## _wp1058

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---

### I. Introduction — A Horse Race
- Central question: why does the real exchange rate matter for economic growth?
- Two competing views:
  - Washington Consensus (WC) view:
    - Real exchange rate misalignment implies macroeconomic disequilibrium that is bad for growth.
    - Overvaluation is the main danger; undervaluation is also considered a harmful misalignment to be corrected.
    - Misalignment measured as deviation of actual real exchange rate from the rate consistent with medium-term fundamentals (FEER/ERER approach).
  - Rodrik (2008) view:
    - Undervaluation (relative to PPP after controlling for per capita income) raises medium-term growth by expanding an otherwise inefficiently small tradable sector.
    - Empirical findings emphasized by Rodrik:
      - A. Growth over the medium term is much higher in countries with more undervalued exchange rates (sample 1950–2004).
      - B. The effect is linear and similar for both under- and overvaluation: overvaluation hurts growth, undervaluation helps.
- Horizon of analysis: medium term (five-year periods).
- Main empirical diagnostic reported:
  - WC and Rodrik views are observationally equivalent in the main growth regressions due to identification problems: determinants of misalignment can also be independent drivers of growth.
  - Nevertheless, empirical confirmation that overvaluations are bad and undervaluations are good for growth is reported (consistent with Rodrik, but also interpretable within WC with additional assumptions).

### II. Two Measures of Misalignment
- PPP_it^ε (Rodrik undervaluation index):
  - Defined as the residual from e_it = α_0 + α_1 y_it + α_t (e_it = log real exchange rate, y_it = log real GDP per capita, α_t = time dummies).
  - Data: Penn World Tables 6.2.
  - Sample construction:
    - Exclude Iraq, Laos, People’s Republic of Korea.
    - Divide sample into developing vs developed by real per capita GDP cut-off of USD 6000.
    - Five-year averages; dataset: 181 countries over eleven 5-year periods from 1950–54 through 2000–04.
  - By construction PPP_it^ε is centered at 0 with a standard deviation of 0.48.
- FEER_it^ε (FEER undervaluation index):
  - FEER controls for additional fundamentals beyond income per capita: terms of trade, openness, investment, government consumption.
  - FEER follows the CGER/ERER reduced-form, single-equation spirit with listed fundamentals (CPI-based real effective exchange rate typically used in CGER).

### III. Exchange Rate Regression (Selected Coefficients and Statistics)
- Real exchange rate regression reported coefficients (columns: Full Sample, Restricted Sample, Rodrik 2008, FEER):
  - Real GDP per capita:
    - Full Sample: -0.23*** (t = -21.72)
    - Restricted Sample: -0.24*** (t = -20.80)
    - Rodrik 2008: -0.24*** ("around 20")
    - FEER: -0.20*** (t = -13.14)
  - Terms of Trade (FEER column): -0.28*** (t = -3.34)
  - Openness (FEER column): 0.055** (t = 2.21)
  - Government Consumption (FEER column): 0.40*** (t = 2.72)
  - Investment (FEER column): -1.30*** (t = -6.28)
- Model statistics:
  - R-squared:
    - Full Sample: 0.19
    - Restricted Sample: 0.22
    - FEER: 0.31
  - Observations:
    - Full Sample: 1488
    - Restricted Sample: 1183
    - FEER: 1086
- Notes preserved:
  - Real exchange rate, real GDP per capita, and terms of trade are in logarithm terms.
  - For regressors in log terms, coefficient of positive 1 implies an increase of one percentage point in the variable depreciates the exchange rate by one percentage point.
  - For regressors expressed as a share of GDP (openness, government consumption, investment), coefficient of positive 1 implies an increase of the variable from 0 to 1 percent of GDP depreciates the exchange rate by 1 percentage point.
  - Robust t-statistics in parentheses. Significance: *** 1% level; ** 5% level; * 10% level.

### IV. Identification: Why PPP and FEER Results Look Similar
- Key empirical identification issue:
  - Determinants of misalignment (fundamentals X_it) are also likely independent drivers of growth, creating an omitted-variable/identification problem.
- Diagnostic algebraic result:
  - PPP_it^ε and FEER_it^ε are highly correlated; PPP_it^ε − FEER_it^ε equals combinations of α and β terms and X_it and y_t (equation (3) in source).
- Empirical descriptors:
  - FEER-based undervaluation index standard deviation = 0.46.
  - Correlation between PPP_it^ε̂ and FEER_it^ε̂ = 0.96.
- Practical consequence:
  - If WC (FEER) is true but PPP is estimated, coefficient on PPP_it^ε in the misspecified model will be nearly identical to the coefficient on FEER_it^ε in the true model because omitted fundamentals and fixed effects absorb differences.
  - Two wrongs can make a right: omission/misallocation of X_it between exchange rate and growth equations can yield similar empirical effects for misalignment.

### V. Growth Regression Frameworks and Empirical Comparisons
- Two growth specifications:
  - Rodrik (PPP-based): 5-year average growth regressed on PPP_it^ε̂, initial income, other growth determinants, country/time fixed effects (equation (4)).
  - WC/FEER-based: 5-year average growth regressed on FEER_it^ε̂, initial income, other growth determinants, country/time fixed effects (equation (5)).
- Horse-race attempt:
  - Regression with both PPP_it^ε̂ and FEER_it^ε̂ is ill-defined because of the algebraic identity linking the two measures (equation (6) leads to u''_it = 0).
- Empirical comparison findings:
  - Undervaluation is significantly and positively associated with growth in developing countries whether measured by PPP_it^ε̂ or FEER_it^ε̂.
  - Estimated coefficient on undervaluation from PPP-based model is almost equal to that from FEER-based model (1̂β ≈ 1̂β′).
  - Rodrik (2008) reported coefficient on undervaluation = 0.017 with t = 5.21 in full sample (1303 observations), and 0.026 and 5.84 in developing subsample (790 observations).
  - Table 2 illustrative observations: 629, 549, 549, 549, 549, 549 across columns.
  - Example: PPP-based estimated coefficient on investment = 0.074 (Column 4). Using 1̂β′ and 2̂α′ with investment coefficient -1.3 predicts a misspecified coefficient 0.074 – 0.021*(-1.3) = 0.10 (arithmetic shown in text).
  - Interpretation note from Table 2: A 10 percent overvaluation lowers growth by 0.2 percentage point.

### VI. Piecewise-linear Misalignment Interactions (Section 3)
- Specification: baseline growth regression augmented with interaction dummies D1–D6 for misalignment ranges:
  - D1: extreme undervaluation of 100% or more.
  - D2: large undervaluation between 50% and 100%.
  - D3: small/moderate undervaluation of 50% or less.
  - D4: small/moderate overvaluation of 50% or less (omitted base case).
  - D5: large overvaluation between 50% and 100%.
  - D6: extreme overvaluation of 100% or more.
- Regression results (developing countries; dependent variable = log difference of per capita real GDP):
  - Ln initial income:
    - Column (1): -0.058*** (-7.02)
    - Column (2): -0.057*** (-7.03)
    - Column (3): -0.067*** (-6.10)
    - Column (4): -0.060*** (-7.24)
  - D1*ln UNDERVAL:
    - (1): 0.056*** (3.26)
    - (2): 0.055*** (3.07)
    - (3): 0.027** (2.07)
    - (4): 0.024* (1.62)
  - D2*ln UNDERVAL:
    - (1): 0.031*** (3.34)
    - (2): 0.023** (2.39)
    - (3): 0.031*** (2.64)
    - (4): 0.025*** (2.75)
  - D3*ln UNDERVAL:
    - (1): 0.011 (0.84)
    - (2): 0.008 (0.60)
    - (3): 0.014 (0.75)
    - (4): 0.024* (1.81)
  - D4*ln UNDERVAL:
    - (1): 0.033** (2.14)
    - (2): 0.035** (2.30)
    - (3): 0.018 (0.78)
    - (4): 0.010 (0.65)
  - D5*ln UNDERVAL:
    - (1): 0.027** (1.94)
    - (2): 0.029** (2.10)
    - (3): 0.027** (1.92)
    - (4): 0.032** (2.34)
  - D6*ln UNDERVAL:
    - (1): 0.022*** (2.68)
    - (2): 0.021*** (2.53)
    - (3): 0.021*** (2.70)
    - (4): 0.021*** (2.60)
  - Ln Terms of Trade:
    - (3): -0.003 (-0.29)
    - (4): 0.004 (0.42)
  - Openness:
    - (3): 0.016** (2.15)
    - (4): 0.016** (2.16)
  - Government Consumption:
    - (3): 0.012 (0.33)
    - (4): 0.003 (0.09)
  - Lag Investment:
    - (3): 0.061*** (2.47)
    - (4): 0.077*** (2.99)
- Observations:
  - Columns (1) and (2): 549
  - Column (3): 629
  - Column (4): 549
- Two misalignment measures used across specifications: Underval_FEER and Underval_PPP. Time and country fixed-effects included. Significance: *** 1% level; ** 5% level; * 10% level.

### VII. Linearity and Symmetry Tests (Table 4)
- Hypothesis tests report limited evidence of differences across misalignment categories; overall support for “overvaluation is bad and undervaluation is good for growth.”
- Selected test statistics and p-values:
  - Only extreme over- and undervaluations matter:
    - Underval_FEER: F(3,437)=4.17 p-value=0.00
    - Underval_PPP: F(3,437)=2.63 p-value=0.05
  - Only overvaluations matter, effect linear in degree of overvaluation:
    - Underval_FEER: F(5,437)=1.92 p-value=0.09
    - Underval_PPP: F(5,437)=2.99 p-value=0.01
  - No effect of overvaluation:
    - Underval_FEER: F(3,437)=4.32 p-value=0.00
    - Underval_PPP: F(3,437)=4.47 p-value=0.00
  - Only undervaluations matter, effect linear in degree of undervaluation:
    - Underval_FEER: F(5,437)=2.68 p-value=0.02
    - Underval_PPP: F(5,437)=2.20 p-value=0.05
  - No effect of undervaluation:
    - Underval_FEER: F(3,437)=3.61 p-value=0.01
    - Underval_PPP: F(3,437)=3.51 p-value=0.02

### VIII. Main Empirical Conclusions
- Three principal conclusions:
  1. It is very difficult to disentangle empirically which misalignment measure (PPP-based vs FEER-based) is most relevant for growth because the difference between concepts is closely related to factors that also drive growth directly.
  2. Insofar as direct and indirect effects of other drivers can be disentangled, there is some evidence in favor of the WC view: deviations from PPP are not important once deviations from equilibrium are controlled for.
  3. Further empirical progress would require plausible specifications of both the real exchange rate and growth regressions; specification searches may not settle the issue due to reverse causality and elusive fully satisfactory specifications.
- Empirical regularity across specifications:
  - Overvaluation is detrimental and undervaluation is beneficial for growth; the relationship appears linear in the data, consistent with Rodrik (2008).
  - Either misalignment measure (PPP-based or FEER-based) can be included in growth regressions with similar estimated coefficients; differences in misalignment values are offset by differences in implied effects of fundamentals on growth.

### IX. Suggestive Evidence, Policy Implications, and Limitations
- Suggestive evidence favoring WC interpretation:
  - If fundamentals affecting equilibrium RER differ in timing or mechanism from those driving growth (e.g., contemporaneous vs lagged investment), accounting for these can make FEER_it^ε̂ more important and render PPP_it^ε̂ insignificant. This requires debatable identifying assumptions and raises endogeneity concerns.
- Policy implications differ by view:
  - If Rodrik view correct (undervaluation good for growth):
    - Consider growth benefits of undervaluation when influencing fundamentals.
    - Inward transfers causing overvaluation relative to PPP (“Dutch disease”) may harm growth.
    - Policies like capital controls or intervention rules that limit real appreciation could help long-run growth.
  - If WC view correct:
    - Emphasize policies consistent with medium-term internal and external balance rather than deliberate undervaluation.
    - CGER methodology can help identify RER problems.
- Limitations and directions for research:
  - Strong assumptions required to distinguish hypotheses convincingly; important heterogeneity likely exists.
  - Different sources of undervaluation (savings-driven vs terms-of-trade shocks) may have different growth implications; aggregate cross-country regressions may be too restrictive.
  - Progress likely requires disaggregated evidence to identify channels and causality.

*Source: IMF Working Paper WP/10/58, "The Real Exchange Rate and Growth Revisited: The Washington Consensus Strikes Back?" (Section 1–3) by Andrew Berg and Yanliang Miao.*

### Section 1

### _wp1058 - Section 1

### I. Introduction – A Horse Race
- Central question: why does the real exchange rate matter for economic growth?
- Two competing views:
  - Washington Consensus (WC) view:
    - Real exchange rate misalignment implies macroeconomic disequilibrium that is bad for growth.
    - Overvaluation is the main danger; undervaluation is also considered a harmful misalignment to be corrected.
    - Misalignment measured as deviation of actual real exchange rate from the rate consistent with medium-term fundamentals (FEER/ERER approach).
  - Rodrik (2008) view:
    - Undervaluation (relative to PPP after controlling for per capita income) raises medium-term growth by expanding an otherwise inefficiently small tradable sector.
    - Two empirical findings emphasized by Rodrik:
      - A. Growth over the medium term is much higher in countries with more undervalued exchange rates (sample 1950–2004).
      - B. The effect is linear and similar for both under- and overvaluation: overvaluation hurts growth, undervaluation helps.
- Policy implications noted (not the focus here): real exchange rate is not a direct policy instrument; deliberate undervaluation raises questions of feasibility and “beggar thy neighbor” effects.
- Horizon of analysis: medium term (five-year periods).
- Main result reported in this section:
  - WC and Rodrik views are observationally equivalent in the main growth regressions: an identification problem arises because determinants of misalignment can also be independent drivers of growth.
  - Nevertheless, empirical confirmation that overvaluations are bad and undervaluations are good for growth (consistent with Rodrik, but also interpretable within WC with additional assumptions).

### II. Two Measures of Misalignment
- Objective: construct two alternative estimates of exchange rate undervaluation and compare their roles in growth regressions.
- Definitions:
  - PPP_it ε (Rodrik undervaluation index):
    - Defined as the residual from the regression:
      PPP_it ε follows exactly Rodrik (2008) and measures the deviation of the real exchange rate from PPP, adjusted for per capita income.
    - Formally, PPP_it ε is the residual from:
      e_it = α_0 + α_1 y_it + α_t
      (where e_it is the log of the real exchange rate for country i at time t, y_it is the log of real GDP per capita, and α_t is a full set of time dummies).
    - Data: Penn World Tables 6.2 (Heston, Summers, and Atena 2006).
    - Sample construction:
      - Exclude outliers Iraq, Laos, and the People’s Republic of Korea (following Rodrik).
      - Divide sample into developing and developed subsamples using a real per capita GDP cut-off of USD 6000.
      - Use five-year averages for each data series.
      - Dataset consists of observations on 181 countries over eleven 5-year time periods from 1950–54 through 2000–04.
    - By construction, PPP_it ε is centered at 0 with a standard deviation of 0.48.
    - Note: reproducing Rodrik undervaluation index in the 160 countries sample yields the same standard deviation of 0.48.
  - FEER_it ε (FEER undervaluation index):
    - FEER: fundamental equilibrium real exchange rate (Nurkse 1945 notion).
    - FEER_it ε controls for additional fundamental determinants of the equilibrium exchange rate beyond income per capita (terms of trade, openness, investment, government consumption), hence measures deviation of the real exchange rate from a full set of equilibrium determinants.
    - The CGER/ERER reduced form approach involves single-equation estimation of the real exchange rate consistent with fundamentals over the medium term; CPI-based real effective exchange rate typically used in CGER (IMF 2008). The FEER approach here follows that spirit with the listed fundamentals.

### Empirical Details and Key Regression Results (Table 1 highlights)
- Exchange rate regression (dependent variable: Real Exchange Rate).
- Reported coefficients (columns correspond to Full Sample, Restricted Sample, Rodrik 2008, FEER):
  - Real GDP per capita:
    - Full Sample: -0.23*** (t = -21.72)
    - Restricted Sample: -0.24*** (t = -20.80)
    - Rodrik 2008: -0.24*** ("around 20")
    - FEER: -0.20*** (t = -13.14)
  - Terms of Trade (FEER column):
    - Coefficient: -0.28*** (t = -3.34)
  - Openness (FEER column):
    - Coefficient: 0.055** (t = 2.21)
  - Government Consumption (FEER column):
    - Coefficient: 0.40*** (t = 2.72)
  - Investment (FEER column):
    - Coefficient: -1.30*** (t = -6.28)
- Model statistics:
  - R-squared:
    - Full Sample: 0.19
    - Restricted Sample: 0.22
    - FEER: 0.31
  - Observations:
    - Full Sample: 1488
    - Restricted Sample: 1183
    - FEER: 1086
- Notes preserved from source:
  - Real exchange rate, real GDP per capita, and terms of trade are in logarithm terms.
  - For regressors in logarithm terms, coefficient of positive 1 implies an increase of one percentage point in the variable depreciates the exchange rate by one percentage point.
  - For regressors expressed as a share of GDP (openness, government consumption, investment), a coefficient of positive 1 implies an increase of the variable from 0 to 1 percent of GDP depreciates the exchange rate by 1 percentage point.
  - Full sample: same sample as Rodrik (2008), excluding Iraq, Laos, and North Korea.
  - Restricted sample: subset of full sample for which terms of trade data are available (see Christiansen et al. (2009)).
  - Robust t-statistics in parentheses.
  - Significance notation: *** significant at 1% level; ** significant at 5% level; * significant at 10% level.

### III. Identification and the Horse Race Between Misalignment Definitions
- Research design:
  - Compare growth regressions that include either PPP_it ε or FEER_it ε as measures of misalignment.
  - Key identification challenge: determinants of misalignment (fundamentals) are also likely independent drivers of growth, making it hard to disentangle whether misalignment itself or the fundamentals matter for growth.
- Main diagnostic conclusion:
  - WC and Rodrik views are observationally equivalent in the primary growth regressions examined: similar empirical implications make disentangling the theories difficult without strong additional identifying assumptions.
  - Some regression evidence (when imposing fairly strong identifying assumptions) suggests deviations from fundamentals (FEER-based misalignment) may be more important than deviations from PPP.

### IV. Undervaluation vs Overvaluation
- Empirical confirmation in the data:
  - Both overvaluations are detrimental and undervaluations are beneficial for growth.
  - This finding aligns squarely with Rodrik’s results (undervaluation raises growth, overvaluation lowers growth), but can also be interpreted within WC under certain explanations (the paper notes this requires some “gymnastics” from the WC viewpoint).
- Methodological note:
  - Analysis treats undervaluation and overvaluation effects, linearity, and symmetry hypotheses and explores them in subsequent regression sections (Section 4 in source).

### V. Data and Sample Construction Specifics (preserved)
- Data source: Penn World Tables 6.2 (Heston, Summers, and Atina 2006).
- Sample exclusions: Iraq, Laos, People’s Republic of Korea.
- Income cutoff for subsamples: USD 6000 real per capita GDP to divide developing vs developed.
- Temporal aggregation: five-year averages used to construct panel covering eleven 5-year periods from 1950–54 through 2000–04.
- Sample counts reported: observations = 1488 (Full Sample), 1183 (Restricted Sample), 1086 (FEER regression).

*Source: IMF Working Paper WP/10/58, "The Real Exchange Rate and Growth Revisited: The Washington Consensus Strikes Back?" (Section 1) by Andrew Berg and Yanliang Miao.*

### Section 2

### Section 2

### Methodology: FEER and PPP-based Undervaluation Measures
- The fundamental equilibrium exchange rate (FEER) is estimated by fitting the equation:
  - FEER_it = α0 + α1 y_it + α2' X_it + α3' ? + α4' ? + ε_it  (equation (2) as presented)
  - In the main specification X_it (the “other fundamentals”) are: the log of terms of trade (ToT), government consumption as a share of GDP, investment as a share of GDP, and openness.
- Terms of trade (ToT) data come from a comprehensive database of commodity terms of trade for around 160 countries from 1960 based on commodity price data and country-specific trade shares for 32 commodities.
- With the exception of ToT, additional variables are from PWT6.2.
- Estimation approach:
  - OLS with time fixed effects is used (following Rodrik (2008)), with the caveat that the real exchange rate is likely nonstationary and panel cointegration techniques (VECM, VAR, DOLS) are common; OLS coefficient estimators are consistent (superconsistent) when relevant cointegrating variables, notably per capita income, are included on the right-hand side. Standard errors may not be well-behaved; panel bootstrap could help but is not undertaken.

### Data and Diagnostic Statistics
- The FEER-based undervaluation index (FEER_it^ε̂) is centered at 0 with a standard deviation of 0.46.
- The PPP-based undervaluation index (PPP_it^ε̂) and FEER_it^ε̂ are highly correlated:
  - Correlation coefficient = 0.96.
- Key equation linking PPP and FEER misalignments:
  - PPP_it^ε̂ − FEER_it^ε̂ = (combinations of α and β terms and X_it and y_t) as shown in equation (3) in the source.

### Regression Frameworks: Two Growth Models
- Rodrik (2008) specification (PPP-based view):
  - 5-year average growth regressed on PPP_it^ε̂, initial income, other growth determinants, and country/time fixed effects (equation (4)).
- Williamson-Collier (WC) specification (FEER-based view):
  - 5-year average growth regressed on FEER_it^ε̂, initial income, other growth determinants, and country/time fixed effects (equation (5)).
- Attempted “horse race” including both misalignment measures:
  - Regression with both PPP_it^ε̂ and FEER_it^ε̂ is ill-defined because of the exact algebraic relationship between the two measures (equation (6) leads to an identity and u''_it = 0).

### Empirical Findings and Numerical Results
- Regression comparisons (summary):
  - Undervaluation is significantly and positively associated with growth in developing countries whether measured by PPP_it^ε̂ or FEER_it^ε̂.
  - The estimated coefficient on undervaluation from the PPP-based model is almost equal to that from the FEER-based model (1̂β ≈ 1̂β′).
- Examples and numeric specifics from the text:
  - The FEER undervaluation index standard deviation = 0.46.
  - Correlation between PPP_it^ε̂ and FEER_it^ε̂ = 0.96.
  - Rodrik (2008) reported a coefficient estimate on undervaluation of 0.017 with a t-statistic of 5.21 in the full sample (1303 observations), and 0.026 and 5.84 in the developing country subsample (790 observations).
  - Note from Table 2 (illustrative numbers): Observations reported as 629, 549, 549, 549, 549, 549 across columns.
  - Example decomposition for investment coefficients:
    - PPP-based specification: estimated coefficient on investment = 0.074 (Column 4).
    - 1̂β′ from Column (4) and 2̂α′ from Column (4) of Table 1 gives a predicted misspecified coefficient of 0.074 – 0.021*(-1.3) = 0.10 (illustrated arithmetic in the text).
  - Note: Developing countries defined as per capita GDP below $6,000 in Table 2 notes.
  - Interpretation note: A 10 percent overvaluation lowers growth by 0.2 percentage point (stated in Table 2 notes).

### Interpretation: Why PPP- and FEER-based Results Look Similar
- Algebraic relationship: Equation (3) shows PPP-based misalignment differs from FEER-based misalignment because of (i) fundamentals that appreciate equilibrium RER (the X_it term) and (ii) inclusion of fundamentals leading to different estimates of common determinants (per capita income, constant, time fixed effects).
- Omitted-variable equivalence:
  - If the WC model (FEER-based) is true but the PPP model is estimated, coefficient on PPP_it^ε̂ in the misspecified model will be nearly identical to the coefficient on FEER_it^ε̂ in the true model; differences are absorbed via coefficients on X_it and fixed effects (Γ_it).
  - Two wrongs can make a right: when X_it both directly affects growth and affects equilibrium RER, omission or misallocation of X_it between the exchange rate and growth equations can yield similar empirical effects for misalignment.
- Identification difficulty:
  - It is empirically difficult to disentangle which misalignment concept matters for growth because the difference between concepts is closely related to factors that also directly drive growth.
  - Excluding X_it from the growth regression (as in Rodrik’s baseline) allows a horse-race to be run; results can change (e.g., FEER_it^ε̂ coefficient increases and PPP_it^ε̂ can take unexpected sign), but this depends on the a priori plausibility of excluding X_it.
- Attempts at differentiation:
  - One plausible differentiation: treat investment as contemporaneously affecting equilibrium RER but with a lagged (time-to-build) effect on growth. Implementing this (Column 6 of Table 2) leaves FEER_it^ε̂ coefficient magnitude similar and PPP_it^ε̂ near 0 (difference not significant). However, this relies on debatable assumptions and can introduce endogeneity concerns.

### Conclusions and Robustness
- Three principal conclusions drawn:
  1. It is very difficult to disentangle empirically which measure of misalignment (PPP-based vs FEER-based) is most relevant for growth because the difference between the misalignment concepts is closely related to factors that may drive growth directly.
  2. Insofar as the direct and indirect effects of other drivers can be disentangled, there is some evidence in favor of the WC view: deviations from PPP are not important once deviations from equilibrium are controlled for.
  3. Making further empirical progress would require plausible specifications of both the real exchange rate and growth regressions; such specification searches are outside the paper’s scope and may not settle the issue due to challenges like reverse causality and elusive fully satisfactory specifications.
- Undervaluation vs overvaluation:
  - The WC view predicts both undervaluation and overvaluation should be bad for growth (sign of coefficient on misalignment should switch with sign of misalignment).
  - Rodrik (2008) predicts overvaluation bad for growth and undervaluation good (sign constant; symmetric relationship).
  - Empirical finding: fairly broad support for Rodrik (2008)’s interpretation — cannot reject coefficient invariance to sign of misalignment; this result holds across misalignment concepts and when dropping X variables as robustness check.

*Source: _wp1058 - Section 2*

### Section 3

### _wp1058 - Section 3

### Empirical specification: piecewise-linear misalignment interactions
- The baseline growth regression for developing countries is augmented with interaction dummies for exchange rate misalignment to allow a piecewise-linear relationship:
  - Equation (8) augments growth with D1,...,D6 interaction dummies where:
    - D1 is the dummy for extreme undervaluation of 100% or more;
    - D2 for large undervaluation between 50% and 100%;
    - D3 for small/moderate undervaluation of 50% or less;
    - D4 for small/moderate overvaluation of 50% or less (the omitted base case is moderate overvaluation of 50% or less — the missing D4);
    - D5 for large overvaluation between 50% and 100%;
    - D6 for extreme overvaluation of 100% or more.
- Specification includes initial conditions, a full set of time and country fixed-effects, exchange rate misalignments, and fundamentals.

### Regression results (Table 3): coefficients on misalignment and controls
- Dependent variable: log difference of per capita real GDP. Sample: Developing countries only (per capita GDP below $6000).
- Selected coefficient estimates (robust t-statistics in parentheses):
  - Ln initial income:
    - Column (1): -0.058*** (-7.02)
    - Column (2): -0.057*** (-7.03)
    - Column (3): -0.067*** (-6.10)
    - Column (4): -0.060*** (-7.24)
  - D1*ln UNDERVAL:
    - (1): 0.056*** (3.26)
    - (2): 0.055*** (3.07)
    - (3): 0.027** (2.07)
    - (4): 0.024* (1.62)
  - D2*ln UNDERVAL:
    - (1): 0.031*** (3.34)
    - (2): 0.023** (2.39)
    - (3): 0.031*** (2.64)
    - (4): 0.025*** (2.75)
  - D3*ln UNDERVAL:
    - (1): 0.011 (0.84)
    - (2): 0.008 (0.60)
    - (3): 0.014 (0.75)
    - (4): 0.024* (1.81)
  - D4*ln UNDERVAL:
    - (1): 0.033** (2.14)
    - (2): 0.035** (2.30)
    - (3): 0.018 (0.78)
    - (4): 0.010 (0.65)
  - D5*ln UNDERVAL:
    - (1): 0.027** (1.94)
    - (2): 0.029** (2.10)
    - (3): 0.027** (1.92)
    - (4): 0.032** (2.34)
  - D6*ln UNDERVAL:
    - (1): 0.022*** (2.68)
    - (2): 0.021*** (2.53)
    - (3): 0.021*** (2.70)
    - (4): 0.021*** (2.60)
  - Ln Terms of Trade:
    - (3): -0.003 (-0.29)
    - (4): 0.004 (0.42)
  - Openness:
    - (3): 0.016** (2.15)
    - (4): 0.016** (2.16)
  - Government Consumption:
    - (3): 0.012 (0.33)
    - (4): 0.003 (0.09)
  - Lag Investment:
    - (3): 0.061*** (2.47)
    - (4): 0.077*** (2.99)
- Observations:
  - Columns (1) and (2): 549 observations
  - Column (3): 629 observations
  - Column (4): 549 observations
- Notes: Two misalignment measures are used across specifications: Underval_FEER and Underval_PPP. Time dummies and country dummies are included in all specifications. Significance: *** 1% level; ** 5% level; * 10% level.

### Linearity and symmetry hypothesis tests (Table 4)
- A set of hypothesis tests shows little evidence of significant differences across misalignment categories; overall “overvaluation is bad and undervaluation is good for growth” is supported by tests.
- Reported test statistics (as presented):
  - Only extreme over- and undervaluations matter, possibly differently:
    - Underval_FEER: F(3,437)=4.17 p-value=0.00
    - Underval_PPP: F(3,437)=2.63 p-value=0.05
  - Only overvaluations matter, and effect is linear in degree of overvaluation:
    - Underval_FEER: F(5,437)=1.92 p-value=0.09
    - Underval_PPP: F(5,437)=2.99 p-value=0.01
  - No effect of overvaluation:
    - Underval_FEER: F(3,437)=4.32 p-value=0.00
    - Underval_PPP: F(3,437)=4.47 p-value=0.00
  - Only undervaluations matter, and effect is linear in degree of undervaluation:
    - Underval_FEER: F(5,437)=2.68 p-value=0.02
    - Underval_PPP: F(5,437)=2.20 p-value=0.05
  - No effect of undervaluation:
    - Underval_FEER: F(3,437)=3.61 p-value=0.01
    - Underval_PPP: F(3,437)=3.51 p-value=0.02
- Notes: Tests are based on growth regressions that include initial conditions, time and country fixed-effects, exchange rate misalignments, and fundamentals.

### Main findings and interpretation
- Empirical regularity:
  - Overvaluation is found to be bad for growth; undervaluation is found to be good for growth in the sample and specifications reported.
  - Linearity: The relationship between misalignment and growth appears linear in the data, consistent with Rodrik (2008).
- On competing frameworks:
  - Rodrik (2008) view: An exchange rate undervalued relative to PPP (after adjusting for per capita income) promotes growth by supporting a larger traded goods sector and compensating for institutional weaknesses.
  - Washington Consensus (WC) view: Deviations from equilibrium are bad for growth — overvaluation implies external imbalance; undervaluation implies internal imbalance and excessive inflation.
- Comparison of misalignment measures:
  - Two misalignment measures are compared: a PPP-based misalignment (Rodrik) and a FEER-based misalignment (deviation from fundamentals).
  - It is empirically difficult to disentangle which misalignment measure matters more because the fundamentals that define FEER also directly affect growth.
  - Either measure can be included in growth regressions with estimated coefficients that are about the same; differences in misalignment values are offset by differences in the implied effects of fundamentals on growth.
  - Hence, in terms of misalignment effects on growth, the answer is similar regardless of the misalignment definition used; the effects of fundamentals on growth are also invariant to the definition of misalignment.

### Suggestive evidence and policy implications
- Suggestive evidence favoring the WC interpretation:
  - Under the assumption that the set of fundamentals determining the equilibrium real exchange rate differs from those driving growth directly (e.g., lagged investment as the growth regression investment variable vs. concurrent investment for equilibrium exchange rate regression), variations in misalignment after accounting for fundamentals appear to matter for growth.
  - Conditional on this WC-type misalignment, deviations from PPP do not matter.
- Policy implications differ sharply by view:
  - If undervaluation (including PPP-driven undervaluation) is good for growth (Rodrik view):
    - Policymakers should consider the growth benefits of undervaluation when influencing fundamentals.
    - Inward transfers that cause overvaluation relative to PPP (“Dutch disease”) may have perverse consequences on growth.
    - Policies such as capital controls or intervention rules that limit real appreciation could help long-run growth.
  - If the WC view is correct:
    - Policy emphasis should be on running policies consistent with medium-term internal and external balance, rather than deliberately generating undervaluation.
    - Approaches like the IMF’s “CGER” methodology can help identify problems.

### Limitations and directions for further research
- Identification and specification challenges:
  - Strong assumptions are required to distinguish the Rodrik and WC hypotheses convincingly.
  - Important heterogeneity likely exists in the relationship between the real exchange rate and growth; omitted variables (e.g., high domestic savings) may drive both the real exchange rate and growth, biasing results.
  - Different sources of undervaluation (savings-driven vs. terms-of-trade shocks) may have different implications for growth; the aggregate specification may be too restrictive.
- Recommendations for future work:
  - Different growth regressions might help but the approach has severe limitations.
  - Progress likely requires stepping away from aggregate cross-country growth regressions toward more disaggregated evidence to identify channels and causality.

*Source: _wp1058 - Section 3 (Tables 3 and 4, conclusion and discussion of empirical results).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp1058.pdf_