## Section 5 concludes. (wpiea2019259-print-pdf)

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---

### The Model — overview
- Static Ricardian framework extending Eaton-Kortum (EK) to incorporate: multiple sectors, product-level quality, and intensive, extensive, and quality margins of trade.
- Driving mechanism: heterogeneity in quality and efficiency across export lines and countries determines export levels.

### Consumers (preferences and demand)
- Representative-agent utility aggregation:
  - c_n = [ Σ_{k=1}^K ω_k^{1/ε} c_nk^{1−1/ε} ]^{ε/(ε−1)}  (equation (1))
  - c_nk = [ ∫_0^1 e^{β_k q_nk} c_nk(j)^{1−1/η_k} dj ]^{η_k/(η_k−1)}  (equation (2))
  - Budget: w_n = Σ_{k=1}^K ∫_0^1 p_nk(j) c_nk(j) dj  (equation (3))
- Key parameters and roles:
  - β_k: sector-specific parameter multiplying quality q_nk in utility weights.
  - ε, η_k > 0: elasticity of substitution between sectors and within sector-k, respectively.
  - ω_k > 0: sector-k weight in utility.
- First-order conditions (demand):
  - Intra-sector: e^{β_k q_nk} c_nk(j) / c_nk = [ p_nk(j) / e^{β_k q_nk} P_nk ]^{−η_k}  (equation (4))
  - Inter-sector: c_nk / c_n = ω_k ( P_nk / P_n )^{−ε}  (equation (5))
- Quality-adjusted price indices:
  - P_nk = [ ∫_0^1 ( p_nk(j) e^{β_k q_nk} )^{1−η_k} dj ]^{1/(1−η_k)}  (equation (6))
  - P_n = [ Σ_{k=1}^K ω_k P_nk^{1−ε} ]^{1/(1−ε)}  (equation (7))
- Interpretation:
  - Consumers care about effective units of quality e^{β_k q_nk} c_nk(j); relevant decision variable is price per unit of effective quality p_nk(j)/e^{β_k q_nk}.
  - Lower price-to-quality ratio increases demand; both intra- and inter-sector aggregations use prices adjusted for quality.

### Producers (technology and pricing)
- Output function for good j in sectork produced in countryn:
  - Y_nk(j) = z_nk(j) L_nk(j) e^{α_k q_nk}  (equation (8))
  - L_nk(j): labor input; z_nk(j): efficiency draw; α_k: sector-specific parameter for cost impact of quality.
- Under perfect competition, free-on-board producer price from country i sold to n:
  - p_nik(j) = e^{α_k q_nik} w_i / z_ik(j)  (equation (9))
- Distinction:
  - Producer price p_nik(j) can differ from consumer price p_nk(j) (e.g., trade costs).
  - Quality at origin q_nik can differ from quality consumed q_nk in destination.

### Trade (stochastic productivity and bilateral patterns)
- Efficiency draws:
  - z_nk(j) ~ Fréchet with F_nk(z) = exp(−Υ_nk z^{−θ_k})  (equation (10))
  - Υ_nk > 0: scale parameter (technology level, absolute advantage).
  - θ_k > 1: shape parameter (degree of efficiency heterogeneity); lower θ_k → larger heterogeneity → stronger comparative advantage effects.
- Iceberg trade costs:
  - For each unit shipped from i to n in sectork, only 1/d_nik units arrive; d_nnk = 1.
- Price per unit of effective quality from origin i to destination n:
  - p_nik(j) / e^{β_k q_nik} = w_i / z_ik(j) e^{(α_k − β_k) q_nik}  (equation (11))
  - For higher-quality goods to be preferred, require β_k > α_k (utility effect dominates cost effect); if β_k < α_k, higher quality hurts exports.
- Consumer price-to-quality ratio is the minimum across origins:
  - p_nk(j) / e^{β_k q_nk} = min_{i=1,...,N} [ d_nik w_i / z_ik(j) e^{(β_k − α_k) q_nik} ]  (equation (12))
- Distribution of price-to-quality ratios:
  - Origin-conditional: G_nik(ρ) = 1 − F_ik( d_nik w_i ρ e^{(β_k − α_k) q_nik} )  (equation (13))
  - Unconditional (what country n actually buys): G_nk(ρ) = 1 − exp(−Φ_nk ρ^{θ_k})  (equation (14))
  - Φ_nk = Π_{i=1}^N Υ_ik [ d_nik w_i e^{(β_k − α_k) q_nik} ]^{−θ_k}
- Sector price index in closed form:
  - P_nk = γ_k Φ_nk^{−1/θ_k}, with γ_k = Γ( (θ_k + 1 − η_k)/θ_k )^{1/(1−η_k)}  (equation (15)), η_k < 1 + θ_k
- Probability that country i provides the best price adjusted for quality in sectork to n:
  - π_nik = Υ_ik [ d_nik w_i e^{(β_k − α_k) q_nik} ]^{−θ_k} / Φ_nk  (equation (16))
  - π_nik depends on geographical barriers d_nik, input prices w_i, technology Υ_ik, and quality q_nik.
- Bilateral trade value relation:
  - Share of countryn’s spending on industry k from source i equals π_nik:
    - X_nik P_nk c_nk L_n = π_nik  (equation (17))
  - Implies fraction of goods purchased from i equals probability i is lowest price-to-quality supplier; law of large numbers ensures spending share equals π_nik.

### Exports and Quality Across Asian Nations — empirical strategy
- Objective: assess contribution of changes in product quality to evolution of exports across 2-digit sectors for six Asian nations: China, India, Indonesia, Malaysia, South Korea, and Thailand.
- Methodology notes:
  - Generate model predictions by sector and compare to data.
  - Assess capacity of quality to predict export changes averaged over different time intervals (from a decade to entire sample) to reduce measurement bias and business cycle effects.
  - Focus on export shares (sectoral shares) rather than aggregate exports to minimize country-specific unobservables and to identify sectors gaining or losing importance.
- Contextual statistics:
  - Average annual growth rates (1970—2010): China 9.4 percent, India 5.6 percent, Indonesia 5.4 percent, Malaysia 7.7 percent, South Korea 6.5 percent, Thailand 6.1 percent.
  - Note: other Asian economies with similar growth rates in 1970—2010 include Singapore (7.6%), Hong Kong (6.1%), Vietnam (6.5%), and Cambodia (5.5%); Singapore and Hong Kong excluded because average quality levels already too close to the frontier in 1985.

### Methodology and data (Section 3.1)
- Data coverage and choices:
  - Exports and quality numbers: SITC, revision 1, at the two digit level; total of 60 product lines from 1962 to 2010.
  - Main analysis time interval: 1970—2010 (quality available for Germany only from 1970 onwards).
  - One product line discarded: product 35 (electric energy) — eliminated because only 18 observations were available.
  - Reference country (nation o): Germany (DEU); destination economy (n): the rest of the world.
  - Exports volumes: Comtrade mirror data (CIF exports reported by the destination country / importer).
  - Quality index: from Henn et al. (2017), downloaded from the Export Diversification and Quality Databases at the IMF.
  - Wages proxy: economy-wide marginal product of labor calculated from employment, labor shares and nominal GDP values from PWT 8.0.
  - Assumption on trade costs to the rest of the world: d_nik / d_nok = 1.
  - Zero-export observations excluded from estimation because the quality index is not available for those cases.

### Parameter assignment, identification, and estimation
- Previous estimates in the literature not used because this study focuses on SITC two-digit sectors while other papers use classifications (e.g., ISIC) for which domestic production numbers are available.
- To avoid converting ISIC to SITC, a version of the Eaton and Kortum-derived expressions that does not require domestic production and demand is used.
- Key model expression linking relative sector-k exports from country i and reference country o: equation (18) is used to generate predictions using relative values and country o’s export numbers.
- Regression specification (equation (19)) estimated by OLS using only non-zero export data:
  - ln (X_nik,t / X_nok,t) = γ_k0 + γ_k1i E_i + γ_k3i t + γ_k4 ln (w_it / w_ot) + γ_k5 (q_nik,t − q_nok,t) + ε_ikt
  - Country fixed effects dummies (E_i) and country-specific time trends proxy ln(Υ_ik / Υ_ok) and other omitted variables.
  - q_nik,t − q_nok,t: difference in relative product quality between country i and Germany in sector k at time t.
  - w_it: measured as country i’s marginal product of labor divided by the average quality across product-lines.
- Lagged quality (q_nik,t−1 − q_nok,t−1) used in robustness checks to address potential endogeneity.

### Estimation outcomes (summary statistics)
- Number of observations available varies from 104 to 246 depending on sector.
- Fit (R-squared) ranges from 0.61 to 0.97 across sectors (in lagged-quality appendix results).
- Estimated coefficients for quality (ˆγ_k5):
  - Significant at standard levels for 60.0% of the products (main specification).
  - Sign is positive in 77.8% of the significant cases (main specification).
  - Interpretation: evidence that quality upgrading and exports move together in 46.7% of the products (main specification).
- Notable data treatment: for product line 84, observations for the years 1970 to 1972 were treated as outliers and eliminated (inclusion raised coefficient from 4.15 to 8.00 and caused overprediction).

### Prediction method and fit measures
- Prediction (equation (20)):
  - ˆS_nik,t+1 = [ e^{ˆγ_k5 [(q_nik,t+1 − q_nik,t) − (q_nok,t+1 − q_nok,t)]} X_nik,t ] / Σ_{v∈K} [ e^{ˆγ_v5 [(q_niv,t+1 − q_niv,t) − (q_nov,t+1 − q_nov,t)]} X_niv,t ]
- Predicted and actual increases in export shares from t to t+1:
  - ˆI_nik,t+1 = ˆS_nik,t+1 − S_nik,t
  - I_nik,t+1 = S_nik,t+1 − S_nik,t
- Overall fit assessed via pseudo-R^2 (equation (21)) and weighted-R^2 (equation (22)):
  - pseudo-R^2 = 1 − [ Σ_{k∈K} Σ_{τ∈Ψ} (I*_nik(τ) − ˆI*_nik(τ))^2 ] / [ Σ_{k∈K} Σ_{τ∈Ψ} (I*_nik(τ))^2 ]
  - weighted-R^2 = 1 − [ Σ_{k∈K} Σ_{τ∈Ψ} S*_nik(τ) (I*_nik(τ) − ˆI*_nik(τ))^2 ] / [ Σ_{k∈K} Σ_{τ∈Ψ} S*_nik(τ) [I*_nik(τ)]^2 ]
- Seven subsamples for fit measurement:
  - Five cross sections: 1970—2010; 1970—1979; 1980—1989; 1990—1999; 2000—2010.
  - Two panels: Ψ = {1970—1989, 1990—2010}; Ψ = {1970—1979, 1980—1989, 1990—1999, 2000—2010}.
- Rationale: comparing different time horizons assesses whether longer commitment to quality upgrading matters for significant improvements in export volumes.

### Empirical patterns and diagnostics (selected country summaries and fit statistics)
- General diagnostics:
  - Quality index (export-weighted average) rises over time in all economies; Indonesia and Malaysia show a U-shape.
  - Quality converges towards the frontier (equals 1 by construction) in all countries except Malaysia during the last decade.
  - Germany remains very close to the quality frontier at all times.
  - Marginal productivity of labor rises rapidly in Asia; China saw particularly rapid productivity growth; India was a relatively weak performer.
  - Germany, South Korea and Malaysia, in that order, enjoy higher productivity levels than the other countries.

- China (1970—2010 and subsamples):
  - Pseudo-R^2 = 0.534; Weighted-R^2 = 0.649 (1970—2010).
  - 1990 split: pseudo-R^2 = 0.316; weighted-R^2 = 0.416.
  - Decades: pseudo-R^2 = 0.166; weighted-R^2 = 0.244.
  - Decade cross sections:
    - 1970-1979: pseudo-R^2 = -0.015; weighted-R^2 = -0.022
    - 1980-1989: pseudo-R^2 = 0.141; weighted-R^2 = 0.151
    - 1990-1999: pseudo-R^2 = 0.203; weighted-R^2 = 0.128
    - 2000-2010: pseudo-R^2 = 0.504; weighted-R^2 = 0.660
  - Additional facts:
    - Largest exporters (shares above 6 percent) during 1970—2010: sectors 84, 89, 72, 65, 33, 71.
    - 24 industries (40 percent) showed positive increases in export share; 49 industries (82 percent) increased relative quality.
    - No industry with relative quality decline experienced an increase in export share.
    - Model predicted about half of the observed change for largest variations (sectors 65, 71, 72); some sectors (e.g., 26, 85) not well predicted.

- India:
  - Export shares above 6 percent in 1970—2010: industries 66, 65, 84 and 28.
  - 36 products (60 percent) show positive increases in export share between 1970 and 2010.
  - 45 products (75 percent) experienced increases in average relative quality.
  - Full-period cross section: pseudo-R^2 = 0.026; weighted-R^2 = 0.048.
  - Subsamples: pseudo-R^2 = 0.058 (1990 split) and pseudo-R^2 = 0.032 (Decades).
  - Decade cross sections: 1970s pseudo-R^2 = 0.157 and weighted-R^2 = 0.172; 1990s pseudo-R^2 = 0.162 and weighted-R^2 = 0.240.
  - Conclusion: quality upgrading correlated with export-share changes in some decades, but correlation becomes negligible over 40-year averages.

- Indonesia:
  - Petroleum (industry 33) and gas (sector 34) accounted for 41.5 percent of total exports (1970—2010 average).
  - 25 industries (42 percent) experienced average positive increases in both relative quality and export share; 11 products (18 percent) had both variables negative.
  - Predictions mostly have the right sign but tend to underestimate changes; some sectors (e.g., 34) show overprediction; sectors 71 and 72 predictions go in the wrong direction.
  - Goodness-of-fit: pseudo-R^2 = 0.070 (1970—2010), 0.097 (1990 split), 0.069 (Decades); weighted-R^2 = 0.069, 0.208, 0.178 respectively.
  - Explanatory power unstable across decades; strong in the 1970s and 1980s, disappears in the 1990s and 2000s.

- Malaysia:
  - Sector 72 (electrical machinery) average share = 24 percent (1970—2010).
  - 73 percent of sectors achieved positive average annual increases in relative quality; 53 percent achieved positive increases in export share (1970—2010).
  - Full-period fit: pseudo-R^2 = 0.389; weighted-R^2 = 0.486.
  - Panel subsamples: pseudo-R^2 explains 19.6 percent (1990 split) and 8.6 percent (Decades).
  - Decade cross sections: 1970s pseudo-R^2 = 0.162 and weighted-R^2 = 0.038; 1990s pseudo-R^2 = 0.502 and weighted-R^2 = 0.581.
  - Interpretation: long commitment to quality upgrading necessary to achieve strong export-volume benefits.

- South Korea:
  - 51 sectors (85 percent) show a rise in relative quality.
  - Sector 72 average export share = 20.6 percent (1970—2010). Sectors 71, 72 and 73 account for about 35 percent of total exports.
  - Full-period fit: pseudo-R^2 = 0.455; weighted-R^2 = 0.504 (1970—2010).
  - 1990 split: pseudo-R^2 = 0.319; weighted-R^2 = 0.455.
  - Decades: pseudo-R^2 = 0.134; weighted-R^2 = 0.171.
  - 2000—2010 cross section: pseudo-R^2 = 0.336; weighted-R^2 = 0.560.
  - Conclusion: quality upgrading has yielded high explanatory power for export-share changes; consistent benefits across decades.

- Thailand:
  - Machinery (sectors 71 and 72) combined export share = 20.8 percent (1970—2010).
  - Three agriculture/fishing products had export shares above 6 percent: sectors 3, 4 and 5.
  - Over 50 percent of industries increased export share 1970—2010; 77 percent saw positive quality upgrading.
  - 28 industries show positive increases in both relative quality and export share; 10 show the opposite — 63 percent of sectors suggest a positive relationship.
  - Full-period fit: pseudo-R^2 = 0.455; weighted-R^2 = 0.504 (1970—2010).
  - 1990-split panel: pseudo-R^2 = 0.176; weighted-R^2 = 0.192.
  - Decades panel: pseudo-R^2 = 0.087; weighted-R^2 = 0.088.
  - Within-decade evidence: 1970s, 1980s, and 1990s contributed importantly to the positive correlation; 1980s and 1990s show >25 percent of within-decade variation explained by changes in relative quality.

### Robustness: lagged-quality specification
- Replace contemporaneous quality change with lagged change q_nik,t−1 − q_nok,t−1 in regression (19); estimate by OLS using only non-zero export data; compute predictions and pseudo-R^2 / weighted-R^2 as before.
- Appendix (Table A) sector-level lagged-quality estimates:
  - Number of observations per sector ranges from 99 to 240.
  - Coefficient of determination R2 ranges from 0.65 to 0.97 across sectors.
  - Estimated coefficients significant for 58.3% of products; positive sign in 74.3% of significant cases.
  - Evidence of quality and export rising together in 43.3% of products under the lagged specification.
  - Industries 00—43 (more commodity-exposed) vs sectors 51—96 (less commodity-reliant): significance of estimated coefficients occurs for 48.1% vs 66.7% of products, and quality and exports rise together in 37.0% vs 48.5% respectively.
- Aggregate fit generally falls slightly relative to main results; Indonesia shows clearest deterioration (quality upgrading has almost no role except in the 1970s cross section). Main findings for other countries remain robust.

### Conclusion and policy implications
- Main empirical conclusion:
  - Quality upgrading is a key factor in explaining changes in sectoral export shares in China, Malaysia, South Korea, and Thailand. In India and Indonesia the role of quality upgrading is less critical, reflecting sectoral structures (commodities in Indonesia; services-driven growth in India while the dataset covers goods only).
- Policy implications:
  - Efforts directed to improve product quality can potentially offer a high return to expand exports.
  - Because other factors (input costs, productivity) also impact export performance and their relative contributions vary across countries, quality upgrading should be pursued preferably when the quality ladder is sufficiently long.
  - A long-term commitment to quality upgrading lasting several years seems necessary to achieve a significant impact on export volumes.

*Source: wpiea2019259-print-pdf - Section 5 concludes (and Section 3.1 "Methodology and data").*

### Section 5 concludes.

### Section 5 concludes.

### The Model — overview
- Static Ricardian framework extending Eaton-Kortum (EK) to incorporate: multiple sectors, product-level quality, and intensive, extensive, and quality margins of trade.
- Driving mechanism: heterogeneity in quality and efficiency across export lines and countries determines export levels.

### Consumers (preferences and demand)
- Representative-agent utility aggregation:
  - c_n = [ Σ_{k=1}^K ω_k^{1/ε} c_nk^{1−1/ε} ]^{ε/(ε−1)}  (equation (1))
  - c_nk = [ ∫_0^1 e^{β_k q_nk} c_nk(j)^{1−1/η_k} dj ]^{η_k/(η_k−1)}  (equation (2))
  - Budget: w_n = Σ_{k=1}^K ∫_0^1 p_nk(j) c_nk(j) dj  (equation (3))
- Key parameters and roles:
  - β_k: sector-specific parameter multiplying quality q_nk in utility weights.
  - ε, η_k > 0: elasticity of substitution between sectors and within sector-k, respectively.
  - ω_k > 0: sector-k weight in utility.
- First-order conditions (demand):
  - Intra-sector: e^{β_k q_nk} c_nk(j) / c_nk = [ p_nk(j) / e^{β_k q_nk} P_nk ]^{−η_k}  (equation (4))
  - Inter-sector: c_nk / c_n = ω_k ( P_nk / P_n )^{−ε}  (equation (5))
- Quality-adjusted price indices:
  - P_nk = [ ∫_0^1 ( p_nk(j) e^{β_k q_nk} )^{1−η_k} dj ]^{1/(1−η_k)}  (equation (6))
  - P_n = [ Σ_{k=1}^K ω_k P_nk^{1−ε} ]^{1/(1−ε)}  (equation (7))
- Interpretation:
  - Consumers care about effective units of quality e^{β_k q_nk} c_nk(j); relevant decision variable is price per unit of effective quality p_nk(j)/e^{β_k q_nk}.
  - Lower price-to-quality ratio increases demand; both intra- and inter-sector aggregations use prices adjusted for quality.

### Producers (technology and pricing)
- Output function for good j in sectork produced in countryn:
  - Y_nk(j) = z_nk(j) L_nk(j) e^{α_k q_nk}  (equation (8))
  - L_nk(j): labor input; z_nk(j): efficiency draw; α_k: sector-specific parameter for cost impact of quality.
- Under perfect competition, free-on-board producer price from country i sold to n:
  - p_nik(j) = e^{α_k q_nik} w_i / z_ik(j)  (equation (9))
- Distinction:
  - Producer price p_nik(j) can differ from consumer price p_nk(j) (e.g., trade costs).
  - Quality at origin q_nik can differ from quality consumed q_nk in destination.

### Trade (stochastic productivity and bilateral patterns)
- Efficiency draws:
  - z_nk(j) ~ Fréchet with F_nk(z) = exp(−Υ_nk z^{−θ_k})  (equation (10))
  - Υ_nk > 0: scale parameter (technology level, absolute advantage).
  - θ_k > 1: shape parameter (degree of efficiency heterogeneity); lower θ_k → larger heterogeneity → stronger comparative advantage effects.
- Iceberg trade costs:
  - For each unit shipped from i to n in sectork, only 1/d_nik units arrive; d_nnk = 1.
- Price per unit of effective quality from origin i to destination n:
  - p_nik(j) / e^{β_k q_nik} = w_i / z_ik(j) e^{(α_k − β_k) q_nik}  (equation (11))
  - For higher-quality goods to be preferred, require β_k > α_k (utility effect dominates cost effect); if β_k < α_k, higher quality hurts exports.
- Consumer price-to-quality ratio is the minimum across origins:
  - p_nk(j) / e^{β_k q_nk} = min_{i=1,...,N} [ d_nik w_i / z_ik(j) e^{(β_k − α_k) q_nik} ]  (equation (12))
- Distribution of price-to-quality ratios:
  - Origin-conditional: G_nik(ρ) = 1 − F_ik( d_nik w_i ρ e^{(β_k − α_k) q_nik} )  (equation (13))
  - Unconditional (what country n actually buys): G_nk(ρ) = 1 − exp(−Φ_nk ρ^{θ_k})  (equation (14))
  - Φ_nk = Π_{i=1}^N Υ_ik [ d_nik w_i e^{(β_k − α_k) q_nik} ]^{−θ_k}
- Sector price index in closed form:
  - P_nk = γ_k Φ_nk^{−1/θ_k}, with γ_k = Γ( (θ_k + 1 − η_k)/θ_k )^{1/(1−η_k)}  (equation (15)), η_k < 1 + θ_k
- Probability that country i provides the best price adjusted for quality in sectork to n:
  - π_nik = Υ_ik [ d_nik w_i e^{(β_k − α_k) q_nik} ]^{−θ_k} / Φ_nk  (equation (16))
  - π_nik depends on geographical barriers d_nik, input prices w_i, technology Υ_ik, and quality q_nik.
- Bilateral trade value relation:
  - Share of countryn’s spending on industry k from source i equals π_nik:
    - X_nik P_nk c_nk L_n = π_nik  (equation (17))
  - Implies fraction of goods purchased from i equals probability i is lowest price-to-quality supplier; law of large numbers ensures spending share equals π_nik.

### Exports and Quality Across Asian Nations (empirical strategy)
- Objective: assess contribution of changes in product quality to evolution of exports across 2-digit sectors for six Asian nations: China, India, Indonesia, Malaysia, South Korea, and Thailand.
- Methodology notes:
  - Generate model predictions by sector and compare to data.
  - Assess capacity of quality to predict export changes averaged over different time intervals (from a decade to entire sample) to reduce measurement bias and business cycle effects.
  - Focus on export shares (sectoral shares) rather than aggregate exports to minimize country-specific unobservables and to identify sectors gaining or losing importance.
- Contextual statistics:
  - Average annual growth rates (1970—2010): China 9.4 percent, India 5.6 percent, Indonesia 5.4 percent, Malaysia 7.7 percent, South Korea 6.5 percent, Thailand 6.1 percent.
  - Note: other Asian economies with similar growth rates in 1970—2010 include Singapore (7.6%), Hong Kong (6.1%), Vietnam (6.5%), and Cambodia (5.5%); Singapore and Hong Kong excluded because average quality levels already too close to the frontier in 1985.

*Source: wpiea2019259-print-pdf - Section 5 concludes.*

### 3.1  Methodology and data

### 3.1  Methodology and data

### Data coverage and choices
- Exports and quality numbers: SITC, revision 1, at the two digit level; total of 60 product lines from 1962 to 2010.
- Main analysis time interval: 1970—2010 (quality available for Germany only from 1970 onwards).
- One product line discarded: product 35 (electric energy) — eliminated because only 18 observations were available.
- Reference country (nation o): Germany (DEU); destination economy (n): the rest of the world.
- Exports volumes: Comtrade mirror data (CIF exports reported by the destination country / importer).
- Quality index: from Henn et al. (2017), downloaded from the Export Diversification and Quality Databases at the IMF.
- Wages proxy: economy-wide marginal product of labor calculated from employment, labor shares and nominal GDP values from PWT 8.0.
- Assumption on trade costs to the rest of the world: d_nik / d_nok = 1.
- Zero-export observations excluded from estimation because the quality index is not available for those cases.

### Parameter assignment and identification
- Previous estimates in the literature not used because this study focuses on SITC two-digit sectors while other papers use classifications (e.g., ISIC) for which domestic production numbers are available.
- To avoid converting ISIC to SITC (and thereby losing time-series length), a version of the Eaton and Kortum-derived expressions that does not require domestic production and demand is used.
- Key model expression linking relative sector-k exports from country i and reference country o (equation numbers preserved from source): equation (18) is used to generate predictions using relative values and country o’s export numbers.

### Regression specification and estimation
- Panel of six Asian countries used to estimate, for each 2-digit sector k, the regression (equation (19)):
  - ln (X_nik,t / X_nok,t) = γ_k0 + γ_k1i E_i + γ_k3i t + γ_k4 ln (w_it / w_ot) + γ_k5 (q_nik,t − q_nok,t) + ε_ikt
  - Country fixed effects dummies (E_i) and country-specific time trends proxy log(Υ_ik / Υ_ok) and other omitted variables.
  - q_nik,t − q_nok,t: difference in relative product quality between country i and Germany in sector k at time t.
  - w_it: measured as country i’s marginal product of labor divided by the average quality across product-lines.
- Regression estimated by OLS using only non-zero export data.
- Lagged quality (q_nik,t−1 − q_nok,t−1) is used later in Robustness to address potential endogeneity.

### Estimation outcomes (summary statistics from Table 1)
- Number of observations available varies from 104 to 246 depending on sector.
- Fit (R-squared) ranges from 0.61 to 0.97 across sectors.
- Estimated coefficients for quality (ˆγ_k5):
  - Significant at standard levels for 60.0% of the products.
  - Sign is positive in 77.8% of the significant cases.
  - Interpretation: evidence that quality upgrading and exports move together in 46.7% of the products.
- Notable data treatment: for product line 84, observations for the years 1970 to 1972 were treated as outliers and eliminated (inclusion raised coefficient from 4.15 to 8.00 and caused overprediction).

### Prediction method
- Using estimates ˆγ_k5 (an estimate of θ_k (β_k − α_k)), predicted export shares to the rest of the world for product k in economy i at t+1 are computed from equation (20):
  - ˆS_nik,t+1 = [ e^{ˆγ_k5 [(q_nik,t+1 − q_nik,t) − (q_nok,t+1 − q_nok,t)]} X_nik,t ] / Σ_{v∈K} [ e^{ˆγ_v5 [(q_niv,t+1 − q_niv,t) − (q_nov,t+1 − q_nov,t)]} X_niv,t ]
- Predicted and actual increases in export shares from t to t+1:
  - ˆI_nik,t+1 = ˆS_nik,t+1 − S_nik,t
  - I_nik,t+1 = S_nik,t+1 − S_nik,t

### Fit measures and subsamples
- Overall fit assessed via a pseudo-R^2 (equation (21)):
  - pseudo-R^2 = 1 − [ Σ_{k∈K} Σ_{τ∈Ψ} (I*_nik(τ) − ˆI*_nik(τ))^2 ] / [ Σ_{k∈K} Σ_{τ∈Ψ} (I*_nik(τ))^2 ]
  - Ψ is the set of periods; I*_nik(τ) and ˆI*_nik(τ) represent averages of I_nik,t and ˆI_nik,t in period τ.
  - Pseudo-R^2 bounded above by one, not bounded below; choosing changes in export shares with mean close to zero reduces likelihood of negative values.
- Weighted-R^2 (equation (22)) multiplies each sectoral squared-error by its average sectoral export-share S*_nik(τ):
  - weighted-R^2 = 1 − [ Σ_{k∈K} Σ_{τ∈Ψ} S*_nik(τ) (I*_nik(τ) − ˆI*_nik(τ))^2 ] / [ Σ_{k∈K} Σ_{τ∈Ψ} S*_nik(τ) [I*_nik(τ)]^2 ]
- Seven subsamples for fit measurement:
  - Five cross sections: 1970—2010; 1970—1979; 1980—1989; 1990—1999; 2000—2010 (each Ψ composed of one element).
  - Two panels: Ψ = {1970—1989, 1990—2010} (two twenty-year periods split around 1990); Ψ = {1970—1979, 1980—1989, 1990—1999, 2000—2010} (four decades).
- Rationale: comparing different time horizons assesses whether longer commitment to quality upgrading matters for significant improvements in export volumes.

### Empirical patterns and diagnostic observations (as described for sample countries)
- Figure 1 observations (quality and marginal productivity over time):
  - Quality index (export-weighted average) rises over time in all economies; Indonesia and Malaysia show a U-shape.
  - Quality converges towards the frontier (equals 1 by construction) in all countries except Malaysia during the last decade.
  - Germany remains very close to the quality frontier at all times.
  - Marginal productivity of labor rises rapidly in Asia; China saw particularly rapid productivity growth; India was a relatively weak performer.
  - Germany, South Korea and Malaysia, in that order, enjoy higher productivity levels than the other countries.
- Example results for China (summary from Figure 2):
  - For 1970—2010:
    - Pseudo-R^2 = 0.534
    - Weighted-R^2 = 0.649
  - Decade and split-period fits decline relative to the 40-year horizon (table entries for China):
    - 1990 split: pseudo-R^2 = 0.316; weighted-R^2 = 0.416
    - Decades: pseudo-R^2 = 0.166; weighted-R^2 = 0.244
    - 1970-1979: pseudo-R^2 = -0.015; weighted-R^2 = -0.022
    - 1980-1989: pseudo-R^2 = 0.141; weighted-R^2 = 0.151
    - 1990-1999: pseudo-R^2 = 0.203; weighted-R^2 = 0.128
    - 2000-2010: pseudo-R^2 = 0.504; weighted-R^2 = 0.660
  - Empirical notes for China:
    - Largest exporters (shares above 6 percent) during 1970—2010: sectors 84, 89, 72, 65, 33, 71.
    - 24 industries (40 percent) showed positive increases in export share; 49 industries (82 percent) increased relative quality.
    - No industry with relative quality decline experienced an increase in export share.
    - Many commodity-related sectors increased quality but did not increase shares (e.g., 1, 2, 4).
    - Model predicted about half of the observed change for largest variations (sectors 65, 71, 72); some sectors (e.g., 26, 85) not well predicted.

*Source: Section 3.1 "Methodology and data" from the provided IMF content unit (wpiea2019259-print-pdf).*

### 0.316 and 0.416, respectively, when we focus on 20-year periods (denoted by “1990

### wpiea2019259-print-pdf - 0.316 and 0.416, respectively, when we focus on 20-year periods (denoted by “1990

### Summary of the paper
- The paper extends a Ricardian trade model (Eaton and Kortum (2002)) to incorporate sectoral heterogeneity and changes in product quality, and estimates the impact of product-quality upgrading on sectoral export shares using 2-digit SITC data for six fast-growing Asian economies during 1970—2010: China, India, Indonesia, Malaysia, South Korea and Thailand.
- The empirical approach uses sectoral changes in relative quality to predict changes in sectoral export shares and evaluates fit using pseudo-R2 and weighted-R2 measures.
- Key high-level quantitative statements from the analysis:
  - 0.316 and 0.416, respectively, when we focus on 20-year periods (denoted by “1990 split”) and 0.166 and 0.244 when we assess the fit using decades (denoted by “Decades”).
  - In the lagged-quality robustness exercise, estimated R2 values go from 0.65 to 0.97 across sectors; estimated coefficients are significant for 58.3% of products, with positive sign in 74.3% of significant cases, yielding evidence of quality and exports moving together in 43.3% of products.

### Country-by-country empirical findings
- China
  - Quality upgrading impact is more evident over longer horizons; fit decreases when using shorter averaging horizons, suggesting a long-term view is necessary for quality strategies.
  - For period 2000—2010 after China joined the World Trade Organization, pseudo-R2 = 0.504 and weighted-R2 = 0.660.

- India
  - Export shares above 6 percent in 1970—2010: industries 66, 65, 84 and 28.
  - 36 products (60 percent) show positive increases in export share between 1970 and 2010.
  - 45 products (75 percent) experienced increases in average relative quality.
  - Full-period cross section: pseudo-R2 = 0.026 and weighted-R2 = 0.048.
  - Subsamples: pseudo-R2 = 0.058 (1990 split) and pseudo-R2 = 0.032 (Decades).
  - Decade cross sections: 1970s pseudo-R2 = 0.157 and weighted-R2 = 0.172; 1990s pseudo-R2 = 0.162 and weighted-R2 = 0.240.
  - Conclusion: quality upgrading correlated with export-share changes in some decades, but correlation becomes negligible over 40-year averages.

- Indonesia
  - Heavily commodity-reliant: petroleum (industry 33) and gas (sector 34) accounted for 41.5 percent of total exports (1970—2010 average).
  - During 1970—2010, 25 industries (42 percent) experienced average positive increases in both relative quality and export share; 11 products (18 percent) had both variables negative.
  - Predictions mostly have the right sign but tend to underestimate changes; some sectors (e.g., 34) show overprediction; sectors 71 and 72 predictions go in the wrong direction.
  - Goodness-of-fit: pseudo-R2 = 0.070 (1970—2010), 0.097 (1990 split), 0.069 (Decades); weighted-R2 = 0.069, 0.208, 0.178 respectively.
  - The explanatory power is unstable across decades; strong in the 1970s and 1980s, disappears in the 1990s and 2000s.

- Malaysia
  - Sector 72 (electrical machinery) average share = 24 percent (1970—2010), more than double any other sector.
  - 73 percent of sectors achieved positive average annual increases in relative quality; 53 percent achieved positive increases in export share (1970—2010).
  - Full-period fit: pseudo-R2 = 0.389 and weighted-R2 = 0.486.
  - Panel subsamples: pseudo-R2 explains 19.6 percent (1990 split) and 8.6 percent (Decades) of export-share variation.
  - Decade cross sections: 1970s pseudo-R2 = 0.162 and weighted-R2 = 0.038; 1990s pseudo-R2 = 0.502 and weighted-R2 = 0.581.
  - Interpretation: long commitment to quality upgrading necessary to achieve strong export-volume benefits.

- South Korea
  - 51 sectors (85 percent) show a rise in relative quality (largest share across sample countries).
  - Sector 72 average export share = 20.6 percent (1970—2010). Sectors 71, 72 and 73 account for about 35 percent of total exports.
  - Full-period fit: pseudo-R2 = 0.455 and weighted-R2 = 0.504 (1970—2010).
  - 1990 split: pseudo-R2 = 0.319 and weighted-R2 = 0.455.
  - Decades: pseudo-R2 = 0.134 and weighted-R2 = 0.171.
  - 2000—2010 cross section: pseudo-R2 = 0.336 and weighted-R2 = 0.560.
  - Conclusion: quality upgrading has yielded high explanatory power for export-share changes; consistent benefits across decades.

- Thailand
  - Machinery (sectors 71 and 72) combined export share = 20.8 percent (1970—2010).
  - Three agriculture/fishing products had export shares above 6 percent: sectors 3, 4 and 5.
  - Over 50 percent of industries increased export share 1970—2010; 77 percent saw positive quality upgrading.
  - 28 industries show positive increases in both relative quality and export share; 10 show the opposite — 63 percent of sectors suggest a positive relationship.
  - Full-period fit: pseudo-R2 = 0.455 and weighted-R2 = 0.504 (1970—2010).
  - 1990-split panel: pseudo-R2 = 0.176 and weighted-R2 = 0.192.
  - Decades panel: pseudo-R2 = 0.087 and weighted-R2 = 0.088.
  - Within-decade evidence: 1970s, 1980s, and 1990s contributed importantly to the positive correlation; 1980s and 1990s show >25 percent of within-decade variation explained by changes in relative quality.

### Robustness: lagged-quality specification
- Approach: estimate regression (19) replacing contemporaneous quality change q_nik,t − q_nok,t with lagged change q_nik,t−1 − q_nok,t−1 to estimate coefficient γ_k5, assuming last year’s product quality determines this year’s exports. Estimation by OLS using only non-zero export data; predictions and pseudo-R2 / weighted-R2 computed as before.
- Table A (appendix) reports sector-level lagged-quality estimates:
  - Number of observations per sector ranges from 99 to 240.
  - Coefficient of determination R2 ranges from 0.65 to 0.97 across sectors.
  - Estimated coefficients significant for 58.3% of products; positive sign in 74.3% of significant cases.
  - Evidence of quality and export rising together in 43.3% of products under the lagged specification.
  - Industries 00—43 (more commodity-exposed) vs sectors 51—96 (less commodity-reliant): significance of estimated coefficients occurs for 48.1% vs 66.7% of products, and quality and exports rise together in 37.0% vs 48.5% respectively.
- Aggregate fit generally falls slightly relative to main results; Indonesia shows the clearest deterioration (quality upgrading has almost no role except in the 1970s cross section). Main findings for other countries remain robust.

### Conclusion and policy implications
- Main empirical conclusion:
  - Quality upgrading is a key factor in explaining changes in sectoral export shares in China, Malaysia, South Korea, and Thailand. In India and Indonesia the role of quality upgrading is less critical, reflecting sectoral structures (commodities in Indonesia; services-driven growth in India while the dataset covers goods only).
- Policy implications (as stated by the authors):
  - Efforts directed to improve product quality can potentially offer a high return to expand exports.
  - Because other factors (input costs, productivity) also impact export performance and their relative contributions vary across countries, quality upgrading should be pursued preferably when the quality ladder is sufficiently long.
  - A long-term commitment to quality upgrading lasting several years seems necessary to achieve a significant impact on export volumes.

*Source: wpiea2019259-print-pdf (chapter/section content extracted from the provided PDF).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019259-print-pdf.pdf_