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---

### 2 Motivational facts and empirical regularities
- Key empirical findings:
  - "2.3 and 15.1 percent of the total decline in hours per worker over this period."
  - Leisure gains from trade vary widely: small open economies (Switzerland, the Netherlands) enjoy more leisure hours from trade than economies such as the US or Japan.
  - Potential leisure response to complete trade shutdown: for the median country in the sample, workers would optimally increase their supply of hours by 10 percent (23 working days per year).
  - Correlations documented:
    - Average annual hours worked per capita and the import share: correlation is -0.51.
    - Average annual hours worked per capita and remoteness: correlation is 0.61.
  - Long-run margin of adjustment: decline in per capita hours driven mainly along the intensive margin (hours per worker); extensive margin (employment rate) is quite stable.

- Interpretation of empirical relationships:
  - Trade ↔ Income: trade is positively correlated with income; causal effect of trade on income documented in literature.
  - Income ↔ Hours: hours worked and income are negatively correlated; households in high-income countries work significantly less than those in low-income countries.
  - Distance/remoteness: greater remoteness (sum of weighted distances where weights are GDP) associated with more hours worked.

- Main empirical implication:
  - If trade affects hours through income, effects should appear primarily on the intensive margin (hours per worker) rather than the extensive margin (employment rate).

### 3 Theory — preferences, labor supply, and trade structure
- Preferences and labor supply:
  - Representative household utility:
    - U_i(C_i,H_i) = { C_i^{1−η} −1 / (1−η) − ψ_i H_i^{1+1/ε_i} / (1+1/ε_i) if η ≠ 1;  log C_i − ψ_i H_i^{1+1/ε_i} / (1+1/ε_i) if η = 1 }.
  - Budget constraint: C_i = w_i P_i H_i.
  - Labor supply (combined FOC and budget constraint):
    - H_i = ˜ψ_i (w_i / P_i)^ρ, with ˜ψ_i = ψ_i^{−ε/(1+εη)} and ρ = −(η−1)ε/(1+εη).
  - Interpretation of ρ:
    - If η > 1 ⇒ ρ < 0: income effect dominates substitution; increases in real wages decrease hours.
    - If η < 1 ⇒ ρ > 0: substitution effect dominates.
    - If η = 1 ⇒ ρ = 0: no reaction of hours to real wages.
  - Cross-country/time-series evidence suggests η > 1 and ρ < 0.

- Eaton and Kortum (2002) environment (incorporation):
  - Consumption aggregator: C_i = ( ∫_0^1 c_i(u)^{(σ−1)/σ} du )^{σ/(σ−1)}, with σ > 1.
  - Production: unit cost = w_i / z_i(u); z_i(u) ~ Fréchet: F_i(z) = exp(−T_i z^{−θ}), T_i > 0, θ > 1.
  - Iceberg trade costs d_in ≥ 1; delivered producer price p_in(u) = w_n d_in / z_n(u); consumer price p_i(u) = min_n p_in(u).
  - Equilibrium objects:
    - Price index: P_i ≡ γ Φ_i^{−1/θ}, Φ_i ≡ Σ_{n=1}^N T_n (w_n d_in)^{−θ}, γ = [Γ(1−σ/θ + 1)]^{1/(1−σ)}; constraint σ < θ + 1.
    - Trade share: π_in ≡ X_in / X_i = T_n (w_n d_in)^{−θ} / Φ_i, Σ_n π_in = 1.
    - Trade balance: w_i H_i = Σ_{n=1}^N π_in w_n H_n.
  - Uniqueness condition: θ > −ρ (trade elasticity θ must exceed magnitude of elasticity of hours to wages).

### 3.3 Accounting for hours worked — structural link and comparative statics
- Domestic trade share:
  - πii = Ti(wi)−θ / PN n=1 Tn(wndin)−θ . (9)
- Real wage expression (relation with domestic trade share and Ti):
  - wi / Pi = πii−1/θ Ti1/θ . (10)
  - Economic interpretation: decline in πii (greater openness) increases real wages by lowering price index; effects mediated by θ.

- Equilibrium hours (substitute (10) into labor supply):
  - Hi = ˜ψi πii−ρ/θ Tiρ/θ . (11)
  - Interpretation:
    - Hi depends on idiosyncratic preference ˜ψi, domestic trade share πii, and average efficiency Ti.
    - If ρ < 0 (income effects dominate), an increase in πii (less trade) increases hours worked.
    - Sensitivity measured by −ρ/θ.

- Aggregate income and consumption:
  - Yi = Ci = ˜ψi πii−(1+ρ)/θ Ti(1+ρ)/θ . (12)
  - With elastic labor supply (ρ < 0), real GDP and consumption are strictly smaller than with inelastic labor supply.
  - Standard case ρ = 0 → effect of πii on income is −1/θ (Eaton and Kortum (2002) baseline).

- Autarky and leisure gains:
  - Autarky: din → +∞ ∀i,n ⇒ πii = 1.
  - Hours in autarky: HAutarky i = ˜ψi Tiρ/θ . (13)
  - General equilibrium response of hours to trade changes:
    - cHi = bπii−ρ/θ , (14) where bx ≡ x′/x.
  - Baseline leisure gains from autarky to trade:
    - HTrade i / HAutarky i = πii−ρ/θ .

- Model extensions (elasticity scaling, sign preserved):
  - Baseline: Hi = πii−ρ/θ
  - Including capital: Hi = πii−ρ/(1+αρ)θ ; α is capital share.
  - Multiple sectors: Hi = ΠS s=1 (πsii)−ωs i ρ/θ ; ωs is consumption share.
  - Intermediate inputs: Hi = πii−ρ/λθ ; λ is labor share in production of intermediate inputs.
  - Firm entry and exit (Melitz): Hi = πii−(σ−1)ρ/(σ−1−ρ)θ ; σ > 1.
  - Short notes:
    - Capital multiplies elasticity by 1/(1+αρ).
    - Multiple sectors weight effects by ωs.
    - Intermediate inputs amplify by 1/λ.
    - Firm entry/exit attenuates elasticity by (σ−1)/(σ−1−ρ) (< 1 when income effects dominate).

### 4.2 Identification strategy — geography-based time-varying IV
- Identification challenge:
  - OLS suffers endogeneity because Tit affects πii and Tit affects hours (equation (11)), inducing negative bias on βH; concurrent reforms also threaten identification.
- IV approach:
  - Time-varying instrument based on geography and evolution of air transportation technology (Feyrer (2019)); exploits 1950–1995 air/sea cost developments.
  - Gravity equation specification:
    - logImportsint = λi + λn + λt − θ log dint, with log dint = βair,t log airdistin + βsea,t log seadistin.
    - Estimated via: logImportsint = λi + λn + λt + βair,t log airdistin + βsea,t log seadistin + εint. (19)
  - Predicted trade instrument (weights-based):
    - logPredictedTradeit = log Σi̸=n ωin eˆβair,t logairdistin + ˆβsea,t logseadistin. (20)
  - Weights ωin: baseline uses average bilateral trade share between n and i (first 5 years of data); robustness to alternative weights.

- Instrument construction details:
  - Trade flows: IMF Direction of Trade Statistics (DOTS), balanced.
  - Air distance: CEPII great circle distances.
  - Sea distance: Feyrer (2019) algorithm minimizing travel time.
  - Time coverage for instrument construction: 1950–1995 (instrument variability concentrated 1955–1972 per Feyrer (2019)).

- Instrument validity arguments:
  - Predicted trade built solely on geography and transport technology; argued orthogonal to:
    - Domestic productivity growth Tit (air transport tech improvements common across countries).
    - Time-varying domestic policies and institutions τit (instrument depends on geography/transport; country fixed effects remove time-invariant factors).
    - Time-varying leisure tastes lit (most air-transported goods are high value-added; required violation would need disproportionate effects on leisure-complementary goods; time fixed effects remove common shifts).

- Data:
  - Country-year panel of 45 countries spanning 1950 to 1995 (instrument-driven coverage).
  - Hours, population, real GDP: Penn World Table (PWT) version 9.0.
  - Hours worked: actual annual hours per worker (employees plus self-employed), excludes paid unworked hours, commuting time, and work time lost due to strikes.
  - Domestic trade share = 1 − Tradeit / Expenditureit (equation (22)); baseline = 1 − imports-to-GDP at current prices.
  - Sample restrictions: drop countries with domestic share outside 0.5 - 1 and those with population < 1,000,000; robustness checks on OECD and balanced panels.

### 4 Empirical estimates — trade → hours per worker and income
- Main within (country and year FE) OLS and IV estimates (Table 2, sample: Observations 321; Countries 45):
  - Panel A (Second stage: log hours per worker on log domestic trade share):
    - OLS: 0.253* (standard error (0.128))
    - IV: 0.507** (standard error (0.217))
  - Panel B (First stage):
    - log predicted trade → log domestic trade share: -0.160*** (standard error (0.041))
    - F-stat: 15.45; First stage R2: 0.182
  - Panel C (Reduced form):
    - log hours per worker on log predicted trade: -0.081** (standard error (0.039))
- Interpretation: IV estimate (0.507) almost doubles OLS (0.253), statistically significant at 5 percent; being more closed to trade (higher domestic trade share) causally increases hours worked.

- Long-differences IV results (Table 3):
  - Second stage coefficients on ∆ log domestic trade share:
    - 10 years (weights): 0.337 (s.e. (0.320))
    - 15 years (weights): 0.497 (s.e. (0.324))
    - 35 years (weights): 0.585** (s.e. (0.221))
    - 10 years (gravity): 0.529 (s.e. (0.462))
    - 15 years (gravity): 0.663* (s.e. (0.361))
    - 35 years (gravity): 0.611*** (s.e. (0.178))
  - First stage improves with longer horizons; gravity-based instrument performs best over 35-year differences.
  - Interpretation: trade → hours effect materializes over long periods (10 years and more).

- Income channel — trade → GDP per worker (Table 4):
  - IV estimates (within FE):
    - OLS: log domestic trade share coefficient -0.722* (s.e. (0.427))
    - IV (hours-sample): log domestic trade share -3.619** (s.e. (1.500)); reduced form log predicted trade 0.579*** (s.e. (0.147)); R2 0.165
    - IV (expanded sample): log domestic trade share -3.544** (s.e. (1.549)); Observations 631; Countries 87
  - Interpretation: instrumented estimates show sizeable negative coefficient (~ -3.6) of log domestic trade share on log GDP per worker, indicating being more closed reduces income per worker; supports model assumption that trade raises income and income effects dominate substitution effects.

- Summary empirical conclusions:
  - Predicted trade instrument provides exogenous variation in domestic trade shares.
  - Trade raises income per worker (IV: log domestic trade share ~ -3.619**).
  - Higher income reduces hours per worker; causal effect: higher domestic trade share (more closed) leads to more hours worked (IV = 0.507**).
  - Trade → hours effect is slow-moving and primarily appears over long horizons (10–35 years).

### 5.2 Impact of trade on the employment rate
- Research question: causal effect of domestic trade share on the employment rate (sample expands to 87 countries where employment data exist).
- Main results (Table 5):
  - Column 1 (OLS, hours-sample): log domestic trade share 0.0248 (s.e. 0.149) — not significant; Observations 321; Countries 45.
  - Column 2 (IV, hours-sample): log domestic trade share 0.814* (s.e. 0.477) — marginally significant at 10 percent; F-stat first stage 15.45.
  - Column 3 (IV, larger employment-rate sample): log domestic trade share 0.343 (s.e. 0.402) — not significant; Observations 631; Countries 87; F-stat 12.33.
  - Column 4 (IV, 35-year differences): ∆ log domestic trade share 35 years: 0.705 (s.e. 0.505) — not significant; Observations 197; Countries 37; F-stat 11.35.
- Interpretation:
  - No robust evidence that trade materially affects the employment rate.
  - Results align with stylized fact: decline in per capita hours driven by intensive margin; extensive margin stationary.

### 5 Quantitative exercises, calibration, and welfare gains
- Calibration used in quantitative exercises:
  - η = 1.73
  - ε = 0.35
  - ρ = −0.16 (implied)
  - θ = 1
  - α = 1/3, λ = 2/3, σ = 6
- Estimated elasticities and empirical identification:
  - A one percentage point increase in the domestic trade share causes a 0.51 percent increase in hours per worker.
  - Backed-out uncompensated elasticity of hours to wages: −0.16.
  - Trade elasticity used: θ = 1.

- Welfare (utility) gains methodology:
  - Welfare loss metric: percentage change in utility associated with moving from trade in 2014 to autarky (absolute value), based on equation (15) and calibrated parameters.
  - Sufficient statistics: domestic trade share, elasticity of hours to wages, trade elasticity.

- Quantitative findings — hours and leisure:
  - Between 1950 and 2014, increase in trade generated between 19 and 91 hours of additional leisure per worker per year across countries.
  - The leisure time generated by trade represents around 7 percent of the total decline in hours per worker over this period.
  - Autarky counterfactual: median household would increase hours by around 10 percent (≈ 23 working days per year); magnitude may three-fold for largely open countries.
  - Including firm entry-and-exit margin slightly reduces leisure gains due to a small crowding-out effect (reduced labor supply lowers number of firms, reduces labor demand and wages).

- Selected country results (increase in annual hours per worker when moving to autarky; Table 9 selected entries):
  - Australia: baseline 5.4 percent; 12.2 days.
  - Austria: baseline 13.1 percent; 26.6 days.
  - Belgium: baseline 17.9 percent; 35.3 days.
  - Ireland: baseline 26.5 percent; 60.2 days.
  - Luxembourg: baseline 30.8 percent; 57.9 days.
  - United States: baseline 3.9 percent; 8.6 days.
  - Note: percentage change in annual hours expressed in work days assuming daily 8 hour shift; calculations assume ρ = −0.16, θ = 1, α = 1/3, λ = 2/3 and σ = 6. Source: WIOD.

- Welfare loss from moving from trade to autarky (Table 10 selected entries):
  - Columns: (1) inelastic labor, (2) elastic labor, (3) (2) − (1).
  - Ireland: (1) 85.53, (2) 90.57, (3) 5.04
  - Luxembourg: (1) 109.77, (2) 118.37, (3) 8.59
  - Malta: (1) 87.67, (2) 92.98, (3) 5.31
  - Hungary: (1) 62.81, (2) 65.43, (3) 2.62
  - Estonia: (1) 49.99, (2) 51.62, (3) 1.62
  - United States: (1) 8.29, (2) 8.33, (3) 0.04
  - Median additional welfare gain by allowing elastic labor supply (column 3): 0.38 percentage points.
  - Average additional gain: 1 percentage point.
  - Note: calculations based on equation (15), η = 1.73, ε = 0.35 (ρ = −0.16), θ = 1. Source: WIOD.

- Conclusions and implications:
  - Trade leads to a decline in labor supply and increase in leisure through income effects; income effects outweigh substitution effects given ρ = −0.16.
  - Leisure gains from trade are empirically meaningful and contribute to historical decline in hours worked; allowing elastic labor supply raises estimated welfare gains on average by up to one percentage point.
  - Heterogeneity across countries: more trade-open economies experience larger leisure gains.
  - Distributional aspects not addressed here; referenced follow-up finds leisure accrues more to lower-income workers and disproportionately to female and less-educated workers.

### Appendices — existence/uniqueness, extensions, robustness, and data
- Preferences and balanced growth (Appendix A):
  - Utility specification compatible with balanced growth: if real wages grow at constant rate γ, hours grow at γ_H = γ/ρ and consumption at γ_C = γ/(1+ρ).
  - Numerical example: ρ = −0.16; if real wages grow at 2 percent (γ = 2 percent), annual decline in hours = 0.32 percent; consumption growth = 1.68 percent (1.02^(−0.16) = 0.9968).

- Existence and uniqueness (Appendix B):
  - Constructs excess demand Z(w): continuous, homogeneous degree zero, satisfies Walras’ Law.
  - Necessary condition for uniqueness: ε(1−η)−θ(1+εη) < 0 ⇔ −ρ < θ.

- Model extensions (Appendix C) summarized:
  - Including physical capital: hours elasticity scaled by 1/(1+αρ); equilibrium hours link to K_i.
  - Multiple sectors: sectoral weights ω_s enter elasticity; H_i = Π_s (π^s_ii)^{−ρω^s_i/θ}.
  - Intermediate inputs: labor share λ amplifies effect by 1/λ.
  - Firm entry/exit (Melitz-style): hours elasticity multiplied by (σ−1)/(σ−1−ρ) (< 1 when income effects dominate).

- Welfare variation (Appendix D):
  - Closed-form expressions for equivalent variation as function of π_ii and T_i; limiting case η → 1 recovers Ŵ_i = π̂_ii^{−1/θ} − 1.
  - Analytical result: welfare gains from trade are always larger with elastic labor supply (comparisons provided for η > 1 and η < 1).

- Robustness checks and empirical additions (Appendix E):
  - Adding controls for log TFP and log capital per worker: domestic trade share coefficient changes from 0.51 to 0.58; TFP and capital not statistically significant at 10 percent; sample: 42 countries, observations = 303.
  - OECD-only sample (17 countries): coefficient on log domestic trade share (hours) 0.355* (s.e. 0.194); (GDP per worker) -4.230*** (s.e. 1.276); Observations = 158; first-stage F-stat = 22.8.
  - Instrument robustness to alternative initial weights (initial bilateral trade, initial population, initial trade volume): second-stage IV coefficients on log domestic trade share: 0.507** (s.e. 0.217), 0.802*** (s.e. 0.203), 1.031*** (s.e. 0.258) respectively.
  - Reduced-form of log predicted trade on log hours per worker: -0.081** (s.e. 0.039), -0.129*** (s.e. 0.035), -0.139*** (s.e. 0.040) respectively.

- Supplementary data and descriptive statistics (Appendix F):
  - Hours per worker: obs = 324, mean = 2,042.32, s.d. = 51.27, min = 439.92, max = 2,921.48.
  - Employment rate: obs = 633, mean = 0.370, s.d. = 0.080, min = 0.18, max = 0.56.
  - Domestic trade share: obs = 673, mean = 0.83, s.d. = 0.11, min = 0.50, max = 0.99.
  - log predicted trade: obs = 673, mean = 4.02, s.d. = 3.15, min = -1.58, max = 12.10.
  - log GDP per worker: obs = 633, mean = 9.44, s.d. = 0.99, min = 6.18, max = 13.06.

_Italic: Source — wpiea2024016-print-pdf_

### 2.3 and 15.1 percent of the total decline in hours per worker over this period.

### 2 Motivational Facts

### Key empirical findings
- "2.3 and 15.1 percent of the total decline in hours per worker over this period."
- The leisure gains from trade vary widely across countries. Small open economies, such as Switzerland and the Netherlands, enjoy more leisure hours from trade than economies such as the US or Japan.
- Potential leisure loss from complete trade shutdown: for the median country in the sample, workers would optimally increase their supply of hours by 10 percent (23 working days per year) to compensate for the income lost due to the complete trade shutdown.
- Correlations documented:
  - Average annual hours worked per capita and the import share: correlation is -0.51.
  - Average annual hours worked per capita and remoteness: correlation is 0.61.
- Long-run margin of adjustment: the decline in per capita hours is driven mainly along the intensive margin (hours per worker), while the extensive margin (employment rate) is quite stable over time.

### Interpretation of empirical relationships
- Trade ↔ Income: trade is positively correlated with income; a causal effect of trade on income has been well documented in the literature.
- Income ↔ Hours: hours worked and income are negatively correlated. Evidence shows households in high-income countries work significantly less than those in low-income countries.
- Distance/remoteness as trade determinant: greater remoteness (sum of weighted distances where weights are GDP) is associated with more hours worked, consistent with distance reducing trade flows.

### Main empirical implication
- If trade affects hours worked through income, then effects should be observed primarily along the intensive margin (hours per worker) rather than the extensive margin (employment rate).

---

### 3 Theory

### Preferences and labor supply
- Representative household utility:
  - U_i(C_i,H_i) = { C_i^{1−η} −1 / (1−η) − ψ_i H_i^{1+1/ε_i} / (1+1/ε_i) if η ≠ 1;  log C_i − ψ_i H_i^{1+1/ε_i} / (1+1/ε_i) if η = 1 }.
  - Definitions: C_i = aggregate consumption; H_i = number of hours worked; η ≥ 0 = inverse of the intertemporal elasticity of substitution; ε ≥ 0 = Frisch elasticity; ψ_i = scalar weighing disutility of working.
- Budget constraint: C_i = w_i P_i H_i, where w_i is nominal wage and P_i is the price index of domestically consumed goods.
- First-order condition combined with budget constraint yields labor supply:
  - H_i = ˜ψ_i (w_i / P_i)^{−(η−1)ε/(1+εη)} = ̃ψ_i (w_i / P_i)^ρ, with ̃ψ_i = ψ_i^{−ε/(1+εη)} and ρ = −(η−1)ε/(1+εη).
- Interpretation of ρ:
  - If η > 1, then ρ < 0: income effect dominates substitution; increases in real wages decrease hours worked.
  - If η < 1, then ρ > 0: substitution effect dominates; increases in real wages increase hours worked.
  - If η = 1, then ρ = 0: income and substitution effects cancel and hours do not react to real wages.
- Cross-country and time series evidence suggest η > 1 and ρ < 0.

### Incorporation into the Eaton and Kortum (2002) framework
- Consumption aggregator: C_i = ( ∫_0^1 c_i(u)^{(σ−1)/σ} du )^{σ/(σ−1)}, with σ > 1 (goods are gross substitutes).
- Production:
  - Firms produce y_i(u) using linear technology in labor; unit cost = w_i / z_i(u).
  - Productivities z_i(u) drawn i.i.d. from Fréchet distribution: Pr(z_i ≤ z) = F_i(z) = exp(−T_i z^{−θ}), with T_i > 0 and θ > 1.
- Trade costs:
  - "Iceberg costs" d_in ≥ 1; d_ii = 1; cross-border arbitrage implies d_in ≤ d_ik d_kn.
  - Delivered producer price p_in(u) = w_n d_in / z_n(u); consumer price p_i(u) = min_n p_in(u).
- Equilibrium objects (as derived from Eaton and Kortum (2002)):
  - Price index: P_i ≡ γ Φ_i^{−1/θ}, with Φ_i ≡ Σ_{n=1}^N T_n (w_n d_in)^{−θ} and γ = [Γ(1−σ/θ + 1)]^{1/(1−σ)}. Constraint imposed: σ < θ + 1.
  - Trade share: π_in ≡ X_in / X_i = T_n (w_n d_in)^{−θ} / Φ_i, with Σ_n π_in = 1.
  - Trade balance: w_i H_i = Σ_{n=1}^N π_in w_n H_n.
- Equilibrium requires consistency between labor supply H_i (from preferences) and the trade-derived price index and trade shares. Uniqueness condition: θ > −ρ (i.e., the absolute magnitude of the elasticity of hours to wages must be smaller than that of the trade elasticity). It is assumed θ > 1 and labor supply reacts less than one-to-one with respect to changes in real wages.

---

*Source: wpiea2024016-print-pdf*

### 3.3    Accounting for hours worked

### 3.3    Accounting for hours worked

### Structural link between trade and hours worked
- Domestic trade share definition (from trade share (7)):
  - πii = Ti(wi)−θ / PN n=1 Tn(wndin)−θ . (9)
- Relation between domestic trade share and price index (6) leads to the real wage expression:
  - wi / Pi = πii−1/θ Ti1/θ . (10)
- Key economic interpretation:
  - Real wage is a function of the domestic trade share πii and average efficiency Ti.
  - A decline in πii (greater openness) increases real wages by lowering the price index.
  - Both effects are mediated by the trade elasticity θ.

### Equilibrium of hours worked
- Substituting real wage (10) into labor supply (4) yields:
  - Hi = ˜ψi πii−ρ/θ Tiρ/θ . (11)
- Interpretation and comparative statics:
  - Hi depends on idiosyncratic preference ˜ψi, domestic trade share πii, and average efficiency Ti.
  - If income effects dominate substitution effects (ρ < 0), an increase in πii (less trade) increases hours worked.
  - Sensitivity measured by −ρ/θ: numerator = elasticity of hours to wages; denominator = elasticity of real wages to trade.
  - Effect of Ti has same magnitude as πii but opposite sign: with ρ < 0, higher Ti → fewer hours worked.

### Aggregate income and consumption
- Substituting (10) and hours equilibrium into the budget constraint yields aggregate income (equal to consumption):
  - Yi = Ci = ˜ψi πii−(1+ρ)/θ Ti(1+ρ)/θ . (12)
- Comparative notes:
  - Incorporates labor supply adjustments; more general than Eaton and Kortum (2002) and Waugh (2010).
  - With elastic labor supply (ρ < 0), real GDP and consumption are strictly smaller than with inelastic labor supply.
  - Standard case ρ = 0 → effect of domestic trade share on income is −1/θ, matching Eaton and Kortum (2002).

### Autarky and leisure gains from trade
- Define autarky: din → +∞ ∀i,n ⇒ πii = 1.
  - Hours in autarky: HAutarky i = ˜ψi Tiρ/θ . (13)
  - Hours worked are strictly higher in autarky than with trade.
- General equilibrium response of hours to trade changes:
  - cHi = bπii−ρ/θ , (14) where bx ≡ x′/x.
  - Change in hours depends only on three sufficient statistics: domestic trade share, elasticity of hours to wages ρ, and trade elasticity θ.
- Baseline leisure gains moving from autarky (πii = 1) to trade (πii < 1):
  - HTrade i / HAutarky i = πii−ρ/θ .

### Model extensions and their effect on hours-to-trade elasticity
- Extensions only scale the elasticity; sign preserved. Table 1 summary (equations reproduced exactly as in source):
  - Baseline: Hi = πii−ρ/θ
  - Including capital: Hi = πii−ρ/(1+αρ)θ ; α is the capital share
  - Multiple sectors: Hi = ΠS s=1 (πsii)−ωs i ρ/θ ; ωs is the consumption share for sectors
  - Intermediate inputs: Hi = πii−ρ/λθ ; λ is the labor share in the in production of int. inputs
  - Firm entry and exit: Hi = πii−(σ−1)ρ/(σ−1−ρ)θ ; σ > 1 is the elasticity of substitution across varieties
- Short notes on each extension:
  - Capital: elasticity of hours to trade multiplied by 1/(1+αρ); channel is domestic and strengthens trade–hours link when income effects dominate.
  - Multiple sectors: Cobb-Douglas consumption across sectors (ωs) increases real wage gains from lower trade costs, reinforcing hours response.
  - Intermediate inputs: composite input with labor share λ amplifies response by factor 1/λ.
  - Firm entry/exit (Melitz-type): endogenous entry/exit induces crowding-out on real wages and hours; elasticity multiplied by (σ−1)/(σ−1−ρ), which is smaller than one for the relevant case (income effects dominate). The crowding-out declines as σ becomes large.

*Source: IMF working paper section “3.3    Accounting for hours worked” from wpiea2024016-print-pdf.*

### 4.2    The identification strategy

### 4.2    The identification strategy

### Identification challenge and IV approach
- OLS estimation of equation (17) would suffer from endogeneity because domestic productivity (Tit) affects the domestic trade share (πii) and higher domestic productivity leads to lower hours worked (equation (11)), inducing a negative bias on βH in OLS.
- Additional endogeneity may arise from concurrent institutional reforms (e.g., free trade agreements coupled with labor market reforms).
- To remove these sources of endogeneity, the paper relies on an IV approach.

### Time-varying instrument based on geography
- The instrument follows Feyrer (2019) and exploits the development of air transportation technology between 1950 to 1995 as an exogenous shifter of trade costs.
- Countries with shorter air routes relative to sea routes benefited more from reductions in air freight costs; capturing this variation gives the instrument a time dimension and geographic exogeneity.
- The instrument leverages a gravity-equation structure for bilateral trade flows:
  - logImportsint = λi + λn + λt − θ log dint, with log dint = βair,t log airdistin + βsea,t log seadistin.
  - Estimated via specification (19): logImportsint = λi + λn + λt + βair,t log airdistin + βsea,t log seadistin + εint.
- Predicted trade (instrument) is constructed as a weighted average of all bilateral imports:
  - logPredictedTradeit = log Σi̸=n ωin eˆβair,t logairdistin + ˆβsea,t logseadistin (equation (20)).
- Alternative gravity-based formulation (Feyrer 2019) is noted (equation (21)), but for within (country fixed-effect) analysis the weights-based instrument (20) is favored to avoid violating the exclusion restriction because domestic trade share is a non-linear function of trade flows.

### Instrument construction details and weights
- ωin weights: baseline uses the average bilateral trade share between n and i, relative to total imports of i, of the first 5 years of available data.
- Results are robust to alternative weights (exporter’s initial population or initial trade volume).
- Trade flows data source: IMF Direction of Trade Statistics (DOTS), balanced as average of four recordings by bilateral partner.
- Air distance: CEPII great circle distances. Sea distance: Feyrer (2019)’s algorithm minimizing travel time.
- Time coverage for instrument construction: 1950–1995 (instrument variability concentrated 1955–1972 per Feyrer (2019)).

### Instrument validity / exclusion restriction
- Predicted trade is strongly correlated with Trade and is built solely on geographic distance and evolving air/sea transport technology, making it orthogonal to changes in Expenditure not caused by trade.
- Instrument argued to be orthogonal to:
  - Domestic productivity growth (Tit): air transport technology improvements are assumed common across countries and uncorrelated with country-specific productivity.
  - Time-varying domestic policies and institutions (τit): construction depends solely on geography and transport technology; country fixed effects remove time-invariant cultural/institutional factors (ψ̃i).
  - Time-varying leisure tastes (lit): most air-transported goods are high value-added (pharmaceuticals and organic chemicals, luxury goods, precious metals and jewelry, perishables), so a violation would require disproportionate instrument effects on leisure-complementary goods; time fixed effects remove common preference shifts.

### Data
- Country-year panel of 45 countries spanning 1950 to 1995 (time coverage limited by instrument construction).
- Key data sources and definitions:
  - Hours worked, population, real GDP: Penn World Table (PWT) version 9.0.
  - Hours worked: actual annual hours per worker (employees plus self-employed), excludes paid unworked hours, commuting time, and work time lost due to strikes.
  - Domestic trade share = 1 − Tradeit / Expenditureit (equation (22)); baseline constructed as one minus imports-to-GDP at current prices (consistent with Waugh and Ravikumar (2016)).
- Sample restrictions:
  - Drop countries with a domestic share outside interval 0.5 - 1 and those with less than one million inhabitants.
  - Robustness: replicate analysis on OECD subsample and balanced-panel subsamples; results robust.
- Instrument inputs:
  - Trade flows from DOTS (balanced), airdist from CEPII, seadist from Feyrer (2019).
- Panel is unbalanced; author checks balanced subsample and finds no significant differences.

### Econometric findings: trade → hours per worker (main estimates)
- Within (country and year fixed effects) OLS and IV (instrument: log predicted trade from equation (20)) — Table 2:
  - Panel A: Second stage coefficients on log domestic trade share:
    - OLS: 0.253* (standard error (0.128))
    - IV: 0.507** (standard error (0.217))
  - Panel B: First stage:
    - Coefficient of log predicted trade on log domestic trade share: -0.160*** (standard error (0.041))
    - F-stat: 15.45
    - First stage R2: 0.182
  - Panel C: Reduced form:
    - log hours per worker on log predicted trade: -0.081** (standard error (0.039))
  - Sample: Observations 321; Countries 45.
- Interpretation: IV estimate (0.507) almost doubles OLS (0.253), statistically significant at 5 percent; being more closed to trade (higher domestic trade share) causally increases hours worked.

### Long-differences results (Table 3)
- IV estimates using 10-, 15-, and 35-year differences; instruments: predicted trade (weights, eq. (20)) and gravity formulation (eq. (21)):
  - Panel A (Second stage, key coefficients on ∆ log domestic trade share):
    - 10 years (weights): 0.337 (standard error (0.320))
    - 15 years (weights): 0.497 (standard error (0.324))
    - 35 years (weights): 0.585** (standard error (0.221))
    - 10 years (gravity): 0.529 (standard error (0.462))
    - 15 years (gravity): 0.663* (standard error (0.361))
    - 35 years (gravity): 0.611*** (standard error (0.178))
  - Panel B (First stage, key coefficients on ∆ log predicted trade):
    - 10 years (weights): -0.048 (standard error (0.033))
    - 15 years (weights): -0.058 (standard error (0.035))
    - 35 years (weights): -0.108** (standard error (0.0498))
    - 10 years (gravity): -0.052* (standard error (0.026))
    - 15 years (gravity): -0.060** (standard error (0.026))
    - 35 years (gravity): -0.105** (standard error (0.038))
  - Observations and diagnostics:
    - Observations by column: 230, 194, 69, 230, 194, 69 (respectively for columns (1)–(6))
    - Countries: 36, 35, 24, 36, 35, 24
    - F-stat (Kleiberg-Paap) by column: 2.633, 7.438, 8.994, 2.090, 5.934, 13.72
    - First stage R2 by column: 0.085, 0.110, 0.135, 0.096, 0.129, 0.223
- Interpretation:
  - The impact of trade on hours worked materializes over long periods (10 years and more).
  - Longer differencing horizons yield larger F-stats and larger first stage R2; gravity-based instrument performs best over 35-year differences.

### Income channel: trade → GDP per worker (Table 4)
- Regressions of log GDP per worker on log domestic trade share (equation (18)); country and year fixed effects:
  - Panel A (Second stage / reduced form):
    - OLS (column 1): log domestic trade share coefficient -0.722* (standard error (0.427))
    - IV (column 2, sample with hours data): log domestic trade share -3.619** (standard error (1.500)); log predicted trade coefficient in reduced form 0.579*** (standard error (0.147)); R2 0.165
    - IV (column 3, expanded sample): log domestic trade share -3.544** (standard error (1.549)); Observations 631; Countries 87
    - Column 4 (reduced form): (reported in table as part of Panel A/Panel B structure)
  - Panel B (First stage):
    - log predicted trade → log domestic trade share: -0.160*** (standard error (0.041)) in column 2; -0.115*** (standard error (0.037)) in another first-stage reported
    - F-stat values reported: 15.45 (column 2) and 2.33 (other specification)
  - Sample sizes:
    - Columns: Observations 321, 321, 631, 321; Countries 45, 45, 87, 45
- Interpretation:
  - Instrumented estimates show a sizeable negative coefficient of log domestic trade share on log GDP per worker (≈ -3.6), indicating that being more closed to trade reduces income per worker.
  - These income effects support the structural model assumption that trade raises income and that income effects dominate substitution effects, implying higher hours per worker in more closed economies.

### Summary of empirical conclusions
- Predicted trade (geography-based, time-varying instrument) provides exogenous variation in domestic trade shares.
- Trade raises income per worker (IV estimates: log domestic trade share ~ -3.619**), and higher income reduces hours per worker.
- Causal effect: a higher domestic trade share (more closed economy) leads to more hours worked; IV estimate of effect on log hours per worker is 0.507** (within estimator, Table 2).
- The trade → hours effect is slow-moving and primarily appears over long horizons (10–35 years).

*Source: 4.2 The identification strategy (from provided IMF content unit).*

### 5.2    The impact of trade on the employment rate

### 5.2    The impact of trade on the employment rate

### Research question and data
- Objective: Estimate the causal effect of the domestic trade share on the employment rate by replacing hours per worker with the employment rate as the dependent variable.
- Sample differences: 87 countries report employment rate data compared to 45 countries reporting hours per worker.
- Panel: 5-year intervals of data between 1950 and 1995 for 87 countries (columns use subsamples as noted below).

### Main econometric results (Table 5)
- Dependent variables reported:
  - log employment rate (OLS and IV, sample limited to countries with hours data)
  - ∆ log employment rate (35 years) (IV, long-differences)
- Key reported coefficients and statistics:
  - Column 1 (OLS, sample with hours data):
    - log domestic trade share: 0.0248 (standard error 0.149) — not significant.
    - Observations: 321
    - Country FE: yes; Year FE: yes
    - Countries: 45
  - Column 2 (IV, sample with hours data; instrument = log predicted trade):
    - log domestic trade share: 0.814* (standard error 0.477) — marginally significant at the 10 percent level.
    - Observations: 321
    - Country FE: yes; Year FE: yes
    - F-stat in first stage: 15.45
    - Countries: 45
  - Column 3 (IV, sample with all countries reporting employment rates):
    - log domestic trade share: 0.343 (standard error 0.402) — not significant (no significance even at 10 percent).
    - Observations: 631
    - Country FE: yes; Year FE: yes
    - F-stat in first stage: 12.33
    - Countries: 87
  - Column 4 (IV, 35-year long differences):
    - ∆ log domestic trade share 35 years: 0.705 (standard error 0.505) — not significant.
    - Observations: 197
    - Year FE: yes; Country FE: yes
    - F-stat in first stage: 11.35
    - Countries: 37
- Instrument strength: The F-stat for the instrument is above the conventional threshold of 10 in all IV regressions reported.

### Interpretation and substantive finding
- Point estimates:
  - OLS: small and statistically insignificant effect of domestic trade share on employment rate.
  - IV (sample with hours data): positive coefficient (0.814) that implies an increase in trade may cause lower employment, but only marginally significant at the 10 percent level.
  - IV (larger employment-rate sample) and IV long-differences: no statistically significant effect of trade on the employment rate.
- Aggregate conclusion: No robust evidence that trade materially affects the employment rate. The empirical results indicate that the decline in per capita hours is driven by the intensive margin (hours per worker) rather than the extensive margin (employment rate).
- Consistency with stylized facts: This finding aligns with the long-run behavior described in Section 2—long-run decline of per capita hours is driven by the intensive margin, while the extensive margin is stationary throughout the second half of the 20th century.

*Source: wpiea2024016-print-pdf - 5.2    The impact of trade on the employment rate*

### 5.6 percentage points larger than the baseline.  Finally, columns 7 and 8 present the leisure gains

### 5.6 percentage points larger than the baseline.  Finally, columns 7 and 8 present the leisure gains

### Model parameters, identification, and elasticities
- Calibration and parameter values used:
  - η = 1.73
  - ε = 0.35
  - ρ = −0.16 (implied by η and ε)
  - θ = 1
  - α = 1/3, λ = 2/3, σ = 6 (used in hours calculations)
- Empirical identification:
  - A time-varying geographic instrument is used to identify exogenous variation in trade openness and estimate the elasticity of hours to trade.
- Estimated elasticities:
  - A one percentage point increase in the domestic trade share causes a 0.51 percent increase in hours per worker.
  - Backed-out elasticity of hours to wages (uncompensated elasticity): −0.16.
  - Trade elasticity employed in quantitative exercises: θ = 1.

### Welfare (utility) gains from trade — methodology and key metrics
- Welfare loss metric: percentage change in utility associated with moving from trade in 2014 to autarky (absolute value).
- Calculations are based on equation (15) and the calibrated parameters listed above.
- Sufficient statistics for leisure gains from trade: domestic trade share, elasticity of hours to wages, and trade elasticity.

### Quantitative findings — hours and leisure
- Across countries, the increase in trade between 1950 and 2014 generated between 19 and 91 hours of additional leisure time per worker per year.
- The leisure time generated by trade represents around 7 percent of the total decline in hours per worker over this period.
- If countries moved to autarky, the median household would increase their supply of hours by around 10 percent; the magnitude may three-fold for countries that are largely open to trade.
- When a margin of firm entry-and-exit is included in the model, leisure gains are slightly smaller than in the baseline due to a small crowding-out effect: reduced labor supply lowers the number of firms in equilibrium, which reduces labor demand and wages, partially offsetting leisure gains. This crowding out is small across all countries.

### Selected country results — increase in annual hours per worker when moving to autarky (Table 9, selected entries)
- Australia: baseline 5.4 percent; expressed as 12.2 days (annual hours change).
- Austria: baseline 13.1 percent; 26.6 days.
- Belgium: baseline 17.9 percent; 35.3 days.
- Ireland: baseline 26.5 percent; 60.2 days.
- Luxembourg: baseline 30.8 percent; 57.9 days.
- United States: baseline 3.9 percent; 8.6 days.
- Note: Table 9 reports percentage change in annual hours worked moving from trade openness in 2014 to autarky, and the percentage expressed in work days assuming a daily 8 hour shift. Calculations assume ρ = −0.16, θ = 1, α = 1/3, λ = 2/3 and σ = 6. Source: WIOD. na: not available.

### Selected country results — welfare loss from moving from trade to autarky (Table 10, selected entries)
- Columns: (1) inelastic labor, (2) elastic labor, (3) (2) − (1) percentage point difference.
- Ireland: (1) 85.53, (2) 90.57, (3) 5.04
- Luxembourg: (1) 109.77, (2) 118.37, (3) 8.59
- Malta: (1) 87.67, (2) 92.98, (3) 5.31
- Hungary: (1) 62.81, (2) 65.43, (3) 2.62
- Estonia: (1) 49.99, (2) 51.62, (3) 1.62
- United States: (1) 8.29, (2) 8.33, (3) 0.04
- Median/average comparisons:
  - For the median country, the additional gain in welfare by including an elastic labor supply (column 3) is 0.38 percentage points.
  - For the average country, this additional gain is 1 percentage point.
- Note: Columns 1 and 2 show the percentage change in utility loss of moving from trade in 2014 to autarky for the model with inelastic and elastic labor supply, respectively. All calculations are based on equation (15), assuming η = 1.73 and ε = 0.35 (which implies ρ = −0.16), and θ = 1. Source: WIOD.

### Conclusions and implications
- Trade leads to a decline in labor supply and an increase in leisure through income effects; income effects outweigh substitution effects given the estimated uncompensated elasticity of hours to wages is −0.16.
- Leisure gains from trade are empirically meaningful: trade-generated leisure represents a nontrivial share of the historical decline in hours worked and raises workers’ welfare.
- Allowing labor supply to be elastic increases estimated welfare gains from trade on average by up to one percentage point; the effect is heterogeneous across countries and larger for more trade-open economies.
- The analysis does not address intra-household allocation of additional leisure; follow-up work (Depetris-Chauvin and Velasquez, 2024) investigates heterogeneity across age, gender, and education, finding that most leisure accrues to lower-income workers (young and older), and female and less-educated workers tend to benefit relatively more.

*Source: wpiea2024016-print-pdf*

### References

### wpiea2024016-print-pdf - References and Online Appendix

### Preferences and balanced growth (Appendix A)
- Utility specification (1) is compatible with a balanced growth path if consumption, real wages, and hours grow at constant rates and satisfy the budget constraint and labor supply equation.
- If real wages grow at constant rate γ, hours grow at rate γ_H = γ/ρ and consumption at rate γ_C = γ/(1+ρ).
- Parameter estimates and numerical example:
  - Estimated ρ = -0.16 (Section 5.3).
  - If real wages grow at 2 percent (γ = 2 percent), annual decline in hours worked = 0.32 percent; consumption growth = 1.68 percent.
  - Computation shown: 1.02^(−0.16) = 0.9968.
  - Example assumption for interest rate calculation: η = 1.1 and β = 0.97 yields a stationary interest rate of 5 percent.

### Existence and uniqueness of equilibrium (Appendix B)
- Constructs an excess demand function Z(w) from the trade share equation and labor supply, with Z(w) shown to be:
  - Continuous,
  - Homogeneous of degree zero (Z(tw) = t^0 Z(w) = Z(w)),
  - Satisfying Walras’ Law (Z(w)·w = 0).
- Gross substitutes property requires ∂Z(w_i)/∂w_k > 0.
- A necessary condition for uniqueness: ε(1−η)−θ(1+εη) < 0, equivalently ε(1−η)/(1+εη) < θ, which can be expressed as −ρ < θ (trade elasticity θ must exceed magnitude of elasticity of hours to wages).
- Existence and uniqueness then follow by invoking propositions from Mas-Colell et al. (1995).

### Model extensions (Appendix C)
- C.1 Including physical capital
  - Aggregate real income Y_i = w_i/P_i · H_i + r_i/P_i · K_i, with r_i = α/(1−α) · w_i H_i K_i^(−1).
  - Under balanced growth and fixed savings share, consumption can be written C_i = κ w_i/P_i H_i.
  - Price index and trade share become:
    - P_i ≡ γ Φ_i^(−1/θ), Φ_i ≡ Σ_n T_n (r_n^α w_n^(1−α) d_in)^(−θ).
    - π_in ≡ (T_n (r_n^α w_n^(1−α) d_in)^(−θ))/Φ_i.
  - Real wage expression: w_i/P_i = (1−α) π_ii^(−1/θ) T_i^(1/θ) (K_i/H_i)^α.
  - Equilibrium hours:
    - H_i = ψ̃_i π_ii^(−ρ/(1+αρ)θ) T_i^(ρ/(1+αρ)θ) K_i^(αρ/(1+αρ)).
  - Aggregate income:
    - Y_i = ψ̃_i π_ii^(−(1+ρ)/(1+αρ)θ) T_i^(1+ρ)/(1+αρ)θ · K_i^(−α(1+ρ)/(1+αρ)).
  - Key implications:
    - Inclusion of capital links hours to capital stock; impact of capital on hours is independent of trade elasticity.
    - Sensitivity of hours to domestic trade share is multiplied by 1/(1+αρ); if α = 0 model reduces to main text.
    - For plausible parameter values (|ρ| < 1, α ≈ 1/3) 1/(1+αρ) is expected to be close to one.
  - Empirical note: Appendix E includes capital as control and finds domestic trade share coefficient broadly unchanged.

- C.2 Multiple sectors and intermediate inputs
  - Multiple sectors (s = 1,...,S) with Cobb-Douglas upper-tier weights ω_s and Dixit-Stiglitz lower-tier with σ > 1:
    - Price index P_i = Π_s (P^s_i)^{ω^s_i}.
    - Real wage: w_i/P_i = Σ_s (T^s_i)^{ω^s_i/θ} (π^s_ii)^{−ω^s_i/θ}.
    - Equilibrium hours: H_i = Π_s (π^s_ii)^{−ρω^s_i/θ} (T^s_i)^{ρω^s_i/θ}.
    - Changes in hours: bH_i = Σ_s (bπ^s_ii)^{−ρω^s_i/θ}.
    - Income effects from trade are weighted by sectoral preference shares ω^s_i.
  - Intermediate inputs (composite intermediate with labor share λ):
    - Intermediate price c_i = w_i^λ P_i^{1−λ}.
    - Real wage: w_i/P_i = T_i^{1/(λθ)} π_ii^{−1/(λθ)}.
    - Hours: H_i = π_ii^{−ρ/(λθ)} T_i^{ρ/(λθ)}.
    - Lower labor share λ amplifies income gains from trade and leisure gains.

- C.3 Firm entry and exit margin (Melitz-style)
  - Firms draw productivities φ from Pareto with shape θ > σ−1; exporting requires φ ≥ φ^*_{in}.
  - Equilibrium number of firms depends on H_i:
    - N_i = (σ−1) b_i^θ / (φ^*_{ii})^{θ/(σ) } f_e H_i (expression in text: N_i = (σ−1)b^{θ}_i/(φ^*_{ii})^{θ/(σ)} f_e H_i).
  - Trade shares become market-size dependent; trade share formula (isomorphic to main model) shown in equation (37).
  - Real wage with firm entry/exit:
    - w_i/P_i = π_ii^{−(σ−1)/(σ−1−ρ)θ} T̃_i^{(σ−1)/(σ−1−ρ)θ}, where T̃_i aggregates fixed-cost and technology terms.
  - Hours and trade:
    - H_i = π_ii^{−(σ−1)ρ/(σ−1−ρ)θ} T̃_i^{(σ−1)ρ/(σ−1−ρ)θ}.
  - Key implication: firm exit attenuates the elasticity of hours with respect to trade; elasticity multiplied by (σ−1)/(σ−1−ρ) < 1 when income effects dominate.

### Welfare variation and gains from trade (Appendix D)
- Expenditure function defined: e_i(P_i,u_i) = min_{c_in} Σ_n p_in c_in subject to u({c_in}) ≥ U.
- Welfare gains from trade (compensating/equivalent variation) cW_i derived in closed form as function of trade costs via π_ii and T_i.
- Under T′_i ≡ T_i the equivalent variation simplifies to:
  - cW_i = [ b π_ii^{−(1+ε)/(1+ηε)} · (1 − (1−η)ε/(1+ε)) − b π_ii^{−(1+ε)(1−η)/(1+ηε)} + (1−η)ε/(1+ε) ]^{1/(1−η)} − 1
  (expression presented in the Appendix; algebraic rearrangement shown step-by-step).
- Limiting case η → 1 recovers Eaton and Kortum result: Ŵ_i = π̂_ii^{−1/θ} − 1.
- The Appendix demonstrates that welfare gains from trade are always larger when labor supply is elastic (comparison between elastic and inelastic cases), providing analytical inequalities for cases η > 1 and η < 1.
- Alternative expressions relate welfare gains to observed changes in wages, prices, and hours, using the model’s mapping w_i/P_i = π_ii^{−1/θ} T_i^{1/θ}.

### Robustness checks and empirical additions (Appendix E)
- Adds controls for TFP and capital per worker to baseline regression (equation (17)) and reports that domestic trade share coefficient remains broadly unchanged:
  - Coefficient on domestic trade share changes from 0.51 to 0.58 when controlling for log TFP and log capital per worker.
  - Both log TFP and log capital per worker are not statistically significant at 10 percent in this specification.
  - Sample: 42 countries, 5-year intervals between 1950 and 1995, observations = 303.
  - First-stage F-statistics reported: 15.4 and 8.7 (two specifications).
- OECD-only sample robustness (17 OECD countries, ~50 percent of original observations):
  - Dependent variables: log hours per worker and log GDP per worker.
  - Coefficient on log domestic trade share (hours): 0.355* (standard error 0.194).
  - Coefficient on log domestic trade share (GDP per worker): -4.230*** (standard error 1.276).
  - Observations = 158; first-stage F-stat = 22.8.
- Instrument construction robustness:
  - Alternative instruments use different initial weights in predicted trade:
    - Initial bilateral trade (baseline), initial population (1950), initial total trade (1950).
  - Second-stage IV estimates (log hours per worker on log domestic trade share):
    - Baseline coefficient 0.507** (s.e. 0.217).
    - Using initial population: 0.802*** (s.e. 0.203).
    - Using initial trade volume: 1.031*** (s.e. 0.258).
  - Reduced-form coefficients of log predicted trade on log hours per worker are negative and significant:
    - Initial bilateral trade reduced-form: -0.081** (s.e. 0.039).
    - Initial population reduced-form: -0.129*** (s.e. 0.035).
    - Initial trade volume reduced-form: -0.139*** (s.e. 0.040).
  - Sample sizes and diagnostics:
    - Observations = 321 in these specifications; F-stats: 15.45, 17.07, 9.16 (reported in table).
- Empirical message: instrument exploits variation correlated with trade but orthogonal to measured TFP and investment; inclusion of TFP and capital does not materially alter main coefficient estimates.

### Supplementary data, tables, and figures (Appendix F)
- Country list (45 countries; OECD subset indicated).
- Main descriptive statistics (sample 1950–1995; countries with population > 1 million and domestic share between 0.5 and 1):
  - Hours per worker: obs = 324, mean = 2,042.32, s.d. = 51.27, min = 439.92, max = 2,921.48.
  - Employment rate: obs = 633, mean = 0.370, s.d. = 0.080, min = 0.18, max = 0.56.
  - Domestic trade share: obs = 673, mean = 0.83, s.d. = 0.11, min = 0.50, max = 0.99.
  - log predicted trade: obs = 673, mean = 4.02, s.d. = 3.15, min = -1.58, max = 12.10.
  - log GDP per worker: obs = 633, mean = 9.44, s.d. = 0.99, min = 6.18, max = 13.06.
- Figures (described):
  - Trade and income (Figure 3): trade–income relationship; hours per capita and income panels using Bick et al. (2018) and PWT.
  - Hours worked margins (Figure 4): hours per worker and employment rate, with 5-year moving averages and country means.

*Italic: Source — The Leisure Gains from International Trade, Working Paper No. WP/2024/016 (References and Online Appendix content from wpiea2024016-print-pdf).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024016-print-pdf.pdf_