L) and capital share (s^K), the MFP index (MFP) of a sector i is given by:

MFPi,t	=	Yi,t
			(	si,tL + si,t-1L	)			(	si,tK+ si,t-1K	)
		Li,t		2		X	Ki,t		2

MFP growth is typically measured as a log growth rate. The log growth rate of MFP (ln(MFP) for a sector is given by:

ln(MFPi,t)	=	ln(Yi,t)	-	[	(	si,tL + si,t-1L	)	ln(Li,t)	+	(	si,tK + si,t-1K	)	ln(Ki,t)	]
						2					2

Therefore, log MFP growth is calculated as the difference between log GVA growth and the weighted sum of the log growth rates of the labour and capital indices.

Labour and Capital Contributions to GVA Growth

GVA growth is typically decomposed into contributions of labour and capital, with MFP growth explaining the remainder. This is shown using a log transformation, as it allows the relationship to be presented additively

The labour contribution (CON_i^L) of a sector i to its log GVA growth (ln(Y_i,t)) is given by:

(	si,tL+  si,t -1L	)	ln(Li,t)
	2

The capital contribution (CON_i^K) of a sector i to its log GVA growth (ln(Yi,t)) is given by:

(	si,tK+  si,t -1K	)	ln(Ki,t)
	2

Therefore, log GVA growth (ln(Y_i,t)) can be decomposed as follows:

ln(Yi,t)

=

CONi,tL + CONi,tK + ln(MFPi,t)

Nominal Unit Labour Cost

The Nominal Unit Labour Cost (ULC) measures hourly employee compensation relative to real labour productivity. Growth in an economy’s unit labour cost suggests that the cost of labour in the economy is rising relative to labour productivity, decreasing competitiveness. On the other hand, a decline in unit labour cost suggests that the cost of labour is declining relative to labour productivity, increasing competitiveness.

The nominal unit labour cost (ULC) of a sector i is given by:

ULCi,t	=	(	COEi,t	)		(	COEi,t	)
			HWi,tEMP		=		HWi,tEMP
		(	GVAi,tCL	)			LPi,t
			HWi,t

Capital Intensity and Capital Deepening

Capital intensity is the ratio of capital services to hours worked in the economy (i.e. capital services per hour). The higher the capital to hours ratio, the more capital intensive the production process becomes. The capital intensity (CI) of a sector i is given by:

CIi,t	=	CSi,t
		HWi,t

Capital deepening is defined as the growth of capital intensity. The capital deepening (CD) of a sector i is given by:

CDi,t	=	Ki,t
		Li,t

It is also possible to show the contribution of capital deepening to labour productivity growth by weighting capital deepening by the two-period average capital share. This is given by:

LPi,t	=	CDi,t	(	si,tK+ si,t-1K	)
				2		X MFPi,t
LPi,t-1

Sector Contributions to Aggregate Labour Productivity Growth

It is possible to decompose labour productivity growth for an aggregate such as the total economy into the contributions of its subsectors. In this publication, this is achieved using the Generalised Exactly Additive Decomposition (GEAD) model.

In the GEAD model, sector contributions to aggregate labour productivity growth can be decomposed into two components: a productivity effect and a reallocation effect. Sectors can increase aggregate labour productivity by increasing their own labour productivity, which is known as the productivity effect. However, sectors can also increase aggregate labour productivity by becoming relatively larger in the economy if they are themselves more productive than the aggregate, or relatively smaller if they are less productive than the aggregate. This is known as the reallocation effect.

There are several steps required to calculate sector contributions to aggregate labour productivity growth.

Firstly, the output price deflator (P) is calculated by:

Pi,t	=	GVAi,tCP
		GVAi,tCL

Next, several ratios are calculated which compare sector variables to their overall aggregate as follows:

pi,t	=	Pi,t	;	li,t	=	HWi,t
		Pt				HWt

Finally, labour productivity growth (G) is given by:

Gi,t	=	LPi,t	-	1
		LPi,t-1

Labour productivity growth (G) for an aggregate with i = 1, ..., I subsectors can then be decomposed using:

Gt

=

∑i

φi,t

+

ωi,t

The productivity effect (φ) is defined in this publication as the part of aggregate labour productivity growth that is explained only by changes in the labour productivity of subsectors of the overall aggregate:

φt	=	∑i	Gi,t	(	GVAi,t-1CP	)
					GVAt-1CP

The reallocation effect (ω) is defined in this publication as the part of aggregate labour productivity growth that is explained by changes in the relative size of sectors, both in terms of output and hours worked:

ωt

=

∑i

[

Gi,t

(

LPi,t-1

)

(

pi,tli,t - pi,t-1li,t-1

)

+

(

LPi,t-1

)

(

pi,tli,t - pi,t-1li,t-1

)

]

LPt-1

LPt-1

The contribution (CON_i^LP) of an individual sector i to aggregate labour productivity growth is then given by:

CONi,tLP

=

φi,t

+

ωi,t

Quality-Adjusted Labour Input (QALI)

While using hours worked is appropriate to measure the quantity of labour input, it fails to capture the differences in the quality of those hours, as not all hours worked are equally productive. For example, an hour of work by a surgeon is arguably more productive than an hour of work by cleaner. The Quality-Adjusted Labour Input (QALI) methodology attempts to quantify the change in the quality of hours worked by weighting hours growth by the earnings associated with those hours. The underlying assumption is that workers with higher earnings are providing higher quality and more productive labour input. The difference between the QALI and hours growth estimates is generally referred to as the composition effect, which is used to measure changes in the quality of hours worked.

The index is provided at both the ten sector (A10) and total economy levels. While the aggregate measures of hours worked and earnings are sourced from the National Accounts, the data used to capture differences in hours worked (by Sex, Age and Level of Education) is taken from the European Union Survey on Income and Living Conditions (EU-SILC). Given the relatively small sample size associated with each category in the EU-SILC, the data is presented at the A10 level. Due to these constraints, the results are labelled as Experimental Statistics rather than the Official Statistics seen elsewhere in the publication.

QALI Categories

The labour force of each sector is broken down into specific categories depending on age, sex and education level. There are three categories for age (18-29, 30-49, 50+), two categories for sex (Male and Female) and three categories for education level (Junior Certificate, Leaving Certificate and Post-Leaving Certificate). This means that there are eighteen categories of hours worked for each sector.

Sex	Age	Education
Male Female	18-29 30-49 50+	Junior Certificate Leaving Certificate Post-Leaving Certificate

Calculating the QALI Index

The QALI Index is calculated as a Tornqvist index at the age, sex and education category level for each sector. The QALI Index (QALI) of a sector i with categories j = 1, ..., J is given by:

						(	si,j,tCOE + sCOE	)
QALIi,t	=	πj	[	HWi,j,t	]		2
				HWi,j,t-1

The weights for the QALI Index are calculated as the two-period average shares of COE for each category within the overall sector, where the annual shares (s_i,j^COE) are calculated as:

si,j,tCOE	=	COEi,j,t
		∑jCOEi,j,t

For higher level aggregates with i = 1, ..., I subsectors, such as the Total Economy, the aggregate QALI index QALI_t is given by:

						(	si,j,tcs + si,j,t-1cs	)
QALIt	=	πi,j	[	HWi,j,t	]		2
				HWi,j,t-1

Calculating the Composition Effect

The composition effect (COMP^HW) measures changes in the quality of the labour force between periods. It is calculated as the ratio of the QALI and hours worked indices as follows:

COMPi,tHW	=		QALIi,t
		[	HWi,t	]
			HWi,t-1

The composition effect is usually presented as a log growth rate, using:

ln(COMPi,tHW)	=	ln	(QALIi,t)	-	ln	(	HWi,t	)
							HWi,t-1

KLEMS Indicators

KLEMS is an acronym referring to Capital (K), Labour (L), Energy (E), Materials (M) and Services (S). While the main indicators in this publication use Gross Value Added (GVA) as the level of production in the economy, KLEMS indicators additionally consider the intermediate inputs consumed in the production process. Therefore, KLEMS indicators use  (which includes intermediate consumption) as the measure of the total level of production for each sector in the economy and facilitate a more nuanced analysis of the factors contributing to output growth than the traditional GVA-centric approach.

Using the KLEMS approach, Gross Output growth can be decomposed into not only the contributions of Capital and Labour, but also the contributions of the intermediate inputs of Energy, Materials and Services. This results in a different measure of Multifactor Productivity (MFP) growth than found when using the GVA-centric approach, which should therefore exclude the effects of changes in the level of intermediate consumption.

Data on Gross Output and intermediate consumption is taken from the  publication. The data used to categorise the intermediate consumption is taken from the Use Table of the , which give a detailed breakdown of intermediate consumption of products and services by economic sector. Gross Output and intermediate consumption are both adjusted to exclude inter-industry deliveries of intermediate inputs to avoid overstating the output of each sector.

Calculating KLEMS Indicators

In order to calculate the KLEMS indicators relating to Gross Output growth, an approach similar to that for the GVA indicators is used. There are three main steps involved in the calculation of the KLEMS indicators:

1. Allocation of intermediate consumption to the Energy, Materials and Services categories
2. Calculation of Gross Output Shares
3. Calculation of KLEMS contributions to Gross Output growth

Allocation of Intermediate Consumption to EMS Categories

Intermediate consumption from the Supply and Use Tables is split into the categories of Energy, Materials and Services based on Statistical Classification of Products by Activity (CPA) codes as follows:

Energy	Materials	Services
CPA 05-09, 19 and 35	CPA 01-03, 10-18, 20-33, 36-43	CPA 45-98

Calculating Gross Output Shares

In the same way that GVA is split into labour and capital shares, Gross Output can be split into shares relating to each of the KLEMS components.

The Gross Output Labour Share (s_tL) and Capital Share (s_t^K) for a sector i are calculated as the proportions of labour and capital compensation to Gross Output:

si,tL	=	COMPi,tL	;	si,tK	=	COMPi,tK
		GOi,t				GOi,t

The Gross Output Energy Share (s_i,t^E), Materials Share (s_i,t^M) and Services Share (s_i,t^S) are similarly calculated as:

si,tE	=	Ei,t	;	si,tM	=	Mi,t	;	si,ts	Si,t
		GOi,t				GOi,t			GOi,t

The two-period average Gross Output shares are calculated as:

stL	=	stL + st-1L
		2

Calculating KLEMS Contributions to Gross Output Growth

In order to calculate the KLEMS contributions to Gross Output growth, all of the variables involved (other than hours worked) must first be converted to chain-linked volumes. Having measured each of the variables in chain-linked volumes, the KLEMS decomposition of Gross Output growth for a sector i is given by: 

GOi,tCL

=

[

Li,t

]

stL

X

[

Ki,tCL

]

stK

X

[

Ei,tCL

]

stE

X

[

Mi,tCL

]

stM

X

[

Si,tCL

]

stS

X

[

MFPi,t

]

GOi,t-1CL

Li,t-1

Ki,t-1CL

Ei,t-1CL

Mi,t-1CL

Si,t-1CL

MFPi,t-1

The contributions of each of the KLEMS components and MFP growth to Gross Output growth is traditionally presented using a log transformation:

ln

(

GOi,tCL

)

=

CONi,tL

+

CONi,tK

+

CONi,tE

+

CONi,tM

+

CONi,tS

+

ln

(

MFPi,t

)

GOi,t-1CL

MFPi,t-1

The contributions of each component to Gross Output growth, such as the contribution of Energy, are given by:

CONi,tE	=	stE	X	ln	(	Ei,tCL	)
						Ei,t-1CL