## _wp11141

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---

### I. Introduction — framing and key implications
- Two channels by which changes in the nominal exchange rate affect domestic consumer prices in Singapore:
  - Classic exchange rate pass-through via domestic prices of imported goods (first stage).
  - Influence on exporters' profit margins, resource utilization and domestic price pressures (second stage).
- Two-stage characterization:
  - First stage: changes in the nominal exchange rate are reflected in import prices in local currency terms.
  - Second stage: changes in domestic import prices are passed on—in whole or in part—to the consumer.
- Purpose and methods:
  - Update estimates for Singapore and assess asymmetric pass-through effects over the business cycle.
  - Use a new approach to estimating business cycle components of non-stationary series (Corbae and Ouliaris, 2006) and band-pass spectral regression techniques.
- Reported empirical implications:
  - First stage: importers pass on a smaller share of cost savings (increases) from a stronger (weaker) exchange rate during an upturn (downturn).
  - Second stage: retailers tend to be more aggressive in passing on import cost increases during strong economic conditions.
- Policy implication summarized:
  - The exchange rate remains an effective tool in curbing imported price inflation: effects of a change in the exchange rate are fully passed on to domestic import prices within a year.
  - Given asymmetric pass-through effects, monetary/exchange rate policy could “lean against the wind” during robust cyclical expansions to moderate inflation.

### II. Literature review — context and stylized facts
- First-stage pass-through across economies:
  - Complete pass-through tends to occur in small, open economies where importers are price-takers (examples: Australia, Singapore).
  - Industrial countries typically show incomplete first-stage pass-through: Campa and Goldberg (2005) report average long-run pass-through elasticities of approximately 64 percent for a sample of 23 OECD countries.
- Evidence of a decline in pass-through:
  - Empirical observation reported: 0.2 percent increase in US import prices, down from 0.5 percent in the 1970s and 1980s.
  - Several hypotheses for declining pass-through: stable low inflation and credible inflation-targeting; changing firm pricing behavior and competition; shifts in import composition toward differentiated goods; multinational pricing strategies; increased nontraded local cost components.

### III. First-stage exchange rate pass-through — estimation results (1980:3–2010:3)
- Unit roots and cointegration:
  - All series in equation consistent with the unit root hypothesis (ADF and FD tests).
  - Residual-based cointegration tests and Johansen (1988) eigen-based procedure suggest a long-run relationship.
- Long-run cointegrating estimates (unconstrained):
  - t_fwpi: α = 0.6929 (Std. Err. 0.0787; t-stat 8.8040)
  - t_exr: λ = -0.9294 (Std. Err. 0.0820; t-stat -11.339)
  - LR Test for α = 1: Chi-square (1) = 6.6329; p-value = 0.0100
  - LR Test for λ = -1: Chi-square (1) = 0.6412; p-value = 0.4233
- Long-run estimates with λ constrained to -1:
  - t_fwpi: α = 0.7295 (Std. Err. 0.02312; t-stat 31.5492)
  - t_exr: λ = -1 (constrained)
- Interpretation of long-run first stage:
  - Long-run pass-through elasticity for exchange rate: 0.93 (λ ≈ -0.93); null of λ = -1 cannot be rejected.
  - Pass-through of foreign prices to domestic import prices significantly different from one: a 1 percent increase in foreign price increases domestic import prices by only 0.70 percent on average in the long run (α ≈ 0.70).
- Weak exogeneity:
  - Null that FWPI and EXR are weakly exogenous to IPI (together with λ = -1) cannot be rejected; p-value = 0.2128.
- Short-run error-correction dynamics (constrained λ = -1):
  - Error-correction term coefficient = -0.1865 (Std. Err. 0.0414; t-stat -4.5107; p-value 0.0000)
  - Constant = 0.817E-03 (Std. Err. 0.222E-02; t-stat -0.3677; p-value 0.7138)
  - 2008 Crisis dummy = -0.1195 (Std. Err. 0.0157; t-stat -8.2096; p-value 0.0000)
  - Adjusted R-squared = 0.5650
  - Interpretation: full first-stage pass-through occurs within 6 quarters (error-correction parameter estimate: 0.18).
- Business-cycle (band [1/6, 1/3], 6 to 32 quarters) estimates:
  - t_fwpi: α = 1.2891 (Std. Err. 0.2250; t-stat 5.7301)
  - t_exr: λ = -0.5176 (Std. Err. 0.1845; t-stat -2.8049)
  - Tests for difference from long-run:
    - Test δ1 = 0.70: t-Statistic 2.5000; p-value 0.0138
    - Test δ2 = -0.93: t-Statistic 2.0423; p-value 0.0433
  - Interpretation: exchange rate pass-through over the business cycle is 0.51 (λ ≈ -0.5176) and significantly smaller than the long-run estimate of 0.93; foreign wholesale price variations have a greater effect at business-cycle frequencies.
- Asymmetric band-pass pass-through by business-cycle state (definitions):
  - 1t_gap+ = 1 if output gap in previous quarter ≥ 1 percent; 0 otherwise.
  - 1t_gap- = 1 if output gap in previous quarter ≤ -1 percent; 0 otherwise.
- Asymmetric band-pass estimates (Table 3):
  - EXR base δ1 = -0.7114 (Std. Err. 0.1689; t-stat -4.2117; p-value 0.000)
  - EXR × gap+ δ2 = 0.4547 (Std. Err. 0.2466; t-stat 1.8442; p-value 0.067)
  - FWPI δ3 = 1.2842 (Std. Err. 0.2385; t-stat 5.3846; p-value 0.000)
  - Adjusted R-squared = 0.5046
- Asymmetric interpretation:
  - When actual GDP is above potential by at least 1 percent, a 1 percent appreciation results in a 0.26 percent fall in domestic import prices (δ1 + δ2 = -0.7114 + 0.4547 = -0.2567).
  - When real GDP is near potential, a 1 percent appreciation results in a 0.71 percent decline in domestic import prices (δ1 = -0.7114).
  - Importers pass on a smaller portion of exchange-related cost savings during robust expansions.

### IV. Second-stage pass-through — estimation results and dynamics (1991:1–2007:4; reduced sample 2000:3–2007:4)
- Long-run mark-up model (log-linear): cpi_t = λ + β ipi_t + γ ulc_t; under unit homogeneity in competitive markets β + γ = 1.
- Long-run unconstrained estimates (1991:1–2007:4):
  - ulc_t β = 0.750 (Std. Err. 0.237; t-stat 3.163)
  - ipi_t γ = 0.554 (Std. Err. 0.177; t-stat 3.128)
  - constant α = -1.404 (Std. Err. 1.771; t-stat 0.793)
  - LR test H0: β + γ = 1: Chi-sq (1) = 10.459; p-value = 0.498 (null accepted)
- Long-run constrained estimates (β + γ = 1) (preferred):
  - ulc_t β = 0.575 (Std. Err. 0.081; t-stat 7.109)
  - ipi_t γ = 0.425 (Std. Err. 0.081; t-stat 5.253)
  - constant α = 0.005 (Std. Err. 0.010; t-stat 0.506)
- Short-run error-correction estimates (1991:1–2007:4) (Table 5):
  - Error-correction term α1 = -0.032 (Std. Err. 0.008; t-stat -4.243; p-value 0.000)
  - Δipi_t α30 = 0.061 (Std. Err. 0.022; t-stat 2.753; p-value 0.008)
  - Δipi_t-1 α31 = 0.032 (Std. Err. 0.019; t-stat 1.723; p-value 0.090)
  - gap_t-1 α51 = 0.001 (Std. Err. 0.000; t-stat 5.962; p-value 0.000)
  - Δgap α60 = 0.001 (Std. Err. 0.000; t-stat 5.514; p-value 0.000)
  - Adjusted R-squared = 0.724
- Short-run estimates for reduced sample 2000:3–2007:4 (Table 6):
  - Error-correction term α1 = -0.063 (Std. Err. 0.025; t-stat -2.535; p-value 0.019)
  - Δulc_t α20 = 0.055 (Std. Err. 0.028; t-stat 2.002; p-value 0.058)
  - Δipi_t-1 α31 = 0.134 (Std. Err. 0.034; t-stat 3.954; p-value 0.001)
  - Δgap_t α60 = 0.003 (Std. Err. 0.001; t-stat 4.678; p-value 0.000)
  - Adjusted R-squared = 0.801
  - Rolling regressions indicate a parameter break around 2000:3; model re-estimated for 2000:3–2007:4.
- Long-run elasticities (constrained):
  - A 1 percent increase in ULC leads to a 0.58 percent increase in the CPI (β = 0.575).
  - A 1 percent increase in IPI leads to a 0.42 percent increase in the CPI (γ = 0.425).
- Simulation implication:
  - First-stage pass-through completes by the sixth quarter.
  - Second-stage response to an IPI shock is limited and protracted: by the end of the second year, only about 60 percent of the long-run impact of the IPI shock is passed through to consumer prices.

### IV.D. Asymmetric second-stage pass-through over the business cycle (band-pass, 2000:3–2007:4)
- Band-pass cyclical regression specification includes:
  - sign1 = 1 if change in import prices in current quarter ≥ 0; 0 otherwise.
  - sign2 = 1 if change in import prices in current quarter < 0; 0 otherwise.
  - gap dummies as in first stage.
- Estimated cyclical coefficients (Table 8):
  - IPI cyclical δ1 = 0.075 (Std. Err. 0.023; t-stat 3.229; p-value 0.004)
  - IPI × sign × gap+ δ2 = 0.164 (Std. Err. 0.078; t-stat 2.099; p-value 0.048)
  - ULC cyclical δ43 = 0.028 (Std. Err. 0.019; t-stat 1.438; p-value 0.165)
  - CPI lag δ50 = 0.597 (Std. Err. 0.116; t-stat 5.136; p-value 0.000)
  - Adjusted R-squared = 0.876
- Interpretation of asymmetry:
  - For import price increases during strong growth, pass-through to cyclical CPI is larger: δ1 + δ2 = 0.075 + 0.164 = 0.239 (i.e., a 1 percent increase in import prices leads to a 0.239 percent cyclical CPI response when growth is strong).
  - Absence of significant interaction for negative import-price changes indicates weaker or statistically insignificant pass-through differences when import prices fall, consistent with downward price stickiness.

### V. Combined two-stage system — simulations and quantitative scenarios
- Structure: two ECM equations combined for system simulations to trace exchange rate → import price → CPI.
- Representative simulation outcomes:
  - Simulation 1: One percent appreciation in the exchange rate
    - By the fourth quarter, CPI declines by 0.1 percent, equivalent to around 25 percent of the full pass-through.
    - By the end of the second year, cumulative CPI impact is 0.22 percent below baseline, or about 50 percent of the overall pass-through.
    - Long-run consumer price index would be 0.42 percent below baseline for a 1 percent appreciation in the exchange rate.
  - Simulation 2: One percent increase in the foreign price of imports (FWPI)
    - Domestic import costs ultimately increase by 0.76 percent.
    - To fully offset this import-price increase, the exchange rate would need to be revalued by 0.76 percent.
    - When that revaluation is introduced in the quarter following the foreign price shock, impact on IPI is dampened significantly by the exchange rate appreciation.
    - Domestic CPI peaks only at 0.1 percent above baseline into the second year when the exchange rate is allowed to appreciate; if the S$NEER is held constant, CPI responses are larger.
- Quantitative magnitudes highlighted:
  - Combined two-stage simulations indicate that average second-stage pass-through is fairly low and protracted: about 60 percent of long-run impact passed to CPI by end of second year.
  - Asymmetric cyclical outcome for import price increases: a 1 percent foreign price increase that causes a 1 percent rise in domestic import price leads to a 0.24 percent increase in the CPI in the short run under robust economic conditions; average across episodes second-stage pass-through is 0.13 percent; over other phases consumer prices rise by approximately 0.08 percent.

### VI. Major empirical findings — consolidated
- Distinct stages and speeds:
  - First-stage: exchange rate changes are quickly reflected in domestic import prices; pass-through to import prices complete by end of the sixth quarter.
  - Second-stage: pass-through from import prices to CPI is more protracted and incomplete in the short/medium run.
- Asymmetric business-cycle behavior:
  - During robust economic conditions, retailers pass on a larger share of import cost increases to consumers: short-run second-stage pass-through for import price increases during strong growth is 0.239 (δ1 + δ2).
  - Average short-run second-stage pass-through across episodes is more muted at 0.13 percent; other phases see about 0.08 percent CPI response for the same import cost increase.
- Speed of adjustment:
  - About 60 percent of the long-run impact of an IPI shock is passed on to consumer prices by the end of the second year.
  - Conditional on the asymmetric cyclical impact, roughly 60 percent of long-term pass-through is completed within the first quarter of the shock onset in the asymmetric case.
- Cross-country comparison:
  - Singapore’s overall exchange rate pass-through to domestic inflation appears similar to that of other developed countries due to the protracted second stage (comparative literature: Gagnon and Ihrig (2004); Liu and Tsang (2008)).

### VII. Policy implications and recommendations
- Exchange-rate policy:
  - The nominal exchange rate remains an effective tool to mitigate external price pressures because importers ultimately pass on full cost savings from a stronger exchange rate.
- Monetary policy stance given asymmetries:
  - Monetary policy in Singapore may need to “lean strongly against the wind” during robust cyclical expansions that are accompanied by increases in import costs.
  - During robust cyclical expansion with rising foreign inflationary pressures, an even stronger monetary response is needed to counteract overall cyclical exchange rate pass-through effects.
- Caveat:
  - These monetary policy implications are drawn solely from exchange rate pass-through effects; exchange rate movements also affect domestic prices through export earnings (not examined). A general equilibrium macro econometric model would be needed to assess the overall impact on consumer prices taking both channels into account.

### VIII. Methodology and data notes
- Two-stage empirical approach: first stage models exchange rate → import price pass-through; second stage models import price → CPI pass-through; ECM specifications combined for system simulations.
- Business-cycle asymmetries analyzed using band-pass extraction for nonstationary series via Corbae and Ouliaris (2006) approximation to the ideal band pass filter.
- Unit root and cointegration testing:
  - First-stage (1980:3–2010:3) ADF statistics: ipi ADF t-statistic = -2.1968 (p-value 0.2086); fwpi ADF t-statistic = -0.5617 (p-value 0.8737); exr ADF t-stat = -2.233 (p-value 0.165).
  - Johansen cointegration tests indicate 1 cointegrating equation at the 0.05 level for both first-stage and second-stage systems (lags interval 1 to 2; Akaike and Schwarz criteria reported).
  - Second-stage unit root tests (1991:1–2007:4): cpi ADF t-stat = -0.468 (p-value 0.892); ulc ADF t-stat = -0.962 (p-value 0.764); ipi ADF t-stat = -2.145 (p-value 0.228). FD test statistics and p-values show nonstationarity by ADF and FD tests; cointegration confirmed (FD p-value = 0.1312).
- Band-pass frequency for business-cycle analysis: [1/6, 1/3] corresponding to 6 to 32 quarters.

*Source: _wp11141 - 0.24 percent increase in consumer prices, or equivalently, 60 percent of the long-term*

### REFERENCES .............................................................................................................

### _wp11141 - REFERENCES .............................................................................................................

### I. INTRODUCTION
- Changes in the nominal exchange rate affect domestic consumer prices in Singapore through two channels:
  - Classic exchange rate pass-through via domestic prices of imported goods (first stage).
  - Influence on exporters' profit margins, affecting resource utilization and domestic price pressures (second stage).
- Two-stage characterization of classic pass-through:
  - First stage: changes in the nominal exchange rate are reflected in import prices in local currency terms.
  - Second stage: changes in domestic import prices are passed on—in whole or in part—to the consumer.
- Empirical background and previous findings:
  - MAS (2001c) concluded that exchange rate pass-through is complete, with exchange rate changes taking less than four quarters to reflect themselves in the local price of imported goods.
  - Second stage pass-through was found to be more sluggish, with changes in domestic import prices having a far more muted impact on consumer prices.
- Purpose and methods of the paper:
  - Update estimates for Singapore and assess asymmetric pass-through effects over the business cycle.
  - Use a new approach to estimating business cycle components of non-stationary series (see Corbae and Ouliaris, 2006) and band-pass spectral regression techniques.
- Key empirical implications reported:
  - In the first stage, importers pass on a smaller share of cost savings (increases) from a stronger (weaker) exchange rate during an upturn (downturn).
  - In the second stage, retailers tend to be more aggressive in passing on import cost increases during strong economic conditions.
- Policy implications for Singapore’s exchange rate policy (centered since 1981 on managing the nominal effective exchange rate (S$NEER) to promote price stability):
  - The exchange rate remains an effective tool in curbing imported price inflation: effects of a change in the exchange rate are fully passed on to domestic import prices within a year.
  - Given asymmetric pass-through effects, monetary/exchange rate policy could “lean against the wind” during robust cyclical expansions to moderate inflation, with this case strengthened by Singapore’s cyclical fluctuations being positively associated with the global business cycle and hence rising foreign prices.
- Paper organization:
  - Section 2: literature survey.
  - Sections 3 and 4: empirical results for first and second stage pass-through, respectively, including asymmetric modeling.
  - Section 5: combined two-stage empirical model and simulations.
  - Section 6: conclusion.

### II. LITERATURE REVIEW
- Focus of literature:
  - Vast empirical literature on exchange rate pass-through, mostly on the relationship between exchange rate and import prices (first stage).
  - Second stage pass-through (import prices to consumer prices) is less frequently studied in isolation.
  - Rare examination of pass-through over the business cycle; this paper aims to fill that gap.
- Findings on first stage pass-through across economies:
  - Complete pass-through tends to occur in small, open economies where importers are price-takers.
    - Examples cited: Dwyer and Leong (2001) find complete pass-through for Australia; MAS (2001c) reports similar results for Singapore.
  - In industrial countries, first stage pass-through tends to be incomplete.
    - Campa and Goldberg (2005) find average (long-run) pass-through elasticities of approximately 64 percent for a sample of 23 OECD countries in the post Bretton-Woods period.
    - Campa, Goldberg and Gonzalez-Minguez (2005) report a similar estimate for the euro-area.
- Evidence of a decline in pass-through:
  - Several econometric studies report a declining exchange rate pass-through in industrial countries, commencing around the early 1990s.
  - Example: Marazzi and Sheets (2007) find that for the 1990s a one percent depreciation in the US dollar leads to a ... (text truncated in source).

*Source: _wp11141 - REFERENCES*

### 0.2 percent increase in US import prices, down from 0.5 percent in the 1970s and 1980s.

### _wp11141 - 0.2 percent increase in US import prices, down from 0.5 percent in the 1970s and 1980s.

### Decline in Exchange Rate Pass-Through: Evidence and Hypotheses
- Empirical observation: 0.2 percent increase in US import prices, down from 0.5 percent in the 1970s and 1980s.
- Bailliu and Fujii (2004) find a significant decline in first stage pass-through since 1990 using a panel of 11 industrial countries including the US, UK and Australia.
- Proposed explanations for declining exchange rate pass-through:
  - Taylor (2000): Stable, low inflation with credible inflation-targeting reduces firms' tendency to pass on exchange-rate-related cost increases.
  - Devereux and Yetman (2002): High inflation raises the cost of maintaining fixed prices relative to menu costs, suggesting pass-through should increase with inflation.
  - Dornbusch (1987): Improvements in competitive conditions since the 1980s reduce pass-through.
  - Marazzi and Sheets (2007): Direct competition or threat of competition with China makes exporters hesitant to shift dollar-denominated prices.
  - Olivei (2002): Larger presence of multilateral corporations and intra-company transfer pricing reduces responsiveness to exchange rate movements.
  - Campa and Goldberg (2005): Shift in import bundle toward differentiated manufactured goods reduces sensitivity to exchange rate movements.
  - Engel (2002): Local cost components (nontraded services) in traded goods produce incomplete pass-through to consumer prices.
- Empirical note: Not all small open economies have complete first-stage pass-through (example: Hong Kong’s long-run pass-through elasticity at 65 percent per Liu and Tsang (2008)).

### III. First Stage Exchange Rate Pass-Through — Analytical Framework
- Long-run specification (textual form): IPI with FWPI and EXR; complete first stage pass-through in the long-run occurs if β = 1.
- Logarithmic transformed model (textual): domestic import prices depend on foreign wholesale prices (elasticity α) and exchange rate (elasticity λ). For a small open economy such as Singapore, first stage pass-through is expected to be complete, i.e., λ = -1.

### III. First Stage Exchange Rate Pass-Through — Estimation Results (Singapore, quarterly 1980:3–2010:3)
- Unit root and cointegration:
  - All series in equation 1.2 consistent with the unit root hypothesis (ADF and FD tests).
  - Residual-based cointegration tests and Johansen (1988) eigen-based procedure suggest a long-run relationship.
- Long-run pass-through estimates (Table 1):
  - Unconstrained long-run cointegrating equation:
    - t_fwpi: α = 0.6929 (Std. Err. 0.0787; t-stat 8.8040)
    - t_exr: λ = -0.9294 (Std. Err. 0.0820; t-stat -11.339)
    - LR Test for α = 1: Chi-square (1) = 6.6329; p-value = 0.0100
    - LR Test for λ = -1: Chi-square (1) = 0.6412; p-value = 0.4233
  - Estimates with λ constrained to -1:
    - t_fwpi: α = 0.7295 (Std. Err. 0.02312; t-stat 31.5492)
    - t_exr: λ = -1 (constrained)
  - Interpretation:
    - Long-run pass-through elasticity for exchange rate: 0.93 (λ ≈ -0.93); null of λ = -1 cannot be rejected.
    - Pass-through of foreign prices to domestic import prices significantly different from one: a 1 percent increase in foreign price increases domestic import prices by only 0.70 percent on average in the long run (α ≈ 0.70).
- Weak exogeneity:
  - Null hypothesis that FWPI and EXR are weakly exogenous to IPI (together with λ = -1) cannot be rejected; p-value = 0.2128.
- Short-run error-correction model (constrained λ = -1) and dynamics (equation 1.3):
  - Error-correction parameter estimate: 0.18 (Table 1(b))
  - Interpretation: full first-stage pass-through occurs within 6 quarters.
- Error-correction model results (Table 1(b)):
  - Error-correction term coefficient = -0.1865 (Std. Err. 0.0414; t-stat -4.5107; p-value 0.0000)
  - Constant = 0.817E-03 (Std. Err. 0.222E-02; t-stat -0.3677; p-value 0.7138)
  - 2008 Crisis dummy = -0.1195 (Std. Err. 0.0157; t-stat -8.2096; p-value 0.0000)
  - Adjusted R-squared = 0.5650
  - Model includes 2 lags and a dummy for 2008:4.

### III(c). Pass-Through over the Business Cycle (frequency band [1/6, 1/3], 6 to 32 quarters)
- Band-pass regression estimates (Table 2):
  - t_fwpi: α = 1.2891 (Std. Err. 0.2250; t-stat 5.7301)
  - t_exr: λ = -0.5176 (Std. Err. 0.1845; t-stat -2.8049)
  - Tests for difference from long-run:
    - Test δ1 = 0.70: t-Statistic 2.5000; p-value 0.0138
    - Test δ2 = -0.93: t-Statistic 2.0423; p-value 0.0433
  - Interpretation:
    - Exchange rate pass-through over the business cycle is 0.51 (λ ≈ -0.5176) and significantly smaller than the long-run estimate of 0.93.
    - Variations in foreign wholesale prices have a greater effect on domestic prices at business-cycle frequencies than at zero/long-run frequencies.
- Asymmetric pass-through by business-cycle state:
  - Dummy definitions:
    - 1t_gap+ = 1 if output gap in previous quarter ≥ 1 percent, 0 otherwise.
    - 1t_gap- = 1 if output gap in previous quarter ≤ -1 percent, 0 otherwise.
  - Table 3 (asymmetric pass-through results, band [6,32] quarters):
    - ()h_lt_c EXR δ1 = -0.7114 (Std. Err. 0.1689; t-stat -4.2117; p-value 0.000)
    - 1t gap+ interaction δ2 = 0.4547 (Std. Err. 0.2466; t-stat 1.8442; p-value 0.067)
    - ()h_lt_c FWPI δ3 = 1.2842 (Std. Err. 0.2385; t-stat 5.3846; p-value 0.000)
    - Adjusted R-squared = 0.5046
  - Interpretation of asymmetric results:
    - When actual GDP is above potential by at least 1 percent, a 1 percent appreciation results in a 0.26 percent fall in domestic import prices (δ1 + δ2 = -0.7114 + 0.4547 = -0.2567).
    - When real GDP is near potential, a 1 percent appreciation results in a 0.71 percent decline in domestic import prices (δ1 = -0.7114).
    - Importers pass on a smaller portion of exchange-related cost savings during robust expansions.

### IV. Second Stage Pass-Through — Analytical Framework
- Long-run mark-up model (textual): CPI is a mark-up over domestic unit labor cost (ULC) and IPI.
- Log-linear form (equation 1.6): cpi_t = λ + β ipi_t + γ ulc_t (textual mapping where λ = log(α) and β, γ are elasticities).
- Unit homogeneity condition in competitive markets: β + γ = 1.

### IV.B. Second Stage Estimation Results (long-run and short-run)
- Long-run estimates (1991:1–2007:4) (Table 4):
  - (a) Unconstrained estimates:
    - ulc_t β = 0.750 (Std. Err. 0.237; t-stat 3.163)
    - ipi_t γ = 0.554 (Std. Err. 0.177; t-stat 3.128)
    - Constant α = -1.404 (Std. Err. 1.771; t-stat 0.793)
    - LR test H0: β + γ = 1: Chi-sq (1) = 10.459; p-value = 0.498 (null accepted)
  - (b) Constrained estimates β + γ = 1 (preferred long-run specification):
    - ulc_t β = 0.575 (Std. Err. 0.081; t-stat 7.109)
    - ipi_t γ = 0.425 (Std. Err. 0.081; t-stat 5.253)
    - constant α = 0.005 (Std. Err. 0.010; t-stat 0.506)
- Short-run error-correction estimation 1991:1–2007:4 (Table 5):
  - Dependent variable: Δcpi_t
  - Key coefficients:
    - Error-correction term α1 = -0.032 (Std. Err. 0.008; t-stat -4.243; p-value 0.000)
    - Δulc_t-3 α23 = 0.026 (Std. Err. 0.017; t-stat 1.471; p-value 0.147)
    - Δulc_t-5 α25 = 0.023 (Std. Err. 0.016; t-stat 1.484; p-value 0.143)
    - Δipi_t α30 = 0.061 (Std. Err. 0.022; t-stat 2.753; p-value 0.008)
    - Δipi_t-1 α31 = 0.032 (Std. Err. 0.019; t-stat 1.723; p-value 0.090)
    - gap_t-1 α51 = 0.001 (Std. Err. 0.000; t-stat 5.962; p-value 0.000)
    - Δgap α60 = 0.001 (Std. Err. 0.000; t-stat 5.514; p-value 0.000)
    - Adjusted R-squared = 0.724
- Short-run estimates for reduced sample 2000:3–2007:4 (Table 6):
  - Dependent variable: Δcpi_t
  - Key coefficients:
    - Error-correction term α1 = -0.063 (Std. Err. 0.025; t-stat -2.535; p-value 0.019)
    - Δulc_t α20 = 0.055 (Std. Err. 0.028; t-stat 2.002; p-value 0.058)
    - Δipi_t-1 α31 = 0.134 (Std. Err. 0.034; t-stat 3.954; p-value 0.001)
    - Δgap_t α60 = 0.003 (Std. Err. 0.001; t-stat 4.678; p-value 0.000)
    - Δgap_t-3 α63 = 0.001 (Std. Err. 0.000; t-stat 1.707; p-value 0.102)
    - Adjusted R-squared = 0.801
  - Rolling regressions indicate a parameter break around 2000:3; model re-estimated for 2000:3–2007:4.

### IV.C. Implications of Second Stage Results and Simulation
- Long-run elasticities:
  - A 1 percent increase in ULC leads to a 0.58 percent increase in the CPI (constrained estimate: β = 0.575).
  - A 1 percent increase in IPI leads to a 0.42 percent increase in the CPI (constrained estimate: γ = 0.425).
- Reasons for larger ULC elasticity:
  - Rising share of service items in CPI basket from 39 percent in 1987-88 to 51 percent in 2003-04 reduces relative weight of import costs.
- Simulation of 1 percent shocks:
  - First stage pass-through completes by the sixth quarter.
  - Second stage (CPI response to IPI shock) is limited and protracted:
    - By the end of the second year, only about 60 percent of the long-run impact of the IPI shock is passed through to consumer prices.
    - Subsequent adjustment slows significantly over time and becomes more drawn-out.
- Explanatory factors for limited/protracted second-stage pass-through:
  - Multi-layer supply chain: wholesalers and retailers have differing mark-ups, menu costs, and market conditions.
  - Competitive pressures lead wholesalers and retailers to absorb part of import cost increases to preserve market share.
  - Retail price includes import cost plus nontradable components; import cost rise translates into smaller proportionate increase in total product cost.
  - Retailers may use profit margins as buffers; significant menu costs can delay adjustments.
  - Monetary authority (MAS) actions to dampen import-price impacts may lower public expectations of permanence of external shocks.

### IV.D. Asymmetric Second Stage Pass-Through Over the Business Cycle
- Band-pass cyclical regression for CPI (equation 1.8) incorporates:
  - Dummy sign1 = 1 if change in import prices in current quarter ≥ 0 (otherwise 0).
  - Dummy sign2 = 1 if change in import prices in current quarter < 0 (otherwise 0).
  - gap dummies same as first stage.
- Four possible asymmetric scenarios (Table 7) described conceptually (A, B, C, D) depending on direction of import price change and state of economy.
- Second-stage asymmetric regression results 2000:3–2007:4 (Table 8):
  - Dependent variable: cyclical CPI component
  - ()h_lt_c IPI δ1 = 0.075 (Std. Err. 0.023; t-stat 3.229; p-value 0.004)
  - ()h_ltt_c IPIsigngap+ interaction δ2 = 0.164 (Std. Err. 0.078; t-stat 2.099; p-value 0.048)
  - ()h_lt_c ULC δ43 = 0.028 (Std. Err. 0.019; t-stat 1.438; p-value 0.165)
  - ()h_lt_c CPI lag δ50 = 0.597 (Std. Err. 0.116; t-stat 5.136; p-value 0.000)
  - Adjusted R-squared = 0.876
- Interpretation:
  - An asymmetric outcome arises for import price increases: given strong economic growth, a 1 percent increase in import prices leads to (text truncated in source), but coefficients indicate larger pass-through to CPI for import price increases when growth is strong (δ1 + δ2 = 0.075 + 0.164 = 0.239).
  - The absence of a significant coefficient for the interaction with negative import-price changes suggests weaker or statistically insignificant pass-through differences when import prices fall, consistent with downward price stickiness.

*Italic: Source: _wp11141 - 0.2 percent increase in US import prices, down from 0.5 percent in the 1970s and 1980s.*

### 0.24 percent increase in consumer prices, or equivalently, 60 percent of the long-term

### _wp11141 - 0.24 percent increase in consumer prices, or equivalently, 60 percent of the long-term

### Major empirical findings on pass-through
- First- and second-stage pass-through are distinct: changes in the exchange rate are quickly reflected in domestic import prices at the first stage, with the pass-through to import prices complete by the end of the sixth quarter.
- Second-stage pass-through (import prices to consumer prices) is more protracted, producing a fairly low overall exchange rate pass-through to the consumer price index (CPI).
- Asymmetric business-cycle results:
  - During robust economic conditions, retailers pass on a larger share of import cost increases to consumers: a 1 percent increase in foreign prices causing a 1 percent rise in domestic import price leads to a 0.24 percent increase in the CPI in the short run.
  - Average (across episodes) second-stage pass-through is more muted at 0.13 percent.
  - Over other phases of the business cycle, consumer prices rise by only 0.08 percent approximately in response to the same import cost increase.
- Speed of adjustment:
  - The average adjustment implies about 60 percent of the long-run impact is passed on to consumer prices by the end of the second year.
  - Conditional on the asymmetric (cyclical) impact, the same amount of pass-through (about 60 percent of the long-term impact) is completed within the first quarter of the onset of the shock.
- First-stage asymmetry during cyclical expansion:
  - A 1 percent appreciation leads to a 0.24 percent decline in domestic import prices during an expansion, compared to a 0.34 percent decline in the average pass-through outcome.

### Quantitative simulation results (combined two-stage system)
- The combined ECM system (coefficients on lagged change variables not shown) includes the two equations (notation preserved from source):
  - Δip̂i_t = 0.186 (… ) − 0.729 (… )  (equation structure and coefficients as presented)
  - Δcpi_t = 0.063 (… ) − 0.575 (… ) − 0.425 (… )  (equation structure and coefficients as presented)
- Simulation 1: One percent appreciation in the exchange rate
  - By the fourth quarter, CPI declines by 0.1 percent, equivalent to around 25 percent of the full pass-through.
  - By the end of the second year, cumulative CPI impact is 0.22 percent below baseline, or about 50 percent of the overall pass-through.
  - Long-run (first-stage complete) consumer price index would be 0.42 percent below baseline for a 1 percent appreciation in the exchange rate (footnote logic preserved).
- Simulation 2: One percent increase in the foreign price of imports (FWPI)
  - Domestic import costs ultimately increase by 0.76 percent.
  - To fully offset this import-price increase, the exchange rate would need to be revalued by 0.76 percent.
  - When that revaluation is introduced in the quarter following the foreign price shock, the impact of the foreign price shock on IPI is dampened significantly by the exchange rate appreciation.
  - Domestic CPI peaks only at 0.1 percent above baseline into the second year of the impact when the exchange rate is allowed to appreciate, reflecting staggered consumer price increases due to sluggish second-stage pass-through.
  - If the S$NEER is held constant (no appreciation), the filtering impact of the exchange rate is isolated and CPI responses are larger (Figure 3 results summarized).

### Cross-country and literature context
- The extent of Singapore’s overall exchange rate pass-through to domestic inflation appears similar to that of other developed countries due to the protracted second stage.
- Literature comparisons cited:
  - Gagnon and Ihrig (2004) estimate pass-through for industrial countries at roughly 0.2 percent for a 1 percent change in the exchange rate.
  - Liu and Tsang (2008) find for Hong Kong pass-through about 0.1 in the short run and 0.2 in the medium term.

### Policy implications and recommendations
- Nominal exchange rate remains an effective tool to mitigate external price pressures: importers ultimately pass on the full cost savings from a stronger exchange rate.
- Because of asymmetric pass-through:
  - Monetary policy in Singapore may need to “lean strongly against the wind” during robust cyclical expansions that are accompanied by increases in import costs.
  - During robust cyclical expansion with rising foreign inflationary pressures, an even stronger monetary response is needed to counteract overall cyclical exchange rate pass-through effects.
- Caveat: These monetary policy implications are drawn solely from exchange rate pass-through effects; exchange rate movements also affect domestic prices through export earnings (not examined). A general equilibrium macro econometric model would be needed to assess the overall impact on consumer prices taking both channels into account.

### Methodology and data notes
- Two-stage empirical approach: first stage models exchange rate to import price pass-through; second stage models import price to CPI pass-through. The two ECM specifications are combined for system simulations.
- Business-cycle asymmetries were analyzed by extracting business cycle components from nonstationary series using the approximation to the ideal band pass filter proposed in Corbae and Ouliaris (2006).
- Unit root and cointegration testing (selected results reported):
  - First-stage unit root tests (1980:3-2010:3): ipi ADF t-statistic = -2.1968 (p-value 0.2086); fwpi ADF t-statistic = -0.5617 (p-value 0.8737); exr ADF t-stat = -2.233 (p-value 0.165). FD test statistics reported and p-values show stationarity rejection by ADF and FD tests.
  - Johansen cointegration tests indicate 1 cointegrating equation at the 0.05 level for both first-stage and second-stage systems (lags interval 1 to 2; Akaike and Schwarz criteria reported).
  - Second-stage unit root tests (1991:1–2007:4): cpi ADF t-stat = -0.468 (p-value 0.892); ulc ADF t-stat = -0.962 (p-value 0.764); ipi ADF t-stat = -2.145 (p-value 0.228). FD test statistics and p-values show nonstationarity by ADF and FD tests, and cointegration confirmed (FD p-value = 0.1312).
- Business cycle extraction uses frequency-domain detrending and FD testing to avoid leakage from I(1) components (detailed assumptions and Lemma summaries provided).

*Italic: Summary derived from the content of _wp11141 - 0.24 percent increase in consumer prices, or equivalently, 60 percent of the long-term.*

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