## Quarterly Projection Model for Vietnam: A Hybrid Approach for Monetary Policy Implementation — Section V concludes

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### II. Stylized facts and model motivation
- Vietnam: small open economy with high trade and FDI contribution; signed 15 Free Trade Agreements as of December 2020.
- Export sector shift to manufacturing (electronics and apparel); trading value exceeded 200 percent of GDP.
- Real GDP growth:
  - "7-8 percent on average" before the global financial crisis (GFC).
  - Slowed to "5-6 percent during 2009-2014".
  - Recovered to "6-7 percent during 2014-2019".
- Post-WTO accession (early 2007) capital inflows produced asset price bubbles, rapid nominal credit growth, high inflation and exchange rate depreciation.
- Authorities’ 2011 reform package targeted banking, state owned enterprises and public investment; macro stability improved since 2014.
- SBV operational rules/instruments:
  - inflation target set exogenously by the National Assembly, achieved mainly via policy interest rates;
  - exchange rate objective that partly changes with economic conditions;
  - annual indicative nominal credit growth set and announced publicly by the SBV.
- Monetary regime features:
  - exchange rate flexibility introduced since 2016; central parity announced daily with trading band of +/‒3 percent (since January 2016);
  - overnight interbank rates below repo rate since 2012 due to excess liquidity;
  - fresh food ≈ 17 percent of CPI basket, administered prices and fuel ≈ 19 percent, remainder is core (data as of 2020);
  - CPI inflation remained below the 4 percent target for most recent years (up to 2019).
- External and fiscal context:
  - persistent trade balance surpluses from 2012 due to export-led FDI sector;
  - trade turnovers in 2019: USA 15 percent, Eurozone 13 percent, China 23 percent;
  - net oil importer since 2015; net imported value USD 5.5 billion in 2019;
  - public and publicly guaranteed debt declined from 60 percent in 2016 to 53 percent in 2019 (below 65 percent statutory limit).
- Model motivation:
  - QPM captures Vietnam’s hybrid monetary policy (inflation targeting, partial exchange rate management, indicative nominal credit growth target).
  - Headline inflation decomposed into core and non-core because drivers differ.

### III. Model structure — overview
- Model class and features:
  - semi-structural quarterly New Keynesian type with nominal and real rigidities, rational expectations, forward-looking endogenous monetary policy.
  - Extensions: two Phillips curves (core and non-core), credit dynamics, and monetary toolkit with indicative nominal credit growth and nominal exchange rate objective.
- Main blocks: real economy, price dynamics, exchange rate, nominal interest rate, nominal credit growth, foreign economy (exogenous).
- Calibration: Vietnam-specific features, sample averages, views on cyclical developments, impulse response analyses, in-sample forecasting; shock standard deviations set to match observed variances.
- Table 1 provides calibrated dynamic coefficients (selected values reproduced below).

### A. Inflation (model specification)
- Headline CPI identity:
  - p_t = w·p_t^C + (1−w)·p_t^NC + ε_t^p
  - Parameter w = 0.631 (observed weight of core component as of 2019).
- Core inflation Phillips curve (annualized q-o-q core inflation π_t^C):
  - π_t^C = a_11 E_t π_{t+1}^C + (1−a_11)[a_12 π_{t−1}^C + (1−a_12)(π_{t−1} + Δ r p̅_{t−1}^C)] + a_13 rmc_{t−1}^C + ε_t^{πC}
  - rmc_t^C = a_14·ŷ_t + (1−a_14)·(ẑ_t − r p̂_t^C)
  - relative price r p_t^C = p_t^C − p_t decomposed as trend plus cyclical component; trend growth Δ r p̅_t^C follows AR(1).
- Non-core inflation Phillips curve (annualized q-o-q non-core inflation π_t^NC):
  - π_t^NC = a_21·E_t π_{t+1}^NC + (1−a_21−a_22)·π_{t−1}^NC + a_22·π_t^{IO} + a_23· rmc_{t−1}^NC + ε_t^{πNC}
  - rmc_t^NC = a_24·ŷ_t + (1−a_24)·(ẑ_t − r p̂_t^NC)
  - Imported oil inflation π_t^{IO} affects non-core inflation.
- Key distinctions:
  - Non-core inflation has lower inertia and higher supply-shock volatility than core.

### B. Interest rate, exchange rate and credit growth (policy block)
- Interest rate rule (forward-looking Taylor-type):
  - i_t = g_1 i_{t−1} + (1−g_1)[i_t^N + g_2(E_t π_{t+1}^4 − π_{t+1}^{4,Tar}) + g_3 ŷ_t + g_4(Δs_t − Δs_t^{Obj})] + ε_t^i
  - Overnight interbank rate used as observation.
  - Calibration note: expected inflation deviation weight roughly four-to-five times higher than other responses.
- Exchange rate objective:
  - Δs_t^{Obj} = c_1 Δs_{t−1}^{Obj} + (1−c_1)[Δ z̅_t + π_{t}^{4,Tar} − π^* − c_2(E_t π_{t+1}^4 − π_{t+1}^{4,Tar}) − c_3 ẑ_t] + ε_t^{ΔsObj}
  - c_2 < c_3: real exchange rate misalignment more important than expected inflation deviation for the objective.
- Market nominal exchange rate:
  - s_t = e_1·(s_{t−1} + Δs_t^{Obj}/4) + (1−e_1)·[ e_2·E_t s_{t+1} + (1−e_2)·(s_{t−1} + (Δ z̅_t + π_{t}^{4} − π^*)/2) + ... + (i_t^* − i_t + prem_t)/4 ] + ε_t^s
  - e_1 measures degree of policy control (e_1 = 1 implies a peg); e_2 calibrates forward- vs backward-looking UIP (calibrating e_2 = 1 removes backward-looking part).
  - ε_t^{ΔsObj} is policy shock to exchange rate objective; ε_t^s is white noise exchange rate shock.
- Credit channel and lending rates:
  - i_t^C = h_1·i_{t−1}^C + (1−h_1)[(i_t + E_t i_{t+1} + E_t i_{t+2} + E_t i_{t+3})/4 + prem_t^C] + ε_t^{iC}
  - Real credit interest rate gap r̂_t^C influences credit demand.
- Nominal credit growth dynamics:
  - Δc_t = d_1·Δc_{t−1} + (1−d_1)(Δc_{t}^{4,Ind} + d_2·ŷ_t − d_3· r̂_{t−1}^C) + ε_t^{Δc}
  - Δc_{t}^{4,Ind} is year-on-year indicative nominal credit growth set exogenously by the SBV.
  - Indicative credit growth evolves toward neutral credit growth:
    - Δc_{t}^{4,N} = k_1·Δc_{t−1}^{4,N} + (1−k_1)·Δc_{t}^{4,Ind} + ε_t^{ΔcN}
- Credit contribution to monetary conditions:
  - Δ r ĉ_t = Δ r c_t − (Δ c_{t}^{4,N} − π_{t}^{4,Tar} − Δ ȳ_t^4)
- All three instruments (interest rate, exchange rate, credit growth) enter a monetary condition index affecting aggregate demand.

### C. Aggregate demand (IS curve and monetary conditions)
- Output gap equation:
  - ŷ_t = b_1·ŷ_{t−1} − b_2·mci_t + b_3·ŷ_t^* + ε_t^{ŷ}
- Monetary conditions index:
  - mci_t = b_4· r̂_t − b_5· Δ r ĉ_t − (1−b_4 − b_5)·ẑ_t
- Components:
  - ŷ_t^* = effective foreign output gap (weighted average of partner gaps).
  - b_2 > 0; looser monetary stance normalized to negative mci_t values.
- Calibrated persistence and foreign demand effects via b_1 and b_3.

### Calibrated parameters (selected values from Table 1)
- Core inflation:
  - a_11 = 0.55
  - a_12 = 0.8
  - a_13 = 0.15
  - a_14 = 0.7
- Non-core inflation:
  - a_21 = 0.5
- Interest rate (Taylor rule):
  - g_1 = 0.7
  - g_2 = 1.1
  - g_3 = 0.2
  - g_4 = 0.3
- Output gap / monetary transmission:
  - b_1 = 0.65
  - b_2 = 0.1
  - b_3 = 0.2
  - b_4 = 0.5
  - b_5 = 0.2
- Exchange rate objective parameter c_1: value not fully provided in the excerpt.

### D. External sector — setup and assumptions
- Trade openness: imports plus exports to GDP > 200 percent in recent years.
- Global economy approximated by USA, Eurozone, China; these three represent about half of international trade in goods and services.
- Foreign demand ŷ_t^* is weighted average of partners' output gaps; foreign inflation a weighted average transformed into USD.
- Foreign interest rate i_t^* approximated by Federal funds rate (mid-level); global oil prices modeled on Brent USD quotations.
- All foreign variables exogenous and modeled as AR(1) with steady states reflecting sample averages; foreign outlooks provided exogenously for forecasting.

### IV. Model results — overview
- Presentation: IRFs, historical decomposition (output gap and inflation), in-sample forecasting accuracy and data fit.
- IRFs trace 20 quarters (five years) deviations to one-unit structural shocks unless stated otherwise.

### A. Impulse response functions — key quantitative findings
- Aggregate demand shock:
  - Output gap increases by about 0.9 percentage points initially; effects dissipate over two years.
  - Nominal interest rate peaks up to 0.3 percentage points.
  - Exchange rate appreciates less than in model without exchange rate objective due to objective adjustment toward more depreciation.
  - Real interest rate gap initially negative then reverses; credit-to-GDP ratio spikes initially then becomes positive before gradual closing.
- Core inflation shock:
  - Minor spillovers to non-core prices; headline inflation driven largely by core.
  - Output gap declines slightly.
  - Mild nominal exchange rate depreciation.
  - Real-term gaps (real interest rate, real exchange rate, credit) negative in initial quarters due mainly to inflation effects.
- Non-core inflation shocks:
  - Less persistent than core shocks.
  - Non-core weight in consumption basket almost twice lower than core, yielding smaller aggregate effects.
- Exchange rate shock:
  - One-unit shock → immediate depreciation ≈ 5.5 percent (quarterly annualized terms); overshooting then reversed by nominal appreciation.
  - Depreciation passes to higher inflation, especially non-core.
  - Interest rate increases ≈ 0.6 percentage points in first quarter.
  - Exchange rate change objective attenuates fluctuations relative to model without objective.
- Credit growth shock (shock size 10 percentage points):
  - Credit-to-GDP growth gap raises output gap by 0.2 percentage points over first year.
  - Central bank reacts with interest rate hike > 0.1 percentage points at peak.
  - Nominal exchange rate appreciates initially; exchange rate change objective adjusted toward slight depreciation.

### B. Historical decomposition and filtration (2007Q1–2019Q4)
- Kalman filtration applied for 2007Q1–2019Q4; 2020 excluded.
- Output gap trajectory:
  - Strongly positive before the GFC.
  - Mild fluctuations around zero during/after the GFC.
  - Persistently (though marginally) negative during 2012–early-2017.
  - Above-trend evolutions in the recent period (pre-2020).
- Contributions to output gap:
  - Lag component: important cumulative contributions.
  - Foreign effective demand: favorable 2007–mid-2008, negative during GFC, positive 2017–2019.
  - Credit gap: notable contributions; post-GFC credit gap mostly countercyclical.
  - Real interest rate and real exchange rate gaps: almost neutral in second half of sample.
  - Unmodelled factors (fiscal policy, consumer confidence) captured by aggregate demand shock.

### Inflation decomposition: dominant role of inflation expectations
- Inflation expectations dominate core inflation dynamics; both backward- and forward-looking components important in hybrid specification.
- Expectations reflect accumulated past and expected real marginal costs, reducing apparent role of aggregate demand pressures.
- Output gap and real exchange rate gap have minor roles, consistent with limited macro transmission and high sacrifice ratio in empirical literature.
- Temporal evolution:
  - 2007-2013: higher relative weight of lagged inflation.
  - Second half of sample: forward-looking component becomes as important as backward-looking.
- Real marginal costs and sectoral differences:
  - Real marginal costs = weighted average of domestic (output gap) and imported (real exchange rate gap) components.
  - Contribution of real marginal costs to inflation is limited (weak transmission).
  - Aggregate supply shocks to core inflation stronger during 2008-2012; smaller in recent years.
- Non-core inflation:
  - Higher volatility and ampler fluctuations than core.
  - Non-modelled non-core supply shocks important, including in second half of sample.
  - Imported oil prices have non-negligible weight in non-core developments.
  - Real marginal costs contribution to non-core inflation also limited.
- Comovement evidence:
  - Real marginal costs and inflation co-move, especially in early sample with higher volatility; narrowing of inflation fluctuations 2013-2019 aligns with estimated real marginal costs patterns.

### In-sample simulations and forecasting accuracy
- Recursive 1- to 8-quarter forecasts for 2008Q1–2019Q4 conditioned on full-sample paths of foreign variables, trends, inflation target, indicative credit growth and exchange rate objective.
- Model performance:
  - QPM matches data reasonably well and captures turning points, including high-volatility initial subsample.
  - Policy signal examples:
    - Model recommended lowering interest rate during end-2014–2015 (core inflation below target).
    - For 2017–early-2018 recursive forecasts predicted higher interest rate than ex-post values given expectations of core inflation returning above 4 percent headline target.
  - Non-core inflation approximated well despite unpredictability (scale differences noted).
- RMSFE ratios (QPM RMSFE / random walk RMSFE) — value < 1 indicates QPM outperforms random walk:
  - GDP (yoy): 0.63, 0.52, 0.45, 0.41, 0.41, 0.42, 0.41, 0.39
  - CPI (yoy): 0.32, 0.34, 0.36, 0.38, 0.38, 0.41, 0.44, 0.46
  - Core (yoy): 0.34, 0.40, 0.45, 0.49, 0.50, 0.54, 0.59, 0.62
  - Non-core (yoy): 0.34, 0.33, 0.31, 0.33, 0.32, 0.35, 0.37, 0.39
  - Interest rate (%): 0.84, 0.74, 0.69, 0.69, 0.63, 0.58, 0.57, 0.55
  - Nominal ER (yoy): 0.94, 1.01, 1.04, 1.04, 0.92, 0.83, 0.79, 0.78
- Findings:
  - QPM outperforms random walk for virtually all variables and horizons; especially large margin for CPI due to strong non-core predictions.
  - Model performs relatively worse at shorter horizons for GDP growth, interest rate, nominal ER.
  - In practice, next-quarter values often exogenised to near-term forecasts from satellite tools, making QPM a robust medium-term policy tool.

### Model features, policy operationalization and conclusion
- QPM: semi-structural model nesting New Keynesian core, allowing real short- to medium-term effects of monetary policy.
- Vietnam-specific extensions:
  - high trade openness;
  - inflation decomposition (core/non-core) with sector-specific dynamics;
  - explicit credit role in aggregate demand;
  - hybrid monetary policy reflecting SBV practice.
- Monetary policy operationalization:
  - price stability primary objective with three operational rules/instruments:
    - (i) inflation target (exogenous) achieved mainly via policy interest rate guided by Taylor-type rule;
    - (ii) exchange rate objective endogenized in model;
    - (iii) annual indicative nominal credit growth announced by SBV.
  - Endogenous interactions: interest rate reacts to exchange rate dynamics; exchange rate objective adjusted for inflation deviations.
- Flexibility and applicability:
  - QPM reflects current/planned SBV regime and can be recalibrated or extended as SBV modernizes policy framework.
  - Intended as a tool to build analytical and institutional capacity to advance SBV’s modernization efforts.

*Source: IMF Working Paper — Quarterly Projection Model for Vietnam: A Hybrid Approach of Monetary Policy Implementation (wpiea2022125-print-pdf — Section V concludes).*

### Section V concludes.

### wpiea2022125-print-pdf - Section V concludes.

### II. STYLIZED FACTS AND MODEL MOTIVATION
- Vietnam is a small open economy with high contribution of international trade and foreign direct investments (FDIs) to economic growth.
- Vietnam signed up 15 Free Trade Agreements as of December 2020.
- The export sector shifted from commodities to manufacturing (electronics and apparel) and trading value exceeded 200 percent of GDP.
- Real GDP growth:
  - "7-8 percent on average" before the global financial crisis (GFC).
  - Slowed to "5-6 percent during 2009-2014".
  - Recovered to "6-7 percent during 2014-2019".
- Post-WTO accession (early 2007) massive capital inflows contributed to asset price bubbles, rapid nominal credit growth, high inflation and exchange rate depreciation.
- Authorities’ 2011 reform package focused on banking, state owned enterprises and public investment reforms; macroeconomic stability improved since 2014.
- SBV monetary policy main characteristics and operational rules/instruments included:
  - (i) inflation target set exogenously by the National Assembly and achieved mainly via policy interest rates;
  - (ii) exchange rate objective that partly changes with economic conditions;
  - (iii) annual indicative nominal credit growth set and announced publicly by the SBV for the aggregate banking system.
- Monetary regime features:
  - Gradual introduction of exchange rate flexibility since 2016; central parity exchange rate announced daily with a trading band of +/‒3 percent (since January 2016).
  - Overnight interbank rates have slid well below the repo rate since 2012 due to excess liquidity.
  - By law, fresh food ≈ 17 percent of the CPI basket, goods with administered prices and fuel ≈ 19 percent, remaining is core (data as of 2020).
  - CPI inflation remained below the 4 percent target for most recent years (up to 2019).
- External and fiscal context:
  - Persistent trade balance surpluses starting 2012 due to strong export-led FDI sector.
  - Trade turnovers (combined exports and imports) in 2019: USA 15 percent, Eurozone 13 percent, China 23 percent.
  - Vietnam became a net oil importer in 2015; net imported value reached USD 5.5 billion in 2019.
  - Public and publicly guaranteed debt declined from 60 percent in 2016 to 53 percent in 2019, below the 65 percent statutory limit.
- Model motivation:
  - QPM (Quarterly Projection Model) is designed to capture Vietnam’s hybrid monetary policy implementation: inflation targeting, partial exchange rate management, and an indicative nominal credit growth target.
  - Headline inflation decomposition into core and non-core components is required because different items are driven by different factors.

### III. MODEL STRUCTURE — overview
- Model class and features:
  - A semi-structural quarterly New Keynesian type model with nominal and real rigidities, rational expectations, and forward-looking endogenous monetary policy.
  - Extensions relative to canonical QPM include:
    - Decomposition of headline inflation into core and non-core (two Phillips curves).
    - Incorporation of credit dynamics as determinant of monetary conditions.
    - Enrichment of monetary toolkit with indicative nominal credit growth targets and nominal exchange rate objective.
- Main interconnected blocks: real economy, price dynamics, exchange rate developments, nominal interest rate, nominal credit growth, and foreign economy (global economy exogenous).
- Calibration approach:
  - Parameters calibrated to Vietnam-specific features, sample averages, views about cyclical developments, impulse response analyses, and in-sample forecasting performance.
  - Standard deviations of modelled shocks set to account for observed variance in available data.
  - Table 1 provides calibrated values for key dynamic coefficients.

### A. Inflation (model specification)
- Headline CPI identity:
  - p_t = w·p_t^C + (1−w)·p_t^NC + ε_t^p
  - Parameter w = 0.631 (observed weight of core component as of 2019).
- Core inflation Phillips curve (annualized quarter-on-quarter core inflation π_t^C):
  - π_t^C = a_11 E_t π_{t+1}^C + (1−a_11)[a_12 π_{t−1}^C + (1−a_12)(π_{t−1} + Δ r p̅_{t−1}^C)] + a_13 rmc_{t−1}^C + ε_t^{πC}
  - Real marginal costs for core: rmc_t^C = a_14·ŷ_t + (1−a_14)·(ẑ_t − r p̂_t^C)
  - Relative price of core: r p_t^C = p_t^C − p_t; decomposed as r p_t^C = r p̅_t^C + r p̂_t^C.
  - Relative price trend growth Δ r p̅_t^C follows AR(1).
- Non-core inflation Phillips curve (annualized quarter-on-quarter non-core inflation π_t^NC):
  - π_t^NC = a_21·E_t π_{t+1}^NC + (1−a_21−a_22)·π_{t−1}^NC + a_22·π_t^{IO} + a_23· rmc_{t−1}^NC + ε_t^{πNC}
  - Non-core real marginal costs: rmc_t^NC = a_24·ŷ_t + (1−a_24)·(ẑ_t − r p̂_t^NC)
  - Imported oil inflation π_t^{IO} (annualized quarter-on-quarter price of imported oil in domestic currency) affects non-core inflation.
- Key modeling distinctions:
  - Lower inertia in non-core inflation than core.
  - Higher volatility of supply shocks for non-core inflation.

### B. Interest Rate, Exchange Rate and Credit Growth (policy block)
- Interest rate rule (forward-looking Taylor-type):
  - i_t = g_1 i_{t−1} + (1−g_1)[i_t^N + g_2(E_t π_{t+1}^4 − π_{t+1}^{4,Tar}) + g_3 ŷ_t + g_4(Δs_t − Δs_t^{Obj})] + ε_t^i
  - i_t^N is neutral interest rate; ε_t^i captures deviations from the reaction function.
  - Overnight interbank rate is used as observation for the interest rate rule.
  - Calibration notes: expected inflation deviation weight is roughly four-to-five times higher than other responses.
- Exchange rate objective:
  - Δs_t^{Obj} = c_1 Δs_{t−1}^{Obj} + (1−c_1)[Δ z̅_t + π_{t}^{4,Tar} − π^* − c_2(E_t π_{t+1}^4 − π_{t+1}^{4,Tar}) − c_3 ẑ_t] + ε_t^{ΔsObj}
  - Objective reflects fundamentals: trend real effective exchange rate growth Δ z̅_t, inflation target, foreign steady-state inflation π^*, and real exchange rate gap ẑ_t.
  - Calibration: c_2 < c_3 (expected inflation deviation less important than real exchange rate misalignment for guiding exchange rate objective).
- Market nominal exchange rate (partial SBV control and UIP):
  - s_t = e_1·(s_{t−1} + Δs_t^{Obj}/4) + (1−e_1)·[ e_2·E_t s_{t+1} + (1−e_2)·(s_{t−1} + (Δ z̅_t + π_{t}^{4} − π^*)/2) + ... + (i_t^* − i_t + prem_t)/4 ] + ε_t^s
  - Parameter e_1 measures importance of exchange rate change objective (e_1 = 1 implies a peg).
  - e_2 calibrates forward-looking vs backward-looking UIP components; by calibrating e_2 = 1, backward-looking part is removed.
  - ε_t^{ΔsObj} is a policy shock to the exchange rate objective; ε_t^s is a white noise exchange rate shock.
- Credit channel and lending rates:
  - Lending rate: i_t^C = h_1·i_{t−1}^C + (1−h_1)[(i_t + E_t i_{t+1} + E_t i_{t+2} + E_t i_{t+3})/4 + prem_t^C] + ε_t^{iC}
  - Real credit interest rate via a Fisher-type equation; real credit interest rate gap r̂_t^C influences credit demand.
- Nominal credit growth dynamics:
  - Δc_t = d_1·Δc_{t−1} + (1−d_1)(Δc_{t}^{4,Ind} + d_2·ŷ_t − d_3· r̂_{t−1}^C) + ε_t^{Δc}
  - Δc_t is annualized quarter-on-quarter growth in nominal credit volume.
  - Δc_{t}^{4,Ind} is the year-on-year indicative nominal credit growth set exogenously by the SBV.
  - Indicative credit growth evolves toward neutral credit growth:
    - Δc_{t}^{4,N} = k_1·Δc_{t−1}^{4,N} + (1−k_1)·Δc_{t}^{4,Ind} + ε_t^{ΔcN}
- Credit component of monetary conditions:
  - Δ r ĉ_t = Δ r c_t − (Δ c_{t}^{4,N} − π_{t}^{4,Tar} − Δ ȳ_t^4)
  - Real credit growth Δ r c_t expressed as ratio to nominal GDP; equilibrium implied by neutral annual credit growth, inflation target and year-on-year potential growth.
- All three instruments (interest rate, exchange rate, credit growth) enter a monetary condition index and affect aggregate demand.

### C. Aggregate Demand (IS curve and monetary conditions)
- Output gap equation (extended IS curve):
  - ŷ_t = b_1·ŷ_{t−1} − b_2·mci_t + b_3·ŷ_t^* + ε_t^{ŷ}
  - Monetary conditions index:
    - mci_t = b_4· r̂_t − b_5· Δ r ĉ_t − (1−b_4 − b_5)·ẑ_t
  - Components:
    - ŷ_t^* is effective foreign output gap.
    - ε_t^{ŷ} is aggregate demand shock (unmodelled influences).
  - Interpretation:
    - b_2 > 0; looser monetary stance normalized to negative mci_t values (looseness via lower interest rates, higher credit growth, or faster exchange rate depreciation).
- Calibrated persistence and foreign demand effects included via b_1 and b_3.

### Calibrated parameters (selected values from Table 1)
- Core inflation parameters:
  - a_11 = 0.55
  - a_12 = 0.8
  - a_13 = 0.15
  - a_14 = 0.7
- Non-core inflation parameter:
  - a_21 = 0.5
- Interest rate (Taylor rule) parameters:
  - g_1 = 0.7
  - g_2 = 1.1
  - g_3 = 0.2
  - g_4 = 0.3
- Output gap / monetary transmission parameters:
  - b_1 = 0.65
  - b_2 = 0.1
  - b_3 = 0.2
  - b_4 = 0.5
  - b_5 = 0.2
- Exchange rate objective parameter (c_1) value not fully provided in excerpt.

*Source: IMF Working Paper — Quarterly Projection Model for Vietnam: A Hybrid Approach of Monetary Policy Implementation (wpiea2022125-print-pdf — Section V concludes).*

### 0.5 Credit

### 0.5 Credit

### D. External Sector — model setup and assumptions
- Vietnam is a small open economy with imports plus exports to GDP summing over 200% in recent years.
- The global economy is approximated by three main trading partners: the USA, Eurozone and China.
- The share of the three foreign economies represents about half of the international trade in goods and services in recent years.
- Foreign demand variable (ŷt∗) entering the IS curve (equation (15)) is defined as a weighted average of the three partners’ output gaps.
- Foreign inflation is a weighted average of inflation rates in the foreign economies; effective foreign inflation is transformed into USD.
- Foreign interest rate (it∗) in the exchange rate equation (10) is approximated by the Federal funds rate (mid-level).
- Global oil prices are modeled based on Brent quotations denominated in USD.
- All foreign variables are considered exogenous and modeled as AR(1) processes with steady state values reflecting sample averages.
- For forecasting exercises, foreign outlooks are provided exogenously based on relevant sources.

### IV. Model results — overview
- Presentation includes: dynamic responses to structural shocks (IRFs), historical decomposition (output gap and inflation), and in-sample forecasting accuracy and data fit.
- IRFs trace dynamic effects over 20 quarters (five years) expressed as deviations from equilibrium to one-unit structural shocks unless stated otherwise.

### A. Impulse Response Functions — key quantitative findings
- Aggregate demand shock (Figure 7):
  - Output gap increases by about 0.9 percentage points in the initial period; effects dissipate over two years.
  - Central bank raises nominal interest rate up to 0.3 percentage points at the peak.
  - Exchange rate appreciates less than in a model without an exchange rate objective due to adjustment of the exchange rate objective toward a more depreciated currency.
  - Real interest rate gap initially negative then reverses; credit-to-GDP ratio spikes initially and then becomes positive before gradual closing-up.

- Core inflation shock (Figure 8):
  - Spillovers generate a minor increase in non-core prices; headline inflation driven largely by core inflation.
  - Output gap declines by a small amount.
  - Shock results in a mild nominal exchange rate depreciation.
  - Real-term gaps (real interest rate, real exchange rate, credit) are negative during initial quarters owing mainly to inflation effects.

- Non-core inflation shocks:
  - Effects are generally less persistent than core inflation shocks.
  - Weight of non-core component in the representative consumption basket is almost twice lower compared to core goods, yielding quantitatively smaller aggregate effects.

- Exchange rate shock (Figure 9):
  - A one-unit shock leads to an immediate depreciation of about 5.5 percent (in quarterly annualized terms); overshooting is gradually reversed via subsequent nominal appreciation.
  - Depreciation passes through to higher inflation, especially in the non-core segment (calibrated larger sensitivity).
  - Interest rate increases by about 0.6 percentage points in the first quarter, steering the economy back to medium-term equilibrium.
  - Exchange rate change objective attenuates fluctuations across variables relative to a model without this objective (Figure 10).

- Credit growth shock (Figure 11) — shock size set to 10 percentage points:
  - Credit-to-GDP growth gap raises output gap by 0.2 percentage points over the first year following the shock.
  - Central bank reacts with an interest rate hike of more than 0.1 percentage points at the peak.
  - Nominal exchange rate appreciates initially; exchange rate change objective adjusted toward slight depreciation.

### B. Historical decomposition and filtration (2007Q1–2019Q4)
- Kalman filtration applied for sample 2007Q1 to 2019Q4; 2020 excluded due to COVID-19 complexities.
- Output gap trajectory (Figure 12) implied by filtration:
  - Strongly positive values before the global financial crisis (GFC).
  - Mild fluctuations around zero during and after the GFC.
  - Persistently (though marginally) negative output gap during 2012–early-2017.
  - Above-trend evolutions in the recent period (pre-2020).
- Contributions to output gap (aggregate demand equation (15)):
  - Lag component (cumulative impact of past structural determinants) displays important contributions.
  - Foreign effective demand played a significant role: favorable during 2007–mid-2008, negative during the GFC, and positive during 2017–2019 (synchronized excess demand in China, US and Eurozone).
  - Notable credit gap contributions reflect the credit channel extension; after the GFC credit gap is mostly countercyclical.
  - Real interest rate gap and real exchange rate gap components were almost neutral during the second half of the sample, reflecting relative stability of nominal interbank rate, nominal exchange rate, and inflation.
  - Unmodelled factors (e.g., fiscal policy, consumer confidence) are captured by the aggregate demand shock.

*Source: Quarterly Projection Model for Vietnam: A Hybrid Approach of Monetary Policy Implementation (IMF Working Paper excerpt).*

### 13. It  shows  the  dominant  contribution  of  inflation  expectations:  in  line  with  the  hybrid

### Quarterly Projection Model for Vietnam: A Hybrid Approach for Monetary Policy Implementation — Working Paper No. WP/2022/125

### Inflation decomposition: dominant role of inflation expectations
- Inflation expectations provide a dominant contribution to core inflation dynamics; both backward- and forward-looking components are important under the hybrid specification of the formation mechanism.
- Expectations reflect accumulation of past (backward-looking) and expected (forward-looking) real marginal costs, which reduces the apparent role of aggregate demand pressures in driving prices.
- The output gap and real exchange rate gap have a minor role, consistent with a historical account of limited macroeconomic transmission in the Vietnam economy and a high sacrifice ratio as estimated in the empirical literature (see Section I).
- Temporal evolution of components:
  - During 2007-2013 the relative weight of lagged inflation was somewhat higher.
  - In the second half of the sample the forward-looking (rational expectations) component becomes as important as the backward-looking one.
- Policy context influencing expectations:
  - Broad achievement of the SBV price stability objective in recent years, with close-to- and below-target headline inflation dynamics, contributed to better anchoring of inflation expectations.

### Real marginal costs and sectoral differences
- Real marginal costs are a weighted average of domestic (output gap) and imported (real exchange rate gap) components.
- The contribution of real marginal costs to inflation is limited, reflecting:
  - Weak transmission through aggregate demand and exchange rate channels for the core goods segment.
  - Instances where output and real exchange rate gaps have opposite signs and partly counterbalance each other.
- Aggregate supply shocks to core inflation:
  - Were more pronounced during the period of high macroeconomic instability in 2008-2012.
  - Were of significantly smaller magnitude in recent years.
- Non-core inflation decomposition:
  - Non-core inflation exhibits relatively ampler fluctuations and higher volatility than core inflation.
  - Non-modelled factors (non-core supply shocks) play a more important role, including over the second half of the sample.
  - Imported oil prices have non-negligible weights in non-core price developments.
  - Similar to the core goods segment, the contribution of real marginal costs to non-core inflation is limited.
- Comovement evidence:
  - Figure 15 depicts co-movement between inflation rates and real marginal costs for core and non-core segments (2007Q1–2019Q4), particularly during the initial half of the sample with higher macroeconomic volatility.
  - Estimated real marginal costs align with the narrowing of inflation fluctuations over 2013-2019 compared to 2007-2012.

### In-sample simulations and forecasting accuracy
- Recursive one- to eight-quarter ahead forecasts were run for 2008Q1-2019Q4, conditioning on full-sample estimates for trajectories of:
  - foreign variables, output trend, real exchange rate trend, inflation target, indicative nominal credit growth target, and nominal exchange rate objective.
- Model performance:
  - For most variables the model matches actual data reasonably well and captures relevant turning points, including during the initial subsample with higher volatility.
  - Recent-period policy signal:
    - Model simulations recommended lowering the interest rate during end-2014–2015, consistent with core inflation registering below-target values.
    - For 2017–early-2018 recursive forecasts predicted higher interest rate compared to ex-post values, given model expectations of core inflation returning and temporarily exceeding the 4 percent headline inflation target.
  - The model approximates non-core inflation dynamics well despite the less-predictable nature of that segment (noting scale differences between core and non-core figures).
- Numerical assessment: root mean square forecast errors (RMSFE) of the QPM relative to a random walk model (ratio QPM RMSFE / random walk RMSFE) — a value below one indicates QPM outperforms random walk.
  - Table 2: Root mean square forecast errors relative to random walk model (1Q–8Q)
    - GDP (yoy): 0.63, 0.52, 0.45, 0.41, 0.41, 0.42, 0.41, 0.39
    - CPI (yoy): 0.32, 0.34, 0.36, 0.38, 0.38, 0.41, 0.44, 0.46
    - Core (yoy): 0.34, 0.40, 0.45, 0.49, 0.50, 0.54, 0.59, 0.62
    - Non-core (yoy): 0.34, 0.33, 0.31, 0.33, 0.32, 0.35, 0.37, 0.39
    - Interest rate (%): 0.84, 0.74, 0.69, 0.69, 0.63, 0.58, 0.57, 0.55
    - Nominal ER (yoy): 0.94, 1.01, 1.04, 1.04, 0.92, 0.83, 0.79, 0.78
  - Findings:
    - For virtually all variables and horizons the QPM outperforms the random walk; the margin is especially large for CPI inflation, driven by an exceptionally good prediction record for the non-core segment.
    - The model performs relatively worse at shorter horizons compared to longer ones for GDP growth, interest rate, and nominal exchange rate dynamics.
    - In practical real-time use, next-quarter values for most variables would often be exogenised to near-term forecasts estimated with satellite tools; combined with robust near-term forecasting methods, the QPM functions as a well-designed medium-term tool for policy analysis and recommendations.

### Model features and conclusion
- The QPM is a semi-structural family of models that nests a New Keynesian core with rigidities, allowing monetary policy to have real short- to medium-term effects.
- Vietnam-specific extensions:
  - Significant openness to international trade.
  - Decomposition of headline inflation into core and non-core segments with sector-specific dynamics.
  - Explicit role for credit developments in driving aggregate demand.
  - A hybrid monetary policy regime reflecting Vietnam’s monetary policy framework.
- Monetary policy operationalization within the model:
  - Price stability is the primary objective with three operational rules/instruments:
    - (i) inflation target (exogenous government goal) achieved primarily with a policy interest rate guided by a Taylor-type rule;
    - (ii) exchange rate objective with a corresponding operational rule endogenized in the model;
    - (iii) annual indicative nominal credit growth for the aggregate banking system, set and announced by the SBV.
  - Endogenous interactions and spillovers: interest rate reacts to exchange rate dynamics; exchange rate objective is adjusted for inflation deviations from target.
- Flexibility and applicability:
  - The QPM reflects the current and planned SBV monetary policy regime and can be recalibrated, adjusted, or extended as the SBV modernizes its policy framework.
  - The model is presented as a tool to build analytical and institutional capacity to further advance SBV’s modernization efforts.

*Source: IMF Working Paper — Quarterly Projection Model for Vietnam: A Hybrid Approach of Monetary Policy Implementation (Working Paper No. WP/2022/125)*

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_Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022125-print-pdf.pdf_