## _wp05229 - References

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---

### Introduction
- Research question: How predictable are exchange rates across different time horizons, with focus on business cycle frequencies (three to seven years).
- Key perspectives:
  - Short term: nominal rate considered completely unpredictable; best predictor of tomorrow's rate is its current value (Meese and Rogoff (1983) as cited).
  - Medium term: real exchange rates tend to move toward an “equilibrium” value defined by real factors; slow return to PPP is one of the “six puzzles” of international finance (Obstfeld and Rogoff (2000) as cited).
  - Empirical determinants noted: country’s stage of development (Balassa-Samuelson effects), trends in net foreign asset positions, commodity prices.
- Motivation: integrate equilibrium determinants of real exchange rates into a single micro-founded model by allowing imperfect substitutability between domestic and foreign traded manufactured goods.
- Scope: focus on medium-term (business cycle) determination of exchange rates; Balassa-Samuelson effects incorporated by concentrating on relative prices of manufactures.
- Paper organization: theoretical model (Section II), data and specification (Section III), results (Section IV), conclusion (Section V).

### Exchange Rate Model — Overview and assumptions
- Model type: static, two-country flexible-price model (home and larger foreign country; starred variables denote foreign).
- Goods and factors:
  - Three goods per country: Nontraded consumption good (N), Traded manufactured good (M), Traded commodity (C) used in production.
  - Home and foreign goods differentiated (six goods total: N, N*, M, M*, C, C*).
  - Two factors with fixed endowments: Labor (used in traded and nontraded goods) and Land (used to produce commodities).
- Exclusions and market structure:
  - Capital excluded.
  - Prices fully flexible; markets competitive.
- Key parameters and assumptions:
  - Elasticity of substitution between manufactures: ε, with ε greater than unity.
  - Home labor endowment: one unit.
  - Foreign labor endowment: s units, with s assumed greater than one.
  - Parameters α, φC, φC* are between zero and one.
  - λ is assumed to be less than one.
  - Utility parameters β, γ, and ε are positive.

### Production
- Technologies: constant-returns-to-scale Leontief technologies between labor and commodities for nontraded and manufactured goods; sectors differ only in productivity.
- Notation:
  - Yi (Y*i) denote home (foreign) output in sector i.
  - Ti (T*i) are productivity shocks.
  - Ii (I*i) are inputs of commodities by sector i.
- Labor resource constraints:
  - 1 = L_NT + L_M
  - s = L_NT* + L_M*
- Price relationships:
  - Price of nontraded goods and manufactures in home country written in terms of productivity and commodity parameters (equations (4) and (5) in source).
  - Relative price of nontraded to manufactured goods driven by relative productivities in the two sectors — the Balassa-Samuelson effect.

### Commodity sector
- Production function: Y_C = T_C A (equation (6) form); analogous starred expression for foreign.
- Land intensity depends on relative rental price of land (price of commodities) to wages.
- Appendix I implication:
  - Commodity prices depend on world labor force (1 + s), commodity intensity of production (φc), productivity of land (T_c), and relative price and productivity of manufactures.
  - λ < 1, reflecting that shocks to commodity output produce larger-than-proportional changes in prices.
- Output and trade:
  - Output of home commodity (Y_C), home consumption (C_C), and exports of home commodity (X_C) depend only on world labor supply and shocks to productivity of land (per model implications).

### Consumption and trade structure
- Preferences:
  - Cobb-Douglas between nontraded and manufactured goods.
  - CES across home and foreign manufactured goods with elasticity of substitution ε > 1.
  - Utility specified in equation (8) with parameters β, γ, ε positive.
- Nonmanufacturing current account balance:
  - Z = P_C X_C + TR (transfers TR priced in foreign manufactures); related identity forms (equation (9)).
- CES demand implications produce relative demand/prices of manufactured goods (equation (11) and following).
- Budget and trade-balance combinations yield expressions for relative prices of manufactured goods (equations (12)–(14)).

### Key equations and intuition
- General expression for relative prices of manufactured goods provided in full and log-linearized forms (equation (14) and derivation).
- Special cases:
  - No home bias (γ + γ* = 1): relative price simplifies as in equation (14’).
  - Balanced initial trade and P_M = 1 with γ relations simplifies to equation (14’’).
  - Equal-size countries and no commodities reduce to equation (14’’’): P_M*/P_M = Y_M*/Y_M^ε.
- Modeling insight: imperfect substitutability across manufactured goods plus explicit commodity channel captures:
  - Importance of relative supply of home vs foreign manufactured goods.
  - Role of nonmanufactures trade balance and export/import composition.
  - Effects of net foreign asset payments and terms of trade via commodity prices.

### Appendix II — Theoretical estimating equation and interpretation
- Basic estimating equation: equation (15). Notation: bars denote equilibrium values; hats are changes from equilibrium values. TRCPCPZ cc + − = * * .
- Numerator (sources of disturbances moving the relative price of manufactures):
  - Relative supply and demand for home and foreign manufactured goods: a rise in home goods quantity depresses their relative price on world markets.
  - Disturbances to balance on commodity trade and transfers (comprising interest payments on international investment positions and uncompensated transfers).
  - Relative importance of terms depends on importance of manufactures trade vs other flows in trade accounts.
- Denominator (how much the relative price of manufactures varies in response to shocks):
  - First term: expenditure-creating effect — rise in relative price of home manufactures increases home income and import demand.
  - Second term: expenditure switching — higher ε raises the impact of relative price on trade balance, depending on home bias and ratio of exports to imports of manufactures.
- Measurement and coefficient composition implications:
  - Relevant variables: relative output of manufactured goods; changes in nominal exports and imports of commodities (not terms of trade); trends in interest payments on international investments (rather than the path of net foreign assets).
  - Coefficients depend on country-specific effects (composition of trade, home bias).

### Data and specification (empirical implementation)
- Real exchange rate constructed using manufacturing output deflators (manufacturing-based real exchange rate).
- Sample: 10 advanced economies — Australia, Canada, Denmark, the euro area, Japan, Norway, New Zealand, Sweden, the United Kingdom, and the United States — period 1980 to 2001.
- Elasticity of substitution:
  - Initial estimates unsuccessful; literature often finds coefficient close to 1.
  - Pragmatic choice: set ε = 1.05.
- Right-hand side variables (from equation (15)) grouped as:
  - RYM: log difference between real manufacturing output of home and foreign countries.
  - TOT: commodity effects captured by log difference between export and import prices of commodities, augmented by theory-specific weights (export price multiplied by ratio of commodity exports to noncommodity imports; import price multiplied by ratio of commodity imports to noncommodity imports).
  - External financial position / transfer effects:
    - Separate flow receipts from gross foreign assets (ra*FA) and flow payments on gross foreign liabilities (rl*FL), each divided by noncommodity imports; derive separate rates of return on external assets and liabilities.
    - First measure: rNFA = ra*FA – rl*FL (synthetic interest rate on net foreign assets r shorthand).
    - Second measure: decompose net flow income into variation driven by stock of net foreign assets ( rNFA ) and remainder driven by variation in implied rates of return ( ()rr− NFA ).
    - Third measure: rely only on variation in the stock of net foreign assets ( rNFA ).
    - Uncompensated international transfers not introduced because negligible for sample countries.
- Panel estimation with country-specific fixed effects:
  - Equation (16): 0123itiitITitit REER RYM TOT rNFA u β β β β = + + + ++
  - Equation (17): 01234 () itiititititit REER RYM TOT rNFA r r NFA u β β β β β = + + + ++ − +
  - Equation (18): 0123 itiitititit REER RYM TOT rNFA u β β β β = + + ++
- Unit-root properties:
  - All variables viewed as I(1) on basis of unit root tests (Table 1). IPS test often rejects unit root; Breitung provides better support for unit roots; Hadri test strongly rejects null of I(0) for all series.
- Estimation method:
  - Panel DOLS (Kao and Chiang (2000); Mark and Sul (2000)).
  - General regression format (equation (19)): 012 m itiitit kit km q z z β β β ε + = − = + + ∆ + ∑
  - Leads and lags of differenced series included to address asymptotic bias; DOLS preferred over FMOLS.

### Estimation results — cointegration and long-run coefficients
- Table 2: long-run coefficients for manufacturing-based REER (DOLS; N = 10, T = 22). Key findings:
  - Column (1):
    - RYM: -0.71 (t = -2.74)
    - Z: 1.01 (t = 3.32)
    - Wald Test (p-value): 0.67 (0.41)
  - Column (2):
    - RYM: -0.64 (-2.58)
    - TOT: 0.58 (1.49)
    - r NFA: 1.75 (3.59)
    - Wald Test (p-value): 4.13 (0.13)
  - Column (3):
    - RYM: -0.68 (-3.20)
    - TOT: 0.78 (2.33)
    - rNFA: 2.59 (5.53)
    - ()rr− NFA: 0.63 (1.17)
    - Wald Test (p-value): 18.45 (0.0004)
  - Column (4):
    - RYM: -0.69 (-3.11)
    - TOT: 0.85 (2.42)
    - rNFA: 2.29 (5.30)
    - Wald Test (p-value): 11.13 (0.0038)
- Interpretation of coefficients:
  - Coefficient on RYM strongly significant and around -0.7, consistent with predicted supply effect.
  - When all external items combined (column (1)), coefficient estimate close to 1 as predicted by theory; Wald test does not reject equality at the 10 percent level (test statistic = 0.67 implying p-value = 0.41).
  - Columns (2)–(4): when NFA decomposed further, cross-coefficient restrictions strongly rejected at the 1 percent level.
  - Coefficients on TOT ~ 0.8 in columns (3) and (4); smaller and not statistically significant in column (2).
  - Coefficient estimates on NFA variables are about twice as large as coefficient on Z variable.
  - Stronger statistical significance of NFA variables than TOT may reflect persistence of underlying shocks and finite sample; model focuses on long-run relationship and may capture long-run relationship better for NFA variables if TOT shocks are more short-lived.
- Panel cointegration tests (Pedroni):
  - Table 3 statistics (N = 10, T = 22). Selected entries:
    - Panel ADF: -2.91**, -2.10**, -0.81, -1.90*
    - Group ADF: -3.27**, -2.00**, -0.75, -2.23**
  - Strongest evidence for cointegration comes from ADF-type tests; other tests often fail to reject null of no cointegration.

### Convergence dynamics, nonlinearity, and forecastability
- Error-correction specification (equation (20)) allowing nonlinear effect with residual raised to the third power:
  - () 3 01121 314151 itiitititititit REER RES RES RYM TOT NFA u γ γ γ γ γ γ − − − − ∆ = + + + ∆ + ∆ + ∆ +
- Linear specification results:
  - When deviation terms included only linearly, half-life of deviations is two to three years.
- Nonlinear findings:
  - Including both linear and cubic residual terms yields statistically significant evidence of nonlinearity.
  - Significant cubic term implies larger deviations revert faster to trend.
  - Threshold model (equation (21)) estimated with endogenous threshold T minimizing SSR:
    - 0 1121314151 itiitititititit REER RES NRES W RYM TOT NFA u γ γ γ γ γ γ − − − − ∆ = + + + ∆ + ∆ + ∆ +
    - Indicator variables defined by residuals relative to threshold.
  - Estimated threshold widths:
    - Table 4: threshold width = 0.151 (15 percent on each side of equilibrium).
    - Table 5: threshold width = 0.089 (9 percent on each side of equilibrium).
  - Convergence speed and magnitudes:
    - Table 4 (based on column (2) cointegrating relation): optimal threshold RESW = 0.151.
      - Column (1): RES∆ = -0.22 (-4.48); REER∆ = 0.28 (3.87)
      - Column (3): RES∆ = -0.12 (-1.55); ()3RES∆ = -4.37 (-4.60)
      - Column (4): RESN∆ = -0.17 (-2.46); RESW∆ = -0.26 (-4.08)
    - Table 5 (based on column (3) cointegrating relation): optimal threshold RESW = 0.089.
      - Column (1): RES∆ = -0.29 (-5.33); REER∆ = 0.29 (4.07)
      - Column (3): RES∆ = -0.20 (-2.77); ()3RES∆ = -3.56 (-4.88)
      - Column (4): r∆NFA = -0.80 (-2.17); ()rr∆− NFA = 0.31 (1.69)
    - Outside threshold convergence is faster than inside; inside-threshold convergence slower and in some specifications statistically not different from zero.
    - Nonlinear convergence coefficient larger by 0.03–0.04 compared with linear specification in column (1), implying half-life outside threshold shorter by three to six months than linear estimate.
- Forecastability (Table 6: Mean Squared Error):
  - Forecast Horizon / Random Walk / Cointegration (2) / Cointegration (3)
    - 1 Year: 0.004 / 0.017 / 0.015
    - 2 Years: 0.010 / 0.017 / 0.017
    - 3 Years: 0.014 / 0.016 / 0.018
    - 4 Years: 0.018 / 0.017 / 0.020
    - 5 Years: 0.023 / 0.018 / 0.018
  - Structural equations (cointegrating regressions of columns (2) and (3) of Table 2) outperform random-walk model at four- or five-year horizons.

### Key empirical magnitudes and methodological choices
- Sample: manufacturing-based REER for 10 advanced economies for 1980–2001; panel estimation uses N = 10, T = 22.
- Elasticity of substitution set to ε = 1.05.
- Half-life of deviations under linear error-correction: two to three years.
- Threshold widths estimated: 0.151 (15 percent) in Table 4 and 0.089 (9 percent) in Table 5 on each side of equilibrium.
- Wald test statistic (column (1) equality of two coefficients): 0.67 with p-value = 0.41.

### Tables and selected test statistics (summarized)
- Table 1: Unit root tests (selected variables):
  - REER: -1.41a, 8.06b, 2.08, -0.83
  - REERMAN: -1.23a, 8.76b, 6.06b, 0.26
  - TOT: -3.84b, 3.21b, -8.34b, -1.27a
  - r NFA: -0.93, 7.95b, -4.32b, -2.25b
  - ()rr− NFA: -0.12, 7.85b, -8.38, -3.42b
  - Note: a denotes significance at 10 percent level. b denotes significance at 5 percent level.
- Table 2: Panel DOLS long-run coefficients (selected):
  - Column (1): RYM = -0.71 (-2.74), Z = 1.01 (3.32)
  - Column (2): RYM = -0.64 (-2.58), TOT = 0.58 (1.49), r NFA = 1.75 (3.59)
  - Column (3): RYM = -0.68 (-3.20), TOT = 0.78 (2.33), rNFA = 2.59 (5.53), ()rr− NFA = 0.63 (1.17)
  - Column (4): RYM = -0.69 (-3.11), TOT = 0.85 (2.42), rNFA = 2.29 (5.30)
- Table 3: Panel cointegration statistics (selected):
  - Panel ADF: -2.91**, -2.10**, -0.81, -1.90*
  - Group ADF: -3.27**, -2.00**, -0.75, -2.23**
  - Note: A *(**) indicates significance at the 10 (5) percent level.
- Table 4: Error-correction estimates (optimal RESW = 0.151; selected coefficients):
  - RES∆ = -0.22 (-4.48); ()3RES∆ = -4.37 (-4.60); RESW∆ = -0.26 (-4.08)
  - REER∆ ≈ 0.26–0.29 with t-statistics ≈ 3.6–3.9
- Table 5: Error-correction estimates (optimal RESW = 0.089; selected coefficients):
  - RES∆ = -0.29 (-5.33); ()3RES∆ = -3.56 (-4.88)
  - r∆NFA ≈ -0.80 (-2.17) in columns including flow decomposition
- Table 6: Forecast Errors (Mean Squared Error) (see Forecastability section for full listing).

### Conclusions and implications
- The two-country flexible-price micro-founded model implies equilibrium real exchange rate depends on:
  - Relative supply of manufactured goods.
  - Interest payments on debt.
  - Commodity prices.
- Model flexibility:
  - Accounts for country differences in relative size, trade composition, home bias in consumption, and elasticity of substitution, while yielding analytically tractable estimating equation with cross-country coefficient restrictions.
- Empirical findings:
  - Variables are correctly signed and statistically significant at conventional levels.
  - Regressions produce implied paths of real exchange rate consistent with heuristic policy discussions.
  - There is a relatively large level of uncertainty about the equilibrium value.
  - Strong evidence that the rate of convergence to equilibrium depends on size of deviation — larger misalignments revert faster.
- Practical value:
  - Provides a theoretically sound, tractable alternative to PPP-based approaches for medium-term exchange rate determination.
  - Useful for assessing deviations from fundamentals and for estimating likely path and rate of return to underlying equilibrium.
  - Applicable beyond industrial countries to developing nations given generality of theoretical model.

*Source: Appendix II, _wp05229 - Appendix II, this results in the following specification.*

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

### _wp05229 - References..............................................................................................................

### Introduction
- Research question: How predictable are exchange rates across different time horizons, with focus on business cycle frequencies (three to seven years).
- Key perspectives:
  - Short term (days or weeks): nominal rate is considered completely unpredictable; best predictor of tomorrow's rate is its current value (reference: Meese and Rogoff (1983) as cited).
  - Medium term: real exchange rates tend to move toward an “equilibrium” value defined by real factors, often linked to purchasing power parity (PPP). The slow rate of return to PPP is listed as one of the “six puzzles” of international finance (reference: Obstfeld and Rogoff (2000) as cited).
  - Empirical determinants noted: country’s stage of development (Balassa-Samuelson effects), trends in net foreign asset positions, commodity prices.
- Motivation: Integrate underlying factors determining equilibrium real exchange rates into a single micro-founded model by allowing imperfect substitutability between domestic and foreign traded manufactured goods.
- Scope: Focus on medium-term (business cycle) determination of exchange rates; Balassa-Samuelson effects incorporated by concentrating on relative prices of manufactures.
- Paper organization (as stated): theoretical model (Section II), data and specification (Section III), results (Section IV), conclusion (Section V).

### Exchange Rate Model — Overview and Assumptions
- Model type: static, two-country flexible-price model with two countries (home and a larger foreign country, starred variables denote foreign).
- Production: three goods per country:
  - Nontraded consumption good (N)
  - Traded manufactured good (M)
  - Traded commodity (C) used in production of other goods
- Goods differentiation: home and foreign goods are differentiated (six goods total: N, N*, M, M*, C, C*).
- Factors of production: two factors with fixed endowments:
  - Labor (used to produce traded and nontraded goods)
  - Land (used to produce commodities)
- Exclusions and market structure:
  - Capital excluded to avoid accumulation complications.
  - Prices fully flexible; markets competitive.

### Production
- Technologies: constant-returns-to-scale Leontief technologies between labor and commodities for nontraded and manufactured goods; differ only in productivity.
- Notation highlights from the model:
  - Yi (Y*i) denote home (foreign) output in sector i.
  - Ti (Ti*) are productivity shocks.
  - Ii (I*i) are inputs of commodities by sector i.
  - α, φC, and φC* are positive parameters between zero and one.
- Labor endowments:
  - Home country endowed with one unit of labor.
  - Foreign country endowed with s units of labor, with s assumed greater than one.
- Resource constraint expressions (as given):
  - 1 = L_NT + L_M
  - s = L_NT* + L_M*
- Under Leontief constraints binding, relationships among outputs, productivity and labor inputs are given (equation references preserved in the source).
- Price relationships:
  - Price of nontraded goods and manufactures in home country written in terms of productivity and commodity parameters (see equations (4) and (5) in source).
  - Relative price of nontraded to manufactured goods is driven by relative productivities in the two sectors — the Balassa-Samuelson effect.

### Commodity Sector
- Commodities (C, C*) produced using a linear production function with land (A, A*) and productivity shock T_C (T_C*):
  - Y_C = T_C A  (equation (6) form)
- Intensity of land use depends on relative rental price of land (price of commodities) to wages.
- Appendix I derivation implication summarized as:
  - Commodity prices depend on world labor force (1 + s), commodity intensity of production (φc), productivity of land (T_c), and relative price and productivity of manufactures.
  - λ is introduced and assumed to be less than one, reflecting that shocks to commodity output produce larger-than-proportional changes in prices.
- Output of home commodity (Y_C), home consumption (C_C), and exports of home commodity (X_C) depend only on world labor supply and shocks to productivity of land (per model implications).

### Consumption and Trade
- Preferences:
  - Cobb-Douglas between nontraded and manufactured goods.
  - CES across home and foreign manufactured goods with elasticity of substitution ε, where ε is greater than unity.
  - Utility specified (equation (8) form) with parameters β, γ, ε positive.
- Nonmanufacturing current account balance defined to include commodity trade and transfers TR (priced in foreign manufactures):
  - Z = P_C X_C + TR  and related identity forms (equation (9) format).
- Production equals consumption in manufactured goods as in equation (10) structure.
- CES demand implications:
  - Relative demand/prices of manufactured goods implied by CES structure (equation (11) and following).
- Budget and trade-balance combinations lead to expressions for relative prices of the two manufactured goods (equations (12)–(14) progression).

### Key Equations and Intuition (as presented)
- General expression for relative prices of manufactured goods is given in log-linearized and full forms (see equation (14) and its derivation).
- Special cases and intuition:
  - No home bias (γ + γ* = 1): relative price simplifies as in equation (14’).
  - If initial equilibrium has balanced trade in manufactures and nonmanufactures and initial P_M = 1, and γ and γ* relate to s as /(1)*   1/(1),ss  ands γγ=+=+ (as stated), expression simplifies to equation (14’’) where relative supply and nonmanufactures trade balance matter.
  - Equal-size countries and no commodities reduce expression to equation (14’’’): P_M*/P_M = Y_M*/Y_M^ε (as presented).
- Modeling insight: allowing imperfect substitutability across manufactured goods and explicit commodity channel yields a flexible framework capturing:
  - Importance of relative supply of home vs foreign manufactured goods.
  - Role of nonmanufactures trade balance and composition of exports/imports.
  - Effects of net foreign asset payments and terms of trade via commodity prices.

### Model Features and Parameters (explicit values/assumptions preserved)
- Elasticity of substitution between manufactures: ε, with ε greater than unity.
- Foreign country labor endowment: s units, with s assumed greater than one.
- Home country labor endowment: one unit.
- Parameters α, φC, φC* are between zero and one.
- λ is assumed to be less than one.
- Utility parameters β, γ, and ε are positive; foreign utility assumes same ε and β, with γ and γ* depending on relative sizes, production structure, and trade composition.
- Production of commodities uses a linear function Y_C = T_C A (as presented).

### Organization and Further Materials (as listed)
- Appendices listed in the source:
  - I. Derivation of Relative Price of Commodities
  - II. Derivation of Log-Linearized Exchange Rate Equation
  - III. Data Sources
- Tables listed in the source (titles preserved as in the content unit):
  - 1. Unit Root Tests
  - 2. Panel Estimates of Long-Run Coefficients
  - 3. Panel Cointegration Statistics
  - 4. Panel Estimates of Error-Correction Model
  - 5. More Panel Estimates of Error-Correction Model
  - 6. Forecast Errors

*Content based solely on the provided PDF excerpt.*

### Appendix II, this results in the following specification:

### Appendix II, this results in the following specification:

### Theoretical estimating equation and interpretation
- Equation (15) is the basic estimating equation of the paper. Bars above terms represent equilibrium values; hats are changes from equilibrium values. TRCPCPZ cc + − = * * .  
- Numerator (sources of disturbances moving the relative price of manufactures):
  - Relative supply and demand for home and foreign manufactured goods: a rise in the quantity of home goods depresses their relative price on world markets.
  - Disturbances to the balance on commodity trade and transfers (comprising interest payments on international investment positions and uncompensated transfers). The relative importance of these terms depends on the relative importance of trade in manufactures and other flows in the overall trade accounts.
- Denominator (how much the relative price of manufactures varies in response to shocks):
  - First term: expenditure-creating effect — a rise in the relative price of home manufactures increases home income and import demand.
  - Second term: expenditure switching — higher elasticity of substitution raises the impact of relative price on the trade balance, depending on home bias in consumption and the ratio of exports to imports of manufactures.
- Measurement and coefficient composition implications from theory:
  - Relevant variables are relative output of manufactured goods; changes in nominal exports and imports of commodities (rather than the terms of trade); and trends in interest payments on international investments (rather than the path of net foreign assets).
  - Coefficients depend on country-specific effects such as composition of trade and home bias of consumption.

### Data and specification
- Real exchange rate constructed using manufacturing output deflators (manufacturing-based real exchange rate), not consumer prices.
- Manufacturing-based exchange rate constructed for 10 advanced economies: Australia, Canada, Denmark, the euro area, Japan, Norway, New Zealand, Sweden, the United Kingdom, and the United States for the period from 1980 to 2001.
- Elasticity of substitution:
  - Initial attempts to estimate the elasticity were unsuccessful; literature often finds a coefficient close to 1.
  - Pragmatic choice: set elasticity equal to 1.05.
- Right-hand side variables (from equation (15)) divided into three groups:
  - RYM: log difference between real manufacturing output of home and foreign countries.
  - TOT: commodity effects captured by the log difference between export and import prices of commodities, each augmented as indicated by theory; commodity export price multiplied by the ratio of commodity exports to noncommodity imports; commodity import price multiplied by the ratio of commodity imports to noncommodity imports.
  - External financial position / transfer effects:
    - Separate flow receipts from gross foreign assets (ra*FA) and flow payments on gross foreign liabilities (rl*FL), each divided by noncommodity imports; derive separate rates of return on external assets and liabilities.
    - First measure: rNFA = ra*FA – rl*FL (synthetic interest rate on net foreign assets r as shorthand).
    - Second measure: decompose net flow income into variation driven by stock of net foreign assets ( rNFA ) and the remainder driven by variation in implied rates of return ( ()rr− NFA ).
    - Third measure: rely only on variation in the stock of net foreign assets ( rNFA ).
    - Uncompensated international transfers not introduced because they are negligible for countries in the sample.
- Panel estimation equations with country-specific fixed effects:
  - Equation (16): 0123itiitITitit REER RYM TOT rNFA u β β β β = + + + ++
  - Equation (17): 01234 () itiititititit REER RYM TOT rNFA r r NFA u β β β β β = + + + ++ − +
  - Equation (18): 0123 itiitititit REER RYM TOT rNFA u β β β β = + + ++
  - Note: all variables viewed as I(1) processes on the basis of various unit root tests (Table 1). IPS test often rejects unit root; Breitung provides better support for unit roots; Hadri test strongly rejects null hypothesis of I(0) for all series.
- Estimation method:
  - Use panel dynamic ordinary least squares estimation (panel DOLS) in line with Kao and Chiang (2000) and Mark and Sul (2000).
  - General regression format (equation (19)): 012 m itiitit kit km q z z β β β ε + = − = + + ∆ + ∑
  - Leads and lags of differenced series included to address asymptotic bias; DOLS preferred over FMOLS for bias reduction and better t-statistic behavior.

### Estimation results — cointegration and coefficients
- Table 2 reports long-run coefficients for the manufacturing-based real exchange rate (corresponding to equation (19)).
  - Column (1): all external balance items combined into one term (Z).
  - Columns (2)–(4): external items broken into TOT and NFA terms; columns differ in treatment of NFA.
    - Column (2): NFA term measures actual net flow income on foreign assets (rNFA).
    - Column (3): net flow income decomposed into part driven by changes in stock of net foreign assets ( rNFA ) and remainder driven by changes in rate of return ( ()rr− NFA ).
    - Column (4): term that reflects variation in rate of return is dropped.
- Main coefficient findings:
  - Coefficient on RYM is strongly significant and estimates are around -0.7, consistent with predicted supply effect.
  - When all external items combined (column (1)), coefficient estimate is close to 1, equal to the value predicted by theory. Wald test does not reject hypothesis that these two coefficients are identical in size at the 10 percent significance level (test statistic = 0.67 implying p-value = 0.41).
  - In column (2) cross-coefficient restrictions hold up (hypothesis that coefficients on RYM identical to coefficients on TOT and NFA not rejected at 10-percent significance).
  - In columns (3) and (4) where NFA is broken down further, cross-coefficient restrictions are strongly rejected at the 1 percent significance level.
  - Coefficient estimates on TOT ~ 0.8 in columns (3) and (4); smaller and not statistically significant in column (2).
  - Coefficient estimates on NFA variables are about twice as large as coefficient on Z variable.
  - Stronger statistical significance of NFA variables than TOT may reflect persistence of underlying shocks and finite sample; model focuses on long-run relationship and may capture long-run relationship better for NFA variables if TOT shocks are more short-lived.
- Panel cointegration tests (Pedroni 2000, 1999) — Table 3:
  - Residual-based tests assume null of no cointegration.
  - “Panel” statistics impose common coefficients; “group” statistics represent group mean of individual test statistics.
  - Under alternative, panel v-statistic diverges to +∞ (right-tail test) while other statistics diverge to -∞ (left-tail tests).
  - Strongest evidence in support of cointegration comes from ADF-type tests; other tests often fail to reject null of no cointegration.

### Convergence dynamics, nonlinearity, and forecastability
- Error correction / convergence specification:
  - Second-stage error correction equation allowing nonlinear effect with residual raised to the third power (equation (20)):
    - () 3 01121 314151 itiitititititit REER RES RES RYM TOT NFA u γ γ γ γ γ γ − − − − ∆ = + + + ∆ + ∆ + ∆ +
  - Residuals constructed from cointegrating regression using level-variables without leads and lags.
- Linear specification results:
  - When deviation terms included only in linear format, half-life of deviations is two to three years (shorter than many PPP literature estimates, probably reflecting specification allowing long-run equilibrium to vary over time).
- Nonlinear findings:
  - When residual terms included in both linear and cubic formats, statistically significant evidence of nonlinearity found.
  - Significant cubic term implies: the farther the exchange rate drifts from the long-term trend, the faster it reverts to the trend — unusually large deviations get corrected more rapidly.
  - Optimal nonlinear threshold model (equation (21)) estimated with endogenous threshold T that minimizes sum of squared residuals:
    - 0 1121314151 itiitititititit REER RES NRES W RYM TOT NFA u γ γ γ γ γ γ − − − − ∆ = + + + ∆ + ∆ + ∆ +
    - Indicator definitions based on residuals relative to threshold.
  - Estimated threshold widths:
    - Table 4: threshold width = 15 percent on each side of equilibrium.
    - Table 5: threshold width = 9 percent on each side of equilibrium.
  - Convergence speed:
    - Faster outside threshold than inside; inside threshold convergence is slower and in Table 4 statistically different from zero, while in Table 5 statistically not different from zero.
    - Coefficient of nonlinear convergence larger by 0.03–0.04 compared with linear specification in column (1), implying half-life outside threshold is shorter by three to six months than half-life estimated by linear specification.
    - Outside threshold, deviations decline more rapidly than most PPP literature estimates; inside threshold convergence slower or near zero.
- Forecastability:
  - Table 6 compares mean squared error for random walk hypothesis with mean squared errors based on cointegrating regressions of columns (2) and (3) of Table 2; realized values of independent variables used (as in Meese and Rogoff (1983)).
  - Structural equations outperform random-walk model in four- or five-year horizon.
  - Implication: estimated cointegrating relationship offers a relevant benchmark for assessing long-term trends in the real exchange rate.

### Key empirical magnitudes and methodological choices
- Sample and periods:
  - Manufacturing-based real exchange rate constructed for 10 advanced economies for 1980–2001.
  - Model estimated using data for 11 industrial countries/currency areas (cointegration estimation described on panel of countries).
- Elasticity of substitution set to 1.05.
- Half-life of deviations under linear error-correction: two to three years.
- Threshold widths estimated at 15 percent (Table 4) and 9 percent (Table 5) on each side of equilibrium.
- Wald test statistic noted: 0.67 with p-value = 0.41 for equality of two coefficients in column (1).

### Conclusions and implications
- The two-country flexible-price micro-founded model implies equilibrium real exchange rate depends on:
  - Relative supply of manufactured goods.
  - Interest payments on debt.
  - Commodity prices.
- Model flexibility:
  - Accounts for country differences in relative size, composition of trade, home bias in consumption, and elasticity of substitution, while yielding an analytically tractable estimating equation with cross-country coefficient restrictions.
- Empirical findings:
  - Variables are correctly signed and statistically significant at conventional levels.
  - Regressions produce implied paths of real exchange rate consistent with heuristic policy discussions.
  - There is a relatively large level of uncertainty about the equilibrium value.
  - Strong evidence that rate of convergence to equilibrium depends on size of deviation — larger misalignments revert faster.
- Practical value:
  - Provides a theoretically sound, tractable alternative to PPP-based approaches for medium-term exchange rate determination.
  - Useful for assessing degree to which actual exchange rates deviate from fundamentals and for estimating likely path and rate of return to the underlying equilibrium.
  - Applicable beyond industrial countries to exchange rates of developing nations given generality of theoretical model.

*Source: Appendix II, _wp05229 - Appendix II, this results in the following specification.*

### REFERENCES

### _wp05229 - REFERENCES

### References
- Bibliographic list of foundational literature on purchasing power parity, real exchange rates, cointegration, commodity currencies, net foreign assets, and equilibrium exchange rates including works by Balassa, Cashin, Céspedes, Sahay, Chen, Rogoff, Choudhri, Khan, Clark, MacDonald, Faruqee, Froot, Gagnon, Im, Pesaran, Shin, Isard, Kao, Lane, Milesi-Ferretti, Lee, Tang, MacDonald, Nagayasu, Ricci, Mark, Sul, Meese, Obstfeld, Pedroni, Rogoff, Samuelson, Stock, Watson, and Williamson as listed in the source.

### Appendix I — Derivation of Relative Price of Commodities
- Land intensity depends on relative price of land to wages expressed by:
  - λ_C = (P_C A_C) / (W_C) and λ*_C = (P*_C A*_C) / (W*_C) (A1)
- Output of commodities:
  - Y_C = P_C TA_C / W_C and Y*_C = P*_C T A*_C / W*_C (A2)
- Demand for commodities proportional to labor inputs times Leontief coefficients:
  - Ys_C = φ_Cc (1) and Xs_C = φ_Cc (1) etc. (A3)
- Relative price expressions:
  - Pc = [(1/(1+φ_Cc)) (MM_PPTTA λ / ...)] and analogous starred expressions (A4)

### Appendix II — Derivation of Log-linearized Exchange Rate Equation
- Log-linearization of equation (14) leads to intermediate approximations:
  - Equation (A5) is the log-linearized form.
  - Approximation for left-hand side when P_M = 1 in equilibrium:
    - 1ˆ((* (1 *))(1 *) ( 1)) M M PP ε γγγε − ∆+−≈− − (A6)
  - Numerator manipulations yield expressions summarized in (A7).
  - Denominator approximations summarized in (A8).
- Combining numerator and denominator manipulations yields equation (14) in the text.

### Appendix III — Data Sources
- Manufacturing deflators and output: OECD’s STAN database; when unavailable, OECD’s ANIA data for industry.
- Trade weights for effective exchange rates: UN’s UNCTAD database.
- Output, prices, and trade composition of commodities: UN’s UNCTAD database.
- Income flows: IFS.
- External assets and liabilities: Lane and Milessi-Ferretti (2001).
- Implied rates of return on assets and liabilities calculated by combining income flows with asset and liability positions.

### Table 1: Unit Root Tests (selected variables and statistics)
- Columns: (1) Im, Pesaran and Shin (1995); (2) Hadri (2000); (3) Levin and Lin (1992); (4) Breitung (2000).
- REER: -1.41a, 8.06b, 2.08, -0.83
- REERMAN: -1.23a, 8.76b, 6.06b, 0.26
- TNT: -0.96, 11.31b, 8.99b, 1.01
- RPMAN: 0.58, 9.58b, 10.44b, 1.49a
- RYM: -0.71, 10.21b, 9.90b, 0.85
- Z: -1.63a, 6.67b, -6.36b, -1.34a
- TOT: -3.84b, 3.21b, -8.34b, -1.27a
- r NFA: -0.93, 7.95b, -4.32b, -2.25b
- rNFA: 1.70a, 15.36b, -0.25, 0.56
- ()rr− NFA: -0.12, 7.85b, -8.38, -3.42b
- rA: -0.91, 9.61b, 8.67b, 0.05
- rL: -2.48b, 6.07b, 7.55b, -0.08
- Note: a denotes significance at 10 percent level. b denotes significance at 5 percent level.

### Table 2: Panel Estimates of Long-run Coefficients
- Dependent Variable: Manufacturing-based REER; N = 10, T = 22. Panel estimates based on Stock-Watson Dynamic OLS (DOLS); corrected t-statistics in parentheses.
- Column (1):
  - RYM: -0.71 (-2.74)
  - Z: 1.01 (3.32)
  - Wald Test (p-value): 0.67 (0.41)
- Column (2):
  - RYM: -0.64 (-2.58)
  - TOT: 0.58 (1.49)
  - r NFA: 1.75 (3.59)
  - Wald Test (p-value): 4.13 (0.13)
- Column (3):
  - RYM: -0.68 (-3.20)
  - TOT: 0.78 (2.33)
  - rNFA: 2.59 (5.53)
  - ()rr− NFA: 0.63 (1.17)
  - Wald Test (p-value): 18.45 (0.0004)
- Column (4):
  - RYM: -0.69 (-3.11)
  - TOT: 0.85 (2.42)
  - rNFA: 2.29 (5.30)
  - Wald Test (p-value): 11.13 (0.0038)

### Table 3: Panel Cointegration Statistics (N = 10, T = 22)
- Panel v: 0.87, 0.23, -0.34, 0.52
- Panel ρ: -0.58, 0.30, 1.39, 0.46
- Panel Phillips-Perron: -1.86*, -1.48, -0.33, -1.05
- Panel ADF: -2.91**, -2.10**, -0.81, -1.90*
- Group ρ: 0.40, 1.48, 2.52, 1.53
- Group Phillips-Perron: -1.69*, -1.02, 0.16, -0.73
- Group ADF: -3.27**, -2.00**, -0.75, -2.23**
- Number of Regressors:
  - k = 2; k = 3; k = 4; k = 3
- Note: Panel cointegration tests based on Pedroni (1997,1999). A *(**) indicates significance at the 10 (5) percent level.
- Specifications:
  - (1) RYMAN and Z as regressors;
  - (2) RYMAN, ZNFA and ZTOT as regressors;
  - (3) RYMAN, ZNFA and ZTOT as regressors;
  - (4) RYMAN, ZTOT, and ZRBARNFA as regressors

### Table 4: Panel Estimates of Error-Correction Model (Dependent Variable: Manufacturing-based REER; N = 10, T = 22)
- Panel estimation of second-stage error correction model based on cointegrating relation of column (2); t-statistics in parentheses. The optimal threshold for RESW is 0.151.
- Column (1):
  - RES∆: -0.22 (-4.48)
  - REER∆: 0.28 (3.87)
  - RYM∆: 0.15 (0.96)
  - TOT∆: 0.20 (1.63)
  - NFA∆: -0.05 (-0.25)
- Column (2):
  - REER∆: 0.26 (3.61)
  - RYM∆: 0.23 (1.51)
  - TOT∆: 0.23 (1.91)
  - NFA∆: 0.01 (0.03)
- Column (3):
  - RES∆: -0.12 (-1.55)
  - ()3RES∆: -4.37 (-4.60)
  - REER∆: 0.28 (3.86)
  - RYM∆: 0.18 (1.17)
  - TOT∆: 0.20 (1.67)
  - NFA∆: -0.05 (-0.26)
- Column (4):
  - RESN∆: -0.17 (-2.46)
  - RESW∆: -0.26 (-4.08)
  - REER∆: 0.29 (3.92)
  - RYM∆: 0.15 (0.99)
  - TOT∆: 0.20 (1.58)
  - NFA∆: -0.06 (-0.31)

### Table 5: More Panel Estimates of Error-Correction Model (Dependent Variable: Manufacturing-based REER; N = 10, T = 22)
- Panel estimation of second-stage error correction model based on cointegrating relation of column (3); t-statistics in parentheses. The optimal threshold for RESW is 0.089.
- Column (1):
  - RES∆: -0.29 (-5.33)
  - REER∆: 0.29 (4.07)
  - RYM∆: 0.20 (1.37)
  - TOT∆: 0.18 (1.44)
- Column (2):
  - REER∆: 0.25 (3.56)
  - RYM∆: 0.45 (2.92)
  - TOT∆: 0.19 (1.55)
  - r∆NFA: -0.82 (-2.24)
  - ()rr∆− NFA: 0.30 (1.62)
- Column (3):
  - RES∆: -0.20 (-2.77)
  - ()3RES∆: -3.56 (-4.88)
  - REER∆: 0.30 (4.16)
  - RYM∆: 0.31 (1.97)
  - TOT∆: 0.15 (1.23)
  - r∆NFA: -0.63 (-1.72)
  - ()rr∆− NFA: 0.35 (1.84)
- Column (4):
  - REER∆: 0.30 (1.57)
  - RYM∆: 0.24 (1.57)
  - TOT∆: 0.17 (1.36)
  - r∆NFA: -0.80 (-2.17)
  - ()rr∆− NFA: 0.31 (1.69)

### Table 6: Forecast Errors (Mean Squared Error)
- Forecast Horizon / Random Walk / Cointegration (2) / Cointegration (3)
  - 1 Year: 0.004 / 0.017 / 0.015
  - 2 Years: 0.010 / 0.017 / 0.017
  - 3 Years: 0.014 / 0.016 / 0.018
  - 4 Years: 0.018 / 0.017 / 0.020
  - 5 Years: 0.023 / 0.018 / 0.018
- Note: Panel estimation of second-stage error correction model; structural forecast is based on cointegrating relationship of columns (2) and (3) in Table 2.

*Content derived from _wp05229 - REFERENCES (source PDF).*

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