## 1. ARDL Model

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### Overview and motivation
- Turkey experienced sizable swings of the real effective exchange rate (REER) over the last 20 years; REER appreciated by close to 25% over the ten years before the 2008-09 global financial crisis and relinquished most of these gains through end-2017.
- During the REER appreciation phase the current account deficit widened to over 5% of GDP.
- Cross-country studies confirm stability of the REER–real trade balance link; country-specific estimates for Turkey show wide dispersion.
- Literature survey points:
  - Export and import elasticities reported range in the range of 0.3 to 0.9 (absolute values).
  - Income elasticities were typically higher than the absolute value of REER elasticities and larger than one.
  - Recent studies find income is a more important determinant of trade flows than the REER.

### Data and stylized facts
- Sample: quarterly data over the period 1998-2017. The sample ends in 2017 (analysis carried out summer 2017 and finalized by mid-2018).
- REER construction:
  - CBRT publishes consumption-based REER starting in 2003; authors construct longer CPI-based REER series and back-cast pre-2003 levels.
  - Calculations align closely with TurkStat’s published REER series from 2003 onward.
- Trade series:
  - Exports and imports include goods and services.
  - Nominal and real values taken from TurkStat’s national accounts and used in expenditure-side GDP compilation.
- Empirical patterns:
  - Scatter plots suggest reasonably linear relationships between real exports/imports and REER, with structural break around the switch from secular REER appreciation to depreciation.
  - Real trade balance is negatively correlated with REER in the full sample and in each sub-sample.
  - Prior to Q3 2008 the link between real imports and REER was very strong and exports showed little negative response to REER appreciation; after Q3 2008 the sign of the correlation between exports and REER turned negative while imports’ responsiveness weakened.

### Analytical framework (partial-equilibrium trade-elasticities approach)
- REER definition (two-country case): Q′ = P · S · (1/ P̃ ) where P = domestic CPI; P̃ = CPI in trade partner; S = exchange rate expressed as domestic currency units per one unit of foreign currency. Increase of Q′ corresponds to real appreciation of the Lira.
- Real trade balance identity: TB = X − M = X − M̃ / Q′ (Equation (1)); TB, X in chain-linked Turkish Lira (reference year = 2009); M̃ = real imports in chain-linked foreign currency.
- Behavioral functions:
  - Imports: M̃ = M̃(Y, Q′) with ∂M̃/∂Y > 0 and ∂M̃/∂Q′ > 0.
  - Exports: X = X(Ỹ, Q′) with ∂X/∂Ỹ > 0 and ∂X/∂Q′ < 0.
- Elasticity definitions (REER elasticities defined positive):
  - ηX = −(∂X/∂Q′)·(Q′/X) > 0
  - ηM̃ = (∂M̃/∂Q′)·(Q′/M̃) > 0
  - Income elasticities:
    - εX = (∂X/∂Ỹ)·(Ỹ/X) > 0
    - εM̃ = (∂M̃/∂Y)·(Y/M̃) > 0
- Growth decomposition (Equation (7)):
  - ẗb = 1/(1−α) [ εM̃ · ȳ − α εX · ȳ̃ + q̇′ ( α ηX + ηM̃ − 1 ) ] where α = X / M.
  - Decomposes contributions into Income Effect and Substitution Effect.
- Marshall-Lerner condition (zero income effect): REER depreciation (q̇′ < 0) improves real trade balance in levels if α ηX + ηM̃ > 1 (Equation (9)).
- Role of domestic-foreign income growth differential: income differential helps narrow trade deficit if ȳ / ȳ̃ < α εX / εM̃ (Equation (10)).

### ARDL specification and estimation approach
- ARDL form (Equation (11)): yt = α0 + ∑_{i=1}^p αi yt−i + ∑_{i=0}^p β′i xt−i + εt
  - y = Turkey’s real exports (Lira) or real imports (USD), both in logs.
  - x = log of REER and log of real income (domestic or trade partners).
  - p = lag length chosen to ensure uncorrelated residuals.
- Long-run elasticities derived (Equation (12)):
  - y* = α0 / (1 − ∑_{i=1}^p αi ) + δ′ x* , δ = ( ∑_{i=0}^p βi ) / (1 − ∑_{i=1}^p αi ).
- Error-correction form (Equation (13)):
  - ∆yt = −θ( yt−1 − α0/θ − δ′ xt−1 ) + ∑_{i=1}^{p−1} γi ∆yt−i + ∑_{i=0}^{p−1} ρ′i ∆xt−i + ut, where θ = 1 − ∑_{i=1}^p αi is the fraction of last period’s disequilibrium eliminated in the current one.
- Estimation choices and robustness:
  - Fit ARDL models on full sample and sub-samples to detect structural breaks.
  - Estimate full-sample ARDL with REER interaction terms.
  - Use Stata’s ardl package; Pesaran and Shin (1998) result invoked on consistency regardless of regressors’ order of integration.

### Empirical strategy highlights
- Complementary techniques to address structural breaks and time variation:
  - Rolling estimation
  - Sub-sample estimation
  - ARDL with REER interaction term (full sample)
  - NARDL (non-linear ARDL)
- Purpose: detect, control for, and interpret structural breaks in REER–trade links to obtain robust long-run elasticities.

---

### 2. NARDL Model

### Model formulation and estimation approach
- NARDL allows short- and long-run nonlinearities via positive and negative partial sum decompositions:
  - X_t = X_0 + X_t^+ + X_t^−
  - X_t^+ = Σ_{j=1}^t ΔX_j^+ = Σ_{j=1}^t max(ΔX_j, 0)
  - X_t^− = Σ_{j=1}^t ΔX_j^− = Σ_{j=1}^t min(ΔX_j, 0)
- Asymmetric distributed-lag parameters are θ_j^+ and θ_j^−.
- NARDL corrects for weak endogeneity of nonstationary regressors; appropriate lag choice removes residual autocorrelation.
- Estimation applied to real exports, imports, and trade balance, allowing asymmetry only in long-run REER elasticities.
- Stata package by Shin, Yu, and Greenwood-Nimmo (2014) used to report long-run coefficients from equilibrium-correction forms.

### Long-run export elasticities — main results
- Full-sample ARDL: long-run REER elasticity of real exports statistically insignificant.
- Evidence of structural break in REER–exports relationship around second half of 2008 (recursive Wald tests).
- Sub-sample ARDL selected results (samples: 1998q1-2017q4; 1998q1-2008q2; 2008q3-2017q4):
  - Error-correction coeff.: -0.46*** (0.09); -0.59*** (0.13); -0.35*** (0.13)
  - Long-run coeff. ln REER: 0.04 (0.10); 0.14 (0.14); -0.73 (0.51)
  - ln Foreign Income: 3.06*** (0.10); 2.87*** (0.21); 2.03*** (0.74)
  - R^2: 0.98; 0.97; 0.94
  - N: 76; 38; 38
  - Bounds test F-stat: 8.68***; 7.67***; 3.40***
- Full-sample ARDL with REER interaction term:
  - Error-correction coeff.: -0.38*** (0.08)
  - Long-run coeff. ln REER: -0.39 (0.29)
  - lnREER×Dummy (pre-2008q3=1): 0.24* (0.13)
  - ln Foreign Income: 2.71*** (0.24)
  - R^2: 0.98; N: 79; Bounds test F-stat: 8.16***
- NARDL full-sample results for exports (Table 3):
  - lnREER^+: 0.041 (F-statistics 0.099, P-value 0.754)
  - lnREER^−: -0.234 (F-statistics 1.771, P-value 0.188)
  - ln Foreign Income (USD): 1.851*** (F-statistics 9.577, P-value 0.003)
  - R^2: 0.334
  - F_PSS: 4.724*** (existence of asymmetric cointegrating long-run relationship)
  - W_LR: 0.275** (Wald test of long-run symmetry)
  - B-G 1st order F-stat: 0.32; B-G 2nd order F-stat: 0.75
- Interpretation and robustness:
  - Evidence of asymmetry: REER elasticity of exports is positive during appreciation periods and negative during depreciation periods.
  - Wald test rejects equality lnREER^+ = lnREER^− at the 99 percent confidence level.
  - Both lnREER^+ and lnREER^− coefficients are not statistically significant at the 90 percent confidence level.
  - Rolling estimation indicates post-2011 observations important for sign switch; long-run REER depreciation intensified to over 2% per year around that time.
  - Long-run foreign demand (income) elasticity of exports is large and significant (greater than 2 across sub-samples); full-sample ARDL with interaction gives 2.7.
  - Speed of adjustment: post-crisis error-correction implies around 1/3 of any misalignment is corrected each quarter (from post-crisis error-correction coefficient).
  - Specification tests: ARDL regressions pass no-residual-autocorrelation and cointegration tests (Breusch-Godfrey LM and Bounds Test). NARDL has weaker goodness-of-fit (lower R^2).
  - Robustness: findings robust to alternative export specification that nets out energy and gold.

### Explanations for export asymmetry
- Structural break linked to switch in secular REER trend from appreciation to depreciation toward end-2008.
- Possible drivers:
  - Asymmetric exchange rate pass-through to prices (market share theory, downward price rigidities, binding quantity constraints).
  - TFP dynamics: strong positive TFP growth prior to 2007, slipping to slightly negative average thereafter; structural reforms pre-2006 raised productivity, reforms waned thereafter.
  - If REER appreciation was driven by positive TFP differential, buoyant exports during appreciation are consistent with trade models; overshooting of REER depreciation relative to slightly negative post-2006 TFP can explain sustained export buoyancy after the global financial crisis.
- Literature notes asymmetric pass-through and non-linearities in other studies; export price elasticity often higher during depreciation than appreciation.

### Long-run import elasticities — main results
- ARDL sub-sample and full-sample selected results (samples: 1998q1-2017q4; 1998q1-2008q2; 2008q3-2017q4):
  - Error-correction coeff.: -0.20** (0.09); -0.29** (0.14); -0.27* (0.14)
  - Long-run coeff. ln REER: 1.36*** (0.27); 1.31*** (0.45); 1.01* (0.57)
  - ln Domestic Income: 1.15*** (0.07); 1.49*** (0.37); 1.02*** (0.27)
  - R^2: 0.99; 0.99; 0.94
  - N: 76; 40; 38
  - Bounds test F-stat: 2.79***; 1.56*; 2.02*
- Full-sample ARDL with REER interaction:
  - Error-correction coeff.: -0.64*** (0.06)
  - Long-run coeff. ln REER: 1.42*** (0.19)
  - lnREER×Dummy (pre-2008q3=1): 0.24 (0.18)
  - ln Domestic Income: 1.07*** (0.07)
  - R^2: 0.99; N: 78; Bounds test F-stat: 32.68***
- NARDL results for imports:
  - Long-run REER elasticity of real imports is statistically significant and positive in both secular appreciation and depreciation periods.
  - Wald test lnREER^+ = lnREER^− rejected at the 99 percent confidence level, suggesting asymmetry: long-run REER elasticity of imports may be smaller in periods of REER depreciation.
- Stability and robustness:
  - Recursive Wald tests do not give conclusive evidence of coefficient instability for imports.
  - Rolling estimates show some instability but estimates remain positive and theory-consistent.
  - Overall, REER–imports link is more stable than REER–exports over 1998-2017.

### Exchange rate pass-through and price effects
- Evidence of high exchange rate pass-through to import prices in Turkey; related studies report coefficients from 0.8 to 1.
- Paper notes: "A high exchange rate pass-through to prices suggests a strong demand-pull effect for Turkish imports."
- Only 3% of Turkish imports are invoiced in Lira.
- Long-run REER depreciation intensified to over 2% per year toward the end of the sample period.

### NARDL long-run trade elasticities of real imports (Table 6)
- lnREER+ coefficient: 1.409***; F-statistics: 102.40; P-value: 0.000
- lnREER− coefficient: 1.151***; F-statistics: 34.95; P-value: 0.000
- ln Domestic Income (Lira) coefficient: 0.642***; F-statistics: 12.97; P-value: 0.001
- R2: 0.909
- F_PSS: 3.148***
- W_LR: 0.258*** (Wald test of long-run symmetry lnREER+ = lnREER−)
- Breusch-Godfrey 1st order F-stat: 0.20; 2nd order F-stat: 0.61
- Notes: lnREER+ and lnREER− denote partial sum processes of positive and negative changes of lnREER.

### Long-run income elasticity and speed of adjustment of imports
- Long-run domestic demand elasticity of real imports is statistically significant and larger than 1 in all sub-samples; rolling estimates remain broadly stable post-crisis.
- Full-sample ARDL with REER interaction points to long-run domestic demand elasticity of real imports of around one in the full sample.
- In contrast to exports, long-run sensitivity of real imports to changes in income and REER are of similar magnitudes.
- Speed of adjustment: post-crisis error-correction suggests around 1/4 of any misalignment between actual and equilibrium real imports is corrected each quarter (Table 4).

### Specification tests and robustness
- ARDL regressions pass specification tests of no residual autocorrelation (Breusch-Godfrey LM) and existence of cointegration (Bounds Test F-statistics).
- High R-squares of ARDL and NARDL indicate good fit.
- Rolling estimation shows relative stability of estimated domestic demand for imports.
- Findings robust to alternative specification net of energy and gold.

### Role of REER in trade-balance adjustment (Marshall-Lerner and dynamics)
- Marshall-Lerner condition constructed from rolling REER elasticities: REER depreciation has had a positive impact on the real trade balance once data from late-2011 onwards is included.
- Positive REER contribution coincides with period when long-run REER depreciation intensified to over 2% per year.
- Export expansion contributed to narrowing the real trade balance; import compression through price elasticity remained a dominant factor.
- Between 2009 and mid-2011 the Marshall-Lerner condition is not met, suggesting Lira devaluation likely initially worsened the real trade balance (J-curve).
- Despite positive REER contribution post-2008, post-2008 improvement fell short of pre-crisis deterioration.
- Domestic-foreign income growth differential frequently contributed to widening the real trade balance, partly offsetting REER effect; rolling estimates show domestic-to-foreign income growth ratio exceeded the appropriately scaled ratio of income elasticities of exports and imports in most rolling sub-samples.

### Summary of findings (Section VI)
- REER was an important determinant of real trade balances in Turkey over 1998-2017.
- Secular REER appreciation through 2008:Q3 transmitted mainly via boosted imports (higher purchasing power); exports also thrived driven by positive TFP differential with partners.
- Post-crisis REER depreciation transmitted via both export promotion and import compression via price elasticities; depreciation appears to have overshot slightly negative TFP growth post-2006.
- Novel finding: structural break in REER elasticity of real exports linked to switch from long-run REER appreciation to depreciation toward end-2008.
- Pattern of higher income elasticity of exports than imports persists post-2008, but its positive effect on real trade balance was more than offset by post-crisis widening of the domestic-foreign income growth differential driven by rapid private sector credit growth and stepped up public-private partnerships (PPP) activity.
- Additional observation: opening wedge between nominal current account-to-GDP and real trade balance-to-GDP ratios starting mid-2010; potential contributors include low/negative TFP growth, pressures from rising corporate external debt rollover needs, a rate of Lira-USD depreciation above GDP deflator growth, and a widening country risk premium affecting the income balance.

### Robustness: trade flows net of energy and gold (Appendix A)
- Excluding energy and gold does not change main findings.
- Real Exports Net of Energy and Gold (ARDL):
  - Error-correction coeff. (1998q1-2017q4): -0.44*** (0.09)
  - Long-run coeff. ln REER (1998q1-2017q4): 0.00 (0.10)
  - ln Foreign Income coefficients: 3.00*** (0.11)
  - R2: 0.98; N: 76; Bounds Test F-stat: 7.66***
- Real Imports Net of Energy and Gold (ARDL):
  - Error-correction coeff. (1998q1-2017q4): -0.29*** (0.08)
  - Long-run coeff. ln REER (1998q1-2017q4): 1.77*** (0.18)
  - ln Domestic Income coefficients: 1.21*** (0.07)
  - R2: 0.99; N: 76; Bounds Test F-stat: 5.41***
- Key robustness takeaways:
  - Demand for imports net of gold and energy is much more sensitive to REER changes than total import demand.
  - Income elasticities of total imports and net-of-energy-and-gold imports are not significantly different.
  - Misalignments between actual and fundamentals-consistent real non-gold, non-energy imports are closed up to 3 times faster than for total imports.

### Data construction and sources (Appendix B highlights)
- REER constructed using top 20 trade partners: Germany, United Kingdom, Iraq, Italy, USA, France, UAE, Spain, Iran, Netherlands, Saudi Arabia, Israel, Egypt, Switzerland, Romania, Poland, Belgium, Bulgaria, China, Algeria (Russia excluded because trade is mostly in energy).
- Weights wi are combined shares of top 20 partners in Turkey’s exports and imports averaged over 2007-17.
- REER backcast methodology uses quarter-on-same-quarter previous year gross growth rates from CPI ratios and bilateral nominal exchange rates.
- Foreign income index: real GDP series transformed to base year 2009, converted to constant 2009 US dollars by dividing local currency real GDP by average nominal exchange rate in 2009; trade-weighted algebraic mean used.
- IMF WEO annual data mapped into quarterly values where quarterly CPI/GDP missing (zero quarter-on-quarter growth within each year assumed).
- Turkey real exports and imports: chain-linked Turkish Lira (reference year = 2009), include goods and services. Exports used in Lira; imports used in USD after transforming via identity M = ˜M / Q′M where ˜M is real imports in chain-linked Lira and Q′ is CPI-based REER.
- Real trade balance excluding gold and energy constructed by converting nominal US dollar amounts to chain-linked US dollars using Fund staff estimates of deflators.

*Source: wpiea2019131 — 1. ARDL Model and 2. NARDL Model (chapter excerpts from the supplied PDF).*

### 1.    ARDL Model   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    13

### 1. ARDL Model

### Overview and motivation
- Turkey experienced sizable swings of the real effective exchange rate (REER) over the last 20 years, making it a suitable case study of the importance of REER adjustments in restoring external balance.
- The REER appreciated by close to 25% over the ten years before the 2008-09 global financial crisis, before relinquishing most of these gains through end-2017.
- During the REER appreciation phase, the current account deficit widened to over 5% of GDP.
- Cross-country studies tend to confirm the stability of the link between REER and real trade balances; however, country-specific studies for Turkey show wide dispersion and sometimes discordant findings.
- Literature summary points:
  - Absolute values of export and import elasticities reported in surveyed studies range in the range of 0.3 to 0.9.
  - Income elasticities were typically higher than the absolute value of the REER elasticities and larger than one.
  - Recent studies find that income is a more important determinant of trade flows than the REER.

### Data and stylized facts
- Sample: quarterly data over the period 1998-2017.
  - The sample ends in 2017, as the empirical analysis was carried out in the summer of 2017 and finalized by mid-2018.
- REER construction:
  - CBRT publishes consumption-based REER starting in 2003; the authors construct longer CPI-based REER series and back-cast pre-2003 levels (Appendix B.1).
  - Calculations align closely with TurkStat’s published REER series from 2003 onward.
- Trade series:
  - Exports and imports include both goods and services.
  - Nominal and real values are taken from TurkStat’s national accounts and are the same series used in the expenditure-side GDP compilation.
- Empirical patterns:
  - Scatter plots of real exports and imports against the REER suggest reasonably linear relationships, but structural breaks around the change from secular REER appreciation to depreciation are visible.
  - Real trade balance is negatively correlated with the REER in the full sample and in each of the two sub-samples.
  - Prior to Q3 2008, the link between real imports and the REER was very strong and exports showed little negative response to REER appreciation; after Q3 2008, the sign of the correlation between exports and the REER turned negative, aiding trade balance correction but imports’ responsiveness weakened.

### Analytical framework (partial-equilibrium trade-elasticities approach)
- REER definition and role:
  - REER (Q′) is defined as the ratio of the domestic price level to a trade-weighted index of foreign price levels, each converted into Turkish Lira using bilateral nominal exchange rates.
  - In the two-country case:
    - Q′ = P · S · (1/ P̃ ) where P—domestic CPI; P̃—CPI in trade partner; S—exchange rate expressed as domestic currency units per one unit of foreign currency.
  - Increase of REER corresponds to real appreciation of the Lira.
- Real trade balance identity:
  - TB = X − M = X − M̃ / Q′ (Equation (1))
    - TB — real trade balance in chain-linked Turkish Lira (reference year = 2009)
    - X — real exports in chain-linked Turkish Lira (reference year = 2009)
    - M̃ — real imports in chain-linked foreign currency
    - Q′ — transforms foreign consumer goods baskets into equivalent domestic ones
- Behavioral functions:
  - Imports: M̃ = M̃(Y, Q′) with ∂M̃/∂Y > 0 and ∂M̃/∂Q′ > 0 (Equation (2))
    - Y — Turkey’s real GDP in chain-linked Turkish Lira
  - Exports: X = X(Ỹ, Q′) with ∂X/∂Ỹ > 0 and ∂X/∂Q′ < 0 (Equation (3))
    - Ỹ — foreign real GDP
- Elasticity definitions:
  - REER elasticities (defined to be positive):
    - ηX = −(∂X/∂Q′)·(Q′/X) > 0
    - ηM̃ = (∂M̃/∂Q′)·(Q′/M̃) > 0
  - Income elasticities:
    - εX = (∂X/∂Ỹ)·(Ỹ/X) > 0
    - εM̃ = (∂M̃/∂Y)·(Y/M̃) > 0
- Growth decomposition:
  - Growth rate of real trade balance (definitions):
    - ȳ = (dY/dt) / Y ; ȳ̃ = (dỸ/dt) / Ỹ ; q̇′ = (dQ′/dt) / Q′
    - ẗb = (dTB/dt) / TB
  - Derived expression (Equation (7)):
    - ẗb = 1/(1−α) [ εM̃ · ȳ − α εX · ȳ̃ + q̇′ ( α ηX + ηM̃ − 1 ) ]
      - where α = X / M
    - Decomposes contributions into Income Effect and Substitution Effect.
  - Marshall-Lerner condition (special case with zero income effect):
    - For REER depreciation (q̇′ < 0) to improve real trade balance in levels requires α ηX + ηM̃ > 1 (Equation (9)).
  - Role of domestic-foreign income growth differential:
    - The income differential helps narrow the trade deficit if ȳ / ȳ̃ < α εX / εM̃ (Equation (10)).

### ARDL model specification and estimation approach
- Motivation:
  - The wide range of estimates of trade elasticities in Turkey suggests structural breaks; thus the authors apply techniques to detect and control for structural breaks, including rolling, sub-sample, ARDL regressions, ARDL with REER interaction terms, and NARDL regressions.
- ARDL setup:
  - ARDL form (Equation (11)):
    - yt = α0 + ∑_{i=1}^p αi yt−i + ∑_{i=0}^p β′i xt−i + εt
      - y — Turkey’s real exports (Lira) or real imports (USD), both in logs
      - x — log of REER and log of real income (domestic or trade partners)
      - p — lag length chosen to ensure uncorrelated residuals
  - Long-run elasticities derived from ARDL (Equation (12)):
    - y* = α0 / (1 − ∑_{i=1}^p αi ) + δ′ x* , where
    - δ = ( ∑_{i=0}^p βi ) / (1 − ∑_{i=1}^p αi )
  - Error-correction form (Equation (13)):
    - ∆yt = −θ( yt−1 − α0/θ − δ′ xt−1 ) + ∑_{i=1}^{p−1} γi ∆yt−i + ∑_{i=0}^{p−1} ρ′i ∆xt−i + ut
      - θ = 1 − ∑_{i=1}^p αi — fraction of last period’s disequilibrium eliminated in the current one.
- Estimation choices and robustness:
  - The authors fit ARDL models on full sample and different sub-samples to detect structural breaks.
  - They estimate full-sample ARDL models with REER interaction terms to exploit more data for coefficients less affected by breaks.
  - Use of Stata’s ardl package to report long-run coefficients derived from the equilibrium-correction form.
  - Pesaran and Shin (1998) result invoked: ARDL estimates are consistent irrespective of whether regressors are exogenous/endogenous or have unit roots.

### Empirical strategy highlights
- Complementary techniques used to address structural breaks and time variation:
  - Rolling estimation
  - Sub-sample estimation
  - ARDL with REER interaction term (full sample)
  - NARDL (non-linear ARDL) regressions
- Purpose: detect, control for, and interpret structural breaks in links between REER and real trade flows to obtain robust long-run export and import elasticities.

*Source: wpiea2019131 - 1.    ARDL Model (chapter from the supplied PDF).*

### 2.   NARDL Model

### 2.   NARDL Model

### Model formulation and estimation approach
- NARDL extends ARDL to allow short- and long-run nonlinearities via positive and negative partial sum decompositions of explanatory variables (Equation (14) in source).
- Decompositions:
  - X_t = X_0 + X_t^+ + X_t^−
  - X_t^+ = Σ_{j=1}^t ΔX_j^+ = Σ_{j=1}^t max(ΔX_j, 0)
  - X_t^− = Σ_{j=1}^t ΔX_j^− = Σ_{j=1}^t min(ΔX_j, 0)
- Asymmetric distributed-lag parameters are θ_j^+ and θ_j^−.
- NARDL corrects for weak endogeneity of nonstationary explanatory variables; appropriate lag choice removes residual autocorrelation.
- Estimation applied to real exports, imports, and trade balance, allowing asymmetry only in long-run REER elasticities.
- Stata package by Shin, Yu, and Greenwood-Nimmo (2014) used to report long-run coefficients derived from equilibrium-correction forms.

### Long-Run Export Elasticities (results and interpretation)
- Full-sample ARDL finds the long-run REER elasticity of real exports statistically insignificant.
- Evidence of a structural break in REER–exports relationship around second half of 2008 (recursive Wald tests; Figure 5).
- Sub-sample ARDL (Table 1) — selected results:
  - Sample: 1998q1-2017q4, 1998q1-2008q2, 2008q3-2017q4
  - Error-correction coeff.: -0.46*** (0.09); -0.59*** (0.13); -0.35*** (0.13)
  - Long-run coeff. ln REER: 0.04 (0.10); 0.14 (0.14); -0.73 (0.51)
  - ln Foreign Income: 3.06*** (0.10); 2.87*** (0.21); 2.03*** (0.74)
  - R^2: 0.98; 0.97; 0.94
  - N: 76; 38; 38
  - Bounds test F-stat: 8.68***; 7.67***; 3.40***
  - B-G 1st order F-stat: 0.14; 0.06; 0.70
  - B-G 2nd order F-stat: 0.55; 0.17; 0.46
- Full-sample ARDL with REER interaction term (Table 2):
  - Error-correction coeff.: -0.38*** (0.08)
  - Long-run coeff. ln REER: -0.39 (0.29)
  - lnREER×Dummy (pre-2008q3=1): 0.24* (0.13)
  - ln Foreign Income: 2.71*** (0.24)
  - R^2: 0.98
  - N: 79
  - Bounds test F-stat: 8.16***
  - B-G 1st order F-stat: 0.75; B-G 2nd order F-stat: 0.98
- NARDL full-sample results for exports (Table 3):
  - lnREER^+: 0.041 (F-statistics 0.099, P-value 0.754)
  - lnREER^−: -0.234 (F-statistics 1.771, P-value 0.188)
  - ln Foreign Income (USD): 1.851*** (F-statistics 9.577, P-value 0.003)
  - R^2: 0.334
  - F_PSS: 4.724*** (PSS F-statistic for existence of asymmetric cointegrating long-run relationship)
  - W_LR: 0.275** (Wald test of long-run symmetry; p-value reported in bracket in source)
  - B-G 1st order F-stat: 0.32; B-G 2nd order F-stat: 0.75
- Interpretation and robustness:
  - Results indicate asymmetry: REER elasticity of exports is positive during appreciation periods and negative during depreciation periods.
  - Wald test rejects equality lnREER^+ = lnREER^− at the 99 percent confidence level.
  - Both lnREER^+ and lnREER^− coefficients are not statistically significant at the 90 percent confidence level.
  - Rolling estimation points to post-2011 observations being important for the sign switch in REER elasticity of exports; long-run REER depreciation intensified to over 2% per year around that time (Figure 7).
  - Long-run foreign demand (income) elasticity of exports is large and significant (greater than 2 across sub-samples); full-sample ARDL with interaction gives 2.7.
  - Speed of adjustment: post-crisis error-correction implies around 1/3 of any misalignment is corrected each quarter (from post-crisis error-correction coefficient).
  - Specification tests: ARDL regressions pass tests for no residual autocorrelation and cointegration (Breusch-Godfrey LM and Bounds Test). NARDL has weaker goodness-of-fit (lower R^2), signaling caution.
  - Robustness: findings robust to alternative export specification that nets out energy and gold (Appendix A).

### Explanations for export asymmetry
- Structural break linked to switch in secular REER trend from appreciation to depreciation toward end-2008.
- Possible drivers:
  - Asymmetric exchange rate pass-through to prices (market share theory, downward price rigidities, binding quantity constraints — Pollard and Coughlin (2004)).
  - TFP dynamics: strong positive TFP growth prior to 2007, slipping to slightly negative average thereafter (Annex I in IMF (2018)); structural reforms pre-2006 increased productivity, waning reforms after attributed to TFP slowdown (IMF (2015), IMF (2018)).
  - If REER appreciation was driven by positive TFP differential, buoyant exports during appreciation are consistent with trade models (Eaton and Kortum, 2002; Melitz and Ottaviano, 2008). Overshooting of REER depreciation relative to slightly negative post-2006 TFP can explain sustained export buoyancy after the global financial crisis.
- Literature context: asymmetric pass-through and non-linearities documented in other studies (Caselli (2016), Kal et al. (2015), Bussiere (2013), Delatte and López-Villavicencio (2012)); export price elasticity often higher during depreciation than appreciation.

### Long-Run Import Elasticities (results and interpretation)
- ARDL sub-sample and full-sample results (Table 4) — selected results:
  - Samples: 1998q1-2017q4, 1998q1-2008q2, 2008q3-2017q4
  - Error-correction coeff.: -0.20** (0.09); -0.29** (0.14); -0.27* (0.14)
  - Long-run coeff. ln REER: 1.36*** (0.27); 1.31*** (0.45); 1.01* (0.57)
  - ln Domestic Income: 1.15*** (0.07); 1.49*** (0.37); 1.02*** (0.27)
  - R^2: 0.99; 0.99; 0.94
  - N: 76; 40; 38
  - Bounds test F-stat: 2.79***; 1.56*; 2.02*
  - B-G 1st order F-stat: 0.00; 1.60; 1.04
  - B-G 2nd order F-stat: 0.62; 0.80; 0.80
- Full-sample ARDL with REER interaction (Table 5):
  - Error-correction coeff.: -0.64*** (0.06)
  - Long-run coeff. ln REER: 1.42*** (0.19)
  - lnREER×Dummy (pre-2008q3=1): 0.24 (0.18)
  - ln Domestic Income: 1.07*** (0.07)
  - R^2: 0.99
  - N: 78
  - Bounds test F-stat: 32.68***
  - B-G 1st order F-stat: 0.06; B-G 2nd order F-stat: 0.91
- NARDL results for imports (summary from source):
  - Long-run REER elasticity of real imports is statistically significant and positive in both secular appreciation and depreciation periods.
  - Wald test of equality lnREER^+ = lnREER^− rejects the null at the 99 percent confidence level, suggesting asymmetry: long-run REER elasticity of imports may be smaller in periods of REER depreciation.
- Stability and robustness:
  - Recursive Wald tests do not provide conclusive evidence of coefficient instability for imports (Figure 8). Statistic marginally significant at 90% in year prior to global financial crisis but falls below threshold as more post-crisis data included.
  - Rolling estimates show some coefficient instability when including start and end of post-crisis period, but estimates remain positive as predicted by theory (Figure 9).
  - Overall, link between REER and imports is in line with theoretical priors and more stable than REER–exports relationship over 1998-2017.

*Source: IMF working paper chapter "2.   NARDL Model" (wpiea2019131).*

### 2017. There is some evidence that the REER elasticity of real imports may be smaller in pe-

### wpiea2019131 - 2017. There is some evidence that the REER elasticity of real imports may be smaller in pe-

### Exchange rate pass-through and price effects
- Evidence of high exchange rate pass-through to import prices in Turkey; reported coefficients in related studies range from 0.8 to 1.
- The paper notes: "A high exchange rate pass-through to prices suggests a strong demand-pull effect for Turkish imports."
- Only 3% of Turkish imports are invoiced in Lira.
- The long-run REER depreciation intensified to over 2% per year toward the end of the sample period.

### Long-run trade elasticities of real imports (NARDL results — Table 6)
- lnREER+ coefficient: 1.409***; F-statistics: 102.40; P-value: 0.000
- lnREER− coefficient: 1.151***; F-statistics: 34.95; P-value: 0.000
- ln Domestic Income (Lira) coefficient: 0.642***; F-statistics: 12.97; P-value: 0.001
- R2: 0.909
- F_PSS: 3.148***
- W_LR: 0.258*** (Wald test of long-run symmetry lnREER+ = lnREER−; p-value reported in bracket in source)
- Breusch-Godfrey 1st order F-stat: 0.20
- Breusch-Godfrey 2nd order F-stat: 0.61
- Notes from table: lnREER+ and lnREER− denote the partial sum process of positive and negative changes of lnREER.

### Long-run income elasticity and speed of adjustment of imports
- Long-run domestic demand elasticity of real imports is statistically significant and larger than 1 in all sub-samples (rolling estimates remain broadly stable in the post-crisis period).
- Full-sample ARDL model with REER interaction term points to a long-run domestic demand elasticity of real imports of around one in the full sample.
- In contrast to exports, long-run sensitivity of real imports to changes in income and REER are of similar magnitudes.
- Speed of adjustment: the post-crisis estimate of the error-correction coefficient suggests that around 1/4 of any misalignment between the actual and equilibrium real imports is corrected in each quarter (Table 4).

### Specification tests and robustness
- Estimated ARDL regressions pass specification tests of no residual autocorrelation (Breusch-Godfrey Lagrange multiplier) and existence of long-run cointegrating relationship (Bounds Test F-statistics).
- High R-squares of ARDL and NARDL models indicate good fit to underlying data.
- Rolling estimation of the error-correction and long-run elasticities points to relative stability of estimated domestic demand for imports.
- Findings are robust to an alternative specification of real imports that nets out energy and gold.

### Role of REER in trade-balance adjustment (Marshall-Lerner condition and dynamics)
- Marshall-Lerner condition constructed from rolling window REER elasticities: REER depreciation has had a positive impact on the real trade balance once data from late-2011 onwards is included.
- The positive REER contribution coincides with the period when long-run REER depreciation intensified to over 2% per year.
- Export expansion has contributed to narrowing the real trade balance; however, import compression through price elasticity has remained a dominant factor.
- Between 2009 and mid-2011, the Marshall-Lerner condition is not met, suggesting Lira devaluation likely initially worsened the real trade balance (J-curve interpretation).
- Despite positive REER contribution post-2008, the post-2008 improvement has fallen short of its pre-crisis deterioration.
- The domestic-foreign income growth differential has frequently contributed to widening the real trade balance, partly offsetting the REER effect. Rolling estimates show the ratio of domestic to foreign income growth rates has exceeded the appropriately scaled ratio of income elasticities of exports and imports in most rolling sub-samples.

### Summary of findings (Section VI)
- REER has been an important determinant of real trade balances in Turkey over 1998-2017.
- In the secular REER appreciation through 2008:Q3, transmission operated mainly through boosted imports (higher purchasing power); exports also thrived driven by positive TFP differential with trade partners.
- In the post-crisis REER depreciation period, transmission operated through both export promotion and import compression via price elasticities; depreciation appears to have overshot slightly negative TFP growth post-2006.
- Novel finding: evidence of a structural break in the REER elasticity of real exports linked to the switch from long-run REER appreciation to depreciation toward end-2008.
- Pattern of higher income elasticity of exports than imports persists post-2008, but its positive effect on the real trade balance was more than offset by post-crisis widening of the domestic-foreign income growth differential driven by rapid private sector credit growth and stepped up public-private partnerships (PPP) activity.
- Additional observation: an opening wedge between nominal current account-to-GDP and real trade balance-to-GDP ratios starting mid-2010; potential contributors include low/negative total factor productivity growth, pressures from rising corporate external debt rollover needs, a rate of Lira-USD depreciation above GDP deflator growth, and a widening country risk premium affecting the income balance.

### Robustness: trade flows net of energy and gold (Appendix A)
- Excluding energy and gold does not change main findings.
- Table A1 (Real Exports Net of Energy and Gold, ARDL model):
  - Error-correction coeff. (1998q1-2017q4): -0.44*** (0.09)
  - Error-correction coeff. (1998q1-2008q2): -0.76*** (0.14)
  - Error-correction coeff. (2008q1-2017q4): -0.36*** (0.13)
  - Long-run coeff. ln REER (1998q1-2017q4): 0.00 (0.10)
  - Long-run coeff. ln REER (1998q1-2008q2): 0.07 (0.10)
  - Long-run coeff. ln REER (2008q1-2017q4): -0.48 (0.45)
  - ln Foreign Income coefficients: 3.00*** (0.11); 2.83*** (0.19); 2.38*** (0.70)
  - R2: 0.98; 0.97; 0.94
  - N: 76; 38; 40
  - Bounds Test F-stat: 7.66***; 10.39***; 2.95*
  - B-G 1st Order F-stat: 0.09; 0.00; 0.08
  - B-G 2nd Order F-stat: 0.42; 2.07; 0.83
- Table A2 (Real Imports Net of Energy and Gold, ARDL model):
  - Error-correction coeff. (1998q1-2017q4): -0.29*** (0.08)
  - Error-correction coeff. (1998q1-2008q2): -0.27** (0.13)
  - Error-correction coeff. (2008q3-2017q4): -0.86*** (0.08)
  - Long-run coeff. ln REER (1998q1-2017q4): 1.77*** (0.18)
  - Long-run coeff. ln REER (1998q1-2008q2): 1.94*** (0.52)
  - Long-run coeff. ln REER (2008q3-2017q4): 1.49*** (0.17)
  - ln Domestic Income coefficients: 1.21*** (0.07); 1.31*** (0.44); 1.07*** (0.09)
  - R2: 0.99; 0.99; 0.94
  - N: 76; 39; 38
  - Bounds Test F-stat: 5.41***; 1.74***; 40.01***
  - B-G 1st Order F-stat: 1.13; 1.06; 0.09
  - B-G 2nd Order F-stat: 2.29; 1.02; 0.42
- Key robustness takeaways:
  - Demand for imports net of gold and energy is much more sensitive to REER changes than total import demand.
  - Income elasticities of total imports and the subset net of energy and gold are not significantly different.
  - Misalignments between actual and fundamentals-consistent real non-gold, non-energy imports are closed up to 3 times faster than for total imports.

### Data construction and sources (Appendix B highlights)
- REER constructed using top 20 trade partners: Germany, United Kingdom, Iraq, Italy, USA, France, UAE, Spain, Iran, Netherlands, Saudi Arabia, Israel, Egypt, Switzerland, Romania, Poland, Belgium, Bulgaria, China, Algeria. Russia excluded because trade is mostly in energy.
- Weights wi are combined shares of the top 20 partners in Turkey’s exports and imports averaged over 2007-17.
- REER backcast methodology: quarter-on-same quarter of previous year gross growth rates given by specified product of CPI ratios and nominal bilateral exchange rate terms.
- Foreign income index: real GDP series transformed to base year 2009, converted to constant 2009 US dollars by dividing local currency real GDP by average nominal exchange rate (local currency per one US dollar) in 2009; trade-weighted algebraic mean used.
- For partners lacking quarterly CPI/GDP, IMF WEO annual data mapped into quarterly values assuming zero quarter-on-quarter growth within each year.
- Turkey real exports and imports data: chain-linked Turkish Lira (reference year = 2009), include goods and services. Exports used in Lira, imports used in USD after transforming via identity M = ˜M / Q′M where ˜M is real imports in chain-linked Lira and Q′ is CPI-based REER.
- Real trade balance excluding gold and energy constructed by first constructing real exports and imports of these commodities using nominal US dollar amounts and converting to chain-linked US dollars using Fund staff estimates of deflators.

*Source: IMF working paper wpiea2019131 (2017).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019131.pdf_