## 1belea2020002

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---

### Introduction and purpose
- Uses a structural stochastic “Buffer-Stock” model of the government to assess Belgium’s fiscal stance and trade-offs between short-term costs of fiscal tightening and long-term gains from higher fiscal buffers.
- Medium-term analysis suggests that once the on-going global outbreak of COVID-19 fades out, a gradual consolidation would strike the right balance.

### Key historical facts and fiscal context
- Belgian public debt has fluctuated between 75 and 140 percent of GDP over the last 40 years.
- Primary deficits rose starting in 1974 to reach more than 8 percent of GDP in 1981.
- A multi-year tightening program with a structural tightening close to 10 percent of GDP occurred between 1981 and 1987; debt stabilized close to 140 percent of GDP thereafter.
- A structural tightening of more than 5 percent of GDP during 1992–98 allowed debt to decline to around 87 percent of GDP by 2007.
- Following the global financial crisis, public debt rose again; a gradual tightening of the structural primary balance of 1¾ percent of GDP between 2011 and 2017 helped stabilize debt, but debt remained high (around 100 percent).

### Model characterization and normative implications
- Government maximizes household utility by choosing a change in structural primary balance subject to a debt constraint and market-access risk; key state variables are government debt, the output gap, and the structural primary balance.
- Model features:
  - Rising interest rate in public debt (calibrated to empirical evidence).
  - Risk premium increases with the change in debt.
  - A probability to lose market access that depends on the level and change of government debt.
  - Hysteresis: recessions reduce potential output (human and physical capital losses).
  - One-year implementation delay in fiscal policy.
- Normative implications:
  - Recommends higher fiscal surplus at higher debt levels to preserve sustainability.
  - Recommends counter-cyclical fiscal stance to smooth fluctuations.
  - Highly indebted governments should react less to shocks because the marginal value of an extra unit of buffer is large.

### Empirical behavior of Belgian fiscal policy
- Historical behavior:
  - Government ran sizeable surpluses when debt was high in the 1990s, giving room for fiscal easing in the 2000s.
  - Analyses (Bohn (1998) test, Mauro et al. (2015)) indicate a significant and positive reaction of primary surpluses to rising debt in Belgium.
- Limited cyclical smoothing:
  - Analysis of 1995–2018 data suggests the government did not generally react to the cycle much; the 2009 fiscal stimulus was an exception.
  - No significant positive correlation found between changes in output gaps and changes in structural primary balances (including lagged output gap).

### Model-based medium-term recommendation (2020–25)
- Simulation setup:
  - Takes 2019 as given; computes optimal fiscal path over 2020–25.
  - Assumes a negative shock in 2020 to reflect the unfolding global outbreak of COVID-19 (consistent with an expected output loss of about ½ percentage point of GDP in 2020 embedded in staff’s baseline projections).
  - One-off COVID-19 related spending is excluded from the structural primary balance considered here.
  - Model solution adjusted for ongoing low interest rate environment in line with staff’s baseline projections over 2020–25; beyond 2025 the interest rate-growth differential is assumed to increase linearly over fifteen years to reach a long-run historical average.
- Recommended adjustments by 2025 relative to 2019:
  - Improve overall primary balance by 1½ percent of GDP.
  - Improve structural primary balance by ¾ percent of GDP.
- Implementation timing:
  - Consolidation in structural terms assumed feasible starting in 2021, with a neutral stance in 2020 due to caretaker government status, elapsed year, and ongoing shock.
- Debt outcome and costs:
  - Model-advised medium-term consolidation helps to bring debt down by around 10 percent of GDP relative to its 2019 level, at a moderate and temporary output cost.
  - Benefits of lower debt (lower risk premium and higher capacity to offset shocks) are permanent.

### Fiscal effort and composition
- Overall fiscal effort required to achieve the recommended medium-term structural adjustment is around 2 ½ percent of GDP.
- Baseline staff projection (without corrective measures) suggests structural primary balance will decline by close to 2 percent of GDP by 2025 due to rising spending pressures related to aging.
- Each year, the fiscal effort should combine measures avoiding or compensating slippages and additional measures to increase the structural primary balance.
- Note: pension spending contributes to aggregate demand; avoiding pension spending increases (or offsetting them by cuts elsewhere) implies avoiding a fiscal expansion when debt is high and the output gap is closed, and should not be viewed as fiscal tightening.

### Sensitivities and robustness
- Recommendation to improve structural primary balance holds under a broad range of assumptions.
- Results are:
  - Not very sensitive to the elasticity of debt to interest rate.
  - Not very sensitive to parameters governing market-access risk (optimal policy reacts preemptively).
  - Sensitive to interest and growth rate assumptions: if growth were permanently higher (or lower), the appropriate fiscal stance should be easier (tighter).
  - Somewhat larger consolidation recommended if fiscal multipliers or automatic stabilizers are higher.
  - Slightly lower consolidation recommended if hysteresis were higher to reduce the risk of recession induced by consolidation.

### Comparison with alternative heuristics
- Carnot (2014) rule of thumb (average of a primary gap indicator and a macroeconomic score) recommends a sharper medium-term consolidation for the same initial conditions (high debt, closed output gap, negative structural primary balance) because it does not internalize the record-low interest rate environment.
- An alternative Buffer-Stock model variant with faster normalization of interest rates would also recommend a more ambitious path.

### Concluding assessment
- Once the current crisis is over, rebuilding fiscal buffers is essential to help Belgium confront the next shock from a stronger fiscal position.
- Reducing debt increases the government’s capacity to react to shocks later; this short-term cost is, in the case of Belgium, worth the effort as it increases future welfare and reduces the risk of long-lasting effects from large crises.
- Historical data show limited past cyclical response by Belgian governments; a credible medium-term fiscal consolidation that anchors public debt on a downward path would improve future ability to offset downturns while maintaining debt sustainability.

### Appendix I — Model details (selected elements)
- Government value function maximizes expected utility over consumption and labor with state variables: debt-to-potential-GDP ratio d_t, output gap gap_t, and structural primary balance pb_st_t.
- Per-period utility: c_t^(1−σ)/(1−σ) − ξ y_t*^(1−σ) L_t^(1+η)/(1+η), with ξ calibrated so utility peaks when output equals potential.
- Market pressure specification:
  - Probability to lose market access: P(lmg) = [1 + e^{m_p(d1(1−d_t/d−d2(d_t−d_{t−1})))}]^{-1}, where d1 governs debt limit uncertainty, d2 governs effect of debt change on market-access risk, and d̄ is the debt level at which the probability to lose market access is 50 percent (given no change in debt).
  - If market access is lost, government must keep debt constant under an adverse shock of d3 σ, where σ is the standard deviation of economic shocks.

### Budget constraint and debt accumulation dynamic
- Government budget constraint follows a standard debt accumulation dynamic with a deterministic stock-flow adjustment sf_t that can capture planned one-offs.
- Debt dynamics depend on the growth-adjusted interest rate (1 + r) and on growth (1 + g_t), and include terms for past debt d_{t-1}, change in debt Δd_t, the primary balance pbt, and the stock-flow adjustment sf_t.

### Output, potential output, and hysteresis
- Output produced by linear production function in labor: Y_t = A_t L_t.
- Potential output Ȳ_t is output when labor is at its equilibrium level L̄: Ȳ_t = A_t L̄.
- Productivity A_t is affected by a permanent hysteresis effect of crisis: when production is below perceived potential, unemployed workers' skills, networks, and morale can decay.
- Hysteresis parameter h ≥ 0 represents the size of hysteresis (a permanent loss of potential output level). A threshold h_th determines when hysteresis kicks in.
- Calibrated effect aligns with Mourougane (2017): large hysteresis effects on potential GDP level but no effect on long-run potential growth.
- Source sets A = L = 1 and g* as potential growth absent hysteresis.

### Output gap, shocks, and the fiscal multiplier
- Output deviates from potential due to shocks v_t and because of the primary balance.
- Sensitivity of output gap to the primary balance is set equal to the fiscal multiplier m1 when the economy is at output equilibrium.
- Fiscal multiplier depends on the output gap itself; multipliers are larger in downturns with an additional term having coefficient m2.
- Responsiveness formalized as:
  - ∂gapp(pbt, v_t) / ∂pbt = −m1 (1 − m2 gapp(pbt, v_t))
- Equilibrium between output gap and primary balance is two-way: structural primary balance decisions affect the output gap, and output gap changes affect cyclical primary balance via automatic stabilizers.

### Primary balance decomposition and approximate solution
- Primary balance pbt is the sum of a cyclical component and a structural component decided by the government:
  - pbt = pbt_st + g.gapp_t
- For small shocks, an approximation shows automatic stabilizers reduce the effect of shocks and changes in the primary balance:
  - gapp_t ≈ v_t − m1 pbt_st / (1 + m1 g)
- In this approximation, the structural balance that offsets the underlying shock process is v_t / m1; it is larger when the fiscal multiplier is lower.
- Parameter m1 captures a causal effect of the primary balance on the output gap. Literature interpretations sometimes use m1/(1 + m1.a) to reflect the multiplier net of automatic stabilizers.

### Aggregate resource constraint and fiscal adjustment costs
- Aggregate consumption c_t (private and public) satisfies:
  - c_t = y_t (1 − χ(Δpbt_st)^2)
- The last term represents fiscal adjustment costs modeled as direct resource costs relative to output.
- Adjustment costs reflect implementation costs of changing spending plans, costs associated with tax uncertainty, and difficulty reversing fiscal decisions.

### Calibration for Belgium (Table 1: Baseline Calibration)
- Welfare function:
  - Discount factor β 0.99
  - Risk aversion σ 2
  - Labor elasticity η 1/0.3
  - Weight of labor ξ 1
- Fiscal parameters:
  - Fiscal multiplier when the gap is null m1 0.50
  - Fiscal multiplier sensitivity to shocks m2 3
  - Automatic stabilizers (primary balance semi-elasticity to the gap) a 0.66
  - Adjustment cost χ 3
- Interest rate and debt parameters:
  - Growth-adjusted interest rate when debt is 90 percent of GDP 1.02%
  - Effect of debt level on the risk premium α1 1.5%
  - Effect of debt change on the risk premium α2 0.5%
  - Debt level at which the risk to lose market access is 50% d 150%
  - Debt limit accuracy d1 3
  - Effect of debt change on the risk to lose market access is d2 1
  - Adverse scenario coefficient in case of loss of market access d3 -1%
- Economy parameters:
  - Potential GDP per capita growth 0.9%
  - Shock persistence ρ 0.70
  - Shock size σ 1.8%
  - Hysteresis 10%
  - Hysteresis threshold -1%

### Calibration notes and parameter provenance
- Potential growth assumption is an average of WEO potential growth over 2017–21.
- Growth–interest rate differential is calibrated with 20-year averages of historical data.
- Shock parameters (size σ and persistence ρ) are estimated with past shocks reflecting the output gap and the primary balance; the source gives a formula for v_t in terms of past gapp and Δb_t incorporating m1 and m2.
- Fiscal multiplier calibration is set to 0.5 as assumed in the recommended scenario in the staff report.
- Automatic stabilizer coefficient is taken from Price et al. (2015).
- Most parameters are taken from Fournier and Lieberknecht (2020); some parameters reflect cross-country empirical evidence (e.g., elasticity of debt to interest rate, risk aversion).

*March 18, 2020. BELGIUM, INTERNATIONAL MONETARY FUND.*

### References ___________________________________________________________________________ 13

### 1belea2020002 - References ___________________________________________________________________________ 13

### Introduction and purpose
- Uses a structural stochastic “Buffer-Stock” model of the government to assess Belgium’s fiscal stance and trade-offs between short-term costs of fiscal tightening and long-term gains from higher fiscal buffers.
- Medium-term analysis suggests that once the on-going global outbreak of COVID-19 fades out, a gradual consolidation would strike the right balance.

### Key historical facts and fiscal context
- Belgian public debt has fluctuated between 75 and 140 percent of GDP over the last 40 years.
- Primary deficits rose starting in 1974 to reach more than 8 percent of GDP in 1981.
- A multi-year tightening program with a structural tightening close to 10 percent of GDP occurred between 1981 and 1987; debt stabilized close to 140 percent of GDP thereafter.
- A structural tightening of more than 5 percent of GDP during 1992–98 allowed debt to decline to around 87 percent of GDP by 2007.
- Following the global financial crisis, public debt rose again; a gradual tightening of the structural primary balance of 1¾ percent of GDP between 2011 and 2017 helped stabilize debt, but debt remained high (around 100 percent).

### Model characterization and implications
- The government maximizes household utility by choosing a change in structural primary balance subject to a debt constraint and market-access risk; key state variables are government debt, the output gap, and the structural primary balance.
- Model features:
  - Rising interest rate in public debt (calibrated to empirical evidence).
  - Risk premium increases with the change in debt.
  - A probability to lose market access that depends on the level and change of government debt.
  - Hysteresis: recessions reduce potential output (human and physical capital losses).
  - One-year implementation delay in fiscal policy.
- Normative implications:
  - Recommends higher fiscal surplus at higher debt levels to preserve sustainability.
  - Recommends counter-cyclical fiscal stance to smooth fluctuations.
  - Highly indebted governments should react less to shocks because the marginal value of an extra unit of buffer is large.

### Empirical behavior of Belgian fiscal policy
- Historical behavior:
  - Government ran sizeable surpluses when debt was high in the 1990s, giving room for fiscal easing in the 2000s.
  - Analyses (Bohn (1998) test, Mauro et al. (2015)) indicate a significant and positive reaction of primary surpluses to rising debt in Belgium.
- Limited cyclical smoothing:
  - Analysis of 1995–2018 data suggests the government did not generally react to the cycle much; the 2009 fiscal stimulus was an exception.
  - No significant positive correlation found between changes in output gaps and changes in structural primary balances (including lagged output gap).

### Model-based medium-term recommendation (2020–25)
- Simulation setup:
  - Takes 2019 as given; computes optimal fiscal path over 2020–25.
  - Assumes a negative shock in 2020 to reflect the unfolding global outbreak of COVID-19 (consistent with an expected output loss of about ½ percentage point of GDP in 2020 embedded in staff’s baseline projections).
  - One-off COVID-19 related spending is excluded from the structural primary balance considered here.
  - Model solution adjusted for ongoing low interest rate environment in line with staff’s baseline projections over 2020–25; beyond 2025 the interest rate-growth differential is assumed to increase linearly over fifteen years to reach a long-run historical average.
- Recommended adjustments by 2025 relative to 2019:
  - Improve overall primary balance by 1½ percent of GDP.
  - Improve structural primary balance by ¾ percent of GDP.
- Implementation timing:
  - Consolidation in structural terms assumed feasible starting in 2021, with a neutral stance in 2020 due to caretaker government status, elapsed year, and ongoing shock.
- Debt outcome and costs:
  - Model-advised medium-term consolidation helps to bring debt down by around 10 percent of GDP relative to its 2019 level, at a moderate and temporary output cost.
  - Benefits of lower debt (lower risk premium and higher capacity to offset shocks) are permanent.

### Fiscal effort and composition
- Overall fiscal effort required to achieve the recommended medium-term structural adjustment is around 2 ½ percent of GDP.
- Baseline staff projection (without corrective measures) suggests structural primary balance will decline by close to 2 percent of GDP by 2025 due to rising spending pressures related to aging.
- Each year, the fiscal effort should combine measures avoiding or compensating slippages and additional measures to increase the structural primary balance.
- Note: pension spending contributes to aggregate demand; avoiding pension spending increases (or offsetting them by cuts elsewhere) implies avoiding a fiscal expansion when debt is high and the output gap is closed, and should not be viewed as fiscal tightening.

### Sensitivities and robustness
- Recommendation to improve structural primary balance holds under a broad range of assumptions.
- Results are:
  - Not very sensitive to the elasticity of debt to interest rate.
  - Not very sensitive to parameters governing market-access risk (optimal policy reacts preemptively).
  - Sensitive to interest and growth rate assumptions: if growth were permanently higher (or lower), the appropriate fiscal stance should be easier (tighter).
  - Somewhat larger consolidation recommended if fiscal multipliers or automatic stabilizers are higher.
  - Slightly lower consolidation recommended if hysteresis were higher to reduce the risk of recession induced by consolidation.

### Comparison with alternative heuristics
- Carnot (2014) rule of thumb (average of a primary gap indicator and a macroeconomic score) recommends a sharper medium-term consolidation for the same initial conditions (high debt, closed output gap, negative structural primary balance) because it does not internalize the record-low interest rate environment.
- An alternative Buffer-Stock model variant with faster normalization of interest rates would also recommend a more ambitious path.

### Concluding assessment
- Once the current crisis is over, rebuilding fiscal buffers is essential to help Belgium confront the next shock from a stronger fiscal position.
- Reducing debt increases the government’s capacity to react to shocks later; this short-term cost is, in the case of Belgium, worth the effort as it increases future welfare and reduces the risk of long-lasting effects from large crises.
- Historical data show limited past cyclical response by Belgian governments; a credible medium-term fiscal consolidation that anchors public debt on a downward path would improve future ability to offset downturns while maintaining debt sustainability.

### Appendix I — Model details (selected elements)
- Government value function maximizes expected utility over consumption and labor with state variables: debt-to-potential-GDP ratio d_t, output gap gap_t, and structural primary balance pb_st_t.
- Per-period utility: c_t^(1−σ)/(1−σ) − ξ y_t*^(1−σ) L_t^(1+η)/(1+η), with ξ calibrated so utility peaks when output equals potential.
- Market pressure specification:
  - Probability to lose market access: P(lmg) = [1 + e^{m_p(d1(1−d_t/d−d2(d_t−d_{t−1})))}]^{-1}, where d1 governs debt limit uncertainty, d2 governs effect of debt change on market-access risk, and d̄ is the debt level at which the probability to lose market access is 50 percent (given no change in debt).
  - If market access is lost, government must keep debt constant under an adverse shock of d3 σ, where σ is the standard deviation of economic shocks.

*March 18, 2020. BELGIUM, INTERNATIONAL MONETARY FUND.*

### 4.      The budget constraint of the government is governed by a standard debt

### 4.      The budget constraint of the government is governed by a standard debt

### Budget constraint and debt accumulation dynamic
- The government's budget constraint follows a standard debt accumulation dynamic with a deterministic stock-flow adjustment sf_t that can capture planned one-offs.
- Debt dynamics are expressed with dependence on the growth-adjusted interest rate (1 + r) and on growth (1 + g_t), and include terms for past debt d_{t-1}, change in debt Δd_t, the primary balance pbt, and the stock-flow adjustment sf_t (equation notation as in source).

### Output, potential output, and hysteresis
- Output is produced by a linear production function in labor: Y_t = A_t L_t.
- Potential output Ȳ_t is output when labor is at its equilibrium level L̄: Ȳ_t = A_t L̄.
- Productivity A_t is affected by a permanent hysteresis effect of crisis: when production is below perceived potential, unemployed workers' skills, networks, and morale can decay (Blanchard and Summers, 1987; DeLong and Summers, 2012).
- Hysteresis is governed by parameter h ≥ 0 which represents the size of hysteresis (a permanent loss of potential output level). A threshold h_th determines when hysteresis kicks in.
- The calibrated effect on output level aligns with Mourougane (2017): large hysteresis effects on potential GDP level but no effect on long-run potential growth.
- The source sets A = L = 1 and g* as potential growth absent hysteresis.

### Output gap, shocks, and the fiscal multiplier
- Output deviates from potential due to shocks v_t and because of the primary balance.
- The sensitivity of the output gap to the primary balance is the derivative with respect to the primary balance and is set equal to the usual fiscal multiplier m1 when the economy is at output equilibrium.
- The fiscal multiplier depends on the output gap itself; multipliers are larger in downturns. An additional term with coefficient m2 magnifies the multiplier in downturns.
- The responsiveness is formalized as:
  - ∂gapp(pbt, v_t) / ∂pbt = −m1 (1 − m2 gapp(pbt, v_t))
- The equilibrium between output gap and primary balance is two-way: structural primary balance decisions affect the output gap, and output gap changes affect cyclical primary balance via automatic stabilizers.

### Primary balance decomposition and approximate solution
- Primary balance pbt is the sum of a cyclical component and a structural component decided by the government:
  - pbt = pbt_st + g.gapp_t  (with a denoting automatic stabilizer coefficient in text)
- For small shocks, an approximation shows automatic stabilizers reduce the effect of shocks and changes in the primary balance:
  - gapp_t ≈ v_t − m1 pbt_st / (1 + m1 g)
- In this approximation, the structural balance that offsets the underlying shock process is v_t / m1; it is larger when the fiscal multiplier is lower.
- The parameter m1 captures a causal effect of the primary balance on the output gap. Literature interpretations sometimes use m1/(1 + m1.a) to reflect the multiplier net of automatic stabilizers.

### Aggregate resource constraint and fiscal adjustment costs
- Aggregate consumption c_t (private and public) satisfies:
  - c_t = y_t (1 − χ(Δpbt_st)^2)
- The last term represents fiscal adjustment costs modeled as direct resource costs relative to output.
- Adjustment costs reflect implementation costs of changing spending plans, costs associated with tax uncertainty, and difficulty reversing fiscal decisions.

### Calibration for Belgium (Table 1: Baseline Calibration)
- Welfare function:
  - Discount factor β 0.99
  - Risk aversion σ 2
  - Labor elasticity η 1/0.3
  - Weight of labor ξ 1
- Fiscal parameters:
  - Fiscal multiplier when the gap is null m1 0.50
  - Fiscal multiplier sensitivity to shocks m2 3
  - Automatic stabilizers (primary balance semi-elasticity to the gap) a 0.66
  - Adjustment cost χ 3
- Interest rate and debt parameters:
  - Growth-adjusted interest rate when debt is 90 percent of GDP 1.02%
  - Effect of debt level on the risk premium α1 1.5%
  - Effect of debt change on the risk premium α2 0.5%
  - Debt level at which the risk to lose market access is 50% d 150%
  - Debt limit accuracy d1 3
  - Effect of debt change on the risk to lose market access is d2 1
  - Adverse scenario coefficient in case of loss of market access d3 -1%
- Economy parameters:
  - Potential GDP per capita growth 0.9%
  - Shock persistence ρ 0.70
  - Shock size σ 1.8%
  - Hysteresis 10%
  - Hysteresis threshold -1%

### Calibration notes and parameter provenance
- Potential growth assumption is an average of WEO potential growth over 2017–21.
- The growth–interest rate differential is calibrated with 20-year averages of historical data.
- Shock parameters (size σ and persistence ρ) are estimated with past shocks reflecting the output gap and the primary balance; the source gives a formula for v_t in terms of past gapp and Δb_t incorporating m1 and m2.
- The fiscal multiplier calibration is set to 0.5 as assumed in the recommended scenario in the staff report.
- The automatic stabilizer coefficient is taken from Price et al. (2015).
- Most parameters are taken from Fournier and Lieberknecht (2020); some parameters reflect cross-country empirical evidence (e.g., elasticity of debt to interest rate, risk aversion).

*Source: IMF — chapter content on fiscal model and calibration for Belgium (Table 1 values and model description).*

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_Source: https://www.imf.org/-/media/files/publications/cr/2020/english/1belea2020002.pdf_