## _wp10279

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### I. Introduction and Key Empirical Observations
- Context:
  - Despite strong growth and trade liberalization, Chile’s income inequality remained mostly unaltered: average real GDP growth = 5 percent; average per capita real GDP increased 3.6 percent; Gini coefficient decreased from 55.9 in 1990 to 55.0 in 2009.
- Focus:
  - Effects of one mainly exogenous variable—the terms of trade (ToT)—on income distribution measured by the wage gap between skilled and unskilled workers.
- Chilean empirical observations (1996–2009):
  - Co-movement between ToT (index 2003=100) and relative wages (managers/unskilled).
  - Most of the increase in the wage gap results from larger wage increases to skilled workers, especially after the ToT surge around 2005–2006.
- Framing:
  - Resource-rich, small open economies: ToT shocks can redistribute income across factors depending on factor intensities, especially of non-tradable goods.

### II. Theory — Galiani–Heymann–Magud Model (overview)
- Structure:
  - Three goods: tradable primary (natural-resource intensive, A), tradable manufactures (M), non-tradable good (N).
  - Factors: T (land, specific to A), L (unskilled labor, mobile across all sectors), H (skilled labor, mobile between M and N).
  - Non-tradable goods assumed skilled-intensive while manufactures are unskilled-intensive (baseline configuration).
- Mechanism of a positive ToT shock:
  - Owner of the natural resource (land) benefits; higher ToT raises income → spending shifts to non-tradables → relative price of non-tradables rises.
  - Zero-profit conditions and factor intensities imply factors intensive in non-tradables gain; if N is skilled-intensive, skilled workers benefit and unskilled workers lose.
  - Labor-market clearing: demand for unskilled labor falls in manufacturing and rises in agriculture and non-tradables; aggregate unskilled wage may need to fall.
- Testable formal relationship:
  - h/w = F(ToT), where h = skilled wage, w = unskilled earnings, ToT = terms of trade.
  - F′(·) > 0 if NT is skilled-intensive; F′(·) < 0 if NT is unskilled-intensive.
- Extensions discussed (not empirically tested here): alternative fiscal redistributive policies, skilled-intensive manufactures, capital, imports as inputs, alternative preferences, capital account dynamics.

### III. Data and Econometric Methodology
- Data sources and construction:
  - ToT: Central Bank of Chile (ratio of export price index to import price index, 2003=100), quarterly 1996:1–2009:4.
  - Wages: National Statistical Institute (INE) monthly series 1993:4–2009:12; skilled proxied by average income of managers, unskilled by category “unskilled”; monthly incomes averaged to quarterly frequencies.
  - Industry-level wage-gap series available for 1993:4–2005:12 for disaggregated exercises.
  - Controls: real GDP per capita growth (from BCCh), volatility measures as 3-quarter moving average of standard deviations of ToT.
- Descriptive statistics (Table 2) — preserve values as presented:
  - Terms of Trade (index, 2003=100): Mean 119:80; Median 96:53; Maximum 191:43; Minimum 79:97; Std. Dev. 37:29; Observations 56.
  - Relative Wage (q-o-q percent change): Mean 6:92; Median 3:64; Maximum 8:91; Minimum 6:0; Std. Dev. 1:02; Observations 67.
  - GDP per capita growth rate (q-o-q percent change): Mean 2:2; Median 2:3; Maximum 10:2; Minimum −5:8; Std. Dev. 2:9; Observations 66.
- Estimation approach:
  - ToT treated as exogenous for a small open economy.
  - OLS on logged variables so coefficients represent elasticities.
  - Stationarity and cointegration diagnostics: 7 unit root tests; Johansen cointegration tests support long-term cointegration with a constant but no trend.

### IV. Aggregate and Sectoral Empirical Results
- Aggregate economy (Table 3):
  - Baseline: Terms of Trade (−1) coefficient = 0:43 ∗∗∗ (column (1)); statistically significant at 1 percent.
  - Interpretation: a 1 percent increase in the ToT increases the wage gap by close to 0.5 percent.
  - R2 = 0:75; Number of Observations = 55.
  - Robustness: controlling for Growth of GDP per capita (−1) coefficient = −1:13 ∗∗ (column (2)) and Std. Dev. of ToT (−1) coefficient = 0:02 (column (3)); R2 rises to 0:79; Number of Observations = 55/54.
- Sectoral shares in GDP (Table 4):
  - Manufacturing 18:2 percent; Financial Sector 17:2 percent; Personal Services 12:1 percent; Commerce 11:4 percent; Transportation and Telecommunications 10:5 percent; Mining 8:2 percent; Construction 7:7 percent; Rest 14:7 percent.
- Financial Services (skilled-intensive, Panel A of Table 5):
  - Terms of Trade (−1) coefficient = 0:53 ∗ (column (1)); 0:64 ∗∗ (column (2)); 0:76 ∗∗ (column (3)).
  - Growth of GDP per capita (−1) = −1:88 ∗∗ (column (2)); Std. Dev. of ToT (−1) = −0:12 ∗∗∗ (column (3)).
  - R2 ranges 0:12 → 0:32; Number of Observations = 39.
  - Interpretation: a 1 percent increase in ToT increases the wage gap by more than 0.5 percent in Financial Services; volatility reduces this benefit.
- Manufacturing (unskilled-intensive, Panel B of Table 5):
  - Terms of Trade (−1) coefficient = −0:31 ∗∗∗ across columns.
  - Std. Dev. of ToT (−1) = 0:01 ∗∗ (column (3)).
  - R2 ≈ 0:59 → 0:64; Number of Observations = 39.
  - Interpretation: a 1 percent increase in ToT results in a 0.31 percent decrease in the wage gap in manufacturing.
- Construction and Commerce (unskilled-intensive, Panels C and D of Table 5):
  - Construction: Terms of Trade (−1) = −0:51 ∗∗ → −0:61 ∗∗ across specifications; R2 up to 0:23; Observations = 39.
  - Commerce: Terms of Trade (−1) = −0:27 ∗∗∗ → −0:25 ∗∗∗; R2 up to 0:68; Observations = 39.
  - Interpretation: these unskilled-intensive sectors show reductions in the wage gap when ToT improve.
- EGW, Mining, Personal Services (Table 6):
  - EGW (skilled-intensive): Terms of Trade (−1) ≈ 0:17 → 0:26 (column (3) shows 0:26 ∗); Std. Dev. of ToT (−1) = −0:06 ∗∗∗ (column (3)); R2 up to 0:21; Observations = 39.
  - Mining (unskilled-intensive): Terms of Trade (−1) ≈ −0:21 → −0:14 (not always significant); R2 up to 0:14; Observations = 39.
  - Personal Services (unskilled-intensive): Terms of Trade (−1) ≈ −0:05/−0:04 (not significant); Growth of GDP per capita (−1) = 0:43 ∗∗ → 0:33 ∗; R2 up to 0:12; Observations = 39.
- Robustness checks:
  - Alternative definitions of skilled/unskilled wages, controls for GDP per capita growth, lagged wage gap, and ToT volatility tested; main results remain robust.
  - Unit root concerns addressed via Johansen cointegration tests supporting a long-run relation.

### V. Main Empirical and Conceptual Findings (Condensed)
- If non-tradable goods are (relatively) skilled-intensive, positive ToT shocks benefit skilled workers.
- In Chile:
  - Wage gap widens in skilled-intensive sectors (more so when ToT volatility is lower).
  - Wage gap narrows in unskilled-intensive sectors.
- A small open economy exposed to ToT shocks benefits from increasing the share of skilled workers; investing in human capital is emphasized.
- As economies grow, non-tradable sectors tend to expand and become more skilled-intensive, increasing the share of population benefiting from positive external shocks.
- Innovation and higher TFP growth help tradable import-competing activities become exportable; less skewed factor intensities reduce real-wage adjustment costs during reallocation.
- Greater labor-market flexibility helps skilled workers absorb external real shocks and mitigates distributional effects.

### VI. Policy Implications and Recommendations
- Invest in human capital:
  - Increase share of skilled workers so more individuals benefit from positive external shocks.
  - A larger skilled share expands the taxable base, reducing per-individual redistribution costs if taxes on skilled workers finance transfers.
  - Tax skilled workers during “good times” to build “rainy day” funds for negative external shocks.
- Improve manufacturing competitiveness (non-protectionist):
  - Increase exportability of manufactures and their competitiveness.
  - If manufactures become more skilled-intensive, more workers benefit from ToT improvements.
- Consider relative factor intensities:
  - Less skewed factor intensities across sectors reduce required adjustments in unskilled wages to clear labor markets after ToT shocks.
- Enhance labor-market flexibility:
  - Facilitate movement of skilled (and unskilled) workers between non-tradable and tradable sectors to broaden sharing of ToT shock benefits.
- Address ToT volatility:
  - Lower volatility amplifies skilled workers’ ability to capture benefits from positive ToT shocks (volatility coefficients often negative and significant).
- Complementary policies:
  - Combining higher human capital investment and improved tradable-sector competitiveness reduces adverse distributional impacts of favorable external shocks.

### VII. Theoretical Propositions, Comparative Statics, and Additional Remarks (select highlights)
- Proposition 1:
  - If N is relatively H-intensive compared with M (or M is relatively L-intensive), ∆ > 0. An exogenous increase in pN (relative to pM) increases H earnings and decreases L wages in terms of both goods N and M.
- Proposition 2 (three-good, three-factor):
  - Increase in pA raises return to T such that ˆt > ˆpA > 0 and ˆt > ˆpN.
  - Agricultural output increases (ˆyA > 0); import-competing output decreases (ˆyM < 0); consumption shifts toward M (ˆcM > 0).
  - If H is used more intensively in N than in M (and labor share in agriculture is small), skilled-labor purchasing power increases and unskilled-labor purchasing power decreases.
  - Threshold conditions determine whether H’s purchasing power increases or decreases; threshold is provided in the Appendix.
- Selected analytical remarks:
  - Remark 1: Use of M as a production input does not alter income-distribution of ToT shifts.
  - Remark 3: Transitory ToT shocks can produce different short/medium-run distributive effects due to spending dynamics; neutrality is more realistic for permanent changes.
  - Remark 7: ToT improvement implies real appreciation (ˆe = −(1−γ_A) ˆp_A < 0); in the baseline there is no “Dutch disease” affecting an import-competing sector in the simple structure.
  - Remark 8: Economy with sector-specific factors illustrates how mobility, factor intensities, and reallocation generate distributional outcomes and potential Dutch-disease–like effects.
  - Remark 9: International transfers (relaxation of external constraint) tend to redistribute income toward the factor used intensively in the non-traded sector; two- and three-good economy outcomes differ in the identity of the most adversely affected factor.

*Source: Authors’ calculations using data from Central Bank of Chile, Chile’s National Bureau of Statistics, and CASEN Survey as presented in the content unit.*

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

### _wp10279 - References         .....................................................................................................

### Figures
- 1. Terms of Trade vs. Relative Wages ..................................................................................4
- 2. Terms of Trade vs. Relative Wages ..................................................................................4
- 3. Relative Wages .................................................................................................................5

### Tables
- 1. Labor Intensities by Sector ...............................................................................................5
- 2. Descriptive Statistics .........................................................................................................8
- 3. Regression Output for the Aggregate Economy .............................................................10
- 4. Relative Importance of the Sectors in the Overall Economy ..........................................10
- 5. Regression Output for the Financial Services, Manufacturing, Construction,  
         and Commerce Sectors ...................................................................................................12
- 6. Regression Output for the EGW, Mining, and Personal Services Sectors .....................13

### Appendix
- Appendix

*Source: _wp10279 - References         .....................................................................................................*

### 1. The Galiani-Heymann-Magud Model .............................................................................17

### 1. The Galiani-Heymann-Magud Model .............................................................................17

### I. Introduction
- Despite strong growth and trade liberalization in the last two decades, Chile’s income inequality remains mostly unaltered: average real GDP growth has been 5 percent, average per capita real GDP increased 3.6 percent, and the Gini coefficient decreased from 55.9 in 1990 to 55.0 in 2009.
- This study focuses on the effects of one mainly exogenous variable—the terms of trade—on income distribution, measured by the wage gap between skilled and unskilled workers.
- Key empirical observations (Chile, 1996–2009):
  - Co-movement between terms of trade (index 2003=100) and relative wages (managers/unskilled).
  - Most of the increase in the wage gap results from larger wage increases to skilled workers, especially after the terms of trade surge around 2005–2006.
- Motivation and framing:
  - Resource-rich, small open economies may see globalization and terms of trade shocks redistribute income across factors.
  - Non-tradable goods’ factor intensities are central to the distributional impact of terms of trade shocks.
- Summary empirical approach:
  - Use Chilean data on terms of trade and wages (1993–2009), regress wage gap of skilled vs. unskilled workers on terms of trade, and disaggregate analysis by industry.

### II. Theory (Model overview following Galiani, Heymann, and Magud (2010))
- Model setting:
  - Three goods: tradable primary goods (natural-resource intensive), tradable manufactures, and a non-tradable good.
  - Primary good uses land and unskilled labor. Manufactures and non-tradables use skilled and unskilled labor.
  - Non-tradable goods are assumed skilled-intensive while manufactures are unskilled-intensive.
- Mechanism of a positive terms of trade (ToT) shock:
  - Owner of the natural resource (land) benefits (standard Stolper–Samuelson result).
  - Positive ToT shock raises income and spending on non-tradable goods → increases relative price of non-tradables.
  - Zero-profit conditions imply factors intensive in non-tradables gain; if non-tradables are skilled-intensive, skilled workers benefit at the expense of unskilled workers.
  - Labor market clearing effects: demand for unskilled labor falls in manufacturing and rises in agriculture and non-tradables; aggregate unskilled wage may need to fall to clear the market.
- Formal relationship tested:
  - h/w = F(ToT), where h = skilled wage, w = unskilled earnings, ToT = terms of trade.
  - F′(·) > 0 if NT is skilled-intensive and F′(·) < 0 if NT is unskilled-intensive.
- Extensions (not empirically tested here but discussed in Galiani, Heymann, and Magud (2010)):
  - Alternative redistributive fiscal policies (e.g., export taxes) can under some conditions ameliorate or exacerbate distributional effects of ToT shocks.
  - Model extensions include skilled-intensive manufactures, capital, imports as inputs, alternative preferences, and capital account dynamics.

### III. Data and Econometric Methodology
- Data sources and construction:
  - Terms of trade (ToT): Central Bank of Chile (ratio of export price index to import price index, 2003=100), quarterly 1996:1–2009:4.
  - Wages: National Statistical Institute (INE) monthly series 1993:4–2009:12; skilled proxied by average income of managers, unskilled by category “unskilled”; monthly incomes averaged to quarterly frequencies for consistency.
  - Industry-level wage-gap series available for 1993:4–2005:12 for disaggregated exercises.
  - Controls: real GDP per capita growth (from BCCh), volatility measures as 3-quarter moving average of standard deviations of ToT.
- Descriptive statistics (Table 2):
  - Terms of Trade (index, 2003=100): Mean 119:80; Median 96:53; Maximum 191:43; Minimum 79:97; Std. Dev. 37:29; Observations 56.
  - Relative Wage (q-o-q percent change): Mean 6:92; Median 3:64; Maximum 8:91; Minimum 6:0; Std. Dev. 1:02; Observations 67.
  - GDP per capita growth rate (q-o-q percent change): Mean 2:2; Median 2:3; Maximum 10:2; Minimum −5:8; Std. Dev. 2:9; Observations 66.
- Estimation approach:
  - Assume ToT exogenous for a small open economy; estimate OLS regressions on logged variables (wage ratio and ToT) so coefficients represent elasticities.
  - Conduct stationarity and cointegration diagnostics (7 unit root tests; Johansen cointegration tests support long-term cointegration with a constant but no trend).

### IV. Results
- Aggregate economy (Table 3):
  - Baseline: Terms of Trade (−1) coefficient = 0:43 ∗∗∗ (column (1)); statistically significant at 1 percent.
  - Interpretation: a 1 percent increase in the terms of trade increases the wage gap by close to 0.5 percent.
  - R2 = 0:75; Number of Observations = 55.
  - Robustness: results hold controlling for Growth of GDP per capita (−1) with coefficient −1:13 ∗∗ (column (2)) and Std. Dev. of ToT (−1) with coefficient 0:02 (column (3)); R2 rises to 0:79; Number of Observations = 55/54.
- Industry-level results (sector shares in GDP, Table 4):
  - Manufacturing 18:2 percent; Financial Sector 17:2 percent; Personal Services 12:1 percent; Commerce 11:4 percent; Transportation and Telecommunications 10:5 percent; Mining 8:2 percent; Construction 7:7 percent; Rest 14:7 percent.
- Financial Services (skilled-intensive, Panel A of Table 5):
  - Terms of Trade (−1) coefficient = 0:53 ∗ (column (1)); 0:64 ∗∗ (column (2) controlling for GDP growth); 0:76 ∗∗ (column (3) including volatility).
  - Growth of GDP per capita (−1) = −1:88 ∗∗ (column (2)); Std. Dev. of ToT (−1) = −0:12 ∗∗∗ (column (3)).
  - R2 ranges 0:12 → 0:32; Number of Observations = 39.
  - Interpretation: For Financial Services, a 1 percent increase in ToT increases the wage gap by more than 0.5 percent; volatility reduces this benefit.
- Manufacturing (unskilled-intensive, Panel B of Table 5):
  - Terms of Trade (−1) coefficient = −0:31 ∗∗∗ across columns.
  - Growth of GDP per capita (−1) ≈ 0:09/0:05 (not significant); Std. Dev. of ToT (−1) = 0:01 ∗∗ (column (3)).
  - R2 ≈ 0:59 → 0:64; Number of Observations = 39.
  - Interpretation: A 1 percent increase in ToT results in a 0.31 percent decrease in the wage gap in manufacturing.
- Construction and Commerce (unskilled-intensive, Panels C and D of Table 5):
  - Construction: Terms of Trade (−1) = −0:51 ∗∗ → −0:61 ∗∗ across specifications; R2 up to 0:23; Number of Observations = 39.
  - Commerce: Terms of Trade (−1) = −0:27 ∗∗∗ → −0:25 ∗∗∗; R2 up to 0:68; Number of Observations = 39.
  - Interpretation: These unskilled-intensive sectors show wage-gap improvements (reductions) when ToT improve.
- EGW, Mining, Personal Services (Table 6):
  - Electricity, Gas, and Water (EGW, skilled-intensive): Terms of Trade (−1) coefficients ≈ 0:17 → 0:26 (column (3) shows 0:26 ∗); Std. Dev. of ToT (−1) = −0:06 ∗∗∗ (column (3)); R2 up to 0:21; Observations = 39.
  - Mining (unskilled-intensive): Terms of Trade (−1) coefficients ≈ −0:21 → −0:14 (not always significant); R2 up to 0:14; Observations = 39.
  - Personal Services (unskilled-intensive): Terms of Trade (−1) ≈ −0:05/−0:04 (not significant); Growth of GDP per capita (−1) = 0:43 ∗∗ → 0:33 ∗; R2 up to 0:12; Observations = 39.
- Robustness checks:
  - Alternative definitions of skilled/unskilled wages, controls for GDP per capita growth, lagged wage gap, and ToT volatility were tested; main results remain robust.
  - Unit root concerns addressed via Johansen cointegration tests supporting a long-run relation.

### V. Discussion and Policy Implications
- Main policy-relevant findings:
  - Positive ToT shocks in a resource-rich small open economy can worsen the wage gap when non-tradable goods are skilled-intensive, redistributing income toward skilled workers.
  - The size of the non-tradable sector magnifies distributional consequences; in Chile non-tradables are relatively skilled-intensive (CASEN 2006).
- Policy recommendations and implications drawn from results:
  - Invest in human capital:
    - Increasing the share of skilled workers raises the number of individuals who benefit from positive external shocks.
    - A larger share of skilled workers increases the taxable base, potentially lowering per-individual redistribution costs if taxes on skilled workers are used to transfer during shocks.
    - Taxing skilled workers during “good times” can help build a “rainy day” fund for negative external shocks.
  - Improve manufacturing competitiveness (non-protectionist approach):
    - Making manufactures more competitive and exportable increases the share of the economy that benefits when manufactures’ relative prices rise.
    - If manufactures become more skilled-intensive, a larger share of workers would benefit from ToT improvements.
  - Consider relative factor intensities:
    - Less skewed factor intensities across sectors reduce required adjustments in unskilled wages to clear labor markets after ToT shocks.
    - More balanced relative factor intensity implies smaller distributional adjustments.
  - Enhance labor market flexibility:
    - Greater flexibility facilitates movement of skilled (and to a lesser extent unskilled) workers between non-tradable and tradable sectors, enabling broader sharing of ToT shock benefits.
- Additional notes:
  - Volatility of ToT matters: lower volatility amplifies skilled workers’ ability to capture benefits from positive ToT shocks (volatility coefficients often negative and significant).
  - The results support complementary policies: raising human capital and enhancing tradable-sector competitiveness jointly reduce adverse distributional impacts of favorable external shocks.

*Source: Authors’ calculations using data from Central Bank of Chile, Chile’s National Bureau of Statistics, and CASEN Survey as presented in the content unit.*

### Section IImentions this; Galiani, Heymann,

### _wp10279 - Section IImentions this; Galiani, Heymann,

### Main empirical and conceptual findings
- For countries in which non-tradable goods are (relatively) skilled-intensive, positive terms of trade shocks benefit skilled workers.
- In the Chilean economy as a whole the wage gap between skilled and unskilled workers:
  - widens in skilled-intensive sectors (the more so the lower the volatility of the terms of trade), and
  - narrows in unskilled-intensive sectors.
- A small open economy mainly exposed to terms of trade shocks would benefit from increasing the share of skilled workers in the labor force, underscoring the relevance of investing in human capital.
- As the economy grows the non-tradable sector tends to increase and become more skilled-intensive, so a larger share of the population will benefit from positive external shocks.
- Innovation and higher TFP growth boost every sector and may help import-competing tradable goods become exportable goods; when relative factor intensity is not too skewed, factor reallocation can be attained at a lower cost in terms of real wages.
- A more flexible labor market helps skilled workers absorb external real shocks; greater labor-market flexibility reduces the prominence of rigid contracts and diminishes income-distributional effects of terms of trade shocks.
- Illustrative micro-structure example: for a 0.55 ratio of skilled to unskilled labor in the non-tradable sector the unskilled workers wage drop would be smaller than if that ratio would be 0.95.

### Policy implications and recommendations
- Increase the share of skilled workers via investment in human capital.
- Promote innovation to raise TFP growth, improving long-term competitiveness and facilitating structural change in tradable sectors.
- Improve labor-market flexibility and reduce asymmetries and rigid contracts to:
  - ease factor reallocation across sectors after external shocks, and
  - mitigate adverse distributional impacts of terms of trade shocks.
- Pursue policies that balance relative factor intensity across sectors to lower real-wage adjustment costs during reallocation.

### Theoretical model sketch and implications (Galiani–Heymann–Magud model)
- Structure:
  - Three goods produced: agricultural (A), manufactures (M), and non-traded (N); quantities yA, yM, yN.
  - Exogenous world price pA for agricultural good; price of imported good M, pM, serves as numeraire (pM = 0).
  - Factors: T (agricultural land), L (raw/unskilled labor, mobile across all sectors), H (skilled labor, mobile between manufactures and non-traded).
  - Production functions: yA = f(T;L) (A.1); yN = g(H;L) (A.2); yM = s(H;L) (A.3).
  - Price-cost equalities (proportional changes):
    - ˆpA = θTA ˆt + θLA ˆw (A.4)
    - ˆpN = θHN ˆh + θLN ˆw (A.5)
    - ˆpM = 0 = θHM ˆh + θLM ˆw (A.6)
  - Factor market equilibrium (proportional change form):
    - ˆT = 0 = ˆpA + ˆyA − ˆt (A.7)
    - ˆL = 0 = λLA(ˆpA + ˆyA) + λLN(ˆpN + ˆyN) + λLM ˆyM − ˆw (A.8)
    - ˆH = 0 = λHN(ˆpN + ˆyN) + λHM ˆyM − ˆh (A.9)
  - Homothetic Cobb–Douglas preferences u(cA;cM;cN) = cA^γA cM^γM cN^γN (A.10); γA + γM = 1.
  - Budget constraint: I = pA cA + pN cN + pM cM (A.11).
  - Consumption equilibrium (proportional changes): ˆpA + ˆcA = ˆcM = ˆpN + ˆcN = ˆpN + ˆyN (A.12).
  - Trade-balance condition (proportional changes):
    - χA(ˆpA + ˆyA) + χM ˆyM = γA(ˆpA + ˆcA) + γM ˆcM (A.13).

- Key algebraic results and definitions:
  - Define ∆ = θHN − θHM = θLM − θLN.
  - Proportionate changes for factor returns when ˆpN changes:
    - ˆh = θLM ∆ ˆpN (A.14)
    - ˆw = − θHM ∆ ˆpN (A.15)
  - These equations imply a Stolper–Samuelson type distributive tension between H and L when ˆpN changes.

### Propositions and comparative-statics results
- Proposition 1
  - If the production of the non-traded good N is relatively intensive in human capital (factor H) compared with the manufactured good M (or equivalently, if sector M is relatively labor intensive), then ∆ > 0.
  - If an exogenous increase in the price of good N relative to imported good M occurs, then:
    - Earnings of skilled workers H increase unambiguously in terms of both goods N and M.
    - The wage of factor L falls in terms of both goods N and M.

- Proposition 2 (three-good, three-factor economy; increase in international relative price of agricultural good A)
  - The return to factor T (specific to production of A) increases unambiguously, and the proportional change of the return to T is greater than the proportional change in the price of the exported good:
    - ˆt > ˆpA > 0; and ˆt > ˆpN.
  - Production reallocation:
    - Agricultural output increases: ˆyA > 0.
    - Output of the import-competing sector decreases: ˆyM < 0.
  - Consumption and trade:
    - Consumption of traded goods switches towards good M: ˆcM > 0.
    - Economy increases its volume (and value) of imports since cM increases while yM falls.
  - Distributional consequences when H is used more intensively in N than in M (and conditional on labor share in agriculture being “small”):
    1. The price of the non-traded good increases in terms of the manufactured good M.
    2. The price of skilled labor (factor H) increases relative to the prices of goods M and N.
    3. The return to unskilled labor L, used intensively in production of import-competing goods M, decreases in terms of the three goods.
  - Relative to an aggregate consumption price index (ˆp = γ′A ˆpA + γ′M ˆpM + γ′N ˆpN):
    - The purchasing power of the return to unskilled labor decreases (ˆw − ˆp < 0) if non-traded goods are sufficiently skilled-labor intensive.
    - The purchasing power of the return to unskilled labor increases (ˆw − ˆp > 0) if non-traded goods are not sufficiently skilled-labor intensive.
  - The “wedge” in factor intensity increases with the share of exportable goods consumed and decreases with the share of exportable tradable goods production and the share of land used in production of exportable goods.

*Source: _wp10279 - Section IImentions this; Galiani, Heymann,*

### 2. The purchasing power of the return to skilled-labor increases (decreases),

### 2. The purchasing power of the return to skilled-labor increases (decreases),

### Main result and threshold condition
- The purchasing power of the return to skilled-labor increases (ˆh−ˆp>0) if non-tradable goods are sufficiently skilled-labor intensive; it decreases (ˆh−ˆp<0) if non-tradable goods are not sufficiently skilled-labor intensive.
- The threshold determining “sufficiently skilled-labor intensive” is shown in the Appendix.

### Mechanisms: factor-intensity wedge and consumption/production shares
- The “wedge” in factor intensity increases via:
  - an increase in the share of exportable goods consumed; and
  - decreases in the share of exportable tradable goods production and the share of land used in the production of exportable goods.

### Specific analytical remarks
- Remark 1 (Imports as production inputs)
  - The use of good M as a production input, and not only as a consumption good, does not alter the income-distribution of the terms-of-trade shift.
- Remark 2 (Non-unitary demand elasticities)
  - If consumption demands are not characterized by unitary elasticities, changes in factor earnings would differ.
  - Example: if demand for the non-traded good is highly income elastic, spending share in that good rises with higher export prices, tending to increase earnings of the specific factor H. In such an economy, after a positive shock on the price of agricultural good A, an “urban” factor could receive larger benefits in terms of income.
- Remark 3 (Transitory non-neutralities)
  - In a multi-period setup, short- and medium-run impacts of a positive terms-of-trade shock may differ due to spending dynamics.
  - Example: if higher export prices initially induce larger savings by agricultural producers (creating a trade surplus) and domestic expenditures rise with delay, the initial effect on “urban” groups can be a loss of purchasing power because agricultural consumption becomes more expensive while incomes do not immediately adjust.
  - Consequently, neutrality of factor price changes does not hold for transitory shocks; neutrality is more realistic for permanent changes in the terms of trade.
- Remark 4 (Distributive effects with different factor intensities in the urban sectors)
  - If services are more unskilled-labor intensive than manufacturing (a different configuration), then:
    - factor H faces a decline in its earnings in terms of the three goods,
    - the wage of L rises relative to the urban goods,
    - these shifts associate with an increase in the relative price of N relative to M.
- Remark 5 (Effects of terms of trade in an economy with manufacturing exports)
  - Consider an economy exporting good M and importing A (e.g., with lower land-labor ratio). For a positive terms-of-trade shock (ˆp_M>0, ˆp_A=0):
    - skilled-labor (or physical capital) increases its income unambiguously;
    - land decreases its income unambiguously;
    - unskilled-labor increases its relative income provided that agricultural goods represent a sufficiently high share in its consumption basket relative to manufactures; it decreases otherwise.
  - Results reverse if the terms-of-trade shock is negative (i.e., ˆp_M=0, ˆp_A>0).

### Two-good economy and homothetic preferences
- Remark 6 (Effects of heterogeneous consumption baskets with homothetic preferences)
  - With homothetic preferences and heterogeneity in consumption baskets (agents owning a single factor; Cobb–Douglas preferences identical within groups but differing across them, utility parameters γ_i^j, j=A;N;M, i=t;w;h), aggregate expenditure functions imply:
    - ˆp_j + ˆc_j = γ_t^j ˆt + γ_w^j ˆw + γ_h^j ˆh; j=A;N;M (A.16)
  - Equal proportional changes in all factor earnings also apply:
    - ˆt = ˆw = ˆh = ˆp_A = ˆp_N.
  - Welfare of all agents increases with an improvement of the international terms of trade, but agents with consumption preferences biased towards good M (higher γ_I^M for I = w; h; t) benefit relatively more.

### Real exchange rate and absence of “Dutch disease” in baseline
- Remark 7 (Terms-of-trade improvement: real appreciation, but no “Dutch disease")
  - An increase in the international price of good A implies an unambiguous rise in the price of the non-traded good relative to an index of consumer prices of traded goods:
    - ˆe = γ_A ˆp_A + γ_M ˆp_M − ˆp_N = −(1−γ_A) ˆp_A < 0 (A.17)
  - Thus, terms-of-trade improvement brings real appreciation (e).
  - In this economy there is no import-competing sector that may be affected by a “Dutch disease"; given the structure, all groups benefit or lose together according to international relative prices.

### Economy with sector-specific factors (sharp illustration)
- Remark 8 (Economy with sector-specific factors)
  - Set-up: three sectors (agriculture, manufactures, services) each use a different specific factor: land (T), unskilled labor (L), skilled labor (H). Thus θ_LA = θ_HM = θ_LN = 0, and cost-price equalities reduce to:
    - ˆp_A = ˆt; ˆp_M = 0 = ˆw; ˆp_N = ˆh (A.18)
  - No factor substitutability implies:
    - ˆy_A = ˆy_M = ˆy_N = 0 (A.19)
  - Balance of payments and demand conditions:
    - γ_A (ˆp_A + ˆc_A) + γ_M ˆc_M = χ_A ˆp_A = ˆp_N + ˆc_N = ˆp_N (A.20)
  - Aggregate consumption of traded goods:
    - γ_A ˆc_A + γ_M ˆc_M = (χ_A − γ_A) ˆp_A
  - Outcomes summarized:
    - A higher price of good A raises consumption of the imported good while consumption of A declines. Aggregate volume of consumption moves with the terms-of-trade effect. If χ_A − γ_A > 0 (A exported good), an increase in p_A increases volume of goods consumed.
    - For given production structure, magnitude of change in consumption index (welfare indicator) is larger the smaller the weight of the exported good in the consumption basket. If γ_A → 0 (exported good not consumed domestically), higher international prices raise domestic incomes without a direct impact on consumer prices.
    - The factor used in manufactures (unskilled labor L) reduces its purchasing power in terms of the two other goods, A and N.
    - The agricultural factor maintains earnings in terms of good A, and gains purchasing power relative to other goods.
    - The income of the factor used in the non-traded sector, H, increases relative to M but decreases in terms of A. Net change in H’s real purchasing power is ambiguous and depends on the terms-of-trade effect.
  - Consumption-weighted price index p:
    - ˆp = γ'_A ˆp_A + γ'_N ˆp_N = (γ'_A + γ'_N χ_A) ˆp_A (A.21)
    - where γ'_i = γ_i /(1+γ_N) stands for the expenditure share of good i.
  - Purchasing power of factor H increases when p_A rises if and only if the agricultural good is exported (χ_A − γ_A > 0). This also implies an increase in the relative price of the non-traded good (real appreciation).
    - ˆh − ˆp = ˆp_N − ˆp = (1 − γ'_N)(χ_A − γ_A) ˆp_A (A.22)
  - Interpretation:
    - Higher p_A benefits the specific factor in its production and reduces real income of producers of M (whose international relative price decreases).
    - Non-traded sector sees increased demand due to higher incomes of A producers, but factors used in M contract spending; in the two-sector case this offset is absent and earnings in N rise proportionally to p_A; here the increase is less than proportional.
  - Reallocation with factor mobility:
    - With mobility, sector A attracts more labor, increasing output and productivity of its specific factor, amplifying earnings of factor T.
    - Factor L sees additional demand from expanding agricultural sector (tending to raise income in terms of M), but sector M faces competition for resources from non-traded activities; consequences depend on factor intensities in urban industries M and N.
    - If sector N uses intensively skilled labor H, it demands more of H while contraction of M liberates predominantly L. If demand for L from agriculture is weak, wages of L decline while factors intensive in non-traded goods gain—this pull of resources by the non-traded sector away from import-competing activity is a symptom of “Dutch disease.”
  - Policy implication: international shocks that on average increase real income may create redistributive effects that leave significant population segments worse off; redistributive policy interventions can take different forms and often influence trade policy choices.

### Distributive effects of international transfers
- Remark 9 (Distributive effects of international transfers)
  - A relaxation of the “external constraint” (e.g., a lump-sum receipt of tradable resources) tends to redistribute income towards the factor used intensively in the non-traded sector.
  - In the two-good economy:
    - ˆh > ˆp_N > ˆw > 0 > ˆt (A.23)
    - Thus, transfer reduces real income of the factor specific to the export-oriented activity.
  - In the three-good economy:
    - The factor intensive in the import-competing sector (rather than factor T specific to the export sector) experiences the strongest distributive loss.

*Source: _wp10279 - 2. The purchasing power of the return to skilled-labor increases (decreases),*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10279.pdf_