## _wp1343

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---

### I. INTRODUCTION
- Research question and approach:
  - Examines whether structural transformation (labor reallocation across agriculture, manufacturing, services) contributes to the decline in aggregate output volatility observed in the U.S. and OECD countries.
  - Uses a model in which labor reallocation emerges endogenously from changes in sectoral labor productivities.
- Methodology:
  - Calibrates the model to the U.S. to discipline preference parameters, keeps deep parameters fixed, and feeds country-specific sectoral labor productivity processes to generate time paths of labor shares for OECD countries.
  - Performs counterfactual experiments that constrain endogenous labor mobility by feeding identical permanent productivity components across sectors while keeping transitory components unchanged; this shuts down most secular labor shifts while preserving cyclical properties.
- Framing:
  - Motivated by the “Great Moderation” and literature on decline in output volatility; emphasizes endogenous labor reallocation, three-sector setup (agriculture, manufacturing, services), and cross-country continuous volatility paths.

### II. EMPIRICAL EVIDENCE
- Data and sample:
  - Annual data for 21 OECD countries over the period 1970–2006.
  - Countries: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Italy, Japan, Korea, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Turkey, United Kingdom, and the United States.
- Volatility measurement:
  - Volatility of variable Y at date t computed as the standard deviation of growth rates over a 10-year backward-looking window (rolling window).
- Sectoral volatility facts:
  - Agriculture is more volatile than manufacturing, which is more volatile than services.
  - Labor productivity is about half as volatile in services as in manufacturing and is nearly twice as volatile in agriculture as in manufacturing across OECD countries.
  - Facts robust to varying the window for computing volatilities.
- Structural transformation patterns:
  - Follows Kuznets (1966) three-stage description: large agricultural employment → shift to manufacturing → shift from manufacturing to services.
  - Illustrative employment shares at beginning of sample (1970):
    - 63% in agriculture in Turkey.
    - nearly 50% in South Korea.
    - 41% in Greece.
    - 30% in Portugal and Spain.
  - Contemporary examples: U.S., U.K., and Canada now have more than 70% of employment in the service sector and less than 3% in agriculture.
- Correlations and regressions:
  - Cross-country correlation between employment share of service sector and aggregate output volatility: −0.68 across countries and −0.56 in the panel.
  - Correlation between output volatility and GDP per capita: −0.54 across countries and −0.45 in the panel.
  - Regression: when regressing output volatility on both employment share of services and GDP per capita, GDP per capita is not significant while employment share of services is significant.
  - Controlling for financial development (GDP share of credit to the private sector) does not remove the significant effect of the employment share of services.
  - Results robust to varying volatility window and replacing volatility measure by standard deviation of de-trended series.
- Empirical implication:
  - Evidence consistent with the hypothesis that labor reallocation toward services is associated with reduced aggregate output volatility in OECD countries over 1970–2006.

### III. THE MODEL
- Model type and environment:
  - Indivisible labor model of structural transformation (three sectors: agriculture (a), manufacturing (m), services (s)); production Yi = Ai Li with Ai exogenous sectoral labor productivity.
  - Continuum of identical infinitely-lived households; population grows at exogenous rate η; indivisible labor: agents either work full-time or not at all; employment probability πt; sectoral employment probabilities πi,t = Li,t/Nt.
  - Employment-to-population calibration benchmark: employment to population ratio = 66%.
  - De-trended series obtained as log series minus HP filter with λ=100 (annual observations).
- Preferences and demand:
  - Planner objective: U(ca,t, ct, ht) = ω log(ca,t − ̄a) + (1−ω) log(c t) + φ log(1−ht), 0<ω,φ<1.
  - Composite manufacturing + services CES aggregator:
    - c = [ θ c_m^{(ε−1)/ε} + (1−θ)(c_s + ̄s)^{(ε−1)/ε} ]^{ε/(ε−1)}
  - Parameters: 0<θ<1; 0<ε<1; ̄s>0 implies income elasticity of services > 1.
  - Two channels generating labor reallocation: low elasticity of substitution (ε<1) and non-homothetic preferences (̄a and ̄s).
- Planner problem and analytical solution:
  - Planner chooses {πa,t; πm,t; πs,t} subject to ca,t ≤ Aa,t πa,t; cm,t ≤ Am,t πm,t; cs,t ≤ As,t πs,t and πa,t+πm,t+πs,t = πt.
  - Solved in two stages: first for πm and πs given πa; then optimize πa.
  - First-stage relation:
    - πs + ̄s/As πm = ( (1−θ)/θ )^ε ( log(1− ̄h_m) / log(1− ̄h_s) )^ε ( As/Am )^{ε−1 }
  - Closed-form πa (second stage):
    - πa = ( ̄a/Aa )(1+Ψ)(1−ω) + ω(π+ ̄s/As)(αm/αa + Ψ αs/αa)
      divided by
      ω(αm/αa + Ψ αs/αa) + (1+Ψ)(1−ω)
    - Ψ = ( (1−θ)/θ )^ε ( log(1− ̄h_m) / log(1− ̄h_s) )^ε ( As/Am )^{ε−1 }
    - αi = log(1− ̄h_i), i∈{a,m,s}
  - Special case (equal α across sectors): πa = (1−ω) ̄a/Aa + ω(π + ̄s/As); long-run agricultural share dictated by ω as ̄a/Aa and ̄s/As vanish with rising Aa and As.
- Mechanisms:
  - Sector with lower hours per worker attracts more labor (less disutility).
  - With ε<1, planner shifts resources out of most productive sector toward less productive one to preserve balanced consumption.
  - Upward trend in As increases labor share to services; amplified by ̄s>0.

### IV. CALIBRATION (U.S. 1970–2006) AND MODEL FIT
- Calibration particulars:
  - Time unit: year. Initial productivities normalized to one.
  - Hours-worked per worker parameters (from 10-Sector Database aggregated to three sectors):
    - ̄h_a = 0.49
    - ̄h_m = 0.54
    - ̄h_s = 0.46
    - Interpretation: service sector employee works on average 15% less hours than manufacturing employee, and 7% less than agriculture employee.
  - ω set to imply long-run agriculture employment share of 1%.
  - θ set to 0.02.
  - Joint calibration of ̄a, ̄s, and ε by iterating to match initial labor shares and time path of service labor share.
- Calibrated values highlighted:
  - ̄s = 0.94
  - ε = 0.41
- Table 1 parameter row as presented in source:
  - A_i,0 ̄h_a ̄h_m ̄h_s ω ̄a ̄s θε
  - 1.49.54.46.01.02.94.02.41
- Model fit:
  - Time path of sectoral labor allocation implied by model closely matches U.S. data over 1970–2006.
  - Model captures structural transformation pattern, including full time path of agriculture employment share even though only initial share was targeted.
  - When applied to OECD countries, model does well overall but underperforms for Germany, South Korea, and Turkey (model captures reallocation out of agriculture well but fails to predict observed magnitude of reallocation out of manufacturing; trade and open-economy forces likely important).

### V. COUNTERFACTUAL EXPERIMENTS AND RESULTS
- Counterfactual design:
  - Decompose sectoral labor productivities into trend and cyclical components via HP-filter: A_i = A^trend_i + A^cycle_i, i = a,m,s.
  - Two counterfactuals preserve cyclical components and initial levels but set trends equal across sectors to limit secular reallocation toward services.
- Counterfactual 1 (manufacturing trend → services trend):
  - Initial: A^1_{i,0} = A_{i,0}, i = a,m,s.
  - For t = 2,...,T: A^1_{a,t} = A_{a,t}; A^1_{m,t} = A^trend_{s,t} + A^cycle_{m,t}; A^1_{s,t} = A_{s,t}.
  - Intention: keep agriculture and services productivity trends unchanged; set manufacturing trend equal to services trend while keeping manufacturing cyclical component unchanged.
- Counterfactual 2 (agriculture and manufacturing trends → services trend):
  - Initial: A^2_{i,0} = A_{i,0}, i = a,m,s.
  - For t = 2,...,T: A^2_{a,t} = A^trend_{s,t} + A^cycle_{a,t}; A^2_{m,t} = A^trend_{s,t} + A^cycle_{m,t}; A^2_{s,t} = A_{s,t}.
  - Intention: set trend for both agriculture and manufacturing equal to services trend, preserving cyclical components.
- Key quantitative results (1970–2006):
  - Baseline (model):
    - Change in employment share of services (first to last period): +25.5 percentage points.
    - Average decline in volatility of aggregate output across OECD countries: about 38%.
  - Counterfactual 1:
    - Change in employment share of services: +18.4 percentage points.
    - Decline in volatility of aggregate output: 26%.
  - Counterfactual 2:
    - Change in employment share of services: around +12.2 percentage points.
    - Decline in volatility of aggregate output: 17.8% (about one-half of the benchmark drop).
- Interpretations:
  - Limiting labor shift from manufacturing to services reduces the decline in aggregate output volatility by roughly one-third (from 38% to 26%).
  - Further restricting the shift out of agriculture raises this fraction to about one-half (38% to 17.8%).
  - Reallocation of labor toward the relatively stable service sector, driven by sectoral labor productivity growth differentials, played an important role in the decline in aggregate output volatility in OECD countries during 1970–2006.
- Additional notes:
  - Complete shutdown of labor reallocation toward services is infeasible in these counterfactuals due to the greater-than-one income elasticity of demand for services.

### VI. CONCLUSION AND SUGGESTED EXTENSION
- Main conclusion:
  - Structural transformation (secular reallocation of labor toward services) contributed significantly to the decline in aggregate output volatility in the OECD between 1970 and 2006.
- Quantitative magnitudes summarized:
  - Benchmark: services employment share ↑ 25.5 percentage points; aggregate volatility ↓ ~38%.
  - Counterfactual 1: services employment share ↑ 18.4 percentage points; aggregate volatility ↓ 26%.
  - Counterfactual 2: services employment share ↑ ~12.2 percentage points; aggregate volatility ↓ 17.8%.
- Suggested extension:
  - Extend data back to the early 1950s for all OECD countries to better capture earlier structural transformation in countries where agriculture employment was already low by 1970; this requires uncovering sectoral labor productivities in less-advanced countries using model-based methods.

*Source: _wp1343 — https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp1343.pdf*

### References .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .

### _wp1343 - References .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .

### I. INTRODUCTION
- Research question and approach:
  - Examines whether structural transformation (labor reallocation across agriculture, manufacturing, services) contributes to the decline in aggregate output volatility observed in the U.S. and OECD countries.
  - Uses a model in which labor reallocation emerges endogenously from changes in sectoral labor productivities, differing from prior studies that take composition as given.
- Key methodological features:
  - Calibrates the model to the U.S. to discipline preference parameters, then keeps deep parameters fixed and feeds country-specific sectoral labor productivity processes to generate time paths of labor shares for OECD countries.
  - Performs counterfactual experiments that constrain endogenous labor mobility by feeding identical permanent productivity components across sectors while keeping transitory components unchanged; this shuts down most secular labor shifts while preserving cyclical properties.
- Framing and literature links:
  - Motivated by the “Great Moderation” (sharp decline in output volatility in the U.S. and most OECD countries) and debates in the literature (McConnell and Pérez-Quirós (2000); Stock and Watson (2002); Alcala and Sancho (2004); Eggers and Ioannides (2006); Duarte and Restuccia (2010); Da-Rocha and Restuccia (2006); Moro (2012)).
  - Highlights differences from prior work: endogenous labor reallocation driven by productivity differentials; three-sector model (agriculture, manufacturing, services); focus on continuous volatility path across OECD rather than U.S.-only steady-state comparisons or isolated breaks.

### II. EMPIRICAL EVIDENCE
- Data and sample:
  - Annual data for 21 OECD countries over the period 1970–2006.
  - Countries covered: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Italy, Japan, Korea, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Turkey, United Kingdom, and the United States.
- Volatility measurement:
  - Volatility of variable Y at date t computed as the standard deviation of growth rates over a 10-year backward-looking window (rolling window). (Definition and formula for σ described in the source.)
- Sectoral volatility facts:
  - Agriculture is more volatile than manufacturing, which is more volatile than services.
  - Labor productivity is about half as volatile in services as in manufacturing and is nearly twice as volatile in agriculture as in manufacturing across OECD countries.
  - These facts are robust to varying the window for computing volatilities.
- Structural transformation patterns:
  - Follows Kuznets (1966) three-stage description: large agricultural employment → shift to manufacturing → shift from manufacturing to services.
  - Illustrative employment shares at beginning of sample (1970):
    - 63% in agriculture in Turkey.
    - nearly 50% in South Korea.
    - 41% in Greece.
    - 30% in Portugal and Spain.
  - Contemporary examples: U.S., U.K., and Canada now have more than 70% of employment in the service sector and less than 3% in agriculture.
- Correlations and regressions:
  - Cross-country correlation between employment share of service sector and aggregate output volatility: −0.68 across countries and −0.56 in the panel.
  - Correlation between output volatility and GDP per capita: −0.54 across countries and −0.45 in the panel.
  - Regression evidence: when regressing output volatility on both employment share of services and GDP per capita, GDP per capita is not significant while the employment share of services is significant.
  - Controlling for financial development (GDP share of credit to the private sector) does not remove the significant effect of the employment share of services on output volatility.
  - Robustness: results unchanged when varying volatility window and when replacing volatility measure by standard deviation of de-trended series.
- Empirical implication:
  - Evidence is consistent with the hypothesis that labor reallocation toward services is associated with reduced aggregate output volatility in OECD countries over 1970–2006, though correlation need not imply causation.

### III. THE MODEL
- Model type and inspiration:
  - Indivisible labor model of structural transformation, modified from Duarte and Restuccia (2010) to include indivisible labor as in Da-Rocha and Restuccia (2006).
  - Uses sectoral employment data (instead of sectoral hours) due to limited comprehensive sectoral hours data across the sample.
- Calibration and simulation strategy:
  - Step 1: Calibrate model to the U.S. experience to pin down preference/deep parameters.
  - Step 2: Keep deep parameters fixed and input country-specific sectoral labor productivity processes to generate labor shares in agriculture, manufacturing, services for individual OECD countries.
  - Counterfactuals: Decompose sectoral labor productivities into permanent (drivers of structural shifts) and transitory (exogenous cyclical shocks) components; feed the same permanent component across sectors while keeping transitory components unchanged to reduce secular labor shifts and evaluate the impact on aggregate output volatility.
- Empirical target and scope:
  - Model aims to broadly match time paths of labor shares in the U.S. and other OECD countries and to quantify the contribution of structural transformation to the observed decline in output volatility.
- Main model-based finding preview:
  - Labor reallocation toward the service sector was volatility-reducing in the OECD during 1970–2006 (as produced by the model and counterfactual exercises described).

*Source: _wp1343 - References — https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp1343.pdf*

### conclusion that output volatility decreases with the level of development.

### _wp1343 - conclusion that output volatility decreases with the level of development.

### Economic environment
- Economy with 3 sectors: agriculture (a), manufacturing (m), services (s).
- Production technology (linear, labor only):
  - Yi = Ai Li, i∈{a,m,s}
  - Ai is sector-specific labor productivity (exogenous); Li is labor input to sector i.
- Population and labor supply:
  - Continuum of identical infinitely-lived households of measure one.
  - Population grows at exogenous rate η.
  - Households endowed with unit of time each period; indivisible labor model (agents either work full-time or not at all).
  - Employment probability per agent in period t: πt; sectoral employment probabilities πi,t = Li,t/Nt; conditional on working: ni,t = Li,t/Lt.
  - Employment-to-population calibration benchmark: employment to population ratio = 66%.
- Data choice and treatment:
  - Use employment data (rather than hours worked) due to limited hours-worked coverage across the sample.
  - De-trended series obtained by difference between log of original series and HP filter on log series with smoothing parameter λ=100 (standard for annual observations).

### Preferences and demand structure
- Planner objective (per-capita terms with indivisible labor extensive margin):
  - U(ca,t, ct, ht) = ω log(ca,t − ̄a) + (1−ω) log(c t) + φ log(1−ht), 0<ω,φ<1.
  - ̄a is subsistence level of agricultural goods (implies income elasticity of agricultural goods < 1).
- Composite manufacturing + services CES aggregator:
  - c = [ θ c_m^{(ε−1)/ε} + (1−θ)(c_s + ̄s)^{(ε−1)/ε} ]^{ε/(ε−1)}
  - Parameters: 0<θ<1; 0<ε<1; ̄s>0 implies income elasticity of services > 1 (drives resources to services as income rises).
- Two standard channels generating labor reallocation:
  - Low elasticity of substitution among goods (ε<1).
  - Non-homothetic preferences (̄a and ̄s).

### Analytical solution and structural transformation mechanics
- Planner chooses sectoral employment shares {πa,t; πm,t; πs,t} subject to capacity constraints ca,t ≤ Aa,t πa,t; cm,t ≤ Am,t πm,t; cs,t ≤ As,t πs,t and πa,t+πm,t+πs,t = πt.
- Problem solved in two stages:
  1. For given πa, solve for πm and πs (πm + πs = π − πa).
  2. Optimize πa given πm(πa), πs(πa).
- First-stage optimal reallocation relation (static):
  - πs + ̄s/As πm = ( (1−θ)/θ )^ε ( log(1− ̄h_m) / log(1− ̄h_s) )^ε ( As/Am )^{ε−1 }
- Implications and intuitions:
  - If hours worked per worker differ across sectors, sector with lower hours worked tends to attract more labor (less disutility).
  - With ε<1 (low elasticity), planner shifts resources out of most productive sector toward less productive one to maintain a balanced consumption bundle.
  - An upward trend in As increases labor share to services; effect amplified by ̄s>0.
- Closed-form solution for agriculture labor share (second stage):
  - πa = ( ̄a/Aa )(1+Ψ)(1−ω) + ω(π+ ̄s/As)(αm/αa + Ψ αs/αa) 
    divided by
    ω(αm/αa + Ψ αs/αa) + (1+Ψ)(1−ω)
  - Ψ = ( (1−θ)/θ )^ε ( log(1− ̄h_m) / log(1− ̄h_s) )^ε ( As/Am )^{ε−1 }
  - αi = log(1− ̄h_i), i∈{a,m,s}.
- Special case (equal α across sectors):
  - πa = (1−ω) ̄a/Aa + ω(π + ̄s/As)
  - Long-run: as Aa and As increase, ̄a/Aa and ̄s/As vanish; long-run agricultural labor share dictated by ω.

### Calibration (U.S. 1970–2006)
- Time unit: year. Initial productivities normalized to one as choice of units.
- Hours-worked per worker parameters (computed from 10-Sector Database aggregated to three sectors, adjusted to daily fraction and discretionary time):
  - ̄h_a = 0.49
  - ̄h_m = 0.54
  - ̄h_s = 0.46
  - Interpretation: service sector employee works on average 15% less hours than manufacturing employee, and 7% less than agriculture employee.
- Targeting and parameter choices:
  - ω set so as to imply a long-run share of employment in agriculture of 1%.
  - θ set to 0.02.
  - Calibration procedure: jointly calibrate ̄a, ̄s, and ε via iterative matching:
    - Given initial ε, choose ̄a and ̄s to match initial labor shares in agriculture (Equation (11)) and services (Equation (7)).
    - Recompute ε to match time path of service sector labor share (Equation (7)); iterate to convergence.
- Calibrated parameter highlights:
  - ̄s calibrated at 0.94 (close to literature values 0.89 and 0.77 reported).
  - ε calibrated at 0.41 (close to values 0.44 and 0.40 in Rogerson (2008) and Duarte and Restuccia (2010)).
- Table 1 parameter row (as presented in source):
  - A_i,0 ̄h_a ̄h_m ̄h_s ω ̄a ̄s θε
  - 1.49.54.46.01.02.94.02.41

### Model fit and results
- Model calibrated to U.S. over 1970–2006:
  - Time path of sectoral labor allocation implied by model closely matches U.S. data.
  - Model captures structural transformation pattern, including full time path of agriculture employment share (even though only initial share was targeted).
- Use of model to replicate OECD country labor-share time paths is the next step (applied to remaining OECD countries over 1970–... in the source).

*Source: _wp1343 - conclusion that output volatility decreases with the level of development.*

### 2006. Now that I have put discipline on preference parameters,

### _wp1343 - 2006. Now that I have put discipline on preference parameters,

### Model calibration and methodology
- Model: three-sector indivisible labor model with sectors agriculture (a), manufacturing (m), services (s).
- Calibration target (for each country): initial labor share in agriculture, initial labor share in services, and initial aggregate productivity relative to the U.S.
- Initial sectoral labor productivities A^j_{i,0} are set to match the three targets; subsequent sectoral labor productivities evolve according to A^j_{i,t+1} = (1+τ^j_{i,t}) A^j_{i,t} (Equation (12)).
- Preference parameter allowed to vary across countries: s̄ (interpreted as shortcut to modeling home production of service goods); s̄ is set so as to keep the ratio s̄/A_s constant across countries.
- Data panel: OECD countries listed (Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Italy, Japan, Korea, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Turkey, United Kingdom, and the United States). Panel covers annual observations for the period 1970-2006. This makes a total of 771 observations for each variable.
- Definitions and measurement:
  - Working-age population: ages 15-64 (N).
  - Labor force: total civilian labor force (L).
  - Employment by sector: L_a, L_m, L_s (including self-employment).
  - Sector definitions: ISIC II divisions (agriculture: 1-5; industry: 10-45; services: 50-99).
  - Sectoral productivity: A_i = VA_i / L_i, i = a,m,s (value added per person employed, constant $US and constant PPP).

### Model performance versus data (qualitative and diagnostics)
- U.S. benchmark calibration: model is calibrated to match the U.S. experience during 1970–2006 and used to generate time paths for other OECD countries.
- General fit:
  - The model does a good job mimicking structural transformation in OECD countries overall.
  - Notable exceptions where the model underperforms: Germany, South Korea, and Turkey.
    - Germany and South Korea: model captures reallocation out of agriculture well but fails to predict the observed magnitude of reallocation out of manufacturing. Trade likely played a major role in South Korea; the closed-economy model does not capture this (consistent with Betts, Giri, and Verma (2011)).
    - Turkey: model is not successful explaining structural transformation; at the beginning of the sample period more than 60% of the labor force was in agriculture (substantially higher than in a typical OECD country).
- Aggregate output volatility relationship:
  - The model replicates the negative relationship between aggregate output volatility and employment share of the service sector found in the data (Figure 3), with some country-specific overestimation of volatility (notably Turkey and Germany).

### Counterfactual experiments (design)
- Purpose: quantify the contribution of secular labor reallocation across sectors (structural transformation) to the decline in aggregate output volatility in OECD countries during 1970–2006.
- Key modeling element: decompose sectoral labor productivities into trend and cyclical components via HP-filter:
  - A_i = A^trend_i + A^cycle_i, i = a,m,s (Equation (13)).
- Two counterfactuals designed to limit long-run labor reallocation while preserving short-run (cyclical) dynamics and initial levels:
  - Counterfactual 1:
    - Initial values: A^1_{i,0} = A_{i,0}, i = a,m,s (Equation (14)).
    - For t = 2,...,T: A^1_{a,t} = A_{a,t}; A^1_{m,t} = A^trend_{s,t} + A^cycle_{m,t}; A^1_{s,t} = A_{s,t} (Equation (15)).
    - Intention: keep agriculture and services productivity trends unchanged; set manufacturing trend equal to services trend while keeping manufacturing cyclical component unchanged.
  - Counterfactual 2:
    - Initial values: A^2_{i,0} = A_{i,0}, i = a,m,s (Equation (16)).
    - For t = 2,...,T: A^2_{a,t} = A^trend_{s,t} + A^cycle_{a,t}; A^2_{m,t} = A^trend_{s,t} + A^cycle_{m,t}; A^2_{s,t} = A_{s,t} (Equation (17)).
    - Intention: set the trend for both agriculture and manufacturing equal to the services trend, preserving cyclical components.
- Rationale: by imposing identical trends across sectors one limits systematic reallocation of labor toward services while preserving cyclical variability; initial labor shares match baseline due to unchanged initial productivities.

### Counterfactual experiment results and key statistics (Table 2 and text)
- Baseline (model) over sample period 1970–2006:
  - Change in employment share of services (first to last period): +25.5 percentage points.
  - Average decline in volatility of aggregate output across OECD countries: about 38%.
- Counterfactual 1 (manufacturing trend set to services trend):
  - Change in employment share of services: +18.4 percentage points.
  - Decline in volatility of aggregate output: 26%.
- Counterfactual 2 (manufacturing and agriculture trends set to services trend):
  - Change in employment share of services: around +12.2 percentage points.
  - Decline in volatility of aggregate output: 17.8% (about one-half of the benchmark drop).
- Interpretations:
  - Limiting labor shift from manufacturing to services reduces the decline in aggregate output volatility by roughly one-third (from 38% to 26%) between the first and last period of the sample.
  - Further restricting the shift out of agriculture raises this fraction to about one-half (38% to 17.8%).
  - Conclusion: reallocation of labor toward the relatively stable service sector, driven by sectoral labor productivity growth differentials, played an important role in the decline in aggregate output volatility in OECD countries during 1970–2006.
- Additional note: complete shutdown of labor reallocation toward services is infeasible in these counterfactuals due to the greater-than-one income elasticity of demand for services.

### Empirical and data summary points (from appendices and figures)
- Panel covers annual observations for 1970-2006 (771 observations per variable).
- Employment age range: 15-64.
- Sectoral productivity computed as VA_i / L_i (i = a,m,s) using constant $US and constant PPP (OECD base year).
- Observed country-level facts highlighted in the paper include:
  - Countries with high initial agricultural employment (e.g., Turkey > 60% at start) exhibit distinct structural transformation patterns that the model struggles to reproduce.
  - Trade and open-economy forces (not modeled here) are important in explaining manufacturing employment dynamics in some countries (e.g., South Korea).

### Conclusion and suggested extension
- Main finding: structural transformation (secular reallocation of labor toward services) contributed significantly to the decline in aggregate output volatility in the OECD between 1970 and 2006.
- Quantitative magnitudes:
  - Benchmark: services employment share ↑ 25.5 percentage points; aggregate volatility ↓ ~38%.
  - Counterfactual 1: services employment share ↑ 18.4 percentage points; aggregate volatility ↓ 26%.
  - Counterfactual 2: services employment share ↑ ~12.2 percentage points; aggregate volatility ↓ 17.8%.
- Suggested extension: extend the data back to the early 1950s for all OECD countries (to better capture earlier structural transformation in countries like the U.S., the U.K., and Canada where agriculture employment was already typically less than 10% by 1970). This would require uncovering sectoral labor productivities in less-advanced countries (e.g., Poland, Uruguay, Czech Republic) potentially through model-based methods.

*Source: _wp1343 - 2006. Now that I have put discipline on preference parameters,*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp1343.pdf_