## wp18134 - 1.      Inflation in very small open economies with pegged exchange rate is mostly

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### Key contributions and research question
- Inflation in very small open economies with a pegged exchange rate is mostly imported; Barbados is a price taker and pegs to the US.
- Paper investigates the role of expectations and domestic factors for inflation dynamics in Barbados.
- Contributions:
  - (i) Identifies the mechanism with which inflation expectations are formed in Barbados;
  - (ii) Adds forward looking inflation expectations as a main channel through which external monetary shocks are transmitted;
  - (iii) Measures the importance of domestic shocks, especially monetary shocks.
- Literature position: external factors expected to dominate price dynamics; novelty claimed in estimating the process of expectation formation for Barbados and estimating relative importance of domestic shocks.

### Recent trends in headline inflation (empirical facts and stylized evidence)
- Long-run and volatility:
  - Average inflation: 3.6 percent (36-year sample).
  - Volatility range: between 12 and -4 percent YoY.
  - Inflation follows a first order autocorrelation process; CPI index is I(1) but headline inflation is I(0); ARMA(1,1) indicated by correlograms and portmanteau (Q) statistics.
- External shock episodes (oil and food) highlighted:
  - Oil-related episodes:
    - 1990-91: oil price doubled in two months (first Gulf war).
    - 1997-98: oil price collapsed below US$12 per barrel by end-1998.
    - 1999-01: WTI rose an additional 38 percent by November 2000; US recession March 2001.
    - 2003: Venezuela unrest and second Gulf war increased oil prices moderately.
    - 2005-08: oil increased from US$55 to US$142 per barrel.
    - 2014-17: WTI decreased from US$100 to US$30 between July 2014 and January 2016.
    - 2017-now: oil prices rose from as low as US$30 to US$70 per barrel.
  - Food-related episodes:
    - 2007-08: food price spike; reversed from summer 2008.
    - 2014-15: international food prices decreased by 14 percent between August 2014 and May 2015.
- Trade exposure and import partner composition (percent of total imports; snapshot rows shown for 1990 1995 2000 2005 2010 2016):
  - USA: 33.8 40.7 41.6 35.9 43.9 39.1
  - Trinidad: 10.8 10.8 16.4 21.2 7.2 13.4
  - China: 2.9 4.8 7.3
  - UK: 11.1 9.8 8.1 5.4 5.4 4.8
  - Japan: 5.3 6.7 5.2 7.6 3.6 2.7
  - Canada: 5.7 5.0 4.1 3.4 4.4 2.3
  - Germany: 2.1 2.3 2.0
  - Antigua: 5.3
  - France: 2.1
  - Jamaica: 2.4 2.2
  - Venezuela: 4.0 4.0
  - Total (largest 11 exporters): 80.5 81.5 75.4 76.4 71.4 71.6
- Trade concentration and partner note:
  - United States is the largest trading partner with a share of 40 percent of total imports (period context).
  - Import sources have become less concentrated: largest 11 exporters share decreased from 80 to 70 percent over the last 25 years.
- Domestic policy/tax shocks linked to inflation:
  - 1982 SBA with IMF: fiscal adjustment lowered inflation from 10 to 5 percent in 12 months after Sept 1982.
  - 1992 SBA with IMF: fiscal adjustment lowered inflation from 8 to -0.5 percent in 12 months after Sept 1992.
  - 1997: introduction of a 15 percent VAT generated a sharp increase in inflation.
  - 2011: VAT increased to 17.5 percent, fueling inflation.
  - Late 2016: NSRL introduced at 2 percent; in 2017 NSRL increased to 10 percent, further impacting inflation.

### Analytical framework and model structure
- Theoretical basis:
  - New-Keynesian small open economy model (Galí and Monacelli, 2005) modified to include imported-price (terms of trade) effects and explicit price-setting to derive a modified Phillips curve.
- Firms’ price setting and Phillips curve:
  - New prices set by discounting future expected marginal costs above a constant mark-up (equation forms preserved in source).
  - Log-linearization yields a New-Keynesian Phillips curve where current inflation depends on forward-looking inflation expectations and real marginal costs.
  - CPI aggregation via CES aggregator; CPI is weighted average of changed and unchanged prices.
  - Modified Phillips curve incorporating imported inputs and output gap (equation (7) form):
    - Current inflation depends on forward-looking expectations, real marginal costs, output gap xt, share of foreign inputs α, and imported inflation component πf_t.
  - Interpretation: improvements in terms of trade (πf_t > 0) can increase domestic inflation via expenditure switching; effect stronger with higher openness α and lower import-price elasticity.
- Monetary authority and exchange rate regime:
  - Barbadian dollar pegged to US dollar; monetary authority can in principle only target foreign reserves.
  - With pegged exchange rate and capital mobility: permanent increase in money supply temporarily raises output and lowers interest rates, but leads to capital outflows and reserve loss unless sterilized; domestic interest rate converges to US risk-adjusted rate.
  - Capital controls reduce elasticity of capital inflows, permitting short-term influence on output and inflation while maintaining temporary FX disequilibrium.
  - CBB short-term objective modeled as minimizing loss:
    - Loss: ( ) 2 2 tt L   xα    β π  π=    −
    - Short term deviations of money base from trend consistent with long-run FX equilibrium allow minimizing output gap and indirectly inflation deviations.

### Empirical strategy and baseline specification
- Estimation approach:
  - Disentangle domestic and external determinants of inflation using a variant of the Neo-Keynesian Phillips curve and estimate via OLS.
- Baseline empirical equation structure (annotated in source):
  - πt = function of lagged inflation, inflation expectations (backward- and forward-looking), import deflator, oil inflation, US inflation, output gap, monetary stance, and residuals (exact annotated form preserved in source).
- Variable proxies and expectations formation:
  - Inflation expectations proxied by weighted average of backward-looking past inflation πt-1 and forward-looking US expected inflation π^US_e_t-1.
  - External determinants: annual change in import deflator (idef_t), annual change in oil prices (π^oil_t), US inflation (π^US_t).
  - Domestic determinants: output gap (ogap_t), monetary stance (mst_t) defined as deviation in base money from HP-trend consistent with FX equilibrium.
- Estimation motivation: setup consistent with linear rational expectation structural models and accommodates varying agent information sets.

### Empirical findings (baseline and caveats)
- Baseline OLS (M01) results:
  - A 1 percent increase in lagged inflation generates a 0.87 pp increase in current inflation.
  - Oil prices have a 0.004 pp impact on current inflation (very small but highly significant).
  - Import prices have a 0.044 pp impact on current inflation (relatively larger and highly significant).
  - A 1 percent increase in the output gap generates a 0.048 pp increase in current inflation.
  - All other variables in the baseline regression have impacts not statistically different from zero.
- Key baseline takeaways:
  - Past inflation is the main determinant of current inflation.
  - External factors appear to have low explanatory power in baseline.
  - Domestic factors appear irrelevant in baseline — later shown to be partially incorrect.
- Identification concerns motivating further estimation:
  - External variables likely collinear (terms of trade proxies).
  - Domestic variables likely endogenous (correlated with dependent variable).
  - Baseline estimates therefore likely inefficient and potentially inconsistent.

### Identification strategy: orthogonalization and SUR estimation
- Addressing collinearity:
  - Extract orthogonal factors from external variables via two auxiliary regressions to obtain fitted residuals:
    - ˆres_US_t: portion of US inflation not explained by expectations and oil prices.
    - res_t_idef: portion of Barbados import prices not explained by US inflation (and hence US inflation expectations and oil prices).
- Addressing endogeneity:
  - Estimate a Seemingly Unrelated Regression (SUR) system to account for endogeneity among domestic variables and cross-equation error correlation.
  - Models estimated: Unconstrained SUR (M02) and Constrained SUR (M03/CSUR); sample Apr-1984 / Dec-2017.

### SUR results and parameter changes (M02 and CSUR)
- Unconstrained SUR (M02) highlights:
  - US inflation expectations impact on current inflation: 0.11 pp (significant only at the 10.9 percent level).
  - Oil prices impact increased to 0.007 pp.
  - Import-price residual impact: 0.04 pp (still highly significant).
  - US inflation residual impact: 0.1 pp (now significant at 5 percent level).
  - Domestic determinants retain similar parameter values but monetary stance has much smaller standard errors — domestic factors now statistically different from zero though overall explanatory power remains low.
- Constrained SUR (CSUR) specification:
  - Restricting backward- and forward-looking expectation weights to sum to one yields equal standard errors and makes forward-looking expectations statistically different from zero.
  - Formal test for ˆα2 + ˆα3 = 1 has χ^2(1) distribution with p-value 0.827 (cannot reject null).

### Historical decomposition of headline inflation (CSUR-based) — aggregate and period contributions
- Method:
  - Solve the CSUR inflation difference equation by forward iteration to decompose headline inflation into initial value plus cumulative external and domestic shocks (equation (9) logic).
- Selected exact period figures and contributions (CSUR-based):
  - Inflation peaked at 10.6 percent in September 2008.
  - 2007-10: average inflation 5.6 percent; external factors contributed 3.8 pp; domestic factors contributed 0.5 pp.
  - 2011-14: inflation averaged 4.2 percent; external factors contributed 3.2 pp; domestic factors contributed 0.1 pp.
  - 2015-17: inflation averaged 1.5 percent; external factors contributed -0.5 pp; domestic factors contributed 1.0 pp.
- Model unexplained residuals and under/over-estimation:
  - Model underestimates inflation by up to 4 percentage points in run up to the financial crisis (possible missing proxies for external demand).
  - Additional underestimation in 2010-12 and recent years possibly due to VAT increases, growth deceleration, deteriorating terms of trade not captured by import deflator, and tax policy changes (NSRL and others).

### Relative roles of external vs domestic factors; components
- External factors:
  - External factors are the key determinants on average; contributions vary over time.
  - Over full 1984-17 sample, external factors contribute on average 3 pp of the 3.5 percent average inflation.
  - Forward-looking inflation expectations are the single largest and almost constant positive contributor over the full sample (except 2015-17), reflecting convergence to US inflation under the peg to the US$.
  - Oil prices explain much of short-term volatility (notably 2007-09 and 2014-17).
  - Other import prices not affected by US inflation and oil prices have large impact on short-term dynamics, especially in the latter sample.
  - The component of US inflation not affected by expectations or oil prices subtracts about 0.7 pp to inflation on average.
- Expectations:
  - Estimated inflation-expectations formation weights: 0.87 (backward-looking) and 0.13 (forward-looking).
  - Cumulative forward-looking expectations contribution: on average expectations contribute an almost constant 3 pp to inflation over the full sample.
- Domestic factors:
  - Domestic factors matter but much less than external shocks.
  - Over full 1984-17 sample, domestic factors contribute on average 10 bps of the 3.1 percent average inflation (explicitly reported in text).
  - Among domestic factors, monetary stance is the largest contributor.
  - Monetary shocks contributed up to 90 bps in the run up to the crisis and up to 60 bps in more recent deficit-financing episodes.
  - Output gap has small or negligible average impact; relevant only in select periods (e.g., GDP about 2 pp above trend pre-crisis; 2 pp below trend by 2010). Deviations from trend smaller than 1 pp considered irrelevant.

### Overall conclusions (key findings summarized)
- Methodology:
  - Decomposed inflation determinants in Barbados between external and domestic factors via a New-Keynesian Phillips curve estimated with a SUR system, minimizing collinearity among external factors and allowing endogeneity among domestic factors.
- Main findings:
  - External factors are the largest determinants of inflation in Barbados; over full 1984-17 sample external factors contribute on average 3 pp of the 3.5 percent average inflation.
  - Estimated inflation-expectation formation: weights 0.87 (backward-looking) and 0.13 (forward-looking).
  - Expectations identified as an important channel transmitting base-country (US) monetary shocks to Barbados; forward-looking expectations contribute on average about 3 pp to inflation.
  - Domestic factors affect inflation but much less than external shocks; monetary shocks are the dominant domestic contributor, though small relative to external shocks.
  - Demand shocks have very small impact on inflation, consistent with a CPI dominated by tradable goods and measurement difficulties for the output gap in Barbados.
- Institutional/contextual notes:
  - The peg to the US$ and absence of published local inflation expectations justify the external forward-looking component.
  - Capital controls and institutional features reduce but do not eliminate the Central Bank of Barbados’s monetary influence on inflation; capital controls do not typically deliver full monetary policy independence.

### Appendix A — Data and variable construction (dataset overview and variable definitions)
- Sample and frequency:
  - Monthly observations over the 1984m5-2017m12 interval.
- Headline inflation (πt):
  - Calculated as the 12-month difference in the log of the seasonally adjusted monthly CPI index.
  - CPI is the product of a splicing process of three differently rebased series published by the Central Bank of Barbados.
  - Seasonally adjusted using a time invariant additive linear factor model.
- Forward-looking inflation expectations (π^US_e_t):
  - University of Michigan one year US inflation expectations. Data source: Haver.
- Oil price inflation (π^oil_t):
  - Calculated as the 12-month difference in the log of the seasonally adjusted monthly average FOB cost of US imports from Venezuela.
  - Seasonally adjusted using a time invariant additive linear factor model. Data source: Haver.
  - Statistical note: 95.8 correlation with WTI-based inflation series; chosen series extends sample by 3 years.
- Import deflator (idef_t):
  - Constructed as idef_t = (product over j of (p_{jt} * e_{jt})^{q_{jt}}), rebased to 100 in 2016m5.
  - q_{jt}: import share from country j (UN comtrade), linearly interpolated to monthly.
  - p_{jt}: monthly export deflator or CPI of country j (IFS and Haver), rebased to 100 in 2016m5.
  - e_{jt}: US$/LCU average monthly exchange rate (IFS and Haver).
  - S_t: time varying number of exporting countries to Barbados (UN comtrade).
  - Note: BSS publishes quarterly import/export price indices not available for full sample.
- US inflation (π^US_t):
  - 12-month difference in log of seasonally adjusted monthly CPI index. Data sources: IFS and Haver.
- Output gap (ogap_t):
  - Annual GDP deflator converted to monthly via Denton (1971) using CPI as higher-frequency indicator.
  - Annual nominal GDP converted to monthly via Denton (1971) using monthly GDP deflator; “stock” option used.
  - Monthly real GDP = monthly nominal GDP / monthly GDP deflator.
  - Output gap = log difference between seasonally adjusted real GDP and trend GDP estimated with HP filter.
  - Seasonally adjusted via time invariant additive linear factor model. Data: IFS and Haver as published by Barbados Statistical Service.
- Monetary stance (mst_t):
  - Log difference between seasonally adjusted base money and its trend estimated with HP filter.
  - Seasonally adjusted via time invariant additive linear factor model. Data source: Central Bank of Barbados.

### Appendix B — Historical decomposition derivation (methodological notes)
- Solution approach:
  - Uses forward iteration solutions for linear first-order non-autonomous difference equations to derive the CSUR model’s first-equation solution.
  - Rearrangement yields historical decomposition separating:
    - demeaned inflation component,
    - external factors (US inflation, forward-looking expectations, oil price inflation, import deflator contributions),
    - domestic factors (ogap, mst),
    - unexplained residual res_t.
  - Decomposition explicitly lists summation over lags and indexed coefficients consistent with source formulas.

*Italic source attribution: IMF Working Paper “wp18134 - 1.      Inflation in very small open economies with pegged exchange rate is mostly” (source content provided).*

### 1.      Inflation in very small open economies with pegged exchange rate is mostly

### wp18134 - 1.      Inflation in very small open economies with pegged exchange rate is mostly

### Key contributions and research question
- Inflation in very small open economies with a pegged exchange rate is mostly imported; Barbados is a price taker and pegs to the US.
- Paper investigates the role of expectations and domestic factors for inflation dynamics in Barbados.
- Contributions:
  - (i) Identifies the mechanism with which inflation expectations are formed in Barbados;
  - (ii) Adds forward looking inflation expectations as a main channel through which external monetary shocks are transmitted;
  - (iii) Measures the importance of domestic shocks, especially monetary shocks.
- Literature position: external factors expected to dominate price dynamics; paper claims novelty in estimating the process of expectation formation for Barbados and estimating relative importance of domestic shocks.

### Recent trends in headline inflation (empirical facts and stylized evidence)
- Inflation in Barbados over the last 36 years:
  - Average inflation: 3.6 percent.
  - Volatility range: between 12 and -4 percent YoY.
  - Inflation appears to follow a first order autocorrelation process; CPI index is I(1) but headline inflation is I(0); correlogram/partial correlogram and portmanteau (Q) statistics indicate ARMA(1,1).
- External shocks identified and linked to inflation dynamics:
  - Oil-related episodes:
    - 1990-91 first Gulf war: oil price doubled in two months; spike short-lived.
    - 1997-98 East Asian crisis: oil price collapsed below US$12 per barrel by end-1998.
    - 1999-01 resumed growth and US recession: WTI rose an additional 38 percent by November 2000; then fell with global slowdown; US recession March 2001.
    - 2003 Venezuela unrest and second Gulf war: oil production drops; oil prices and Barbados’ inflation increased moderately.
    - 2005-08 geopolitical instability and speculative investment: oil increased from US$55 to US$142 per barrel.
    - 2014-17 downturn: WTI decreased from US$100 to US$30 between July 2014 and January 2016.
    - 2017-now: oil prices rose from as low as US$30 to US$70 per barrel.
  - Food-related episodes:
    - 2007-08 food price spike: driven by supply shocks (poor harvests), demand (rapid world growth), policy (export bans), and financial elements (US$ depreciation); spike short-lived and reversed from summer 2008.
    - 2014-15 food price drop: international food prices decreased by 14 percent between August 2014 and May 2015.
- Trade exposure and import partner composition (percent of total imports, 1990-2016 snapshot rows shown):
  - Table excerpt (1990 1995 2000 2005 2010 2016):
    - USA: 33.8 40.7 41.6 35.9 43.9 39.1
    - Trinidad: 10.8 10.8 16.4 21.2 7.2 13.4
    - China: 2.9 4.8 7.3
    - UK: 11.1 9.8 8.1 5.4 5.4 4.8
    - Japan: 5.3 6.7 5.2 7.6 3.6 2.7
    - Canada: 5.7 5.0 4.1 3.4 4.4 2.3
    - Germany: 2.1 2.3 2.0
    - Antigua: 5.3
    - France: 2.1
    - Jamaica: 2.4 2.2
    - Venezuela: 4.0 4.0
    - Total (largest 11 exporters): 80.5 81.5 75.4 76.4 71.4 71.6
  - Notes: United States is the largest trading partner with a share of 40 percent of total imports (period context); import sources have become less concentrated (largest 11 exporters share decreased from 80 to 70 percent in the last 25 years).
- Domestic policy and tax shocks as inflation drivers:
  - 1982 and 1992 SBAs with IMF: fiscal adjustment lowered inflation (from 10 to 5 percent in 12 months after Sept 1982; from 8 to -0.5 percent in 12 months after Sept 1992).
  - 1997 introduction of a 15 percent VAT generated a sharp increase in inflation.
  - VAT increased to 17.5 percent in 2011, again fueling inflation.
  - Late 2016 National Social Responsibility Levy (NSRL) introduced at 2 percent; in 2017 NSRL increased to 10 percent, further impacting inflation.

### Analytical framework and model structure
- Theoretical approach: New-Keynesian small open economy model (Galí and Monacelli, 2005) modified to include imported-price (terms of trade) effects and an explicit price-setting process to derive a modified Phillips curve.
- Firms’ price setting:
  - New prices set by discounting future expected marginal costs above a constant mark-up:
    - Equation (1) (as given): 0 (1   )  (  )  {   }             kn ttt k k pE mc
  - Rewritten forms and log-linearizations lead to a New-Keynesian Phillips curve where current inflation depends on forward-looking inflation expectations and real marginal costs.
  - CPI aggregation: CPI is weighted average of changed and unchanged prices with CES aggregator; log-linearized forms given (equations (3), (4), (5)).
  - New-Keynesian Phillips curve form:
    - Equation (6): 1 {  }            tt   tt Emc
  - Incorporating imported inputs and output gap:
    - Equation (7): 1 {  }                     f tt   ttt Ex
    - Where xt is the output gap,  is share of foreign inputs, and f t is component of imported inflation in domestic inflation (terms of trade effect).
  - Interpretation: improvements in terms of trade (f t > 0) can increase domestic inflation via expenditure switching to foreign goods; effect stronger with higher openness () and lower import-price elasticity.
- Monetary authority and exchange rate regime:
  - Barbadian dollar pegged to US dollar; monetary authority can in principle only target foreign reserves.
  - With pegged exchange rate and capital mobility, permanent increase in money supply temporarily raises output and lowers interest rates, but leads to capital outflows and reserve loss unless sterilized; eventual convergence of domestic interest rate to US risk-adjusted rate.
  - Capital controls provide some monetary independence by reducing elasticity of capital inflows to domestic interest rate changes, allowing short-term influence on output and inflation while maintaining temporary FX disequilibrium.
  - CBB (monetary authority) objective in short term modeled as minimizing loss function:
    - Loss: ( ) 2 2 tt L   x           
    - Short term deviations of money base from trend consistent with long-run FX equilibrium allow minimizing output gap and indirectly inflation deviations.

### Empirical strategy and baseline specification
- Approach: Disentangle domestic and external determinants of inflation using a variant of the Neo-Keynesian Phillips curve and estimate via OLS.
- Baseline empirical equation (annotated form in text):
  -  ,12   1    3   145678 domestic determinants inflation expectations external determinants                         US eUS tttttttt idef oilogap mst  u
- Variable definitions and proxies:
  - Inflation expectations:
    - Formed on all available information at time t; proxied by a weighted average of backward- and forward-looking expectations.
    - Backward-looking expectations: past inflation 1( ) t.
    - Forward-looking expectations: expected inflation in the US ,1(   )  US e t.
    - Lagged inflation included because of ARMA(1,1) evidence; expectations therefore contain both domestic and external determinants.
    - Expectation terms expected to be positively related to inflation.
  - External determinants:
    - Proxy for terms of trade / NEER: annual change in the import deflator ( t idef ) and key components: annual change in oil prices ( t oil ) and US inflation (  US t ).
    - External determinants expected to be positively related to inflation.
  - Domestic determinants:
    - Output-gap ( t ogap ) as in equation (7).
    - Monetary stance ( t mst ) defined as deviation in the volume of base money from the steady state trend consistent with FX market equilibrium.
    - Domestic determinants expected to be positively related to inflation.
- Motivation: empirical setup consistent with a large class of linear rational expectation structural models and accommodates various agent information sets.

### Empirical findings (summary from text)
- Consistent with past literature, external factors dominate price dynamics in Barbados.
- The model and estimation strategy allow comparison of the roles of:
  - Inflation expectations (composed of domestic lagged inflation and US expected inflation),
  - External determinants (import deflator, oil price changes, US inflation),
  - Domestic determinants (output gap, monetary stance).
- Specific coefficients and numerical estimation results are not reported in the supplied excerpt.

*Italic source attribution: IMF Working Paper “wp18134 - 1.      Inflation in very small open economies with pegged exchange rate is mostly” (source content provided).*

### 20.      Results of our baseline equation are reported in the first column of Table 2. A

### wp18134 - 20.      Results of our baseline equation are reported in the first column of Table 2. A

### Baseline estimation results (M01 - OLS)
- A 1 percent increase in lagged inflation generates a 0.87 pp increase in current inflation.
- Oil prices have a 0.004 pp impact on current inflation (very small but highly significant).
- Import prices have a 0.044 pp impact on current inflation (relatively larger and highly significant).
- A 1 percent increase in the output gap generates a 0.048 pp increase in current inflation.
- All other variables in the baseline regression have impacts not statistically different from zero.
- Key takeaways from baseline: (i) past inflation is the main determinant of current inflation; (ii) external factors have low explanatory power; and (iii) domestic factors are irrelevant — a set of inferences later shown to be partially incorrect.

### Collinearity and endogeneity concerns; identification strategy
- Issues identified:
  - External variables likely collinear (they proxy import prices / terms of trade).
  - Domestic variables likely endogenous (correlated with the dependent variable).
  - Baseline estimates therefore likely inefficient and potentially inconsistent.
- Addressing collinearity:
  - Extract orthogonal factors from external variables by estimating two auxiliary regressions to obtain fitted residuals:
    - ,ˆUS res_t: portion of US inflation not explained by expectations and oil prices.
    - •res_t_idef: portion of Barbados import prices not explained by US inflation (and hence US inflation expectations and oil prices).
- Addressing endogeneity:
  - Estimate a seemingly unrelated regression (SUR) system to account for endogeneity among domestic variables and cross-equation error correlation.
  - Unconstrained SUR (M02) and constrained SUR (M03/CSUR) reported in Table 2 sample Apr-1984 / Dec-2017.

### SUR results and parameter changes (M02 and CSUR)
- Unconstrained SUR (M02) findings:
  - US inflation expectations impact on current inflation: 0.11 pp (significant only at the 10.9 percent level).
  - Oil prices impact increased to 0.007 pp.
  - Import-price residual (not affected by US inflation and oil prices) impact: 0.04 pp (still highly significant).
  - US inflation residual (not affected by expectations or oil prices) impact: 0.1 pp (now significant at 5 percent level).
  - Domestic determinants retain similar parameters but monetary stance has much smaller standard errors — domestic factors now statistically different from zero though explanatory power remains low.
- Constrained SUR (CSUR) findings:
  - Restricting backward- and forward-looking expectation weights to sum to one yields equal standard errors for the two parameters and makes forward-looking expectations statistically different from zero.
  - Formal test for ˆα2 + ˆα3 = 1 has a χ^2(1) distribution with p-value 0.827 (cannot reject null).

### Historical decomposition of headline inflation (CSUR-based)
- Method:
  - Solve the CSUR inflation difference equation by forward iteration to decompose headline inflation into initial value plus cumulative external and domestic shocks (equation (9)).
- Aggregate and period contributions (selected exact figures preserved):
  - Inflation peaked at 10.6 percent in September 2008.
  - 2007-10: average inflation 5.6 percent; external factors contributed 3.8 pp; domestic factors contributed 0.5 pp.
  - 2011-14: inflation averaged 4.2 percent; external factors contributed 3.2 pp; domestic factors contributed 0.1 pp.
  - 2015-17: inflation averaged 1.5 percent; external factors contributed -0.5 pp; domestic factors contributed 1.0 pp.
- Unexplained residuals:
  - Model underestimates inflation by up to 4 percentage points in the run up to the financial crisis (possible missing proxies for external demand).
  - Additional underestimation in 2010-12 and recent years possibly due to VAT increases, growth deceleration, deteriorating terms of trade not captured by the import deflator, and tax policy changes (NSRL and others).

### Relative roles of external and domestic factors; component contributions
- External factors:
  - On average, external factors are the key determinants of headline inflation, with contributions varying over time.
  - Over the full 1984-17 sample, external factors contribute on average 3 pp of the 3.5 percent average inflation.
  - Forward-looking inflation expectations are the single largest and almost constant positive contributor over the full sample (except 2015-17), reflecting convergence to US inflation under the peg to the US$.
  - Oil prices explain much of short-term volatility (notably 2007-09 and 2014-17).
  - Other import prices not affected by US inflation and oil prices have a large impact on short-term dynamics, especially in the latter sample.
  - The component of US inflation not affected by expectations or oil prices subtracts about 0.7 pp to inflation on average.
- Expectations:
  - Estimated inflation-expectations formation: weights 0.87 (backward-looking) and 0.13 (forward-looking).
  - The cumulative forward-looking expectations contribution is large: on average expectations contribute an almost constant 3 pp to inflation over the full sample.
- Domestic factors:
  - Domestic factors matter but much less than external shocks.
  - Over the full 1984-17 sample, external factors contribute on average 10 bps of the 3.1 percent average inflation (text reports this figure explicitly).
  - Among domestic factors, the monetary stance is the largest contributor to domestic inflation.
  - Monetary shocks contributed up to 90 bps in the run up to the crisis and up to 60 bps in more recent deficit-financing episodes.
  - The output gap has small or negligible average impact, relevant only in select periods (e.g., GDP about 2 pp above trend pre-crisis; 2 pp below trend by 2010). Deviations from trend smaller than 1 pp are considered irrelevant.

### Overall conclusions (V. CONCLUSIONS — key findings summarized)
- Methodology:
  - Decomposed inflation determinants in Barbados between external and domestic factors via a New-Keynesian Phillips curve estimated with a SUR system, minimizing collinearity among external factors and allowing endogeneity among domestic factors.
- Main contributions and findings:
  - External factors are the largest determinants of inflation in Barbados; over full 1984-17 sample external factors contribute on average 3 pp of the 3.5 percent average inflation.
  - First contribution: estimated the inflation-expectation formation process for Barbados — expectations are a weighted average with weights 0.87 (backward-looking) and 0.13 (forward-looking).
  - Second contribution: identify expectations as an important channel transmitting base-country (US) monetary shocks to Barbados; forward-looking expectations contribute on average about 3 pp to inflation.
  - Third contribution: domestic factors do affect inflation, but much less than external shocks; monetary shocks are the dominant domestic contributor, though small relative to external shocks.
  - Demand shocks have a very small impact on inflation, consistent with a CPI dominated by tradable goods and the difficulty of estimating the output gap in Barbados.
- Institutional/contextual notes:
  - The peg to the US$ and the absence of published local inflation expectations justify the external forward-looking component.
  - Capital controls and institutional features reduce but do not eliminate the CBB’s monetary influence on inflation; capital controls do not typically deliver full monetary policy independence.

*Sources: IMF calculations as reported in wp18134 (Sample: Apr-1984 / Dec-2017).*

### Appendix A. Data description

### Appendix A. Data description

### Dataset overview
- Monthly observations over the 1984m5-2017m12 interval.
- Includes domestic and external factors affecting headline inflation: forward-looking component of inflation expectations, oil prices, US inflation, import prices, estimates of the output gap and the monetary stance.

### Headline inflation (πt)
- Calculated as the 12-month difference in the log of the seasonally adjusted monthly CPI index.
- CPI series is the product of a splicing process of three differently rebased series separately published by the Central Bank of Barbados.
- The CPI series is seasonally adjusted using a time invariant additive linear factor model.

### Forward-looking inflation expectations (π^US_e_t)
- University of Michigan one year US inflation expectations.
- Data source: Haver.

### Oil price inflation (π^oil_t)
- Calculated as the 12-month difference in the log of the seasonally adjusted monthly average FOB cost of US imports from Venezuela.
- Series is seasonally adjusted using a time invariant additive linear factor model.
- Data source: Haver.
- Statistical note: the oil price inflation series has a 95.8 correlation with the inflation calculated with the Western Texas Intermediate (WTI) series used in Downes et al. (2017).
- Rationale for choice: monthly average FOB cost of US imports from Venezuela is a longer series, allowing the estimation sample to increase by 3 years relative to WTI.

### Import deflator (idef_t)
- Constructed as an index defined by equation (A1):
  - idef_t = (product over j of (p_{jt} * e_{jt})^{q_{jt}}), rebased to 100 in 2016m5.
- Components and sources:
  - q_{jt} is the import share from country j at time t. Data from UN comtrade database (https://comtrade.un.org) and linearly interpolated to produce monthly observations.
  - p_{jt} is either the monthly export deflator (when available) or the CPI index (as substitute) of country j at time t. Data from IFS and Haver and rebased to 100 in 2016m5.
  - e_{jt} is the US$/LCU average monthly exchange rate of country j at time t. Data from IFS and Haver.
  - S_t is the time varying number of exporting countries to Barbados according to the UN comtrade database (https://comtrade.un.org).
- Footnote: The BSS publishes quarterly import and export price indices but they are not available for the full sample of the dataset.

### US inflation (π^US_t)
- Calculated as the 12-month difference in the log of the seasonally adjusted monthly CPI index.
- Data sources: IFS and Haver.

### Output gap (ogap_t)
- Estimation steps:
  - Convert the annual GDP deflator to a monthly series using Denton (1971) with the CPI index as the higher frequency indicator series.
  - Convert annual nominal GDP to a monthly series using Denton (1971) with the monthly GDP deflator as the higher frequency indicator series, using the “stock” option so monthly observations correspond to annual GDP estimates.
  - Generate monthly real GDP as the ratio of monthly nominal GDP and monthly GDP deflator.
  - Calculate the output gap as the log difference between the seasonally adjusted real GDP and trend GDP estimated with HP filter.
- Seasonally adjusted using a time invariant additive linear factor model.
- Data come from IFS and Haver as published by the Barbados Statistical Service.

### Monetary stance (mst_t)
- Calculated as the log difference between the seasonally adjusted base money and its trend estimated with the HP filter.
- Seasonally adjusted using a time invariant additive linear factor model.
- Data source: Central Bank of Barbados.

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### Appendix B. Derivation of the Historical Decomposition

### Solution of linear difference equations
- General linear first-order autonomous difference equation (B.1):
  - y_t = a y_{t-1} + b, for t = 0,1,...
  - Solution for a ≠ 1 shown in (B.2); steady state value of y is b/(1-a).
- General linear first-order non-autonomous difference equation (B.3):
  - y_t = a_t y_{t-1} + b_t, for t = 0,1,...
  - Solution via forward iteration given by (B4).

### Application to the CSUR model first equation
- The first equation of the CSUR model is “partially” non-autonomous (constant coefficient, variable intercept). Solution derived from (B4) and presented in (B5).
- Substitution of relevant terms from the first equation of the CSUR system yields expression (B6) (symbols and indexed coefficients preserved as in source).
- Rearrangement produces the historical decomposition in (B7), separating:
  - demeaned inflation component,
  - external factors (including US inflation, forward-looking expectations, oil price inflation, import deflator contributions),
  - domestic factors (ogap, mst),
  - unexplained residual (res_t).
- The decomposition in (B7) explicitly lists summation terms over lags and cross-sectional contributors (indexed j and t as in the source formulas), with coefficient structure and residual terms preserved.

*Source: Appendix A and Appendix B from wp18134 - Appendix A. Data description (IMF working paper).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18134.pdf_