This publication is categorised as a Frontier Series Output. Particular care must be taken when interpreting the statistics in this release as it may use new methods which are under development and/or data sources which may be incomplete, for example, new administrative data sources.
All calculations used in this publication follow the methodology outlined by the OECD in their Measuring Productivity manual unless otherwise stated.
Sectors in this publication are classified using the Statistical Classification of Economic Activities in the European Community, also known as NACE classifications.
This publication separates the economy into two distinct sectors: Foreign and Domestic & Other. 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 and Other sectors.
The sectors classified as Foreign MNE-dominated in this publication are:
It should be noted that Rental & Leasing Services (NACE 77) is not classified as Foreign MNE-dominated in other CSO National Accounts publications. It is classified as such in the CSO’s Productivity statistics due to the concentration of foreign-owned capital in the sector.
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.
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 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 (LP) measures output in the economy relative to labour input. It is calculated as Gross Value Added in chain-linked volumes (GVACL) divided by total hours worked (HW) in the economy.
| LPt | = | GVAtCL |
| HWt |
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 (γLP) 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 | ) |
| GVACL | 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.
As log growth rates are logarithmic transformations of ordinary growth rates, they can be easily transformed back to ordinary growth rates using and exponential transformation. For example, the log growth rate of Labour Productivity (βLPt) can be transformed to the ordinary growth rate of Labour Productivity (yLPt) using:
| γLPt | = | exp(βLPt) | - | 1 |
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.
Labour Compensation (COMPL) 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 (GMIL) and Net Taxes less Subsidies on Production (NTSL):
| COMPtL | = | COEt+GMItL+NTStL |
Capital Compensation (COMPL) consists of Gross Operating Surplus (GOS) and the capital shares of both Gross Mixed Income (GMIK) and Net Taxes less Subsidies on Production (NTSK):
| 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.
The labour component of Gross Mixed Income (GMIL) 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 (GMIK) is then calculated as the remainder of total GMI:
| GMItK | = | GMIt | - | GMItL |
The labour component of Net Taxes less Subsidies on Production (NTSL) 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 (NTSL) is then calculated as the remainder of total net taxes less subsidies on production:
| NTStK | = | NTSt | - | NTStL |
Having calculated labour compensation (COMPL) and capital compensation (COMPK), the labour share (sL) 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 (sK) is then calculated as one minus the labour share:
| stK | = | 1 - stL |
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:
Data on capital stocks is taken from the Estimates of the Capital Stock of Fixed Assets publication.
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:
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.
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 (ri) is given by:
| ri,t | = | COMPi,tK + ∑j[CAPi,j,tCL X (qi,j,t - qi,j,t-)] - ∑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 (COMPi,tK) and capital gains/losses (∑j[CAPi,j,tCL X (qi,j,t - qi,j,t-1)] less depreciation (∑j[CAPi,j,tCL X (qi,j,t X di,j,t]) divided by the total capital stock for the sector (∑j[CAPi,j,tCL x qi,j,t]).
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 (qi,j,t x [ri,t + di,j,t]) and the capital gains/losses on the asset.
Having calculated the user cost (μi,j) of asset type j for sector i, the value of the capital services (CSi,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 |
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 (si,jCS) 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 (CSIi) 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 | |||||||
| CAPCL |
For higher level aggregates with i = 1, ..., I subsectors, such as the Total Economy, the aggregate capital services index CSIt is given by:
| CSIt | = | πi,j | [ | ] | ( | si,j,tCS + si,j,t-1CS | ) | |
| CAPi,j,tCL | 2 | |||||||
| CAPi,j,t-1CL |
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(CSIi)) for sector i with asset types j = 1, ..., J is given by:
|
ln(CSIi,t) |
= |
∑j | ( | si,j,tCS+sCS | ) | ln | ( | CAPi,j,tCL | ) |
| 2 | CAPCL |
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.
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.
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 is given by:
| ( | si,j,tCS + sCS | ) | ||||||||
| Ki,t | = | CSIi,t | = | πj | [ | CAPi,j,tCL | ] | 2 | ||
| CAPi,j,t-1CL |
Having constructed the GVA index (Y), the labour index (L) and capital index (K), as well as the labour share (sL) and capital share (sK), the MFP index (MFP) of a sector i is given by:
| MFPi,t | = |
Yi,t | ||||||||
| ( | si,tL + L | ) | ( | si,tK+ K | ) | |||||
| 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.
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 (CONiL) of a sector i to its log GVA growth (ln(Yi,t)) is given by:
| ( | si,tL+ si,t -1L | ) | ln(Li,t) |
| 2 |
The capital contribution (CONiK) 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(Yi,t)) can be decomposed as follows:
| ln(Yi,t) | = | CONi,tL + CONi,tK + ln(MFPi,t) |
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 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 | ||||||
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 | [ | Gi,t | ( | GVAi,t-1CP | ) | + | Gi,t | ( | LPi,t-1 | ) | + | ( | pi,tli,t - pi,t-1li,t-1 | ) | + | ( | LPi,t-1 | ) | + | ( | pi,tli,t - pi,t-1li,t-1 | ) | ] |
| GVAt-1CP | LPt-1 | LPt-1 |
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 (CONiLP) of an individual sector i to aggregate labour productivity growth is then given by:
| CONi,tLP | = | φi,t | + | ωi,t |
The seasonal adjustments are completed by applying the X-13-ARIMA model, developed by the U.S. Census Bureau to the unadjusted data. This methodology estimates seasonal factors while also taking into consideration factors that impact on the quality of the seasonal adjustment such as:
For additional information on the use of X-13-ARIMA see US Census Bureau information on X-13ARIMA-SEATS Seasonal Adjustment Program.
Seasonally adjusted aggregates can be computed either by aggregating the seasonally adjusted components (indirect adjustment) or adjusting the aggregate and the components independently (direct adjustment). In this publication, seasonal adjustment is conducted using the indirect seasonal adjustment approach. This approach is in line with CSO’s Policy on Seasonal Adjustment and Eurostat’s Recommendations on Seasonal Adjustment. The indirect approach can give the best results when the component series show very different seasonal patterns, which is a feature of some data series in the Irish National Accounts. Under this indirect approach, individual time series are independently adjusted at the component level. These individual series are then aggregated to compute seasonally adjusted results for GVA, Labour Compensation etc. As part of the seasonal adjustment process using the US Census Bureau’s X-13-ARIMA framework, RegARIMA models are identified for each series based on unadjusted data spanning Q1 2010 to Q3 2023. These models are then applied to the entire series (Q1 2010 to Q3 2023). Seasonal factors and the parameters of the RegARIMA models are updated each quarter.
As this release provides a higher level of disaggregation for some sectors compared to the Quarterly National Accounts (QNA), the seasonal adjustment process can lead to inconsistencies between this release and the QNA. For example, the sum of Manufacturing – Domestic GVA and Manufacturing – Foreign GVA in this release will not exactly match the seasonally-adjusted Manufacturing GVA in the QNA.
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