## wp18149

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### I. Purpose, motivation, and FPAS role
- Paper describes a basic version of a new core forecasting model to be used at the Central Bank of Sri Lanka (CBSL) within a Forecasting and Policy Analysis System (FPAS).
- Rationale and FPAS components:
  - Transition from monetary targeting (MT) to flexible inflation targeting (FIT); CBSL currently operates an “enhanced” hybrid MT–FIT framework.
  - FPAS elements: (i) dedicated forecasting team, (ii) database infrastructure, (iii) near-term forecasting and nowcasting tools, (iv) core quarterly projection model (QPM), (v) regular forecast meetings, (vi) clear reporting process.
  - FPAS functions: (i) collect key macro variables, (ii) produce consistent model-based forecasts with uncertainty and alternative scenarios, (iii) report to Monetary Policy Committee and Monetary Board.

### II. QPM model class, mechanisms, and transmission channels
- Model class and focus:
  - Semi-structural small open economy quarterly projection model (QPM) based on New-Keynesian paradigm; gap model around exogenously given equilibrium; includes nominal and real rigidities.
- Four basic relationships:
  - IS curve: aggregate demand depends negatively on real interest rate and positively on real exchange rate and foreign output.
  - New-Keynesian Phillips Curve: aggregate supply reacts to excess demand and intermediate goods prices.
  - Policy rule: central bank sets policy rate to pursue inflation objective (possibly weighted with exchange rate objective).
  - UIP: exchange rate determined by current and future interest rate differentials adjusted by country risk premium.
- Monetary transmission channels:
  - Interest rate channel: real interest rate affects intertemporal substitution and demand.
  - Exchange rate channel: policy rate affects exchange rate, competitiveness, import prices, and inflation.
  - Expectation channel: policy shapes agents’ expectations influencing current spending and price-setting.

### III. Key model components and equations (selected)
- Output and equilibrium growth:
  - Output gap y^_t depends on a1·y^_{t−1}, a2·y^_{t+1}, −a3·r^_t, a4·foreign output gap, −a5·z^_t, and shock ε^{y^}_t (equation (1)).
  - Equilibrium growth Δy_t: autoregressive with parameter a6 and shock ε^{Δy}_t (equation (2)).
- Disaggregated inflation structure:
  - CPI composition weights: core consumption goods and services = a14 = 68.9 percent; volatile food = a13 = 18.5 percent; energy and transport = residual (1−a14−a13).
  - Headline inflation π_t = a14·π_t^c + a13·π_t^vf + (1−a14−a13)·π_t^ft + π_t^dfsc (equation (3)).
  - Core inflation dynamics include parameters a15, a16, a17, a18, a19 (equation (15)).
- Monetary policy and exchange rate rules:
  - Interest-rate rule (inflation and output stabilization): i_t^info = a7·i_{t−1} + (1−a7)·(i_t^{ffnn} + a8·π̂_t + a9·ŷ_t) + ε^f_t (equation (7)).
  - Weight between inflation-targeting and exchange rate rules: i_t = a12·i_t^info + (1−a12)·i_t^{nfi} (equation (10)); a12 reflects relative importance of inflation objective.
  - Exchange rate dynamics via UIP and smoothing with parameters a10, a11 and target depreciation dynamics (equations (8)–(11)).

### IV. Data, treatment of noisy GDP, and external block
- Domestic data: Real GDP, Colombo CPI and components, Average Weighted Call Market Rate (nominal interest rate), nominal exchange rate (US$/Rs); GDP and inflation from DCS; other domestic data from CBSL.
- Foreign data: Fed Fund rate, Brent oil price, FAO food price index; foreign forecasts from Mantis.
- Seasonal adjustment: X12 software.
- Handling noisy GDP:
  - Introduces “Adjusted GDP” variable as the noise-free GDP level; observed DCS GDP are treated as observed series with measurement error computed in the model filtration stage.
  - Revision facts: DCS first release ≈ ten weeks after quarter end; estimates may be revised up to six times within three years.
  - Example 2015 quarterly revisions (percent YoY): Q1 first release 6.0; 1st Revision 4.4; 2nd Revision 4.9; 3rd Revision 4.4. Q2 first release 6.7; 1st Revision 6.0; 2nd Revision 7.0. Q3 first release 4.8; 1st Revision 5.6. Q4 first release 2.5.
- External block: U.S. output gap, U.S. CPI, U.S. interest rates, world oil and food prices treated as exogenous autoregressive mean-reverting processes.

### V. Calibration strategy and key calibrated steady states
- Calibration rationale:
  - Model has about 50 parameters and several unobserved variables; data sample limited (2001–2015 ≈ 56 quarterly observations) and includes structural breaks (civil war ended May 2009).
  - Iterative calibration with diagnostics: impulse responses, in-sample forecast simulations, filter decomposition. Greater emphasis on post-2009 performance.
- Key calibrated steady states:
  - Steady state inflation rate = 5 percent.
  - Steady state real GDP growth rate = 6.0 percent.
  - Steady state real exchange rate appreciation = 2 percent.
  - Resulting nominal depreciation in steady state = 1 percent.
  - Country risk premium = 5 percentage points per annum.
  - Foreign inflation = 2 percent.
  - Foreign real interest rate = 1 percent.
  - Steady state inflation of real oil prices = 7.5 percent.
  - Steady state inflation of real food prices = 7 percent.

### VI. Calibration of behavioral parameters (selected) and Bayesian ML tuning
- Chosen calibration (examples):
  - Output gap: a1 = 0.6 (lagged), a2 = 0.3 (expected), a3 (real interest elasticity) relatively low.
  - Phillips curves and sectoral parameters: core forward component = 0.27; backward component = 0.25; real exchange rate parameter = 0.15; energy spillover = 0.06; imported food direct effect = 0.02.
  - Energy & transport: imported inflation parameter = 0.25; sectoral real marginal costs = 0.5; backward component = 0.1.
  - Volatile food: higher reversion weight on lag.
  - Interest-rate rule: weight on inflation gap a8 = 0.8; weight on output gap a9 = 0.1; interest rate smoothing a7 = 0.8.
  - Weight on inflation-targeting vs exchange rate smoothing a12 = 0.8 (captures partial attention to exchange rate while emphasizing FIT).
- Bayesian maximum likelihood fine-tuning (selected ML estimates vs calibrated values):
  - a1 (c1_l_y_gap): Calibrated 0.60, ML Estimate 0.5480
  - a2 (c2_l_y_gap): Calibrated 0.30, ML Estimate 0.2000
  - a3 (c3_l_y_gap): Calibrated 0.05, ML Estimate 0.0354
  - a4 (c4_l_y_gap): Calibrated 0.10, ML Estimate 0.0938
  - a5 (c5_l_y_gap): Calibrated 0.08, ML Estimate 0.0637
  - a7 (c1_rn): Calibrated 0.80, ML Estimate 0.8133
  - a8 (c2_rn): Calibrated 0.80, ML Estimate 0.7744
  - a9 (c3_rn): Calibrated 0.10, ML Estimate 0.0988
  - a11 (c2_dl_s_pol): Calibrated 1.00, ML Estimate 0.8220
  - a12 (w_rn_rule): Calibrated 0.80, ML Estimate 0.8066
  - a15 (c1_dl_cpi_core): Calibrated 0.27, ML Estimate 0.2509
  - a16 (c2_dl_cpi_core): Calibrated 0.25, ML Estimate 0.2743
  - a17 (c3_dl_cpi_core): Calibrated 0.15, ML Estimate 0.1366
  - a18 (c4_dl_cpi_core): Calibrated 0.06, ML Estimate 0.0435
  - a19 (c5_dl_cpi_core): Calibrated 0.02, ML Estimate 0.0288
  - a20 (c1_dl_cpi_vfood): Calibrated 0.10, ML Estimate 0.2680
  - a21 (c2_dl_cpi_vfood): Calibrated 2.00, ML Estimate 1.2902
  - a22 (c1_dl_cpi_et): Calibrated 0.10, ML Estimate 0.2089
  - a23 (c2_dl_cpi_et): Calibrated 0.25, ML Estimate 0.1807
  - a24 (c3_dl_cpi_et): Calibrated 0.50, ML Estimate 0.1664
  - a25 (c4_dl_cpi_et): Calibrated 0.50, ML Estimate 0.4487
  - a31 (c1_e_l_s): Calibrated 0.90, ML Estimate 0.8722
- Estimation outcome:
  - Improved in-sample forecasting performance for inflation and GDP growth; estimated model generally better than calibrated baseline on selected metrics.

### VII. Shock identification, structural shocks, and standard deviations (selected)
- Structural shocks and standard deviations (selected entries from Table 5):
  - ε^{y^} — shock_l_y_gap — Demand shock — 1.00
  - ε^{f} — shock_rn — MP shock — 1.00
  - ε^{π_{cc}} — shock_dl_cpi_core — Core inflation shock — 1.50
  - ε^{π_{vvvv}} — shock_dl_cpi_vfood — Volatile food inflation shock — 13.00
  - ε^{π_{ett}} — shock_dl_cpi_et — Energy & transport inflation shock — 15.00
  - ε^{Δs} — shock_dl_s — UIP shock — 3.00
  - ε^{Δy} — shock_dl_y_tnd — Potential growth shock — 0.30
  - ε^{ρ} — shock_prem — Risk premium shock — 0.20
  - ε^{q^_proil_gap} — shock_l_roil_gap — Real oil price gap shock — 18.00
  - ε^{q^_rfood_gap} — shock_l_rfood_gap — Real food price gap shock — 5.00

### VIII. Impulse response stylized findings
- Demand shock (positive):
  - Immediate increase in domestic demand and core prices; monetary tightening needed to stabilize inflation; higher interest rate leads to temporary exchange rate appreciation and contraction in activity.
- Monetary policy tightening shock:
  - Policy rate increase attracts foreign funds (appreciation), raises loan and deposit rates, reduces spending, and contracts real activity; reduces imported production costs and demand-sensitive inflation temporarily.
- Temporary exchange rate depreciation shock:
  - Raises import and domestic commodity prices (Energy & Transport, non-volatile food), increases production costs, improves competitiveness and activity, generating inflationary pressures; requires restrictive monetary conditions to cool activity and re-appreciate exchange rate.
- Policy responses vary by inflation component:
  - Strongest and most persistent reactions to core inflation shocks.
  - Smallest reactions to volatile food shocks due to their temporary nature.

### IX. Historical decompositions and narrative consistency
- Model identifies drivers consistent with stylized facts:
  - High inflation 2007–2009 mainly due to growing domestic non-core prices and large domestic supply shocks (administered energy above underlying).
  - Imported disinflation during the global financial crisis contributed to domestic disinflation in 2009.
  - Post-2010: domestic supply shocks, looser monetary stance, and rupee depreciation led to higher inflation; stabilization and disinflation from 2013 onward.
  - Output gap: overheating from 2006 until global financial crisis; post-2009 civil war end supported domestic demand; since 2013 tight policy and weakening demand opened output gap.

### X. Forecast performance metrics (selected RMSEs and ratios)
- Table 1 — RMSE for Headline Inflation (% YoY) — without vs with inflation components in QPM:
  - Without components: 1.0 (1Q), 2.0 (2Q), 2.8 (3Q), 3.4 (4Q), 3.5 (5Q), 3.4 (6Q).
  - With components: 1.3 (1Q), 2.0 (2Q), 2.4 (3Q), 2.8 (4Q), 2.8 (5Q), 2.9 (6Q).
- RMSE ratios versus random walk (selected variables, horizons 1Q–8Q):
  - Real GDP growth (percent, YoY): 1Q 0.69, 2Q 0.60, 3Q 0.52, 4Q 0.47, 5Q 0.46, 6Q 0.48, 7Q 0.50, 8Q 0.54
  - CCPI Inflation (percent, YoY): 1Q 0.52, 2Q 0.50, 3Q 0.49, 4Q 0.49, 5Q 0.46, 6Q 0.47, 7Q 0.49, 8Q 0.51
  - LKR per USD FX rate (100*log): 1Q 0.88, 2Q 0.80, 3Q 0.77, 4Q 0.74, 5Q 0.72, 6Q 0.71, 7Q 0.70, 8Q 0.69
  - Nominal Interest Rate (percent p.a.): 1Q 1.09, 2Q 0.71, 3Q 0.61, 4Q 0.59, 5Q 0.53, 6Q 0.48, 7Q 0.45, 8Q 0.43
- Model performance summary:
  - Model forecasts inflation and real growth precisely in many periods; underperforms during large unpredictable domestic shocks (e.g., 2007–mid-2008 high inflation, 2010–2011 rupee appreciation, post-civil-war growth surge, flood-affected low growth).
  - Model performs well when small or foreign shocks dominate; underperforms for large domestic shocks.

### XI. Directions for future extensions
- Fiscal block:
  - Capture government spending, tax changes, government borrowing, and effects on equilibrium interest rates and external balance; important given large and persistent fiscal deficits.
- Financial sector block:
  - Incorporate financial frictions, macro-financial linkages, and banking-sector frameworks (e.g., Bernanke et al. (1999), Gertler and Kiyotaki (2010), Gertler and Karadi (2011)).
- Data and estimation improvements:
  - Move from judgment-based parameter choices to greater estimation using Sri Lankan data; incorporate micro-foundations to improve model performance.

### XII. Appendix A — model inventory (selected tables and parameter values)
- Representative equations numbered (1) through (81) define output gap, interest rate rules, UIP, disaggregated inflation, relative prices, trend processes, and measurement identities.
- Table 4 — model variables (selected):
  - y (l_y): Real output (100*log)
  - Δy (dl_y): Real output growth (percent, QoQ annualized)
  - y^ (l_y_gap): Real output gap (%)
  - i (rn): Nominal interest rate (percent p.a.)
  - π (dl_cpi): Inflation (percent, QoQ annualized)
  - π_{cc} (dl_cpi_core): Core Inflation (percent, QoQ annualized)
  - s (l_s): Nominal exchange rate LKR per USD (100*log)
  - z (l_z): Real exchange rate (100*log)
- Table 5 — structural shocks and standard deviations (see section IX).
- Table 6 — selected parameter values (examples preserved verbatim):
  - ss_dl_z_tnd = 2.000
  - ss_pie_tar = 4.879
  - ss_prem = 5.000
  - ss_dl_y_tnd = 6.500
  - a1 (c1_l_y_gap) = 0.548
  - a2 (c2_l_y_gap) = 0.200
  - a3 (c3_l_y_gap) = 0.035
  - a4 (c4_l_y_gap) = 0.094
  - a5 (c5_l_y_gap) = 0.064
  - a6 (c1_dl_y_tnd) = 0.900
  - a7 (c1_rn) = 0.813
  - a8 (c2_rn) = 0.774
  - a9 (c3_rn) = 0.099
  - a10 (c1_dl_s_pol) = 0.500
  - a11 (c2_dl_s_pol) = 0.822
  - a12 (w_rn_rule) = 0.807
  - a13 (w_vfood) = 0.185
  - a14 (w_core) = 0.689
  - a15 (c1_dl_cpi_core) = 0.251
  - a16 (c2_dl_cpi_core) = 0.274
  - a17 (c3_dl_cpi_core) = 0.137
  - a18 (c4_dl_cpi_core) = 0.043
  - a19 (c5_dl_cpi_core) = 0.029
  - a20 (c1_dl_cpi_vfood) = 0.268
  - a21 (c2_dl_cpi_vfood) = 1.290
  - a22 (c1_dl_cpi_et) = 0.209
  - a23 (c2_dl_cpi_et) = 0.181
  - a24 (c3_dl_cpi_et) = 0.166
  - a25 (c4_dl_cpi_et) = 0.449
  - a26 (c1_dl_cpi_disc) = 0.079
  - a27 (c1_dl_rp_vfood_tnd) = 0.900
  - a28 (c1_dl_rp_et_tnd) = 0.900
  - a29 (c1_pie_tar) = 1.000
  - a31 (c1_e_l_s) = 0.872
  - a32 (c1_prem) = 0.950
  - a33 (c1_l_y_gap_f) = 0.910
  - a34 (c1_rn_f) = 0.500
  - a35 (c1_rr_tnd_f) = 0.500
  - a36 (c1_dl_cpi_f) = 0.285
  - a37 (ss_dl_roil_tnd) = 7.500
  - a40 (ss_dl_rfood_tnd) = 7.000
  - a41 (c1_l_rfood_gap) = 0.900
  - a42 (c1_dl_rfood_tnd) = 0.950

*Source: wp18149 — References and Appendix A (Complete Model) as provided in the source content.*

### References .............................................................................................................

### References

### I. Introduction — purpose and motivation
- The paper describes a basic version of a new core forecasting model to be used at the Central Bank of Sri Lanka (CBSL) for forecasting and monetary policy analysis.
- The modeling work is part of a joint project between the CBSL and the International Monetary Fund (IMF) to develop a modern Forecasting and Policy Analysis System (FPAS) at the CBSL.
- Key rationale:
  - Transition of the monetary policy framework from monetary targeting (MT) to flexible inflation targeting (FIT) is underway; CBSL currently operates under an “enhanced” monetary policy framework that is a hybrid of MT and FIT.
  - The evolution of the CBSL into an increasingly transparent and forward-looking institution is imperative to the successful transition to FIT.
  - Structural models provide forward-looking guidance on policy actions required to align inflation with its medium-term objective while stabilizing real output at its potential level.
  - Simple structural models can bridge information gaps with the public regarding the rationale of the monetary policy stance (Alichi et al., 2015; Hammond, 2012).

### II. The Forecasting and Policy Analysis System (FPAS) — components and role
- FPAS elements described:
  - (i) a team fully dedicated to forecasting with clearly defined responsibilities,
  - (ii) a database infrastructure,
  - (iii) a set of near-term forecasting and nowcasting tools,
  - (iv) a core quarterly projection model (QPM) which embodies policymakers’ view about transmission mechanisms and relevant shocks,
  - (v) a regular schedule of meetings to update the forecast and interact with senior management,
  - (vi) a reporting process that presents the analysis in a clear and straightforward manner to policy makers.
- The FPAS combines quantitative tools with processes to use these tools efficiently in policy decision-making.
- Central banks adopting (flexible) inflation targeting capitalize on FPAS to discipline policy analysis; FPAS involves:
  - (i) collecting and organizing key macroeconomic variables,
  - (ii) developing a consistent, model-based macroeconomic forecast including measures of uncertainty and alternative risk and policy scenarios,
  - (iii) reporting and communicating the forecast to the Monetary Policy Committee and the Monetary Board (Andrle et al., 2013; CBSL, 2017).

### III. Structure of the paper and model-related sections
- Organization of the paper:
  - Section II: progress of economic modelling at the CBSL and motivation for developing a semi-structural model.
  - Section III: description of the new QPM model and the theory and practical aspects underpinning the creation of this customized model.
  - Section IV: means of calibration and fine-tuning of the QPM.
  - Section V: analysis of the dynamic properties of the model and assessment of model performance using “in-sample” simulations.
  - Section VI: areas for future research.
  - Section VII: concluding remarks.
- The FPAS QPM is positioned as the core quarterly projection model used for medium-term projections and policy analysis.

### IV. Historical background and motivation for modeling at CBSL
- Sri Lanka’s economic transformation:
  - Independence in 1948; transition from an agriculture-based primary commodity producer to a predominantly service-based light manufacturing economy.
  - Per capita income increased from around US dollars 100 at independence to reach the upper threshold of the lower middle-income economy status.
- CBSL institutional context:
  - CBSL established in 1950.
  - First 25 years featured a fixed exchange rate system, strict capital controls, underdeveloped money and capital markets, occasional external shocks, and subsidized credit to selected sectors.
- Ongoing modeling motivation:
  - Rapid structural transformation, especially in the post-conflict era, and efforts to become an exporter and investment destination create new challenges requiring changes to the macroeconomic framework.
  - Use of structural models is indispensable for transparency, communication, and forward-looking policy guidance.

### V. Figures, tables, boxes, and appendices referenced (as listed)
- Figures:
  - Figure 1. Model Structure
  - Figure 2. Impact of Civil War End on Potential Output and Risk Premium
  - Figure 3. Domestic Headline and World Commodity Inflation
  - Figure 4. Demand Shock
  - Figure 5. Monetary Policy Tightening
  - Figure 6. Temporary Exchange Rate Shock
  - Figure 7. Policy Response to the Different Supply Shocks
  - Figure 8. Shock Decomposition of Annual Inflation
  - Figure 9. Shock Decomposition of Real Output Gap
  - Figure 10. In-sample Forecast of the Main Macro Variables
- Tables:
  - Table 1. Comparison of RMSE for Headline Inflation with
  - Table 2. Prior Distributions and Estimated Values
  - Table 3. RMSE Comparison of the Main Model Variables
  - Table 4. Model Variables
  - Table 5. Model Structural Shocks
  - Table 6. Model Parameters
- Boxes:
  - Box 1. Handling Noisy GDP data
- Appendix:
  - Appendix A. Complete Model

*Source: wp18149 - References (IMF working paper content provided).*

### introduction of open economy policies in 1977 required an overhaul of the entire

### wp18149 - introduction of open economy policies in 1977 required an overhaul of the entire

### Historical reforms and CBSL responses
- Introduction of open economy policies in 1977 required an overhaul of the entire policymaking machinery.
- CBSL key responses included:
  - introduction of monetary targeting in the early 1980s,
  - automation of the clearing house,
  - active facilitation of the development of domestic financial markets.
- Judging by available macroeconomic statistics, the post-1977 period saw:
  - the economy became more volatile,
  - inflation cycles became larger.

### Technical capacity and modelling history at CBSL
- Legal basis: Monetary Law Act No 58 of 1949 established the Economic Research Department and empowered CBSL to “promote and sponsor the training of technical personnel on the subjects of money, banking, statistics, finance, and other economic subjects”.
- Early multisectoral and macroeconometric work by CBSL staff:
  - Sirisena (1976): multisectoral model using input-output analysis and linear programming.
  - Karunasena (1986): “A Macroeconometric Model for Sri Lanka” — large-scale macroeconometric model.
  - Wijesinghe (1986): multisectoral intertemporal optimization model.
- Later modelling and studies (late 1990s–2015) included assessments of inflation targeting feasibility, transmission channels, and monetary policy impacts; selected authors and years cited in source include Thenuwara (1998), Mahadeva and Thenuwara (2000), Jayamaha et al (2002), Amarasekara (2005, 2008), Weerasinghe et al (2005), Perera (2008 and 2009), Wimalasuriya (2009), Ratnasiri (2011), Jayawickrema and Perera (2013), Anand, Ding and Peiris (2011), Ehelepola (2014, 2015), Jegajeevan (2014), Karunaratne and Pathberiya (2014).

### Modernization, institutional change, and policy tools
- Late 1990s catalysts for reform:
  - global developments in central banking emphasizing price stability,
  - managed floating exchange rate regime becoming unviable,
  - rapid development of financial markets and need to regulate unregulated sectors,
  - financial innovation including electronic payments and fund transfer systems and millennium bug concerns,
  - exigencies from a terrorist attack in 1996 prompting efficiency improvements.
- CBSL Modernization Project supported by IMF, World Bank, and Sveriges Riksbank led to:
  - establishment of the Monetary Policy Committee (MPC),
  - floating of the Rupee,
  - introduction of active open market operations (active OMOs).
- Forward-looking inputs introduced:
  - Inflation Expectations Survey (mid-2000s),
  - Business Outlook Survey and Purchasing Managers’ Index (PMI) Survey (recent).

### Motivation for building a semi-structural core forecasting model (QPM)
- In moving toward a Flexible Inflation Targeting (FIT) regime, need for:
  - anchoring inflation expectations while minimizing large fluctuations in economic growth,
  - monitoring recent developments and probable future paths of inflation,
  - attention to systematic components and short-term indicators to comprehend linkages and policy impacts.
- Existing tools: CBSL used VAR and VEC models for near-term assessment; these are flexible but limited for structural policy inference.
- Benefits of a core (semi-)structural model:
  - transparency and simplicity,
  - expresses variables as gaps and trends,
  - tractable and intuitive for monetary policy analysis,
  - aids interpretation of forecasts, risk assessment, policy response design, and exploration of monetary transmission.
- Objective: present a concise customized semi-structural core forecasting model for CBSL FPAS to form a baseline medium-term outlook, assess risks, and analyze policy responses; model designed to be refined and extended over time.

### QPM model description and main mechanisms
- Model class and focus:
  - semi-structural small open economy quarterly projection model (QPM) based on New-Keynesian paradigm,
  - gap model focusing on business cycle fluctuations around exogenously given equilibrium,
  - incorporates nominal and real rigidities.
- Four basic relationships define underlying mechanism:
  - Aggregate demand depending negatively on real interest rate and positively on real exchange rate (IS curve — Euler equation).
  - Aggregate supply reacting in short run to excess demand and prices of intermediary goods (New–Keynesian Phillips curve).
  - Central bank sets policy rate to achieve inflation objective (and perhaps other objectives).
  - Exchange rate determined by current and future interest rate differentials adjusted by country risk premium (uncovered interest rate parity).
- Monetary transmission channels in the model:
  - Interest rate channel: real interest rate changes affect intertemporal substitution and demand (consumption, investment).
  - Exchange rate channel: policy rate changes influence currency attractiveness, depreciation/appreciation, competitiveness of tradables, and import prices with demand and supply-side inflation effects.
  - Expectation channel: policy shapes agents’ expectations about growth, prices, and future interest rates, affecting current saving, investment, and price-setting.

### Key model components and structure
- Output and equilibrium growth:
  - Output gap yt̂ is model-consistent and depends on past gap, expected future gap, real interest rate gap r̂t, foreign output gap ŷtff, and real exchange rate gap ẑt; demand shock εtŷ.
  - Equilibrium growth Δyt modeled as autoregressive converging to steady state growth with parameter a6 and shock εtΔy (equation (2)).
- Disaggregated aggregate supply and inflation components:
  - Three inflation components with respective weights:
    - core consumption goods and services: 68.8 percent of CPI basket,
    - volatile food: 15.2 percent,
    - regulated transport and energy goods and services: treated as residual.
  - Headline inflation πt is weighted average:
    - πt = a14·πt c + a13·πt vf + (1−a14−a13)·πt ft + πt dfsc (equation (3)).
  - Core inflation πt c (equation (4)) driven by:
    - output gap ŷt, lagged core inflation πt−1 c, forward-looking core inflation Et[πt+1 c], real exchange rate gap and relative sectoral prices, imported food inflation Δpt ffood,d,fi,i,c, and sectoral energy/transport spillovers rpp̂t ft/c.
  - Energy and transport inflation πt ft (equation (5)) driven by:
    - lagged and forward-looking inflation, imported oil price inflation Δpt−1 foil,foi,ft, real oil price gap q̂t−1 foil,ft, sectoral relative price gap rpp̂t−1 ft/c, and shock εtπet.
  - Volatile food inflation πt vf (equation (6)) modeled as mean-reverting with lagged inflation, steady-state mean, sectoral relative price gap rpp̂t−1 vf/c, and shock εtπvv.
- Sectoral relative prices and trends:
  - Relative price rpp t j = pt j − pt c decomposed into cyclical rpp̂ t j and trend rpp̄ t j components; trends evolve as autoregressive mean-reverting processes with shocks.
- Monetary policy specification and UIP:
  - Interest rate rule for inflation and output stabilization:
    - iitinfo = a7·it−1 + (1−a7)·(itffnn + a8·π̂t + a9·ŷt) + εtf (equation (7)).
    - π̂t = πt+4 − πt (7a).
    - itffnn = rt + πt+1 4 (7b) (policy-neutral rate).
  - UIP-based exchange rate dynamics:
    - iitinfo = itff + 4(st f − st nfi) + ρt + εtΔs (equation (8)).
  - Exchange rate smoothing regime and depreciation target:
    - itnfi = itff + 4·(st f − st ifo) + ρt + εtΔs (9).
    - Δst ifo = 4·(st ifo − st−1) (9a).
    - Δst ifo = a10·Δst−1 ifo + (1−a10)·(−Δzt + πt − πssff + a11·ẑt−1) + εtΔs ppp (9b).
  - Actual policy rate combines objectives:
    - it = a12·itinfo + (1−a12)·itnfi (10). Parameter a12 reflects relative importance of inflation objective; a12 = 1 implies full inflation targeting, a12 = 0 implies full exchange rate smoothing.
  - Current exchange rate is combination:
    - st = a12·st nfi + (1−a12)·st ifo (11).
- Real exchange rate and long-run UIP:
  - Real exchange rate zt = pt − st − pt fforeign (12).
  - Long-run UIP in real terms:
    - rt = r t fforeign − Δzt+1 + ρt (13).

### External sector and parameterization
- External block:
  - U.S. output gap, U.S. CPI inflation, U.S. interest rates used as proxies for global demand, inflationary pressures, and global liquidity.
  - World oil and food prices included.
  - External variables treated as exogenous autoregressive mean-reverting processes around steady states.
- Data sources and treatment:
  - Domestic data: real GDP, Colombo Consumer Price Index (CCPI) and components, Average Weighted Call Market Rate (nominal interest rate), nominal exchange rate (US$/Rs) — GDP and inflation data from DCS; other domestic data from CBSL.
  - Foreign data: Fed Fund rate, Brent oil price, FAO world food price index, etc.
  - Forecasts of foreign variables obtained from Mantis forecast database.
  - Seasonal adjustment: X12 software package used for seasonal variables.
  - Data continuity methods:
    - splicing technique for different base-year series,
    - rebasing historical series to recent compilation methodology where DCS changed methodology and base years,
    - combined observed GDP series obtained by rebasing GDP levels based on base years 1996 and 2002 to the new base year.
- Model role within FPAS:
  - QPM is a core semi-structural forecasting model intended to work alongside BVARs and leading indicator models to produce medium-term projections and analyze macroeconomic risks for monetary policy formulation.

### Forecasting performance note
- Table 1: Comparison of RMSE for Headline Inflation with and without inflation components in the QPM (Headline Inflation, % YoY)
  - without inflation components in QPM: 1.0 (1Q), 2.0 (2Q), 2.8 (3Q), 3.4 (4Q), 3.5 (5Q), 3.4 (6Q).
  - with inflation components in QPM: 1.3 (1Q), 2.0 (2Q), 2.4 (3Q), 2.8 (4Q), 2.8 (5Q), 2.9 (6Q).

*Source: wp18149 - introduction of open economy policies in 1977 required an overhaul of the entire*

### 2010. In the meantime, noise in the combined series is treated by adding a measurement error

### wp18149 - 2010. In the meantime, noise in the combined series is treated by adding a measurement error

### Handling Noisy GDP data
- GDP estimation faces a tradeoff between estimate accuracy and timeliness; initial estimates are released on scheduled timelines and are subject to revision.
- Real GDP compilation in Sri Lanka is carried out by the Department of Census and Statistics (DCS) in compliance with SNA 2008.
- The first set of real GDP estimates for a particular quarter is released by the DCS approximately ten weeks after that quarter has ended.
- Revision policy: estimates are subject to revise not more than six times during three years from the first release of a particular estimate.
- Example quarterly revisions (Table 5: Quarterly Gross Domestic Product at Constant (2010) Prices: 2015):
  - 2015 Q1: First release 6.0; 1st Revision 4.4; 2nd Revision 4.9; 3rd Revision 4.4
  - 2015 Q2: First release 6.7; 1st Revision 6.0; 2nd Revision 7.0
  - 2015 Q3: First release 4.8; 1st Revision 5.6
  - 2015 Q4: First release 2.5
- Noisy and preliminary initial GDP estimates can be substantially different from later revisions due to noise and news in the compilation process; this inconsistency can affect policy making and must be handled in macroeconomic modeling and forecasting.
- Methods to address noisy macroeconomic data discussed:
  - Filter-based methods (e.g., Kalman filter) — Kalman filter allows estimation to adjust as revised data become available (Howrey, 1978).
  - State space models — measurement equation becomes part of estimation; success depends on the structure of the measurement equations imposed; weakly-structured measurement equations can yield less accurate forecasts than ignoring noise (Ghosh and Lien, 2001; Fukuda, 2007).
  - Factor models — minimize impact of noise when noise is idiosyncratic and uncorrelated across variables (Bernanke and Bovin, 2003); but added noise from using many variables may outweigh benefits (Faust and Wright, 2009).
- QPM approach:
  - Introduces an additional variable “Adjusted GDP” considered as the actual level of GDP free of any noise.
  - GDP figures published by DCS are treated as observed GDP; observed GDP adjusted for noise (Adjusted GDP) is given as input to the model’s transition equations.
  - GDP measurement error is computed within the model during the filtration stage.

### Summary of the Data used in the Model (Table 4)
- Domestic Block variables and notations:
  - Real Gross Domestic Product — l_y (Data source: DCS)
  - Colombo Consumer Price Index — l_cpi (DCS)
    - Core Inflation — l_cpi_core (DCS)
    - Volatile Food Inflation — l_cpi_vfood (DCS)
    - Energy and Transport Inflation — l_cpi_et (DCS)
  - Average Weighted Call Money Rate — rn (CBSL)
  - Nominal LKR per USD Exchange Rate — l_s (CBSL)
- Foreign Block variables and notations:
  - Fed Funds Rate — rn_f (FRED Federal Reserve Bank of St. Louis)
  - U.S. Output Gap — l_y_gap_f (Mantis)
  - U.S. CPI — l_cpi_f (OECD statistics)
  - Brent Oil Price — l_oil (Bloomberg)
  - FAO Food Price Index — l_food (FAO)

### Calibration techniques
- Model parameters are calibrated rather than estimated because:
  - Small, semi-structural models for developing countries face limitations: short and noisy data samples and structural breaks complicate identification.
  - The model has about 50 parameters (including standard deviations of shocks) and several unobserved variables, making estimation inadvisable.
- Structural break context:
  - Civil war ended in May 2009 represents a distinctive structural break for Sri Lanka.
  - QPM is not capable of explicitly accounting for structural breaks or fully explaining drivers and dynamics of structural changes due to modest structure, focus on deviations/gaps from long-term equilibria, and linear nature.
  - QPM nonetheless useful to identify:
    - A temporary increase in potential output growth of about 1.5 percentage points right after the end of the war.
    - A decline in country risk premium from a peak of 6 percentage points per annum in 2007 to around 2 percentage points per annum in 2013.
- Data sample and implications:
  - Sample period between 2001 and 2015 yields about 14 years of quarterly data (56 data points), including periods affected by the civil war and the global financial crisis.
- Calibration process:
  - Iterative; in every iteration the model’s calibration is examined using diagnostic tools until satisfactory calibration is achieved.
  - Diagnostic tools used:
    - Impulse response functions for assessing dynamic properties of the model.
    - In-sample historical forecast simulations for assessing model’s forecasting performance.
    - Filter decomposition to compare model’s interpretation of past events with experts’ views and stylized facts.
- Emphasis during calibration:
  - Greater emphasis on model performance after the civil war (post-2009) than before 2009.

### Calibration of main behavioral equations
- Parameter choice informed by modeling experience of other countries, particularly emerging markets, and adapted to Sri Lanka’s characteristics.
- Output gap equation parameters:
  - Coefficient on lagged output gap:
    - Literature suggests it lies between 0.5 and 0.9, with lower values for less mature, more volatile economies.
    - Chosen value for Sri Lanka: 0.6.
  - Coefficient on expected output gap:
    - Typically small; chosen value for Sri Lanka: 0.3.
  - Parameters on real interest rate gap, real exchange rate gap, and foreign output gap:
    - Depend on monetary transmission effectiveness, importance of exchange rate channel, and degree of openness.
    - Relatively low values selected for Sri Lanka to reflect: relatively weak interest rate channel, tightly managed exchange rate regime, and non-diversified export dependence.
- Inflation dynamics:
  - Modeled using three Phillips Curve equations tracking core inflation, volatile food inflation, and energy and transport inflation individually.
  - In the Phillips Curve for core inflation, the parameter on output gap depends on how much core inflation is influenced by real demand pressures and affects the “sacrifice ratio” of the economy.

*Source: wp18149 (2010) — IMF working paper content provided in the supplied PDF chapter/section.*

### 0.27 for this parameter since price dynamics of core items are mainly driven by domestic

### wp18149 - 0.27 for this parameter since price dynamics of core items are mainly driven by domestic

### Calibration of sectoral Phillips curves and transmission parameters
- Core inflation:
  - Parameter on forward component set to 0.27.
  - Parameter on backward component set to 0.25 to match high volatility of observed data.
  - Real exchange rate parameter set to 0.15 to reflect strong pass-through.
  - Spillover effect from energy prices set to 0.06.
  - Direct effect of imported food price dynamics set to 0.02 due to small weight of non-volatile food in core basket.
- Energy & Transport (domestic administered energy inflation follows world oil price dynamics):
  - Imported inflation component parameter set to 0.25.
  - Sectoral real marginal costs parameter set to 0.5.
  - Backward component (price rigidity) parameter set to 0.1.
- Volatile food inflation:
  - Parameterized to respond to its lagged value with a relatively higher weight to reflect fast reversion to long-term trend.

### Monetary policy rule calibration
- Interest-rate rule parameters:
  - Parameter on inflation gap set to 0.8 reflecting CBSL’s gradual move towards a flexible inflation targeting regime (FIT).
  - Parameter on output gap set to 0.1.
  - Interest rate smoothing parameter set to 0.8, consistent with past smooth path and estimates for emerging markets.
- Weight on inflation-targeting interest rate rule versus exchange rate rule (parameter 푎푎12) set to 0.8 to capture CBSL’s partial attention to exchange rate volatility while emphasizing inflation targeting.
- Note on future recalibration:
  - As FIT credibility strengthens, forward-looking components in Phillips curves may be increased.
  - Strengthening of interest rate channel and weakening of exchange rate channel may be required (parameters at real interest rate and real exchange rate gaps in the IS curve and parameters driving exchange rate pass-through in Phillips Curves).

### Calibration of steady states
- Steady state inflation rate set to 5 percent (coincides with recent medium-term inflation targets of the CBSL; same steady state for all sectors).
- Steady state of real GDP growth rate calibrated at 6.0 percent (average since 2003).
- Steady state real exchange rate appreciation set to 2 percent (historical average ~2.6 percent; long-term equilibrium assumed somewhat lower).
- Resulting nominal depreciation in steady state: 1 percent (given 5 percent domestic inflation and 2 percent foreign inflation).
- Country risk premium calibrated at 5 percentage points per annum to match historical interest rate differential.
- External sector steady states:
  - Foreign inflation set to 2 percent.
  - Foreign real interest rate set to 1 percent.
  - Steady state inflation of real oil prices set to 7.5 percent.
  - Steady state inflation of real food prices set to 7 percent.

### Fine-tuning via Bayesian Maximum Likelihood Estimation
- Bayesian estimation used to fine-tune calibration with relatively narrow priors centered on calibrated values; aim to find a nearby point that explains data better without large deviations.
- Selected estimated parameters and ML estimates (subset from Table 2, means of priors set to calibrated values):
  - 푎푎1 (c1_l_y_gap): Calibrated 0.60, ML Estimate 0.5480
  - 푎푎2 (c2_l_y_gap): Calibrated 0.30, ML Estimate 0.2000
  - 푎푎3 (c3_l_y_gap): Calibrated 0.05, ML Estimate 0.0354
  - 푎푎4 (c4_l_y_gap): Calibrated 0.10, ML Estimate 0.0938
  - 푎푎5 (c5_l_y_gap): Calibrated 0.08, ML Estimate 0.0637
  - 푎푎7 (c1_rn): Calibrated 0.80, ML Estimate 0.8133
  - 푎푎8 (c2_rn): Calibrated 0.80, ML Estimate 0.7744
  - 푎푎9 (c3_rn): Calibrated 0.10, ML Estimate 0.0988
  - 푎푎11 (c2_dl_s_pol): Calibrated 1.00, ML Estimate 0.8220
  - 푎푎12 (w_rn_rule): Calibrated 0.80, ML Estimate 0.8066
  - 푎푎26 (c1_dl_cpi_disc): Calibrated 0.50, ML Estimate 0.0787
  - 푎푎15 (c1_dl_cpi_core): Calibrated 0.27, ML Estimate 0.2509
  - 푎푎16 (c2_dl_cpi_core): Calibrated 0.25, ML Estimate 0.2743
  - 푎푎17 (c3_dl_cpi_core): Calibrated 0.15, ML Estimate 0.1366
  - 푎푎18 (c4_dl_cpi_core): Calibrated 0.06, ML Estimate 0.0435
  - 푎푎19 (c5_dl_cpi_core): Calibrated 0.02, ML Estimate 0.0288
  - 푎푎20 (c1_dl_cpi_vfood): Calibrated 0.10, ML Estimate 0.2680
  - 푎푎21 (c2_dl_cpi_vfood): Calibrated 2.00, ML Estimate 1.2902
  - 푎푎22 (c1_dl_cpi_et): Calibrated 0.10, ML Estimate 0.2089
  - 푎푎23 (c2_dl_cpi_et): Calibrated 0.25, ML Estimate 0.1807
  - 푎푎24 (c3_dl_cpi_et): Calibrated 0.50, ML Estimate 0.1664
  - 푎푎25 (c4_dl_cpi_et): Calibrated 0.50, ML Estimate 0.4487
  - 푎푎31 (c1_e_l_s): Calibrated 0.90, ML Estimate 0.8722
- Estimation outcome:
  - Improved in-sample forecasting performance for inflation and GDP growth.
  - RMSE comparisons (selected quarters) show estimated model better than original for core inflation and real GDP; similar for interest and exchange rates.

### Dynamic properties and impulse responses
- Impulse Response Function (IRF) framework: responses to a 1 percent unexpected shock in first period measured relative to steady state.
- Demand shock:
  - Positive output shock increases aggregate domestic demand and core prices immediately due to excess demand.
  - Monetary tightening required to mitigate demand-side inflation; higher interest rate leads to temporary nominal exchange rate appreciation via UIP, reducing activity and inflation.
- Monetary policy tightening shock:
  - Unexpected policy rate increase attracts foreign investors (exchange rate appreciation).
  - Higher loan and deposit rates encourage postponing spending, increasing savings; contraction in real activity.
  - Stronger currency and tighter policy reduce imported production costs and demand-sensitive inflations temporarily.
- Temporary exchange rate shock (depreciation):
  - Depreciation raises import prices, increases domestic commodity prices (Energy & Transport and non-volatile food), and raises production costs across sectors.
  - Improved competitiveness heats economic activity generating excess demand and inflationary pressure; CBSL needs to cool activity and appreciate currency via restrictive monetary conditions.
- Policy responses differ by inflation component:
  - Strongest policy reaction to core inflation shocks (highest and most persistent impact).
  - Volatile food shocks elicit smallest and relatively modest policy reaction due to temporary nature.

### Historical shock decomposition and model interpretation of history
- Model identifies past inflationary drivers consistent with stylized facts:
  - Foreign real economy and weak exchange rate contributed positively until the financial crisis.
  - High inflation between 2007 and 2009 mainly due to growing domestic non-core prices and large domestic supply shocks (domestic administered energy inflation above underlying factors).
  - Imported disinflation during financial crisis led to large domestic disinflation in 2009, amplified by negative foreign economy shocks.
  - Stable exchange rate and weak foreign demand kept inflation stable until 2012 despite commodity price increases.
  - Domestic supply shocks, looser monetary stance, and rupee depreciation led to higher inflation post-2010; stabilization and subsequent disinflation from 2013 onward.
- Real output gap decomposition:
  - Weak domestic demand and weak currency, plus strong foreign demand, kept output gap close to zero in early 2000s.
  - Economy overheated from 2006 until the global financial crisis; crisis-induced decline in foreign demand and tight monetary stance caused overvaluation until 2012 devaluation.
  - Improvement in domestic demand from 2009 after civil war end offset some effects.
  - Since 2013, tight monetary policy and decreasing domestic and foreign demand resulted in a permanently opened output gap.

### Historical forecast performance and model evaluation
- In-sample forecast protocol: observed variables known until simulation start; exogenous external variables treated as known over 8-quarter horizon.
- Forecast performance:
  - Model forecasts inflation and real growth precisely in many periods but underperforms during large, unpredictable domestic shocks (e.g., 2007–mid-2008 high inflation, 2010–2011 rupee appreciation, post-civil-war growth surge, and flood-affected low growth).
  - Conclusion: model performs very well when small or foreign shocks dominate; underperforms for large domestic shocks.
- RMSE comparison (Table 3) for main variables (selected quarters show estimated model improvements; exact quarterly RMSEs reported in source).
- RMSE ratios versus random walk (Table 6) — model outperforms random walk for most horizons and variables (ratios shown exactly in source):
  - Real GDP growth (percent, YoY): 1Q 0.69, 2Q 0.60, 3Q 0.52, 4Q 0.47, 5Q 0.46, 6Q 0.48, 7Q 0.50, 8Q 0.54
  - CCPI Inflation (percent, YoY): 1Q 0.52, 2Q 0.50, 3Q 0.49, 4Q 0.49, 5Q 0.46, 6Q 0.47, 7Q 0.49, 8Q 0.51
  - LKR per USD FX rate (100*log): 1Q 0.88, 2Q 0.80, 3Q 0.77, 4Q 0.74, 5Q 0.72, 6Q 0.71, 7Q 0.70, 8Q 0.69
  - Nominal Interest Rate (percent p.a.): 1Q 1.09, 2Q 0.71, 3Q 0.61, 4Q 0.59, 5Q 0.53, 6Q 0.48, 7Q 0.45, 8Q 0.43

### Directions for future analysis and model extensions
- Fiscal block addition:
  - Capture effects of government spending, countercyclical fiscal policy, tax structure changes, government borrowings on equilibrium interest rates and external balance.
  - Important given large and persistent fiscal deficits in Sri Lanka.
- Financial sector block addition:
  - Incorporate financial frictions, effects of financial distortions on interest rates and investments, and macro-financial linkages.
  - Rationale: CBSL’s dual focus on price stability and financial system stability; growing importance of money to GDP and credit to GDP ratios and credit cycles.
  - Suggested micro-foundations include Bernanke et al. (1999) financial accelerator and banking-sector frameworks of Gertler and Kiyotaki (2010), Gertler and Karadi (2011).
- Data and estimation improvements:
  - Current parameter values largely judgment-based due to limited data.
  - Future work: estimate parameters using Sri Lankan data to incorporate micro foundations and improve model performance.

### Conclusion
- QPM is a semi-structural open economy macroeconomic model (DSGE principles) developed under FPAS for CBSL to support forward-looking monetary policy analysis and forecasting.
- Model allows forecasting of key macro variables and policy simulations; historical decompositions and impulse-response analyses demonstrate policy implications for achieving medium-term price stability.
- QPM is intended as the main macro model for CBSL within a broader toolkit including nowcasting and near-term forecasting models, facilitating transition from monetary targeting to flexible inflation targeting.

*Source: wp18149 (IMF Working Paper content provided in the supplied PDF excerpt)*

### REFERENCES

### REFERENCES

### Key cited works
- Alichi, A., Benes, J., Felman, J., Feng, I., Freedman, C., Laxton, D., Tanner, E., Vavra, D., Wang, H., “Frontiers of Monetary Policymaking: Adding the Exchange Rate as a Tool to Combat Deflationary Risks in the Czech Republic”, IMF Working Paper 15/74, 2015
- Andrle, M., Berg, A., Morales, R.A., Portillo, R. and Vlcek, J., “Forecasting and Monetary Policy Analysis in Low-Income Countries: Food and non-Food Inflation in Kenya”, IMF Working Paper 13/61, 2013.
- Amarasekara, C., “Interest Rate Pass-through in Sri Lanka”, Staff Studies, Vol. 35, Nos 1 and 2, Central Bank of Sri Lanka, 2005.
- An, S., Schorfheide, F., “Bayesian Analysis of DSGE Models”, Econometric Reviews, 26:2-4, p.113-172, 2007.
- Benes, J., Clinton, K., George, A., John, J., Kamenik, O., Laxton, D., Mitra, P., Nadhanael, G., Wang, H., Zhang, F., “Inflation-Forecast Targeting for India: An Outline of the Analytical Framework”, Reserve Bank of India, Working Paper 07/2016, 2016.
- Berg, A., Karam, P. and Laxton D., “Practical Model-Based Monetary Policy Analysis: A How-to Guide”, IMF Working Paper 06/081, 2006.
- Bernanke, B.S., and Bovin, J., “Monetary Policy in a data-rich environment”, Journal of Monetary Economics, 2003.
- Bernanke, B.S., Gertler, M., and Gilchrist, S., “The financial accelerator in a quantitative business cycle framework”, Handbook of Macroeconomics, Elsevier, Volume 1, Part C, Pages 1341-1393, 1999.
- Gertler, M., and Karadi, P., "A model of unconventional monetary policy," Journal of Monetary Economics, Elsevier, vol. 58(1), pages 17-34, 2011.
- Laxton, D., Scott, A., Rose, D., “Developing a Structured Forecasting and Policy Analysis System to Support Inflation-Forecast Targeting (IFT)”, IMF Working Paper 09/65, 2009.
- (Additional country- and Central Bank–level studies focused on Sri Lanka, model-based policy analysis, inflation targeting feasibility and transmission mechanisms are listed in the full references section.)

---

### APPENDIX A. COMPLETE MODEL

### Model scope and structure
- The appendix provides a complete DSGE-style model specification comprised of model equations (numbered (1) through (81)), a model variable glossary (Table 4), model structural shocks with standard deviations (Table 5), and calibrated model parameters with values (Table 6).
- Equations include behavioral relations for output gap, interest rate formation and rules, exchange rate dynamics, disaggregated inflation (core, volatile food, energy & transport), relative price trends, and measurement/construction identities for quarterly and annualized growth rates.

### Representative model equations (numbered in source)
- (1) y^_t = a1 ⋅ y^_{t−1} + a2 ⋅ y^_{t+1} − a3 ⋅ r^_t + a4 ⋅ y^_{t}^{fff...} − a5 ⋅ z^_t + ε^_{t}^{y^}
- (2) i_{t}^{ifoo} = a7 ⋅ i_{t−1} + (1−a7) ⋅ (i_{t}^{ffnn} + a8 ⋅ π^_t + a9 ⋅ y^_t) + ε_{t}^{ff}
- (3) i_{t}^{ifoo} = i_{t}^{fffff} + 4⋅(f s_t − s_{t}^{nfii}) + ρ_t + ε_t^{Δs}
- (10) π^_t = π_{t+4} − π_t
- (11) i_{t}^{ffnn} = r_t + π_{t+1}/4
- (12) r_t = i_t − π_{t+1}/4
- (14) π_{t}^{dffssc} = a26 ⋅ π_{t−1}^{dffssc} + ε_{t}^{πddd c}
- (15) π_{t}^{cc} = a15 ⋅ y^_t + a16 ⋅ π_{t−1}^{cc} + (1−a16−a19) ⋅ π_{t+1}^{cc} − a17 ⋅ (z^_t − a13 ⋅ rpp^_t vf/c − (1−a13−a14) ⋅ rpp^_t fftt/c) + a18 ⋅ rpp^_t fftt/c + a19 ⋅ Δp_{t}^{ffff d,fii,cc} + ε_{t}^{πcc}
- (29) Δy_t = a6 ⋅ Δy_{t−1} + (1−a6) ⋅ Δy^{sss} + ε_{t}^{Δy}
- (33) π_t = a29 ⋅ π_{t−1} + (1−a29) ⋅ π^{sss} + ε_{t}^{π}
- (34) y_t = y^_t + y_t (identity)
- (40) π_{t} = 4⋅(p_t − p_{t−1})
- (51) π_{t}^{vvf} = π_t + (1−a13)⋅Δrpp_{t}^{vvf/c} − (1−a14−a13)⋅Δrpp_{t}^{fftt/c}
- (73) q^_t fftt = q^_t fftt − z^_t + a13 ⋅ rpp^_t vf/c − (a13 + a14) ⋅ rpp^_t fftt/c
- (80) Δp_{t}^{ffff d,fii,cc} = Δp_{t}^{ffff d} + Δs_t − Δq_{t}^{ffff d} + Δz_t − a13 ⋅ Δrpp_{t}^{vvf/c} − (1−a13−a14) ⋅ Δrpp_{t}^{fftt/c}
- (81) (last equation listed) — model identities and measurement conversions continue through equation (81) in the source.

(Note: full equation text and indices are given verbatim in the source; above bullets preserve the referenced equation numbers and key structural components.)

### Table 4 — Model Variables (selected entries)
- y (l_y): Real output (100*log)
- Δy (dl_y): Real output growth (percent, QoQ annualized)
- Δ4 y (d4l_y): Real output growth (percent, YoY)
- y^ (l_y_gap): Real output gap (%)
- i (rn): Nominal interest rate (percent p.a.)
- i_{ffnn} (rn_neutral): Policy neutral rate (percent p.a.)
- r (rr): Real interest rate (percent p.a.)
- π (dl_cpi): Inflation (percent, QoQ annualized)
- π_{cc} (dl_cpi_core): Core Inflation (percent, QoQ annualized)
- π_{vvf} (dl_cpi_vfood): Volatile Food Inflation (percent, QoQ annualized)
- π_{fftt} (dl_cpi_et): Energy & Transport Inflation (percent, QoQ annualized)
- s (l_s): Nominal exchange rate LKR per USD (100*log)
- Δs (dl_s): Nominal depreciation of LKR per USD (percent, QoQ annualized)
- z (l_z): Real exchange rate (100*log)
- ρ (prem): Risk premium (percent p.a.)
- q_{foss} (l_roil): Brent oil price (100*log)
- q_{food} (l_food): FAO food price (100*log)

(Full Table 4 in the source contains the complete mapping of model variable names to descriptions and units.)

### Table 5 — Model Structural Shocks (Shock name — Model name — Description — StDev)
- ε^{y^} — shock_l_y_gap — Demand shock — 1.00
- ε^{f} — shock_rn — MP shock — 1.00
- ε^{π_{cc}} — shock_dl_cpi_core — Core inflation shock — 1.50
- ε^{π_{vvvv}} — shock_dl_cpi_vfood — Volatile food inflation shock — 13.00
- ε^{π_{ett}} — shock_dl_cpi_et — Energy & transport inflation shock — 15.00
- ε^{π_{ddd c}} — shock_dl_cpi_disc — CPI discrepancy shock — 0.70
- ε^{Δs} — shock_dl_s — UIP shock — 3.00
- ε^{Δy} — shock_dl_y_tnd — Potential growth shock — 0.30
- ε^{Δz} — shock_dl_z_tnd — Eq. RER shock — 0.30
- ε^{ρ} — shock_prem — Risk premium shock — 0.20
- ε^{π} — shock_pie_tar — Inflation target shocks — 0.20
- ε^{Δs_pppp} — shock_dl_s_pol — Exchange rate policy shock — 3.00
- ε^{Δfivv/c} — shock_dl_rp_vfood_tnd — Volatile food VS core relative price trend shock — 0.30
- ε^{Δet/c} — shock_dl_rp_et_tnd — Energy & transport VS core relative price trend shock — 0.50
- ε^{y^_f} — shock_l_y_gap_f — Foreign demand shock — 0.51
- ε^{f_rn} — shock_rn_f — Foreign MP shock — 0.37
- ε^{rr_tnd_f} — shock_rr_tnd_f — Foreign eq. real interest rate shock — 0.07
- ε^{π_f} — shock_dl_cpi_f — Foreign inflation shock — 2.27
- ε^{q^_proil_gap} — shock_l_roil_gap — Real oil price gap shock — 18.00
- ε^{Δroil_tnd} — shock_dl_roil_tnd — Eq. real oil price growth shock — 1.00
- ε^{q^_rfood_gap} — shock_l_rfood_gap — Real food price gap shock — 5.00
- ε^{Δrfood_tnd} — shock_dl_rfood_tnd — Eq. real food price growth shock — 0.50

### Table 6 — Model Parameters (Parameter — Model name — Description — Value) (selected entries)
- ss_dl_z_tnd — Steady-state of RER depreciation — 2.000
- ss_pie_tar — Steady-state of headline inflation target — 4.879
- ss_prem — Steady-state of the country risk premium — 5.000
- ss_dl_y_tnd — Steady-state of the potential output growth — 6.500
- ss_rr_tnd_f — Steady-state of the foreign real interest rate — 1.000
- ss_dl_cpi_f — Steady-state of the foreign inflation — 2.000
- ss_dl_rp_vfood_tnd — Steady-state of the change in volatile food relative price — 0.000
- ss_dl_rp_et_tnd — Steady-state of the change in energy and transport relative price — 0.000
- a1 (c1_l_y_gap) — Backward-lookingness in demand — 0.548
- a2 (c2_l_y_gap) — Forward-lookingness in demand — 0.200
- a3 (c3_l_y_gap) — Elasticity of demand on real interest rate — 0.035
- a4 (c4_l_y_gap) — Elasticity of demand on foreign demand — 0.094
- a5 (c5_l_y_gap) — Elasticity of demand on real exchange rate — 0.064
- a6 (c1_dl_y_tnd) — Persistence of potential real GDP growth — 0.900
- a7 (c1_rn) — Interest rate smoothing in IT consistent monetary policy rule — 0.813
- a8 (c2_rn) — Weight on inflation objective in in IT consistent monetary policy rule — 0.774
- a9 (c3_rn) — Weight on output objective in in IT consistent monetary policy rule — 0.099
- a10 (c1_dl_s_pol) — Weight on exchange rate smoothing in FX policy rule — 0.500
- a11 (c2_dl_s_pol) — Weight on real exchange rate misalignment in FX policy rule — 0.822
- a12 (w_rn_rule) — Relative importance of IT in decision maker preferences — 0.807
- a13 (w_vfood) — Weight of volatile food in CPI — 0.185
- a14 (w_core) — Weight of energy and transport in CPI — 0.689
- a15 (c1_dl_cpi_core) — Elasticity of core inflation on excess demand — 0.251
- a16 (c2_dl_cpi_core) — Backward-lookingness in core inflation — 0.274
- a17 (c3_dl_cpi_core) — Elasticity of core inflation on imports as a part of real marginal costs — 0.137
- a18 (c4_dl_cpi_core) — Elasticity of core prices on energy and transport prices — 0.043
- a19 (c5_dl_cpi_core) — Elasticity of core inflation on imported food inflation — 0.029
- a20 (c1_dl_cpi_vfood) — Persistence of volatile food inflation — 0.268
- a21 (c2_dl_cpi_vfood) — Elasticity of volatile food inflation of relative price gap — 1.290
- a22 (c1_dl_cpi_et) — Persistence of energy and transport inflation — 0.209
- a23 (c2_dl_cpi_et) — Elasticity of energy and transport inflation on imported oil inflation — 0.181
- a24 (c3_dl_cpi_et) — Elasticity of energy and transport inflation on oil price gap — 0.166
- a25 (c4_dl_cpi_et) — Elasticity of volatile food inflation of relative price gap — 0.449
- a26 (c1_dl_cpi_disc) — Persistence of discrepancy in headline inflation identity — 0.079
- a27 (c1_dl_rp_vfood_tnd) — Persistence of volatile food relative price trend — 0.900
- a28 (c1_dl_rp_et_tnd) — Persistence of energy and transport relative price trend — 0.900
- a29 (c1_pie_tar) — Persistence of inflation target — 1.000
- a30 (c1_dl_z_tnd) — Persistence of equilibrium real exchange rate appreciation — 0.900
- a31 (c1_e_l_s) — Forward-lookingness in exchange rate — 0.872
- a32 (c1_prem) — Persistence of country risk premium — 0.950
- a33 (c1_l_y_gap_f) — Persistence of foreign output gap — 0.910
- a34 (c1_rn_f) — Persistence of foreign nominal interest rate — 0.500
- a35 (c1_rr_tnd_f) — Persistence of foreign equilibrium real interest rate — 0.500
- a36 (c1_dl_cpi_f) — Persistence of foreign inflation — 0.285
- a37 (ss_dl_roil_tnd) — Long-run inflation of (real) oil prices — 7.500
- a38 (c1_l_roil_gap) — Persistence of gap in world oil prices — 0.750
- a39 (c1_dl_roil_tnd) — Persistence of equilibrium world oil price inflation — 0.950
- a40 (ss_dl_rfood_tnd) — Long-run inflation of (real) food prices — 7.000
- a41 (c1_l_rfood_gap) — Persistence of gap in world food prices — 0.900
- a42 (c1_dl_rfood_tnd) — Persistence of equilibrium world food price inflation — 0.950

(Full Table 6 in the source provides the complete parameter list and values used in model calibration.)

*Source: wp18149 - REFERENCES (Appendix A: Complete Model) — model equations, variable glossary, structural shocks, and parameter calibration as provided in the source content.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18149.pdf_