## wpiea2021190-print-pdf

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---

### I. Purpose and scope
- Purpose: develop a parsimonious, semi-structural model of the Moroccan economy to assess propagation of key shocks, medium- and long-term impacts, and effects of alternative domestic macroeconomic policy responses.
- Calibrate model to capture key stylized facts of Morocco’s economy and present scenarios of policy responses to the Covid-19 pandemic under different monetary policy regimes.
- Monetary regimes considered:
  - peg exchange rate regime;
  - intermediate regime: peg with a band (the current one);
  - inflation targeting regime with flexible exchange rate.
- Modeling choices:
  - Focus on a few variables consistent with the New Keynesian framework to retain theoretical consistency and parsimony.
  - Fiscal authority chooses a single policy variable: the cyclically adjusted primary balance.
- Organization: Section II describes the model, Section III discusses calibration, Section IV applies the model to Covid-19 recovery scenarios, Section V concludes.

### II. Model structure and key features
- Model type and form:
  - Semi-structural, steady-state (transitional steady-state solution), gap-format (variables expressed as deviations from trend).
  - Annual frequency; includes a rudimentary fiscal and debt-accounting block.
  - Theoretical blend: New Keynesian nominal and real rigidities with RBC/DSGE methods and rational expectations; allows backward- and forward-looking expectations and substantial inertia.
- Five building blocks:
  - Aggregate demand split into agricultural (exogenous) and nonagricultural parts (IS curve).
  - Prices: core and non-core CPI components; Phillips curve for core inflation; non-core prices determined by oil prices, agricultural production, and exogenous shocks.
  - Monetary policy: accommodates peg-with-band (nominal exchange rate exogenous), and inflation-targeting (domestic interest rate instrument); limited capital mobility makes market interest rate a weighted average of policy and UIP-implied rates.
  - Fiscal policy: fiscal reaction function with cyclically adjusted primary deficit and gross debt stabilization around threshold (policy-consistent threshold cited as 60 percent of GDP).
  - Debt dynamics and financing: authorities choose domestic or foreign-currency debt accumulation; net debt affects market interest rates; rising gross public debt above threshold raises risk premium and neutral real interest rate; effect partly offset by increased international reserves.

### III. Core equations and mechanisms (selected)
- Nonagricultural IS curve (gapped form preserved):
  - ŷ_t^{NAgr} = a_1 ŷ_{t-1}^{NAgr} + a_2 E_t ŷ_{t+1}^{NAgr} − a_3 mci_t + a_4 f_t^{imp} + a_5 ŷ_t^{*} + ε_t^{y}
  - mci_t = a_6 (r̂_t^{mix} + cr_spread_t) + (1 − a_6)(− ẑ_t)
- Real exchange rate (log) definition:
  - ∆z_t = ∆s_t MAD/EUR + π_t^{*} − π_t
  - An increase in z_t implies a more depreciated domestic currency in real terms.
- Fiscal impulse (preserved form):
  - f_t^{imp} = (cad_t − cad_{t−1}) + f4 ε_{t bbar}. (Equation (3))
- Core Phillips curve (preserved form):
  - π_t^{Core} = b1 π_{t−1}^{Core} + (1−b1) E_t π_{t+1}^{Core} + b2 rmc_t + ε_{t π,Core}. (Equation (4))
  - rmc_t = b3 ŷ_t^{NAgr} + (1−b3) ẑ_t^{Core}. (Equation (5))
- Non-core inflation:
  - π_t^{NCore} = b4 π_{t−1}^{NCore} + (1−b4)(π_{t}^{Tar,NCore} − b5 ŷ_t^{Agr} − b6 (1− w_{CPI}) r p̂_t) + b7 ∆π_t^{Oil} + ε_{t π,NCore}. (Equation (6))
- Exchange rate band and UIP (preserved forms):
  - s_t^{MAD/EUR} = ω_{PEG} s_{t,MAD/EUR,PEG} + (1−ω_{PEG}) s_{t,MAD/EUR,FL}. (Equation (7))
  - s_{t,MAD/EUR,FL} = E_t s_{t+1,MAD/EUR} + i_{t}^{EUR} − i_t + prem_t + ε_{t s}. (Equation (9))
- Monetary policy (peg and IT forms preserved, parameters preserved):
  - Peg-weighted policy equation (text display, Equation (11)) with parameters ω_{PEG}, c1, c2, c3, c4, c5 and monetary shock ε_{t i}.
  - IT forward-looking rule: i_t = c1^{IT} i_{t−1} + (1− c1^{IT})( ĩ_t + c2^{IT}( E_t π_{t+1} − π^{Tar})) + ε_{t i}. (Equation (13))
- Risk premium dynamics preserved:
  - prem_t = c4 prem_{t−1} + (1−c4)[ prem̅ + c5[( b_t − b_{t}^{tar} ) − ( res_t − res_{t}^{tar} )]] + ε_{t prem}. (Equation (12))

### IV. Calibration: key parameter values and steady states (preserved exactly)
- Aggregate-demand and output-gap parameters:
  - a2: 0.3 — Output gap persistence.
  - Forward-looking part of aggregate demand: 0.1.
  - Elasticity of the output gap wrt monetary conditions: 0.125.
  - Elasticity of the output gap wrt the fiscal impulse: 0.6.
  - Elasticity of the output gap wrt foreign demand: 0.35.
- Inflation and marginal cost parameters:
  - Core inflation persistence: 0.35.
  - Elasticity of core inflation wrt marginal cost: 0.065.
- Monetary policy parameters (ω_{PEG} and variants):
  - ω_{PEG}: 0.8 — Current regime (degree economy insulated from external developments).
  - ω_{PEG}: 0.5 — Regime with more extensive use of ER band.
  - ω_{PEG}: 0.0 — Floating exchange rate and inflation targeting.
  - c1: 0.5 — Central bank sterilization capacity under the peg.
  - c2: 0.6 — Central bank interest rate smoothing under the peg.
  - c3: 0.2 — Central bank inflation aversion under the peg.
  - c4: 0.75 — Risk premium persistence.
  - c5: 0.03 — Elasticity of the risk premium with respect to debt and international reserves (calibrated; 3 basis point for each 1-percent increase in debt).
  - Under IT:
    - c1^{IT}: 0.3 — Central bank interest rate smoothing under IT.
    - c2^{IT}: 2.5 — Central bank inflation aversion under IT.
- Fiscal policy parameters:
  - f7: 0.6 — Fiscal policy smoothing.
  - f8: 0.05 — Debt aversion.
  - f9: 0.5 — Debt smoothing.
  - f10: 0.2 — Reaction of fiscal policy to the output gap.
- Steady-state parameters:
  - prem̅: 1 — Long-term risk premium.
  - ∆z̅: 0 — Long-term (trend) real appreciation.
  - ∆y̅_{NAgr}, ∆y̅_{Agr}: 4 — Long-term nonagricultural and agricultural GDP growth.
  - π̃: 2 — Implied inflation target.
  - b̅_{t}^{tar}: 0.6 — Long-term debt-to-GDP ratio (60 percent).
  - b̅_{1Y,tar}: 0.05 — One-year debt-to-GDP ratio.
  - b̅_{5Y,tar}: 0.4 — Five-year debt-to-GDP ratio.

### V. Calibration validation and estimation approach
- Validation methods:
  - Compare model-based impulse response functions (IRFs) with empirical IRFs where available; expert judgment for Morocco where empirical IRFs unavailable.
  - Estimate unobserved variables via multivariate (diffuse) Kalman filter for nonstationary variables.
  - Recursive forecasts: 8-years-ahead forecasts repeated from 2004 to 2019 to assess predictive ability.
- Estimation of unobserved variables via model + Kalman filter: output gap, exchange rate gap, interest rate gap.

### VI. Impulse responses — shocks analyzed and principal findings
- Shocks considered:
  - Aggregate demand shock: unexpected positive nonagricultural output gap of 1 percentage point for one year.
  - Risk premium shock: unexpected increase in foreign interest rates by 1 percentage point for one year.
  - Fiscal shock: unexpected one-year increase of the primary deficit by 1 percentage point of GDP.
- Key IRF findings (preserved dynamics and timing):
  - Temporary positive aggregate demand shock (1 percentage point):
    - Headline primary balance moves to surplus due to greater tax revenues and lower cyclically adjusted spending, although cyclically adjusted primary balance deficit initially increases.
    - Debt-to-GDP ratio initially falls; fiscal authority then slowly moves to a deficit to return to steady state.
    - Nominal exchange rate unchanged; domestic inflation increases; real exchange rate appreciates; monetary policy tightens.
    - Output gap closes in about five years; gross debt, inflation, and exchange rate take longer due to gradual fiscal response.
  - Risk premium shock (1 percentage point rise in foreign interest rates for one year):
    - Real domestic interest rate increases; monetary policy tightens.
    - Output impact relatively small compared with increase in debt-to-GDP ratio.
    - Fiscal authority tightens gradually; primary balance improves by 10-15 basis points relative to baseline.
    - Return to steady state takes more than 10 years despite one-year shock.
  - Fiscal expansion (one-year increase of primary deficit by 1 percent of GDP):
    - Authorities bring gross debt back via long series of primary surpluses, withholding aggregate demand.
    - Long-run multiplier negative: temporary stimulus depresses aggregate demand and reduces inflationary pressure.
    - Debt-to-GDP ratio starts declining only in the 8th year after the initial stimulus.

### VII. Policy-relevant exercise: Covid-19 downside scenario and policy options
- Baseline staff expectations (context):
  - Morocco expected to recover from 2020 shocks: growth rebounds from −7 percent in 2020 to 4.5 percent in 2021 and 3.9 percent in 2022.
  - Harvest returns to historical average; vaccination progress; monetary and fiscal policies remain supportive.
  - Output gap fully reabsorbed and inflation returns to 2 percent only in 2025.
- Downside scenario assumptions:
  - Slower vaccination progress and persistent virus circulation necessitate extended lockdowns for most of 2021 in Morocco and main trading partners.
  - GDP growth slows to 1.5 percent in 2021, keeping output gap below baseline by about 2 percentage points.
  - GDP growth gradually returns to baseline in following years but with damage to output potential.
- Central bank context in 2020:
  - Policy interest rate cut by 75 bps in 2020 to 1.5 percent.
  - Exchange rate band expanded to ±5 percent in March 2020.
  - Dirham depreciated by 6 percent against the basket in March 2020, then partially recovered.

### VIII. Monetary regime simulations and outcomes (ω_{PEG} scenarios preserved)
- Simulated regimes (ω_{PEG} parameter values preserved):
  - Peg regime: ω_{PEG} = 0.8
  - Intermediate ER regime (full use of band): ω_{PEG} = 0.5
  - Inflation targeting (IT) regime: ω_{PEG} = 0
- Simulation outcomes (preserved comparative findings):
  - Peg regime (ω_{PEG} = 0.8):
    - Central bank lowers interest rates by around 30 basis points.
    - Fall in market interest rates partly offset by increased risk premium from higher debt-to-GDP.
    - Dirham depreciates only marginally.
    - Output gap slow to close.
    - Debt-to-GDP ratio remains elevated by about 2½ percentage points relative to baseline.
  - Intermediate ER regime (ω_{PEG} = 0.5):
    - Central bank cuts interest rate by almost 100 basis points.
    - Much larger nominal and real depreciation (close to full use of band).
    - Inflation closer to baseline; output recovers somewhat faster.
    - Debt-to-GDP ratio starts to decline in 2023 but remains close to 200 basis points above baseline.
  - IT regime (ω_{PEG} = 0):
    - Central bank reduces policy rate more gradually than in intermediate regime (rate cut about 20 bps smaller in 2021; policy rates same only in 2023).
    - Greater nominal (and real) depreciation offsets deflationary shock, allowing inflation to reach 2-percent target in 2023.
    - Looser monetary conditions limit output losses; output gap closes two years earlier than under other regimes.
    - Stronger GDP growth helps keep debt-to-GDP ratio close to baseline by 2025.

### IX. Fiscal stimulus simulations and interactions with monetary regimes
- Fiscal deterioration from 2020 shocks (preserved magnitudes):
  - Overall fiscal deficit rose from about 4 percent of GDP in 2019 to about 7 percent in 2020.
  - Central government debt-to-GDP rose by 12 percentage points, from 65 to 77 percent at end-2020.
  - Gross financing needs rose to about 17 percent of GDP in 2020, from 11 percent in 2019.
- Fiscal stimulus simulated (preserved policy design and numbers):
  - Extension of wage subsidies and cash transfers to households in informal sectors for 2021.
  - Increase in capital spending.
  - Offset measures: accelerate tax reform and reduce wage bill.
  - Overall fiscal deficit increases to slightly above 8 percent of GDP in 2021.
  - Estimated fiscal impulse of about 1.5 percent of GDP in 2021 (increase of cyclically adjusted primary fiscal deficit).
- Fiscal stimulus outcomes by regime (preserved findings):
  - Under exchange rate peg:
    - Public debt climbs above 80 percent of GDP in 2021 and 2022 and continues increasing thereafter at a slower rate.
    - Gross financing needs increase to about 19 percent in 2021; financed mostly via increased placement of Treasury bonds with local financial institutions.
    - Higher public debt increases risk premium, negatively affecting domestic demand (crowding out).
    - Despite crowding out, fiscal stimulus helps sustain recovery in 2021 (smaller output gap vs downside scenario).
  - Under IT combined with fiscal stimulus:
    - Debt-to-GDP ratio stabilizes as early as in 2023.
    - Reasons: smaller increase in financing costs, faster growth from stronger monetary easing via greater exchange rate depreciation, and smaller crowding out of private demand.
    - Combined fiscal and monetary responses under IT offset about half of the impact of the negative shock on GDP growth and allow faster closure of the output gap, likely reducing risk of scarring.

### X. Model validation findings and limitations
- Estimation and historical consistency:
  - Morocco’s economy somewhat overheated before the GFC; nonagricultural output gap estimated close to IMF WEO output gap.
  - Overheating driven by low interest rates and undervalued exchange rate.
  - Fiscal balance worsened after the GFC; GDP growth slowed markedly after the crisis due to supply-side developments outside model scope.
  - Inflation peaked in 2008 driven by overheated economy, undervalued exchange rate, and global food-price increase; pressures dissipated quickly.
  - Real exchange rate remained slightly overvalued in recent years.
- Recursive forecast performance:
  - Model predicts most turning points in output and inflation.
  - Missed turning points attributable to exogenous factors outside model scope (post-GFC growth slowdown, domestic price shock of 2015–16, gradual fiscal consolidation after the GFC).

### XI. Conclusions and policy implications
- The semi-structural model:
  - Provides a simple, transparent framework consistent with New Keynesian theory to analyze monetary, exchange rate, and fiscal interactions for Morocco.
  - Is tractable for policy analysis under alternative monetary regimes and financing constraints.
- Policy-relevant implications (preserved from simulations):
  - Greater exchange-rate flexibility (intermediate or IT regimes) increases central bank room to ease monetary conditions, can speed output recovery, and can reduce the fiscal cost of borrowing relative to a strict peg.
  - Under constrained fiscal space, a combination of targeted fiscal support and a more flexible exchange-rate/monetary regime can mitigate output losses and reduce scarring, while helping stabilize debt dynamics sooner.
- Model utility:
  - Simplicity facilitates intuitive understanding and usability for frequent policy analysis.
  - Validation via IRFs, consistency checks of unobservables, and recursive forecasts supports practical application to Morocco’s Covid-19 recovery policy design.

*Source: IMF working paper wpiea2021190-print-pdf (content unit provided).*

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

### wpiea2021190-print-pdf - References .............................................................................................................

### I. Introduction
- Purpose: develop a parsimonious, semi-structural model of the Moroccan economy to assess propagation of key shocks, medium- and long-term impacts, and effects of alternative domestic macroeconomic policy responses.
- Calibrate model to capture key stylized facts of Morocco’s economy and present scenarios of policy responses to the Covid-19 pandemic under different monetary policy regimes.
- Monetary regimes considered:
  - peg exchange rate regime;
  - intermediate regime: peg with a band (the current one);
  - inflation targeting regime with flexible exchange rate.
- Modeling choices:
  - Focus on a few variables consistent with the New Keynesian framework to retain theoretical consistency and parsimony.
  - Drop sectors/variables less relevant or difficult to model for Morocco.
  - Fiscal authority chooses a single policy variable: the cyclically adjusted primary balance.
- Relationship to other models:
  - More complex DSGE models exist for Morocco (e.g., MOPAM by Bank Al-Maghrib, Sarr, Benlamine, and Munkacsi (2019)), but the presented model aims for greater simplicity and higher usability for frequent policy analysis.
- Organization: Section II describes the model, Section III discusses calibration, Section IV applies the model to Covid-19 recovery scenarios, Section V concludes.

### II. The Model — Structure and Key Features
- Model type: semi-structural, steady-state (transitional steady-state solution), gap-format (variables expressed as deviations from trend).
- Frequency: recast to annual frequency; extended to include a rudimentary fiscal and debt-accounting block.
- Theoretical blend: New Keynesian emphasis on nominal and real rigidities and aggregate demand with RBC/DSGE methods and rational expectations; allows backward- and forward-looking expectations and substantial inertia to match data.
- Five building blocks (summarized in Figure 1):
  - Aggregate demand split into agricultural (exogenous) and nonagricultural parts (IS curve).
  - Prices: core and non-core CPI components; Phillips curve for core inflation; non-core prices determined by oil prices, agricultural production, and exogenous shocks.
  - Monetary policy: reflects exchange rate peg with horizontal band and relatively closed capital account — nominal exchange rate is a key exogenous monetary policy variable; limited capital mobility allows central bank influence on market interest rate via a weighted average of policy rate and UIP-implied rate. Model can also accommodate an inflation-targeting regime with domestic interest rate as main instrument (forward-looking reaction function and exchange rate reflecting UIP).
  - Fiscal policy: fiscal reaction function where fiscal authority chooses a cyclically adjusted primary deficit, stabilizes output with countercyclical stance while stabilizing gross debt around a threshold (noted policy objective: stabilize debt around 60 percent of GDP).
  - Debt dynamics and financing: authorities choose accumulation of domestic or foreign-currency-denominated debt; net debt (gross public debt less central bank foreign reserves) affects market interest rates; when gross public sector debt rises above its threshold level, risk premium increases and so does the neutral real interest rate; effect can be partly offset by an increase of international reserves above steady-state.

### A. Aggregate Demand (IS curve)
- Nonagricultural IS relationship (equation preserved as in source):
  - ŷ_t^{NAgr} = a_1 ŷ_{t-1}^{NAgr} + a_2 E_t ŷ_{t+1}^{NAgr} − a_3 mci_t + a_4 f_t^{imp} + a_5 ŷ_t^{*} + ε_t^{y}
- Definitions and components:
  - ŷ_t^{NAgr}: nonagricultural output gap (deviation of log real output from trend).
  - mci_t: real monetary conditions index.
  - f_t^{imp}: fiscal impulse.
  - ŷ_t^{*}: foreign output gap.
  - ε_t^{y}: aggregate demand shock.
  - E_t denotes model-consistent ("rational") forward-looking expectations.
  - Gapped variables: x̂_t = x_t − x̃_t (actual minus estimated trend).
- All parameters a_i, b_i, e_i, f_i, g_i are positive.

- Real monetary conditions index (preserved equation form):
  - mci_t = a_6 (r̂_t^{mix} + cr_spread_t) + (1 − a_6)(− ẑ_t)
- Definitions and components for mci:
  - r̂_t^{mix}: weighted average deviation of one-year and longer-term domestic real government bond rates from trend.
  - cr_spread_t: exogenous credit spread.
  - ẑ_t: deviation of the real exchange rate from its trend.
  - Simplifying assumption: one-year bond rate equals the domestic monetary policy rate.

### Model Implementation Notes and Policy-Relevant Mechanisms
- Agricultural output treated as exogenous and separate from the IS-driven nonagricultural demand.
- Inflation decomposition: core inflation driven by Phillips curve with dependence on past and expected inflation, output gap, exchange rate, and pass-through from non-core; non-core driven by oil, agricultural production, exogenous shocks.
- Monetary regime specifications:
  - Under peg-with-band: nominal exchange rate is exogenous; limited capital mobility implies market interest rate is a weighted average of central bank policy rate and UIP-implied rate (foreign interest rate plus country risk premium).
  - Under inflation targeting: domestic interest rate acts as main policy instrument; exchange rate follows UIP.
- Fiscal policy objective operationalized via cyclically adjusted primary deficit and explicit gross debt stabilization around a threshold (policy-consistent threshold cited as 60 percent of GDP under recent arrangements).
- Debt dynamics: gross public debt, central bank foreign reserves, net debt concept, and their influence on risk premium and neutral real interest rate are explicitly modeled.

*Source: IMF working paper wpiea2021190-print-pdf (content unit provided).*

### Section II.C), while the longer-term rate is derived adding a term premium to the domestic

### wpiea2021190-print-pdf - Section II.C), while the longer-term rate is derived adding a term premium to the domestic

### Monetary policy, aggregate demand, and key definitions
- Real exchange rate log definition and interpretation:
  - ∆푧푡 = ∆푠푡𝑀퐴퐷/퐸푈푅 + 휋푡∗ − 휋푡, where 푠푡 are units of domestic currency, the dirham, per euro; 휋푡∗ is foreign CPI inflation and 휋푡 is domestic CPI inflation.
  - An increase (decrease) in 푧푡 implies a more depreciated (appreciated) value of the domestic currency in real terms.
- Fiscal impulse definition:
  - 푓푡𝑖𝑚푝 = (푐푎푑푡 − 푐푎푑푡−1) + 푓4휀푡𝑏𝑡𝑎𝑟. (Equation (3))
  - Positive (negative) 푓4 captures expansionary (contractionary) effects of a larger debt threshold.
- Monetary conditions index and transmission:
  - Monetary policy affects aggregate demand through the real exchange rate gap and real interest rate gap aggregated in 푚푐푖푡.
  - Tighter monetary policy (higher 푚푐푖푡) reduces the output gap via higher real interest rate (higher 푟̂푡) or an appreciated real exchange rate (lower 푧̂푡).
  - Fiscal policy affects aggregate demand directly through the fiscal impulse; parameter 푎4 is the impact multiplier.
- Short- and longer-term interest rates:
  - Central banks control the short end; policy rate equals short-term interbank/treasury bill rate.
  - Longer-term rate with maturity k quarters: 푖𝑡𝑘 = 푖𝑡𝑀푃 + ∑_{푖=1}^{푘} 퐸𝑡 푖_{𝑡+𝑖}_{𝑀푃} + 푝푟푒푚 (text description).

### Aggregate supply: core and noncore inflation dynamics
- Core inflation Phillips curve:
  - 휋𝑡𝐶표𝑟𝑒 = 푏1 휋𝑡−1𝐶표𝑟𝑒 + (1−푏1) 𝐸𝑡 휋𝑡+1𝐶표𝑟𝑒 + 푏2 푟𝑚𝑐𝑡 + 휀𝑡𝜋,𝐶표𝑟𝑒. (Equation (4))
  - 푟𝑚𝑐𝑡 = 푏3 𝑦̂𝑡𝑁𝐴𝑔𝑟 + (1−푏3) 𝑧̂𝑡𝐶표𝑟𝑒. (Equation (5))
  - Core-based real exchange rate: ∆푧𝑡𝐶표𝑟𝑒 = ∆푠𝑡𝑀퐴퐷/퐸푈푅 + 휋𝑡∗ − 휋𝑡𝐶표𝑟𝑒.
  - Calibrated 푏1 represents share of backward-looking agents; product 푏2∙푏3 measures Phillips curve slope w.r.t non-agricultural output gap.
- Noncore inflation (regulated, commodity, volatile food prices):
  - 휋𝑡𝑁𝐶표𝑟𝑒 = 푏4 휋𝑡−1𝑁𝐶표𝑟𝑒 + (1−푏4)(휋𝑡𝑇𝑎𝑟,𝑁𝐶표𝑟𝑒 − 푏5 𝑦̂𝑡𝐴𝑔𝑟 − 푏6 (1− 𝑤𝐶𝑃𝐼) 𝑟𝑝̂𝑡 ) + 푏7 ∆휋𝑡𝑂𝑖𝑙 + 휀𝑡𝜋,𝑁𝐶표𝑟𝑒. (Equation (6))
  - Variables: 𝑦̂𝑡𝐴𝑔𝑟 = agricultural output gap; 𝑟𝑝̂𝑡 = relative price gap between noncore and core; ∆휋𝑡𝑂𝑖𝑙 = imported oil price inflation.
- Total inflation aggregation:
  - 휋𝑡 = 𝑤𝐶𝑃𝐼 휋𝑡𝐶표𝑟𝑒 + (1−𝑤𝐶𝑃𝐼) 휋𝑡𝑁𝐶표𝑟𝑒.
- Model supply-side assumptions:
  - Aggregate supply largely exogenous; economy grows along calibrated potential output path.
  - Potential growth can be altered by equilibrium real interest rate or non-Keynesian expectations of future fiscal policy.

### Exchange rate regime, UIP, and monetary policy reaction function
- Current regime (peg plus band):
  - Morocco: exchange rate peg with horizontal band of ±5 percent and relatively closed capital account.
  - Dirham nominal exchange rate (interim regime) is weighted average of currency-basket-based peg and market-driven fluctuation:
    - 푠𝑡𝑀퐴퐷/퐸푈푅 = 휔𝑃𝐸𝐺 푠𝑡𝑀퐴퐷/퐸푈푅,𝑃𝐸𝐺 + (1−휔𝑃𝐸𝐺) 푠𝑡𝑀퐴퐷/퐸푈푅,𝐹𝐿. (Equation (7))
  - Currency basket definition and weights:
    - 푠𝑡𝐵𝑎𝑠𝑘𝑒𝑡 = 휔𝑠 푠𝑡𝑀퐴퐷/퐸푈푅,𝑃𝐸𝐺 + (1−휔𝑠) 푠𝑡𝑀퐴퐷/𝑈𝑆𝐷,𝑃𝐸𝐺 = 푠𝑡𝑀퐴퐷/퐸푈푅,𝑃𝐸𝐺 + (1−휔𝑠) 푠𝑡𝐸𝑈𝑅/𝑈𝑆𝐷. (Equation (8))
    - Weights equal to 60 and 40 percent vis-à-vis the Euro and US dollar, respectively (text reference).
  - Fluctuation-band (market-driven) component via uncovered interest parity (UIP):
    - 푠𝑡𝑀퐴퐷/퐸푈푅,𝐹𝐿 = 𝐸𝑡 푠𝑡+1𝑀퐴퐷/퐸푈푅 + 푖𝑡𝐸𝑈𝑅 − 푖𝑡 + 푝푟𝑒𝑚𝑡 + 휀𝑡𝑠. (Equation (9))
    - Volatile part depends on expected nominal exchange rate, foreign and domestic interest rate differentials 푖𝑡𝐸𝑈𝑅 − 푖𝑡 and risk premium 푝푟𝑒𝑚𝑡; 휀𝑡𝑠 is transitory shock.
  - Realignment under peg requires internal devaluation if real exchange rate misaligned; peg enforces medium-term PPP:
    - ∆푧̃ = ∆푠̃𝑀퐴퐷/퐸푈푅 + 휋𝑇𝑎𝑟,𝐸푈푅 − 휋𝑇𝑎𝑟. (Equation (10))
    - If nominal peg (∆푠̃𝑀퐴퐷/퐸푈푅 = 0) and desire to keep competitiveness (∆푧̃ = 0), then 휋𝑇𝑎𝑟,𝐸푈푅 = 휋𝑇𝑎𝑟.
- Policy reaction function and interest rate composition:
  - Interest rate that enters IS has two components: peg-based (weight 휔𝑃𝐸𝐺) and shadow flexible-exchange-rate-based (weight 1−휔𝑃𝐸𝐺).
  - Peg-based interest rate is weighted average of policy-rate-for-inflation-control (weighted by 푐1) and financial-market-driven shadow UIP term (weighted by 1−푐1).
  - Full policy equation (text display, Equation (11)) preserves parameters 휔𝑃𝐸𝐺, 푐1, 푐2, 푐3, and their IT analogs, and includes monetary shock 휀𝑡𝑖.
  - Parameter 푐1 proxies the effect of capital controls (ability to set domestic interest rate different from foreign rate).
- Risk premium dynamics:
  - 푝푟𝑒𝑚𝑡 = 푐4 푝푟𝑒𝑚𝑡−1 + (1−푐4)[푝푟𝑒𝑚̅ + 푐5[(푏𝑡 − 푏𝑡𝑡𝑎𝑟) − (𝑟𝑒𝑠𝑡 − 𝑟𝑒𝑠𝑡𝑡𝑎𝑟)]] + 휀𝑡𝑝𝑟𝑒𝑚. (Equation (12))
  - 푝푟𝑒𝑚̅̅̅̅̅̅̅ is steady-state level; (1−푐4)∗푐5 is elasticity of risk premium vis-à-vis public net debt.
  - Calibration note: debt elasticity of risk premium calibrated to be 0.03 (3 basis point for each 1-percent increase in debt) per calibration section (text footnote).
- Inflation-targeting regime alternative:
  - Under IT, inflation target 휋𝑇𝑎𝑟 is nominal anchor; central bank follows forward-looking rule:
    - 푖𝑡 = 푐1𝐼𝑇 푖𝑡−1 + (1−푐1𝐼𝑇)(푖̃𝑡 + 푐2𝐼𝑇(𝐸𝑡 휋𝑡+1 − 휋𝑇𝑎𝑟)) + 휀𝑡𝑖. (Equation (13))
  - In IT, nominal exchange rate becomes endogenous and follows UIP also in short run:
    - ∆푠𝑡 = [𝐸𝑡 ∆푠𝑡+1 + 푖𝑡𝐸𝑈𝑅 + 푝푟𝑒𝑚𝑡] + 휀𝑡𝑠. (Equation (14))

### Fiscal block: rules, debt dynamics, and financing structure
- Fiscal policy aggregation and role:
  - Fiscal authority chooses cyclically adjusted primary balance (푐푎푑𝑡) as sole policy variable, guided by cyclical position and debt-to-GDP ratio.
  - Model aggregates fiscal operations; supply side (potential growth) is exogenous and constant for simulations.
- Fiscal policy reaction function:
  - 푐푎푑𝑡 = 푓7(푐푎푑𝑡−1 − 푓10 𝑦̂𝑡) + (1−푓7)(푐푎푑𝑡𝑡𝑎𝑟 − 푓8 𝑏𝑡𝑑𝑒𝑣) + 휀𝑡𝑐𝑑. (Equation (13) in text)
  - Trade-offs: smooth fiscal balance vs. stabilize gross public debt around threshold 푐푎푑𝑡𝑡𝑎𝑟, with debt deviation 𝑏𝑡𝑑𝑒𝑣 influencing tighter policy.
  - Debt deviation process: 𝑏𝑡𝑑𝑒𝑣 = 푓9(𝑏𝑡 − 𝑏𝑡𝑡𝑎𝑟) + (1−푓9) 𝐸𝑡 𝑏𝑡+1𝑑𝑒𝑣. (Equation (15))
- Debt decomposition and laws of motion:
  - Gross public debt: 푏𝑡 = 푏𝑡1𝑌 + 푏𝑡5𝑌 + 푏𝑡𝐹5𝑌. (Equation (16))
  - One-year domestic debt law of motion:
    - 푏𝑡1𝑌 = 휃𝑡1𝑌 (𝑑𝑡 + ∆𝑥𝑡) + 푏𝑡−1 1𝑌 /(1+𝑔𝑡). (Equation (17))
    - 휃𝑡1𝑌 = time-variant share of deficit financed with one-year domestic bonds.
  - Five-year domestic debt accumulation:
    - 푏𝑡5𝑌 = 푏𝑡5𝑌,𝑁𝑒𝑤 + 푏𝑡−1 5𝑌,𝑁𝑒𝑤/(1+𝑔𝑡) + 푏𝑡−2 5𝑌,𝑁𝑒𝑤/[(1+𝑔𝑡)(1+𝑔𝑡−1)] + 푏𝑡−3 5𝑌,𝑁𝑒𝑤/[(1+𝑔𝑡)(1+𝑔𝑡−1)(1+𝑔𝑡−2)] + 푏𝑡−4 5𝑌,𝑁𝑒𝑤/[(1+𝑔𝑡)(1+𝑔𝑡−1)(1+𝑔𝑡−2)(1+𝑔𝑡−3)]. (Equation (18))
    - New five-year issuance:
      - 푏𝑡5𝑌,𝑁𝑒𝑤 = 휃𝑡5𝑌 (𝑑𝑡 + ∆𝑥𝑡) + 푏𝑡−5 5𝑌,𝑁𝑒𝑤 / [(1+𝑔𝑡)(1+𝑔𝑡−1)(1+𝑔𝑡−2)(1+𝑔𝑡−3)(1+𝑔𝑡−4)]. (Equation (19))
    - 휃𝑡5𝑌 is share of deficit financed with five-year bonds; renewal of five-year bond captured by lagged term.
- Financing decision:
  - Government chooses domestic vs. foreign debt composition dynamically via 휃 shares and rollover structure.

### Calibration and model validation approach
- Calibration objectives:
  - Reproduce unobserved variables (potential output, equilibrium real exchange rate) consistent with accepted Moroccan business cycle narrative.
  - Generate reasonable recursive forecasts with inflation and output converging to steady-state over medium term.
- Strategy and constraints:
  - Use previous models for Morocco where available (Benlamine and others 2018; Achour and others 2021) and judgment informed by literature and past staff practice.
  - Iterative fine-tuning to obtain reasonable intuitive paths for unobservables (Geweke 1999; Fukac and Pagan 2010).
  - Rare use of OLS regressions only for autoregressive terms.
- Calibration table:
  - Table 1 lists main parameters and steady-state values (referenced in text for model implementation).

*Source: wpiea2021190-print-pdf - Section II.C), while the longer-term rate is derived adding a term premium to the domestic*

### 0.3 Output gap persistence OLS; iterative adjustment

### 0.3 Output gap persistence OLS; iterative adjustment

### Aggregate-demand and output-gap parameters
- 푎2: 0.3 — Output gap persistence. Method: OLS; iterative adjustment.
- Forward-looking part of aggregate demand: 0.1. Method: Iterative adjustment; comparative studies (label: 푎3).
- Elasticity of the output gap wrt monetary conditions: 0.125. Method: Iterative adjustment; comparative studies (label: 푎4).
- Elasticity of the output gap wrt the fiscal impulse: 0.6. Method: OLS; staff judgment (label: 푎5).
- Elasticity of the output gap wrt foreign demand: 0.35. Method: OLS; iterative adjustment (label: 푎1).

### Inflation and marginal cost parameters
- Core inflation persistence: 0.35. Method: OLS; iterative adjustment (label: 푏2).
- Elasticity of core inflation wrt marginal cost: 0.065. Method: OLS; iterative adjustment.

### Additional parameter labels present in the text
- Iterative adjustment; comparative studies (푎3, 푎4).
- OLS; iterative adjustment (multiple entries as above).

### Monetary Policy Parameters (휔푃퐸퐺 and variants)
- 휔푃퐸퐺: 0.8 — The degree to which the economy is insulated from external developments. Method: Current regime; staff judgment.
- 휔푃퐸퐺: 0.5 — The degree to which the economy is insulated from external developments. Method: Regime with a more extensive use of the ER band; staff judgment.
- 휔푃퐸퐺: 0.0 — The degree to which the economy is insulated from external developments. Method: Floating exchange rate and inflation targeting; staff judgment.

- 푐1: 0.5 — Central bank sterilization capacity under the peg. Method: Staff judgment.
- 푐2: 0.6 — Central bank interest rate smoothing under the peg. Method: OLS; iterative adjustment.
- 푐3: 0.2 — Central bank inflation aversion under the peg. Method: Staff judgment.
- 푐4: 0.75 — Risk premium persistence. Method: Iterative adjustment.
- 푐5: 0.03 — Elasticity of the risk premium with respect to debt and international reserves. Source/method: Schumacher and Żochowski, (2017); iterative adjustment.

- Under IT (inflation targeting) regime:
  - 푐1IT: 0.3 — Central bank interest rate smoothing under IT. Method: Annualized from Benlamine et al, 2018.
  - 푐2IT: 2.5 — Central bank inflation aversion under IT. Source: Benlamine et al, 2018.

### Fiscal Policy Parameters
- 푓7: 0.6 — Fiscal policy smoothing. Method: Iterative adjustment; staff judgment.
- 푓8: 0.05 — Debt aversion. Method: Iterative adjustment; staff judgment.
- 푓9: 0.5 — Debt smoothing. Method: Iterative adjustment; staff judgment.
- 푓10: 0.2 — Reaction of fiscal policy to the output gap. Method: Iterative adjustment; staff judgment.

### Steady-state parameters
- 푝푟푒̅̅̅̅̅̅̅: 1 — Long-term risk premium. Method: Calibrated to match the historic interest rate differential.
- ∆푧̅: 0 — Long-term (trend) real appreciation. Method: Calibrated to match the historical average.
- ∆푦̅푁퐴푔푟, ∆푦̅퐴푔𝑟: 4 — Long-term nonagricultural and agricultural GDP growth. Method: Calibrated to match the historical averages.
- 휋̃: 2 — Implied inflation target. Method: Calibrated to match the PPP with ∆푧̅=0.
- 푏̅𝑡𝑎𝑟: 0.6 — Long-term debt-to-GDP ratio. Method: Calibrated to match the debt threshold in IMF-supported arrangements.
- 푏̅1𝑌,𝑡𝑎𝑟: 0.05 — One-year debt-to-GDP ratio. Method: Calibrated to match the historical average.
- 푏̅5𝑌,𝑡𝑎𝑟: 0.4 — Five-year debt-to-GDP ratio. Method: Calibrated to match the historical average.
- 푟푒푠̅̅̅̅̅푡𝑎𝑟: (label present; value not provided in the supplied excerpt).

*Source: wpiea2021190-print-pdf - 0.3 Output gap persistence OLS; iterative adjustment*

### 0.22 International reserves-to-GDP ratio Calibrated to match the

### wpiea2021190-print-pdf - 0.22 International reserves-to-GDP ratio Calibrated to match the

### Calibration validation and approach
- Validation methods used:
  - Comparison of model-based impulse response functions (IRFs) with empirical IRFs where available; expert judgment where empirical IRFs are not available (Morocco case).
  - Examination of estimation of unobserved variables via a multivariate (Kalman) filter.
  - Assessment of recursive forecasts (8-years-ahead, repeated from 2004 to 2019).
- Monetary policy framework for IRFs: exchange rate peg regime, horizontal band, relatively closed capital account.
- Diffuse Kalman filter used for nonstationary variables (De Jong 1991).

### Impulse responses — shocks analyzed and main findings
- Three shocks considered:
  - Aggregate demand shock: unexpected opening of a positive (non-agricultural) output gap by 1 percentage point for one year.
  - Risk premium shock: unexpected increase in foreign interest rates by 1 percentage point for one year.
  - Fiscal shock: unexpected one-year increase of the primary deficit by 1 percentage point of GDP.

- Temporary positive aggregate demand shock (1 percentage point nonagricultural output gap):
  - Greater tax revenues and lower cyclically adjusted spending bring the headline primary balance into a surplus, although the cyclically adjusted primary balance deficit initially increases because of the positive output gap.
  - Debt-to-GDP ratio initially falls; fiscal authority then slowly moves to a deficit to return to steady state.
  - Nominal exchange rate unchanged; domestic inflation increases, real exchange rate appreciates relative to steady state, tightening monetary policy stance.
  - Output gap closes in about five years; gross debt, inflation, and exchange rate take longer to return to steady state due to gradual fiscal response.
  - Dynamics align with Morocco’s observed behavior over the last 30 years where these variables moved largely from structural changes rather than cyclical forces.

- Risk premium shock (1 percentage point rise in foreign interest rates for one year):
  - Real domestic interest rate increases, tightening monetary policy stance.
  - Adverse output impact relatively small compared to increase in debt-to-GDP ratio.
  - Fiscal authority gradually tightens stance; primary balance improves by 10-15 basis points relative to baseline.
  - Return to steady state takes more than 10 years despite one-year shock; matches post-GFC gradual fiscal consolidation in Morocco.

- Fiscal expansion (one-year increase of primary deficit by 1 percent of GDP):
  - Authorities bring gross debt back via long series of primary surpluses, withholding aggregate demand.
  - Long-run multiplier is negative for the temporary stimulus, depressing aggregate demand and creating downward inflationary pressure.
  - Debt-to-GDP ratio starts declining only in the 8th year after the initial stimulus.
  - Consistent with Morocco’s post-GFC experience where higher energy-related subsidies increased deficits and reforms were gradual (2013-2105 noted in text).

### Estimation of unobserved variables
- Variables estimated via model + multivariate Kalman filter: output gap, exchange rate gap, interest rate gap.
- For linear systems Kalman filter is optimum in least squares sense (Hamilton 1994).
- Findings from estimates:
  - Morocco’s economy somewhat overheated before the GFC; nonagricultural output gap estimated close to IMF WEO output gap.
  - Overheating driven by low interest rates and undervalued exchange rate.
  - Fiscal balance worsened after the GFC; GDP growth slowed markedly after the crisis, likely due to supply-side developments outside the model.
  - Limited demand-side shocks post-GFC.
  - Inflation peaked in 2008 driven by overheated economy, undervalued exchange rate, and global food-price increase; inflationary pressures dissipated quickly.
  - Real exchange rate remained slightly overvalued in recent years, consistent with External Balance Approach findings cited.

### Recursive forecasts and predictive ability
- Recursive forecasting method:
  - Kalman filter to identify initial conditions for each year (t).
  - Series of 8-years-ahead recursive forecasts, shifting initial conditions year-by-year from 2004 to 2019 (six key recursive forecasts).
  - Domestic variables forecast endogenously; foreign variables use actual realizations.
- Performance:
  - Model predicts most turning points in output and inflation.
  - Missed turning points attributable to exogenous factors outside model scope: post-GFC growth slowdown, domestic price shock of 2015–16, gradual fiscal consolidation after the GFC.

### Policy-relevant exercise — downside scenario and policy options
- Baseline staff expectations (context for exercise):
  - Morocco expected to recover from 2020 shocks: growth rebounds from -7 percent in 2020 to 4.5 percent in 2021 and 3.9 percent in 2022.
  - Harvest returns to historical average; vaccination progress; monetary and fiscal policies remain supportive.
  - Output gap fully reabsorbed and inflation returns to 2 percent only in 2025.

- Downside scenario assumptions:
  - Slower vaccination progress and persistent virus circulation necessitate extended lockdowns for most of 2021 in Morocco and main trading partners.
  - GDP growth slows to 1.5 percent in 2021, keeping output gap below baseline by about 2 percentage points.
  - GDP growth gradually returns to baseline in following years but with damage to output potential.

- Question addressed: how could authorities respond given reduced fiscal and monetary space at end-2020?

### Monetary policy scenarios and modelled outcomes
- Central bank context in 2020:
  - Policy interest rate cut by 75 bps in 2020 to 1.5 percent.
  - Exchange rate band expanded to ±5 percent in March 2020.
  - Dirham depreciated by 6 percent against the basket in March 2020, then partially recovered.

- Three exchange rate/monetary regimes simulated via parameter 휔PEG values:
  - Peg regime: 휔PEG = 0.8
  - Intermediate ER regime (full use of band): 휔PEG = 0.5
  - Inflation targeting (IT) regime (exchange rate floats): 휔PEG = 0

- Simulation findings:
  - Peg regime:
    - Central bank lowers interest rates by around 30 basis points.
    - Fall in market interest rates partly offset by increased risk premium from higher debt-to-GDP.
    - Dirham depreciates only marginally.
    - Output gap slow to close.
    - Debt-to-GDP ratio remains elevated by about 2½ percentage points relative to baseline.
  - Intermediate ER regime:
    - Central bank cuts interest rate by almost 100 basis points.
    - Much larger nominal and real depreciation versus peg regime (close to full use of band).
    - Inflation closer to baseline; output recovers somewhat faster.
    - Debt-to-GDP ratio starts to decline in 2023 but remains close to 200 basis points above baseline.
  - IT regime:
    - Central bank reduces policy rate more gradually than in intermediate regime (rate cut about 20 bps smaller in 2021; policy rates same only in 2023).
    - Greater nominal (and real) depreciation offsets deflationary shock, allowing inflation to reach 2-percent target in 2023.
    - Looser monetary conditions limit output losses; output gap closes two years earlier than under other regimes.
    - Stronger GDP growth helps keep debt-to-GDP ratio close to baseline by 2025.

### Fiscal policy simulations and interactions with monetary regimes
- Fiscal deterioration from 2020 shocks:
  - Overall fiscal deficit rose from about 4 percent of GDP in 2019 to about 7 percent in 2020.
  - Central government debt-to-GDP rose by 12 percentage points, from 65 to 77 percent at end-2020.
  - Gross financing needs rose to about 17 percent of GDP in 2020, from 11 percent in 2019.

- Fiscal stimulus simulated:
  - Extension of wage subsidies and cash transfers to households in informal sectors for 2021.
  - Increase in capital spending.
  - Offset measures: accelerate tax reform and reduce wage bill.
  - Overall fiscal deficit increases to slightly above 8 percent of GDP in 2021.
  - Estimated fiscal impulse (increase of cyclically adjusted primary fiscal deficit) of about 1.5 percent of GDP in 2021.

- Fiscal stimulus outcomes by monetary regime:
  - Under exchange rate peg:
    - Public debt climbs above 80 percent of GDP in 2021 and 2022 and continues increasing thereafter at a slower rate.
    - Gross financing needs increase to about 19 percent in 2021; financed mostly via increased placement of Treasury bonds with local financial institutions.
    - Higher public debt increases risk premium, negatively affecting domestic demand (crowding out).
    - Despite crowding out, fiscal stimulus helps sustain recovery in 2021 (smaller output gap vs downside scenario).
  - Under IT regime combined with fiscal stimulus:
    - Debt-to-GDP ratio stabilizes as early as in 2023.
    - Reasons: smaller increase in financing costs (less pronounced rise of interest rates), faster growth from stronger monetary easing via greater exchange rate depreciation, and smaller crowding out effect on private demand.
    - Combined fiscal and monetary responses under IT offset about half of the impact of the negative shock on GDP growth and allow faster closure of the output gap, likely reducing risk of scarring.

### Conclusions and model utility
- The paper presents a simple macro-fiscal semi-structural model consistent with the New Keynesian framework focusing on a few key variables.
- Advantages:
  - Simplicity facilitates intuitive understanding of monetary and fiscal transmission mechanisms.
  - Model can be tailored to different fiscal, monetary, or exchange rate regimes.
- Validation performed via IRFs, consistency checks of unobserved variables with accepted narrative, and recursive forecast accuracy.
- Practical application demonstrated: assessing fiscal and monetary space for Moroccan authorities under alternative monetary policy and exchange rate regimes in response to a slower recovery from Covid-19.

*Source: wpiea2021190-print-pdf - 0.22 International reserves-to-GDP ratio Calibrated to match the*

### REFERENCES

### REFERENCES

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### Appendix A — The Model: structure and key equations
- Model decomposes Total GDP and sectoral output:
  - Total GDP: ŷ_t = w_GDP ŷ_t_NAgr + (1−w_GDP) ŷ_t_Agr
  - Nonagricultural output gap (Dynamic IS curve): ŷ_t_NAgr = a1 ŷ_{t−1}_NAgr + a2 E_t ŷ_{t+1}_NAgr − a3 mci_t + a4 f_t_imp + a5 ŷ_t^* + ε_{t ŷ, NAGR}
  - Agricultural output gap: ŷ_t_Agr = a7 ŷ_{t−1}_Agr + ε_{t ŷ, AGR}
- Monetary conditions and real rates:
  - Monetary conditions index: mci_t = a6 (r̂_t_mix + cr_prem_t) + (1−a6)(−ẑ_t)
  - Real interest rate gap mix: r̂_t_mix = w_i r̂_{t 1Y} + (1−w_i) r̂_{t 5Y}
- Inflation block:
  - Total inflation: π_t = w_CPI π_t_Core + (1−w_CPI) π_t_NCore
  - Core inflation (New-Keynesian Phillips curve): π_t_Core = b1 π_{t−1}_Core + (1−b1) E_t π_{t+1}_Core + b2 rmc_t + ε_{t π,Core}
  - Real marginal cost: rmc_t = b3 ŷ_t_NAgr + (1−b3) ẑ_t_Core
  - Non-core inflation: π_t_NCore = b4 π_{t−1}_NCore + (1−b4)(π_t_Tar,NCore − b5 ŷ_t_Agr − b6 (1−w_CPI) r p̂_t) + b7 ∆π_t_Oil + ε_{t π,NCore}
- Exchange rate and relative prices:
  - Currency basket: ∆s_t = ∆s_t MAD/EUR + (1−ω_s) ∆s_t EUR/USD
  - Relative prices: r p_t = π_t_NCore − π_t_Core
  - Real exchange rate adjusted for relative prices: ẑ_t_Core = ẑ_t + w_CPI r p̂_t
  - PPP condition: z_t = s_t + p_t^* − p_t
- Monetary policy and risk premia:
  - Monetary policy rule: i_t = c1 [ c2 i_{t−1} + (1−c2)( ĩ_t + c3 ( E_t π_{t+1} − π̃ ) ) ] + (1−c1)[ E_t ∆s_{t+1 MAD/EUR} + i_t_EUR + prem_t ] + ε_{t i}
  - Risk premium dynamics: prem_t = c4 prem_{t−1} + (1−c4)[ prem̅ + c5[( b_t − b_t_tar ) − ( res_t − res_t_tar )] ] + ε_{t prem}
- Fiscal block:
  - Fiscal impulse: f_t_imp = ( cad_t − cad_{t−1} ) + f4 ε_{t b_tar}
  - Fiscal reaction function: cad_t = f7 ( cad_{t−1} − f10 ŷ_t ) + (1−f7)( cad_t_tar − f8 b_t_dev ) + ε_{t cd}
  - Cyclically-adjusted primary deficit: cad_t = pd_t + f3 ŷ_t
  - Total deficit: d_t = pd_t + id_t
- Debt and issuance structure:
  - Expected debt deviation path: b_t_dev = f9 ( b_t − b_t_tar ) + (1−f9) E_t b_{t+1}_dev
  - Total government debt decomposition: b_t = b_{t 1Y} + b_{t 5Y} + b_{t F5Y}
  - One-year domestic debt accumulation: b_{t 1Y} = θ_{t 1Y}( d_t + ∆x_t ) + b_{t−1 1Y}/(1+g_t)
  - Five-year domestic debt accumulation and new issuance: b_{t 5Y} and b_{t 5Y,New} defined with multi-period accumulation formulas using growth factors (1+g_t), lagged b_{t−k 5Y,New}, and θ_{t 5Y}( d_t + ∆x_t )
  - Five-year foreign debt accumulation and new issuance: b_{t F5Y} and b_{t F5Y,New} defined with exchange rate adjustments (1+∆s_t MAD/EUR) and growth factors (1+g_t)
- Reserves and interest costs:
  - Foreign reserve accumulation: x_t = ∆x_t + (1+∆s_t MAD/EUR) x_{t−1}/(1+g_t)
  - Reserve reaction function: ∆x_t = g2 ∆x_{t−1} + (1−g2)( ∆x̃_t + g3 ŷ_t − g4 ẑ_t ) + ε_{t x}
  - Total interest cost of debt: id_t = id_{t 1Y} + id_{t 5Y} + id_{t F5Y} − i x_t
  - Interest cost formulas for id_{t 1Y}, id_{t 5Y}, id_{t F5Y} use lagged rates (i_{t−k 5Y}), lagged new issuance, exchange rate adjustments, and growth denominators (1+g_t) terms
  - Interest payment on foreign reserve: i x_t = i_{t−1 EUR} ∙ x_{t−1} ∙ (1+∆s_t MAD/EUR)/(1+g_t)
- Bond rates:
  - One-year domestic bond rate: i_{t 1Y} = i_t + tprem_{t 1Y}
  - Five-year domestic bond rate: i_{t 5Y} = (1/5)∙( i_t + i_{t+1} + i_{t+2} + i_{t+3} + i_{t+4} ) + tprem_{t 5Y}
  - Five-year foreign bond rate: i_{t F5Y} = (1/5)∙( i_{t EUR} + i_{t+1 EUR} + i_{t+2 EUR} + i_{t+3 EUR} + i_{t+4 EUR} + prem_t + prem_{t+1} + prem_{t+2} + prem_{t+3} + prem_{t+4} ) + tprem_{t F5Y}
- Trends and potential growth:
  - Real interest rate trend: r̃_t = h5 r̃_{t−1} + (1−h5)( ∆z̃_{t+1} + r̃_{t EUR} + prem_t )
  - Country risk premium: prem_t = h6 prem_{t−1} + (1−h6)( prem + h12( b_t − b̅ − ( x_t − x̅ ))) + ε_{t prem}
  - Equilibrium real exchange rate trend: ∆z̃_t = h7 ∆z̃_{t−1} + (1−h7) ∆z̅ + ε_{t ∆z}
  - Total trend GDP growth: ∆ỹ_t = w_GDP ∆ỹ_{t NAgr} + (1−w_GDP) ∆ỹ_{t Agr}
  - Potential output growth (nonagricultural): ∆ỹ_{t NAgr} = h8 ∆ỹ_{t−1 NAgr} + (1−h8)( ∆y̅_{NAgr} − h13( r̃_{t 5Y} − r̅ ) ) + ε_{t ∆ỹ, NAgr}
  - Potential output growth (agricultural): ∆ỹ_{t Agr} = h8 ∆ỹ_{t−1 Agr} + (1−h8) ∆y̅_{Agr} + ε_{t ∆ỹ, Agr}

*Source: wpiea2021190-print-pdf - REFERENCES*

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_Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021190-print-pdf.pdf_