## _wp04145

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---

### Key context and data coverage
- Periods and magnitudes:
  - During 1970–2001, Korea’s real per capita GDP grew by five-fold.
  - Export volume grew by about 9,800 percent during 1970–2001.
  - Import volume grew by about 2,400 percent during 1970–2001.
  - In 2002, the share of Korean exports in total world exports was 2.5 percent (double the level in 1979).
  - In 2002, the share of Korean imports in total world imports was 2.4 percent (two and a half times the 1979 level).
- Reestimation sample used in this paper: 1988–2001.
- Comparative prior estimates cited:
  - Bayoumi (1996), annual data 1974–93: income elasticity = 3.1; price elasticity = -0.7.
  - Giorgianni and Milesi-Ferretti (1997), quarterly data 1970–95: income elasticity = 3.2; price elasticity = -2.0.
  - Prior studies for imports: income elasticity around 1.5.

### Main findings on exports (aggregate and by product type)
- Aggregate changes in elasticities (1988–2001 reestimation):
  - The income elasticity of export demand has fallen considerably.
  - The price elasticity of Korea’s export demand has risen dramatically.
- Role of export composition:
  - The shift toward electrical and electronic products (EEPs) is the main factor behind:
    - The large decline in the income elasticity of exports.
    - The large increase in the price elasticity of exports.
- Elasticity patterns by product type (1988–2001):
  - EEPs:
    - Income elasticity: 0.51 (Table 3).
    - Price elasticity: -1.42 (Table 3).
    - Exhibit a low income elasticity and a high price elasticity.
  - Non-EEPs:
    - Income elasticity: 2.52 (Table 3).
    - Price elasticity: 0.51 (Table 3).
    - Exhibit a high income elasticity and a low price elasticity.
  - Total exports (1988–2001): income elasticity = 1.00; price elasticity = -1.46 (Table 2 and Table 3).
- Long-run export demand estimates (selected exact values from Table 2):
  - 1974–87: income elasticity = 3.07; price elasticity = -0.18; R^2 = 0.95; AR(4) p-value <0.01; White p-value = 0.13; ECM_t-1 = -0.62; Number of observations = 54. Standard errors: (0.24)(0.23)(0.13).
  - 1988–2001: income elasticity = 1.00; price elasticity = -1.46; R^2 = 0.99; AR(4) p-value <0.01; White p-value = 0.72; ECM_t-1 = -0.19; Number of observations = 52. Standard errors: (0.70)(0.37)(0.05).
  - 1974–2001: income elasticity = 2.59; price elasticity = -0.17; R^2 = 0.97; AR(4) p-value <0.01; White p-value = 0.05; ECM_t-1 = -0.23; Number of observations = 106. Standard errors: (0.11)(0.13)(0.06).
- Interpretation:
  - The recent changes in long-run elasticities of total export demand are mainly due to the increase in the share of EEPs in total exports.
  - The decline in income elasticity is consistent with Krugman’s “45 degree rule” (Krugman (1989)): fast-growing countries face high income elasticities for exports, whereas slower-growing countries face lower income elasticities.

### Supply-side analysis for EEPs — theoretical motivation and empirical evidence
- Motivation and puzzle:
  - Puzzle: Why is the price elasticity of EEPs exports high while its income elasticity is low?
  - Rejected simple "luxury good" explanation (would imply high income elasticity).
  - Proposed explanation: the estimated relation for EEPs may be identifying a supply function rather than demand.
- Theoretical framework (summary of key assumptions and implications):
  - Export demand assumed perfectly elastic (price taker).
  - Increasing returns to scale exist at the industry level but are external to the representative firm (positive spillovers: learning-by-doing, technological innovations).
  - Aggregate production X = ∫_0^N X_j dj; firm cost C_j = C_j(X_j, X) = φ_j(X_j) ξ(X) with properties 0 < ξ'(X), 0 < φ_j'(X_j), 0 < φ_j''(X_j).
  - If positive external effects of increasing returns at industry level outweigh the increasing marginal cost faced by each firm (condition summarized as εα <−1 in source notation), the industry supply curve can be negatively sloped.
  - Economic implication: external increasing returns can generate a negatively-sloped industry supply curve while firms individually remain price takers.
- Empirical supply-side indicators for EEPs:
  - A steep decline in EEP export unit prices suggests supply-side, not demand-side, explanations in the standard model.
  - Exports of EEPs are strongly cointegrated with total factor productivity (TFP) and potential output.
  - Evidence indicates the existence of increasing returns to scale in EEP production.
- Contrast with non-EEPs:
  - No strong link found between exports of non-EEPs and TFP.
  - Production of non-EEPs shows no evidence of increasing returns to scale.

### Empirical export supply model specification and results (1988–2001)
- Supply model specification:
  - X = f(P, W, TFP, pY) where:
    - P is the export unit price (in Korean won for supply regressions).
    - W is factor prices (real wage index in won).
    - TFP is total factor productivity.
    - pY is potential output (GDP filtered by Hodrick-Prescott).
- Data notes:
  - Export prices: unit value of exports in terms of Korean won.
  - W: real wage index of Korean workers, expressed in won.
  - pY: potential output is GDP of Korea filtered by the Hodrick-Prescott method.
  - TFP: data obtained from Zebregs (2003).
- Long-run export supply estimates (Table 4 exact values):
  - EEPs (1988–2001): p = -1.18; w = -1.26; t f p = 1.49; y p = 2.74; R^2 = 0.99; AR(4) p-value = 0.36; White p-value = 0.40; ECM_t-1 = -0.67; Number of observations = 52. Standard errors: (0.12)(0.42)(0.40)(0.51)(0.13).
  - Non-EEPs (1988–2001): p = -0.79; w = -3.79; t f p = -0.69; y p = 5.28; R^2 = 0.92; AR(4) p-value <0.01; White p-value = 1.00; ECM_t-1 = -0.23; Number of observations = 52. Standard errors: (1.09)(2.00)(0.65)(2.52)(0.11).
  - Total (1988–2001): p = -0.28; w = -1.93; t f p = 1.17; y p = 3.59; R^2 = 0.99; AR(4) p-value <0.01; White p-value = 0.53; ECM_t-1 = -0.18; Number of observations = 52. Standard errors: (0.53)(0.85)(0.47)(1.22)(0.06).
- Empirical interpretation:
  - EEPs exports: significant relations with all explanatory variables; strong positive relation with TFP and Korea’s potential GDP; strong negative relation with unit price of EEP exports — consistent with increasing returns to scale, technological progress, and other positive spillovers at industry level.
  - Non-EEPs: TFP not significant; price elasticity not significant — production of non-EEPs may exhibit constant returns to scale.
  - Total exports: mixed results.

### Imports — standard and extended specifications and results
- Standard import demand specification:
  - M = f( Y, r ) where r ≡ Pm / P and Pm is unit price of Korean imports; P is general price level (CPI).
  - Data: Korean seasonally-adjusted GDP for income; CPI for general price level.
- Long-run import demand estimates (Table 5 exact values):
  - 1974–87: income elasticity = 1.22; price elasticity = -0.65; R^2 = 0.97; AR(4) p-value <0.01; White p-value = 0.78; ECM_t-1 = -0.43; Number of observations = 54. Standard errors: (0.05)(0.16)(0.09).
  - 1988–2001: income elasticity = 1.60; price elasticity = -0.19; R^2 = 0.98; AR(4) p-value <0.01; White p-value = 0.77; ECM_t-1 = -0.26; Number of observations = 55. Standard errors: (0.06)(0.14)(0.10).
  - 1974–2001: income elasticity = 1.31; price elasticity = -0.49; R^2 = 0.99; AR(4) p-value <0.01; White p-value = 0.96; ECM_t-1 = -0.29; Number of observations = 109. Standard errors: (0.04)(0.16)(0.06).
- Interpretation:
  - Income elasticity of import demand has risen slightly; overall estimates stable and broadly consistent with previous studies.
- Alternative import model with multiple scale and price variables:
  - Rationale: Korean imports composed of consumer imports (Mc) and capital imports (Mk); consumer imports depend on Pmc, Pc, and consumption C; capital imports depend on Pmk, Pk, and a targeted production level depending on C, I, and X.
  - Functional form preserved in source: ),,,,,,(),,,,(),,( X I C P P P P M X I C P M M C P P M M C kmkcmckmkkcmcc =+=. Relative-price rewrite: ),,,/,/( X I C P P P M M kmkcmc =.
  - Data: price of imported consumer and capital goods from Korea Customs Service; domestically-produced consumer goods = CPI; domestically-produced capital goods = Producers’ Price Index (PPI); Investment = gross fixed capital formation. All scale variables are real quantities.
- Long-run results with multiple scale and price variables (Table 6 exact values):
  - Coefficients: c = 0.47; i = 0.40; x = 0.35; p_m_c = -0.22; r_p_m_k = -0.30; R^2 = 1.00; AR(4) p-value = 0.38; White p-value = 0.62; ECM_t-1 = -0.76; Number of observations = 56. Standard errors: (0.19)(0.05)(0.06)(0.16)(0.16)(0.14).
- Interpretation:
  - Consumption, fixed investment, and exports are jointly significant determinants of imports.
  - Prices appear less important in determining imports.
  - Total capital formation did not perform well in estimation.

### Comparative context and policy implications
- Comparative elasticities (from Bayoumi (1996), reproduced in source) show Korea’s historical export income elasticity in 1974–93 around 3.12 and price elasticity around -0.52; import income elasticity around 1.36 and price elasticity around 0.61 (table reproduced in source).
- Policy-relevant implications deduced in text:
  - The structural shift toward EEPs with industry-level increasing returns and productivity improvements can explain dramatic export volume growth and falling EEP unit prices.
  - Supply-side drivers (TFP, potential output, increasing returns) should be taken into account when interpreting export responsiveness to foreign income and prices for EEPs.
  - For imports, policies or analyses that focus solely on import prices may miss the primary drivers: consumption, fixed investment, and exports.

### Conclusion and suggestions for further research
- Summary of main findings:
  - Exports: income elasticity of Korean export demand has fallen sharply; price elasticity has risen; changes largely due to increasing share of EEPs. EEPs show low income elasticity and high price elasticity; non-EEPs behave more like earlier total-export estimates and may show constant returns to scale.
  - Supply-based export analysis explains surge in EEP export volume by presence of increasing returns to scale and technological improvement.
  - Imports: standard model results broadly consistent with previous studies; income elasticity of import demand has risen slightly. Alternative model shows consumption, fixed investment, and exports are key determinants; prices less important.
- Suggested future research (text statement):
  - Reexamine trade flows for other Asian NIEs using recent data.
  - A supply-based export analysis may be useful for explaining exports of EEPs in other Asian NIEs.

### Appendix I — mathematical background (selected expressions and conditions)
- Firm cost structure (notation preserved):
  - Cj = C( Xj, X ) = φj( Xj ) ξ( X ).
  - Assumptions on functions in source: 0)(>Xξ, 0)(>Xφ,0)('<Xξ  ,,0)('> j X φ 0)('> j X φ.
- Firm supply relation:
  - Firm supply: Xj = g( P / ξ( X ) ) (where g is inverse of φ').
  - Aggregate supply: N [ g( P / ξ(X) ) ].
  - Inverse supply: )(')( N X X P φ ξ = (source notation preserved).
- Condition for negatively-sloped industry supply as stated in source:
  - If positive external effects of increasing returns at industry level outweigh increasing marginal cost faced by each firm (condition summarized in source as εα <−1), then the industry supply curve can be negatively sloped.

*Source: _wp04145 - References..............................................................................................................*

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

### _wp04145 - References

### Key context and data coverage
- Periods and magnitudes:
  - During 1970–2001, Korea’s real per capita GDP grew by five-fold.
  - Export volume grew by about 9,800 percent during 1970–2001.
  - Import volume grew by about 2,400 percent during 1970–2001.
  - In 2002, the share of Korean exports in total world exports was 2.5 percent (double the level in 1979).
  - In 2002, the share of Korean imports in total world imports was 2.4 percent (two and a half times the 1979 level).
- Reestimation sample used in this paper: 1988–2001.
- Comparative prior estimates cited:
  - Bayoumi (1996), annual data 1974–93: income elasticity = 3.1; price elasticity = -0.7.
  - Giorgianni and Milesi-Ferretti (1997), quarterly data 1970–95: income elasticity = 3.2; price elasticity = -2.0.
  - Prior studies for imports: income elasticity around 1.5.

### Main findings on exports
- Aggregate changes in elasticities (1988–2001 reestimation):
  - The income elasticity of export demand has fallen considerably.
  - The price elasticity of Korea’s export demand has risen dramatically.
- Role of export composition:
  - The shift toward electrical and electronic products (EEPs) is the main factor behind:
    - The large decline in the income elasticity of exports.
    - The large increase in the price elasticity of exports.
- Elasticity patterns by product type:
  - EEPs:
    - Exhibit a low income elasticity.
    - Exhibit a high price elasticity.
  - Non-EEPs:
    - Exhibit a high income elasticity.
    - Exhibit a low price elasticity.
  - The non-EEP elasticity profile is not too different from earlier total-export estimates.
- Interpretation and theoretical consistency:
  - The decline in income elasticity is consistent with Krugman’s “45 degree rule” (Krugman (1989)): fast-growing countries face high income elasticities for exports, whereas slower-growing countries face lower income elasticities.

### Supply-side analysis for EEPs
- Evidence points to supply-side drivers for EEP export behavior:
  - A steep decline in EEP export prices suggests supply-side, not demand-side, explanations in the standard model.
  - Exports of EEPs are strongly cointegrated with total factor productivity (TFP) and potential output.
  - Evidence indicates the existence of increasing returns to scale in EEP production.
- Non-EEPs contrast:
  - No strong link found between exports of non-EEPs and TFP.
  - Production of non-EEPs shows no evidence of increasing returns to scale.

### Main findings on imports
- Reestimated import equation results:
  - Estimates are similar to previous studies, with a slight upward trend in the income elasticity.
- Multivariate scale/price specification:
  - Import demand is jointly correlated with consumption, fixed investment, and exports when multiple scale variables are included.
  - Import prices are not important determinants of imports in the empirical results.

### Paper structure (as presented)
- Section II: Recent developments in Korean foreign trade and graphical description of key variables.
- Section III: Econometric model used throughout the paper.
- Section IV: Issues and results pertaining to exports.
- Section V: Issues and results pertaining to imports.

*Source: _wp04145 - References..............................................................................................................*

### Section VI concludes.

### _wp04145 - Section VI concludes.

### II. GRAPHICAL DESCRIPTION OF KOREAN FOREIGN TRADE — Overview
- Korea is described as "a highly open economy, with a rising trend in both export and import volumes; the share of Korean trade in total world trade has also been increasing."
- Growth patterns:
  - "The growth rates in both exports and imports have flattened, with the former showing a higher decline than the latter."
  - "The economic growth in Korea and the recipients of Korean exports have decelerated, with the former declining faster than the latter."
- Trading-partners note:
  - "The slow decline in the economies of Korea’s trading partners is mainly due to the increasing share of exports to China, which have been growing rapidly in the 1990s. Other than China, Korea’s main trading partners, particularly Japan, grew more slowly in the 1990s than before."

Key graphical indicators (as described)
- Figure 1: Export and Import Volume (1995=100), 1988–2001 (index): exports and imports rising over time (sources: CEIC database; WEO; and IMF staff estimates).
- Figure 2: Korea’s Share of World Trade, 1988–2001 (percent): plotted series for Imports and Exports (sources: CEIC database; WEO; and IMF staff estimates).
- Figure 3: Share of Trade in GDP (in Real Terms), 1988–2001 (percent): series for Exports/GDP, Imports/GDP, (Exports+Imports)/GDP (sources: CEIC database; WEO; and IMF staff estimates).

Table 1 — Real Growth in Exports, Imports, and GDP, 1974–2001 (average annual growth, in percent)
- Columns: Exports | Imports | GDP | Export Recipients’ GDP
- 1974–87: 15.2 | 11.1 | 7.9 | 4.3
- 1988–2001: 11.9 | 10.5 | 6.1 | 4.0
- Difference: -3.3 | -0.6 | -1.8 | -0.3
- Sources: CEIC database; WEO; and IMF staff estimates

### II.B Exports — Composition and unit values
- Structural shift: "Korean exports, which consisted mostly of labor-intensive goods in the past, are now concentrated in capital-intensive goods, of which, electrical and electronic products (EEPs) constitute the bulk of exports."
- Figure 4 (Composition of Exports), 1988–2001 (percent): category shares shown for Others; Chemical Products; Other Machinery and Transport Equipment; Manufactured Goods and Articles; EEPs (sources: CEIC database; and IMF staff estimates).
- Figure 5 (Export Volume: EEPs and Non-EEPs), 1988–2001 (1995=100, index): "the growth of [EEPs] is much faster than that of [Non-EEPs]." (sources: CEIC database; and IMF staff estimates).
- Figure 6 (Export Unit Value: EEPs and Non-EEPs), 1988–2001 (1995=100, index): "the export unit values of the EEPs and non-EEPs have been falling, but the former exhibits a much steeper decline in prices. This suggests that the cost of production of the EEPs have fallen, which may be due to the presence of technological improvements and/or increasing returns to scale." (sources: CEIC database; and IMF staff estimates).

### II.C Imports — Usage and composition
- Figure 7 (Imports Usage: for Domestic Use or Exports), 1996–2001 (percentage): "a high proportion of imports to Korea is for use in export production." (sources: CEIC database; and IMF staff estimates). Note: "Data for years not shown are not available."
- Figure 8 (Imports: Composition), 1990–2002 (percent): "a bulk of imports to Korea are capital or industrial raw materials, with consumer goods accounting for a small proportion." (sources: CEIC database and IMF staff estimates). Note: "Data for years not shown are not available."

### III. ECONOMETRIC SPECIFICATION — Data and methods
- Stationarity testing: "The first step of the empirical analysis involves testing all variables for nonstationarity by the Dickey-Fuller tests. The results show that they largely appear to be I(1) processes."
  - Footnote: "Results of these tests are available from the author on request."
- Estimation strategy:
  - Long-run (cointegrating) relationships estimated first; then short-run relationships via error-correction approach.
  - Long-run estimation method: Dynamic Ordinary Least Squares (DOLS) procedure of Stock and Watson (1993).
  - Formal DOLS specification provided (variable notation preserved): t
    j
    jtj
    j
    jtjttt
    uc+∆Ψ+∆Ψ+∆Ψ+Ψ+=Φ
    ∑∑
    =
    +
    =
    −
    11
    ''''γβαθ,
  - Short-run error-correction regression specified as:
    tttt
    ECMcελδ++∆Ψ+=∆Φ
    −1
    ',
    where δ is a vector of short-run elasticities and ECM is ECM = ttt
    ECMΨ−Φ='θ.

### IV. EXPORTS — Empirical analysis
- Two modeling approaches:
  - A. Standard Demand Model (demand-based framework; supply assumed perfectly elastic).
  - B. Alternative Supply Model (supply-based framework for EEPs with external increasing returns to scale).

A. Standard Demand Model — Framework and data
- Demand equation: real exports X depend on recipients' real income wY, export price xP, and trading-partners’ price level wP:
  - ),( rw PYfX=, where w
    x
    r
    P
    P
    P≡.
- Data sources:
  - "All data between 1988–2001 are official quarterly data from CEIC. Data prior to 1988 are from IMF’s International Financial Statistics and World Economic Outlook databases."
- Price measures:
  - xP is unit price of Korean exports in dollars.
  - wP approximated by trade-weighted average of CPIs for the twelve biggest importers:
    - 12
      1
      exp[ln(*]
      wiii
      i
      PWP   E
      =
      =
      ∑
  - wY is trade-weighted sum of real GDP of Korea’s main trading partners.
- Notation: "Throughout this paper, uppercase letters denote level of variables whereas lowercase letters denote their logarithm."

Results — Long-run export demand elasticities (Table 2)
- Table 2: Long-Run Export Demand Equations — Periods estimated: 1974–87, 1988–2001, 1974–2001.
- Reported coefficients and statistics (coefficients under heading columns y_w p_r R^2 AR(4) White ECM_t-1 Number of Observations). Values shown in table exactly:
  - 1974–87: 3.07  -0.18  0.95  <0.01  0.13  -0.62  54
    - Standard errors (in parentheses): (0.24)(0.23)(0.13)
  - 1988–2001: 1.00  -1.46  0.99  <0.01  0.72  -0.19  52
    - Standard errors: (0.70)(0.37)(0.05)
  - 1974–2001: 2.59  -0.17  0.97  <0.01  0.05  -0.23  106
    - Standard errors: (0.11)(0.13)(0.06)
- Interpretation stated: "Note that the estimates using data during 1974–88 essentially replicate those from previous studies. The results indicate that the long-run income elasticity is declining while the long-run price elasticity is rising."
  - Supporting references noted (examples): Giorgianni and Milesi-Ferretti (1997); Bayoumi (1996).

Disaggregation by product type (Table 3) — EEPs vs Non-EEPs (1988–2001)
- Table 3: Long-Run Export Demand Equations for EEPs, Non-EEPs, and Total, 1988-2001.
- Reported coefficients and statistics for 1988–2001 (values exactly as presented):
  - EEPs: 0.51  -1.42  0.99  <0.01  0.19  -0.53  52
    - Standard errors: (0.47)(0.11)(0.10)
  - Non-EEPs: 2.52  0.51  0.90  <0.01  0.47  -0.37  52
    - Standard errors: (0.99)(0.73)(0.10)
  - Total: 1.00  -1.46  0.99  <0.01  0.72  -0.19  52
    - Standard errors: (0.70)(0.37)(0.05)
- Main findings from Table 3:
  - "The price elasticity of EEPs is high while the income elasticity of EEPs is low."
  - "Conforming to the standard picture of a high income elasticity and a low price elasticity, the estimates for non-EEPs are not very different from those for total exports using 1974–87 data."
  - Implication: "the recent changes in long-run elasticities of total export demand are mainly due to the increase in the share of EEPs in total exports."

Interpretation issue raised
- Puzzle: "Why is the price elasticity of EEPs exports high and its income elasticity low?"
  - Rejected simple "luxury good" explanation because that would imply high income elasticity as well.
  - Proposed plausible explanation: the estimated relation for EEPs may be identifying a supply function rather than demand — supply would render the foreign income variable (a demand factor) insignificant.
  - Supply curve plausibility: "if it is a supply curve, it is a negatively-sloped one. ... Korean production of EEPs have benefited from massive positive spillovers such as learning by doing and technological innovations, as well as increasing returns to scales at the industry level."

B. Alternative Supply Model — Supply-based explanation for EEPs export surge
- Literature: "Much literature asserts that supply factors are important determinants of exports for high-growth country." Examples/refs: Krugman (1989); Halpern and Szekely (1992); Diewert and Morrison (1986).
- Framework — theoretical model summary:
  - Assumptions:
    - Export demand is perfectly elastic (Korean producer of EEPs is a price taker).
    - Increasing returns to scale exist at the industry level but are external to the representative firm (positive spillovers: learning-by-doing, research, innovation).
  - Production setup:
    - Continuum of identical firms indexed j in (0,N].
    - Aggregate production X = ∫_0^N X_j dj.
    - Each firm j faces a cost function C_j = C_j(X_j, X) = φ_j(X) ξ(X) with properties: 0 < ξ'(X), 0 < φ_j'(X_j), 0 < φ_j''(X_j) (signs preserved as in source).
    - For simplicity: define X^(ε)-ξ ≡ X)( and α φ_j ≡ φ_j(XX) with 0 > ε and 1 > α. (Source notation preserved: "For simplicity, let ε ξ − ≡ XX)( and α φ jj XX≡)(, where 0>εand .1>α")
    - Result: "as the aggregate production X increases, the marginal cost confronting each firm declines" — formula retained as in source:
      - 0
        1
        1
        2
        <−=
        ∂∂
        ∂
        −
        −−
        α
        ε
        εα
        j
        j
        XX
        XX
        C
  - Economic implication: Because increasing returns are external (depend on aggregate X), individual firm j has no incentive to expand to capture the increasing returns, preserving price-taking (perfect competition) behavior.
- Objective: "to illustrate such a possibility and to substantiate other points discussed in this subsection, a simple model is constructed" (model structure and implications provided in text).

Final empirical and theoretical synthesis (as presented)
- The supply-based interpretation can "best explain the dramatic surge in export volume of EEPs and the steep fall in the unit price of EEPs during the late 1990s."
- The supply model demonstrates the possibility of a negatively-sloped industry supply curve in the presence of external increasing returns to scale and technological improvements.
- Subsequent analytical elaboration is promised in the section (subsection B) with a theoretical model proving the possibility of a negatively-sloped supply curve.

*Source: _wp04145 - Section VI concludes.*

### Chapter 3 of their book.

### Chapter 3

### Supply-based export model: theory and conditions
- Firm j’s marginal cost facing aggregate production X:
  - ∂/∂Xj (C) = 0)1(2 2 >−= α ε α α j j XX X C  (notation preserved from source)
  - Second derivative with respect to own output jX: 0)1( 2 2 >= ∂ ∂ − − α ε α α j XX Î (stated in text)
- Firm j’s profit maximization problem:
  - Maximize αε jj XXP − −  (expression preserved)
  - First-order condition: 0 1 =− − − α ε α j XXP Î
    - Rearranged: 1 1 − −     = α ε α X P X j
  - Second-order condition: 0)1( 2 <−− − − α ε α α j XX Î , with 1>α (assumption)
- Aggregate (industry) supply:
  - Aggregate supply expression (equation (1) in source):
    - 1 1 0 1 1 0 − − − −     =     == ∫∫ α ε α ε α α X P Ndj X P dj XX NN j
  - Inverse supply function solved for P:
    - 1 )( −− = α ε α N X X P
- Industry supply slope possibility:
  - Industry supply may be downward sloping if:
    - 0 1 )1( 21 1 <     −+     − = ∂ ∂ − − − − − − α ε α ε α α ε α N X N X N X X X P c
  - Condition summarized: εα <−1
  - Interpretation: 1−α is the elasticity of the marginal cost with respect to an additional unit of output; ε measures the degree of positive external spillovers of an additional unit of output. If positive external effects of increasing returns at industry level outweigh increasing marginal cost faced by each firm, supply curve can be negatively sloped.

### Empirical export supply model specification
- Export supply X is modeled as a function of unit price of exports P and parameters α and ε:
  - ),,,( p Y TFP W P X = , where:
    - P is the export unit price
    - W is factor prices, such as the real wage of labor
    - TFP is total factor productivity
    - pY is potential output of the economy (proxy for “positive spillovers”)
- Notes on variables:
  - Potential GDP used because positive spillovers may be intra- or inter-industrial; TFP and potential output may be correlated (collinearity may arise) but estimates remain unbiased and consistent (text statement).

### Data used (exports)
- Export prices: unit value of exports in terms of Korean won
- W: real wage index of Korean workers, expressed in won
- pY: potential output is GDP of Korea filtered by the Hodrick-Prescott method
- TFP: data obtained from Zebregs (2003)

### Results — long-run export elasticities (1988–2001)
- Summary from text:
  - EEPs exports: significant relations with all explanatory variables; strong positive relation with TFP and Korea’s potential GDP; strong negative relation with unit price of EEP exports — evidence of increasing returns to scale, technological progress, and other positive spillovers at industry level.
  - Non-EEPs: TFP not significant; price elasticity not significant — production of non-EEPs may exhibit constant returns to scale.
  - Total exports: mixed results.
- Table 4 (Long-Run Export Supply Equations for EEPs, Non-EEPs, and Total, 1988-2001)
  - Format: Type | p w t f p y p R^2 AR(4) White ECM t-1 Number of observations
  - EEPs: -1.18 -1.26 1.49 2.74 0.99 0.36 0.40 -0.67 52
    - (0.12)(0.42)(0.40)(0.51)(0.13)
  - Non-EEPs: -0.79 -3.79 -0.69 5.28 0.92 <0.01 1.00 -0.23 52
    - (1.09)(2.00)(0.65)(2.52)(0.11)
  - Total: -0.28 -1.93 1.17 3.59 0.99 <0.01 0.53 -0.18 52
    - (0.53)(0.85)(0.47)(1.22)(0.06)
- Notes appended in source (method and diagnostics):
  - All regressions include a constant term. Quarterly data used; data prior to 1988 not available.
  - Dependent variable: export volume in logarithm (x). Independent variables in logarithm (defined in text).
  - Estimation: Dynamic Ordinary Least Squares (Stock and Watson, 1993).
  - Standard errors in parentheses are heteroscedasticity and autocorrelation consistent.
  - AR(4): Lagrange-multiplier test for fourth-order residual autocorrelation; p-values reported.
  - White test: heteroscedasticity test p-values reported.
  - ECM t-1 reports coefficient on lagged error-correction term; standard errors in parentheses.
  - Since variables appear I(1) in level, significance of ECM term suggests cointegration.

### Imports — standard model
- Standard import equation depends on domestic income Y, unit price of Korean imports mP, and general price level P:
  - ),( r P Y f M = , where r ≡ Pm / P (notation preserved)
- Data:
  - Korean consumers’ income: Korea’s seasonally-adjusted GDP
  - General price level: CPI
- Results — long-run import elasticities (Table 5):
  - Table 5. Long-Run Import Demand Equations
    - Type | y p r R^2 AR(4) White ECM t-1 Number of Observations
    - 1974–87: 1.22 -0.65 0.97 <0.01 0.78 -0.43 54
      - (0.05)(0.16)(0.09)
    - 1988–2001: 1.60 -0.19 0.98 <0.01 0.77 -0.26 55
      - (0.06)(0.14)(0.10)
    - 1974–2001: 1.31 -0.49 0.99 <0.01 0.96 -0.29 109
      - (0.04)(0.16)(0.06)
  - Interpretation in text:
    - Income elasticity of import demand has risen slightly; overall estimates stable and broadly consistent with previous studies.
  - Comparative references cited in text (no numeric alteration): Giorgianni and Milesi-Ferretti (1997), Bayoumi (1996).

### Imports — alternative model with multiple scale and price variables
- Rationale:
  - Korean imports are composed of imported consumer goods (Mc) and imported capital goods (Mk). Consumer imports depend on price of imported consumer goods (Pmc), price of domestically-produced consumer goods (Pc), and permanent income approximated by aggregate consumption C. Capital goods demand depends on price of imported capital goods (Pmk), price of domestically-produced capital goods (Pk), and a targeted production level which depends on consumption C, investment I, and exports X.
- Functional expression in source:
  - ),,,,,,(),,,,(),,( X I C P P P P M X I C P M M C P P M M C kmkcmckmkkcmcc =+=.  (notation preserved)
  - Relative-price rewrite: ),,,/,/( X I C P P P M M kmkcmc =  (notation preserved)
- Data:
  - Price of imported consumer and capital goods: Korea Customs Service
  - Price of domestically-produced consumer goods: CPI
  - Price of domestically-produced capital goods: Producers’ Price Index (PPI)
  - Investment: gross fixed capital formation
  - All scale variables are real quantities
- Results — long-run elasticities (Table 6):
  - Table 6. Long-Run Import Demand Equations with Multiple Scale and Price Variables, 1988-2001
    - c i x p m c r p m k r R^2 AR(4) White ECM t-1 Number of Observations
    - 0.47 0.40 0.35 -0.22 -0.30 1.00 0.38 0.62 -0.76 56
      - (0.19)(0.05)(0.06)(0.16)(0.16)(0.14)
  - Interpretation in text:
    - Consumption, fixed investment, and exports are jointly significant determinants of imports.
    - Prices appear less important in determining imports.
- Note: Total capital formation did not perform well in estimation (text statement).

### Comparative table of trade elasticities (from Bayoumi, 1996, reproduced)
- Table 7. Trade Elasticities for Other Countries (reproduced from Bayoumi (1996))
  - Columns: Exports (Income elasticities, Price elasticities) | Imports (Income elasticities, Price elasticities)
  - Selected rows (values preserved):
    - Australia: 1.33 -0.19 | 1.85 0.45
    - Canada: 2.06 0.00 | 2.01 0.49
    - Chile: 2.87 0.10 | 1.70 0.23
    - Hong Kong: 4.11 -0.07 | 1.92 1.01
    - Indonesia: 1.27 -0.32 | 1.66 0.68
    - Japan: 2.10 -0.69 | 0.79 0.55
    - Korea: 3.12 -0.52 | 1.36 0.61
    - Mexico: 1.55 -0.77 | 1.60 1.43
    - Malaysia: 1.86 -0.53 | 1.47 0.01
    - New Zealand: 0.98 -0.51 | 1.70 0.68
    - Philippines: 1.34 0.10 | 1.65 -0.75
    - Singapore: 1.77 -0.21 | 1.05 0.00
    - Taiwan Province of China: 3.28 -0.70 | 1.23 0.66
    - Thailand: 2.73 -0.99 | 1.03 0.75
    - United States: 1.47 -0.85 | 2.46 0.26
    - Panel of all countries: 1.96 -0.80 | 1.46 0.28
  - Note: Table reproduced from Bayoumi (1996) based on annual data for 1974–93.

### Conclusion — summary of main findings
- Reestimation period: primary focus on 1988–2001 (text statement)
- Exports:
  - Income elasticity of Korean export demand has fallen sharply; price elasticity has risen.
  - Changes largely due to increasing share of EEPs (export expansion producers) in total exports.
  - EEPs: low income elasticity, high price elasticity.
  - Non-EEPs: estimates similar to earlier data for total exports; possible constant returns to scale.
  - Supply-based export analysis explains surge in EEP export volume by presence of increasing returns to scale and technological improvement.
- Imports:
  - Standard model results broadly consistent with previous studies; income elasticity of import demand has risen slightly.
  - Alternative model with multiple scale and price variables: consumption, fixed investment, and exports important determinants; prices less important.
- Suggestion for future research:
  - Reexamine trade flows for other Asian NIEs using recent data.
  - A supply-based export analysis may be useful for explaining exports of EEPs in other Asian NIEs.

### Appendix I — mathematical background (general functional form)
- Setup: Each firm j faces cost function depending on aggregate output X:
  - Cj = C( Xj, X ) = φj( Xj ) ξ( X )  (notation as in appendix)
  - Assumptions on functions (preserved text):
    - 0)(>Xξ, 0)(>Xφ,0)('<Xξ  ,,0)('> j X φ 0)('> j X φ.
  - As aggregate production X increases, marginal cost confronting each firm declines:
    - 0)(')(' 2 <= ∂ ∂ ∂ j j XX XX C φ ξ
  - Given aggregate X, each firm faces increasing marginal cost relative to own production jX:
    - 0)('')(
2 2 >= ∂ ∂ j j XX y C φ ξ
- Firm j’s profit maximization:
  - Maximize )()(
jj
XXPXφξ−
  - First-order condition: 0)(')(=− j XXP φ ξ  Î )(' )( j X X P φ ξ =
- Define g(·) as inverse of φ'(·), i.e., Z Z g = ))('( φ for all Z.
- Firm supply: Xj = g( P / ξ( X ) )  (expressed in source as )(X P g X j ξ )
- Aggregate supply and inverse supply:
  - Aggregate supply: ∫∫ g( P / ξ(X) ) dj = N [ g( P / ξ(X) ) ] (notation preserved)
  - Inverse supply: )(')( N X X P φ ξ =
- Condition for negatively-sloped industry supply:
  - 0'')(
1
')('<
    +
    =
∂
∂
N
X
X
NN
X
X
X
P
φ ξ φ ξ
  - Equivalently (multiplying both sides by X):
    - )/(' )/('' )( )(' NX NX N X X X X φ φ ξ ξ >
  - Interpretation: Left-hand side is elasticity of ξ(X) with respect to additional output X (absolute value); right-hand side is elasticity of marginal cost with respect to additional output by an average firm (absolute value). If positive external effects of increasing returns (left) outweigh increasing marginal cost faced by individual firm (right), negatively-sloped supply curve arises.

*Source: Chapter 3 (content unit)._wp04145 - Chapter 3 of their book.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2004/_wp04145.pdf_