Diagnosing the UK Productivity Slowdown: Which Sectors Matter and Why?

This paper explores the slowdown in labour productivity growth in the UK and other advanced economies by decomposing its growth into contributions from different sectors of the economy, looking both at within-industry productivity growth and labour reallocation between sectors. We find that the within-industry contribution is the main source of the slowdown. Comparing trends preand post-2008, the aggregate productivity slowdown can largely be attributed to the manufacturing and the information and communication sectors. Disaggregating further, the UK productivity growth slowdown can be mainly attributed to transport equipment and pharmaceuticals within manufacturing, and computer software and telecommunications within information and communication. Strikingly, these are advanced, high value added sectors considered to be strengths of the UK economy. Looking across other advanced economies, our results confirm that manufacturing and information sectors are the main drivers of the labour productivity growth slowdown. Part of the explanation for the slowdown in in these sectors may relate to the underlying question of how to construct deflators for a modern economy when technological and structural changes are leading to large relative price shifts. The structure and supply chains of the key slowdown sectors also merit further investigation.


Introduction
The 'puzzle' of the productivity slowdown has been extensively explored. This paper extends this body of work by decomposing the aggregate productivity statistics into the different sectors and sub-sectors in order to see how either dispersed or concentrated the slowdown has been. One of the questions often raised in discussions of the slowdown is to what extent it reflects specific sectoral slowdowns or, instead, shifts in activity from high to low productivity sectors. We find that the main contribution to the slowdown is within the manufacturing and information and communication sectors, and within these in certain sub-sectors such as pharmaceuticals and software generally considered to be among the leading industries in the economy.
The term `productivity' itself has a meaning in everyday use that differs from its specific meaning in economics. For example, in business the variable of interest will often be engineering efficiency, or perhaps revenue or value added per hour worked in current price terms, whereas economists are interested in real terms output or value added per hour (i.e. revenue or value added deflated by a price index). This is because deflating by a price index removes general inflationary effects to give a measure (in constant prices) closer to an economic welfare measure: deflators are constant utility constructs (e.g., Diewert 1995). The intuitive way to think about the deflation exercise is as separating the quantity of something sold from its price; how many haircuts or apples are bought and sold is more relevant to economic progress than how many dollars or pounds are involved in the transaction. Yet for aggregate economic measurement, the 'real' quantities need to be added together; and as apples, haircuts, cars and all the myriad other products are counted in different volume units (and indeed the volume units are not obvious in many services such as accountancy or software), they are all converted into monetary terms for the purposes of aggregation. Real GDP is thus a money metric of economic welfare or utility (Hillinger, 2002), not a straightforward measure of quantity. Thomas Schelling (1958) was referring to this when he stated: "[W]hat we call `real' magnitudes are not completely real; only the money magnitudes are real. The `real' ones are hypothetical".
As economic statistics are often generated from collecting data in terms of monetary revenues, the price-quantity split is then constructed by deflating revenues by a price index (industry-level deflators are constructed from product prices). In moving from current price revenue or value added per hour to the real terms labour productivity figures economists are interested in therefore requires using an appropriate price index to deflate current price value added. Similarly, in moving from aggregate labour productivity to individual sectoral level measures, there are choices to be made in calculating labour productivity; is current price output to be deflated using a separate output price index for each sector, or should nominal value added simply be adopted when estimating? In moving from gross output to value added, similarly, the most appropriate input price deflators will differ between sectors. A further choice concerns how to weight the sectors of the economy to add them up to the aggregate level -should the weights use their share in total revenues, or volume or employment shares instead? When sectoral relative prices are changing these will differ substantially (e.g. Abdirahman et al., 2022). The weights, therefore, have an important meaning in the analysis of the sectoral contributions to aggregate labour productivity growth.
For an initial look, we show in Figure 1 current price value added per hour worked in the UK. The figure omits real estate, mining and utilities, which all have substantially higher current price value added per hour due to their distinctive features. After these, finance (brown) and manufacturing (blue) have highest current price value added per hour, and for both the decrease in gradient post-2007 is visually evident; indeed there has been an absolute decline for finance. Slowdowns are also readily visible for Professional, scientific and technical activities (industry M) and wholesale and retail trade (industry G). We test for a break in trend (log change) between 1998-2007 and 2008-2019 in Appendix I Table AI 1, confirming that Water supply (industry E), Construction (industry F), Information communication (industry J), Professional and scientific (industry M), Education (industry P), and Human health (industry Q) experienced a statistically significant slowdown (at the 5% level) in current price terms during the post-crisis period.
Yet the picture is different when we turn to the deflated or 'real terms' value added per hour, where the revenue series for each sector is deflated by a sector-specific output price deflator. These do not have natural units so are rebased to 1997=100. The labour productivity of the information and communication sector has grown substantially in real terms over the entire period, and both manufacturing and agriculture have grown too. Other sectors experienced either modest productivity growth or some decline -particularly mining and quarrying. As our focus is explaining the slowdown after the mid-2000s, we test for a break in growth rates for [1998][1999][2000][2001][2002][2003][2004][2005][2006][2007] compared to 2008-2019; the results in Appendix I Table AI 2 reveal that both manufacturing and information communication nevertheless experienced the most significant slowdowns in real value added per hour growth (at the 1% statistical significance level) over the post-crisis period.
Other industries including wholesale and retail trade, financial services, administrative services, and public administration have also grown significantly more slowly in the period 2008-2019 compared to 1998-2007. These charts nevertheless do not answer the question about the role played by reallocation of activity from high to low productivity sectors and the pure within -sector productivity contribution. To disentangle this question, previous studies have estimated the trend differences (before and after 2008) using different decomposition approaches (see, for Notes: Nominal value added per hour is measured by using the all-industry current price value added divided by total hours worked. There are 20 industries making up the whole economy sector (A-T, see data section for more details). We exclude mining and quarrying, electricity, gas, steam and air conditioning supply, and real estate activities. Real gross value added per hour is measured by using total gross value added in chain volume measure divided by the total hours worked based on the new double deflated data updated since 30 th Sep 2021 by ONS. See ONS Bluebook 2021 for more details.
Source: Authors' calculations by using bb2102industrialanalysis and gdpolowlevelaggregates2021q3 data series from ONS.
Although the recent empirical literature (such as Harris and Moffat (2014) 1 and Craft and Mills (2020), Goodridge, Haskel, and Wallis, 2018) 2 confirms the UK productivity slowdown, this paper updates prior research on UK labour productivity by using recent ONS statistics that have incorporated double deflation for the first time. In Section 2, we clarify how the aggregate data and the sectoral data relate to each other in a diagnostic exploration of the UK productivity slowdown through the lens of sectoral decomposition, discussing the role played by different weights used in deflating nominal value added. We consider issues raised by the existing sectoral decomposition approaches such as Generalized Exactly Additive Decomposition (GEAD) employed in Tang and Wang (2004). 3 In this paper we adopt the Tornqvist method, which has also been used in Goodridge at el., (2018), as it allows output prices and production functions to differ across sectors and we are interested in sectoral differences. We then decompose labour productivity growth into within and reallocation components through each sector.
For the period since 2008 compared with the prior 10 years, we find that shifts between sectors play little role in accounting for the aggregate labour productivity slowdown in the UK, although they do have a small negative effect on productivity when the real estate sector (whose output is mainly imputed rent) is excluded from the calculation. Our data and results (Sections 3 and 4) show that manufacturing and information and communication are those that have experienced the biggest labour productivity slowdowns. Furthermore, we find that the withinsector slowdowns are mainly attributable to transport equipment and pharmaceuticals in manufacturing, and to computer software and telecommunications in information and communication. Strikingly, these are among the sectors generally considered to be strengths of the UK economy.
For comparison, we set out two alternative decomposition methods, the shift share method and GEAD, in Appendix II. The reallocation effects seem to be relatively more important to the aggregate slowdown using the GEAD approach, whereas the shift-share method suggests 1 Harris and Moffat (2014) found that labour productivity for the whole UK economy by the end of 2014 was 13% lower compared to a potential output per worker level had the pre-2007 trend had continued. 2 Craft and Mills (2020) found that the current productivity slowdown has resulted in productivity being 19.7% less than the pre-2008 trend path by 2018. 3 Tang and Wang (2004) adopt the GEAD formula to take into account changes in relative prices. By incorporating price effects into contributions, this approach captures the overall economic significance of different sectors to aggregate labour productivity growth, but not the impact of sectoral real contribution on aggregate labour productivity growth. It has been argued that the generalized exactly additive decomposition approach often produces results being perceived as counterintuitive (Avillez, 2012;Reinsdorf, 2015;De Vries et al., 2021) that it is relatively unimportant, which is similar to what we find under the Tornqvist approach.
The alternative methods therefore highlight the importance the different weights in the decomposition exercise. We suggest that the choice of weights and output price deflators, as well as omitted quality change, therefore plays a part in the story.
In order to see how UK compares with other countries, we also look in Section 5 at 12 other countries including Japan, the US, and several European economies for 1998-2015, using the EU KLEMS database. The reallocation term contributes little to explaining the slowdown in all cases, and the within-industry contribution is also the driver in the other 12 advanced economies. In these countries too, the manufacturing and information and communication  (2021) find that the reallocation effects until 2019 were slightly negative for the US, UK and France, and all countries saw a decline in withinindustry productivity growth since 2011. Relative to these earlier results, our paper adopts a different decomposition approach that relaxes the assumption of an identical production function 4 Other papers using the shift share method are applied in the developing economy context. McMillan and Rodrik (2011) document large gaps in labour productivity between the traditional and modern parts of the economy such that that labour flows from low-productivity to high-productivity activities are a key driver of productivity growth from 1990-2005. Focusing on structural transformation, De Vries et al. (2012) similarly find that reallocation of labour across sectors contributes to aggregate productivity growth for China, India and Russia but not for Brazil 1993-2004. De Vries et al. (2015 find that resources were reallocated to manufacturing activities, enhancing overall productivity during the early post-independence period in 11 Sub-Saharan African countries. Diao et al. (2019) document that the growth acceleration in Latin America more recently is explained by rapid within-sector labour productivity growth, whereas the growth acceleration in Africa is attributed to the reallocation due to structural change. Examining Morocco's structural transformation process 1999-2017, Moussir and Chatri (2020) report that the within industry contribution rather than reallocation accounts for much of the labour productivity growth. decomposition methods, their main focus is on the shift-share method and they use data for the UK that predate the implementation of double deflation. We also consider the whole economy, not just the market sector. 5 Section 7 concludes with a discussion of the implications of our findings.

Aggregate and sectoral labour productivity growth
In this paper we use the Tornqvist decomposition as it allows output prices to differ across sectors/industries, separating productivity growth into within and reallocation components. 6 The sum of real-terms sectoral labour productivity growth weighted by value added in this approach will not be equal to growth in aggregate value added per hour calculated using an aggregate deflator. But as we are interested in the performance of the different sectors, it is the most appropriate choice. We use estimates of industry real gross value added ( ) to construct aggregate real gross value added ( ) through weighted sum of log changes in industry gross value added: and ̄= 0.5( Eq. (1) says the log change in real aggregate gross value added is the weighted aggregate of the log changes in industry real gross value added , and the weight is the share of industry in 5 While Voskoboynikov (2020) also includes whole economy sector into the aggregate labour productivity analysis and finds that the overall contribution of structural change is growth enhancing but decreasing over time, the Tornqvist approach is absent and the author only focuses on the Russia economy. 6 We provide findings based on two alternative methods -the shift-share and Generalized Exactly Additive Decomposition in Appendix II. Out results confirm that the shift-share method provides similar results for the aggregate productivity growth pattern compared to our current approach. By contrast, the Generalized Exactly Additive Decomposition approach provides divergent results. See Appendix II for more details.
nominal gross value added . We using two-period average weights as a Divisia index ̄. Since aggregate total worked hours can be estimated as a simple sum of industry hours = ∑ (4) we can then obtain aggregate labour productivity per hour through taking the change in log of as ∆ln ( ⁄ ) = ∆ − ∆ and so the industry labour productivity growth can be defined as: To define aggregate labour productivity growth from the industry data, we can then implement a share-weighted sum over industries as:

Sectoral Decomposition
To distinguish within industry productivity growth from reallocation or structural change, following Fabricant (1942) where the subscript refers to any of sub-sector, for example, food products, beverages, and tobacco in Manufacturing (in which = 1, 2, … , ). is derived from the change in value added weighted labour productivity growth of sub-sectors , with the share of current price value added in sub-sector in industry as weights , and a residual term measuring the reallocation within industries across subsectors . The in Eq.
(2) is the average share of an industry in overall nominal value added, whereas the in Eq.(10) is the average share of a sub-sector in an industry . Substituting Eq. (11) into Eq.(9) obtains a new reallocation effect, as well as a new within industry contribution effect, of labour moving within an industry across sub-sectors. We apply this decomposition to the high-level sectors of the whole economy, and subsequently to sub-sectors of some of these.

Data
We use sector and sub-sector level data on nominal value added, real value added, and labour input (total hours worked). We use the double deflated Office National Statistics ( The second data source is the EU KLEMS dataset (Jerbashian and Vilalta-Bufi, 2020), January 2022 release. We used data for the US, Japan, France, Belgium, Netherland, Denmark, Germany, Greece, Italy, Portugal, Austria, Sweden, and removed the sectors public administration, defence, education, human health and social work activities, arts, entertainment, recreation; other services and service activities, etc., and activities of extraterritorial organizations and bodies. 8 The 20 A-T sectors include A Agriculture, B Mining and quarrying, C Manufacturing, D Electricity, gas, steam and air conditioning supply, E Water supply; sewerage, waste management and remediation activities, F Construction, G Wholesale and retail trade and repair of motor vehicles and motorcycles, H Transportation and storage, I Accommodation and food service activities, J Information and communication, K Financial and insurance activities, L Real estate activities, M Professional, scientific and technical activities, N Administrative and support service activities, O Public administration and defence; compulsory social security, P Education, Q Human health and social work activities, R Arts, entrainment and recreation, S Other service activities, T Activities of households as employers.
Finally, our analysis looks at the periods 1998-2019 for the UK, and 1998-2015 for international comparison. Data for the 2020-2021 period for the UK is removed due to the disruption caused by the global pandemic.
4. UK results Figure 3 and Table 1 show first of the aggregate labour productivity growth for the whole economy sector ∆ln ( ⁄ ) (grey bars), and the separated two terms as the weighted sum of industry labour productivity ∑̄∆ ln( ⁄ ) (i.e., the pure within-sector contribution) and the aggregate reallocation effect estimated from Eq. (8). For the whole period 1998-2019, on average, Table 1 shows that the aggregate labour productivity growth ∆ln ( ⁄ ) was 1.04% per year, the weighted sum of labour productivity growth ∑̄∆ ln( ⁄ ) was 0.792% per year, and the reallocation term 0.248% per year. The slowdown since 2008 for the whole economy is apparent from the chart in Figure  To explore the slowdown, Table 2 (2) and (3) then decompose these into the contributions from within productivity growth and labour reallocation during the two periods. It shows that about a quarter ((0.086-0.409)/-1.282) of the slowdown is explained by reallocation, and about three quarters ((0.263-1.222)/-1.282) of the slowdown has occurred within the industries.
It is worth noting the difference in aggregate labour productivity growth, as well as the within and reallocation effects, when the real estate sector (L) is excluded. As highlighted in the ONS 2019 Labour Productivity Report, the output of industry real estate is mainly imputed rents for owner-occupiers of housing, while labour input (mainly estate agents) is small. We also show the effect when industry real estate is removed in Tables 1 and 2. As can be seen from Table 1, excluding imputed rental from GVA reduces the aggregate by 0.22 percentage points (from 1.040% to 0.818%), increases the within component and reduces the average reallocation effect by 0.45 percentage points so that it becomes negative rather than positive (i.e., 0.248% to -0.202%). The exclusion thus changes not only to the labour reallocation term, but also whole economy sector productivity performance (see also Riley, Rincon-Aznar, and Samek, 2018). This  industries. Blue is 'within' and red is 'reallocation'.
Source: Data sources as above and authors' calculations.  implies a different scenario in terms of labour reallocation from high to low productive industries during the two distinct periods (1998-2008 and 2008-2018). Imputed rent is a return to capital, largely reflecting the appreciation of land values (Nguyen and Johansson 2022) so there are strong conceptual reasons to exclude it from consideration of labour productivity. We also show results with the public sector omitted. These services present well-known distinctive conceptual and measurement challenges; we include them in the decomposition nevertheless.
Turning to the sectors, Table 3 and Figure 4 look at the disaggregation for the whole period 1998-2019, pre-crisis (1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007), and post-crisis (2008-2019). Comparing columns (2) and (3) in Table 3, agriculture (-7.296%), information and communication (-5.986%), manufacturing (-5.211%), financial and insurance activities (-4.205%), and electricity, gas, steam and air conditioning supply (-2.427%) were the five industries with the largest productivity downturn between the two periods. Figure 4 presents data for contributions of the nominal value added-weighted within-sector labour productivity growth for each industry ranked by the slowdown in growth rates ∆(̄∆ ln( ⁄ ) between the two periods. Focusing on the bottom five industries, it shows again that the slowdown in labour productivity ∆ln ( ⁄ ) in these industries  is the slowdown within the industry; e.g., the slowdown in manufacturing ∆(∆ ⁄ ) is -5.211% (2008-2019 vs. 1998-2008), which consists of a slowdown in within-sector productivity -5.226% and a slowdown in labour reallocation term 0.015%; similarly the slowdown in information and communication is -5.986%, which consists of a slowdown in within-sector productivity growth of 5.933% plus a slowdown from labour reallocation term -0.053%. 9 The reallocation components are small.
Having looked at the productivity pattern across sectors, we now repeat the exercise as above and move to the next level of disaggregation for two of the sectors displaying the biggest slowdowns, namely manufacturing, and information and communication. The results are shown in Table 4 and Figure 5. There are 13 sub-sectors in manufacturing and six in information and communication industries, respectively.  where refers to manufacturing and information communication industries, respectively. A positive term implies movement of labour from low-productivity sub-sector toward high-productivity sub-sector either within manufacturing or information communication, respectively.
Source: Authors' calculations. the second period, and no sub-sectors experiencing an increase. The only subsectors not to experience much of a 'within' slowdown are chemicals and coke/refined petroleum products.
In Figure 6, the top panel shows the contribution to the slowdown from each sub-sector's within component in manufacturing (top panel) and in the information and communication industry (bottom panel). About 60% 10 of the slowdown in manufacturing overall is attributable to transport equipment, machinery and equipment, computer and electronics manufacture, and basic pharmaceuticals. For the information and communication industry, telecommunications and computer programming contribute about 69% of the labour productivity slowdown. It is striking that the most pronounced slowdowns occurred in some industries considered to be UK success stories, and with high nominal value added per hour, such as autos (in transport equipment), pharmaceuticals, and telecommunications.
What about the reallocation between the sub-sectors? Figure 7 confirms that the reallocation contribution is small although positive on average in manufacturing and information and communication.

Comparison with other advanced economies
We explored how the productivity decomposition for the UK compares to some other economies. 11 use Eqs. (8) and (9) to carry out the decomposition exercise for an additional we economies for 1998-2015. 12 Table 5 shows the decomposition results, which reveal that the US economy experienced the highest productivity growth and Italy, Greece, Japan, and Portugal the weakest during the entire period 1998-2015. The average reallocation term is negative for the US and France, which implies that labour was moving from more productive to less productive industries during 1998-2015, while Japan and UK have a positive contribution from labour reallocation.
Nevertheless, the reallocation term is relatively small in all countries, and is negative for all countries once real estate is excluded. Finding the reallocation term to be small is consistent with McMillan and Rodrik (2011) and Moussir and Chatri (2020) who find that labour reallocation made very little contribution to productivity performance in the high-income countries during the period 1990-2005. In Figure 8 we show the correlation between aggregate labour 10 60.39% = (1.017%+0.737%+0.586%+0.807%)/5.211%. 11 Jorgenson and Timmer (2011) highlight that specialisation may generate differences across European countries when relatively small countries trade widely and suggest that it is important to aggregate across European countries as a region rather than nation. While we are aware of this concern, it is worth looking at, similar to Kaldor (1963) and Kuznets (1971), how each nation's labour productivity perform individually and how differences may exist across industries. We also provide other European countries' statistics, including Ireland, Czechia, Estonia, Poland, Romania, Slovenia, and Slovakia in Appendix IV. 12 We restrict this exercise within the time frame 1998-2015 due to across countries data availability.     productivity growth and the within and reallocation terms, confirming that there is indeed a positive and linear correlation between aggregate growth ∆ln ( ⁄ ) and the within contribution ∑̄∆ ln( ⁄ ), but no pattern between the aggregate growth ∆ ln( ⁄ ) and reallocation R.  13 There is a slowdown in average productivity growth in manufacturing (except Denmark and Italy, see Figure 11) and information and communication in each. Although somewhat less pronounced in Japan, Belgium, 13 To save space, we keep the US and UK in the main context, but move other countries into Appendix III. In addition, we provide overall growth patterns between 1998-2008 and 2008-2015 across the 13 economies in Appendix III Tables AIII 1 and AIII 2. and Portugal than in the other countries, manufacturing industry is the main contributor to the growth slowdown with minus 4.721% (US) and minus 4.310% (UK), minus 1.327% (France), minus 2.868% (Netherlands), minus 2.060% (Germany), minus 2.809% (Austria), minus 3.585% (Greece), and minus 4.910% (Sweden), respectively. The information and communication sector also contributes to the overall productivity slowdown in all economies (except Denmark), although it is relatively smaller in Belgium (-0.906%) and France (-0.810%) than other countries.
What industries in the UK are doing better compared to other countries? Figure 10 shows that the better-performing sectors include mining and quarrying (5.910%), activities of households as employers (4.781%), other service activities (3.617%), education (2.305%), and real estate (3.278%). There are some differences across countries in the ranking of the sectors contributing to the overall productivity slowdown. For instance, the slowdown mainly is attributable to wholesale trade (minus 2.125%) and transport and storage (minus 2.039%) in the US; electricity (minus 15.327%) and mining (minus 14.801%) in Japan; and electricity (minus 6.536%) and other service activities (minus 3.416%) in France (see Figure 10 and Figure AIII 1 in Appendix III).
We next decompose manufacturing into 13 sub-sectors. Figure 12 shows the results.
Overall, the sub-sector transport equipment shows a somewhat similar picture contributing notably to the decline across all economies . However, the pattern for other sub-sectors differs across countries. Another notable pattern is that chemicals and computers in the US have post-2008 growth rates of minus 0.785% and minus 1.594%, respectively, which account for almost two-quarters and one-third of the US manufacturing productivity slowdown. While these two sub-sectors perform relatively better in the UK compared to the US, in the UK the computer subsector makes a substantial negative contribution. The pharmaceutical subsector also shows different patterns across countries; the UK shows the biggest slowdown in pharmaceuticals, but productivity growth in this sub-sector accelerates in Japan, Germany, Denmark, Italy, Netherlands, and Greece (see Appendix III Figure AIII 2).
Overall, as Figures 10 and 11 show, the slowdown occurs 'within' sectors rather than reflecting reallocations of labour between sectors, although the reallocation that occurs is negative. The productivity slowdown is common across these 13 advanced economies, and in all countries the decompositions show that the high value added sectors of manufacturing and information and communication make a notable contribution to accounting for the slowdown.
While there is variation among these countries, there is enough consistency for certain subsectors to warrant further investigation: information and communication, and, within manufacturing, transport equipment, computer and electronics manufacture, and pharmaceuticals stand out.

Robustness Check: Difference-in-Difference Estimates
As a final robustness check to examine whether the two sectors definitively account for the labour productivity slowdown in the UK and the other countries, we carry out a difference-in-difference estimation. We adopt a general two-way fixed effects (TWFE) with difference-in-difference estimation to test for difference in mean labour productivity growth rates between the two subperiods as follows: ̄∆ ln( ⁄ ) = + where ̄∆ ln( ⁄ ) is the pure within industry labour productivity contribution estimated by Eq. (9), is a dummy equal to 1 if > 2008 and 0 otherwise, is an indicator equal to 1 if industry is either manufacturing or information communication industry and 0 otherwise, is a year fixed effect, and , is a zero mean error term. As in Stiroh (2002), the estimate captures the mean within-industry labour productivity contribution for industries excluding manufacturing and information (i.e., industries in the control group) in the period prior to 2008, + is the mean within-industry labour productivity contribution for treated industries prior to 2008, measures acceleration/deceleration for control industries after 2008 (including = 2008), + is then the acceleration/deceleration for treated industries after 2008. The notation highlights that is the differential labour productivity growth contribution of manufacturing and information and communication industries relative to others. We cluster robust standard errors at the industry (for the UK) and country-industry pair level (for worldwide) to allow for arbitrary forms of serial correlation and heteroscedasticity.  (1) and (2) (1), (3), and (4) are OLS; columns (2), (5), and (6) are the two-way fixed-effect estimates. Column 6 regroups manufacturing and information industries into control for Denmark since the slowdown in Denmark was not mainly caused by the two industries. See Figure 10 for more details. Robust standard errors are clustered at industry and country-industry pair, respectively, reported in parentheses. *, **, and *** represent significance levels at the 10%, 5% and 1% respectively. and information and communication sectors into the control group for Denmark as a robustness check, as there they do not contribute much to accounting for the overall productivity slowdown (see, Figure AIII 1 in Appendix III). However, the regrouping does not change the overall pattern; we see that manufacturing and information remain as significant and negatively contribute to the aggregate labour productivity, with estimated coefficient -2.268 at the 1% significance level.
We next extend our DiD estimates from Eq. (14) by breaking down the average treatment effect across each year to capture the accumulated dynamic within-sector productivity contribution as well as the assumption of a common trend in the prior period. The specification is identified as follows: where is a dummy taking value 1 if an observation pertains to calendar year k and is in treatment group (manufacturing and information industries) and 0 otherwise, is a dummy taking value 1 if an observation pertains to calendar year m and is in treatment group(manufacturing and information industries) and 0 otherwise. We normalise year 2007 to be our reference year. This specification thus allows us to further examine if any if there was any pre-existing difference in trends between the control and the treated industries . Figure 13 provides the results. Reassuringly, the coefficients on the dummy variables are not Part of the resolution lies in the fact that the within figures in the Tornqvist decomposition use nominal value added shares as weights, and hence the slowdown reflects slower (albeit still quite rapid) revenue growth in the sector. It might seem that using volume weights instead -for example growth in bytes of data used -would give a 'truer' picture of the contribution of telecommunications to productivity growth but this would be misleading in the sense that user value lies in the content carried by the telecoms network, value generated by downstream sectors. It is not immediately obvious how to think about the changing value of bytes of data over time. Does twice the data lead to twice the money-metric utility? Probably not. There are unresolved questions concerning how to think about price indices for markets whose outputs are complements (such as telecoms and sectors using communications intensively) or those whose products demonstrate significant returns to scale and non-rivalry.
One lesson is that interpreting the results of any decomposition must be done with care.
The fundamental issue is that the choice of revenue weights versus volume or employment weights (as in alternative decomposition methods) provide two distinct lenses on the economy.
For the case of telecommunications, Abdirahman et al (2022) show that the greater the use of volume (in terms of bytes of data) rather than revenue weights, the larger the decline in the deflator and the faster the growth in real terms output. The difference can be large when there is rapid change in a sector, due in this example to technological shifts such as greater compression, more bandwidth and faster speeds, such that the relationship between volume and revenue shifts.
The use of a unit value deflator (which uses pure volume weights) rather than the ONS output price deflator might tell a different productivity story.
In this paper, we adopt the Tornqvist decomposition formula to allow for relative price shifts between different sectors of the economy, while also using two alternative methods to demonstrate the importance of different weights employed in the exercise. We demonstrate that within-sector labour productivity growth is the main source accounting for the slowdown in aggregate labour productivity growth, while labour reallocation between sectors accounts for little. We further show that some other high value added sectors -transport equipment manufacture (mainly motor vehicles), pharmaceuticals, and computer, electronic and optical products within manufacturing, and telecommunications and computer programming, consulting and related activities withing in information and communication -experienced the biggest within labour productivity slowdowns in the UK.
Looking at 13 (including the UK) advanced economies, the pattern at the sector level is consistent across countries. Within manufacturing, there is variation across sub-sectors but some common elements with slowdowns in within-industry labour productivity growth in transport equipment, pharmaceuticals and computer and electronics manufacture. Since many of the sub-sectors in this list are regarded as success stories in the UK and worldwide, it is striking that the productivity slowdown is greatest in some of the most technologically-advanced industries.
There are two possible avenues to pursue in exploring the reasons for this pattern. One concerns price deflators: the shift share method, using employment share weights, ensures that the sum of the sectors' labour productivity growth is equal to the aggregate by assuming relative prices between sectors do not change. The difference with the Tornqvist method can be large when there is rapid change in a sector, due for example to technological shifts (such as greater compression, more bandwidth and faster speeds in telecoms) such that the relationship between volume and revenue shifts. Alongside this, our findings call for more detailed investigation of the slowdown sub-sectors and their supply chains, including across countries. There is more work to be done to understand the rapidly-changing advanced sectors of the economy.

Appendix I. Tests for breaks in trend
We test whether the difference in the means is zero. Column (3) in Table A1 provides means for current price value added per hour for the period 1998-0007, whereas column (4) shows them for 2008-2019. The test (columns 5 and 6) confirms that almost all industries, except mining and quarrying (industry B) and real estate (industry L), experienced a significant slowdown during the post-crisis period. Table A2 repeats the tests for real terms data.  Appendix II. Comparison of Shift-Share and Generalized Exactly Additive Approaches The advantage of our Tornqvist decomposition is that is allows for different value-added functions across industries. However, it does so at the cost of additivity and it matters when we more industry detail information are available as reallocation effects by its natural setting in Tornqvist approach become larger. Since our main concern are the of value weights in Tornqvist, the shift-share method that employs labour input weights may provide interesting differences.
Furthermore, the Generalized Exactly Additive Decomposition approach adopted by Tang and Wang (2004) and implemented by ONS may also provide different story since different weights are used. Therefore, in this section we further provide two alternative approaches to measuring productivity growth and slowdown.
The first one, which is called shift-share, is to assume that relative prices between sectors do not change and so the sum of the labour productivity growth across industries is equal to the aggregate one. This enables us to obtain aggregate value added (Y) and aggregate hours worked (H) by summing value added and hours across industries (see, Fabricant, 1942;Haltiwanger, 1997;De Vries et al., 2015;Moussir and Chatri, 2020;De Vries et al., 2021): is the aggregate labour productivity, = ∑ ⁄ is the worked hours of industry to the overall economy. Thus, the first term is the hours worked weighted sum of productivity growth within individual sectors. ∑ ∆ −1 is the the movement of workers to sectors with above-average productivity levels (static reallocation effect, which we will call the cross-sectoral effect) and ∑ ∆ ∆ is the transversal term or interaction term. We combine the last two terms as = ∑ ∆ −1 + ∑ ∆ ∆ to refer the reallocation term. Finally, dividing all terms by −1 we then obtain the growth rate of aggregate labour productivity.
The second one, which is called Generalized Exactly Additive Decomposition (GEAD) approaches and adopted in Tang and Wang (2004), considers the formulation outlined as follows:  frameworks. Furthermore, we note that the shift-share method assumes prices are the same across industries for the aggregate whole economy sector. This assumption seems to be too strong in reality compared to either Tornqvist or GEAD approach.  (14) incorporates the effect of changes in relative prices to capture the overall economic significance of different sectors in the economy, i.e., the weights are different between the two approaches (and of course for our Tornqvist formular too). In the use of GEAD formula, it implies that sector such as mining and oil and gas would have such a strong contribution to aggregate labour productivity growth even without strong sector's productivity performance (Avillez, 2012). This can be easily seen when compared the two charts in Figure A2; shift-share suggests that mining and quarrying leads to aggregate productivity slowdown, whereas GEAD approach indicates accelerating productivity growth post-2008.
From this perspective, it would be difficult to claim which approach is more accurate in capturing economic reality. From our point of view, although the GEAD approach estimate something quite different and is hard to distinguish effects from either labour or output price changes to productivity compared to Tornqvist or shift-share approach, the GEAD approach still very well takes into account changes in relative prices and generate sectoral contribution estimates that are perfectly additive irrespective of how real output is calculated.  Sources: ONS, EU KLEMS National Account Data files, and authors' calculation. We remove industries public administration, defence, education, human health and social work activities, arts, entertainment, recreation; other services and service activities, etc., and activities of extraterritorial organizations and bodies from our aggregation exercise. Industries L represents real estate activities.   Sources: ONS, EU KLEMS National Account Data files, and authors' calculation. We remove industries public administration, defence, education, human health and social work activities, arts, entertainment, recreation; other services and service activities, etc., and activities of extraterritorial organizations and bodies from our aggregation exercise. Industries L represents real estate activities.