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### Appendix A. Derivation of BGP under a Binding Debt Ceiling
- Model setup: agents, timing, and objects
  - Time is discrete.
  - Production function: 푌_t = 퐾_{t−1}^α 퐿^{1−α} (퐴푋_{t−1})^{1−α}.
  - Private and public capital stocks: 퐾_{t−1} and 푋_{t−1}.
  - Depreciation rates: 훿_퐾 for private capital, 훿_푋 for public capital.
  - Public capital productivity parameter: 퐴.
  - Labor supply 퐿 is exogenous and normalized to unity.
  - Private-to-public capital ratio determined by: α( (퐾_t)/(퐴푋_t) )^{α−1} − 훿_퐾 = 푟_퐾.
  - Output proportional to public capital: 푌_t = Φ 푋_{t−1}, where Φ = 퐴( (푟_퐾 + 훿_퐾)/α )^{α/(α−1)}.
- Households and consumption
  - After-tax wage income: (1−τ)(1−α)Φ푋_{t−1}.
  - Consumption: 푐_t = (1−τ)(1−α)Φ푋_{t−1}. Private capital supplied by external owners (no household savings).
- Government behavior and constraints
  - Public capital accumulation: 푋_t = (1−훿_푋)푋_{t−1} + 퐼_t.
  - Flow budget constraint: 퐷_t = 퐺_t + 퐼_t − 푇_t + (1+푟)퐷_{t−1}, with 푇_t = τ(1−α)Φ푋_{t−1}.
  - Government objective: max ∑_{t=0}^{∞} β^t [ (1−ω) u(퐺_t) + ω u(푐_t) ] subject to the budget constraint.
- Fiscal anchor: binding public debt ceiling
  - Debt ceiling: 퐷_t ≤ d̅ 푌_t, where d̅ denotes debt ceiling in percent of output.
  - Economy starts on a BGP with a binding public debt ceiling.
  - Parameter space restricted so equilibrium growth rate g satisfies r < g (so standard lifetime budget constraint is irrelevant; ceiling prevents arbitrarily large deficits).
  - On the BGP: public capital stock, public debt, and output grow at rate g; public investment and current spending are constant shares of output.
- Appendix A characterizes BGP equilibrium under the binding debt ceiling in detail.

### Key modelling assumptions and focus
- Productive public capital is the only public asset; its balance-sheet value reflects financial and social returns.
- Current government consumption 퐺_t does not benefit households; public investment 퐼_t increases productive capacity and benefits both government and households.
- Tax rate τ is fixed; focus is on spending-side fiscal policy and the fiscal anchor’s role.
- This setup provides the benchmark (debt ceiling) against which a public sector net worth target is compared.

### Main equilibrium implications (from Appendix A)
- A binding debt ceiling prevents explosive debt dynamics when r < g by limiting deficits.
- On the BGP with a binding ceiling, policy variables (investment, current spending) are constant shares of output; growth and stock ratios follow from model primitives and the ceiling.

### _Source: Appendix A. Derivation of BGP under a Binding Debt Ceiling — wpiea2024137-print-pdf._

---

### 2.2 Public Sector Net Worth as Fiscal Anchor

- Definition and valuation
  - Public sector net worth: N_t = q_t X_t − D_t. (6)
  - q_t: unit value of public capital; total asset value q_t X_t.
  - Financial-return valuation (unit NPV): τ(1−α)Φ / (r + δ).
  - Social-return valuation (unit NPV): (1−α)Φ / (r + δ).
  - Weighted valuation: q = λ [τ(1−α)Φ / (r + δ)] + (1−λ) [(1−α)Φ / (r + δ)].
    - With τ* = λ τ + (1−λ), 0 ≤ λ ≤ 1, q = τ* (1−α)Φ / (r + δ).
  - Qualitative: public capital more valuable when Φ is higher, and when r and δ are low.
- Net worth target as fiscal anchor
  - Target: N_t = n* Y_t for all t.
  - Equivalent constraint: q X_t − D_t = n* Φ X_{t−1}. (7)
  - The net worth target constrains both liabilities and assets: higher debt must be matched by larger public capital stock and vice versa.
- Government maximization problem under net worth anchor
  - Max Σ β^t [ (1−ω) u(G_t) + ω u(c_t) ] subject to:
    - D_t = G_t + I_t − τ(1−α)Φ X_{t−1} + (1+r) D_{t−1},
    - q X_t − D_t = n* Φ X_{t−1},
    - X_t = (1−δ_X) X_{t−1} + I_t.
  - For simplicity the paper sets ω = 0 (government does not internalize public investment effects on household consumption).
- Two adjustment strategies to raise n*
  - Fiscal expansion: increase public capital stock more than increase in debt (higher investment).
  - Fiscal consolidation: reduce public debt more than accompanying reduction in public capital.
  - Optimal choice depends crucially on real interest rate r.

- Long-run (BGP) properties under net worth anchor
  1. Public debt-to-output ratio is finite: net worth constraint rules out explosive debt dynamics because increases in debt must be matched by proportional increases in productive assets and output.
  2. At a given BGP growth rate, net worth anchor yields a lower debt-to-output ratio than a pure debt anchor. Intuition: same investment rate implies a lower current spending share under net worth targeting, producing a lower primary deficit and hence lower debt ratio.
     - Numerical example parameter values: r = 0.02, r_K = 0.02, α = 1/3, β = 0.98, τ = 0.12, τ* = 0.2, δ_X = 0.1, δ_K = 0.05, A = 0.5, and σ = 3. The implied unit value of public capital is q = 1.21.
  3. At any growth rate, public net worth (as share of output) is higher with a net worth target because higher debt ratios lower net worth; the term q X_t / (Φ X_{t−1}) is the same across economies growing at the same rate.
  4. Raising the net worth target leads to higher long-term growth in a low interest rate environment because fiscal expansion is preferred over fiscal consolidation when r is low.
     - Two-period thought experiment (t = 1,2): original constraint q X_1 − D_1 = n* Y_1. Increase n* so RHS increases by ε > 0; changes satisfy q ΔX − ΔD = ε.
     - For q > 1, ΔX < ΔD at t = 1, so part of new borrowing finances government consumption: ΔG_1 = ΔD − ΔX = (q − 1) ΔX − ε.
     - Gains at t = 2: higher tax revenue τ(1−α)Φ ΔX and additional asset (1−δ_X) ΔX; cost at t = 2: (1 + r) ΔD. Lower r makes net gain from fiscal expansion more likely to be positive.
     - If r and r_K are correlated (r_K falls when r falls), the mechanism is strengthened via effects on Φ and tax revenues.
     - Threshold for r as ε → 0 given in text: r̄ = 1/q [ u′(G_1) / β u′(G_2) (q − 1) + τ(1−α)Φ + 1 − δ_X ]^{−1}, where G_1 and G_2 are equilibrium current spending levels before changing n*.
     - Figure 2 (left chart) provides a numerical example where net worth target and long-term growth are positively associated (parameters same as Figure 1).
  5. Raising public sector net worth does not necessarily increase debt-to-output ratio: higher public investment raises debt but also raises growth which can lower the debt ratio; net effect depends on relative strengths. In the numerical example debt ratio on the BGP declines with rising net worth targets (Figure 2, right chart).
  6. The optimal net worth target is interest-rate dependent: there may exist an n* that maximizes social welfare on the BGP (the n* that yields the welfare-maximizing growth rate). The paper does not determine the optimal n*.

- Dynamics and simulation setup
  - Public capital adjustment cost added: D_t = G_t + I_t (1 + φ/2 (I_t / X_{t−1}) ) − τ(1−α)Φ X_{t−1} + (1 + r) D_{t−1}.
  - Adjustment cost changes BGP values; parameters adjusted for dynamics section.
  - Illustrative parameter space focuses on r < g, though properties hold for r > g as well.
  - When r > g, debt dynamics less favorable; may complement net worth anchor with interim debt-based target. When both net worth constraint (7) and debt constraint (5) bind, X_t / X_{t−1} = (n* + d̅) Φ / q, capping public investment growth.
  - Dynamics parameter values used: r = 0, r_K = 0.02, α = 1/3, β = 0.98, τ = 0.14, τ* = 0.14, δ_X = 0.08, δ_K = 0.05, A = 0.55, φ = 0.1, and σ = 2. The implied unit value of public capital is q = 1.12.

- Scenario 1 — Replacing a debt ceiling with a net worth target
  - Initial setup:
    - BGP under debt ceiling of 60 percent of GDP at t = 0, with growth rate 3.5 percent, and public sector net worth at 36 percent of GDP.
    - Debt ceiling replaced by net worth target n* = 38 percent of GDP at t = 1.
    - Real interest rate assumed to be 0.
  - Outcomes:
    - Economy experiences a strong growth spurt then settles to new BGP with higher growth than under the debt ceiling.
    - Government increases public investment to create net worth; investment financed by new borrowing → temporary increase in public debt.
    - As investment converges and growth rises, public debt falls to just below 60 percent of GDP due to a more favorable r − g differential, even though primary deficit is larger.
    - Conclusion: instituting a public net worth anchor can induce higher public investment and economic growth without jeopardizing debt sustainability.
  - Alternative initial condition:
    - If initial public debt is 50 percent of GDP and starting public net worth 45 percent of GDP, with same n* target, economy converges to same BGP but public debt increases from 50 percent to just below 60 percent of GDP.
  - Endogeneity of r:
    - If interest rates respond to borrowing, qualitative result (higher n* when r is low induces higher investment and growth) holds but quantitative impacts are damped by rate increases as debt rises.

- Scenario 2 — A temporary positive interest rate shock under net worth targeting
  - Setup:
    - Real interest rate initially zero, rises to 2 percent until period 5, then returns to zero. Other parameters as in Section 3.1.
  - Outcomes:
    - Economy undergoes consolidation: public investment drops, growth slows.
    - Primary balance turns positive via spending cuts, lowering public debt-to-output ratio.
    - Variables return to unaltered BGP after exit from high-r episode.
    - Comparison with debt anchor: under a debt anchor higher interest rates would reduce non-interest expenditures to accommodate higher interest expenses without changing debt-to-output ratio; net worth targeting yields larger primary-balance adjustments and is more responsive to interest rate movements.
  - Permanent vs temporary r changes:
    - Permanent r shifts change asset valuations and require adjustment in n* (lower n* appropriate when interest rates rise permanently).
    - Temporary fluctuations do not change asset valuations and require no adjustment in n*.

### Key takeaways from Section 2.2
- Net worth target links assets and liabilities: q X_t − D_t = n* Φ X_{t−1}.
- Low r favors fiscal expansion (investment) to meet higher n*; high r favors consolidation.
- Net worth anchor can deliver higher growth and maintain debt sustainability under plausible parameterizations.

### _Source: IMF Working Paper — Beyond Debt: Net Worth Fiscal Anchors (section 2.2 and related excerpts)._

---

### 4.1 Taking Stock

- Benefits of a medium-to-long-term PSNW anchor
  - Encourages productive public investment and supports intergenerational equity.
  - Improvement in PSNW achievable by running surpluses or shifting expenditure toward productive investment.
  - Incentivizes prioritizing pro-growth public investment instead of politically easier current spending or cutting investment during consolidation.
  - Provides feedback from interest rates to public investment:
    - Lower borrowing rates allow greater public investment.
    - Higher borrowing rates reduce public investment.
  - Simulations show adjustments occur gradually.
  - When combined with prudent debt management (e.g., long debt maturity), PSNW anchor:
    - Shields public finances from sudden/sustained interest increases.
    - Still allows higher public investment leading to higher future growth.

- Comparison with alternative fiscal anchors
  - Golden rule
    - Requires borrowing only to fund public investments (net operating balance target).
    - Drawbacks:
      - Places no bounds on borrowing used to fund investment → sustainability risks.
      - Does not incentivize rigorous cost-benefit analysis; risk of low-quality projects (푞<1).
      - Ambiguity between investment and current spending enables reclassification.
      - Prioritizes physical investment over human capital projects that may be classified as current spending.
    - Net worth anchor addresses these issues by focusing on net worth rather than investment flows alone, providing an upper bound on public debt and making investment sensitive to interest rates.
  - Debt servicing cost rules
    - Debt servicing rules create fiscal space when interest rates decline but are agnostic about use of fiscal space and can lead to excessive adjustments in debt stock in response to minor interest changes.
    - Net worth anchor provides incentives to invest extra fiscal space in productive investments.

- Operational considerations and challenges
  - Defining and measuring productive investment
    - Countries on average lose around a third of potential benefits from infrastructure investment due to inefficiencies.
    - Ex ante assessments often overstate benefits and understate costs.
    - Incentive to strengthen public investment management (PIM) systems: IMF research indicates improving PIM from bottom quartile to top quartile can double the return from public investments.
    - Net worth anchor sets a higher bar than the golden rule and helps prevent reclassification of current spending as investment.
  - What benefits to include in project assessment
    - Purely financial approach could discourage projects with high social returns but low financial returns.
    - Model assumes project value depends on weighted average of financial and social returns; weights reflect policy preferences.
    - Net worth anchor can be complemented by budgetary provisions to safeguard resources for high social-return / low financial-return projects.
  - Valuation of public capital and parameter q
    - Common practice values public capital by investment flow, effectively setting q = 1 regardless of returns; under q = 1 debt-financed public investment is neutral for net worth unless funded by cuts in consumption.
    - Government Financial Statistics Manual recommends valuing assets at market value or an equivalent for non-traded nonfinancial assets.
    - Good PIM practices help secure projects with q > 1, which improve net worth and growth.
  - Choice of discount rate for valuing public nonfinancial assets
    - Favor using a long-term safe interest rate (less volatile).
    - Valuations should be updated periodically as interest rate projections change; temporary shocks do not require reassessment of asset values.
  - Timing and forecasting issues
    - Investment benefits materialize with delay while debt is immediate → temporary rises in debt-to-GDP possible.
    - PSNW targeting is forward-looking; interim higher debt only problematic if it breaches a secondary debt limit.
    - Forecast inaccuracies unavoidable; can be mitigated via conservative assumptions, buffers, independent fiscal councils.
  - Choice between PSNW and public sector financial net worth
    - PSNW (including nonfinancial public assets) is theoretically superior.
    - Authorities may prefer financial net worth initially because it is easier to compute.
    - Scope can be broadened over time as valuation capacity improves.

- Conclusion (paper’s main findings)
  - A net worth target is conducive to public investment and economic growth, particularly in a low interest rate environment.
  - A net worth anchor precludes explosive debt dynamics and guides fiscal policy to react to macroeconomic changes, including interest rate movements.
  - Best used as a medium- to long-term guide and can be complemented with debt-based considerations in the short-to-medium term to preserve countercyclical fiscal space.
  - Operationalization challenges exist but are surmountable.
  - PSNW-based fiscal policy offers substantial potential benefits over traditional debt-based fiscal rules.

- Select quantitative and parameter highlights preserved exactly in the discussion
  - Example parameter sets and implied q values:
    - Long-run comparison example: r = 0.02, r_K = 0.02, α = 1/3, β = 0.98, τ = 0.12, τ* = 0.2, δ_X = 0.1, δ_K = 0.05, A = 0.5, σ = 3 → q = 1.21.
    - Dynamics section: r = 0, r_K = 0.02, α = 1/3, β = 0.98, τ = 0.14, τ* = 0.14, δ_X = 0.08, δ_K = 0.05, A = 0.55, φ = 0.1, σ = 2 → q = 1.12.
  - Scenario 1 baseline and targets:
    - Debt ceiling: 60 percent of GDP at t = 0.
    - Growth rate: 3.5 percent.
    - PSNW initial: 36 percent of GDP.
    - Net worth target introduced: n* = 38 percent of GDP at t = 1.
    - Alternative initial condition example: initial debt 50 percent of GDP, starting PSNW 45 percent of GDP.
  - Scenario 2 shock:
    - Real interest rate rises from 0 to 2 percent until period 5, then returns to 0.

### _Source: 4.1 Taking Stock — wpiea2024137-print-pdf._

### Appendix A. Derivation of BGP under a Binding Debt Ceiling .............................................................

### Appendix A. Derivation of BGP under a Binding Debt Ceiling

### Model setup: agents, timing, and objects
- Time is discrete.
- One final good is produced using private and public (productive) capital and labor:
  - 푌_t = 퐾_{t−1}^α 퐿^{1−α} (퐴푋_{t−1})^{1−α}.
  - 퐾_{t−1} and 푋_{t−1} denote private and public capital stocks at end of period t−1 (used in period t).
  - Depreciation rates: 훿_퐾 for private capital, 훿_푋 for public capital.
  - Public capital productivity parameter: 퐴.
  - Labor supply 퐿 is exogenous and normalized to unity.
- Equilibrium private-to-public capital ratio determined by marginal return equated to exogenous global rate 푟_퐾:
  - α( (퐾_t)/(퐴푋_t) )^{α−1} − 훿_퐾 = 푟_퐾.
- Output is proportional to public capital:
  - 푌_t = Φ 푋_{t−1},
  - where Φ = 퐴( (푟_퐾 + 훿_퐾)/α )^{α/(α−1)} (notation preserved exactly as in text).
- Households:
  - Supply labor, earn wage 푤_t, taxed at rate τ (tax rate fixed).
  - After-tax wage income in period t: (1−τ)(1−α)Φ푋_{t−1}.
  - Households consume all income: 푐_t = (1−τ)(1−α)Φ푋_{t−1}.
  - Private capital supplied by external capital owners (no household savings for simplicity).
- Government:
  - Collects tax revenues 푇_t and spends on government consumption 퐺_t and public investment 퐼_t.
  - Public capital accumulation:
    - 푋_t = (1−훿_푋)푋_{t−1} + 퐼_t.
  - Issues one-period bonds on international market at global interest rate 푟 (treated as constant in this section).
  - Flow budget constraint:
    - 퐷_t = 퐺_t + 퐼_t − 푇_t + (1+푟)퐷_{t−1},
    - where 푇_t = τ(1−α)Φ푋_{t−1} and 퐷_t denotes net public debt at end of period t.
  - Government objective (maximization):
    - max ∑_{t=0}^{∞} β^t [ (1−ω) u(퐺_t) + ω u(푐_t) ],
    - with ω ∈ [0,1] the weight on households, subject to budget constraint.

### Fiscal anchor: binding public debt ceiling
- Debt ceiling constraint introduced:
  - 퐷_t ≤ d̅ 푌_t,
  - where d̅ denotes debt ceiling in percent of output.
- Economy assumed to start on a balanced growth path (BGP) with a binding public debt ceiling.
- Parameter space restricted so that equilibrium endogenous growth rate g satisfies r < g.
  - Under r < g, standard lifetime government budget constraint is irrelevant, but the debt ceiling prevents arbitrarily large deficits.
- On the BGP:
  - Public capital stock, public debt, and output all grow at the same rate g.
  - Public investment and current spending stay constant in shares of output.
- Appendix A characterizes the equilibrium in detail (derivation of the BGP under the binding debt ceiling).

### Key modelling assumptions and focus
- Productive public capital is the only form of public asset in the model; its value on the government balance sheet reflects financial and social returns.
- Current government consumption 퐺_t does not benefit households; public investment 퐼_t increases productive capacity and benefits both government and households.
- Tax policy is abstracted from (tax rate τ fixed) to focus on spending-side fiscal policy and the fiscal anchor’s role.
- The setup provides the benchmark (debt ceiling) against which a public sector net worth target is later compared in the paper.

*Appendix A. Derivation of BGP under a Binding Debt Ceiling — wpiea2024137-print-pdf.*

### 2.2 Public Sector Net Worth as Fiscal Anchor

### 2.2 Public Sector Net Worth as Fiscal Anchor

### Definition and valuation of public sector net worth
- Public sector net worth is defined as the difference between the value of government assets and liabilities:  
  N_t = q_t X_t − D_t. (6)
- In the model, government assets are the public capital stock X_t; net financial liabilities D_t (net debt) incorporate government financial assets.
- q_t denotes the unit value of public capital; total value of public assets at end of period t is q_t X_t.

- Valuation approaches for q_t:
  - Financial-return valuation (government cash flow): unit cash flow per unit of public capital each period is τ(1−α)Φ. Taking depreciation δ and discount rate r into account, the unit net present value is:
    τ(1−α)Φ / (r + δ).
    - Note: the unit net present value is constant over time given constant r.
  - Social-return valuation (combined return to households and government): social return per unit is (1−α)Φ and its net present value is:
    (1−α)Φ / (r + δ).
  - Weighted average of financial and social returns to strike a balance:
    q = λ [τ(1−α)Φ / (r + δ)] + (1−λ) [(1−α)Φ / (r + δ)].
    - Let τ* = λ τ + (1−λ), with 0 ≤ λ ≤ 1, then:
      q = τ* (1−α)Φ / (r + δ).

- Qualitative: Public capital is more valuable when Φ is higher, and when r and δ are low.

### Net worth target as fiscal anchor and government problem
- Fiscal anchor: set target on ratio of public sector net worth to output: N_t = n* Y_t for all t.
- Using expressions for Y_t and N_t, the net worth constraint is equivalently:
  q X_t − D_t = n* Φ X_{t−1}. (7)

- Implication: the net worth target constrains both liabilities and assets. Higher debt must be matched by larger public capital stock, and vice versa.
- Government maximization problem (objective and constraints):
  max Σ β^t [ (1−ω) u(G_t) + ω u(c_t) ] subject to:
  - D_t = G_t + I_t − τ(1−α)Φ X_{t−1} + (1+r) D_{t−1},
  - q X_t − D_t = n* Φ X_{t−1},
  - X_t = (1−δ_X) X_{t−1} + I_t.
  - Note: for simplicity the paper sets ω = 0 (government does not internalize effect of public investment on household consumption; positive ω gives qualitatively similar results).

- Two adjustment strategies to satisfy a higher n*:
  - Fiscal expansion: increase public capital stock more than increase in debt (higher investment).
  - Fiscal consolidation: reduce public debt more than accompanying reduction in public capital.
- The optimal fiscal strategy depends crucially on the real interest rate r.

### Long-Run (BGP) properties of the net worth anchor
- Existence of a Balanced Growth Path (BGP): output, public capital, and public debt grow at the same rate; public investment and current spending constant ratios to output.
- Key properties:
  1. Public debt-to-output ratio is finite: the net worth constraint rules out explosive debt dynamics because increases in debt must be matched by proportional increases in productive assets and output.
  2. At a given BGP growth rate, the net worth anchor yields a lower debt-to-output ratio than a pure debt anchor. Intuition: same investment rate implies a lower current spending share under net worth targeting (spending mix favors investment), producing a lower primary deficit and hence lower debt ratio.
     - Numerical example parameter values used in this exercise: r = 0.02, r_K = 0.02, α = 1/3, β = 0.98, τ = 0.12, τ* = 0.2, δ_X = 0.1, δ_K = 0.05, A = 0.5, and σ = 3. The implied unit value of public capital is q = 1.21.
  3. At any growth rate, public net worth (as share of output) is higher with a net worth target because higher debt ratios lower net worth; the first term q X_t / (Φ X_{t−1}) is the same across economies growing at the same rate.
  4. Raising the net worth target leads to higher long-term growth in a low interest rate environment because fiscal expansion is preferred over fiscal consolidation when r is low. Thought experiment (two periods t = 1,2) summary:
     - Original constraint: q X_1 − D_1 = n* Y_1.
     - Increase n* so RHS increases by ε > 0; resulting changes ΔX and ΔD satisfy q ΔX − ΔD = ε.
     - For q > 1, ΔX < ΔD at t = 1, so part of new borrowing finances government consumption: ΔG_1 = ΔD − ΔX = (q − 1) ΔX − ε.
     - Gains at t = 2: higher tax revenue τ(1−α)Φ ΔX and additional asset (1−δ_X) ΔX; cost at t = 2: (1 + r) ΔD. Lower r makes net gain from fiscal expansion more likely to be positive.
     - If r and r_K are correlated (r_K falls when r falls), conclusion is strengthened because higher r_K reduces private capital relative to public capital, decreasing Φ and tax revenues.
     - Threshold for r as ε → 0 given in text: r̄ = 1/q [ u′(G_1) / β u′(G_2) (q − 1) + τ(1−α)Φ + 1 − δ_X ]^{−1}, where G_1 and G_2 are equilibrium current spending levels before changing n*.
     - Figure 2 (left chart) provides a numerical example where net worth target and long-term growth are positively associated. Parameters same as Figure 1.
  5. Raising public sector net worth does not necessarily increase debt-to-output ratio: higher public investment raises debt but also raises growth which can lower the debt ratio; net effect depends on relative strengths. In the numerical example debt ratio on the BGP declines with rising net worth targets (Figure 2, right chart).
  6. The optimal net worth target is interest-rate dependent: there may exist an n* that maximizes social welfare on the BGP (the n* that yields the welfare-maximizing growth rate). This paper does not determine the optimal n*.

### Dynamics: model extensions and simulation setup
- To study dynamics, the model adds a standard convex capital adjustment cost to public capital:
  - Modified budget constraint:
    D_t = G_t + I_t (1 + φ/2 (I_t / X_{t−1}) ) − τ(1−α)Φ X_{t−1} + (1 + r) D_{t−1}.
- The adjustment cost changes BGP equilibrium values; some parameter values adjusted for this section.
- For illustrative simulations the paper focuses on parameter space with r < g (real interest rate lower than real growth rate), though properties hold for r > g as well.
- It is noted that as debt dynamics become less favorable with r > g, and financial markets often look at debt levels more than net worth, it may be sensible to complement a long-term net worth anchor with an interim debt-based target. When both net worth constraint (7) and debt constraint (5) bind, X_t / X_{t−1} = (n* + d̄) Φ / q, effectively capping public investment growth.

- Parameter values used in the dynamics section: r = 0, r_K = 0.02, α = 1/3, β = 0.98, τ = 0.14, τ* = 0.14, δ_X = 0.08, δ_K = 0.05, A = 0.55, φ = 0.1, and σ = 2. The implied unit value of public capital is q = 1.12.

### Scenario 1 — Replacing a debt ceiling with a net worth target
- Initial setup for illustrative scenario:
  - Economy rests on a BGP under a debt ceiling of 60 percent of GDP at t = 0, with growth rate 3.5 percent, and public sector net worth at 36 percent of GDP.
  - Debt ceiling replaced by net worth target n* = 38 percent of GDP at t = 1.
  - Real interest rate assumed to be 0.
- Dynamics and outcomes:
  - Economy experiences a strong growth spurt and then settles to a new BGP with higher growth than under the debt ceiling.
  - Government increases public investment to create net worth and exploit low interest rate; investment is financed by new borrowing → temporary increase in public debt.
  - As investment converges to BGP and growth rises, public debt falls to just below 60 percent of GDP due to more favorable r − g differential, even though primary deficit is larger.
  - Conclusion: instituting a public net worth anchor can induce higher public investment and economic growth without jeopardizing debt sustainability.
- Alternative initial condition example:
  - If initial public debt is lower (50 percent of GDP) and starting public net worth higher (45 percent of GDP), with same n* target, the economy converges to same BGP but public debt increases from 50 percent to just below 60 percent of GDP. Thus the government need not target a higher net worth than under the debt rule to achieve faster growth.
- Note on endogeneity of r:
  - If interest rates respond endogenously to borrowing, the qualitative property that higher n* when r is low induces higher public investment and growth still holds, but quantitative impacts are damped by interest rate increases as debt rises. Increased investment mitigates rate rises through positive effects on PSNW.

### Scenario 2 — A temporary positive interest rate shock under net worth targeting
- Setup:
  - Real interest rate initially zero, rises to 2 percent until period 5, then returns to zero.
  - Other parameters as in Section 3.1.
- Dynamics and outcomes:
  - The economy undergoes consolidation: public investment drops, growth slows.
  - Primary balance turns positive via spending cuts, lowering public debt-to-output ratio.
  - All variables return to unaltered BGP after exit from high-r episode.
  - Comparison with debt anchor: under a debt anchor higher interest rates would reduce non-interest expenditures to accommodate higher interest expenses without changing debt-to-output ratio; overall adjustment in primary balance is more limited than under net worth targeting. Net worth targeting is therefore more responsive to interest rate movements.
- Distinction between permanent vs temporary r changes:
  - Permanent shift in r changes asset valuations and requires adjustment in n* (lower n* appropriate when interest rates rise permanently, and vice versa).
  - Temporary fluctuations do not change asset valuations and require no adjustment in the net worth target.

*Source: IMF Working Paper — Beyond Debt: Net Worth Fiscal Anchors (section 2.2 and related excerpts).*

### 4.1 Taking Stock

### 4.1 Taking Stock

### Benefits of a medium-to-long-term public sector net worth (PSNW) anchor
- A net worth anchor provides strong benefits to fiscal policy makers by encouraging productive public investment and supporting intergenerational equity.
- Improvement in public sector net worth can be achieved by either running surpluses, or by shifting expenditure towards productive investment.
- A net worth target incentivizes prioritizing pro-growth public investment even when it is politically easier to increase current spending or—when consolidating—cut investment rather than current spending.
- A net worth anchor provides a feedback mechanism from interest rates to levels of public investment:
  - Lower borrowing rates allow greater amounts of public investment.
  - Higher borrowing rates reduce the amount of public investment.
- Historical example logic: in the 2010s, when the real cost of borrowing was far below the real growth rate, a net worth anchor would have resulted in higher public investment; should rates increase (e.g., immediate post pandemic world) or growth decline, net worth targeting would mechanically reduce public investment.
- Simulations show such adjustments occur gradually.
- When combined with prudent debt management (for example, pursuing long maturity of public debt), the net worth anchor:
  - Shields public finances from sudden or sustained increases in interest.
  - Still allows higher public investment that leads to higher future growth.

### Comparison with alternative fiscal anchors
- Relation to the golden rule:
  - The golden rule requires government to borrow only to fund public investments, effectively a net operating balance target (current spending fully funded by revenues).
  - Drawbacks of the golden rule:
    - Places no bounds on borrowing used to fund public investment, incentivizing excessive borrowing and creating sustainability risks.
    - Does not incentivize proper cost-benefit analysis; without strong PFM, risk of low-quality projects (푞<1 in the model).
    - Ambiguity between public investment and current spending can enable creative accounting and reclassification.
    - Prioritizes physical investment over investments in human capital (education, health) that may be classified as current spending but share investment-like benefits.
  - How a net worth anchor addresses these issues:
    - Focuses on net worth rather than just public investment, creating an incentive for productive investments: projects where benefits exceed costs increase net worth; projects with greater costs than benefits reduce net worth and would be excluded.
    - Provides an upper bound on public debt (as shown in Section II), thus keeping fiscal sustainability in check.
    - Unlike the golden rule, the net worth anchor guides the amount of public investment and makes it sensitive to changes in interest rates.
- Relation to debt servicing cost rules:
  - Debt servicing rules (debt servicing as percent of GDP or percent of revenue) can create fiscal space when interest rates decline, as debt service falls even when debt/GDP is high.
  - Drawbacks of debt servicing rules:
    - Agnostic about use of fiscal space; could be used for increased consumption rather than investment.
    - Can lead to excessive adjustments in the debt stock in response to relatively minor changes in interest rates.
  - Net worth anchor advantages over debt servicing rules:
    - Provides feedback from changing interest rates and incentives to invest extra fiscal space in productive, growth-enhancing investments.

### Operational considerations and challenges
- Defining and measuring productive investment:
  - Effectively investing in productive public capital is difficult.
  - On average, countries lose around a third of the potential benefits from infrastructure investment due to inefficiencies.
  - Ex ante assessments often overstate benefits and understate costs, exaggerating benefits to net worth.
  - This poses a practical challenge in countries with weak investment project evaluation capacity, but also increases incentives to strengthen public investment management (PIM) systems.
  - IMF research indicates improving PIM systems from the bottom quartile to the top quartile can double the return from public investments.
  - By requiring investments to demonstrate a positive contribution to net worth, the net worth anchor sets a higher bar than the golden rule and helps prevent reclassification of current spending as investment.
- What benefits to include in project assessment:
  - A purely financial approach could discourage projects with lower financial returns but higher social returns.
  - The model assumes project value depends on a weighted average of financial and social returns, with weights assigned by authorities reflecting policy preferences.
  - Social returns are often harder to quantify; a net worth anchor can be complemented by budgetary provisions that safeguard fiscal resources for high social-return / low financial-return projects.
  - The paper’s weighting approach allows different treatments of social returns depending on political preferences and reliability of social return estimates.
- Valuation of public capital and the parameter 푞:
  - Common practice values public capital stock by investment flow, effectively setting 푞=1 regardless of returns; this makes debt-financed public investment neutral for net worth unless funded by cuts in consumption.
  - The Government Financial Statistics Manual recommends valuing assets at market value or an equivalent for non-traded nonfinancial assets.
  - Good PIM practices are important to secure projects with 푞>1; such projects improve net worth and economic growth.
- Choice of discount rate for valuing public nonfinancial assets:
  - Favor using a long-term safe interest rate because it is less volatile than short-term rates.
  - Valuation of public assets should be updated periodically as interest rate projections change, and the net worth target adjusted accordingly.
  - Temporary shocks to interest rates affect borrowing cost and induce fiscal responses but do not require reassessment of public asset values.
- Timing and forecasting issues:
  - Growth benefits from investment may take time to realize, while debt is incurred immediately; this can temporarily raise public debt-to-GDP.
  - PSNW targeting is forward-looking; qualitative results do not change unless higher interim debt breaches a secondary debt limit.
  - Forecast inaccuracies are unavoidable but can be minimized using past experience; policymakers may apply conservative assumptions or include buffers on financial and social returns.
  - Independent fiscal councils can help cross-check assumptions on investment returns and limit optimistic bias.
- Choice between PSNW and public sector financial net worth:
  - PSNW (includes nonfinancial public assets) is theoretically superior because it encompasses all productive public capital.
  - Authorities may prefer public sector financial net worth initially because it is easier to compute and less ambiguous in valuation.
  - Authorities can progressively broaden scope toward full PSNW by improving capacity to value public nonfinancial assets.

### Conclusion (paper’s main findings)
- A net worth target is conducive to public investment and economic growth, particularly in a low interest rate environment.
- A net worth anchor precludes explosive debt dynamics and guides fiscal policy to react to macroeconomic changes, including interest rate movements.
- A net worth target is best used as a medium- to long-term guide and can be complemented with debt-based considerations over the short-to-medium term to preserve countercyclical fiscal space.
- Operationalization challenges exist but are surmountable.
- Overall, using public sector net worth to guide fiscal policy offers substantial potential benefits over traditional debt-based fiscal rules.

*Source: 4.1 Taking Stock — wpiea2024137-print-pdf*

### References

### References

### Public investment, public capital, and growth
- Abiad, A., D. Furceri, and P. Topalova, 2016, “The Macroeconomic Effects of Public Investment: Evidence from Advanced Economies,” Journal of Macroeconomics, Vol. 50, pp. 224–40.  
- Aschauer, D., 1989, “Does Public Capital Crowd Out Private Capital?” Journal of Monetary Economics, Vol. 24, No. 2, pp. 171–88.  
- Barro, R., 1990, “Government Spending in a Simple Model of Endogenous Growth,” Journal of Political Economy, Vol. 98, No. 5, part 2, pp. S103-S125.  
- Sturm, J., and J. de Haan, 1995, “Is Public Expenditure Really Productive? New Evidence for the US and the Netherlands,” Economic Modelling, Vol. 12, pp. 60–72.  
- Delgado-Tellez, M., E. Gordo, I. Kataryniuk, and J. Perez, 2022, “The Decline in Public Investment: ‘Social Dominance’ or Too-Rigid Fiscal Rules?” Applied Economics, Vol. 54, No. 10, pp. 1123-1136.  

### Public sector balance sheets, net worth, and fiscal anchors
- Alves, M., S. De Clerck, and J. Gamboa-Arbelaez, 2020, “Public Sector Balance Sheet Database: Overview and Guide for Compilers and Users,” IMF Working Paper No. 20/130 (Washington: International Monetary Fund).  
- Brede, M. and Henn, C., 2018. "Finland’s Public Sector Balance Sheet: A Novel Approach to Analysis of Public Finance," IMF Working Papers 2018/078, International Monetary Fund.  
- Henn, C. and Cabezon, E., 2018. "Counting the Oil Money and the Elderly: Norway's Public Sector Balance Sheet," IMF Working Papers 2018/190, International Monetary Fund.  
- El Rayess, M., A. Halstead, J. Harris, J. Yalyea, and A. Tieman, 2019, “Indonesia’s Public Wealth: A Balance Sheet Approach to Fiscal Policy Analysis,” IMF Working Paper No. WP/19/81 (Washington: International Monetary Fund).  
- Koshima, Y., J. Harris, A. Tieman, 2021, “The Cost of Future Policy: Intertemporal Public Sector Balance Sheets in the G7,” IMF Working Paper No. 21/128 (Washington: International Monetary Fund).  
- Yousefi, S., 2019, “Public Sector Balance Sheet Strength and the Macro Economy,” IMF Working Paper No. 19/170 (Washington: International Monetary Fund).  
- Sturzenegger, F., and N. Der Meguerditchian, 2022, "A Balance-Sheet Model of Fiscal Policy in Namibia," Red Nacionale de Investigadores en Economia (RedNIE), April.  
- Hughes, R., 2019, “Seeking Public Value: The Case for Balance Sheet Targeting in Fiscal Policy,” Resolution Foundation briefing, September.  
- Hughes, R., J. Leslie, C. Pacitti, and James Smith, 2019, “Totally (Net) Worth It: The Next Generation of UK Fiscal Rules,” Resolution Foundation, October.  
- Hughes, R., J. Leslie, and C. Pacitti, 2019, “Britannia Waives the Rules? Lessons from UK and International Experience with Fiscal Rules,” Resolution Foundation, October.  
- Crompton, J., 2023, “Does Introducing Net Worth-Based Fiscal Rules Represent ‘a Long Walk for a Small Sandwich?’” Public Finance. https://www.publicfinance.co.uk/opinion/2023/11/does-introducing-net-worth-based-fiscal-rules-represent-long-walk-small-sandwich  
- Zaranko, B., 2023, “Public Sector Net Worth as a Fiscal Target” in Green Budget, (London: Institute for Fiscal Studies).  

### Fiscal policy, debt, interest rates, and rules
- Blanchard, O., 2019, “Public Debt and Low Interest Rates,” American Economic Review, Vol. 109, No. 4, pp. 1197-1229.  
- Blanchard, O., 2023, Fiscal Policy under Low Interest Rates, (Cambridge; Massachusetts: MIT Press).  
- Furman, J., and L. Summers, 2020, A Reconsideration of Fiscal Policy in the Era of Low Interest Rates (unpublished; Harvard University and Peterson Institute for International Economics).  
- Valencia, F., 2015, “Strengthening Mexico’s Fiscal Framework,” IMF Country Report: Selected Issues 15/314, (Washington: International Monetary Fund).  
- Cottarelli, C., 2020, “The Role of Fiscal Rules in Relation with the Green Economy,” (European Parliament: Brussels). https://www.europarl.europa.eu/RegData/etudes/IDAN/2020/651364/IPOL_IDA(2020)651364_EN.pdf  
- Hughes, R., J. Leslie, C. Pacitti, and James Smith, 2019, “Totally (Net) Worth It: The Next Generation of UK Fiscal Rules,” Resolution Foundation, October.  

### Climate, green investment, and fiscal pacts
- Darvas, Z., and G. Wolff, 2021, “A Green Fiscal Pact: Climate Investment in Times of Budget Consolidation,” Policy Contribution No. 18/2021 (Bruegel: Brussels).  
- Cottarelli, C., 2020, “The Role of Fiscal Rules in Relation with the Green Economy,” (European Parliament: Brussels). https://www.europarl.europa.eu/RegData/etudes/IDAN/2020/651364/IPOL_IDA(2020)651364_EN.pdf  

### Country and regional fiscal analyses
- Adedeji, O., 2022, “Pandemic, Debt Accumulation, and a Balance Sheet Approach to Fiscal Analysis in African Countries,” Center for Global Development note, March, https://www.cgdev.org/publication/pandemic-debt-accumulation-and-balance-sheet-approach-fiscal-analysis-african-countries  
- Sturzenegger, F., and N. Der Meguerditchian, 2022, "A Balance-Sheet Model of Fiscal Policy in Namibia," Red Nacionale de Investigadores en Economia (RedNIE), April.  
- El Rayess, M., A. Halstead, J. Harris, J. Yalyea, and A. Tieman, 2019, “Indonesia’s Public Wealth: A Balance Sheet Approach to Fiscal Policy Analysis,” IMF Working Paper No. WP/19/81 (Washington: International Monetary Fund).  
- Valencia, F., 2015, “Strengthening Mexico’s Fiscal Framework,” IMF Country Report: Selected Issues 15/314, (Washington: International Monetary Fund).  

### IMF publications and policy papers
- International Monetary Fund, 2023, “Chapter 2: Managing Expectations: Inflation and Monetary Policy” in World Economic Outlook, April, (Washington).  
- International Monetary Fund, 2018, Fiscal Monitor: Managing Public Wealth, October, (Washington).  
- International Monetary Fund, 2015, “Fiscal Policy and Long-Term Growth,” IMF Policy Paper (Washington).  
- International Monetary Fund, 2015a, “Making Public Investment More Efficient,” IMF Policy Paper (Washington).  
- International Monetary Fund, 2014, Government Finance Statistics Manual 2014, (Washington).  

*References, from wpiea2024137-print-pdf - References*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024137-print-pdf.pdf_