## _wp1361

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### The 2007–2009 Period: regional context, shocks, and policy challenges
- Regional stabilization before shocks:
  - Median inflation in SSA fell from 15 percent in 2000 to 6 percent in 2006.
  - Many SSA countries adopted regimes centered on targets for reserve and broad money, with considerable management of the exchange rate.
  - De facto exchange rate flexibility remained common; money targets frequently missed.
- Large external shocks during 2007–2009:
  - First food and fuel crisis of 2007–2008, spillovers from the global financial crisis in 2008–2009, and a later commodity price spike.
  - Resulted in large swings in inflation and, in some cases, erratic monetary policy responses.
- Limitations of existing regimes:
  - Money-target–centric regimes provided poor frameworks for understanding shock transmission, inflation dynamics, and policy roles.
  - Structural changes (market signals, unstable money demand, greater exposure to capital flows) questioned adequacy of such regimes.
- Shift toward inflation-forecast targeting (IFT) and FPAS elements:
  - IFT: inflation forecast is intermediate target; short-term interest rate often operational target.
  - Central banks under IFT focus on explaining deviations of inflation from target and on policy needed to bring forecasts back in line.
  - Even without full IFT adoption, many central banks adopt FPAS elements (in-house forecasting and policy analysis systems).

### Purpose and framework of the FPAS for low–income countries (application to Kenya)
- Purpose:
  - Blueprint of a Forecasting and Policy Analysis System (FPAS) for LICs, with explicit role for food prices.
- Model class and core equations:
  - New–Keynesian open economy FPAS with micro–foundations and rational expectations.
  - Core equations: forward–looking IS, hybrid Phillips curves, monetary policy rule, uncovered interest parity (UIP).
- Key extension:
  - Two separate Phillips curves—one for food and one for non–food—requiring explicit treatment of relative food prices (domestic, international, and their deviation) and trends in those relative prices.

### Kenyan context, inflation history and monetary policy (selected facts)
- Demographics and income:
  - Population estimated 40 million; GDP per-capita US$1,700 as of 2011 (PPP).
- Growth and structure:
  - Growth averaged about 5 percent over the last decade (slowed during global financial crisis).
  - Services >60 percent of GDP; 75 percent of population relies on agriculture; agriculture accounts for 40–50 percent of total exports.
- External financing and fiscal:
  - Trade balance in deficit; remittances, FDI, and official flows provide bulk of financing; portfolio inflows increasing but slowed during global crisis.
  - Government debt about 45 percent of GDP; about half of government debt in domestic currency; fiscal deficit ~5 percent of GDP; tax revenue ~20 percent of GDP.
- Monetary framework and CPI composition:
  - De jure anchor historically reserve money targeting; increasing attention to short–term interest rates; managed float with volatility.
  - Share of food in consumer basket: 38 percent (Kenya) vs. 50 percent (LIC average).
  - ~40 percent of cereal consumption (of about 5 million metric tons) is imported.
- Inflation and interest rates (selected observations):
  - Headline inflation: ~3 percent at beginning of 2007 → 16 percent by mid 2008 → <4 percent mid 2010 → almost 20 percent end 2011; almost 19 percent in November 2011; 13 percent as of April 2012.
  - Short-term interest rates: fell from 6 percent in 2009 to about 1 percent by early 2011.
  - Central Bank Rate (CBR): 6.25 percent in September 2011 → 18 percent by December 2011.
  - Overnight rate set at CBR plus 600 basis points after September 2011 reform.
- Reserves:
  - Official FX reserves fell by almost US$ 800 million (about 20 percent of the stock) between mid-2008 and early 2009.
  - Kenya borrowed from the IMF Exogenous Shock Facility.

### Model structure, key technical elements and identities (selected equations and definitions)
- CPI and inflation aggregation:
  - p_cpi_t = w p_f_t + (1-w) p_nf_t
  - π_cpi_t = 4(p_cpi_t − p_cpi_{t−1}) = w π_f_t + (1-w) π_nf_t
  - π_4,cpi_t = p_cpi_t − p_cpi_{t−4}
- Relative prices and deviations:
  - rlp_t = p_f_t − p_nf_t
  - dev_t = p_f_t − (p*_f_t + s_t)
  - rlp*_t = p*_f_t − p*_cpi_t
  - z_t = s_t + p*_cpi_t − p_cpi_t
  - Identity: z_t = (1−w) rlp_t − rlp*_t − dev_t
- Trends in relative prices: modeled as autoregressive processes in first (annualized) differences with parameters θ_rlp, θ_rlp', θ_z; implication: dev_t trend can drift.
- Output and potential:
  - y_t = y_t + ygap_t; potential growth follows random walk with time–varying drift g_t.
- IS (output gap):
  - ygap_t = β1 ygap_{t−1} + β2 E_t(ygap_{t+1}) − β3 rmc_{t−1} + β5 ygap*_t + ε_ygap_t
- Real monetary conditions:
  - rmc_t = (1−β4) rrgap_t + β4 (−zgap_t); neutral real rate rr_t follows AR(1).
- Dual Phillips curves:
  - Non–food: π_nf_t − π̄_nf_t = λ1(E_t(π_nf_{t+1}) − π̄_nf_t) + (1−λ1−λ2)(π_nf_{t−1} − π̄_nf_t) + λ2(π_imp_nf,t − π_imp_t) + λ3 rmc_nf_t + ε_πnf_t
  - Food: π_f_t − π̄_f_t = b1(E_t(π_f_{t+1}) − π̄_f_t) + (1−b1−b2)(π_f_{t−1} − π̄_f_t) + b2(π_imp − π_imp_t) + b3 rmc_f_t + ε_πf_t
  - rmc_f_t includes devgap_t, so temporary deviations between domestic and international food prices directly drive food inflation.
- UIP with risk premium prem_t following AR(1).
- Monetary policy rule:
  - rs_t = γ1 rs_{t−1} + (1−γ1)[ rr_t + π_{t+1} + γ2(π_{4,cpi_{t+4}} − π_cpi_{t+4}) + γ3 ygap_t + γ4 ∆s_gap_t ] + ε_rs_t
- Evolution of inflation target:
  - π_t = ρ_π π_{t−1} + (1−ρ_π) π + ε_π_t (captures low–frequency shifts in tolerated inflation).

### Calibration principles, selected parameter values and volatilities (preserved exactly)
- Shares and trends:
  - w = 0.36
  - ∆rlp = 6.5
  - θ_rlp = 0.8
  - ∆z = −4
  - θ_rlp (real growth rate) = 0.65
- Output and IS:
  - g = 4
  - θ_g = 0.5
  - β_1 = 0.6
  - β_2 = 0.1
  - β_3 = 0.15
  - β_4 = 0.6
  - β_5 = 0.15
  - ρ_rr = 0.75
  - rr = 1
- Phillips curves (selected):
  - λ_1 = 0.4, λ_2 = 0.05, λ_3 = 0.2, λ_4 = 0.5
  - b_1 = 0.5, b_2 = 0.05, b_3 = 0.1, b_4 = 0.1, b_5 = 0.7
- Monetary policy and UIP:
  - ρ_prem = 0.75, φ = 0.85, γ_1 = 0.8, γ_2 = 1.4, γ_3 = 0, γ_4 = 0.25
  - π (inflation target) = 5
  - ρ_π = 0.85
- Rest of world (selected):
  - ∆rlp′ = 2, θ_rlp′ = 0.5, β′_1 = 0.5, β′_2 = 0.5, β′_3 = 0.05
  - λ′_1 = 0.6, λ′_2 = 0.06, γ′_1 = 0.75, γ′_2 = 1.7, γ′_3 = 0.25
  - ρ_p^f = 0.75, ρ_rr′ = 0.5, rr′ = 2.5
- Selected shock volatilities:
  - σ_rlp = 2, σ_z = 3, σ_y = 1.5, σ_g = 1, σ_ygap = 1, σ_rr = 0.7
  - σ_π^nf = 1.5, σ_π^nf (food) = 2.5, σ_s = 3.5, σ_prem = 3.5, σ_rs = 1.5
  - σ_π = 1, σ_ygap′ = 0.3, σ_rs′ = 0.3, σ_rr′ = 0.08, σ_π′ = 1.5
  - σ_rlp′ = 0.35, σ_rlpgap′ = 0.3
- Representative calibrated transmission magnitudes:
  - IS channel: β3(1−β4) = 0.06 (small sensitivity of output to interest rates)
  - Phillips curves: non–food sensitivity to output gap λ3 λ4 = 0.1; food sensitivity b3(1−b4−b5) = 0.02
  - Real exchange rate sensitivities: λ3(1−λ4) = 0.1 (non–food) and b3 b4 = 0.04 (food)
  - Food gap pass–through: 1 percent widening of devgap_t yields immediate 0.07 percent increase in food prices (0.13 percent including expectations).

### Solution method, state-space representation and estimation tools
- Model solved using variant of Blanchard and Kahn (1982) algorithm implemented with IRIS Toolbox for Matlab.
- State equation: X_t = T X_{t−1} + R ε_t,  ε_t ~ N(0, Σ_ε).
- Measurement equation: Y_t = Z X_t + H η_t,  η_t ~ N(0, Σ_η).
- Kalman filter and Kalman smoother used to estimate states and decompose series into trend and gap components.
  - Recursive updating and backward-smoothing equations preserved as presented in the source.
- Note on identification:
  - More structural shocks than observed variables implies stochastic specification (Σ_η and Σ_ε) strongly influences impulse responses and interpretation.

### Empirical findings, filtering results, and shock decompositions (selected)
- Trend/gap decompositions:
  - Real exchange rate z_t: smooth trend appreciation with gap spikes (notably 2008).
  - International relative food price rlp*_t: smooth positive trend with large gap movements in 2007–2008 and recent spike (mainly international food price gap shocks).
  - Domestic relative food price rlp_t: trend increased over time; 2008 food inflation partly catching up relative to trend; dev_t oscillates widely with large negative gaps in 2007–2008 and recent spike—those gaps are inflationary via food Phillips curve.
  - Output: fast growth 2003–2007 (six percent average, 7 percent peak in 2007), drop to 2 percent in 2008–2009; gap reopens from 2010 onwards.
  - Real interest rate: largely positive 2001–early 2003, largely negative until mid 2005 and again from mid 2007 to end of sample.
- Shock decomposition highlights:
  - Imported food shocks (non–trend) important for some inflation dynamics in 2008 and recently.
  - Domestic food shocks (harvest shocks) also relevant.
  - Accommodative monetary policy played important role in inflation episodes in 2007–2008 and 2011 spike.
  - 2007–2008: domestic inflationary pressures offset by disinflationary global recession; CBK did not need to tighten.
  - 2011 spike: absent disinflationary global forces; model indicated short-term rates needed to increase; CBK tightened (CBR increases) by end 2011, consistent with model guidance.
- Impulse response findings (selected experiments):
  - Temporary 1 percent increase in international relative food prices (ε_rlpgap* = 1):
    - Large short-lived effect on international food inflation; longer-lived effect on domestic food and CPI inflation due to slower pass–through.
    - Monetary tightening mutes headline inflation via output gap reduction and temporary currency appreciation.
  - Trend shock to international relative food prices (ε_rlp* = 1) not inflationary domestically under model assumptions.
  - Positive trend shock to domestic relative food price (ε_rlp = 1) raises food inflation, lowers non–food inflation, and can leave headline inflation unchanged absent monetary response.
  - Shocks to equilibrium real interest rates can be inflationary because monetary policy adjusts slowly.
- Role of monetary policy and exchange rate:
  - Part of exchange rate depreciation in 2008 and 2011 was consequence of looser monetary policy.
  - Nominal exchange rate depreciation aggravated world food price increases and raised non–food inflation.
- Real marginal costs in food sector:
  - Large increases in 2008 and late 2010–early 2011 driven largely by devgapt (RLPFOODGAP) and REER gap components; output gap plays small role.

### Forecasting performance and model validation
- In-sample forecasting (mechanical forecasts with zero future shocks), sample 2003Q1–2011Q2:
  - Forecasts conditioned on external variables: US output gap, Fed funds rate, trend real Fed funds rate, US CPI inflation, world food price and trend, real exchange rate trend, implicit inflation target.
  - RMSE ratios (RMSE_MF / RMSE_RW) by horizon q1…q8 (selected series preserved exactly):
    - Nominal Repo Rate (per cent p.a.): 0.38 0.45 0.43 0.55 0.55 0.53 0.53 0.56
    - YoY CPI Inflation (per cent): 0.69 0.84 0.80 0.76 0.72 0.66 0.63 0.61
    - Nominal Exch. Rate (KES per USD): 0.44 0.51 0.49 0.50 0.50 0.48 0.47 0.47
    - Output Gap (per cent): 0.64 0.57 0.61 0.72 0.84 0.96 0.96 0.94
  - Interpretation: model RMSE lower than random walk for inflation, nominal exchange rate, and repo rate at all horizons.
  - Limitations: performance weakens during large exogenous shocks or sustained policy misalignments.
- Out-of-sample forecast (real-time exercise Sept 2011 using data to 2011:Q2):
  - Model forecast indicated policy tightening was needed during 2011 inflation surge.
  - Model correctly predicted tightening in 2011Q4 (though under-predicted magnitude); actual tightening larger (motivated by restoring credibility) produced stronger exchange rate appreciation and decelerating overall inflation.
  - Authors argue real-time model-based projection superior for medium-term policy assessment versus mechanical one-step statistics.

### Policy implications, recommendations and practical issues for LICs
- Core recommendations:
  - Incorporate food sector explicitly in FPAS for LICs: separate food and non–food Phillips curves and model relative price trends given large food weight and exposure to imported food.
  - Distinguish trend vs. gap movements in relative prices: temporary deviations (devgap_t) are important inflation drivers and should inform policy response.
  - Calibrate transmission channels to LIC realities: weaker interest-rate channel (small β3) and stronger exchange-rate channel (β4).
  - Use model iteratively: filtration and calibration should reconcile prior beliefs and empirical evidence; avoid overfitting to unmodeled large events.
  - Operationally, characterize policy stance by a single interest rate where possible and improve transparency of standing facilities and policy pivot rates.
- Recognize limitations but value:
  - Limited financial markets, weak transmission, and institutional prerequisites should be inputs for recalibration, not reasons to avoid FPAS.
  - FPAS can provide coherent narratives, decompose drivers of inflation and exchange rate movements, and signal direction of interest rate changes in LICs when suitably adapted.
- Outstanding areas for further study and operational work:
  - Micro structure of the food sector and exposure to domestic/international shocks.
  - Importance of other supply shocks and degree of price/wage stickiness.
  - Implications of limited financial participation and imperfect capital mobility.
  - Role and effects of sterilized foreign exchange interventions.
  - Definition of policy instrument, interbank market functioning, role of money and exchange rate management, scarcity of high-frequency data.
- Suggested next step:
  - Apply the presented model to support monetary policy in Kenya and other LICs conducting forward-looking policy under flexible exchange rates.

*Italic: IMF Working Paper _wp1361 (2007). The Bank of Uganda has also recently announced the adoption of an ”Inflation Targeting Lite” regime.*

### 1. The 2007–2009 Period ................................................................................................

### 1. The 2007–2009 Period ..................................................................................................... 22

### Regional context and past stabilization
- During the first half of the 2000s, sub-Saharan African (SSA) countries succeeded in re-anchoring inflationary expectations, reducing median inflation in the region from 15 percent in 2000 to 6 percent in 2006.
- Fiscal-based stabilization efforts led many SSA countries to adopt policy regimes centered on targets for reserve and broad money—and considerable management of the exchange rate.
- De facto flexibility in exchange rates remained common; money targets are frequently missed in either direction.
- The adoption of monetary aggregates targets was intended to signal that the central bank was “holding the line,” i.e., that stabilization efforts were on track and that fiscal pressures on monetary policy were contained.

### Shocks during 2007–2009 and policy challenges
- The region was buffeted by large external shocks, starting with the first food and fuel crisis of 2007-2008, spillovers from the global financial crisis in 2008-2009 and the latest spike in commodity prices.
- These shocks resulted in large swings in inflation.
- In some cases the monetary policy response has been erratic.
- Existing regimes—with their almost exclusive emphasis on money targets and target misses—have not provided a useful framework for thinking about these shocks, their effects on inflation and the economy, and the role of policy decisions in offsetting or amplifying them.
- Structural changes—enhanced role of market signals, increasing instability in money demand, greater exposure to international capital flows—have called into question the adequacy of existing regimes.

### Shift toward inflation forecast targeting (IFT) and FPAS elements
- Some central banks in the region have moved to, or have announced the adoption of, inflation forecast targeting (IFT), a forward-looking regime in which the inflation forecast is the intermediate target of policy, and a short-term interest rate often serves as the operational target.
- Under IFT, central banks focus on:
  - understanding and explaining why inflation may currently deviate from the target, and
  - determining what policy decisions may be necessary to bring the inflation forecast back in line.
- Even where formal adoption of IFT is not immediate, many central banks are interested in adopting certain elements of inflation targeting, notably the development of in-house forecasting and policy analysis systems (FPAS).

### Role and components of FPAS in IFT-consistent frameworks
- FPAS frameworks are used to discipline policy analysis and typically:
  - collect and help organize high frequency data;
  - use a simple quarterly projection model of the economy that incorporates policymakers’ views about the transmission mechanism and the relevant shocks; and
  - (the source text lists additional uses of FPAS beyond these two points).

*Source: IMF Working Paper — section 1. The 2007–2009 Period*

### 2007. The Bank of Uganda has also recently announced the adoption of an ”Inflation Targeting Lite” regime.

### _wp1361 - 2007. The Bank of Uganda has also recently announced the adoption of an ”Inflation Targeting Lite” regime.

### Purpose and framework
- Purpose: provide a blueprint of a Forecasting and Policy Analysis System (FPAS) for low–income countries (LICs), with an application to Kenya; extend existing frameworks to include an explicit role for food prices.
- Model class: new–Keynesian open economy FPAS with micro–foundations and rational expectations; core equations: forward–looking IS, hybrid Phillips curves, monetary policy rule, uncovered interest parity (UIP).
- Key extension: two separate Phillips curves—one for food and one for non–food—requiring explicit treatment of relative food prices (domestic, international, and their deviation) and trends in those relative prices.

### Kenyan context, inflation history and monetary policy (2007–2011)
- Population and income: estimated 40 million inhabitants; GDP per-capita of US$1,700 as of 2011 (in PPP terms).
- Growth: averaged about 5 percent over the last decade (slowed during global financial crisis).
- Sectoral structure: services contribution to GDP above 60 percent; 75 percent of population relies on agriculture; agriculture accounts for 40-50 percent of total exports.
- Trade and financing: trade balance in deficit; remittances, FDI, and official flows provide bulk of financing; portfolio inflows increasing but slowed during global crisis.
- Fiscal: government debt about 45 percent of GDP; about half of government debt in domestic currency; fiscal deficit hovered around 5 percent of GDP; tax revenue ~20 percent of GDP.
- Monetary framework: de jure anchor historically reserve money targeting; increasing attention to short–term interest rates; managed float exchange rate with considerable volatility.
- CPI and food exposure: share of food in consumer basket 38 percent (Kenya) vs. 50 percent (LIC average); 40 percent of cereal consumption (of about 5 million metric tons) is imported.
- Inflation swings: headline inflation rose from around 3 percent at beginning of 2007 to 16 percent by mid 2008, fell to under 4 percent in mid 2010, and climbed to almost 20 percent at end 2011; inflation reached almost 19 percent in November 2011; inflation stood at 13 percent as of April 2012.
- Policy rates and operations: short term interest rates fell from 6 percent in 2009 to about 1 percent by early 2011; Central Bank Rate (CBR) was 6.25 percent in September 2011 and increased to 18 percent by December 2011; overnight rate was set at the CBR rate plus 600 basis points after September 2011 reform.
- Reserves and external shock: official foreign exchange reserves fell by almost US$ 800 million (about 20 percent of the stock of reserves) between mid-2008 and early 2009; Kenya borrowed from the IMF Exogenous Shock Facility.

### Model structure and key technical elements
- Price aggregation:
  - p_cpi_t = w p_f_t + (1-w) p_nf_t
  - π_cpi_t = 4(p_cpi_t − p_cpi_{t−1}) = w π_f_t + (1-w) π_nf_t
  - π_4,cpi_t = p_cpi_t − p_cpi_{t−4}
- Relative prices defined:
  - rlp_t = p_f_t − p_nf_t (domestic food relative to non–food)
  - dev_t = p_f_t − (p*_f_t + s_t) (deviation domestic vs. international food prices)
  - rlp*_t = p*_f_t − p*_cpi_t (international food relative to international CPI)
  - z_t = s_t + p*_cpi_t − p_cpi_t (real exchange rate)
  - Identity: z_t = (1−w) rlp_t − rlp*_t − dev_t
- Trends in relative prices: autoregressive processes in first (annualized) differences for ∆rlp_t, ∆rlp*_t, ∆z_t with parameters θ_rlp, θ_rlp', θ_z.
  - Implication: trend of dev_t can drift, so long–run domestic food prices need not equal long–run international food prices.
- Output and potential:
  - y_t = y_t + ygap_t; potential growth follows random walk with time–varying drift g_t.
  - IS (output gap): ygap_t = β1 ygap_{t−1} + β2 E_t(ygap_{t+1}) − β3 rmc_{t−1} + β5 ygap*_t + ε_ygap_t
- Real monetary conditions: rmc_t = (1−β4) rrgap_t + β4 (−zgap_t); neutral real rate rr_t follows AR(1).
- Dual Phillips curves:
  - Non–food: π_nf_t − π̄_nf_t = λ1(E_t(π_nf_{t+1}) − π̄_nf_t) + (1−λ1−λ2)(π_nf_{t−1} − π̄_nf_t) + λ2(π_imp_nf,t − π_imp_t) + λ3 rmc_nf_t + ε_πnf_t
  - Food: π_f_t − π̄_f_t = b1(E_t(π_f_{t+1}) − π̄_f_t) + (1−b1−b2)(π_f_{t−1} − π̄_f_t) + b2(π_imp − π_imp_t) + b3 rmc_f_t + ε_πf_t
  - rmc_f_t includes devgap_t, so temporary deviations between domestic and international food prices directly drive food inflation.
- UIP specification with risk premium prem_t following AR(1).
- Monetary policy rule:
  - rs_t = γ1 rs_{t−1} + (1−γ1)[ rr_t + π_{t+1} + γ2(π_{4,cpi_{t+4}} − π_cpi_{t+4}) + γ3 ygap_t + γ4 ∆s_gap_t ] + ε_rs_t
  - Inflation target evolves: π_t = ρ_π π_{t−1} + (1−ρ_π) π + ε_π_t (captures low–frequency shifts in tolerated inflation).

### Calibration, data and implementation
- Calibration principles:
  - Some parameters reflect Kenyan averages (relative price growth, output, real rates, inflation target).
  - Structural views: IS curve relatively backward–looking; small sensitivity of output to interest rates with β3(1−β4) = 0.06; stronger exchange rate channel.
  - Phillips curves: non–food sensitivity to output gap λ3 λ4 = 0.1; food sensitivity b3(1−b4−b5) = 0.02; real exchange rate sensitivities λ3(1−λ4) = 0.1 (non–food) and b3 b4 = 0.04 (food).
  - Food gap pass–through: a 1 percent widening of devgap_t yields immediate 0.07 percent increase in food prices (0.13 percent including expectations).
  - Monetary rule calibrated with strong smoothing, relatively small response to expected inflation, some response to nominal exchange rate, no response to output gap.
- Data:
  - Sample: mixed frequency, from 2000 to 2011.
  - Short term interest rate series: repo rate used from 2000:1 to 2009:1 and 2011:5–2011:6; reverse repo from 2009:3 to 2011:4; 2009:2 used average of the two.
  - CPI methodology change: switch from chained arithmetic mean ("Carli") to geometric mean in 2009; aggregate CPI retroactively revised up to 2005; authors estimated a bias coefficient from overlapping periods and corrected older series.

### Key empirical findings and model exercises
- Filtration and decomposition:
  - Kalman smoother used to decompose series into trend and gap components and to recover sequences of shocks explaining business-cycle dynamics.
  - Real exchange rate z_t: smooth trend appreciation with noticeable gap spikes (notably 2008).
  - International relative food price rlp*_t: smooth positive trend with large gap movements during 2007–2008 and the recent spike (mainly international food price gap shocks).
  - Domestic relative food price rlp_t: trend increased over time but with pre–2007 slowdown; much of 2008 food inflation interpreted as catching up relative to trend; dev_t oscillates widely with large negative gaps in 2007–2008 and recent spike—these gaps are inflationary via the food Phillips curve.
  - Output: fast growth 2003–2007 (six percent average, 7 percent peak in 2007), drop to 2 percent in 2008–2009; most acceleration/deceleration around 2007 explained by output gap movements; gap reopens from 2010 onwards.
  - Real interest rate: large movements; largely positive 2001–early 2003, largely negative until mid 2005 and again from mid 2007 to end of sample; movements mainly in real interest rate gap.
- Shock decomposition and historical interpretation:
  - Imported food shocks (non–trend) accounted for some inflation dynamics in 2008 and recently.
  - Domestic food shocks (harvest shocks) were also relevant.
  - Accommodative monetary policy played an important role in inflation episodes in 2007–2008 and in the 2011 spike.
  - 2007–2008: CBK benefited from "good luck" as domestic inflationary pressures were offset by disinflationary forces associated with global recession—no need for tightening.
  - 2011 spike: disinflationary global forces were absent; model indicated short term interest rates needed to increase to offset inflationary pressures. CBK implemented tightening by end 2011 (CBR increases), validating model usefulness.
- Impulse response experiments:
  - Temporary 1 percent increase in international relative food prices (ε_rlpgap* = 1) produces:
    - Large short–lived effect on international food inflation (level shock causes YoY drop after four quarters).
    - Longer–lived effect on domestic food and CPI inflation since pass–through to domestic food prices is slower.
  - Monetary policy response (central bank raises rates) mutes headline inflation impact via output gap reduction and temporary currency appreciation.
  - Trend shock to international relative food prices (ε_rlp* = 1) is not inflationary domestically because trend movements in international prices do not force trend changes in domestic food prices under model assumptions.
  - Exception: positive shock to trend of domestic relative food price (ε_rlp = 1) increases food inflation, decreases non–food inflation, but leaves headline inflation unchanged absent monetary response.
  - Shocks to equilibrium real interest rates can be inflationary because monetary policy adjusts slowly, opening gaps in real monetary conditions.
- Model validation:
  - Coincidence between model forecast indicating need for tightening in 2011 and actual CBK tightening supports model utility for policy analysis in LICs.

### Policy implications and recommendations
- Incorporate food sector explicitly in FPAS for LICs: separate food and non–food Phillips curves and relative price trends are essential given large food weight and exposure to imported food.
- Distinguish trend vs. gap movements in relative prices: temporary deviations between domestic and international food prices (devgap_t) are important inflation drivers and should inform policy responses.
- Calibrate transmission channels to LIC realities: allow for weaker interest rate channel (small β3) and stronger exchange rate channel (β4) consistent with empirical evidence for LICs.
- Use model for iterative filtering and judgment: iterate calibration and filtration to reconcile prior beliefs about shock importance with empirical evidence; avoid overfitting to unmodeled large events.
- Operational policy framework:
  - Characterize policy stance by a single interest rate where possible; in Kenya the repo/reverse repo rates and later the CBR served as practical indicators.
  - Improve operational framework transparency: align standing facilities and policy pivot rates (as CBK did in September–December 2011) to make policy signals effective.
- Recognize limitations but value of FPAS in LICs:
  - Acknowledge weaker financial markets, limited transmission, and institutional prerequisites, but treat these as inputs for recalibrating FPAS rather than reasons to avoid model use.
  - FPAS can provide a coherent narrative of the economy and signal direction of interest rate changes even in LICs when suitably adapted.

*Italic: IMF Working Paper _wp1361 (2007). The Bank of Uganda has also recently announced the adoption of an ”Inflation Targeting Lite” regime.*

### Appendix III). Since we have 18 different shocks, we regroup them into seven groups:

### _wp1361 - Appendix III). Since we have 18 different shocks, we regroup them into seven groups:

### Shock groups (regrouping)
- There are 18 shocks regrouped into seven groups:
  - Shocks that hit the output gap: εygapt, εrrt.
  - Shocks that hit sectoral inflation rates: επft, επnft, εrlpt.
  - Shocks that affect the international relative price of food: εrlpt, εrlpgapt.
  - Shocks related to monetary policy: εRSt, επt.
  - Shocks that directly affect the exchange rate: εSt, εpremt, εzt.
  - Shocks that originate in the rest of the world: εygap∗t, επ∗t, εRS∗t, εrr∗t.
  - Other (initial conditions).

- Caveats about regrouping:
  - The regrouping can overlap; e.g., some exchange rate shocks reflect international market conditions and developments in the world economy.
  - The model is highly stylized and may miss transmission mechanisms; estimated shocks may therefore correlate.

### How shocks affect model variables (interpretation)
- General points:
  - Some shocks have straightforward effects (e.g., output gap shocks directly raise the output gap).
  - Some effects are complex due to endogenous policy responses (e.g., persistent inflation shocks raise expected inflation and lower real rates, but monetary policy responds by tightening, tightening real monetary conditions and producing a real appreciation that reduces the output gap).
  - Users must understand multiple channels through which shocks affect variables.

- Own shocks (direct shocks to observed variables):
  - Own shocks (e.g., επft and επnft) soak up two types of movements:
    - Movements with clear economic interpretation (e.g., negative food harvest shocks → increase in food inflation → recorded in επft).
    - High frequency dynamics without clear economic interpretation (likely due to model stylization), which may overstate the importance of own shocks.
  - The analysis is complemented by alternative filtration representations.

### Shock decomposition — key findings (selected variables)
- Output gap (Figure 11; three main features):
  - An important share of output gap fluctuations are explained by developments in the international economy: the mid 2000s positive gap was driven in part by strong international output; mid-2008 deceleration was mainly due to the global financial crisis; recovery since mid 2010 was supported by relative improvement in the US economy.
  - Output gap shocks account for much of the 2007 economic boom, associated in part with the increase in the fiscal deficit during that period. Development expenditure increased by 60 percent.
  - The Kenyan economy was supported by an accommodating monetary policy (εRSt < 0, επt > 0) from mid 2008 onwards, which helped offset some fallout from the global financial crisis and became expansionary once the international economy recovered.

- Non–food inflation (Figure 12):
  - Shocks to non–food prices account for part of movements.
  - The benign international environment helped explain some non–food movements, especially during the global financial crisis.
  - Accommodating monetary policy consistently buoyed non–food prices and contributed to the large acceleration in inflation observed in 2011.

- Food inflation (Figure 13):
  - Domestic food price shocks (e.g., drought of 2008–2009) play an important role.
  - International food price shocks explain a large fraction of the upswing/downswing/upswing pattern in food prices.
  - Monetary conditions also affected food inflation.

- Headline inflation (Figure 14):
  - International conditions—including international food prices—and, more importantly, accommodating monetary policy were the two key factors.

- Nominal depreciation relative to long–run value (Δs; Figure 15):
  - Large depreciation observed in 2009 accounted for by monetary policy shocks and shocks to the risk premium associated with a worsening external environment.
  - External improvement contributed to nominal appreciation in early 2010.
  - Since then, monetary policy and exchange rate shocks (possibly associated with balance of payment pressures from higher food and fuel import bill) resulted in depreciation.

### Alternative representations of the filtration exercise
- Two complementary representations:
  - Time path of selected variables: if unobserved, display model-implied path; if observed, compare observed variable with model path in absence of the variable’s own shock (“KF Predicted”).
  - Alternative decomposition based on terms that enter the variable’s equation.

- Real marginal costs in the food sector (rmcf t; Figure 16):
  - Large increases in 2008 and late 2010–early 2011, with an important decline between the spikes.
  - Large share of fluctuations stem from movements in devgapt (appearing as RLPFOODGAP in the figure) and movements in the gap component of the food-based real exchange rate (combination of real exchange rate gap and gap component of domestic relative price of food).
  - Movements in the output gap play a small role.

- Nominal interest rates (Figure 17):
  - Since mid 2007, actual interest rates are consistently below those predicted by the model due to negative monetary policy shocks.
  - The gap is most prominent in 2008–2009 (model called for policy tightening which did not take place) and opens again starting mid 2010.
  - Persistence in interest rates is mainly due to smoothing factor in the policy rule.
  - Model-predicted increases in interest rates in 2008–2009 and 2011 are due to increases in inflation and nominal depreciation (first episode); decreases are due to declines in inflation.

### A Model–Based Interpretation of Recent History
- Purpose:
  - Provide an interpretation of recent history suitable for monetary policy committee use; model-based but should be plausible and complemented by additional variables (trade, balance of payments, fiscal developments) not included here.

- 1. The 2007–2009 Period
  - 2007: Kenyan economy in full expansion; output growth peaked, driven by favorable external environment and positive domestic demand; inflation initially stable; food prices fell due to bumper harvest; benign inflation outlook also due to neutral monetary policy and appreciated real exchange rate.
  - Prospects worsened starting in 2008:
    - Growth dropped dramatically, to about 2 percent in 2008-2009.
    - Slowdown more severe than other EAC countries because external demand shock from the global financial crisis combined with domestic shocks—poor harvests and post-election violence.
    - External position deteriorated as low external demand widened current account deficits and financial/capital inflows halted due to liquidity strains.
    - Nominal exchange rate sharply depreciated—by more than 20 percent in the second half of 2008—allowing the real exchange rate to return to equilibrium.
  - Inflation dynamics:
    - In 2008 inflation overshot its target: it increased to about 17 percent at its peak in mid 2008, from less than 2 percent a year earlier.
    - Inflation fueled by soaring world food and oil prices and domestic shocks.
    - Figure 18 shows sizeable impact of international price shocks on domestic inflation, even if the central bank had responded (which it did not).
  - As the global crisis unfolded and international commodity prices plummeted in second half of 2008 and through 2009, and domestic economy slowed, inflationary pressures subsided.
    - This occurred even though nominal depreciation during this period was the highest since 1998.
    - CBK did not tighten policy; nominal short-term interest rates declined.
    - Fiscal and monetary policy turned countercyclical to support the domestic economy once it decelerated.

- 2. The 2010–2011 Period
  - Real growth rebounded, reaching approximately 5 percent in 2010 and reopening the output gap.
    - Recovery driven by improvement in external demand and accommodating monetary policy.
    - Depreciation pressures peaked in mid 2011 due to balance of payment pressures and low interest rates.
  - Inflation events:
    - Driven by 2009 events, inflation fell to less than 4 percent in mid 2010 before climbing again.
    - Non–food price inflation soared due to nominal exchange rate depreciation; positive output gap also contributed but impact was moderate compared to import prices (real depreciation).
    - Model estimation suggests demand pressures during 2011 were close to the highest within the historical sample.
    - Food price inflation was lifted by exchange rate depreciation, increasing import prices, and fast growth in world food prices in second half of 2010 and early 2011.

### Applying the model for macro forecasting in Kenya (section V)
- Two forecast types studied:
  - Historical in–sample simulations.
  - Out–of–sample forecast.

- A. In–sample forecasting properties
  - In-sample forecasts: mechanical model forecasts created every quarter with zero future shocks starting at smoothed means and using only dataset up to start period; forecasts conditioned on external variables, real exchange rate trend, and implicit inflation target.
  - Conditioning variables:
    - the US output gap,
    - the Fed funds rate and the trend of the real Fed funds rate,
    - US CPI inflation,
    - the world price of food and its trend,
    - the real exchange rate trend,
    - the implicit inflation target.
  - Outcomes compared with actual values or smoothed trajectories (e.g., output gap).
  - Historical forecasting performance reported for four main variables: year-on-year CPI inflation, nominal KES per USD exchange rate, short–term interest rate, and the output gap. Forecasts presented in Figure 19.
  - Sample period covers 2003Q1–2011Q2.
  - Performance by sub-period:
    - Pre–2008:
      - Model captures general tendencies relatively well: predicts increase in nominal interest rates between 2003 and 2005 and relative stability from mid 2005 onwards.
      - Predicts path of nominal exchange rate (benefiting from conditioning on equilibrium real exchange rate path).
      - Correctly predicts sustained expansion in the output gap and some inflation dynamics in 2004–2006.
    - 2008–2010:
      - Simulations capture general directions but not magnitudes due to exogenous shocks (global crisis, adverse weather, post-election violence).
      - Simulations undershoot the inflation surge predicted for 2008; model simulations assume central bank tightened policy, opening a negative output gap not observed in data.
      - Simulations partially capture increase in country risk premium and sharp nominal depreciation in second half of 2008, aided by knowledge of equilibrium real exchange rate.
    - End 2010–2011:
      - As inflation soared by end-2010, model predicts monetary tightening; repo rate forecasts are above actual data.
      - Observed low interest rates are interpreted by model as policy misalignments; predicted tightening rises through this period.
      - Predicted tightening keeps inflation below actual data; smaller observed nominal depreciation also contributes to lower observed inflation.
      - Tight monetary conditions imply a lower output gap than inferred from the full sample.
  - RMSE comparison with random walk (Table 4):
    - RMSEs reported for different horizons using all historical forecasts.
    - Numbers below 1 indicate model RMSE is lower than random walk RMSE.
    - Results suggest model forecasts perform better than random walk for inflation, nominal exchange rate, and repo rate at all horizons.
  - Overall: in–sample forecasting properties satisfactory but limited in presence of large exogenous shocks or sustained policy misalignments.

- B. Out–of–sample forecasting
  - Real-time historical exercise for period of increasing inflation in mid 2011; performed in September 2011 using data up to 2011:Q2 and external assumptions as of September 2011; forecast compared with subsequent actual developments (Figure 20).
  - Authors argue real-time model-based projection is superior for assessing model qualities relevant to medium-term policy over mechanistic measures like one-step RMSEs.
  - Kenya experienced soaring inflation in second half of 2011, driven mainly by food prices.
  - Model analysis: food price inflation was driven in part by surge in world food prices in second half of 2010 and beginning of 2011.

*Source: _wp1361 - Appendix III). Since we have 18 different shocks, we regroup them into seven groups:*

### 2011. Importantly, the world food price increase was aggravated by depreciation of the

### _wp1361 - 2011. Importantly, the world food price increase was aggravated by depreciation of the

### Model forecast and historical performance
- The model forecast indicated that a policy tightening was needed to curb inflationary pressures.
- The model correctly predicted a tightening in 2011Q4, though it under–predicted its magnitude.
- Because the actual tightening was larger (objective to restore credibility not modeled), nominal exchange rate appreciation was stronger than forecast and overall inflation decelerated, although food inflation remained high.
- The model was used for:
  - Filtering key macroeconomic series into trend and gap components.
  - Analyzing impulse response functions and in–sample historical forecasts.
  - Performing an out–of–sample forecast to identify likely policy trajectories given contemporaneous inflationary pressures.

### Monetary policy chronology and actions (Kenya)
- Policy was loosened in response to the global financial crisis of 2008-2009 and maintained beyond that period.
- Rates declined continuously and reached 1 percent by the end of 2011.
- The Central Bank of Kenya (CBK):
  - Provided liquidity through reverse repos until 2011Q1.
  - Started withdrawing liquidity thereafter but kept the repo rate close to 5.75% until mid June 2011.
  - Continued to implement non–standard and discretionary measures in 2011Q3 despite recognizing symptoms of an exchange rate crisis.
  - Implemented a firm monetary tightening in 2011Q4.
- During 2010-2011 commercial banks borrowed from the central bank overnight discount window at low rates and built foreign exchange positions, contributing to a depreciation spiral.

### Drivers of inflation and exchange rate dynamics
- Imported food price shocks contributed to inflation dynamics in 2008 and 2011.
- Nominal exchange rate depreciation aggravated the world food price increase and raised non–food price inflation.
- A positive output gap contributed to the non–food inflation surge, but its impact was moderate compared to depreciation.
- The estimated output gap aligns with the fast credit growth observed during 2010-2011.
- Analysis shows that in both 2008 and 2011 part of the exchange rate depreciation was a consequence of looser monetary policy.
- Narrative financial market evidence corroborated concerns about excessive inflation expectations.

### Policy framework, targets, and interpretation challenges
- CBK's December 2011 Monetary Policy Statement emphasized monetary and credit aggregates as justification for its stance:
  - Quoted: “The programmed growth in money supply ... was considered adequate to support economic growth through expansion of credit to private sector... Generally, broad money supply, M3, remained within the set target . Credit to private sector increased , which was virtually on target.” (Monetary Policy Statement, Dec 2010, pp. 3).
- Reserve money growth overshot its target consistently through 2011, indicating expansionary policies despite broad money and credit aggregates appearing on target.
- Reliance on broad money and credit targets can obscure the true stance of policy when broad money velocity assumptions are optimistic.
- The legacy of monetary aggregate targeting may have led to inconsistent views about policy stance; greater emphasis on interest rates could have revealed the accommodative stance sooner.

### Structural model features (overview)
- Framework: Forecasting and policy analysis system (FPAS) extended to include an explicit role for food prices via two separate Phillips curves (food and non–food).
- Key inclusions:
  - Domestic and foreign relative food prices (trend and gap components).
  - Direct entry of imported inflation into the non–food Phillips curve.
- Applications demonstrated:
  - Decomposition of series into trend and gap components.
  - Quantitative assessment of international shocks and monetary policy contributions.
  - Support for forward–looking monetary policy under a flexible exchange rate regime.

### Outstanding uncertainties and recommended next steps
- Important unresolved features to study in Kenya and other low–income countries:
  - The (micro) structure of the food sector and its exposure to domestic and international shocks.
  - The importance of other supply shocks.
  - The degree of price and wage stickiness.
  - Implications of limited financial participation and imperfect capital mobility for the transmission mechanism.
  - The role and effects of alternative instruments such as sterilized foreign exchange interventions.
- Practical issues for implementation of such models in policy making:
  - Definition of the policy instrument.
  - Functioning of the interbank market.
  - The role of money and exchange rate management in policy making.
  - Scarcity of high-frequency data.
- Suggested next step: Apply the presented model to support monetary policy in Kenya and other low–income countries conducting forward–looking policy under flexible exchange rates.

*Source: _wp1361 - 2011. Importantly, the world food price increase was aggravated by depreciation of the (IMF working paper content).*

### 1.  Solving and Simulating the Model

### 1. Solving and Simulating the Model

### Model structure and solution
- The model is a linear semi-structural forward looking model with model-consistent expectations of the form F(X_{t−1}, X_t, X_{t+1}, ε_t | θ) = 0.
- X_t denotes the vector of endogenous variables; ε_t are exogenous variables (shock innovations); θ denotes model parameters.
- The model is solved using a variant of the Blanchard and Kahn algorithm (Blanchard and Kahn (1982)), implemented using the IRIS Toolbox for Matlab.

### State-space representation (solution form)
- State equation:
  - X_t = T X_{t−1} + R ε_t,  ε_t ~ N(0, Σ_ε).  (A1)
  - Σ_ε is the variance covariance matrix of the shock innovations.
- Measurement equation:
  - Y_t = Z X_t + H η_t,  η_t ~ N(0, Σ_η).  (A2)
  - η_t indicates potential measurement noise; Σ_η denotes the noise covariance.
- Observed variables Y_t include inflation, output, exchange rates, etc.

### Kalman filter (estimation of states and shocks)
- The Kalman filter is applied to system (A1)-(A2) to recursively update estimates of X_t and ε_t based on observations Y_t.
- Recursive updating equations (as presented):
  - X̂_{t+1|t} = T X̂_{t|t} = X̂_{t|t−1} + P_{t|t−1} Z (Z′ P_{t|t−1} Z + Σ_η)^{−1} (Y_t − Z X̂_{t|t−1})
  - P_{t+1|t} = (T − K_t Z′) P_{t|t−1} (T − K_t Z′) + K_t Σ_η K_t′ + Σ_ε
  - K_t = T P_{t|t−1} Z (Z′ P_{t|t−1} Z + Σ_η)^{−1},  for t = 1, ..., T.
- Initialization:
  - X̂_{1|0} = E(X_1)
  - vec(P_{1|0}) = [I_{r^2} − (T ⊗ T)]^{−1} vec(Q)
- P_{t+1|t} is the mean square error of X̂_{t+1|t}.

### Kalman smoother (full-sample state estimates)
- The Kalman smoother constructs X̂_{t|T} using the entire sample via backward recursion:
  - X̂_{t|T} = X̂_{t|t} + J_t [X̂_{t+1|T} − X̂_{t+1|t}]
  - J_t = P_{t|t} T′ P_{t+1|t}^{−1}
  - P_{t|T} = P_{t|t} + J_t (P_{t+1|T} − P_{t+1|t}) J_t′,  for t = T, T−1, ..., 1.
- With:
  - P_{t|t} = P_{t|t−1} − P_{t|t−1} Z (Z′ P_{t|t−1} Z + Σ_η)^{−1} Z′ P_{t|t−1}
  - P_{t|T} is the mean square error of the smoothed estimate X̂_{t+1|T}.
- The Kalman smoother is described as a recursive implementation of minimizing:
  - J = (1/2) ∑_{t=1}^T ε_t′ (R Σ_ε R′) ε_t + (1/2) ∑_{t=1}^T η_t′ (H Σ_η H′) η_t + (X_0 − E[X_0]) P_0 (X_0 − E[X_0]) subject to (A1)-(A2).

### Role of stochastic specification and identification
- In practice there are typically more structural shocks (elements in ε_t and η_t) than observed macroeconomic variables.
- The least squares / Kalman approach places important weight on the stochastic specification: the covariance matrices Σ_η and Σ_ε.
- Implication: both the impulse response behavior of the model and the assumed variance of structural shocks determine the plausibility of particular drivers of the economy and the interpretation of the data.
- Example: an assumption of zero variance for demand shocks would eliminate household preference shocks or government stimulus as plausible explanations for GDP growth or inflation and would result in a severely misspecified model.

### Shock decompositions and reconstruction
- With estimates of exogenous shocks and initial conditions, observed (and state) variables can be decomposed in terms of exogenous shocks via recursion on (A1)-(A2):
  - Y_t = Z ∑_{τ=0}^t T^{t−τ} R ε_{τ|T} + T^{τ−t}_0 X_{0|T} + H η_t.  (A3)
- Implementation of the Kalman filter and smoother is available in IRIS Toolbox for Matlab.

### Calibration (selected parameters and values)
- Relative Prices and their Trends:
  - w: Share of food in the CPI = 0.36 (Kenya National Bureau of Statistics)
  - ∆rlp: Trend growth rate, relative price of food = 6.5 (Historical average)
  - θ_rlp: Persistence, Trend growth, relative price of food = 0.8 (S.P.)
  - ∆z: Trend growth rate, real exchange rate = −4 (Historical average)
  - θ_rlp (real growth rate): 0.65 (S.P.)
- Output and Real Interest Rates:
  - g: Trend growth rate, non–Agricultural GDP = 4 (Historical average)
  - θ_g: Persistence, Trend growth, GDP = 0.5 (S.P.)
  - β_1: Backward looking parameter, IS curve = 0.6
  - β_2: Forward looking parameter, IS curve = 0.1
  - β_3: Output sensitivity to real monetary cond. (rmc) = 0.15
  - β_4: Weight of real exchange rate in rmc = 0.6
  - β_5: Output sensitivity to foreign demand = 0.15
  - ρ_rr: Persistence, equilibrium real interest rate = 0.75
  - rr: Equilibrium real interest rate = 1 (Historical average)
- Non–Food Phillips Curve:
  - λ_1 = 0.4, λ_2 = 0.05, λ_3 = 0.2, λ_4 = 0.5
- Food Phillips Curve:
  - b_1 = 0.5, b_2 = 0.05, b_3 = 0.1, b_4 = 0.1, b_5 = 0.7
- Monetary Policy and Uncovered Interest Parity:
  - ρ_prem = 0.75, φ = 0.85, γ_1 = 0.8, γ_2 = 1.4, γ_3 = 0, γ_4 = 0.25
  - π (Inflation target) = 5
  - ρ_π = 0.85
- Rest of the World (selected):
  - ∆rlp′ = 2, θ_rlp′ = 0.5, β′_1 = 0.5, β′_2 = 0.5, β′_3 = 0.05
  - λ′_1 = 0.6, λ′_2 = 0.06, γ′_1 = 0.75, γ′_2 = 1.7, γ′_3 = 0.25
  - ρ_p^f = 0.75, ρ_rr′ = 0.5, rr′ = 2.5 (Historical average)

### Calibration (volatilities, selected)
- σ_rlp = 2, σ_z = 3, σ_y = 1.5, σ_g = 1, σ_ygap = 1, σ_rr = 0.7
- σ_π^nf = 1.5, σ_π^nf (food) = 2.5, σ_s = 3.5, σ_prem = 3.5, σ_rs = 1.5
- σ_π = 1, σ_ygap′ = 0.3, σ_rs′ = 0.3, σ_rr′ = 0.08, σ_π′ = 1.5
- σ_rlp′ = 0.35, σ_rlpgap′ = 0.3

### In-sample model forecasts vs. random walk (RMSE ratios)
- Reported RMSE ratio = RMSE_MF / RMSE_RW for horizons q1…q8:
  - Nominal Repo Rate (per cent p.a.): 0.38 0.45 0.43 0.55 0.55 0.53 0.53 0.56
  - YoY CPI Inflation (per cent): 0.69 0.84 0.80 0.76 0.72 0.66 0.63 0.61
  - Nominal Exch. Rate (KES per USD): 0.44 0.51 0.49 0.50 0.50 0.48 0.47 0.47
  - Output Gap (per cent): 0.64 0.57 0.61 0.72 0.84 0.96 0.96 0.94

### Impulse responses, decompositions, and diagnostics (high-level)
- The document contains impulse response functions for shocks such as:
  - ε_rlpgap′_t = 1 (international relative price of food gap shock)
  - ε_RS_t = 1 (monetary policy shock)
  - ε_rlp′_t = 1 (international relative price of food, trend shock)
  - ε_rlp_t = 1 (domestic relative price of food, trend shock)
- Trend/gap decompositions shown for:
  - Real exchange rate, Relative food price (Food − Nonfood), Relative international food price (Food − CPI), Food price deviation (Domestic − Intl)
  - Output level/trend and Output gap
  - Real interest rate level/trend and Real interest rate gap
- Shock decompositions illustrated for:
  - Output gap (components: Output gap, Prices, Intl food, Policy, Ex rate, RoW, Other)
  - Non-Food Inflation (same components)
  - Food Inflation (same components)
  - Headline Inflation (same components)
  - Nominal Depreciation (same components)
- Real marginal costs decomposition for Food Price Inflation decomposed into:
  - Output Gap, REER Gap, RLP Gap, RLPFOOD Gap
- Monetary policy rate decomposition includes components:
  - Lagged, Policy Neutral, Inflation Dev., Output Gap, FX, Actual, KF Predicted
- Model diagnostics and comparisons:
  - Impulse responses are presented for the 2007–2008 Global Food Crisis.
  - Conditioned historical simulations and Model Forecast versus Actual Data figures are provided for repo rates, CPI Inflation YoY, nominal exchange rate (KES per USD), money market rates, and food price inflation.

*Source: _wp1361 - 1.  Solving and Simulating the Model (PDF chapter).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp1361.pdf_