## ch3onlineannex

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### Online Annex 3.1 — Insights from Medium-Term Forecasts
- Methodology:
  - Forecast error e_{i,t} defined as actual growth in year t minus the medium-term growth projection for the same year made five years prior.
  - Vintage-by-vintage cross-country regression: e_{i,t} = α_t + ε_{i,t}; estimates of α_t shown with 95 percent confidence intervals.
  - Actual growth smoothed using an end-of-period three-year moving average.
- Alignment with potential growth:
  - Vintage-by-vintage cross-country regression: z_{i,t} = α_t + ε_{i,t}, where z_{i,t} = medium-term growth forecast − forecast of potential growth for country i in year t.
  - Result: differences statistically insignificant except after major crises (example: post-GFC and post-2020 pandemic for EMDEs where output growth forecasts exceeded potential reflecting deep scarring and projected faster catching up).

### Online Annex 3.2 — “How Did We Get Here?”: Labor, Investment, and Allocative Efficiency

H3: Labor inputs — demographic turning points
- Demographic turning points:
  - Online Annex Figure 3.2.1 identifies timing of working-age population share peaks (point 0) for the world’s largest economies.
  - Notable coincidence: period around the GFC coincided with turning points for US, UK, Canada, and China.

H3: Shift-share decomposition of labor force participation (LFP)
- Age groups: 15–24, 25–54, 55–64, 65+.
- Gender-specific LFP decomposition:
  - LFP_{i,t,g} = Σ_a s_{i,t,a,g} × LFP_{i,t,a,g}.
- Change decomposition between 2008 and 2021:
  - Term attributing change to participation rate changes within age groups (population shares held constant).
  - Term capturing population aging effect due to changing population shares (LFP rates held constant at 2008 levels).

H3: Labor force participation regressions and policy roles
- Regression specification:
  - LFP_{i,t,g} = β_g CYCLE_{i,t} + γ_g X_{i,t} + δ_g Z_{i,t,g} + α_{i,g} + α_{t,g} + ε_{i,t,g}.
  - CYCLE: output gap; X: structural variables (trade openness, service/industry employment ratio, urbanization, education shares); Z: policies and institutions (group-specific); country and year fixed effects; some variables lagged by one year.
  - Five groups: young (15–24); prime-age men (25–54); prime-age women (25–54); close-to-retirement (55–64); older workers (65+).
- Data sources and variable definitions (selected):
  - Output Gap: IMF, WEO database.
  - Trade Openness: (X + M)/GDP, IMF WEO.
  - Service/Industry Employment Ratio; Urbanization Rate: World Bank, WDI.
  - Population by Education: Barro-Lee.
  - Labor Tax Wedge: OECD Tax database (single-earner family at 100 percent of average earnings, two children).
  - Unemployment Benefits: OECD net replacement rate.
  - Spending on Labor Market Programs: OECD Social Expenditure; spending per unemployed as percent of GDP per capita.
  - Coordination of Wage Setting: OECD/AIAS (ICTWSS) index 1–5 (higher = more centralized).
  - Retirement Age: International Social Security Association; statutory retirement age.
  - Public Pension Spending; Public Spending on Incapacity: OECD Social Expenditure.
- Selected regression coefficients and significance (standard errors in parentheses; *, **, *** indicate significance at 10 percent, 5 percent, 1 percent):
  - Output Gap (Lagged): 0.122 (Youth) (0.103); −0.0619** (Prime-Age Men) (0.0228); 0.0109 (Prime-Age Women) (0.0662); 0.0337 (Close-to-Retirement) (0.0914); 0.0701** (Older Workers) (0.0238).
  - Trade Openness (Lagged): −0.0316 (Youth) (0.0248); −0.0603*** (Older Workers) (0.0110).
  - Service/Industry Employment Ratio (Lagged): 0.0223*** (Prime-Age Women) (0.00334); 0.0129*** (Older Workers) (0.00164).
  - Secondary Education (All gender, ages 15–24): 0.0622** (0.0242).
  - Secondary Education (Female, ages 25–54): 0.121*** (0.0253).
  - Tertiary Education (All gender, ages 55–64): −0.177* (0.0887) and −0.160*** (0.0228) reported.
  - Labor Tax Wedge: −0.0978*** (Prime-Age Men) (0.0286).
  - Unemployment Benefits: −0.0174*** (Prime-Age Men) (0.00535); −0.0512*** (Prime-Age Women) (0.0151).
  - Spending on Labor Market Programs: 0.774* (Prime-Age Women) (0.363); 1.358** (Close-to-Retirement) (0.505).
  - Union Density: −0.104*** (Prime-Age Men) (0.0334); 0.358*** (Prime-Age Women) (0.0812); −0.346*** (Close-to-Retirement) (0.113).
  - Coordination of Wage Setting: 1.514** (Youth) (0.635); 0.837*** (Prime-Age Women) (0.238); 0.866*** (Close-to-Retirement) (0.225).
  - Spending on Early Childhood Education and Care: 4.310*** (Prime-Age Women) (0.646).
  - Share of Part-Time Employment: 0.302** (Prime-Age Women) (0.103).
  - Retirement Age: 0.735*** (Close-to-Retirement) (0.204); 0.432*** (Older Workers) (0.0560).
  - Public Pension Spending: −1.598*** (Close-to-Retirement) (0.313); −1.102*** (Older Workers) (0.0962).
  - Public Spending on Incapacity: 0.630*** (Older Workers) (0.195).
- Model diagnostics:
  - Observations: 487 (Youth), 394 (Prime-Age Men), 363 (Prime-Age Women), 379 (Close-to-Retirement), 379 (Older Workers).
  - Within R2: 0.30 (Youth), 0.30 (Prime-Age Men), 0.65 (Prime-Age Women), 0.77 (Close-to-Retirement), 0.65 (Older Workers).

H3: Aggregate business investment and fiscal shocks data
- Definition and sample:
  - OECD aggregate business investment = gross fixed capital formation for non-financial corporations deflated using the WEO private investment deflator.
  - Sample restricted to 21 economies with narrative fiscal shocks from Devries and others (2011).
  - Sample period: late 1970s to 2021, assuming zero-fiscal shock in 2020–21.
  - Sample composition: 16 advanced economies (Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Italy, Japan, Netherlands, Portugal, Spain, Sweden, United Kingdom, United States) and 5 EMDEs (Brazil, Chile, Colombia, Costa Rica, Mexico).

H3: Investment growth–output growth IV regression (based on Chapter 4, April 2015 WEO)
- Two-stage IV approach:
  - First stage instruments change in real GDP growth ΔlnY_{it}^{IV} using narrative fiscal shocks (Devries and others 2011).
  - Second stage: ΔlnI_{it} = β ΔlnY_{it}^{IV} + ρ ΔlnI_{it−1} + a_i + τ_t + ε_{it}.
  - Dependent variable: Investment Growth ΔlnI_{it} (change in log real business investment).
- Key reported statistics (Online Annex Table 3.2.3):
  - Coefficient on instrumented GDP growth: 1.985** (column 1) (0.851); 2.878** (column 2) (1.441).
  - Coefficient on lagged investment growth: 0.018 (column 1) (0.090); 0.006 (column 2) (0.098).
  - Country FE: Yes. Year FE: Yes.
  - Observations: 499 (column 1), 488 (column 2).
  - Adjusted R2: 0.668 (column 1), 0.537 (column 2).
  - First-Stage F-statistic: 16.446 (column 1), 10.832 (column 2).
  - p-Value of F-statistic: < 0.0001 (column 1), 0.0011 (column 2).
  - Interpretation: investment–output growth elasticity statistically significant and close to 2; column 2 uses growth rate of total demand (C + X) as alternative measure and yields consistent results.
- First-stage specification notes:
  - ΔlnGDP = −0.661*** FiscalShock + 0.063*** ∆lnI−1 + α_i + λ_t + u.
  - Δln(C+X) = −0.514*** FiscalShock + 0.046** ∆lnI−1 + α_i + λ_t + u.
  - Overidentification tests with fiscal shocks and lagged fiscal shocks as instruments produce Hansen J-statistic p-values exceeding 10 percent.

H3: Firm-level investment analysis (Thomson Reuters Worldscope)
- Data and coverage:
  - Firm-level data aggregated to country-year; finance, insurance, real estate, and government agencies excluded.
  - 95 percent winsorization applied on variables used to construct total investment.
- Representativeness:
  - Aggregated firm-level investment represents around half of total business investment in advanced economies; correlation with total business investment exceeds 0.8 for majority of advanced economies.
  - For emerging markets, aggregated firm-level investment represents up to 30 percent of business investment; correlation exceeds 0.8 for about half of emerging markets.

H3: Construction of net investment rates and intangible capital (Peters and Taylor 2017 approach)
- Intangible investment:
  - IIIt = R&D_it + 0.3 SGA_it (presentation preserved as in source).
- Intangible capital construction:
  - K_{I,it} = S_assets_it + KI_pstock_{it} + OOtherInvestment_K_it (presentation preserved).
  - KI_pstock_{it} update: KI_pstock_{it} = [ (1−δ_k) ] KI_pstock_{it−1} + R&D_it (presentation preserved).
  - OOtherInvestment_K_it update: OOtherInvestment_K_it = (1−δ_ppg) OOtherInvestment_K_it−1 + SGA_it (presentation preserved).
  - Depreciation rates: δ_k = 0.15; δ_ppg = 0.2.
- Descriptive statistics (Worldscope, 2000–2021; winsorized at 5th and 95th percentiles):
  - Gross Tangible Investment Ratio: Median 6.35; Mean 9.66; Standard Deviation 10.43.
  - Intangible Investment Ratio: Median 8.44; Mean 10.88; Standard Deviation 10.66.
  - Total Net Investment Ratio: Median 10.39; Mean 14.04; Standard Deviation 15.54.
  - Tobin’s q: Median 1.16; Mean 1.48; Standard Deviation 0.93.
  - Leverage: Median 23.28; Mean 25.11; Standard Deviation 17.39.
  - Cost of Debt: Median 4.36; Mean 6.87; Standard Deviation 9.49.
  - Profit Margin: Median 4.95; Mean −1.39; Standard Deviation 35.52.
  - Cash Stock over Total Assets: Median 10.57; Mean 13.70; Standard Deviation 12.74.

H3: Firm-level investment regressions — key estimates (Online Annex Table 3.2.5)
- Dependent variable: Net Investment Rate; firm and year fixed effects; standard errors clustered at firm level.
- Tobin’s q (t−1):
  - Advanced economies (AEs), column (1): 0.0403***.
  - Emerging markets (EMMIEs), column (2): 0.0357***.
  - Interpretation preserved: a 1 unit increase in Tobin’s q → 4.03 percentage points increase in net investment rate in AEs, 3.57 percentage points in EMs; post-2008 effect reduced to 2.9 percentage points in AEs and 3.15 percentage points in EMs.
- Uncertainty index (log): a 1 percent increase → approximately 5.82 basis points decline in investment rates (textual statement preserved).
- Selected coefficients (AEs / EMMIEs):
  - Leverage (t−1): −0.1059*** / −0.0757***.
  - Cost of Debt (t−1): −0.0303*** / −0.0277**.
  - Profit Margin (t−1): 0.0137*** / 0.0719***.
  - Cash Stock over Assets (t−1): 0.2673*** / 0.3345***.
  - Post-2008 × Tobin’s q (t−1): −0.0113*** / −0.0042**.
  - Post-2008 × Leverage (t−1): −0.0019 / −0.1030***.
  - Post-2008 × Cost of Debt (t−1): −0.0009 / −0.0757***.
  - Post-2008 × Profit Margin (t−1): −0.0087** / −0.0414***.
  - Post-2008 × Cash Stock over Assets (t−1): −0.0994*** / −0.0504**.
  - GDP Growth (t−1): 0.0885*** (AEs); 0.0140 (EMs).
  - Observations: AEs 214,458; EMMIEs 90,301.
  - Adjusted R2: AEs 0.4985; EMMIEs 0.338.
- Interpretation:
  - Marked reduction in sensitivity of investment rates to Tobin’s q, profit margins, and accumulated cash after 2008, especially in AEs.
  - EMs: firms became more responsive to leverage and cost of debt post-2008.

H3: Evolution of key investment determinants (post-2008 vs pre-2008)
- Observed changes (firm-level, aggregated):
  - Tobin’s q, Cost of Debt, Cash Stock over Assets, and Past GDP Growth declined post-2008 in both AEs and EMs.
  - Leverage and country-level Uncertainty Index increased in both groups.
  - Profit margins increased in AEs but decreased in EMs.
  - Capital inflows over GDP decreased in AEs after 2008; increased in EMs.

H3: Resource misallocation — data, measurement, and findings
- Country sample for misallocation analysis (2000–19, 20 economies): Austria, Belgium, Bulgaria, China, Czechia, Estonia, France, Germany, Italy, Japan, Korea, Poland, Portugal, Romania, Russia, Slovakia, Slovenia, Spain, Switzerland, USA.
- Orbis firm-level data covering 19 broad sectors; Orbis sales generally exceed 60 percent of OECD gross output for included countries except US (~30 percent coverage).
- Allocative efficiency framework (Hsieh and Klenow 2009 notation preserved):
  - Parameters: σ = 3; α_s = 1 − average U.S. labor share in sector s during 2000–19 (EU-KLEMs).
  - SSL_prt ∈ [0,1]; 1 − SSL_prt measures share of sector’s potential TFP lost to misallocation.
- Additive measurement error detection:
  - λ̂_pr interpretation: λ̂_pr = 1 ⇒ no additive measurement error; λ̂_pr = 0 ⇒ pure noise.
  - Selected median λ̂_pr values (2000–09 and 2010–19):
    - United States median λ̂, 2000–09: 0.837 (0.014); 2010–19: 0.898 (0.017).
    - China median λ̂, 2000–09: 0.812 (0.005); 2010–19: 0.728 (0.011).
    - AEs median λ̂, 2000–09: 0.738 (0.010); 2010–19: 0.767 (0.006).
    - EMMIEs median λ̂, 2000–09: 0.833 (0.005); 2010–19: 0.797 (0.004).
    - Sample median λ̂, 2000–09: 0.757 (0.008); 2010–19: 0.768 (0.006).
  - Goods panel example: Goods, 2000–09 medians: U.S. 0.945 (0.012); China 0.884 (0.017); Sample 0.834 (0.005). Goods, 2010–19 medians: U.S. 0.772 (0.016); China 0.835 (0.009); Sample 0.782 (0.003).
  - Conclusion: additive measurement error present but small; service sectors less prone to additive measurement error than goods sectors.
- Correction: adjusted expectations E[λ̂_pr ln(measured variable)] used to compute firms’ total revenue factor productivities and sector-level SSL_prt.

H3: Aggregate TFP and allocative efficiency decomposition
- Aggregate TFP decomposition preserved:
  - ln TFP_pt ≡ ln TFP_pt* + Σ_s θ_spt ln SSL_spt.
  - Growth: ∆ln TFP_pt ≡ ∆ln TFP_pt* + ∆ln SSL_pt, where ∆ln SSL_pt ≡ ∆Σ_s θ_spt ln SSL_spt.
  - Shift-share decomposition: ∆ln SSL_pt ≡ Σ (∆θ_spt) ln SSL_spt + Σ θ_s,p−1 (∆ln SSL_spt) (composition vs within-sector change).
  - Sector GDP shares from EU-KLEMS or OECD-TiVA.

H3: Evidence on adjustment frictions — firm- and sector-level
- Firm-level regression (N = 34,399,920 observations, 2000–19):
  - ∆ln( TLFTRR_{prit} / TLFTRR̄_{prt} ) = γ̂1 ∆ln TFPQ_{prit} + γ̂2 ln( TLFTRR_{prit} / TLFTRR̄_{prt} ) + firm FE + country-sector-year FE + error.
  - Key estimates:
    - Column (1) γ̂1 = 0.727***.
    - Column (2) γ̂1 = 0.703***.
    - Column (3) coefficient on log initial misallocation wedge = −0.595***.
    - Column (4) γ̂1 = 0.703***; log initial misallocation wedge = −0.066***.
    - R2: column (1) 0.160; (2) 0.940; (3) 0.410; (4) 0.940.
  - Interpretations:
    - Firms with faster relative TFPQ growth see an increase in misallocation wedge on impact (γ̂1 > 0).
    - Misallocation wedges revert over time (γ̂2 < 0).
    - Estimated reversion implies about ln 0.5 / ln(1 + γ̂2) ≈ 11 years on average for half-life of wedge reversion.
    - Aggregate implication: about 37 percent of overall misallocation is transitory and 63 percent structural.
    - Robust across countries and groups; U.S. wedges rise less and revert faster (coverage caveat).

- Sector-level regression (N = 586 observations, pooled 2000–09 and 2010–19):
  - ∆_{t+9,t} ln SSL_prt = β̂1 ∆_{t+9,t} ln LG_prt + β̂2 ln SSL_prt + country FE + sector FE + error.
  - LG_prt = dispersion of firm TFPQs (power mean to geometric mean, σ = 3).
  - Key estimates (selected):
    - Log Change in Productivity Dispersion coefficient: −0.470 (column 1); −0.365*** (column 2).
    - Log Initial Allocative Efficiency coefficient: −0.611 (column 3); −0.516*** (column 4).
    - R2: column (1) 0.100; (2) 0.340; (3) 0.430; (4) 0.570.
  - Interpretations:
    - Increase in sector-level productivity dispersion accompanies contemporaneous decline in sector allocative efficiency.
    - Sectors with larger initial inefficiency exhibit mean reversion; estimated half-life from column (4) = 9 years (consistent with firm-level ~11 years).

### Online Annex 3.3 — Assumptions and calculations for medium-term projections (year 2030)

H3: Projecting potential employment growth
- Cohort-based LFP forecast for 83 economies; estimation uses ILO LFP data for four age groups for 1995–2021 (expanded to 1995–2023 in extended estimation).
- Specification preserved:
  - logLFPR_{t,a,g} = α_{a,g} + (1/n_a) Σ β^T_g I_{T(=t−a),t,g,2006}^{T=1932} + γ_{a,g} CYCLE_t + λ_{a,g} X_{t,a,g} + ε_{t,a,g}.
- Determinants include birth-cohort effects, HP-filtered output gap, life expectancy, fertility, education attainment and enrollment.
- Prediction assumptions:
  - No cyclical gap; constant time trends; projected structural factors from UN Population and Development Database; cohort progression and newest cohorts mirror recent cohorts.
- Medium-term potential employment growth estimated using projected LFP growth by 2030 and expected growth of population aged 15+ (assuming stable employment rates).

H3: Constructing baseline medium-term growth projection (top-down decomposition)
- Growth identity: ΔlnY_t = ΔlnTFP_t + (1−α) ΔlnL_t + α ΔlnK_t.
- Capital growth:
  - ΔlnK = s ΔK/public K_public + (1−s) ΔK/private K_private.
  - ΔK/K = I/K − δ (net investment rate after depreciation).
  - Private investment rate projected using accelerator model with estimated investment-growth elasticity β̂ (from IV regression).
  - Net private investment rate formula: NII2030_private K2029_private = β̂(ΔlnY2030 − ΔlnY_{t0}) + NII_{i0}_private K_{i0}_private, using pre-pandemic five-year (2015–19) averages for initial values.
- TFP projection:
  - ΔlnTFP_t ≡ ΔlnTFP_t* + ΔlnSSL_t (efficient TFP change plus allocative efficiency change).
  - Change in allocative efficiency projected using Online Annex Table 3.2.8 estimates and 2019 sector-level misallocation as initial values; aggregation across 20 sample countries with PPP GDP weights.
  - Efficient TFP growth assumed to continue historical downward trend.
  - Combining factors yields expected TFP growth in medium term estimated to be around 0.9 percent.
- Values used (preserved exactly from source) to compute ΔlnY2030:
  - ΔlnTFP2030 = 0.9,
  - ΔlnL_t = 0.32,
  - α = 0.487,
  - s = 0.27,
  - NII2030_public K2029_public = 0.3,
  - β̂ = 0.85,
  - ΔlogY_{t0} = 3.41,
  - NII_{i0}_private K_{i0}_private = 4.24.
- Solving the equation with these values implies global growth likely to be 2.77 percent.

H3: Scenario analyses — methods and assumptions (selected)
- Policies to increase LFP:
  - Uses regression coefficients in Table 3.2.2; scenario has all countries converge on best policies (25th percentile of policy variable distribution).
  - Median increase in aggregate LFP across economies in sample = 3.2 percentage points.
  - Assumes all countries (29 economies in policy regression sample plus remaining 111 economies) see aggregate participation increase by 3.2 percentage points.

- Migration boost to labor supply in advanced economies:
  - Scenario: 1 percent increase in advanced economies’ labor force in 2030, adding about 5.5 million workers.
  - Increase in labor supply computed as (1 − Unemp) * 5.5 million, where Unemp = structural unemployment (average 2015–19).
  - If migrants face higher structural unemployment and a pay/productivity gap of 16.1 percent, effective labor supply impact in AEs = (1 − UnempMig) * 5.5 million * (1 − 0.161).
  - In that case, impact = a more modest increase in global growth of 15 basis points.

- Structural reforms to improve allocative efficiency:
  - Using correlations in Figure 3.14, a 1 percent closing of high-misallocation countries’ policy gap with the U.S. expected to improve structural allocative efficiency by ~1 percent.
  - A 15-percent closing of the structural policy gap with the U.S. (plausible but uncommon) used as a scenario to compute corresponding TFP improvements for the 20-economy misallocation sample and extrapolated globally.

- Improved talent allocation in EMDEs:
  - Hsieh and others (2019) estimate 20 percent of U.S. income-per-worker growth over past 50 years due to improved allocation of talent (0.4 percent growth per year).
  - If EMDEs replicated this trend, given their global share, this translates into a global growth boost of about 0.25 percentage point per year.

- Legacy of high public debt (FSGM-based simulation):
  - Scenario 1: Larger transfers to households 2015–2025 increase public debt-to-GDP by 15 percentage points in AEs and 10 percentage points in EMs; deficits remain high from 2025 onward and debt does not stabilize.
  - Scenario 2: In addition to (1), full debt stabilization over 2025–2030 via reduction in transfers to cover larger interest payments.
  - Scenario 3: In addition to (1), full debt stabilization over 2025–2030 via reduction in public investment.

- Geoeconomic fragmentation (GIMF model simulations):
  - Limited fragmentation: friend-shoring by U.S.-led and China-led blocs reduces their imports from the other bloc by 5–10 percentage points across types of goods.
  - More extensive fragmentation: re-shoring by all countries reduces imports from rest of world by 1–3 percentage points across types of goods.
  - Range of impacts reported across these two scenarios.

*Source: CHAPTER 3 SLOWDOWN IN GLOBAL MT GROWTH — Online Annex (IMF staff compilation).*

### Annex follows the structure of the Chapter. The Chapter draws on a variety of datasets which

### ch3onlineannex - Annex follows the structure of the Chapter. The Chapter draws on a variety of datasets which

### Online Annex 3.1. Insights from Medium-Term Forecasts
- Methodology:
  - Forecast error 푒푒푖푖,푡푡 defined as actual growth in year 푡푡 minus the medium-term growth projection for the same year made five years prior.
  - Vintage-by-vintage cross-country regression: 푒푒푖푖,푡푡 = 훼훼푡푡 + 휀휀푖푖,푡푡. Online Annex Figure 3.1.1 presents estimates of 훼훼푡푡 with 95 percent confidence intervals.
  - Actual growth is smoothed using an end-of-period three-year moving average.
- Alignment with potential growth:
  - Vintage-by-vintage cross-country regression: 푧푧푖푖,푡푡 = 훼훼푡푡 + 휀휀푖푖,푡푡, where 푧푧푖푖,푡푡 = medium-term growth forecast − forecast of potential growth for country 푖푖 in year 푡푡.
  - Result: differences are statistically insignificant except after major crises. Example: after the GFC output growth forecasts exceeded potential growth forecasts reflecting deep scarring and projected faster catching up; similarly after the pandemic shock in 2020 for emerging markets and developing economies.

### Online Annex 3.2. Additional Figures, Data Sources and Technical Details — “How Did We Get Here?”

H3: Labor Inputs — Shrinking Share of the Working-Age Population
- Demographic turning points:
  - Online Annex Figure 3.2.1 identifies timing of demographic turning points for the world’s largest economies.
  - A demographic turning point is the year (shown in parentheses next to country names) when the share of the working-age population peaks and subsequently declines; shown as point 0 on the horizontal axis.
  - Notable: time period around the GFC coincided with turning points for US, UK, Canada, and China.

H3: Shift-Share Analysis of Labor Force Participation Rates
- Age groups used: 15–24, 25–54, 55–64, and 65+.
- Decomposition:
  - Gender-specific LFP rate 퐿퐿퐿퐿퐿퐿푖푖,푡푡푔푔 = sum over age groups a of 푠푠푖푖,푡푡푎푎,푔푔 × 퐿퐿퐿퐿퐿퐿푖푖,푡푡푎푎,푔푔.
  - Change in LFP between 2008 and 2021, ∆퐿퐿퐿퐿퐿퐿푖푖,푡푡푔푔, decomposed into:
    - Term attributing change to participation rate changes within age groups (holding population shares constant).
    - Term capturing population aging effect due to changing population shares (holding LFP rates constant at 2008 levels).

H3: Labor Force Participation and the Role of Policies
- Regression specification:
  - 퐿퐿퐿퐿퐿퐿푖푖,푡푡푔푔 = 훽훽푔푔 퐶퐶퐶퐶퐶퐶퐶퐶푒푒푖푖,푡푡 + 훾훾푔푔 푋푋푖푖,푡푡 + 훿훿푔푔 푍푍푖푖,푡푡푔푔 + 훼훼푖푖푔푔 + 훼훼푡푡푔푔 + 휀휀푖푖,푡푡푔푔.
  - 퐶퐶퐶퐶퐶퐶퐶퐶푒푒푖푖,푡푡 is cyclical position captured by output gap; 푋푋 structural variables (trade openness, service/industry employment ratio, urbanization, education shares); 푍푍 policies and institutions (some group-specific). Country and year fixed effects included. Some variables lagged by one year.
  - Regression run for five groups: young workers (15–24); prime-age men (25–54); prime-age women (25–54); close-to-retirement workers (55–64); older workers (65+).
- Data sources and variable definitions (Online Annex Table 3.2.1):
  - Output Gap: IMF, WEO database.
  - Trade Openness: IMF, WEO database; defined as (X + M)/GDP where X and M are total exports and imports of goods and services.
  - Service/Industry Employment Ratio; Urbanization Rate: World Bank, World Development Indicators database.
  - Population by Education (secondary, tertiary): Barro-Lee Educational Attainment data set.
  - Labor Tax Wedge: OECD, Tax database; defined as ratio between average tax paid by a single-earner family (one parent at 100 percent of average earnings with two children) and the corresponding total labor cost for the employer.
  - Unemployment Benefits: OECD, Benefits and Wages: Statistics; net replacement rate.
  - Spending on Labor Market Programs: OECD, Social Expenditure database; active labor market program spending per unemployed person in percent of GDP per capita.
  - Union Density: OECD, Employment database; net union membership as proportion of wage earners.
  - Coordination of Wage Setting: OECD/AIAS (ICTWSS) index 1–5 (higher = more centralized).
  - Spending on Early Childhood Education and Care: OECD, Social Expenditure database; as percent of GDP.
  - Share of Part-time Employment: OECD, Employment database.
  - Length of Maternity Leave: OECD, Family database; measured in weeks of job-protected leave.
  - Retirement Age: International Social Security Association, Social Security Programs throughout the World; statutory retirement age.
  - Public Pension Spending; Public Spending on Incapacity: OECD, Social Expenditure database.
- Regression results (Online Annex Table 3.2.2) — selected coefficients and significance indicators:
  - Output Gap (Lagged): 0.122 (Youth); –0.0619** (Prime-Age Men); 0.0109 (Prime-Age Women); 0.0337 (Close-to-Retirement); 0.0701** (Older Workers). Standard errors: (0.103)(0.0228)(0.0662)(0.0914)(0.0238).
  - Trade Openness (Lagged): –0.0316 (Youth); 0.00514 (Prime-Age Men); 0.0116 (Prime-Age Women); –0.000912 (Close-to-Retirement); –0.0603*** (Older Workers). Standard errors: (0.0248)(0.00617)(0.0113)(0.0174)(0.0110).
  - Service/Industry Employment Ratio (Lagged): –0.00526 (Youth); 0.0000050 (Prime-Age Men); 0.0223*** (Prime-Age Women); –0.00477 (Close-to-Retirement); 0.0129*** (Older Workers). Standard errors: (0.00936)(0.00206)(0.00334)(0.00582)(0.00164).
  - Urbanization Rate (Lagged): 0.00509 (Youth); 0.0230 (Prime-Age Men); 0.0930* (Prime-Age Women); 0.159 (Close-to-Retirement); –0.0755* (Older Workers). Standard errors: (0.123)(0.0280)(0.0492)(0.0979)(0.0409).
  - Secondary Education (All gender, ages 15–24): 0.0622** (standard error (0.0242)).
  - Secondary Education (Female, ages 25–54): 0.121*** (standard error (0.0253)).
  - Tertiary Education (All gender, ages 55–64): –0.177* and –0.160*** reported (standard errors (0.0887)(0.0228)).
  - Labor Tax Wedge: –0.0632 (Youth); –0.0978*** (Prime-Age Men); 0.0197 (Prime-Age Women); 0.0206 (Close-to-Retirement); –0.0577 (Older Workers). Standard errors: (0.0816)(0.0286)(0.0486)(0.0837)(0.0400).
  - Unemployment Benefits: 0.00680 (Youth); –0.0174*** (Prime-Age Men); –0.0512*** (Prime-Age Women); 0.00197 (Close-to-Retirement); 0.00785 (Older Workers). Standard errors: (0.0156)(0.00535)(0.0151)(0.0413)(0.00644).
  - Spending on Labor Market Programs: 0.227 (Youth); –0.306 (Prime-Age Men); 0.774* (Prime-Age Women); 1.358** (Close-to-Retirement); 0.0650 (Older Workers). Standard errors: (0.729)(0.195)(0.363)(0.505)(0.211).
  - Union Density: –0.0574 (Youth); –0.104*** (Prime-Age Men); 0.358*** (Prime-Age Women); –0.346*** (Close-to-Retirement); 0.0432 (Older Workers). Standard errors: (0.135)(0.0334)(0.0812)(0.113)(0.0470).
  - Coordination of Wage Setting: 1.514** (Youth); 0.375** (Prime-Age Men); 0.837*** (Prime-Age Women); 0.866*** (Close-to-Retirement); –0.0272 (Older Workers). Standard errors: (0.635)(0.128)(0.238)(0.225)(0.129).
  - Spending on Early Childhood Education and Care: 4.310*** (Prime-Age Women). Standard error: (0.646).
  - Share of Part-Time Employment: 0.302** (Prime-Age Women). Standard error: (0.103).
  - Retirement Age: 0.735*** (Close-to-Retirement); 0.432*** (Older Workers). Standard errors: (0.204)(0.0560).
  - Public Pension Spending: –1.598*** (Close-to-Retirement); –1.102*** (Older Workers). Standard errors: (0.313)(0.0962).
  - Public Spending on Incapacity: 0.638 (Close-to-Retirement); 0.630*** (Older Workers). Standard errors: (0.617)(0.195).
- Model diagnostics:
  - Observations: 487 (Youth), 394 (Prime-Age Men), 363 (Prime-Age Women), 379 (Close-to-Retirement), 379 (Older Workers).
  - Within R2: 0.30 (Youth), 0.30 (Prime-Age Men), 0.65 (Prime-Age Women), 0.77 (Close-to-Retirement), 0.65 (Older Workers).
  - Note: Standard errors shown in parentheses. *, ** and *** indicate statistical significance at 10 percent, 5 percent, and 1 percent levels.

H3: Aggregate Business Investment — Business investment and fiscal shocks data
- Definition and sample:
  - In OECD economies, aggregate business investment = gross fixed capital formation for non-financial corporations deflated using the WEO private investment deflator.
  - Sample restricted to 21 OECD economies for which narrative fiscal shocks from Devries and others (2011) are available.
  - Sample period: late 1970s to 2021, assuming zero-fiscal shock in 2020-21.
  - Sample composition: 16 advanced economies (Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Italy, Japan, Netherlands, Portugal, Spain, Sweden, United Kingdom, United States) and 5 emerging markets and developing economies (Brazil, Chile, Colombia, Costa Rica, Mexico).

H3: Investment growth–output growth regression (Instrumental Variables)
- Two-stage IV regression approach (based on Chapter 4, April 2015 WEO):
  - First stage: instrument change in real GDP growth ΔlnY푖푡I V using narrative fiscal shocks (Devries and others 2011).
  - Second stage: ∆lnI푖푡 = 훽 ΔlnY푖푡I V + ρ ∆lnI푖푡−1 + a푖 + τ푡 + ε푖푡.
  - Dependent variable: Investment Growth ∆lnI푖푡 (change in log real business investment).
- Key reported statistics (Online Annex Table 3.2.3):
  - Coefficient on instrumented GDP growth: 1.985** (column 1) and 2.878** (column 2). Standard errors: (0.851)(1.441).
  - Coefficient on lagged investment growth: 0.018 (column 1) and 0.006 (column 2). Standard errors: (0.090)(0.098).
  - Country FE: Yes. Year FE: Yes.
  - Number of observations: 499 (column 1), 488 (column 2).
  - Adjusted R2: 0.668 (column 1), 0.537 (column 2).
  - First-Stage F-statistic: 16.446 (column 1), 10.832 (column 2).
  - p-Value of F-statistic: < 0.0001 (column 1), 0.0011 (column 2).
  - Note: Using narrative fiscal shocks as instruments yields first-stage F-statistics above 15 in column 1 with p-value below 0.1 percent, suggesting instrument relevance. Second-stage results imply investment–output growth elasticity statistically significant and close to 2. Column 2 uses growth rate of total demand (C + X) as alternative measure; results consistent.
- Additional first-stage specification notes (footnote):
  - First-stage regressions: ΔlnGDP = −0.661*** FiscalShock + 0.063*** ∆lnI−1 + αi + λt + u, and Δln(C+X) = −0.514*** FiscalShock + 0.046** ∆lnI−1 + αi + λt + u.
  - Overidentification tests when using fiscal shocks and lagged fiscal shocks as instruments produce Hansen J-statistic p-values exceeding 10 percent, indicating validity of instruments.

H3: Firm-level Investment Analysis
- Data and coverage:
  - Firm-level data from Thomson Reuters Worldscope aggregated to country-year level; finance, insurance, real estate, and government agencies excluded.
  - 95% winsorization applied on variables used to construct total investment.
- Sample lists:
  - Advanced economies sample includes: Australia, Austria, Belgium, Canada, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hong Kong SAR, Iceland, Ireland, Israel, Italy, Japan, Korea, Lithuania, Luxembourg, Netherlands, New Zealand, Norway, Portugal, Singapore, Slovak Republic, Slovenia, Spain, Sweden, Switzerland, United Kingdom, United States. Hong Kong SAR, Iceland, and Singapore excluded in comparison with OECD fixed capital formation.
  - Emerging market sample includes: Brazil, Chile, China, Colombia, Hungary, India, Malaysia, Mexico, Poland, Russia, South Africa, Thailand, Türkiye. India, Malaysia, and Thailand excluded in comparison with OECD fixed capital formation.
- Representativeness:
  - Aggregated firm-level investment represents around half of total business investment in advanced economies; correlation between firm-level aggregate and total business investment exceeds 0.8 for majority of advanced economies in sample.
  - For emerging markets, aggregated firm-level investment represents up to 30 percent of business investment compared to aggregate OECD series; correlation exceeds 0.8 for about half of emerging markets in the sample.

H3: Construction of Net Investment Rates in Thomson Reuters Worldscope
- Rationale:
  - Mismeasurement of intangible capital is a proposed explanation for observed decline in investment rates, especially in advanced economies (e.g., Crouzet and Eberly (2019) finding that accounting for intangible capital can explain 30 to 60 percent of the decline in US investment since 2000).
- Definition and construction:
  - Follows Peters and Taylor (2017).
  - Net investment rate for firm i in year t defined using net tangible investment plus intangible investment measures and capital stocks (formulas in source text).
  - Net Tangible Investment constructed as tangible capital expenditure in Worldscope minus depreciation.
  - Aggregation and inclusion of intangible investment components are explicitly incorporated in the net investment rate construction.

*Source: IMF staff compilation.*

### CHAPTER 3 SLOWDOWN IN GLOBAL MT GROWTH

### CHAPTER 3 SLOWDOWN IN GLOBAL MT GROWTH

### Construction of Intangible Investment and Intangible Capital
- Intangible investment for firm i in year t is constructed as:
  - IIIt aIIg iICe I I IItit = R&D_it + 0.3 SGA_it (presentation preserved as in source).
  - R&D = annual spending on research and development; SGA = annual selling, general and administrative expenses.
- Intangible capital is constructed as:
  - IIIt aIIg iICe K_it = IIIt aIIg iICe S_assets_it + KI_pstock K_it + OOtherInvestment_K_it (presentation preserved as in source).
  - IIIt aIIg iICe S_assets_it refers to the book value of patents, leasehold improvements and trademarks.
  - KI_pstock and OOtherInvestment_K are constructed following Peters and Taylor 2017 as:
    - KI_pstock K_it = [ (1−δ_k n p k T a k g a K) ] K_I_pstockKCe Kge K_it−1 + R&D_it (presentation preserved).
    - OOtherInvestment_K_it = (1−δ_ppg_an i o a t i p n a T K) OOtherInvestment_K_it−1 + SGA_it (presentation preserved).
  - Depreciation rates:
    - δ_k n p k T a k g a K = 0.15
    - δ_ppg_an i o a t i p n a T K = 0.2

### Descriptive Statistics (Thomson Reuters Worldscope, sample period 2000-2021)
- All variables winsorized at the 5th and 95th percentile.
- Online Annex Table 3.2.4 (Median, Mean, Standard Deviation):
  - Gross Tangible Investment Ratio: Median 6.35; Mean 9.66; Standard Deviation 10.43
  - Intangible Investment Ratio: Median 8.44; Mean 10.88; Standard Deviation 10.66
  - Total Net Investment Ratio: Median 10.39; Mean 14.04; Standard Deviation 15.54
  - Tobin’s q: Median 1.16; Mean 1.48; Standard Deviation 0.93
  - Leverage: Median 23.28; Mean 25.11; Standard Deviation 17.39
  - Cost of Debt: Median 4.36; Mean 6.87; Standard Deviation 9.49
  - Profit Margin: Median 4.95; Mean –1.39; Standard Deviation 35.52
  - Cash Stock over Total Assets: Median 10.57; Mean 13.70; Standard Deviation 12.74

### Investment Regression: Key Estimates and Interpretations (Online Annex Table 3.2.5)
- Dependent variable: Net Investment Rate; regressions include firm and year fixed effects; standard errors clustered at firm level.
- Tobin’s q (t-1):
  - Advanced economies (AEs), column (1): coefficient 0.0403***
  - Emerging markets (EMMIEs), column (2): coefficient 0.0357***
  - Interpretation: a 1 unit increase in Tobin’s q leads to a 4.03 percentage points increase in the net investment rate in advanced economies (column 1), and a 3.57 percentage points increase in emerging markets (column 2).
  - Post-2008 effect: increase reduced to 2.9 percentage points in advanced economies and 3.15 percentage points in emerging markets (textual statement preserved).
- Uncertainty index (log):
  - A 1 percent increase in the uncertainty index leads approximately to a 5.82 basis points decline in investment rates (textual statement preserved).
- Coefficient interpretation for other regressors:
  - For coefficient β, a 1 percentage point increase in the regressor leads to (100 × β) basis points increase in the net investment rate (textual rule preserved).
- Selected coefficient estimates (Online Annex Table 3.2.5):
  - Leverage (t-1): AEs −0.1059***; EMMIEs −0.0757***
  - Cost of Debt (t-1): AEs −0.0303***; EMMIEs −0.0277**
  - Profit Margin (t-1): AEs 0.0137***; EMMIEs 0.0719***
  - Cash Stock over Assets (t-1): AEs 0.2673***; EMMIEs 0.3345***
  - Post-2008 × Tobin’s q (t-1): AEs −0.0113***; EMMIEs −0.0042**
  - Post-2008 × Leverage (t-1): AEs −0.0019; EMMIEs −0.1030***
  - Post-2008 × Cost of Debt (t-1): AEs −0.0009; EMMIEs −0.0757***
  - Post-2008 × Profit Margin (t-1): AEs −0.0087**; EMMIEs −0.0414***
  - Post-2008 × Cash Stock over Assets (t-1): AEs −0.0994***; EMMIEs −0.0504**
  - GDP Growth (t-1): AEs 0.0885***; EMMIEs 0.0140
  - GDP Growth (t-2): AEs 0.0551***; EMMIEs 0.1890***
  - GDP Growth (t-3): AEs 0.1294***; EMMIEs 0.2538***
  - Uncertainty Index: AEs −0.0582***; EMMIEs 0.0022
  - Capital Inflow over GDP: AEs 0.0242; EMMIEs 0.1981***
  - Observations: AEs 214,458; EMMIEs 90,301
  - Adjusted R2: AEs 0.4985; EMMIEs 0.338
- Interpretation and patterns:
  - Marked reduction in sensitivity of investment rates to Tobin’s q, profit margins, and accumulated cash after 2008, especially in advanced economies.
  - Emerging markets: firms became more responsive to leverage and cost of debt post-2008.
  - These patterns align with research linking weakened investment relationships to the rise of large firms and decreased competition, and with evidence on rising corporate leverage in emerging markets.

### Evolution of Key Investment Determinants (post-2008 vs pre-2008)
- Method: Post-pre 2008 differences computed at firm-level, aggregated at country level using relative capital share weights; averages for advanced and emerging economies computed using GDP PPP weights.
- Observed changes (text summary preserved):
  - Tobin’s q, Cost of Debt, Cash Stock over Assets, and Past GDP Growth declined post-2008 in both advanced and emerging markets.
  - Leverage and the country-level Uncertainty Index increased in both advanced and emerging markets.
  - Profit margins increased in advanced economies but decreased in emerging markets.
  - Capital inflows over GDP decreased in advanced economies after 2008; conversely, they increased in emerging markets.

### Resource Misallocation — Data Sample and Coverage
- Country sample (20 economies, period 2000–19): Austria, Belgium, Bulgaria, China, Czechia, Estonia, France, Germany, Italy, Japan, Korea, Poland, Portugal, Romania, Russia, Slovakia, Slovenia, Spain, Switzerland, and the USA.
- Firm-level data from Orbis covering 19 broad sectors: Agriculture; Mining; Food; Textiles; Wood Products; Petroleum Products; Chemical Products; Plastics; Basic Metals; Electronics; Machinery; Transport Equipment; Other Manufacturing; Construction; Retail; Hospitality; Information Services; Finance and Real Estate; Professional Services.
- Coverage notes:
  - Sectors span whole economy excluding Utilities, Public Administration, Education, and Arts.
  - For included countries, total firm sales in Orbis consistently exceed 60 percent of value of total gross output reported by OECD, except:
    - United States: Orbis covers only listed firms accounting for about 30 percent of total output.

### Measuring Allocative Efficiency at Sector Level (Hsieh and Klenow 2009 framework)
- Relationships (presentation preserved with original notation):
  - TRFLP_prit ∝ VS_prit^(σ/(σ−1)) K_prit^α_s L_prit^(1−α_s)
  - MRPK_prit ∝ VS_prit K_prit
  - MRPL_prit ∝ VS_prit L_prit
- Parameters and calibration:
  - σ (elasticity of substitution between outputs of different firms) set to 3.
  - α_s set equal to 1 minus average U.S. labor share in sector s during 2000–19 from EU-KLEMs.
- Computation:
  - TFPQ, MRPK, MRPL computed at sector level for 2000–19 using Orbis data on value added, capital stocks, employment.
- Allocative efficiency measure:
  - SSL_prt ∈ [0,1]; 1 − SSL_prt measures the share of sector’s potential TFP lost due to misallocation.

### Detecting and Correcting for Additive Measurement Error
- Additive measurement error detection regression (presentation preserved):
  - ∆ln VS_prit = Φ_pr ∆ln TLFTRR_prit + Ψ_pr ∆ln K_prit^α_s L_prit^(1−α_s) − Ψ_pr (1 − λ_pr) ln TLFTRR_prit × ∆ln K_prit^α_s L_prit^(1−α_s) + G_pr + ξ_prit
- Interpretation of λ̂_pr:
  - λ̂_pr = 1 ⇒ no additive measurement error
  - λ̂_pr = 0 ⇒ measures are pure noise
- Online Annex Table 3.2.6 findings (selected country and group medians, by period and sector type):
  - United States median λ̂, 2000–09: 0.837 (0.014)
  - China median λ̂, 2000–09: 0.812 (0.005)
  - AEs median λ̂, 2000–09: 0.738 (0.010)
  - EMMIEs median λ̂, 2000–09: 0.833 (0.005)
  - Sample median λ̂, 2000–09: 0.757 (0.008)
  - United States median λ̂, 2010–19: 0.898 (0.017)
  - China median λ̂, 2010–19: 0.728 (0.011)
  - AEs median λ̂, 2010–19: 0.767 (0.006)
  - EMMIEs median λ̂, 2010–19: 0.797 (0.004)
  - Sample median λ̂, 2010–19: 0.768 (0.006)
  - Goods and Services panels also reported (examples preserved):
    - Goods, 2000–09 medians: U.S. 0.945 (0.012); China 0.884 (0.017); AEs 0.820 (0.007); EMMIEs 0.884 (0.005); Sample 0.834 (0.005)
    - Goods, 2010–19 medians: U.S. 0.772 (0.016); China 0.835 (0.009); AEs 0.772 (0.004); EMMIEs 0.835 (0.003); Sample 0.782 (0.003)
- Conclusion:
  - Additive measurement error is present but small; λ̂_pr values consistently closer to 1 than 0.
  - Service sectors appear less prone to additive measurement error than goods sectors.
- Correction for additive measurement error:
  - True values recovered using expectations E[λ̂_pr ln(measured variable)] (presentation preserved).
  - These adjusted values used to compute firms’ total revenue factor productivities and sector-level allocative efficiency SSL_prt.

### Aggregate TFP Impact of Changes in Allocative Efficiency
- Aggregate TFP decomposition:
  - ln TFP_pt ≡ ln TFP_pt* + Σ_r θ_prt ln SSL_prt
  - TFP_pt* = “ideal” TFP absent misallocation
  - θ_prt = share of sector s in country C GDP
- Growth decomposition:
  - ∆ln TFP_pt ≡ ∆ln TFP_pt* + ∆ln SSL_pt
  - ∆ln SSL_pt ≡ ∆Σ_r θ_prt ln SSL_prt
  - First term captures innovation and entry; second term captures TFP impact of changes in allocative efficiency.
- Shift-share decomposition of ∆ln SSL_pt:
  - ∆ln SSL_pt ≡ Σ (∆θ_prt) ln SSL_prt + Σ θ_prt−1 (∆ln SSL_prt)
  - First term: impact of changes in sector GDP shares (composition)
  - Second term: changes in within-sector allocative efficiency (holding sector shares constant)
- Sector GDP shares sourced from EU-KLEMS or OECD-TiVA.

### Firm-Level Evidence of Adjustment Frictions (Online Annex Table 3.2.7)
- Hypothesis: adjustment frictions imply firms take time to attract resources after a positive productivity shock → temporary increase in misallocation wedge.
- Firm-level regression (presentation preserved):
  - ∆ln( TLFTRR_prit / TLFTRR̄_prt ) = γ̂1 ∆ln TFPQ_prit + γ̂2 ln( TLFTRR_prit / TLFTRR̄_prt ) + firm FE + country-sector-year FE + error
- Key estimates (Online Annex Table 3.2.7, period 2000–19, N = 34,399,920 observations):
  - Column (1) Log Change in Misallocation Wedge: Log Change in TFPQ coefficient 0.727*** (p-value formatting preserved as in table)
  - Column (2) Log Change in Misallocation Wedge: Log Change in TFPQ coefficient 0.703*** 
  - Column (3) Log Change in Misallocation Wedge: Log Initial Misallocation Wedge coefficient −0.595***
  - Column (4) Log Change in Misallocation Wedge: Log Change in TFPQ 0.703***; Log Initial Misallocation Wedge −0.066***
  - R2 values: Columns (1) 0.160; (2) 0.940; (3) 0.410; (4) 0.940
- Interpretations and quantitative implications:
  - Firms with faster relative TFPQ growth tend to see an increase in their misallocation wedge on impact (γ̂1 > 0).
  - Misallocation wedges revert over time (γ̂2 < 0).
  - Estimated reversion speed implies it takes about ln 0.5 / ln(1 + γ̂2) ≈ 11 years on average for a firm’s misallocation wedge to return half-way to its initial value following a one-time shock (textual computation preserved).
  - Aggregate implication: using regression results, about 37 percent of overall misallocation is due to transitory factors and 63 percent is structural (textual finding preserved).
  - Robustness: result robust across countries and groups; some evidence U.S. wedges rise less and revert faster (noted caveat re: U.S. Orbis coverage).

### Sector-Level Evidence of Adjustment Frictions (Online Annex Table 3.2.8)
- Sector-level regression (presentation preserved):
  - ∆_{t+9,t} ln SSL_prt = β̂1 ∆_{t+9,t} ln LG_prt + β̂2 ln SSL_prt + country FE + sector FE + error
  - LG_prt = dispersion of firm TFPQs computed as ratio of power mean to geometric mean (σ = 3).
  - Regression pooled for two ten-year changes: 2000–09 and 2010–19; N = 586 observations.
- Key estimates (Table 3.2.8):
  - Log Change in Allocative Efficiency regressed on:
    - Log Change in Productivity Dispersion: coefficient −0.470 (column 1), −0.365 (column 2)***
    - Log Initial Allocative Efficiency: coefficient −0.611 (column 3), −0.516 (column 4)***
  - R2 values: column (1) 0.100; (2) 0.340; (3) 0.430; (4) 0.570
- Interpretations:
  - An increase in sector-level dispersion of firm productivities is accompanied by a contemporaneous decline in sector allocative efficiency.
  - Sectors with larger initial inefficiency tend to exhibit stronger mean reversion (allocative efficiency recovers over time).
  - Long-run allocative efficiency converges to ln SSL_pr = −δ̂_p + δ̂_r / β̂2, capturing sector-inherent characteristics and country economic conditions.

*International Monetary Fund | April 2024*

### CHAPTER 3 SLOWDOWN IN GLOBAL MT GROWTH

### CHAPTER 3 SLOWDOWN IN GLOBAL MT GROWTH

### Institutional environment and long-run allocative efficiency
- The country component of long-run structural allocative efficiency is defined and estimated as −훿훿̂푝푝/훽훽̂2.
- In the absence of shocks: ∆푡+9,푡 lnSLL푝푟푡 = 훽̂2(lnSLL푝푟푡 − lnSLL푝푟).
- The approximate half-life in years of a deviation of allocative efficiency from its long-run fundamental is measured by 9×ln0.5 / ln(1+훽̂2).
- Estimates in column (4) of Online Annex Table 3.2.8 imply:
  - half-life = 9 years,
  - comparable to an 11-year half-life of the firm-level misallocation wedge documented earlier.

### Online Annex 3.3 — Assumptions and calculations for medium-term projections
- Purpose: methodology to project trend LFP rate, potential employment growth, growth rates of TFP and capital in the medium-term (year 2030).

#### Projecting potential employment growth in the medium term
- Labor supply forecast uses a cohort-based analysis of trend LFP rates for age and gender groups in 83 economies.
- Specification (as in source):
  - logLFPRt a,g = αa,g + (1/na) ΣβT g IT(=t−a),t g 2006 T=1932 + γa,g CYCLEt + λa,g Xt a,g + εt a,g.
- Data and estimation:
  - LFP data from ILO for four age groups (15–24, 25–54, 55–64, 65 above) for period 1995–2021 (estimation noted for 1995–2021) and for period 1995–2023 in expanded estimation.
  - Cohorts included: birth years 1932 to 2006, grouped in five-year intervals; cohort coefficient divided by number of cohorts in an age group Ia.
  - Determinants: age-gender-specific constant (αa,g), birth-cohort effects (IT), business cycles (measured by HP-filtered output gap), structural factors Xt a,g (life expectancy, fertility, education attainment and enrollment).
  - For women of prime working age: participation negatively correlated with fertility rate; among working-age women positive correlation with years of schooling (Barro and Lee 2021 September update).
- Prediction assumptions:
  - No cyclical gap, constant time trends over the medium term.
  - Uses projected structural factors from the UN Population and Development Database.
  - Natural progression of cohorts; participation profile of new cohorts mirrors most recently observed cohort.
  - Aggregation to country-level participation based on projected population share of each group.
  - Medium-term potential employment growth estimated using projected LFP growth by 2030 and expected growth of population (aged 15 above), assuming stable employment rates.

#### Constructing the baseline scenario for global medium-term growth
- Approach: top-down growth decomposition starting from ΔlnYt = ΔlnTFPt + (1−α)ΔlnLt + αΔlnKt.
- Labor component: forecasted via cohort-based LFP projections (above).
- Focus here on capital component and TFP.

Capital growth projection
- ΔlnKt = s ΔK/public Kpublic + (1−s) ΔK/private Kprivate, where s is share of public capital in total capital.
- ΔK/K = I/K − δ corresponds to net investment rate (after depreciation).
- Projected investment rates from WEO for the medium term are used.
- Private investment rate forecast:
  - Output growth elasticity of private investment rate estimated using accelerator model; net private investment rates regressed on GDP growth using narrative fiscal shocks as instrument; controls for country and time fixed effects.
  - Estimated investment-growth elasticity = 훽̂.
  - Net private investment rate formula (from source equation (1)):
    - NII2030 private K2029 private = 훽̂(ΔlnY2030 − ΔlnYt0) + NIIi0 private K i0 private.
  - Pre-pandemic five-year (2015–19) averages used for initial values of global output growth and net private investment rate.

TFP growth projection
- TFP growth decomposition (as in Online Annex 3.2): ∆lnTFPt ≡ ∆lnTFPt* + ∆lnSLLt (change in efficient TFP plus change in allocative efficiency).
- Change in allocative efficiency in 2030:
  - Based on sector-level allocative efficiency analysis and estimates in Online Annex Table 3.2.8.
  - Projected for country C using E[∆t+9,t lnSLLp t] = Σθp r t (β̂2 lnSLLpr t + r δ̂p + δ̂r), given initial sector-level misallocation in t and assuming no further shocks and constant sector shares.
  - Countries’ 2019 sector-level misallocation used as initial value, allowing for some “depreciation” between 2019 and 2024.
  - Aggregation across 20 sample countries using PPP GDP weights: E[∆lnSLLt] = (1/9) Σωp E[∆t+9,t lnSLLp t]p.
- Efficient TFP growth assumed to continue its historical downward trend.
- Combining factors yields expected TFP growth in the medium term estimated to be around 0.9 percent.

Global output growth projection
- Global GDP growth in 2030 projected with:
  - ΔlnY2030 = ΔlnTFP2030 + (1−α)ΔlnL2030 + α[ s NII2030 public K2029 public + (1−s) NII2030 private K2029 private ].
- Values used (preserved exactly from source):
  - ΔlnTFP2030 = 0.9,
  - ΔlnL t = 0.32,
  - α = 0.487,
  - s = 0.27,
  - NII2030 public K2029 public = 0.3,
  - 훽̂ = 0.85,
  - ΔlogYt0 = 3.41,
  - NIIi0 private K i0 private = 4.24.
- Solving the equation for ΔlnY2030 implies global growth likely to be 2.77 percent.

### Scenario analyses — estimation methods and assumptions
- Policies to increase LFP:
  - Uses regression coefficients in Table 3.2.2.
  - Scenario: all countries converge on best policies defined as 25th percentile of policy variable distribution.
  - Median increase in aggregate LFP across economies in sample = 3.2 percentage points.
  - Assumes all countries (29 economies in policy regression sample plus remaining 111 economies) see aggregate participation rate increase by 3.2 percentage points.

- Migration boost to labor supply in advanced economies:
  - Scenario: additional migrant worker flows and better labor market integration → 1 percent increase in advanced economies’ labor force in 2030, adding about 5.5 million workers.
  - Context: pre-pandemic (2015–19) migration flows in Australia, Canada, EU, UK, and the US ranged from 0.6 to 2.2 percent of their labor forces on average.
  - Year 2022 saw rebound in migration flows, constituting an additional 1 percent of the labor force in Canada and the UK relative to pre-pandemic average.
  - Increase in labor supply computed as (1 − Unemp) * 5.5 million workers, where Unemp = structural unemployment rate proxied by average unemployment rate 2015–19.
  - Absent enhanced integration, migrants may face worse outcomes. Assuming higher structural unemployment for migrants (Amo-Agyei 2020, Table 4) and a pay gap of 16.1 percent (Amo-Agyei 2020, Figure 17) representing productivity differentials, effective labor supply impact in AEs = (1 − UnempMig) * 5.5 million * (1 − 0.161).
  - In this case, impact = a more modest increase in global growth of 15 basis points.

- Structural reforms for improving allocative efficiency:
  - Using correlations in Figure 3.14, a 1 percent closing of high-misallocation countries’ policy gap with the U.S. expected to improve structural allocative efficiency by ~1 percent.
  - Empirically, a 15-percent closing of the structural policy gap with the U.S. is uncommon (≈ top 10 percent of distribution of decadal policy changes between 1988 and 2018) but plausible.
  - Corresponding improvement in TFP computed for 20-economy misallocation sample and extrapolated to global boost if high-misallocation countries achieve a 15-percent policy-gap reduction over next decade.

- Improved talent allocation in emerging market and developing economies:
  - Hsieh and others (2019) estimate 20 percent of income-per-worker growth over past 50 years in U.S. resulted from improved allocation of talent (0.4 percent growth per year).
  - If EMDEs followed same trend, given their share in global economy this translates into global growth boost of about 0.25 percentage point per year.

- Legacy of high public debt:
  - FSGM-based simulation with three scenarios:
    1. Larger transfers to households between 2015 and 2025 increase public debt-to-GDP ratio by 15 percentage points in advanced economies and 10 percentage points in emerging economies; from 2025 onward deficits stay high and debt does not stabilize.
    2. In addition to (1), full debt stabilization over 2025–2030 via reduction in transfers to cover larger interest payments.
    3. In addition to (1), full debt stabilization over 2025–2030 via reduction in public investment.

- Geoeconomic fragmentation:
  - Simulations using the Global Integrated Monetary and Fiscal (GIMF) model.
  - Two fragmentation scenarios:
    - Limited fragmentation: friend-shoring by a U.S.-led and China-led bloc reduces their imports from the other bloc by 5–10 percentage points across types of goods.
    - More extensive fragmentation: re-shoring by all countries and regions reduces imports from rest of world by 1–3 percentage points across types of goods.
  - Range of impacts reflects these two scenarios.

*Source: CHAPTER 3 SLOWDOWN IN GLOBAL MT GROWTH (Online Annex).*

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_Source: https://www.imf.org/-/media/files/publications/weo/2024/april/english/ch3onlineannex.pdf_