## wp18106

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---

### Introduction and motivation
- Low global inflation environment with a secular downward trend in tradable goods inflation as a key driver of falling inflation.
- Improved monetary policy frameworks and global factors likely contribute to structural improvement across many emerging markets.
- Latin American cyclical episodes (including Colombia) show high inflation volatility driven by currency depreciations, food shocks, and increasing economic slack.

### CPI decomposition and modeling framework
- CPI basket decomposed into:
  - tradables
  - non-tradables
  - food
  - regulated prices
- Non-tradables further decomposed into:
  - education
  - rent
  - other
- Regulated prices further decomposed into:
  - fuel
  - transportation
  - public services
- General model: triangular model of the Phillips curve (Gordon) capturing:
  - inertia (lagged inflation)
  - demand shocks proxied by unemployment or the output gap
  - explicit supply-side shocks
- Baseline specification: auto-regressive distributed lag model (ARDL) estimated on quarterly data Q1 2002–Q3 2017.
- Open-economy controls: trade partner weighted CPI growth and NEER movements.
- Baseline supply-side factors:
  - VAT hike dummy
  - El Niño dummy (Southern Oscillation Index two-period sum below -1.25)
  - Real wage shocks (residual from regression of minimum wage increases on output gap, labor productivity growth, and past inflation)
- Include 24-month-ahead inflation expectations; avoid 12-month expectations due to high correlation with current/lagged inflation.

### Key empirical findings (component-level)
- Tradables:
  - More flexible than non-tradables and react more strongly to economic slack.
  - Strong impact of exchange rate movements (significant at the 1 percent level).
  - Output gap has a relatively strong impact on tradable inflation.
  - Inflation expectations have a large positive impact on tradable inflation.
  - El Niño and VAT dummy selected and signed as expected.
- Food:
  - Dominated by supply shocks: international prices, weather (El Niño), and exchange rate.
  - Estimated coefficient for the output gap in the food equation is large and significant.
  - Trade Partner Weighted CPI and El Niño coefficients large in Annex (see values below).
- Non-tradables:
  - Very stable; at times move opposite to tradables.
  - Rent and education strongly influenced by inertia and indexation.
  - “Other” non-tradables more volatile and less indexed; around 50 percent of “other” contains some indexation; only 10 percent of non-tradable goods are not indexed.
  - Rent: mortgage interest rates and price-rent ratio considered; index for new home prices selected.
  - Education: indexation is key; other covariates often appear spurious.
- Regulated prices:
  - Subcomponents behave differently and are driven by formulas/political decisions.
  - Fuel broadly tracks Gulf of Mexico gasoline prices; auxiliary regressions used for subcomponents.

### Aggregate Phillips curve and quantitative estimates
- Contemporaneous output gap (impact effect) point estimates:
  - Headline: 0.098
  - Core: 0.044
  - Core market-determined: 0.096
- Interpretation: contemporaneous estimates suggest a very flat Phillips curve, but dynamics matter.
- Short-to-medium-run (IRF after 6 quarters): estimated Phillips curve coefficient ranges between 0.29 and 0.53.
- Long-run coefficients (Table 3): lie between 0.55 and essentially unity (core market-determined).
- Long-run impacts (Table 3 summary):
  - (a) Long-run Impact of 1 standard deviation increase — Output Gap / Unemployment Gap:
    - Headline: 0.58 / -0.31
    - Core: 0.55 / -0.63
    - Core Market: 0.95 / -1.00
  - (b) Long-run Impact of 1 percentage point increase — Output Gap / Unemployment Gap:
    - Headline: 0.46 / -0.60
    - Core: 0.41 / -1.20
    - Core Market: 0.74 / -1.90
  - (c) Impact of 1 percentage point increase (q-o-q seasonally adjusted growth rates) — Impact / Long-Run:
    - Headline: 0.51 / 0.82
    - Core: 0.14 / 0.46
    - Core Market: 0.11 / 0.54
- Top-down vs bottom-up:
  - Both approaches improve substantially over AR(4) benchmarks in pseudo out-of-sample forecasts.
  - Bottom-up approach provides additional explanatory power and improves forecasting performance relative to top-down.

### Selected regression evidence (headline and core excerpts)
- Headline specification selected coefficients (examples):
  - L1.Headline Inflation: 1.300 0.120 10.83 ***
  - L2.Headline Inflation: -0.683 0.195 -3.50 0.001 ***
  - Output Gap: 0.098 0.062 1.59 0.118
  - Nominal Effective Exchange Rate (Diff): -0.020 0.011 -1.77 0.083 *
  - L1.Nominal Effective Exchange Rate (Diff): -0.034 0.016 -2.12 0.039 **
  - Trade Partner Weighted CPI: 0.348 0.098 3.54 0.001 ***
  - 2 Year Inflation Expectations: 0.174 0.109 1.60 0.116
- Core specification selected coefficients (examples):
  - L1.Core Inflation: 1.358 0.123 11.03 ***
  - L2.Core Inflation: -0.719 0.199 -3.62 0.001 ***
  - L3.Core Inflation: 0.338 0.195 1.73 0.09 *
  - Output Gap: 0.044 0.026 1.68 0.099 *
  - Nominal Effective Exchange Rate (Diff): -0.019 0.004 -5.19 ***
  - El Niño: 0.155 0.091 1.70 0.094 *
  - VAT: 0.858 0.236 3.63 0.001 ***

### Bottom-up sectoral results and diagnostics
- Tradable: Tradeable Inflation lag sum: 0.8648; Output Gap: 0.100; Nominal Effective Exchange Rate (Diff): -0.0403; El Nino: 0.350; VAT: 1.540.
- Non-tradable (excluding Rent & Edu): lag sum: 0.7964.
- Rent: lag sum: 0.7904; Inflation from Last Q4: 0.0600; Trade Partner Weighted CPI: 0.0780.
- Education: lag sum: 0.6754; Inflation from Last Q4: 0.1540; 2yr Inflation Expectations: -0.2960; VAT: 0.6860.
- Core Market Determined: lag sum: 0.8714; Output Gap: 0.0960; Nominal Effective Exchange Rate (Diff): -0.0330; VAT: 1.1000.
- Food: lag sum: 0.6794; Output Gap: 0.3410; Nominal Effective Exchange Rate (Diff): -0.0613; Trade Partner Weighted CPI: 0.6420; El Nino: 1.0550.
- Fuel: Gulf Oil Price Growth: 0.2904; VAT: 11.6392.
- Public Services: lag sum: 0.6664.
- Transportation: lag sum: 0.8294.
- Residual diagnostics: Breusch–Godfrey LM test and Engle’s LM test do not reject H0 of no auto-correlation and no ARCH-effects in residuals for the final specifications.

### Forecasting, baseline projections, and scenario analysis
- Forecast setup:
  - Pseudo out-of-sample evaluation with final specs re-estimated ending 2016 Q2/Q3/Q4; forecast period 2016 Q3/Q4/2017 Q1—2017 Q3.
  - Benchmark: AR(4).
  - Two headline forecasts: top-down (direct) and bottom-up (sum of component forecasts).
- Baseline assumptions for 2018 forecast:
  - Forecast horizon: 2018 Q1 to 2018 Q4.
  - Explanatory variables: January 2018 IMF WEO values.
  - No supply-side shocks other than exchange rate movements as in WEO.
  - Long-term inflation expectations constant at 3.3 percent.
- Baseline projections:
  - Headline inflation projected to converge towards the target level of 3 percent.
  - Bottom-up projects about 3.3 percent in Q4 2018 and is somewhat lower than top-down over the horizon.
  - Non-tradable inflation forecast to come down slowly, falling below 4 percent only at the very end of the horizon.
  - Tradable inflation close to the 3 percent target for the whole year in baseline.
- Four bottom-up scenarios:
  1. 10 percent exchange rate appreciation in Q1 2018 (remainder as WEO baseline) — would push inflation to or below the inflation target.
  2. Weather shock (El Nino) in Q1 and Q2 2018 — mainly affects headline inflation and moves it away from the target; impact moderates relatively quickly.
  3. Lower GDP growth such that output gap at end-2018 is 1 percentage point lower than baseline — modest impact: a 1 percentage point increase in the output gap translates into a decrease in inflation of roughly 0.2 percent over the forecast horizon.
  4. Adverse scenario: 20 percent depreciation and a persistent El Nino shock — would raise headline and core inflation to finish 2018 at close to 7 and 5.5 percent, respectively; driven by much higher food and tradable inflation; non-tradables hardly affected during 2018 but would rise in 2019 due to indexation.

### Role of wage/minimum wage and other robustness checks
- Wage cost push / minimum wage:
  - Generally excluded by information criterion (except rent regression); when included often insignificant.
  - Interpretation: conditional on inertia, demand and supply controls, minimum wage increases add limited explanatory power.
- Robustness checks:
  - Unemployment gap used instead of output gap produces similar results for one standard deviation shocks.
  - q-o-q vs year-on-year: q-o-q seasonally adjusted growth rates give broadly comparable long-run coefficients; q-o-q has greater quarterly volatility which complicates forecasting.
  - Lag selection up to four lags based on BIC; always include four lags of dependent variable.
  - Long-run impacts retrieved from ARDL coefficient polynomials as described in text.

### Key empirical summary and policy implications
- Inflation in Colombia fell from shocks in 2015–2017 as tradable and food inflation returned to target once supply shocks dissipated; core and non-tradable inflation remained elevated longer due to inertia/indexation.
- Triangle Phillips-curve ARDL with supply-shock proxies and international controls is a useful framework for decomposing inflation drivers and forecasting.
- Top-down findings:
  - High inertia.
  - Exchange rate depreciation and world inflation affect domestic inflation with expected signs.
  - Inflation expectations matter.
  - Impact effect of an output gap shock on headline inflation is 0.1 and the long-run impact is at least 0.5.
- Bottom-up findings:
  - Supply-side shocks (El Nino, VAT hike, world inflation) play an important role, especially for tradable and food inflation.
  - Regulated prices follow idiosyncratic processes driven by pricing formulas and political decisions.
- Policy relevance:
  - Combination of component-level Phillips curves outperforms top-down and AR benchmarks in pseudo out-of-sample forecasts.
  - Sensitivity analysis: output gap shocks have moderate effects on inflation; negative supply shocks can push inflation substantially above target, indicating vulnerability to large supply shocks and the importance of monitoring supply-side risks.

*Source: wp18106*

### 1. Key Components of CPI Basket ______________________________________________5

### 1. Key Components of CPI Basket

### Introduction and motivation
- Among a backdrop of low global inflation, a consistent result is that a secular downward trend in tradable goods inflation has been a key driver of falling inflation.
- The downward trend in headline inflation holds for most emerging markets; improved monetary policy frameworks and global factors likely contribute to structural improvement.
- Cyclical episodes in many Latin American countries, including Colombia, have shown high volatility of inflation driven by currency depreciations, food shocks, and increasing economic slack.

### Decomposition of the CPI basket
- The CPI basket is decomposed into:
  - tradables
  - non-tradables
  - food
  - regulated prices
- Non-tradables are further decomposed into:
  - education
  - rent
  - other
- Regulated prices are further decomposed into:
  - fuel
  - transportation
  - public services

### Modelling framework
- The general framework follows the triangular model of the Phillips curve (Gordon).
- The model captures three main drivers of inflation:
  - inertia
  - demand shocks proxied by unemployment or the output gap
  - explicit supply-side shocks

### Empirical approach and literature links
- Follows a bottom-up approach estimating individual Phillips curves for key CPI components, building on Matheson (2006) and Abdih et al. (2016).
- Related evidence:
  - Bryan and Meyer (2010) for the U.S.
  - Julio et al. (2017) for Colombia
  - Julio et al. (2010), Bunn and Ellis (2012), Aron et al. (2014) on heterogeneity in price setting
  - Lopes and Misas (1999) as an earlier careful look at the Phillips curve in Colombia

### Key empirical findings (component-level)
- Prices of tradables, which are more flexible than prices of non-tradables, react more strongly to economic slack than non-tradable prices.
- Supply-side shocks play an important role across bottom-up Phillips curves:
  - weather shocks
  - exchange rate movements
  - international price movements
  - the VAT hike
  - These shocks have important impacts especially on tradable and food inflation.
- Rent and education inflation are strongly influenced by inertia and indexation.
- Regulated prices follow distinct processes; for example, fuel broadly tracks Gulf of Mexico gasoline prices.
- Long-term (24 month) inflation expectations are important determinants of inflation.

### Aggregate Phillips curve and forecast performance
- The aggregate relationship between economic slack and inflation is relatively flat, but:
  - flatter than traditional estimates in some contexts, yet
  - steeper than the recent estimate for the U.S. by Abdih et al. (2016)
  - steeper than the average slope in a sample of 20 advanced countries estimated by Blanchard et al. (2015)
- Both top-down and bottom-up estimations significantly improve on simple autoregressive processes.
- The bottom-up approach has additional explanatory power over the top-down approach.

### Forecasts and scenarios
- Using estimated Phillips curves and IMF World Economic Outlook database inputs (growth, exchange rate, and other variables), the baseline scenario indicates:
  - headline inflation should converge towards the Central Bank’s inflation target by end-2018
  - core inflation would also converge to the target
- Scenario analysis indicates the downward trend in inflation is relatively robust, except in cases of large upward pressure from important inflationary supply-side shocks.

*Source: wp18106 - 1. Key Components of CPI Basket*

### Section IV presents the results. Last Section V presents various model evaluation exercises

### wp18106 - Section IV presents the results. Last Section V presents various model evaluation exercises

### Background and recent developments
- Colombia adopted full-fledged inflation targeting in 1999, with inflation as the nominal anchor, a floating exchange rate, and the short-term interest rate as the main instrument.
- The central bank has kept inflation close to the 3 percent target for extended periods of time.
- Recent shocks with significant inflationary impacts:
  - Sharp depreciation of the peso in 2015−16.
  - Food price shocks in 2016.
  - VAT increase in early 2017.
- Key recent inflation chronology and levels:
  - In February 2015 inflation moved above the 4 percent upper-tolerance limit.
  - Inflation peaked at 9 percent in July 2016.
  - As of Q3 2017, headline inflation is hovering around 4 percent.
- Post-shock dynamics:
  - Tradable and food inflation fell quickly back toward target once supply shocks dissipated.
  - Core and non-tradable inflation remained significantly above 4 percent as of Q3 2017.

### CPI decomposition and component behavior
- Central Bank CPI split into four subcomponents and their population shares:
  - Non-tradable: over 30 percent of the CPI basket.
  - Food: 28 percent.
  - Tradables: 26 percent.
  - Regulated prices: 15 percent.
- Observed dynamics:
  - Tradable inflation is highly volatile (even more so among peer countries).
  - Non-tradable inflation is very stable and at times moves opposite to tradable inflation.
- Further decomposition of non-tradable inflation:
  - Rent (including imputed rent).
  - Education.
  - "Other" — captures the remaining components of the non-tradable basket.
- Indexation and implications:
  - Indexation plays a key role for education and rent, which depend in part on headline inflation at the end of the previous year.
  - The "other" component is somewhat more volatile than rent and education, likely because it is less indexed.
  - Around 50 percent of the "other" component contains some element of indexation.
  - Only 10 percent of non-tradable goods are not indexed in any way.
- Constructed indices:
  - "Purely market-determined core prices" defined as the sum of tradable inflation and the "other" component of non-tradable inflation.
  - This index represents roughly one third of the overall CPI basket.
- Regulated prices decomposition:
  - Regulated subcomponents behave very differently (fuel, public services and transportation) and are driven by formulas and political decisions.

### Conceptual framework and model specification
- Modeling approach:
  - Estimate a "triangle model" of the Phillips curve using quarterly data from Q1 2002 until Q3 2017.
  - Baseline model is an auto-regressive distributed lag model (ARDL) capturing three drivers:
    - Inertia (lagged inflation).
    - Demand shocks proxied by the unemployment or output gap.
    - Explicit supply-side shocks.
  - Include 24-month-ahead inflation expectations to capture forward-looking behavior.
- Open-economy considerations:
  - Include international prices and the exchange rate.
  - Capture international price component via weighted trading partner CPI growth.
  - Use NEER movements owing to lack of a consumption import price basket.
- Baseline supply-side factors:
  - VAT hike dummy.
  - Dummy for extreme weather associated with el Niño (constructed from Southern Oscillation Index; takes value one when the two-period sum lies in the lower decile of the distribution (below -1.25)).
  - Real wage shocks: defined as the residual of a regression of minimum wage increases on the output gap, labor productivity growth and past inflation (i.e., real minimum wage increases in excess of labor productivity growth and not explained by market pressures proxied by the output gap).
- Component-specific variables in bottom-up estimations:
  - Rent inflation: include mortgage interest rates and a lag of the price-rent ratio.
  - Education and rent: include end-of-period headline inflation in the previous year to capture indexation arrangements.
  - Regulated prices: modeled outside the Phillips curve framework in auxiliary regressions that account for idiosyncratic formulaic and political drivers.

### Estimation approach
- Lag selection:
  - Select up to four lags of each variable based on the Bayesian information criterion (BIC).
  - Do not restrict lag length to be uniform across variables.
  - Always include four lags of the dependent variable to control for base effects.
- Interpretation of ARDL estimates:
  - Use estimated ARDL coefficients to retrieve short- and long-run impulse responses.
  - Long-run impact of a change in a forcing variable is given by the ratio of sums of relevant coefficient polynomials (as detailed in the text).
- Significance assessment:
  - Information criterion may not exclude variables that are not statistically significant.
  - Report F-tests on the sum of lag structures to gauge overall significance of included variables.
- Robustness choices:
  - Baseline regressions use the output gap; unemployment gap used in robustness exercises due to concerns about the large informal sector.
  - Avoid using 12-month-ahead expectations because they are highly correlated with current and lagged inflation.
  - In robustness exercises for wage shocks, simpler measures such as just real minimum wage increases produce generally unchanged results.

### Top-down analysis: headline, core, and core market-determined inflation
- General findings from top-down regressions:
  - Inertia is very high: large and significant coefficients on lagged dependent variables.
  - Exchange rate movements have a significant and expected sign: depreciations increase prices.
  - Higher world inflation and higher long-term inflation expectations in Colombia translate into higher inflation.
  - The Phillips curve coefficient (output gap) is positive as expected.
- Differences between headline and core inflation equations:
  - Persistence is even higher for core inflation than headline inflation, consistent with core's higher weight of non-tradables.
  - The estimated impact of exchange rate movements is significantly higher for headline inflation, likely due to Colombia importing roughly 30 percent of its food consumption.
  - The output gap coefficient is positive for both headline and core inflation, but the point estimate is only significant for core inflation.
- Core market-determined inflation index:
  - For the index of core market-determined inflation (tradable + "other"), the estimated coefficient on the output gap is highly significant and larger than for core inflation.
- Magnitude assessment:
  - Impulse response functions and long-term impact calculations are constructed to gauge magnitude, including the long-term impact for a one percent increase in the output gap (procedure described in the text).

*Source: wp18106 - Section IV presents the results. Last Section V presents various model evaluation exercises (IMF working paper).*

### Section III. We can distinguish three measures of the Phillips curve relationship which might

### Section III. We can distinguish three measures of the Phillips curve relationship which might be of interest

### Measures of the Phillips curve and estimated impact coefficients
- Three measures of interest:
  - (i) the impact effect: point estimate on the contemporaneous output gap measure;
  - (ii) the short-to-medium-run impact over a number of quarters;
  - (iii) the long-run impact after all model dynamics have played out.
- Impact (contemporaneous output gap) point estimates:
  - Headline: 0.098
  - Core: 0.044
  - Core market-determined: 0.096
- Interpretation: these impact estimates by themselves suggest a very flat Phillips curve.
- Short-to-medium-run: impulse response functions (IRFs) show slope over several quarters; after 6 quarters estimated Phillips curve coefficient ranges between 0.29 and 0.53.
- Long-run coefficients (Table 3): lie between 0.55 and essentially unity, the latter for the core market-determined index.
- Conclusion: it takes a while for demand pressures to work their way into higher prices.

### Regression evidence (selected coefficients and statistics)
- Headline inflation specification (selected coefficients and statistics):
  - L1.Headline Inflation: 1.300 0.120 10.83 ***
  - L2.Headline Inflation: -0.683 0.195 -3.50 0.001 ***
  - Output Gap: 0.098 0.062 1.59 0.118
  - Nominal Effective Exchange Rate (Diff): -0.020 0.011 -1.77 0.083 *
  - L1.Nominal Effective Exchange Rate (Diff): -0.034 0.016 -2.12 0.039 **
  - Trade Partner Weighted CPI: 0.348 0.098 3.54 0.001 ***
  - 2 Year Inflation Expectations: 0.174 0.109 1.60 0.116
  - Analysis of lag structure, coefficients:
    - Sum(Coeff.) Headline Inflation: 0.785 202.38 0.00 ***
    - Output Gap: 0.098 2.53 0.1182
    - Nominal Effective Exchange Rate (Diff): -0.046 17.20 0.0001 ***
    - Trade Partner Weighted CPI: 0.348 12.55 0.0009 ***
    - 2 Year Inflation Expectations: 0.174 2.55 0.1165
- Core inflation specification (selected coefficients and statistics):
  - L1.Core Inflation: 1.358 0.123 11.03 ***
  - L2.Core Inflation: -0.719 0.199 -3.62 0.001 ***
  - L3.Core Inflation: 0.338 0.195 1.73 0.09 *
  - Output Gap: 0.044 0.026 1.68 0.099 *
  - Nominal Effective Exchange Rate (Diff): -0.019 0.004 -5.19 ***
  - El Niño: 0.155 0.091 1.70 0.094 *
  - VAT: 0.858 0.236 3.63 0.001 ***
  - 2 Year Inflation Expectations: 0.049 0.048 1.02 0.314
  - Analysis of lag structure, coefficients:
    - Sum(Coeff.) Core Inflation: 0.8939 04.38 0.000***
    - Output Gap: 0.044 2.82 0.0989 *
    - Nominal Effective Exchange Rate (Diff): -0.019 26.95 0.000***
    - VAT: 0.858 13.18 0.0006 ***
    - El Niño: 0.155 2.90 0.0943 *
    - 2 Year Inflation Expectations: 0.049 1.03 0.3138

### Table 3: Phillips Curve in Colombia — Long-run and q-o-q impacts
- (a) Long-run Impact of 1 standard deviation increase
  - Output Gap / Unemployment Gap
    - Headline: 0.58 / -0.31
    - Core: 0.55 / -0.63
    - Core Market: 0.95 / -1.00
- (b) Long-run Impact of 1 percentage point increase
  - Output Gap / Unemployment Gap
    - Headline: 0.46 / -0.60
    - Core: 0.41 / -1.20
    - Core Market: 0.74 / -1.90
- (c) Impact of 1 percentage point increase (q-o-q seasonally adjusted growth rates)
  - Impact / Long-Run
    - Headline: 0.51 / 0.82
    - Core: 0.14 / 0.46
    - Core Market: 0.11 / 0.54

### Robustness checks and alternate specifications
- Using unemployment gap rather than output gap:
  - Sign flips (higher unemployment gap implies lower/more negative output gap).
  - Impact of a one standard deviation shock: results very similar when using unemployment gap instead of output gap.
  - The unemployment gap is constructed using a simple Hodrick-Prescott filter for the quarterly data.
- Using quarter-on-quarter (q-o-q) rather than year-on-year growth rates:
  - q-o-q seasonally adjusted growth rates calculated after seasonal adjustment using the census bureau X-12 method.
  - Conceptual preference for q-o-q as it allows cleaner structural interpretation of Phillips coefficient, but baseline not q-o-q due to high quarterly volatility making forecasting less reliable.
  - Table 3c: long-run coefficients using q-o-q growth rates broadly comparable to year-on-year estimates; impact coefficients comparable except for headline inflation (large estimated impact on food inflation when using q-o-q rates).
- Note: possible non-linearities in the Phillips curve could be explored, though limited data for extreme scenarios makes this challenging.

### Role of wage cost push and minimum wage variables
- Consistent result: the measure of wage cost push is never included in the final specification by the information criterion (exception: regression for rent inflation).
- Interpretation: conditional on adequately controlling for inertia (dependent variable lag structure), demand and supply pressures, minimum wage increases do not have much explanatory power in the regressions.
- Empirical context: level of minimum wages in Colombia is high relative to median income (see OECD (2016) referenced); minimum wage growth has tended to follow inflation in the previous year closely; real wage increases controlling for productivity have been moderate in most, but not all, years between 2000 and 2017.
- Various alternative specifications for minimum wage (e.g., simple real minimum wage increases) were tried; the variable was either dropped by the information criterion or, on few occasions included, insignificant.

### Bottom-up approach: sectoral drivers of inflation dynamics
- Purpose: model tradable, non-tradable, food, and regulated price inflation separately to understand drivers in more detail.
- General finding: important role for supply-side shocks in bottom-up Phillips curves — weather shocks, exchange rate movements, international price movements, and the VAT hike have important impacts on inflation, particularly tradable and food inflation.
- Regulated prices: behave according to their own processes (example: fuel broadly tracking Gulf of Mexico gasoline prices).
- Rent and education inflation: strongly influenced by inertia and indexation.

Tradable
- Strong impact of exchange rate movements on tradable prices (significant at the 1 percent level).
- Relatively strong impact of the output gap on tradable inflation.
- Inflation expectations have a large positive impact on tradable inflation.
- El Niño indicator and the VAT dummy were selected by the information criteria and have the expected sign.
- Note: estimated pass-through to headline inflation is driven by tradable effect and impact on food prices; somewhat higher than estimates in referenced IMF work.

Non-tradable
- Non-tradable split into rent, education, and ‘other’.
- Rent equation: additional factors allowed — index for new home prices, real mortgage interest rates, lagged price-to-rent ratio. Only index for new home prices selected in final specification.
- To capture indexation, end of period headline inflation of the previous year included.
- Results: persistence and indexation dominate dynamics of rent inflation.
- World inflation enters with a statistically significant positive coefficient in rent equation, but channel unclear — may be spurious.
- Education inflation: indexation is a key driver; other coefficients appear spurious, indicating education dynamics not fully modeled. Data limitations prevented inclusion of supply/demand variables specific to education market.
- ‘Other’ non-tradables: very high persistence; output gap, exchange rate and indexation not statistically significant.

*Source: wp18106 - Section III. We can distinguish three measures of the Phillips curve relationship which might*

### 5.9 percent, less than the previous year. For higher education, an index of costs which broadly follows CPI

### wp18106 - 5.9 percent, less than the previous year. For higher education, an index of costs which broadly follows CPI

### Education and Rent: drivers and dynamics
- For higher education, an index of costs which broadly follows CPI inflation is calculated as a suggestion for price increases but the universities are free to deviate from the index when setting their price increases.
- Rent and education inflation are strongly influenced by inertia and indexation.
- Disaggregated results explain why a steeper Phillips curve is found for core market prices than for core prices: rent and education prices do not seem to be positively impacted by aggregate demand pressures in a significant way.

### Food: supply shocks and demand role
- Food inflation dynamics are dominated by supply shocks related to international prices, the weather, and the exchange rate.
- The estimated coefficient for the output gap in the food equation is large and significant.
- Section V (forecasting) highlights the key role that supply-side shocks have for food prices.

### Regulated prices: component-specific modeling
- Regulated prices are disaggregated into public services, fuel, and transportation price indices.
- Auxiliary regressions are used for subcomponents to reflect pricing-formula particularities:
  - Fuel price inflation is modeled as a function of lags of the growth rate of Gulf of Mexico gasoline prices, the VAT shock, and headline inflation in the previous year.
  - Public services inflation includes the indexation variable and the El Nino dummy.
  - Transportation includes only the indexation variable (headline inflation at the end of the previous year).
- These specifications fit the data reasonably well and substantially improve forecasting performance relative to a simple AR process.

### Forecasting inflation using Phillips curves — model evaluation
- Pseudo out-of-sample setup:
  - Final specifications re-estimated restricting sample to end in 2016 Q2, 2016 Q3 or 2016 Q4.
  - Forecast period: 2016 Q3/2016 Q4/2017 Q1—2017 Q3.
  - Benchmark: simple autoregressive process AR(4).
- Two headline forecasts constructed:
  - Top-down: directly from CPI inflation regressions.
  - Bottom-up: sum of forecasts for tradable, components of non-tradable, components of regulated, and food.
- Findings:
  - Both top-down and bottom-up forecasts substantially improve on AR(4).
  - Bottom-up forecast improves on top-down.
  - Models are dynamic (use projected values after t+1) to provide meaningful evaluation.
  - RMSE analysis shows food and fuel have the largest absolute RMSEs, reflecting higher volatility, but regression RMSEs are significantly lower than pure AR RMSEs for these components.
  - Residual diagnostics: Breusch–Godfrey LM test and Engle’s LM test do not reject H0 of no auto-correlation and no ARCH-effects in residuals.

### Baseline forecast for 2018 (bottom-up and top-down)
- Data and assumptions:
  - Forecast horizon: 2018 Q1 to 2018 Q4.
  - Explanatory variables: January 2018 IMF WEO values.
  - Assume no supply side shocks other than exchange rate movements as taken from WEO forecasts.
  - Long-term inflation expectations constant at 3.3 percent.
- Projections:
  - Headline inflation projected to converge towards the target level of 3 percent.
  - Bottom-up projects about 3.3 percent in Q4 2018 and is somewhat lower than top-down over the horizon.
  - Non-tradable inflation forecast to come down slowly, falling below 4 percent only at the very end of the forecast horizon.
  - Tradable inflation should be close to the 3 percent target for the whole year in the baseline scenario.

### Forecast scenarios and sensitivity analysis
- Four bottom-up scenarios analyzed:
  1. 10 percent exchange rate appreciation in Q1 2018 with remainder of year as in WEO baseline.
  2. Weather shock (El Nino) in Q1 and Q2 of 2018.
  3. Lower GDP growth than baseline such that the output gap at end-2018 is 1 percentage point lower than under the baseline.
  4. Adverse scenario: 20 percent depreciation and a persistent El Nino shock.
- Scenario impacts:
  - 10 percent appreciation would push inflation to or even below the inflation target.
  - A short weather shock would mainly affect headline inflation and take it away from the target, but the impact would moderate relatively quickly.
  - A worsening in the output gap of 1 percent of GDP by end-2018 would have a modest impact: a 1 percentage point increase in the output gap translates into a decrease in inflation of roughly 0.2 percent over the forecast horizon.
  - The adverse scenario (20 percent depreciation + weather shock) would raise headline and core inflation to finish 2018 at close to 7 and 5.5 percent, respectively, driven by much higher food and tradable inflation; non-tradables would be hardly affected during 2018 but would rise in 2019 due to indexation.

### Key empirical summary and policy implications (from conclusions)
- Inflation in Colombia has been coming down steadily since exchange rate depreciation and food price shocks pushed it well above the target in 2016.
- Tradable and food inflation fell fast as shocks dissipated; core and non-tradable inflation remained higher.
- Triangle Phillips-curve approach: auto-regressive distributed lag model including output gap, lagged inflation, inflation expectations, and supply-shock proxies; includes international prices and exchange rate; lag length selection via BIC.
- Top-down findings:
  - Inertia is very high in Colombia.
  - Exchange rate depreciation and world inflation affect inflation with expected signs.
  - Inflation expectations matter.
  - Coefficient on the output gap is positive for both headline and core inflation.
  - Impact effect of an output gap shock on headline inflation is 0.1 and the long run impact is at least 0.5.
- Bottom-up findings:
  - Important role for supply-side shocks (El Nino, VAT hike, world inflation), especially for tradable and food inflation.
  - Regulated prices follow idiosyncratic processes related to pricing formulas.
- Forecasting performance and policy relevance:
  - Combination of Phillips curves for each subcomponent beats the top-down Phillips curve and AR benchmark in pseudo out-of-sample forecasts.
  - Using IMF WEO global assumptions and Colombia projections, model forecasts headline inflation to fall towards 3 percent in 2018Q4.
  - Sensitivity analysis indicates output gap shocks have moderate effects; negative supply shocks can push inflation substantially above target, highlighting vulnerability to large supply shocks.

### Annex — selected coefficient highlights (Annex Tables)
- Tradeable:
  - Tradeable Inflation lag sum: 0.8648
  - Output Gap: 0.100
  - Nominal Effective Exchange Rate (Diff): -0.0403
  - El Nino: 0.350
  - VAT: 1.540
- Non-Tradeable (Excluding Rent & Edu.):
  - Non-Tradeable Inflation lag sum: 0.7964
- Rent:
  - Rent Inflation lag sum: 0.7904
  - Inflation from Last Q4: 0.0600
  - Trade Partner Weighted CPI: 0.0780
- Education:
  - Education Inflation lag sum: 0.6754
  - Inflation from Last Q4: 0.1540
  - 2yr Inflation Expectations: -0.2960
  - VAT: 0.6860
- Core Market Determined Prices:
  - Core Market Determined Inflation lag sum: 0.8714
  - Output Gap: 0.0960
  - Nominal Effective Exchange Rate (Diff): -0.0330
  - VAT: 1.1000
- Food:
  - Food Inflation lag sum: 0.6794
  - Output Gap: 0.3410
  - Nominal Effective Exchange Rate (Diff): -0.0613
  - Trade Partner Weighted CPI: 0.6420
  - El Nino: 1.0550
- Fuel:
  - Gulf Oil Price Growth: 0.2904
  - VAT: 11.6392
- Public Services:
  - Public Services Inflation lag sum: 0.6664
- Transportation:
  - Transportation Inflation lag sum: 0.8294

*Source: wp18106 (IMF Working Paper content provided).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18106.pdf_