## _wp07296

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### Box 1 — The Purchasing Power Parity Hypothesis: definition, evidence, and implications
- Definition and formal statements
  - Two main variants of PPP:
    - Absolute PPP: S = P*/P
      - S is the nominal exchange rate measured in units of foreign currency per unit of domestic currency.
      - P is the domestic price level.
      - P* is the foreign price level.
    - Relative PPP: S = kP*/P, where k is a constant parameter.
  - Both variants imply a constant real exchange rate: R = SP/P*.
  - Logarithmic form: s = c + p* − p, where s, p, p* are logarithms of S, P, P* and c = log(k) (c = 0 under absolute PPP).
  - Changes imply: ∆s = ∆p* − ∆p.
  - Empirical tests generally focus on relative PPP because aggregate price levels are typically indexed to base years that may differ across countries.

- Empirical evidence (industrial countries, medium-to-long horizons)
  - Flood and Taylor (1996) replication (1974-2006, 21 industrial country currencies vs U.S. dollar):
    - Plots use percentage changes in nominal exchange rates (horizontal axes) and percentage changes in ratios of CPIs (vertical axes).
    - Sample sizes and intervals:
      - 1-year intervals: 672 changes (32 for each of 21 countries).
      - Non-overlapping 8-year intervals: 84 changes (periods 1974-1982, 1982-1990, 1990-1998, 1998-2006).
      - Longer intervals also shown (16- and 32-year intervals).
    - Convergence of scatter plots toward the 45-degree diagonal as the interval lengthens provides strong support for PPP as a long-run hypothesis for these industrial countries over 1974-2006.
  - Meese and Rogoff (1983a, 1983b):
    - Exchange rate models could not significantly outpredict a random walk or the forward exchange rate at horizons up to 12 months.
    - At horizons of a few years or more, macroeconomic variables outperform forward exchange rates and random walk models.
  - Notable exceptions and short-horizon successes:
    - Chen and Rogoff (2003) for three “commodity currencies” (Australian, Canadian, New Zealand dollars).
    - Micro-structural approaches forecast up to three weeks (Evans and Lyons (2002, 2005)).

- Limitations, choice of price indices, and practical implications
  - Different price/cost indices (CPI, wholesale prices, unit labor costs, GDP deflators, export prices) yield different PPP-based equilibrium exchange rates.
  - Historical example: British return to the gold standard, April 1925
    - Wholesale price indices suggested little change in national price ratios since prewar; retail price comparisons implied the pound would be 12 percent overvalued at that parity.
  - Illustration (United Kingdom–Germany, 1970-2000):
    - Five measures of the real exchange rate: GDP deflators, consumer prices, producer prices, export prices, and unit labor costs.
    - Two equilibrium assumptions: average over the preceding 30 years and average over the preceding 10 years.
    - Ten different estimates of misalignment at end-2000: all indicated pound overvaluation, range from around 10 percent to more than 40 percent.

- Interpretation for policy and practice
  - PPP is a useful long-run benchmark and indicates mean reversion in real exchange rates over multi-year horizons.
  - PPP-based equilibrium estimates are sensitive to:
    - Choice of price/cost index.
    - Choice of historical averaging window for equilibrium level.
  - Because of sensitivity and large variation across reasonable specifications, PPP alone may be insufficient for definitive policy choices and should be complemented by other methodologies.

*Source: Excerpt from the IMF working paper chapter titled "Box 1. The Purchasing Power Parity Hypothesis."*

### Box 2 — PPP and the Balassa-Samuelson Hypothesis: theory, evidence, and links to MB
- Definitions and baseline equations
  - Aggregate price levels and sectoral prices:
    - P = P_T^α P_N^(1-α)  (equation (2.1))
    - P* = P*_T^β P*_N^(1-β)  (equation (2.2))
    - Real exchange rate: R = S P / P*  (equation (2.3))
    - Substitution implies (as given): R = S (P*_T / P_T)^α (P*_N / P_N)^(1-α) / (P*/P)^(?)  (equation (2.4) as given)
  - Notation:
    - P_T, P_N = prices of tradable and nontradable goods in country A.
    - P*_T, P*_N = corresponding prices in country B.
    - S = nominal exchange rate in currency B per unit currency A.
    - R = real exchange rate (an increase implies a real appreciation of currency A).

- Balassa-Samuelson hypothesis and implications
  - Hypothesis: relatively fast-growing countries experience relatively rapid productivity growth in tradables sector accompanied by relatively large increases in the ratio of nontradables prices to tradables prices.
  - Under assumptions (S*(P*_T / P_T) constant; differences between α and β second-order), if country A grows faster than country B then R will increase over time (real appreciation of currency A).

- Empirical evidence — time series versus cross-section
  - Time series (OECD and Asia-Pacific):
    - Found strong associations between relative productivity levels and relative prices of tradables and nontradables.
    - Changes in relative prices can give rise to systematic changes in real exchange rates when constructed using tradable/nontradable indices.
    - But time series challenge the notion that rapid growth generally gives rise to real appreciation: productivity growth in tradables often counterbalanced by other developments.
      - Example 1973-1992 (seven Asian economies vs Japan): only Korea and Taiwan experienced significant real appreciations; Indonesia, Malaysia, Thailand had substantial depreciations; Hong Kong and Singapore had very small appreciations.
  - Cross-section evidence (the Penn effect):
    - Strong systematic association between real exchange rates and GDP per capita.
    - Figure 3 (ICP data for 2003, Penn World Tables, 165 countries) regression: log Y = -0.1145 + 0.3851 log X  (t-values: -3.52, 10.94).
    - Some interpret this cross-section regression as an equilibrium relationship and use residuals to construct over/undervaluation measures and to infer expected real appreciation conditional on projected per capita GDP growth.

- Weaknesses, possible explanations, and caveats
  - Weak link: assumption that relative tradable prices across countries remain relatively constant over time is often violated.
  - Possible explanations for changing relative tradable prices:
    - Changes in composition and quality of tradable goods as countries develop.
    - Changes in relative prices across tradable categories interacting with country differences in price index weights.
    - Differential impacts of “goods arbitrage” costs (transportation/distribution or trade liberalization).
  - Literature rejects the "law of one price" for many specific products and disaggregated categories.
  - Despite time series doubts, the cross-section Penn effect is robust regardless of whether Balassa-Samuelson fully explains it.

- Contextual links to macroeconomic frameworks
  - Balassa-Samuelson discussion links to the macroeconomic balance (MB) framework by showing how relative price movements between tradables and nontradables affect real exchange rates, which influence current account positions and external/internal balance assessments.
  - MB framework uses UCUR and relationships between UCUR, R, and equilibrium saving-investment (S-I) balance to infer equilibrium real exchange rates (R*).

- Simple model of the underlying current account (Box 3 — skeletal specifications)
  - Imports/exports with n-quarter lags of R:
    - M_t = M(Y_t, R_t, R_{t-1}, ..., R_{t-n})  (equation (3.1))
    - X_t = X(Y*_t, R_t, R_{t-1}, ..., R_{t-n})  (equation (3.2))
    - CUR_t = X_t − M_t  (equation (3.3))
  - Underlying full-employment levels (Y, Y*) and lagged R realized:
    - M_t = M(Y, R, ..., R)  (equation (3.4))
    - X_t = X(Y*, R, ..., R)  (equation (3.5))
    - UCUR_t = X_t − M_t  (equation (3.6))
  - Definitions reiterated: M = imports, X = exports, Y/Y* = domestic/foreign GDP, Y/Y* with stars = full-employment levels, R = real exchange rate (increase = appreciation).

*Source: Box 2. PPP and the Balassa-Samuelson Hypothesis.*

### Appendix II — calibrated reduced-form model (Bayoumi and Faruqee adaptation) and U.S. 2006 assessment
- Model and intuition
  - Calibrated reduced-form model generalized to allow longer exchange-rate lags and passthrough parameters λ and λ* that can differ from unity.
  - Definitions: CUR, Y, M, X, R, YGAP, YGAP*, α (initial conditions).
  - Appreciation of R lowers domestic-currency value of imports in proportion to λ(M/Y) and reduces domestic-currency value of exports in proportion to (1 − λ*)(X/Y).
  - Appreciation affects import/export volumes through λ m_β (M/Y) and λ* x_β (X/Y) with multi-year realization governed by δ lags (δ^0, δ^1, δ^2,...).
  - UCUR defined by setting YGAP = YGAP* = 0 and replacing lagged R series by prevailing R to obtain UCUR/Y.

- Numerical inputs for 2006 (values used in the calculation)
  - CUR/Y = -.0576
  - X/Y = .1107
  - M/Y = .1683
  - YGAP* = .0007
  - YGAP = -.0018
  - R = 92.42
  - R_{-1} = 92.75
  - R_{-2} = 94.12
  - ln R = 4.526
  - ln R_{-1} = 4.530
  - ln R_{-2} = 4.545

- Parameter calibrations (Bayoumi-Faruqee suggested values)
  - x_β = 0.71
  - m_β = 0.92
  - x_ψ = 1.50
  - m_ψ = 1.50
  - δ^0 = 0.6
  - δ^1 = 0.25
  - δ^2 = 0.15
  - λ = 1
  - λ* = 1

- Estimated results and sensitivity
  - Under these values and parameters:
    - UCUR/Y = -.0573
      - Comparison: CUR/Y = -.0576 (UCUR/Y not much different from CUR/Y in 2006).
    - Small difference reflects dollar depreciation of only 2 percent between 2004 and 2006 (annual averages) and small 2006 output gaps.
  - Sensitivity:
    - If only half of the effects on trade volumes of the dollar’s 13 percent depreciation since 2002 had been realized in 2006, implied UCUR/Y ≈ -.043.
  - Estimate of σ (relating change in ln R to required UCUR/Y adjustment):
    - σ = -15.4 (calculated from equation (A2.5) under baseline parameterization).
    - If λ lowered from 1.0 to 0.4, σ = -13.7.
    - If λ and λ* both lowered to 0.4, σ = -10.8.

- United States — multi-approach assessment for 2006 (high-level findings)
  - PPP findings:
    - IMF’s CPI-based real effective exchange rate index and FRB’s CPI-based “broad index” in 2006: “not much different” than either the average for previous 26 years or the average for the 8-year period prior to post-1995 appreciation — hence PPP suggests dollar reasonably well aligned in 2006.
  - Adjusted-PPP (Penn effect) findings:
    - Based on 2003 cross-section, the United States (0,0) lies approximately 11.5 percent above regression line — implying roughly 11.5 percent overvaluation in 2003.
    - Between 2003 and 2006 IMF’s CPI-based real effective exchange rate index declined by 6.5 percent; FRB index declined by about the same amount.
    - Assuming comparable ICP data for 2006, adjusted-PPP implies dollar about 5 percent above equilibrium adjusted-PPP level in 2006.
  - Tradable sector indicators (U.S. 2006 vs 1995-2005 averages):
    - Unit labor cost and price deflator indexes (1992=100):
      - Average 1995-2005: unit labor cost 107.4; price deflator 109.0; ratio 98.5.
      - 2006: unit labor cost 115.6; price deflator 120.2; ratio 96.2.
      - Interpretation: 2006 ratio below 1995-2005 average — suggests healthy profit picture.
    - After-tax profits per dollar of sales in U.S. manufacturing (in cents):
      - All manufacturing: 5.49 (1995-2005), 8.30 (2006).
      - Nondurable goods: 6.79 (1995-2005), 9.78 (2006).
      - Durable goods: 4.33 (1995-2005), 6.83 (2006).
      - Interpretation: profitability of durables manufacturing by 2006 returned to second-half-1990s levels.
    - U.S. goods exports as percent of GDP:
      - Average 1995-2005: 7.47%
      - 2006: 7.82%
      - Interpretation: exports/GDP ratio in 2006 back up to late-1990s levels.

- Macroeconomic Balance (MB) framework findings for U.S. 2006
  - Current account and UCUR estimates:
    - Current account deficit in 2006 nearly 5.8 percent of GDP.
    - Under assumption that full effects of exchange rate changes on trade volumes realized within two years, Appendix II simple model suggests UCUR was 5.7 percent of GDP.
    - Under slower realization (e.g., only half of effects of 13 percent depreciation since 2002 realized in 2006), estimated UCUR deficit ≈ 4.3 percent of GDP.
    - These UCUR deficits are 2.3 to 3.7 percent of GDP larger than the average current account deficit over previous three decades (a rough regression-based equilibrium S-I approximation).
  - Interpretation: A current account disequilibrium of this magnitude would suggest significant misalignment according to the simple MB model in Appendix II.

*Source: _wp07296 - Appendix II uses a calibrated variant of this skeletal model, as adapted from Bayoumi and Faruqee (excerpt).*

### Appendix II — U.S. Net Foreign Liability position, NFL-stabilizing S-I balance, and overvaluation estimates
- U.S. Net Foreign Liability (NFL) position and implications
  - NFL reached nearly 25 percent of GDP in 2002 and declined to 17 percent of GDP in 2006 (partly because valuation effects of dollar depreciation outweighed ongoing large U.S. current account deficits).
  - Absent further dollar depreciation, NFL position projected to start increasing again at an annual rate of several percentage points of GDP.
  - Countries with positive NFL positions generally need current account surpluses to stabilize; the United States has been an exception by issuing liabilities offering a much lower average rate of return than its foreign assets (per official data).

- Formula for NFL-stabilizing S-I balance and parameter definitions
  - Formula (analogous to Appendix I):
    - (S-I)/Y =  [(iL-g)/(1+g)](FL/Y) - [(iC-g)/(1+g)](FA/Y)   (3)
  - Variable definitions:
    - iL, iC = rates of return on liabilities and claims
    - g = growth rate of GDP
    - FL/Y = liabilities to foreigners as ratio to GDP
    - FA/Y = claims on foreigners as ratio to GDP

- Relevant data and assumptions used to evaluate the formula
  - FA/Y = 0.83
  - FL/Y – FA/Y = 0.17 (estimated NFL/Y ratio for 2006)
  - iL = .04 (average over the 20 years through 2004)
  - iC - iL = .03 (average over 1990-2004)
  - g = .03
  - Notes:
    - Equity holdings account for roughly 60 percent of U.S. gross claims and 40 percent of U.S. gross liabilities.
    - FA/Y ratio assumes most of decline in NFL/Y between 2004 and 2006 reflected rise in FA/Y.
    - iL and iC constructed as sums of investment income and capital gains divided by relevant stocks.
    - Gros (2006) suggests the large official difference between iC and iL may be misleading due to profit-reporting incentives of foreign direct investors.

- Implied S-I balance required to stabilize NFL/Y in 2006 and exchange rate assessment
  - Numbers imply S-I balance required to stabilize NFL/Y in 2006 was a deficit of roughly 2.3 percent of GDP.
  - This required S-I deficit is some 2 to 3.4 percentage points smaller than UCUR deficit estimates.
  - Thus, this MB application suggests the dollar was overvalued in 2006 by at least 20 percent.
  - Appendix II previously indicated the real effective exchange rate of the dollar was overvalued in 2006 by at least 25 percent.

- Comparison with Obstfeld-Rogoff (OR) perspective
  - OR distinguishes tradable/nontradable goods and focuses on shocks to domestic/foreign saving or productivity that might reduce U.S. current account deficit; OR does not take a stand on equilibrium S-I or real exchange rate.
  - OR (November 2005) concluded it seems conservative to suppose the trade-weighted dollar needs to depreciate at least another 20-25% as the current account rebalances.

- Methodology weighting guidance and policy-relevance criteria
  - Prioritize methodologies that:
    - Draw support from models predicting currency crises in emerging markets and factors important for economic growth.
    - Point to situations policymakers/public would view as serious problems and persuasive rationales for exchange rate realignment or policy adjustment.
  - Relatively large weights should be given to:
    - The external sustainability variant of the macroeconomic balance approach (financial capacity).
    - Assessments of tradable goods competitiveness (political capacity).
  - These two approaches are particularly relevant for low income countries where external debt sustainability and a healthy tradable goods sector are prerequisites for sustainable growth.
  - Communication: MB and tradable competitiveness assessments point to intuitively understandable issues (growing external indebtedness, unhealthy tradable sector) that policymakers and the public can readily relate to.
  - Regression residuals or general equilibrium simulations are harder to use persuasively with policymakers/public.

- Conclusions and caveats on methodology use
  - Six different approaches described; four applied to U.S. data. Each involves conceptual simplifications or imprecise parameter estimates; different methods can yield markedly different quantitative estimates.
  - Equilibrium exchange rate assessment requires considerable judgment and multiple methodologies.
  - Prioritize approaches that identify currency-crisis or growth-failure risk (external sustainability MB and tradable competitiveness).
  - Do not use any approach mechanically; MB may be less helpful for countries with strong growth prospects attracting capital inflows and large current account deficits—judgment needed on inflow productivity and prospective unwinding of deficits.
  - No general answer on policy when exchange rate differs substantially from equilibrium level; exchange rate adjustment is not always the best or only remedy — policy advice must fit the overall macroeconomic situation and risks.

*Source: Appendix II and related sections of the supplied IMF content unit.*

### Box 1. The Purchasing Power Parity Hypothesis ......................................................................6

### Box 1. The Purchasing Power Parity Hypothesis

### Definition and formal statements
- Two main variants of PPP:
  - Absolute PPP: S = P*/P  
    - S is the nominal exchange rate measured in units of foreign currency per unit of domestic currency.  
    - P is the domestic price level.  
    - P* is the foreign price level.
  - Relative PPP: S = kP*/P, where k is a constant parameter.
- Both variants imply a constant real exchange rate: R = SP/P*.
- In logarithmic form: s = c + p* − p, where s, p, p* are the logarithms of S, P, P* and c = log(k) (c = 0 under absolute PPP).
- Changes imply: ∆s = ∆p* − ∆p.
- Empirical tests generally focus on relative PPP because data on aggregate price levels are typically indexed to base years that may differ across countries.

### Empirical evidence (industrial countries, medium-to-long horizons)
- Flood and Taylor (1996) replication: annual average data on nominal exchange rates of 21 industrial country currencies versus the U.S. dollar, with corresponding CPIs, for the period 1974-2006.
  - Plots use percentage changes in nominal exchange rates (horizontal axes) and percentage changes in ratios of CPIs (vertical axes).
  - Sample sizes and intervals:
    - 1-year intervals: 672 changes (32 for each of 21 countries).
    - Non-overlapping 8-year intervals: 84 changes (periods 1974-1982, 1982-1990, 1990-1998, 1998-2006).
    - Longer intervals also shown (16- and 32-year intervals).
  - Convergence of scatter plots toward the 45-degree diagonal as the interval lengthens provides strong support for PPP as a long-run hypothesis for these industrial countries over 1974-2006.
- Meese and Rogoff (1983a, 1983b) findings:
  - Economists’ state-of-the-art exchange rate models could not significantly outpredict a random walk or the forward exchange rate at horizons up to 12 months.
  - At horizons of a few years or more, macroeconomic variables outperform forward exchange rates and random walk models in explaining exchange-rate behavior.
- Notable exceptions and short-horizon successes:
  - Chen and Rogoff (2003) for three “commodity currencies” (Australian, Canadian, New Zealand dollars).
  - Micro-structural data approaches exploiting orders and transactions can forecast up to three weeks (Evans and Lyons (2002, 2005)).

### Limitations, choice of price indices, and practical implications
- Different price or cost indices (CPI, wholesale price indices, unit labor costs, GDP deflators, export prices) yield different PPP-based estimates of equilibrium exchange rates.
- Historical example: British return to the gold standard, April 1925
  - Wholesale price indices suggested little change in the ratio of national price levels since prewar, supporting return to prewar parity.
  - Keynes argued retail price comparisons implied the pound would be 12 percent overvalued at that parity.
  - Choice between indices had large real economic consequences.
- Illustration for United Kingdom–Germany (1970-2000):
  - Five measures of the real exchange rate used: GDP deflators, consumer prices, producer prices, export prices, and unit labor costs.
  - Two assumptions about equilibrium real exchange rate: the average over the preceding 30 years and the average over the preceding 10 years.
  - The combination of five measures and two equilibrium assumptions produced ten different estimates of misalignment for the pound at end-2000.
  - All ten estimates indicated the pound was overvalued (or the euro excessively weak), but estimates ranged from around 10 percent to more than 40 percent.

### Interpretation for policy and practice
- PPP is a useful long-run benchmark and shows mean reversion in real exchange rates over multi-year horizons.
- PPP-based equilibrium estimates are sensitive to:
  - Choice of price or cost index.
  - Choice of historical averaging window for the equilibrium level.
- Because of sensitivity and potential for large variation across reasonable specifications, PPP on its own may be insufficient for definitive policy choices (e.g., setting conversion rates or judging misalignment), and should be complemented by other methodologies.

*Source: Excerpt from the IMF working paper chapter titled "Box 1. The Purchasing Power Parity Hypothesis."*

### Box 2.  PPP and the Balassa-Samuelson Hypothesis

### Box 2.  PPP and the Balassa-Samuelson Hypothesis

### Definitions and baseline equations
- Aggregate price levels and sectoral prices are related by:
  - P = P_T^α P_N^(1-α)  (equation (2.1))
  - P* = P*_T^β P*_N^(1-β)  (equation (2.2))
  - Real exchange rate: R = S P / P*  (equation (2.3))
  - Substitution implies: R = S (P*_T / P_T)^α (P*_N / P_N)^(1-α) / (P*/P)^(?)  (equation (2.4) as given)
- Notation:
  - P_T and P_N denote prices of tradable and nontradable goods in country A.
  - P*_T and P*_N are corresponding prices in country B.
  - P and P* are aggregate price levels in the two countries.
  - S is the nominal exchange rate in currency B per unit currency A.
  - R denotes the real exchange rate (an increase in R implies a real appreciation of currency A).

### Balassa-Samuelson hypothesis and implications
- Hypothesis: relatively fast growing countries experience relatively rapid productivity growth in the tradables sector accompanied by relatively large increases in the ratio of nontradables prices to tradables prices.
- Under the Balassa-Samuelson hypothesis, if country A grows faster than country B and under the assumptions that S*(P*_T / P_T) remains constant and that any difference between α and β has second-order effects, then:
  - The value of R will increase over time, implying a real appreciation of currency A.

### Empirical evidence — time series versus cross-section
- Time series studies (OECD and Asia-Pacific economies) have:
  - Found strong associations between relative productivity levels and the relative prices of tradables and nontradables.
  - Found that, other things equal, changes in relative prices of tradables and nontradables give rise to systematic changes in real exchange rates when real exchange rates are constructed using indices of the aggregate prices of tradables and nontradables.
  - However, except for a subset of the transition countries, time series data challenge the notion that relatively rapid economic growth generally gives rise to real exchange rate appreciation. Productivity growth in tradables is often counterbalanced by other developments over time.
    - Example: among seven Asian economies that grew more rapidly than Japan over the period 1973-1992, only Korea and Taiwan experienced significant real appreciations; Indonesia, Malaysia, and Thailand experienced substantial depreciations; Hong Kong and Singapore experienced very small appreciations.
- Cross-section evidence:
  - Cross-section data provide evidence of a strong systematic association between real exchange rates and GDP per capita (the Penn effect).
  - Figure 3 (based on ICP data for 2003, Penn World Tables, annual data for 2003 for 165 countries) shows this association.
    - Regression line (t-values in parentheses): log Y = -0.1145 + 0.3851 log X  (-3.52)  (10.94)
  - Some economists interpret the cross-section regression as an equilibrium relationship between real exchange rates and relative levels of GDP per capita. This is used to construct measures of over- or undervaluation from regression residuals and to inform judgments about expected real appreciation conditional on projected growth of relative per capita GDP.

### Weaknesses, possible explanations, and caveats
- A key weak link in applying the Balassa-Samuelson hypothesis to real exchange rates is the assumption that relative prices of tradable goods across countries remain relatively constant over time. Empirical findings show:
  - Substantial cumulative changes over time in relative prices of tradable goods across countries when prices are measured at the sectoral level (e.g., manufacturing).
- Possible explanations for changing relative tradable prices:
  - Changes in composition of tradable goods production as countries develop toward more sophisticated technologies and higher quality products.
  - Changes in relative prices across categories of tradable goods interacting with country differences in weights of goods in price indices.
  - Differential impacts of changes in costs of “goods arbitrage” (transportation/distribution costs or liberalization of trade restrictions) across countries.
- Literature also rejects the “law of one price” for many specific products and highly disaggregated categories of goods.
- Despite doubts from time series evidence, the cross-section Penn effect remains a robust empirical regularity, independently of whether Balassa-Samuelson explains it.

### Contextual links to macroeconomic frameworks
- The discussion of Balassa-Samuelson links to the macroeconomic balance (MB) framework by highlighting how relative price movements between tradables and nontradables can affect real exchange rates, which in turn influence current account positions and external/internal balance assessments.
- The MB framework uses the underlying current account (UCUR) concept and relationships between UCUR, the real exchange rate (R), and the equilibrium saving-investment (S-I) balance to infer equilibrium real exchange rates (R*).

### Simple model of the underlying current account (Box 3)
- Skeletal import and export specifications (with n calendar quarters for lagged R effects):
  - M_t = M(Y_t, R_t, R_{t-1}, ..., R_{t-n})  (equation (3.1))
  - X_t = X(Y*_t, R_t, R_{t-1}, ..., R_{t-n})  (equation (3.2))
  - CUR_t = X_t − M_t  (equation (3.3))
  - Underlying levels at full-employment (Y, Y*) and with effects of past R realized:
    - M_t = M(Y, R, ..., R)  (equation (3.4))
    - X_t = X(Y*, R, ..., R)  (equation (3.5))
    - UCUR_t = X_t − M_t  (equation (3.6))
- Definitions reiterated:
  - M = imports
  - X = exports
  - Y, Y* = domestic and foreign GDP
  - Y, Y* with stars = full-employment or potential-output levels of GDP
  - R = real exchange rate (an increase in R represents an appreciation of the domestic currency)

*Source: Box 2. PPP and the Balassa-Samuelson Hypothesis.*

### Appendix II uses a calibrated variant of this skeletal model, as adapted from Bayoumi and Faruqee

### _wp07296 - Appendix II uses a calibrated variant of this skeletal model, as adapted from Bayoumi and Faruqee

### Approaches to estimating equilibrium S-I / current account positions
- Panel-regression (Debelle and Faruqee 1996) approach:
  - Focuses on stage of development (output per capita), demographics (dependency ratios), and structural fiscal positions.
  - Subsequent studies extended to larger country groups and longer lists of explanatory variables.
  - Fitted values often reflected estimated country-specific constant terms, making regression-based equilibrium S-I positions close to historical sample averages of S-I.
  - IMF (2006) addresses reliance on country-specific constants and accounts for much of the variation in S-I with less reliance on country-specific constants.
- External Sustainability / MB (macroeconomic balance) framework:
  - Requires assumptions about equilibrium stocks of net foreign assets or liabilities and about equilibrium real interest rates and equity yields; can be problematic because of these heroic assumptions.
  - The MB framework can assess sustainability of prevailing (or projected) net foreign liability positions without assuming equilibrium levels (referred to as the External Sustainability Approach).
  - Useful for countries with moderate to large net foreign liability positions for assessing whether exchange rates are badly misaligned.
  - MB methodology imposes an identity between the current account and either the capital account or the S-I balance.
  - MB focuses on medium-run determinants of exchange rates rather than short-run capital flow-driven volatility.
  - Less helpful for countries with strong growth prospects attracting large capital inflows and large current account deficits; such assessments require judgment about the productivity of inflows and potential future shifts in the current account.

### Assessments of tradable goods sector competitiveness
- Tradable sector assessments use various indicators depending on data availability:
  - Profitability measures (or inferred from unit labor costs and value-added deflators).
  - Trends in export volumes or shares of world exports.
  - Trends in import penetration ratios.
- Lipschitz and McDonald (1992) example:
  - Showed that despite substantial real appreciation of the Italian lira against the Deutschemark between 1979 and 1988, the ratio of unit labor costs to price (value-added deflator) in Italian manufacturing fell relative to Germany—implying improved competitiveness despite real appreciation.
- Emphasis: real exchange rate trends alone can be misleading for competitiveness assessment.

### Assessments based on estimated exchange rate equations
- Historical context:
  - Post-1971 “heroic age” of exchange rate theory produced many reduced-form estimates across flexible-price monetary models, sticky-price monetary models, and portfolio balance frameworks.
  - Meese and Rogoff (1983a, 1983b) found that none of the structural models outperformed a random walk out-of-sample at horizons up to one year.
- Short-run vs. medium/long-run:
  - Short-run exchange rate volatility far exceeds volatility of macroeconomic fundamentals; reduced-form models have limited short-horizon explanatory power.
  - Cointegration and time-series methods (Granger, Engel and Granger) enabled long-run relationship estimation between exchange rates and fundamentals (e.g., Faruqee 1995).
- Mussa/Faruqee-style implementation:
  - Derive reduced-form error-correction specifications consistent with long-run saving-investment equilibrium and an equilibrium NFA position.
  - Look for a long-run (cointegrating) relationship between real exchange rate, net foreign asset position, and variables influencing current account level associated with a given real exchange rate.
  - Example explanatory variables used in IMF (2006) long-run exchange rate equation:
    - net foreign asset position (as a ratio to the average of exports and imports),
    - difference between productivity (output per worker) in tradables and nontradables relative to trading partners,
    - measure of the commodity terms of trade (country-specific weights),
    - level of government consumption (as a ratio to GDP),
    - trade restriction index,
    - measure of extent of price controls (share of administered prices in CPI basket).
- Limitations:
  - Regression-based equilibrium exchange rate estimates require assumptions about equilibrium values of explanatory variables (notably net foreign asset position), which are often uncertain.

### Assessments based on general equilibrium models
- Advantages in principle:
  - Provide a fuller macroeconomic representation, impose accounting identities, and generate endogenous variable solutions consistent with identities.
- Practical limitations:
  - Complete macroeconomic models exist for limited countries.
  - Many macro models are designed for short-term forecasting and lack carefully specified long-run properties.
  - Solution paths are conditional on forecasts for exogenous variables, calibrations, and imposed shocks to replicate historical behavior.
  - Time paths are sensitive to assumptions about persistence of past shocks and future shocks.
- Conclusion: general equilibrium models highlight limitations and imprecision inherent in any equilibrium exchange rate estimation approach.

### Case study: United States (application of four approaches to 2006)
- Scope and comparability:
  - Each approach applied to assessing alignment of the dollar during 2006 for comparability.
  - Applications do not include a general equilibrium model assessment or an estimated exchange rate equation assessment in this presentation.
- Purchasing Power Parity (PPP) findings:
  - IMF’s CPI-based real effective exchange rate index and FRB’s CPI-based “broad index” in 2006: “not much different” than either the average for the previous 26 years or the average for the 8-year period of relative stability prior to the post-1995 appreciation—hence PPP suggests dollar was reasonably well aligned in 2006.
- Adjusted-PPP (Penn effect) findings:
  - Based on Figure 3 for 2003 cross-section, the United States (0,0) point lies approximately 11.5 percent above the regression line—implying roughly 11.5 percent overvaluation in 2003.
  - Between 2003 and 2006 the IMF’s CPI-based real effective exchange rate index declined by 6.5 percent; FRB index declined by about the same amount.
  - Assuming comparable International Comparisons Project data for 2006, the adjusted-PPP approach implies the dollar was only about 5 percent above its equilibrium adjusted-PPP level in 2006.
- Tradable sector indicators (profitability, export performance):
  - Unit labor cost and implicit price deflator for U.S. nonfinancial corporate sector (indexes, 1992=100):
    - Average value 1995-2005:
      - unit labor cost 107.4
      - price deflator 109.0
      - ratio 98.5
    - 2006:
      - unit labor cost 115.6
      - price deflator 120.2
      - ratio 96.2
    - Interpretation: 2006 ratio below its 1995-2005 average—suggests healthy profit picture.
  - After-tax profits per dollar of sales in U.S. manufacturing (in cents):
    - Average value 1995-2005 and 2006:
      - all manufacturing: 5.49 (1995-2005), 8.30 (2006)
      - nondurable goods: 6.79 (1995-2005), 9.78 (2006)
      - durable goods: 4.33 (1995-2005), 6.83 (2006)
    - Interpretation: profitability of durables manufacturing by 2006 returned to levels experienced in the second half of the 1990s.
  - U.S. goods exports as percent of GDP:
    - Average 1995-2005: 7.47%
    - 2006: 7.82%
    - Interpretation: exports/GDP ratio in 2006 back up to levels of the late 1990s.
- Macroeconomic Balance (MB) framework findings:
  - U.S. current account and UCUR estimates:
    - Current account deficit in 2006 nearly 5.8 percent of GDP.
    - Under assumption that full effects of exchange rate changes on trade volumes are observed within two years, the simple model in Appendix II suggests UCUR was 5.7 percent of GDP.
    - Under slower effects (e.g., if only half of the effects of the 13 percent depreciation since 2002 had been realized in 2006), the estimated UCUR deficit would have been 4.3 percent of GDP.
    - These estimated UCUR deficits are 2.3 to 3.7 percent of GDP larger than the average current account deficit over the previous three decades (a rough approximation to equilibrium S-I from regression approach).
  - Interpretation: A current account disequilibrium of this magnitude would suggest significant misalignment according to the simple MB model described in Appendix II.

*Source: _wp07296 - Appendix II uses a calibrated variant of this skeletal model, as adapted from Bayoumi and Faruqee (excerpt).*

### Appendix II, that the real effective exchange rate of the dollar was overvalued in 2006 by at

### Appendix II, that the real effective exchange rate of the dollar was overvalued in 2006 by at least 25 percent

### U.S. Net Foreign Liability (NFL) position and implications
- The U.S. NFL position reached nearly 25 percent of GDP in 2002 and subsequently declined to 17 percent of GDP in 2006, partly because the valuation effects of dollar depreciation outweighed the ongoing effects of large U.S. current account deficits.
- In the absence of further dollar depreciation, the NFL position would be projected to start increasing again at an annual rate of several percentage points of GDP.
- Countries with positive NFL positions generally need to generate current account surpluses (positive net export balances) to stabilize these positions; the United States is an exception in practice because it has been able to issue liabilities to nonresidents that offer a much lower average rate of return than it earns on its foreign assets—at least according to official data.

### Formula for NFL-stabilizing S-I balance and parameter definitions
- Formula (analogous to Appendix I):
  - (S-I)/Y =  [(iL-g)/(1+g)](FL/Y) - [(iC-g)/(1+g)](FA/Y)   (3)
- Variable definitions:
  - iL, iC = rates of return on liabilities and claims
  - g = growth rate of GDP
  - FL/Y = liabilities to foreigners as a ratio to GDP
  - FA/Y = claims on foreigners as a ratio to GDP

### Relevant data and assumptions used to evaluate the formula
- FA/Y = 0.83
- FL/Y – FA/Y = 0.17 (the estimated NFL/Y ratio for 2006)
- iL = .04 (the average over the 20 years through 2004)
- iC - iL = .03 (the average over 1990-2004)
- g = .03
- Notes on data composition:
  - Equity holdings account for roughly 60 percent of U.S. gross claims on nonresidents and 40 percent of U.S. gross liabilities to nonresidents.
  - The FA/Y ratio assumes that most of the decline in NFL/Y between 2004 and 2006 reflected a rise in FA/Y.
  - iL and iC are constructed as sums of investment income and capital gains divided by the relevant stocks of assets or liabilities.
  - Gros (2006) suggests the large difference between iC and iL in the official data may be misleading because foreign direct investors in the United States have incentives to shift reported profits outside the United States.

### Implied S-I balance required to stabilize NFL/Y in 2006 and exchange rate assessment
- Together, the above formula and numbers suggest that the level of the S-I balance required to stabilize the NFL/Y ratio in 2006 was a deficit of roughly 2.3 percent of GDP.
- This required S-I deficit is some 2 to 3.4 percentage points smaller than the estimates of the UCUR deficit.
- Thus, this application of the macroeconomic balance framework suggests that the dollar was overvalued in 2006 by at least 20 percent.
- Appendix II previously indicated that the real effective exchange rate of the dollar was overvalued in 2006 by at least 25 percent.

### Comparison with Obstfeld-Rogoff (OR) perspective
- The Obstfeld-Rogoff (OR) approach distinguishes between tradable and nontradable goods and focuses on shocks to domestic or foreign saving or productivity that might reduce the U.S. current account deficit; it does not take a stand on equilibrium S-I balances or the real exchange rate.
- OR (writing in November 2005) concluded: “Notwithstanding ... [various] qualifications, and given the depreciation that has already occurred in the last couple of years, it still seems quite conservative to suppose that the trade weighted dollar needs to depreciate at least another 20-25% as the current account rebalances.”

### Which assessment methodologies deserve the most weight?
- Criteria for prioritizing methodologies for individual country assessments:
  - Consider methodologies that draw support from theoretical models for predicting currency crises in emerging markets and those that draw on factors important for economic growth.
  - Consider which approaches point to situations policymakers and the public would view as serious problems and persuasive rationales for exchange rate realignment or other policy adjustments.
- Currency crisis literature implications:
  - First generation models link crises to depletion of foreign exchange reserves driven by policies that produce rapid inflation with fixed nominal exchange rates.
  - Second generation models emphasize doubts about a country’s willingness or political capacity to defend its currency.
  - Post-1997 models incorporate balance sheet mismatches (currency and maturity mismatches), adding to vulnerabilities from macroeconomic imbalances.
- Guidance for methodology weighting:
  - Emphasize methodologies that address a country’s ability (financial capacity) or willingness (political capacity) to sustain its exchange rate and resist speculative attacks.
  - Relatively large weights should be given to:
    - The external sustainability variant of the macroeconomic balance approach (bears on financial capacity).
    - Assessments of the competitiveness of the tradable goods sector (bears on political capacity).
  - These two approaches are also particularly relevant for low income countries, where external debt sustainability and a healthy tradable goods sector are prerequisites for sustainable growth.
- Communication and persuasiveness:
  - Macroeconomic balance and tradable goods competitiveness assessments point to intuitively understandable issues (growing external indebtedness, unhealthy tradable goods sector) that policymakers and the public can readily relate to.
  - It is harder to convince policymakers and the public that there is a problem when assessments rely primarily on regression residuals or general equilibrium simulations.

### Conclusions and caveats on methodology use
- Six different approaches for estimating equilibrium exchange rates were described; four were applied to U.S. data. Each methodology involves conceptual simplifications and/or imprecise parameter estimates; different methodologies can generate markedly different quantitative estimates.
- Assessment of equilibrium exchange rates requires considerable judgment; policymakers should inform judgments through multiple methodologies.
- Prioritization guidance:
  - Give emphasis to methodologies that identify when countries are ripe for currency crises or growth failures.
  - The external sustainability variant of the macroeconomic balance approach and assessments of tradable goods competitiveness warrant high priority, especially for identifying risks of speculative attacks and threats to growth.
- Qualifications:
  - Do not use any approach mechanically. The macroeconomic balance approach may be less helpful for countries with bright growth prospects attracting capital inflows mirrored by large current account deficits; judgment is required to assess whether inflows support productive investment and prospective unwinding of deficits.
  - The endorsement of the two approaches is not a criticism of others; institutions may find it useful to maintain multiple methodologies, particularly for multilateral exercises.
- Final policy note:
  - There is no general answer to what to do when an exchange rate differs substantially from its equilibrium level; exchange rate adjustment is not always the best or only answer. Policy advice must be framed within an overall assessment of the prevailing macroeconomic situation and risks to the macroeconomic outlook.

*Source: Appendix II and related sections of the supplied IMF content unit.*

### Appendix I

### _wp07296 - Appendix I

### Assessing the Sustainability of the Net Foreign Liability Position (Methodology)
- Purpose: Compare the UCUR position associated with the prevailing real exchange rate with the current account balance required to stabilize the prevailing (or projected) level and composition of net foreign liabilities (NFL). If UCUR is considerably less than the NFL-stabilizing balance, the NFL position may be unsustainable without a depreciation of the real exchange rate.
- Key variables:
  - S_CUR = the current account balance that sustains the level and composition of net foreign liabilities
  - NFL = net foreign liabilities
  - i = the nominal rate of return on net foreign liabilities, denominated in domestic currency
  - g = the growth rate of domestic nominal GDP
- Balance of payments identity (stock-flow relation) expressed in levels:
  - NFL_t – NFL_{t-1} = i_{t-1} NFL_{t-1} – CUR_t  (A1.1)
- Expressed as ratios to nominal GDP (lower case denotes ratio to GDP):
  - The derivation yields an expression for the current account that sustains the prevailing net foreign liability ratio:
    - S_CUR = (i - g) / (1 + g) * nfl
      - (Equation labeled (A1.4) in the source)

### Decomposition by asset type and rates of return
- When decomposing claims and liabilities into debt and equity, the nfl-sustaining current account balance becomes (expressed in the source as a sum/difference of components each adjusted by (1+g) denominators):
  - S_CUR = [ (i_LD l_D + i_LE l_E) – (i_CD c_D + i_CE c_E) ] / (1 + g)
    - Where (symbols as defined in the source):
      - c_D, c_E = the debt and equity components of claims on foreigners as ratios to GDP
      - l_D, l_E = the debt and equity components of liabilities to foreigners as ratios to GDP
      - i_CD, i_CE = nominal rates of return (domestic currency, inclusive of capital gains) on claims on foreigners
      - i_LD, i_LE = nominal rates of return (domestic currency, inclusive of capital gains) on liabilities to foreigners
- Note: The definition of the current account used here (based on the balance of payments identity) includes official transfers and private remittances; when comparing S_CUR with UCUR derived from net exports models, adjust for transfer payments (important when remittances are large).

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### _wp07296 - Appendix II

### Estimating the U.S. Underlying Current Account Position in 2006 (Model and Intuition)
- Model framework: Calibrated reduced-form model following Bayoumi and Faruqee (1998), generalized to allow longer exchange-rate lags and explicit passthrough parameters λ and λ* that can differ from unity.
- Definitions used:
  - CUR = current account
  - Y = GDP
  - M = imports
  - X = exports
  - R = the real exchange rate
  - YGAP = domestic output gap
  - YGAP* = weighted-average foreign output gap
  - α = constant reflecting initial conditions
- Key modeling features and intuition:
  - Appreciation of R lowers domestic-currency value of imports in proportion to λ(M/Y) (positive for current account) and reduces domestic-currency value of exports in proportion to (1 − λ*)(X/Y).
  - Appreciation also affects import and export volumes through λ m_β (M/Y) and λ* x_β (X/Y) with multi-year realization governed by δ lags (δ^0, δ^1, δ^2,...).
  - UCUR is defined by setting YGAP = YGAP* = 0 and replacing lagged R series by the prevailing R to obtain the underlying current account ratio UCUR/Y.

### Numerical inputs for 2006 (values used in the calculation)
- CUR/Y = -.0576
- X/Y = .1107
- M/Y = .1683
- YGAP* = .0007
- YGAP = -.0018
- R = 92.42
- R_{-1} = 92.75
- R_{-2} = 94.12
- ln R = 4.526
- ln R_{-1} = 4.530
- ln R_{-2} = 4.545

### Parameter calibrations (Bayoumi-Faruqee suggested values)
- x_β = 0.71
- m_β = 0.92
- x_ψ = 1.50
- m_ψ = 1.50
- δ^0 = 0.6
- δ^1 = 0.25
- δ^2 = 0.15
- λ = 1
- λ* = 1

### Estimated results and sensitivity
- Under the listed variable values and parameters, the model implies:
  - UCUR/Y = -.0573
    - Comparison: CUR/Y = -.0576 (so UCUR/Y is not much different from CUR/Y in 2006)
- Interpretation: Small difference reflects that the dollar depreciated by only 2 percent between 2004 and 2006 (based on annual average exchange rates) and that 2006 output gaps were small.
- Sensitivity to slower realization of trade-volume effects:
  - If only half of the effects on trade volumes of the dollar’s 13 percent depreciation since 2002 had been realized in 2006, the implied UCUR/Y ≈ -.043.
- Estimate of σ (used to relate change in ln R to required UCUR/Y adjustment):
  - σ = -15.4 (calculated from equation (A2.5) under the baseline parameterization)
- Sensitivity of σ to passthrough parameters:
  - If λ lowered from 1.0 to 0.4 (consistent with some U.S. estimates), σ = -13.7
  - If λ and λ* both lowered to 0.4, σ = -10.8

*Source: _wp07296 - Appendix I and Appendix II (from the supplied IMF content)*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp07296.pdf_