## wpiea2021273-print-pdf

## Source details

**Canonical URL:** [wpiea2021273-print-pdf](https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021273-print-pdf.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2021/english/wpiea2021273-print-pdf.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2021/english/wpiea2021273-print-pdf.pdf.json)

---

### I. INTRODUCTION — UK productivity context
- UK productivity growth has been lackluster over the decade following the Global Financial Crisis, underperforming other advanced economies.
- The supply-side component that has underperformed the most is total factor productivity (TFP).
- Hypotheses for the TFP growth decline:
  - legacy effects from both the dotcom and global financial crises (GFC),
  - the stagnation of laggard or small-scale firms,
  - the UK’s reliance on the service sector,
  - mismeasurement of intangible investment,
  - diminishing technological opportunities.
- The period is referred to as the “UK’s productivity puzzle”.
- Government strategy and numerical targets:
  - total R&D investment to reach 2.4 percent of GDP by 2027 (from 1.7 percent in 2019),
  - increasing annual public R&D investment to £22 billion (about 0.9 percent of GDP).
- IMF forecasts identify TFP growth as the weaker component of the UK recovery in the medium run (IMF staff forecasts, July 2021 WEO vintage).

### Observed and forecasted supply-side decomposition (high-level)
- Pre/post comparison highlights:
  - Total TFP growth: 1.69 (1998–2007) → 0.46 (2010–2019).
- Prominent hypotheses for post-Covid and Brexit uncertainty:
  - Optimistic scenario: productivity boom via creative destruction; growth from digital and green sectors.
  - Pessimistic scenario: depressed innovation yields persistent scarring; difficulties reallocating workers from affected traditional sectors.

### Key empirical findings on sources of productivity growth
- Aggregate shift in sources (pre-GFC vs post-GFC):
  - Pre-GFC dominant sources (1998–2007 totals):
    - Own innovation (incumbents): 0.85 percentage points (50.3 percent of TFP growth).
    - Creative destruction by incumbents: 0.54 percentage points (31.8 percent).
    - New varieties (entrants): 0.16 percentage points (9.4 percent).
  - Post-GFC dominant sources (2010–2019 totals):
    - New varieties by entrants: 0.22 percentage points (47.5 percent).
    - Own innovation: 0.12 percentage points (26.8 percent).
    - Creative destruction: 0.12 percentage points (25.7 percent).
- Structural and demographic moments (UK 2010–2019, period averages):
  - Total employment: 19.9 (millions).
  - Employment per firm: 9.3.
  - Employment share young firms (<5y): 12.0 percent.
  - Job creation rate: 37.7 percent.
  - Job destruction rate: 32.3 percent.
  - TFP growth rate: 0.46 percent.
  - Employment growth rate: 1.1 percent.

### Sectoral patterns (2010–2019)
- Manufacturing:
  - TFP growth 0.39 percent; employment growth -0.1 percent.
  - Sources: own innovation 52.9 percent, creative destruction 47.1 percent, new varieties 0.0 percent.
- ICT:
  - TFP growth 1.72 percent; employment growth 2.2 percent.
  - Sources: new varieties (entrants) 26.7 percent, creative destruction 39.5 percent, own innovation 33.8 percent.
- Retail:
  - TFP growth 1.65 percent; employment growth 0.3 percent.
  - Sources: own innovation 63.2 percent, creative destruction 28.9 percent, new varieties 7.9 percent.
- Tradable vs non-tradable (2010–2019):
  - Tradables: TFP growth 0.42 percent; employment growth 1.3 percent; sources: new varieties (entrants) 56.1 percent, creative destruction 21.5 percent, own innovation 22.4 percent.
  - Non-tradables: TFP growth 1.27 percent; employment growth 0.8 percent; sources: own innovation 46.9 percent, creative destruction 39.6 percent, new varieties 13.5 percent.

### Inferred model parameters (post-GFC 2010–2019, per existing variety over 5-year period)
- Own-variety improvements by incumbents λi = 0.51.
- Creative destruction by incumbents δi = 0.82 (conditional on no own-improvement).
- Creative destruction by entrants δe = 1.00 (conditional).
- New varieties from entrants κe = 0.06; from incumbents κi = 0.00.
- Pareto shape θ = 84.3.
- Relative quality of new varieties sκ = 0.55.
- Average quality of exiting varieties ψ = 0.17.

### Interpretation of drivers and structural factors
- Incumbent vs entrant dynamics:
  - Post-GFC decline in incumbents’ own improvement and incumbents’ creative destruction suggests incumbent-specific constraints (e.g., legacy deleveraging, regulatory changes).
  - Increased role of entrants post-GFC reflects higher creation of low-quality new varieties; consistent with higher employment growth despite lower aggregate TFP growth.
- Market flexibility and regulatory environment:
  - Higher pre-GFC creative destruction in the UK (relative to US) may reflect more flexible UK product markets.
  - OECD product market regulation indicators show the UK among least stringent but with a shrinking advantage over time.
- Firm heterogeneity and survivorship:
  - A larger productivity gap between firms in the UK (growing post-GFC) may indicate weaker competitive pressures allowing low-quality varieties to persist.
  - Share of one-employee firms rose from 3.6 percent pre-GFC to 4.5 percent post-GFC.
- Sectoral maturity and innovation modes:
  - ICT: faster TFP growth driven more by entrants and creative destruction (disruptive innovation).
  - Manufacturing and retail: growth driven more by incumbents’ own innovation (incremental/within-firm improvements).

### Forward-looking signals (DMP and Covid implications)
- Decision Maker Panel (DMP) survey (2016Q4–2021Q2, ~9,400 firms) signals:
  - Incumbent firms experienced a drop in job creation and a surge in job destruction during Covid.
  - Expected near-term recovery characterized by a large expected increase in job creation and a rise in the share of firms expecting large positive employment shocks—consistent with anticipated creative destruction and factor reallocation.
  - Overall TFP expected to remain below pre-crisis levels in coming years; low firm entry during Covid and declines in R&D investment may reduce future contributions from new varieties and own innovation.
- Short-run distortions:
  - Corporate support policies appear to have temporarily suppressed exits (exiting firms’ share below normal in parts of 2020–2021), delaying cleansing and reallocation.

### Policy implications and recommended interventions
- Guiding principle: match policy mix to dominant innovation mode and sectoral specifics.
- If creative destruction and entrant-led reallocation dominate:
  - Prioritize measures that ease and accelerate factor reallocation:
    - Enhanced active labor market policies focused on in-demand skills (e.g., digital skills).
    - Fast-tracked insolvency proceedings to clear non-viable firms quickly.
    - Make financing available: seed and venture capital for entrants; recapitalization for viable incumbents where appropriate.
  - Mitigate negative reallocation externalities (business-stealing) and smooth transitions for displaced workers and firms.
- If less disruptive forms of innovation prevail (own innovation and incumbent-led improvements):
  - Scale up public R&D spending and subsidies to private R&D, emphasizing basic research with larger positive spillovers per unit of public investment.
  - Strengthen collaboration between private and public researchers and guard against overly broad patents that slow diffusion of basic knowledge.
- Sector-specific tailoring:
  - Digital/ICT sector (high creative destruction, entrant-driven): emphasize reallocation policies, lower entry barriers, fast-track permits and regulatory procedures for new products/services, and support remote-work-enabled business models.
  - Manufacturing and retail (smoother innovation): emphasize R&D support, investment incentives, and measures targeting frictions hindering incumbent innovation.
- Cross-cutting measures:
  - Maintain openness to firm entry and immigrant entrepreneurship as potential sources of new-variety creation.
  - Monitor and, where appropriate, reform product market regulations to balance competitive dynamism with stability.
  - Reassess policy response as updated ONS productivity vintages become available and as post-Covid dynamics crystallize.

### Welfare considerations from innovation composition
- Innovation subsidies yield larger welfare gains when creation of new varieties or own innovation dominate, and smaller (but still positive) gains when creative destruction dominates due to business-stealing externalities and reallocation frictions.
- Optimal policy should internalize the composition of innovation: support R&D and basic research while simultaneously implementing reallocation-friendly institutions when creative destruction is large.

### Appendix highlights
- Model equations:
  - Aggregate output is a CES combination of quality-weighted varieties. Notation and expressions for Y, y_j, l_j, L_f, and W follow the source presentation.
  - Innovation contributions to growth g are expressed in full-form equations grouping new varieties, own innovation, and creative destruction, using parameters κ, λ, δ, ψ and σ.
- Sample description (BSD/IDBR):
  - LBSD longitudinal panel spans 1997–2019.
  - Final UK market economy sample: 46 million firm-year observations of ‘alive’ firms (about 2 million per year) and 14 million firm-year observations of ‘exited’ firms.
  - Manufacturing: SIC2007 2-digit divisions 10–33. Service subsectors and inclusion/exclusion rules detailed in source.
- Role of M&As (2010–2019 period averages), excluding M&A firms:
  - Excluding M&A firms reduces total employment in the sample by about 2 million (or 10 percent).
  - Moments largely invariant; job creation and exit rates tend to be higher when excluding M&A firms.
  - Table 1 moments (Full Sample vs Excluding M&A Firms):
    - Total employment (millions): Full Sample 19.9; Excluding M&A Firms 17.0
    - Job creation rate: Full Sample 37.7%; Excluding M&A Firms 39.5%
    - Job destruction rate: Full Sample 32.3%; Excluding M&A Firms 31.9%
    - Share of small job creation (<3x): Full Sample 33.0%; Excluding M&A Firms 31.2%
    - Exit rate small firms: Full Sample 6.2%; Excluding M&A Firms 6.3%
    - Exit rate large firms: Full Sample 3.4%; Excluding M&A Firms 3.5%

*Source: wpiea2021273-print-pdf — Section 5.*

### References ________________________________________________________________26

### wpiea2021273-print-pdf - References ________________________________________________________________26

### I. INTRODUCTION — UK productivity context
- UK productivity growth has been lackluster over the decade following the Global Financial Crisis, underperforming other advanced economies.
- The supply-side component that has underperformed the most is total factor productivity (TFP) (Chart 1).
- Hypotheses advanced for the TFP growth decline include:
  - legacy effects from both the dotcom and global financial crises (GFC),
  - the stagnation of laggard or small-scale firms,
  - the UK’s reliance on the service sector,
  - mismeasurement of intangible investment,
  - diminishing technological opportunities.
- The literature still refers to this period as the “UK’s productivity puzzle”.

### Observed and forecasted supply-side decomposition
- Chart 1: UK: Gross Value Added, Supply-Side Decomposition (moving average (5) annual growth rate, percent). Source: ONS (January 2021 vintage).
- Chart 2: UK: Real GDP, Supply-Side Decomposition (growth rate, percent). Source: IMF staff forecasts, July 2021 WEO vintage.
- IMF forecasts identify TFP growth as the weaker component of the UK recovery in the medium run, based on experience of past recessions in advanced economies, including those caused by epidemics (IMF, 2021a).

### Post-Covid and Brexit uncertainty
- The evolution of productivity after the structural shocks caused by Covid and Brexit is uncertain.
- Two contrasting views:
  - Optimists: economy may experience a productivity boom via creative destruction; new sectors (digital and green) could be future growth sources.
  - Pessimists: depressed innovation may yield persistent scarring; difficulties reallocating workers from traditional sectors affected by shocks.

### Government strategy and numerical targets
- Government documents cited: Plan for Growth (HM Treasury, 2021) and Innovation Strategy (BEIS, 2021) position innovation as a main pillar of post-Brexit growth strategy.
- Government targets and commitments:
  - total R&D investment to reach 2.4 percent of GDP by 2027 (from 1.7 percent in 2019),
  - increasing annual public R&D investment to £22 billion (about 0.9 percent of GDP).
- Achieving these targets would help reduce economic scarring from an incomplete TFP recovery.
- Other Plan for Growth pillars— infrastructure and skills—are intended to facilitate reallocation of capital and labor toward better-prospect sectors.
- Plan singles out sectors with higher growth potential, including digital and clean energy.

### Policy design considerations: creative destruction vs other innovation sources
- The optimal policy stance depends on dominant channels of productivity growth.
- Creative destruction features:
  - positive knowledge spillovers,
  - negative “business stealing” externality (Atkeson and Burstein, 2019).
- Implications:
  - Optimal subsidy for innovation is lower for creative-destruction-type innovation than for less disruptive forms.
  - Creative destruction increases the need for policies that enable rapid reabsorption of displaced workers and capital, e.g., enhanced active labor market policies and ample financing for viable firms.
- Successful policy design requires understanding the roles of creative destruction versus other sources of growth across the economy.

### Research questions addressed in the paper
- 1. What sources of innovation account for the decline in UK TFP growth over the last decade, compared with the 2000s?
- 2. Do major peers (namely the US) feature similar patterns?
- 3. How do the sources of innovation vary by economic sector?
- 4. What sources are expected to dominate in the post-Covid era?

*Source: wpiea2021273-print-pdf - References ________________________________________________________________26*

### 5.      What are the implications for optimal innovation and growth policies?

### 5.      What are the implications for optimal innovation and growth policies?

### Key empirical findings on sources of productivity growth
- Aggregate shift in sources (pre-GFC vs post-GFC):
  - Total TFP growth: 1.69 (1998–2007) → 0.46 (2010–2019).
  - Pre-GFC dominant sources:
    - Own innovation (incumbents) contributed 0.85 percentage points (50.3 percent of TFP growth).
    - Creative destruction by incumbents contributed 0.54 percentage points (31.8 percent).
    - New varieties (entrants) contributed 0.16 percentage points (9.4 percent).
  - Post-GFC dominant sources:
    - New varieties by entrants contributed 0.22 percentage points and accounted for 47.5 percent of TFP growth.
    - Own innovation fell to 0.12 percentage points (26.8 percent).
    - Creative destruction fell to 0.12 percentage points (25.7 percent).
- Structural and demographic moments (UK 2010–2019, period averages):
  - Total employment: 19.9 (millions).
  - Employment per firm: 9.3.
  - Employment share young firms (<5y): 12.0 percent.
  - Job creation rate: 37.7 percent.
  - Job destruction rate: 32.3 percent.
  - TFP growth rate: 0.46 percent.
  - Employment growth rate: 1.1 percent.
- Sectoral patterns (2010–2019):
  - Manufacturing: TFP growth 0.39 percent; employment growth -0.1 percent; sources: own innovation 52.9 percent, creative destruction 47.1 percent, new varieties 0.0 percent.
  - ICT: TFP growth 1.72 percent; employment growth 2.2 percent; sources: new varieties (entrants) 26.7 percent, creative destruction 39.5 percent, own innovation 33.8 percent.
  - Retail: TFP growth 1.65 percent; employment growth 0.3 percent; sources: own innovation 63.2 percent, creative destruction 28.9 percent, new varieties 7.9 percent.
- Tradable vs non-tradable (2010–2019):
  - Tradables: TFP growth 0.42 percent; employment growth 1.3 percent; sources: new varieties (entrants) 56.1 percent, creative destruction 21.5 percent, own innovation 22.4 percent.
  - Non-tradables: TFP growth 1.27 percent; employment growth 0.8 percent; sources: own innovation 46.9 percent, creative destruction 39.6 percent, new varieties 13.5 percent.
- Inferred model parameters (post-GFC 2010–2019, per existing variety over 5-year period):
  - Own-variety improvements by incumbents λi = 0.51.
  - Creative destruction by incumbents δi = 0.82 (conditional on no own-improvement).
  - Creative destruction by entrants δe = 1.00 (conditional).
  - New varieties from entrants κe = 0.06; from incumbents κi = 0.00.
  - Pareto shape θ = 84.3.
  - Relative quality of new varieties sκ = 0.55.
  - Average quality of exiting varieties ψ = 0.17.

### Interpretation of drivers and structural factors
- Incumbent vs entrant dynamics:
  - Post-GFC decline in incumbents’ absolute contributions (own improvement and incumbents’ creative destruction) suggests incumbent-specific constraints (e.g., legacy deleveraging, regulatory changes).
  - Increased role of entrants in post-GFC period reflects higher creation of low-quality new varieties, consistent with observed higher employment growth despite lower aggregate TFP growth.
- Market flexibility and regulatory environment:
  - Higher pre-GFC creative destruction in the UK (relative to US) may reflect more flexible UK product markets.
  - OECD product market regulation indicators show the UK among least stringent but with a shrinking advantage over time.
- Firm heterogeneity and survivorship:
  - Larger productivity gap between firms in the UK (growing post-GFC) may indicate weaker competitive pressures that allow low-quality varieties to persist.
  - Rising share of one-employee firms (from 3.6 percent pre-GFC to 4.5 percent post-GFC) may reflect gig economy growth and self-employment trends.
- Sectoral maturity and innovation modes:
  - ICT’s faster TFP growth driven more by entrants and creative destruction (disruptive innovation).
  - Manufacturing and retail growth driven more by incumbents’ own innovation (incremental/within-firm improvements).

### Forward-looking signals (DMP and Covid implications)
- Decision Maker Panel (DMP) survey (2016Q4–2021Q2, ~9,400 firms) signals:
  - Incumbent firms experienced a drop in job creation and a surge in job destruction during Covid.
  - Expected near-term recovery characterized by a large expected increase in job creation and a rise in the share of firms expecting large positive employment shocks—consistent with anticipated creative destruction and factor reallocation.
  - Overall TFP expected to remain below pre-crisis levels in coming years; low firm entry during Covid and declines in R&D investment may reduce future contributions from new varieties and own innovation.
- Short-run distortions:
  - Corporate support policies appear to have temporarily suppressed exits (exiting firms’ share below normal in parts of 2020–2021), delaying cleansing and reallocation.

### Policy implications and recommended interventions
- Guiding principle: match policy mix to dominant innovation mode and sectoral specifics.
- If creative destruction and entrant-led reallocation dominate (as post-Covid expectations suggest):
  - Prioritize measures that ease and accelerate factor reallocation:
    - Enhanced active labor market policies focused on in-demand skills (e.g., digital skills).
    - Fast-tracked insolvency proceedings to clear non-viable firms quickly.
    - Make financing available: seed and venture capital for entrants; recapitalization for viable incumbents where appropriate.
  - Provide policies to mitigate negative reallocation externalities (business-stealing) and smooth transitions for displaced workers and firms.
- If less disruptive forms of innovation prevail (own innovation and incumbent-led improvements):
  - Scale up public R&D spending and subsidies to private R&D, with emphasis on basic research that yields larger positive spillovers per unit of public investment.
  - Strengthen collaboration between private and public researchers and guard against overly broad patents that slow diffusion of basic knowledge.
- Sector-specific tailoring:
  - For digital/ICT sector (high creative destruction, entrant-driven): emphasize reallocation policies, lower entry barriers, fast-track permits and regulatory procedures for new products/services, and support remote-work-enabled business models.
  - For manufacturing and retail (smoother innovation): emphasize R&D support, investment incentives, and measures to address sector-specific frictions hindering incumbent innovation.
- Cross-cutting measures:
  - Maintain openness to firm entry and immigrant entrepreneurship as potential sources of new-variety creation.
  - Monitor and, where appropriate, reform product market regulations to balance competitive dynamism with stability.
  - Reassess policy response as updated ONS productivity vintages become available and as post-Covid dynamics crystallize.

### Welfare considerations from innovation composition
- Innovation subsidies have greater welfare gains when creation of new varieties or own innovation dominate, and smaller (but still positive) gains when creative destruction dominates, due to business-stealing externalities and frictions in reemployment and capital reallocation.
- Optimal policy should therefore internalize the composition of innovation: support R&D and basic research while simultaneously implementing reallocation-friendly institutions when creative destruction is large.

*Source: wpiea2021273-print-pdf — Section 5.*

### REFERENCES

### REFERENCES

### Key citations
- Aghion, P., and P. Howitt (1992): “A Model of Growth Through Creative Destruction,” Econometrica, 60(2), 323–351: 1507–1510.
- Atkeson, Andrew, and Ariel Burstein. "Aggregate implications of innovation policy." Journal of Political Economy 127, no. 6 (2019): 2625–2683.
- Barnett, A., Batten, S., Chiu, A., Franklin, J. and Sebastia-Barriel, M., 2014. “The UK productivity puzzle.” Bank of England Quarterly Bulletin, p.Q2.
- Bassanini, Andrea, and Ekkehard Ernst. "Labour market institutions, product market regulation, and innovation: cross-country evidence." OECD Economics Department Working Papers No. 316, (2002).
- Bloom, Nicholas, Philip Bunn, Scarlet Chen, Paul Mizen, Pawel Smietanka, and Gregory Thwaites. “The impact of Brexit on UK firms." Staff Working Paper No. 818, 2019.
- Bloom, Nicholas, Philip Bunn, Paul Mizen, Pawel Smietanka, and Gregory Thwaites. “The impact of Covid-19 on productivity.” NBER Working Paper no. 28233, 2020.
- Broadbent, Ben, Federico Di Pace, Thomas Drechsel, Richard Harrison and Silvana Tenreyro. “The Brexit vote, productivity growth and macroeconomic adjustments in the United Kingdom.” Bank of England Discussion Paper No. 51, 2019.
- Broda, C. and Weinstein, D. E. (2006). Globalization and the Gains from Variety. The Quarterly Journal of Economics, 121(2):541–585.
- Castellani, Davide, Mariacristina Piva, Torben Schubert, and Marco Vivarelli. "Can European productivity make progress?." Intereconomics 53, no. 2 (2018): 75–78.
- Evans, Peter, and Richard Welpton. "'Business Structure Database: The Inter-Departmental Business Register (IDBR) for Research'." Economic & Labour Market Review 3, no. 6 (2009): 71–75.
- Decker, Ryan A., John Haltiwanger, Ron S. Jarmin, and Javier Miranda. "Declining business dynamism: What we know and the way forward." American Economic Review 106, no. 5 (2016): 203–07.
- Department for Business, Energy, and Industrial Strategy (BEIS), 2021. “UK Innovation Strategy: Leading the future by creating it”.
- Garcia‐Macia, Daniel, Chang‐Tai Hsieh, and Peter J. Klenow. "How destructive is innovation?." Econometrica 87, no. 5 (2019): 1507–1541.
- Goodridge, Peter, Jonathan Haskel, and Gavin Wallis. "Can intangible investment explain the UK productivity puzzle?." National Institute Economic Review 224, no. 1 (2013): R48–R58.
- Goodridge, Peter, Jonathan Haskel, and Gavin Wallis. "Accounting for the UK productivity puzzle: a decomposition and predictions." Economica 85, no. 339 (2018): 581–605.
- Haldane, Andrew G., 2017, “Productivity puzzles”, speech by the Chief Economist of the Bank of England.
- HM Treasury, 2021. “Build Back Better: our plan for growth”, HM Treasury Policy Paper.
- International Monetary Fund (IMF, 2021a), World Economic Outlook, April 2021, Chapter 2.
- International Monetary Fund (IMF, 2021b), World Economic Outlook, October 2021, Chapter 3.
- Klette, Tor Jakob, and Samuel Kortum. "Innovating firms and aggregate innovation." Journal of Political Economy 112, no. 5 (2004): 986–1018.
- Lui, Silvia, Russell Black, Josefa Lavandero-Mason, and Mohammad Shafat. "Business dynamism in the UK: New findings using a novel dataset." Economic Statistics Centre of Excellence (ESCoE) Discussion Paper 14 (2020).
- Moral-Benito, Enrique. "Growing by learning: firm-level evidence on the size-productivity nexus." SERIEs 9, no. 1 (2018): 65-90.
- OECD, 2020. OECD Economic Surveys: United Kingdom 2020, Chapter 2: “Boosting productivity in the service sectors”.
- Parker, Simon C. (2018) The Economics of Entrepreneurship, Cambridge University Press: Cambridge.
- Romer, Paul M. "Endogenous technological change." Journal of Political Economy 98, no. 5, Part 2 (1990): S71–S102.

### APPENDIX I. MODEL EQUATIONS
- Static equilibrium:
  - Aggregate output is a CES combination of quality-weighted varieties:
    - Y = [ sum_{j=1}^M q_j^{(σ-1)/σ} y_j^{(σ-1)/σ} ]^{σ/(σ-1)}  (presentation preserved from source)
    - where y_j denotes the quantity and q_j the quality of variety j. M is the number of varieties and σ the elasticity of substitution across varieties.
  - Output of variety j: y_j = l_j, where l_j is labor used to produce variety j.
  - Profit-maximizing labor employed in producing variety j:
    - l_j = (L W^{-σ} q_j^{σ-1})^{1/(σ-1)}  (expression preserved from source)
    - where L is total labor supply and W the real wage.
  - Employment of firm f:
    - L_f = sum_{j in M_f} l_j ≡ ... (expression preserved from source)
    - where M_f denotes the set of varieties produced by firm f.
  - Real wage proportional to aggregate labor productivity:
    - W ∝ [ (1/M) sum_{j=1}^M q_j^{1-σ} ]^{1/(1-σ)} * Y / L  (expression preserved from source)
- Innovation:
  - If a firm innovates on an existing variety, the average proportional improvement in quality weighted by employment:
    - s_q^{(1)} = [ (1 - θ) / (1 - θ^{σ}) ]^{1/σ}  (presentation preserved from source)
    - formal definition: s_q ≡ (q̃)^{1/(1-σ)}  (notation preserved)
    - q̃ is the proportional step size of innovation on a given variety.
  - Expected aggregate productivity growth rate g as function of innovation arrival rates and relative quality step size:
    - g = [ complex expression grouping contributions from new varieties, own innovation, creative destruction ] (equation (1) preserved in full form in source)
    - equation (1) includes parameters κ, λ, δ, ψ and σ with terms identified as contributions from three innovation sources and an endogenous 훿표 denoting rate at which varieties fall below break-even quality threshold ψ.
  - Alternative grouping into entrants and incumbents:
    - g = [ expression (2) grouping entrants and incumbents ] (equation (2) preserved in full form in source)

### APPENDIX II. SAMPLE DESCRIPTION
- Primary data source:
  - UK Business Structure Database (BSD), snapshot of the Inter-Departmental Business Register (IDBR).
  - IDBR covers approximately 99 percent of economic activity.
  - LBSD longitudinal panel spans 1997–2019 and contains data on employment, turnover, year of birth, year of death, and industrial activity based on SIC 2003 and 2007.
  - Firm employment defined by current number of employees, including business proprietors.
- Cleaning and exclusions:
  - Entire time series removed for firms that in at least one year declare legal status as ‘Central Government body’, ‘Local authority’, ‘Non-profit making body’ and ‘Public corporation’.
  - Excluded sectors: D ‘Electricity and gas’; E ‘Water supply, sewerage and waste management’; O ‘Public administration and defense’; P ‘Education’; Q ‘Human Work and Social Care Activities’; T ‘Activities of households as employers’; U ‘Activities of extra-territorial organizations and bodies’.
  - Excluded 5-digit sectors containing less than five firms per SIC 5-digit-year cell; this leads to losing only 8,553 observations.
- Definitions:
  - ‘Alive’ firms: firm-year observations reported as ‘active’ with employment greater than zero, and ‘reactivated’ firms with positive employment and turnover.
  - ‘Exited’ firms: all remaining observations.
  - ‘Active’ firms: enterprises with at least one reporting (legal entity) unit.
  - ‘Reactivated’ firms: reported active in a subsequent year following the one when they declared as ‘dead’; whole time series kept including in-between dormant years.
  - Firms declared ‘dead’ administratively after two years without any trading, following BSD methodology.
- Sample size and sector construction:
  - Final UK market economy sample contains 46 million firm-year observations of ‘alive’ firms (about 2 million per year) and 14 million firm-year observations of ‘exited’ firms.
  - Manufacturing sector: all 5-digit sectors within SIC2007 2-digit divisions 10–33.
  - Services sector includes SIC2007 sections: G ‘Wholesale and retail trade’, I ‘Accommodation & food services activities’, H ‘Transport & storage’, J ‘Information and communication’, K ‘Financial & insurance activities’, L ‘Real estate’, M ‘Professional scientific and technical activities’, N ‘Administrative and support services’, R ‘Arts, entertainment and recreation’, S ‘Other service activities’.
  - Within services, Information and Communication (J) comprises 2-digit divisions 58, 59, 60, 61, 62, 63; to represent the digital economy, sectors 58–60 are excluded, but 5-digit sectors 58210 ‘Publishing of computer games’ and 58290 ‘Other software publishing’ are included.
  - Wholesale and Retail Trade sector includes SIC2007 2-digit categories 45, 46, 47.
  - Professional Services sector includes SIC2007 2-digit categories 69–75.
- Note:
  - Lui et al. (2020) develop an alternative method refining BSD entry and exit statistics using IDBR quarterly data; trends in business dynamism are consistent with those reported herein.

### APPENDIX III. THE ROLE OF MERGERS AND ACQUISITIONS
- Definition of M&As (ONS guidelines):
  - Acquisition: all enterprises within a given enterprise reference group change to another common enterprise reference group, and the latter group already existed.
  - Merger: enterprises coming from two or more reference groups move to a new common group.
- Empirical findings when excluding firms undergoing M&As (2010–2019 period averages):
  - Excluding M&A firms reduces total employment in the sample by about 2 million (or 10 percent).
  - Key moments largely invariant between full sample and sample excluding M&As.
  - Job creation and exit rates tend to be higher when excluding M&A firms, likely because M&A firms are on average larger and older, which more-than-compensates for any disruption effects attributable to M&As.
  - Job destruction is lower without M&As, consistent with M&As tending to lead to redundancies and limited M&A-related employment protection in the UK.
- Table 1. Moments Excluding M&As, 2010–2019 (period averages)
  - Total employment (millions): Full Sample 19.9; Excluding M&A Firms 17.0
  - Job creation rate: Full Sample 37.7%; Excluding M&A Firms 39.5%
  - Job destruction rate: Full Sample 32.3%; Excluding M&A Firms 31.9%
  - Share of small job creation (<3x): Full Sample 33.0%; Excluding M&A Firms 31.2%
  - Exit rate small firms: Full Sample 6.2%; Excluding M&A Firms 6.3%
  - Exit rate large firms: Full Sample 3.4%; Excluding M&A Firms 3.5%
- Source of Table 1: ONS and authors’ calculations.

*Content derived from wpiea2021273-print-pdf - REFERENCES*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021273-print-pdf.pdf_