## Appendix I: Equilibrium and Optimality Conditions ## Source details **Canonical URL:** [Appendix I: Equilibrium and Optimality Conditions](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12274.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12274.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12274.pdf.json) --- ### Motivation, framing, and contribution - Resource revenues are an important source of fiscal revenue and foreign exchange; IMF lists "29 resource-rich developing countries and12prospective countries with identified reserves (International Monetary Fund (2012c))." - High development needs in these countries: average poverty headcount ~60percent (living at $2 a day or below) and only 27percent of total roads are paved. - Policy debate: - Conventional PIH advice: save off-the-ground resource wealth externally in a sovereign wealth fund to preserve wealth and avoid instability (Davis et al. (2001); Barnett and Ossowski (2003); Bems and de Carvalho Filho (2011)). - Countervailing view: invest resource revenue to meet urgent development and capital-scarce needs (UNCTAD Secretariat (2006); Sachs (2007); Collier et al. (2010); Independent Evaluation Office (2011); Baunsgaard et al. (2012); IMF (2012c)). - Paper’s contribution: - Develops a DSGE-style small open real-economy model incorporating public investment inefficiencies, absorptive capacity constraints, weak tax systems, and Dutch disease. - Proposes a "sustainable investing approach": combine raising public investment with saving some resource revenue in a resource fund to fulfill development needs, preserve resource wealth, and maintain economic stability. - Illustrates implications with two country applications (CEMAC region and Angola). ### Key empirical and conceptual features emphasized - Public investment efficiency and absorptive capacity: - Empirical estimates of efficiency generally below 0.5 for countries in sub-Saharan Africa and Latin America (Pritchett (2000); Hurlin and Arestoff (2010)). - Rapid scaling-up can trigger absorptive capacity constraints that reduce returns and drive up costs (Collier et al. (2010); van der Ploeg (2011a); Buffie et al. (2012)). - Example: road per capita length growth rose from 6percent annually in the 1990s to 15percent after 2003 in West China; Shi (2012) finds negative growth effect after expansion. - Modeling: investment efficiency falls when investment expenditure levels exceed a threshold (Arestoff and Hurlin (2006) evidence). - Dutch disease and externalities: - Dutch disease captured via a learning-by-doing externality in the non-resource traded sector; rising government spending pressures non-traded goods, leading to real appreciation and decline in traded-good production (van Wijnbergen (1984)). - Productive public investment can raise productivity in the non-resource traded sector and potentially counteract Dutch disease effects (Sachs (2007); Berg et al. (2010)). - Two key distortions: - Limited access to international capital markets for low-income countries; resource sectors often attract FDI. - Inefficient and weak domestic tax systems amplify costs of self-financed public investment scaling up. ### Model structure and core components - Economy: small open, real economy with three production sectors: non-traded goods (N), non-resource traded goods (T), and a natural resource (O). - Frictions: public investment inefficiencies, absorptive capacity constraints, DSGE investment adjustment costs, closed private capital account assumption (b_t = b for all t), government does not issue additional debt to finance public investment. - Financing focus: resource-revenue-financed public investment scaling up; concessional borrowing (aid) can be accommodated exogenously. - Households: - Utility: E_0 sum_{t=0}^∞ β^t [ 1/(1−σ) (c_t)^{1−σ} − κ/(1+ψ) (l_t)^{1+ψ} ]. - Budget constraint: (1 + τ^c_t) c_t + b_t = (1 − τ^l_t) w_t l_t + R_{t−1} b_{t−1} + Ω^T_t + Ω^N_t + s_t rm^* + z_t. - Consumption aggregator (CES): c_t = [ φ^{1/χ} (c^N_t)^{(χ−1)/χ} + (1−φ)^{1/χ} (c^T_t)^{(χ−1)/χ} ]^{χ/(χ−1)}; price condition 1 = φ (p^N_t)^{1−χ} + (1−φ) (s_t)^{1−χ}. - Firms/sectors: - Resource sector: exogenous y^O_t and p^{O*}_t processes; resource GDP Y^O_t = s_t p^{O*}_t y^O_t; resource revenue T^O_t = s_t ( τ_o p^{O*}_t y^O_t ). - Non-traded sector technology: y^N_t = z^N (k^N_{t−1})^{1−α_N} (l^N_t)^{α_N} (K^G_{t−1})^{α_G}; private capital law of motion with adjustment costs; firm profit Ω^N_t includes a distortion parameter ι rebated lump-sum to firms. - Traded sector: y_Tt = z_Tt (k_Tt−1)^{1−α_T} (l_Tt)^{α_T} (K_Gt−1)^{α_G}; learning-by-doing: ln z_Tt = ρ_zT ln z_Tt−1 + d ln y_Tt−1. - Government: - Flow budget constraint: T_Ot + τ_c t C_t + τ_l t w_t L_t ≡ T_NOt + s_t A^* + s_t (1 + r^*) F^*_{t−1} = p_g t G_t + Z_t + (R_{t−1}) B + s_t F^*_t. - Resource fund F^*_t earns constant real interest r^*; aid A^* is exogenous. - Public capital law of motion with effective public investment: K_Gt = (1−δ_Gt) K_Gt−1 + ˜ϕ_t (G_I t) × G_I t ≡ ˜G_I t. - Time-varying depreciation δ_Gt (maintenance effect) specified as in equation (20). - Absorptive capacity: two efficiency regimes ˜ϕ_t(G_I t) = { ϕ when G_I t < ̄G_I; ̄ϕ when G_I t ≥ ̄G_I } with calibration ϕ = 0.5, ̄ϕ = 0.35, ̄G_I = 1.6 × G_I. - Market clearing and identities: - Non-traded demand: D_N t = φ (C_t + I_N t + I_T t) + ν(p_g t)^{χ} G_t; clearing Y_N t = (p_N t)^{−χ} D_N t. - Current account and balance of payments as in equations (31) and (32). ### Fiscal treatments of resource windfalls (three approaches) - Windfall definition: T_O^* t − T_O^* (in units of foreign goods). - Save in a Sovereign Wealth Fund (SWF): - F^*_t = F^*_{t−1} + (T_O^* t − T_O^*). Spending limited to r^* F^*_{t−1} interest income. - All-investing approach: - F^*_t = F^* ∀ t; G_I t = G_I + (T_O t / p_g t − T_O / p_g). - Sustainable investing approach: - Stable scaling-up path commensurate with resource profile and absorptive capacity. - If short resource horizon and saving: F^*_t = F^*_{t−1} + φ (T_O^* t − T_O^*). - If fund used for stabilization: F^*_t = F^*_{t−1} + (T_O^* t − T_O^*) − (p_g t G_t s_t − p_g G s). - Fiscal instruments to clear budget include transfers and consumption or labor tax rates; some instruments may remain at initial steady-state levels. ### Baseline calibrations and key numerical values (common and country-specific) - Common baseline calibrations: - φ = 0.5; χ = 0.44; ρ = 1; σ = 2; ψ = 10; β = 0.91 (domestic annual interest rate of 10 percent); ρ_zT = d = 0.1; κ_N = κ_T = 25; ρ_yo = 0.9; ρ_po = 1; initial oil price per barrel = $94 a barrel; r^* = 0.027 (2.7 percent). - Absorptive capacity: ϕ = 0.5, ̄ϕ = 0.35, ̄G_I = 1.6 × G_I. - Public capital parameters (CEMAC baseline): α_G = 0.1; δ_G = 0.08; implied K_G initial = 42.5 percent of GDP. - Tax/fiscal (CEMAC): τ_c = 0.18; τ_l = 0.08; τ_o = 0.58 to match initial oil revenue share 0.55; initial resource fund = 1 percent of GDP; initial public debt = 11.6 percent of GDP; ν = 0.6; ν_g = 0.5. - Angola-specific calibrations: - Initial oil production: 606 million barrels; oil output = 47.5 percent of GDP. - τ_o = 0.58 implies oil tax receipts ≈ 80 percent of total government revenue. - Initial stabilization fund = 2 percent of GDP. - φ = 0.4 (private consumption/investment home bias); ν = 0.4; ν_g = 0.2. - Non-oil traded good production ≈ 17 percent of GDP. - Public investment initial = 8.7 percent of GDP; δ_G = 0.07; ϕ = 0.5; α_G = 0.2 targets return to public capital ≈ 10 percent. - Government consumption = 19.5 percent of GDP; government debt = 34.5 percent of GDP; transfers = 2.8 percent of GDP; τc = τl = 0.1; ι = 0.2; σ_po = 0.1 for oil price shocks. ### Baseline scenario outcomes: saving in SWF vs all-investing - SWF (saving all windfall externally): - Fund climbs to 132 percent of GDP in the new steady state. - New steady-state consumption = 5.2 percent higher relative to path without the windfall. - Public capital does not increase (public investment stays at initial steady state). - All-investing (invest all windfall domestically): - Public capital peak (in 2025) = 26 percent higher relative to path without the windfall. - Peak consumption (in 2026) = 4.3 percent above path without windfall (slightly higher than SWF consumption 4.1 percent in an alternative specification). - Welfare: all-investing yields welfare higher by 1.0 percent of initial steady-state consumption each period relative to saving in a SWF (measured over horizon 2012–2040). ### Absorptive capacity and multipliers - Baseline absorptive constraint: efficiency falls from 0.5 to 0.35 when expenditures exceed 60 percent of initial steady-state level. - With binding constraint, peak consumption under all-investing = 4.3 percent above no-windfall. - Non-binding scenario (ϕ = 0.5 ∀ t): - Peak consumption rises to 8.4 percent above no-windfall. - Average periodic utility advantage of all-investing over SWF = 3 percent of initial steady-state consumption. - Present-value cumulative non-oil output multipliers (Mountford and Uhlig (2009) definition): - Baseline all-investing: multiplier = 0.41 at end of 2040. - Non-binding constraints scenario: multiplier = 0.64 at end of 2040. - Multipliers generally low (much smaller than 1) due to inefficiencies and absorptive constraints; investing in implementation capacity could change efficiency over time. ### Return to public capital: scenario analysis - Baseline α_G = 0.1 implying net annual return = 13.4 percent. - Scenario 3 (Low return): - α_G = 0.05 implying annual return = 2.7 percent. - By end-2040, private consumption under SWF = 4.7 percent above no-windfall; under all-investing = 0.8 percent. - Cumulative multiplier in 2040 = 0.28. - Scenario 4 (High return): - α_G = 0.20 implying annual return = 35 percent. - Welfare: average periodic utility with all-investing = 3.2 percent higher than SWF. - Cumulative multiplier in 2040 = 0.67; relax absorptive constraints (ϕ = 0.5 ∀ t) increases multiplier to 1.12. - Policy insight: outcomes highly sensitive to α_G; when returns low, saving in SWF preferable; when returns high and absorptive capacity adequate, investing dominates. ### Cost of fiscal adjustments and endogenous depreciation - All-investing requires fiscal adjustments to sustain capital after windfall: - Example baseline: transfers/GDP must fall to 0.9percent (from 2.7percent); or consumption tax must rise to 0.21 (from 0.18). - Scenario 2 (non-binding constraints): transfers/GDP must be lowered to −0.01 (equivalent to lump-sum tax of 1 percent of GDP) or τ_c raised to 0.24. - Endogenous depreciation specification (equation (20)): - Depreciation rate rises when investment below replacement costs; under all-investing depreciation rises after 2020 to about 10percent. - With fixed δ_G = 8percent, public capital declines more slowly; non-oil GDP and private consumption higher with all-investing across scenarios. - Endogenous depreciation penalizes volatile investment trajectories; volatile capital stocks are less efficient. - Political economy: large fiscal adjustments often infeasible; public capital built with windfalls likely to depreciate over time. ### Sustainable investing approach: design, calibration, and outcomes - Concept: combine external saving and domestic investment to choose sustainable scaling-up magnitude given windfall size and fiscal/structural characteristics; interest income and non-resource revenue finance recurrent costs after windfall. - Investment rule example: GIt = (1 − e^{−γt}) GIns s + e^{−γt} GI0; γ controls speed of transition. - Preferred baseline simulation: - GI0 = 1.6 × GI; GIns s = 1.26 × GI; γ = 0.15; φ = 0.5 saving rate. - Resource fund eventually climbs to 64 percent of GDP. - Public capital permanently 26 percent higher relative to no-windfall path. - Private consumption in new steady state = 4.7 percent higher. - During first 12 years, investment efficiency ϑ = 0.5 under sustainable investing vs 0.35 under all-investing. - No fiscal adjustments needed after windfall exhaustion; consumption tax returns to initial steady-state level. - Welfare: periodic utility advantage of sustainable investing over all-investing = 1.1 percent of initial steady-state consumption. - Trade-offs in alternative sustainable-investing calibrations: - Higher scaling-up (long-run investment 40percent higher): fund insufficient; τ_c must rise to ~0.2 to sustain capital; periodic utility 0.5 percent lower than 26percent scaling-up case. - Lower saving-rate (φ = 0.2 with 26percent scaling-up): initial consumption boom but insufficient fund later; τ_c must rise to ~0.2; new steady-state private consumption 1.7 percent lower than φ = 0.5 case. - Calibration procedure: GI_nss = 1.26GI and φ = 0.5 pinned down by simulations to avoid long-run fiscal adjustments. - Caveats: results conditional on returns to public capital, absorptive capacity, political feasibility. ### Investing volatile resource revenue — Angola application and volatility management - Context: Angola with long revenue horizon, high oil dependence; use stochastic simulations with historical oil price volatility and production path projection. - Stabilization fund rule: allow depositing and withdrawing (equation (28)); non-negative constraint on F^*_t; if buffer insufficient, investment spending cut. - Spend-as-you-go specification: 60percent of additional revenues to investment, 40percent to government consumption. - Comparative volatility (average standard deviations, percent deviations from trend, 2011–2025, 100 simulations): - public investment: Spend-as-You-Go = 16.2; Sustainable Investing = 7.4 - non-resource GDP: Spend-as-You-Go = 1.2; Sustainable Investing = 0.7 - private consumption: Spend-as-You-Go = 1.0; Sustainable Investing = 0.6 - real exchange rate: Spend-as-You-Go = 2.2; Sustainable Investing = 1.4 - Trade-off between investing and external saving: - Aggressive scaling-up builds public capital faster but leaves small stabilization fund and increases vulnerability to negative shocks. - Conservative scaling-up yields larger buffer and less volatility in realized investment. - Angola simulation outcomes (end-2025 averages and bands): - Stabilization fund mean end-2025: Aggressive = 1.1 percent of GDP; Conservative = 37.1 percent of GDP. - Mean realized scaling-up 2016–2025 (aggressive) = 15 percent (pre-determined target 20 percent). - Average depreciation rate (95-percent upper bound): Conservative = 0.08; Aggressive = 0.10. - Public capital above no-windfall path at end-2025: Aggressive = 40percent; Conservative = 31percent. - Tail risk for public capital in 2025: - Aggressive: one-standard-deviation lower band = 7.3 percent; two-standard-deviation lower band = −27.0 percent. - Conservative: one-standard-deviation lower band = 24.8 percent; two-standard-deviation lower band = −4.0 percent. - Non-oil GDP one-standard-deviation interval in 2025 above no-windfall path: - Aggressive = 5.0 to 22.0 percent. - Conservative = 7.5 to 15.0 percent. - Households’ average consumption similar under aggressive and conservative paths on average. - Depreciation channel and robustness: - Endogenous depreciation amplifies negative outcomes when investment falls below replacement. - Fixing δ_G at initial 7 percent improves lower bands of public capital and GDP performance. - Policy implications: - Sustainable investing (investment + resource fund) helps delink government spending from volatile revenues and reduces volatility across macro variables. - Avoid overly aggressive scaling-up: raises instability, lowers investment efficiency, increases depreciation risk, and may not outperform conservative paths. - Design of scaling-up must account for financing of recurrent costs and political feasibility; in practice, public investment likely to be cut rather than taxes or transfers adjusted. ### Policy recommendations and suggested extensions - Policy recommendations: - Adopt a sustainable investing approach: combine a resource fund and a calibrated public investment scaling-up that accounts for absorptive capacity, returns to public capital, and future recurrent cost financing. - Use resource fund as a stabilization buffer when revenue volatility is material. - Sequence and size scaling-ups conservatively if absorptive capacity is limited or fiscal adjustment costs are large. - Prioritize maintenance and recurrent cost financing to avoid endogenous increases in depreciation. - Suggested model extensions and further research: - Analyze other investment types (health, education) that build human capital. - Develop fuller rule-based optimal policy analysis within the model. - Introduce nominal rigidities to address short-run policy issues. - Study interactions with fiscal rules that permit commercial debt as countries access international bond markets. *Source: Appendix I: Equilibrium and Optimality Conditions (excerpts from IMF working paper _wp12274).* ### Appendix I: Equilibrium and Optimality Conditions ............................................................40 ### Appendix I: Equilibrium and Optimality Conditions ### Introduction — motivation and policy framing - Natural resource revenues are an important source of fiscal revenue and foreign exchange; the International Monetary Fund lists "29 resource-rich developing countries and12prospective countries with identified reserves (International Monetary Fund (2012c))." - Among these, average poverty headcount (living at $2 a day or below) is about60percent, and only27percent of total roads are paved. - Conventional permanent-income-based advice: save off-the-ground resource wealth externally in a sovereign wealth fund to preserve wealth and avoid instability (cites: Davis et al. (2001), Barnett and Ossowski (2003), Bems and de Carvalho Filho (2011)). - Emerging countervailing view (mid-2000s): invest resource revenue to meet urgent development and capital-scarce needs (cites: UNCTAD Secretariat (2006), Sachs (2007), Collier et al. (2010), Independent Evaluation Office (2011), Baunsgaard et al. (2012), International Monetary Fund (2012c)). - Theoretical work shows productive government spending can dominate external saving in credit-constrained, capital-scarce economies (cites: Takizawa et al. (2004), Venables (2010), van der Ploeg (2010a), van der Ploeg and Venables (2011), Araujo et al. (2012)). - Historical experience and the "natural resource curse": - Resource-abundant countries have tended to grow more slowly than others (natural resource curse literature: Gelb (1988), Sachs and Warner (1999), Sachs and Warner (2001), van der Ploeg (2011b)). - Example: Gelb (1988) study of six oil-exporting developing countries; Venezuela’s public investment reached40percent on average from 1974 to 1977, yet per capita non-oil GDP growth declined in 1976 and became negative in 1979 (Moreno and Shelton (forthcoming)). - Conclusion: other factors besides capital scarcity and credit constraints (e.g., inefficiencies, absorptive constraints, recurrent cost financing) shape outcomes of investing a windfall. - Paper’s contribution: develop a DSGE-style small open real-economy model that: - Incorporates public investment inefficiencies, absorptive capacity constraints, weak tax systems, and Dutch disease. - Proposes a "sustainable investing approach": combine raising public investment with saving some resource revenue in a resource fund to fulfill development needs, preserve resource wealth, and maintain economic stability. - Uses two country applications (CEMAC region and Angola) to illustrate implications. ### Key empirical and conceptual features emphasized - Public investment efficiency: - Empirical estimates of efficiency (ratio of change in public capital to investment expenditures) are generally below0.5 for countries in sub-Saharan Africa and Latin America (Pritchett (2000); Hurlin and Arestoff (2010)). - Rapid scaling-up can trigger absorptive capacity constraints (supply bottlenecks, poor planning) that drive up costs and reduce returns (Collier et al. (2010); van der Ploeg (2011a); Buffie et al. (2012)). - Empirical example: Shi (2012) finds negative growth effect after road expansion in West China where road per capita length growth rose from6percent annually in 1990s to15percent after 2003. - Modeling approach: investment efficiency falls when investment expenditure levels exceed a threshold (following Arestoff and Hurlin (2006) estimates). - Dutch disease and public investment: - Model captures Dutch disease through a learning-by-doing externality in the non-resource traded sector: rising government spending pressures non-traded goods, leading to real appreciation and decline in traded-good production (van Wijnbergen (1984)). - Productive public investment can raise productivity in the non-resource traded sector, potentially counteracting or reversing Dutch disease effects (Sachs (2007); Berg et al. (2010)). - Two distortions highlighting special role of resource rents: - Limited access to international capital markets for low-income countries; resource sectors often attract FDI because high rents induce investors to overcome sovereign risk. - Inefficient and weak domestic tax systems amplify the costs of self-financed public investment scaling up and the deferred private consumption and investment such scaling implies. ### Sustainable investing approach and policy insights from applications - CEMAC application (Central African Economic and Monetary Community): - Emphasis: secure financing of recurrent costs for sustaining capital when exhaustibility looms in the next 10-20 years. - Key insight: decisions between investing domestically vs saving in a sovereign wealth fund depend on returns to capital and absorptive capacity, but critically on the fiscal adjustment needed to sustain capital beyond the windfall. - Recurrent costs for operation and maintenance are crucial to maintain productivity of public capital (Heller (1974); Rioja (2003)). - Policy implication: when revenue mobilization is difficult or fiscal adjustment is highly distorting, scale back investment scaling-up and save more in a resource fund; the fund’s return helps finance recurrent costs and supports long-term growth. - Angola application: - Emphasis: building a fiscal buffer to invest volatile revenue. - Historical lesson: large fiscal expansions in Angola 2006–2008 driven by oil revenue surges left little buffer when oil prices collapsed in 2008–2009. - Policy implication: use the resource fund as a fiscal buffer to protect the economy from boom-bust commodity price shocks (cites: Collier et al. (2010), van der Ploeg (2010b), Cherif and Hasanov (2012), Van den Bremer and van der Ploeg (2012)). - Stochastic simulations using historical oil price volatility can assess buffer adequacy for a given scaling-up plan and inform invest-vs-save allocations under uncertain revenue flows. - Modeling contribution relative to literature: - Constructs a fully specified dynamic stochastic framework suitable for policy analysis with private-sector decisions and implementable fiscal policies. - Incorporates a detailed fiscal-variable specification to simulate a given fiscal path or simple fiscal rules in allocating resource revenues. - Contrast with prior literature that often solves social planner problems or assumes fiscal instruments that fully correct distortions but may not be practically implementable. ### Model setup — structure and core components - Economy type and sectors: - Small open, real economy with three production sectors: non-traded goods (N), (non-resource) traded goods (T), and a natural resource (O). - Includes standard DSGE investment adjustment costs and frictions common in developing countries: public investment inefficiencies and absorptive capacity constraints. - Assumes closed private capital account and government does not issue additional debt to finance public investment (b_t = b for all t). - Concessional borrowing (aid) can be accommodated exogenously but is largely beyond authorities’ control. - Financing focus: - Primary interest: resource-revenue-financed public investment scaling up in low-income and lower-middle-income countries. - Alternatives involving greater tax finance are examined later, but medium-term scope for tax increases is limited in practice. ### Households — preferences, budget constraint, consumption aggregation - Representative household utility: - Maximize E_0 sum_{t=0}^∞ β^t [ 1/(1−σ) (c_t)^{1−σ} − κ/(1+ψ) (l_t)^{1+ψ} ]. - Parameters: σ and ψ are inverses of intertemporal substitution elasticities for consumption and labor; κ is disutility weight on labor. - Budget constraint (in units of domestic composite consumption): - (1 + τ^c_t) c_t + b_t = (1 − τ^l_t) w_t l_t + R_{t−1} b_{t−1} + Ω^T_t + Ω^N_t + s_t rm^* + z_t. - Notation: τ^c_t and τ^l_t are consumption and labor tax rates; rm^* denotes remittances in units of foreign consumption; z_t denotes government transfers; s_t is CPI-based real exchange rate; Ω^T_t and Ω^N_t are sector profits; b_t are domestic government bonds paying R_t b_t units of consumption at t+1. - Assumption: households do not have access to foreign loans; government does not issue additional debt to finance public investment (b_t = b ∀ t). - Consumption aggregator (CES): - c_t = [ φ^{1/χ} (c^N_t)^{(χ−1)/χ} + (1−φ)^{1/χ} (c^T_t)^{(χ−1)/χ} ]^{χ/(χ−1)}. - Parameters: χ is intratemporal elasticity of substitution; φ indicates consumption home bias. - Price of one unit of composite consumption: 1 = φ (p^N_t)^{1−χ} + (1−φ) (s_t)^{1−χ}. - Law of one price holds for traded goods; composite consumption is numeraire. - Aggregate labor and wage: - Labor aggregator with imperfect mobility: l_t = [ δ^{−1/ρ} (l^N_t)^{(1+ρ)/ρ} + (1−δ)^{−1/ρ} (l^T_t)^{(1+ρ)/ρ} ]^{ρ/(1+ρ)}, where δ is non-traded sector labor share in steady state and ρ > 0 governs mobility. - Aggregate real wage: w_t = [ δ (w^N_t)^{1+ρ} + (1−δ) (w^T_t)^{1+ρ} ]^{1/(1+ρ)}. ### Firms — sectors, technologies, and key equations - Natural resource sector (O): - Resource output process (exogenous): y^O_t / y^O = ( y^O_{t−1} / y^O )^{ρ_{yo}} e^{ε^{yo}_t }, where ρ_{yo} ≤ 1 and ε^{yo}_t ∼ i.i.d. N(0, σ^2_{yo}). - International commodity price process (exogenous): p^{O*}_t / p^{O*} = ( p^{O*}_{t−1} / p^{O*} )^{ρ_{po}} e^{ε^{po}_t }, where ρ_{po} ≤ 1 and ε^{po}_t ∼ i.i.d. N(0, σ^2_{po}). - Resource GDP in units of domestic composite consumption: Y^O_t = s_t p^{O*}_t y^O_t. - Resource production subject to royalty τ_o. - Resource revenue each period: T^O_t = s_t ( τ_o p^{O*}_t y^O_t ) ≡ T^{O*}_t. - Assumption: resource output is exported and not consumed domestically. - Non-traded goods sector (N): - Technology (representative firm, perfectly competitive): y^N_t = z^N (k^N_{t−1})^{1−α_N} (l^N_t)^{α_N} (K^G_{t−1})^{α_G}, where α_G is public capital output elasticity and z^N is productivity scale; constant returns to private inputs and increasing returns in public capital. - Private capital law of motion: k^N_t = (1 − δ_N) k^N_{t−1} + [ 1 − (κ_N / 2) ( i^N_t / i^N_{t−1} − 1 )^2 ] i^N_t, where κ_N ≥ 0 is investment adjustment cost parameter. - Representative firm maximizes net present-value profit weighted by household marginal utility λ_t: - Profit measure Ω^N_t = (1−ι) ( p^N_t y^N_t ) − w^N_t l^N_t − i^N_t + ι p^N_t Y^N_t, where ι captures distortions that discourage firm investment/hiring; these implicit distortions act like a distorting tax but are rebated lump-sum to firms. ### Model assumptions and simplifications relevant for policy analysis - Closed private capital account approximates limited access to international commercial borrowing in low-income countries (empirical high risk premia justify near-closure). - Government does not issue additional debt to finance public investment within baseline analysis; alternative setups (concessional borrowing, aid) can be modeled exogenously. - The model abstracts from a fraction of hand-to-mouth households explicitly; forward-looking households under model assumptions behave similarly to hand-to-mouth in response to shocks given closed private capital account, firm ownership of capital, and no government debt financing. *Source: Appendix I: Equilibrium and Optimality Conditions.* ### 3. Traded Good Sector ### 3. Traded Good Sector ### Traded-good production and productivity - Production function (perfect competition, technology similar to non-traded sector): - y_Tt = z_Tt (k_Tt−1)^{1−α_T} (l_Tt)^{α_T} (K_Gt−1)^{α_G}. (14) - Productivity with learning-by-doing externalities (depends on last period traded output): - ln z_Tt = ρ_zT ln z_Tt−1 + d ln y_Tt−1. (15) - Assumed minor learning-by-doing externality: ρ_zT = d = 0.1. ### Capital accumulation and firm objective - Capital accumulation in traded sector: - k_Tt = (1−δ_T) k_Tt−1 + [1 − κ_T/2 (i_Tt / i_Tt−1 − 1)^2] i_Tt. (16) - Firm maximizes weighted preset-value profits; profit of the traded good sector: - E_t ∑_{t=0}^{∞} β^t λ_t [ (1−ι) s_t y_Tt − w_Tt l_Tt − i_Tt + ι s_t Y_Tt ] ≡ Ω_Tt. (17) - Investment adjustment-cost parameter calibration for traded and non-traded: κ_N = κ_T = 25. ### Factor shares and depreciation (private production) - Sectoral labor income shares set to α_N = 0.45 and α_T = 0.65 (based on capital shares ranges). - Depreciation rates for private capital: δ_N = δ_T = 0.1. --- ### Government: budget constraint, taxes, and resource fund - Flow government budget constraint (aggregate notation): - T_Ot + τ_c t C_t + τ_l t w_t L_t ≡ T_NOt (non-resource tax) - + s_t A^* + s_t (1 + r^*) F^*_{t−1} = p_g t G_t + Z_t + (R_{t−1}) B + s_t F^*_t. (18) - Definitions and parameters in (18): - F^*_t is the asset value of a resource fund earning constant real interest r^*. - A^* is foreign aid. - G_t is government purchases with relative price p_g t. - Z_t is aggregate transfers to households. - Fiscal revenue mobilization feature: - Taxes on non-traded and traded sectors (ι p_Nt y_Nt and ι s_t y_Tt) are rebated to firms and do not appear as government revenues in (18). - Government collects taxes on resource sector revenues and these account as valid financing sources. - Assumption on external borrowing: - Model allows accumulating external assets but abstracts from external commercial borrowing; concessional borrowing treated as aid (A^*). --- ### Investment efficiency and absorptive capacity constraints (public capital) - Public capital law of motion with effective public investment: - K_Gt = (1−δ_Gt) K_Gt−1 + ˜ϕ_t (G_I t) × G_I t ≡ ˜G_I t. (19) - 0 < ˜ϕ_t ≤ 1 governs efficiency of public investment. - Time-varying public capital depreciation (maintenance effect; Rioja (2003) specification): - δ_Gt = { δ_G × δ_G K_Gt−1 / ˜G_I t, when ˜G_I t < δ_G K_Gt−1; δ_G, when ˜G_I t ≥ δ_G K_Gt−1 }. (20) - Absorptive capacity modeled as two efficiency regimes (Arestoff and Hurlin (2006) evidence): - ˜ϕ_t(G_I t) = { ϕ, when G_I t < ̄G_I; ̄ϕ, when G_I t ≥ ̄G_I }. (21) - Calibration: ϕ = 0.5, ̄ϕ = 0.35, ̄G_I = 1.6 × G_I (based on Mexican evidence). - Range of investment efficiency consistent with 0.35−0.5. ### Government purchases aggregation and home bias - Government purchases are a CES basket of traded and non-traded goods: - G_t = [ ν_t^{1/χ} (G_N t)^{(χ−1)/χ} + (1−ν_t)^{1/χ} (G_T t)^{(χ−1)/χ} ]^{χ/(χ−1)}. (22) - Relative price of government consumption to private consumption: - p_g t = [ ν_t (p_N t)^{1−χ} + (1−ν_t) (s_t)^{1−χ} ]^{1/(1−χ)}. (23) - Time-varying home bias for government purchases (additional spending bias ν_g may differ from steady-state ν): - ν_t = ν + (p_g t G_t − p_g G)/(p_g t G_t) (ν_g − ν). (24) --- ### Fiscal policy: treatment of resource windfalls (three approaches) - Resource windfall defined as resource revenue above original steady state: T_O^* t − T_O^* (in units of foreign goods). - Saving in a Sovereign Wealth Fund (SWF): - All windfall saved externally; fund evolves: - F^*_t = F^*_{t−1} + (T_O^* t − T_O^*). (25) - Spending limited to interest income r^* F^*_{t−1} in the budget constraint. - The All-Investing Approach: - Resource fund stays at its initial level: F^*_t = F^* ∀ t. - Public investment follows rule: - G_I t = G_I + (T_O t / p_g t − T_O / p_g). (26) - The Sustainable Investing Approach: - Specifies a relatively stable scaling-up path of public investment, commensurate with resource profile and absorptive capacity. - If short resource horizon and fund used for saving, fixed share φ of windfall is saved: - F^*_t = F^*_{t−1} + φ (T_O^* t − T_O^*). (27) - If fund built for stabilization, saving rate time-varying and fund evolves by: - F^*_t = F^*_{t−1} + (T_O^* t − T_O^*) − (p_g t G_t s_t − p_g G s). (28) - Under all approaches, fiscal instruments that can adjust to clear the budget include transfers and consumption or labor tax rates; those that do not adjust remain at initial steady-state levels. --- ### Market clearing conditions and identities - Total demand for non-traded goods: - D_N t = φ (C_t + I_N t + I_T t) + ν(p_g t)^{χ} G_t. (29) - Non-traded goods market clearing: - Y_N t = (p_N t)^{−χ} D_N t. (30) - Current account deficit: - CAd t = (C_t + I_t + p_G t G_t) − Y_t − s_t (r^* F^*_{t−1} + RM^*). (31) - I_t = I_N t + I_T t; Y_t = p_N t Y_N t + s_t Y_T t + Y_O t. - Balance of payments condition: - CAd t = s_t [ A^* − (F^*_t − F^*_{t−1}) ]. (32) --- ### Equilibrium and calibration: model scope and baseline parameter values - Equilibrium system: private agents' optimality conditions, government budget constraint, fiscal policy rules, market clearing, balance of payments, and exogenous shock processes. - Annual frequency applied to CEMAC region and Angola; Table 1 summarizes baseline calibrations (not reproduced here). - Common parameter calibrations: - Degree of home bias in private consumption and investment: φ = 0.5. - Elasticity of substitution between traded and non-traded goods: χ = 0.44. - Labor mobility parameter: ρ = 1. - Household risk aversion: σ = 2 (intertemporal EIS of 0.5). - Frisch labor elasticity: 0.1 (ψ = 10). - Discount factor: β = 0.91 (domestic annual interest rate of 10 percent). - Learning-by-doing: ρ_zT = d = 0.1. - Investment adjustment costs: κ_N = κ_T = 25. - Resource production shock persistence: ρ_yo = 0.9. - Oil price follows a random walk without drift: ρ_po = 1. - Initial steady-state oil price per barrel: $94 a barrel. - Real return on international financial assets: r^* = 0.027 (2.7 percent). - Absorptive capacity calibration based on Arestoff and Hurlin (2006): - ϕ = 0.5, ̄ϕ = 0.35, ̄G_I = 1.6 × G_I. - Public capital parameters (CEMAC baseline): - Elasticity of public capital to output: α_G = 0.1 (baseline; explore α_G from 0.05 to 0.2). - Public capital depreciation rate: δ_G = 0.08. - Implied public capital in initial steady state: 42.5 percent of GDP. - Tax and fiscal calibration (CEMAC): - Average VAT rate: τ_c = 0.18. - Labor tax rate: τ_l = 0.08. - Oil tax rate set to τ_o = 0.58 to match initial oil revenue share in total revenue of 0.55. - Initial resource fund: 1 percent of GDP. - Initial public debt: 11.6 percent of GDP. - Degree of home bias in government purchases steady state: ν = 0.6; for additional spending ν_g = 0.5. - Angola-specific calibration highlights: - Initial oil production: 606 million barrels; oil output = 47.5 percent of GDP. - Oil tax rate: τ_o = 0.58 implies oil tax receipts ≈ 80 percent of total government revenue. - Initial stabilization fund: 2 percent of GDP. - Private consumption/investment home bias: φ = 0.4. - Government purchases home bias: ν = 0.4; for additional spending ν_g = 0.2. - Non-oil traded good production implied ≈ 17 percent of GDP. - Public investment in initial steady state: 8.7 percent of GDP; depreciation δ_G = 0.07; ϕ = 0.5; α_G = 0.2 targets return to public capital ≈ 10 percent. - Government consumption: 19.5 percent of GDP. - Government debt: 34.5 percent of GDP; household transfers implied 2.8 percent of GDP. - Consumption and labor tax rates: both set at 0.1. - Implied distorting tax rate: ι = 0.2. - Oil price shock standard deviation (for stochastic simulations with ρ_po = 1): σ_po = 0.1. --- ### Investing with a short revenue horizon (policy comparison) - Context: when resource revenues are expected to be exhausted within 10 to 20 years, the Permanent Income Hypothesis (PIH) advice to save in a SWF may be attractive. - The paper compares macroeconomic outcomes under: - Saving in a SWF (equation (25)), and - All-investing in public capital (equation (26)). - Sustainable investing approach (equations (27)–(28)) is proposed to determine a scaling-up magnitude of public investment that is sustainable after resource revenues are exhausted, accounting for productivity and absorptive capacity constraints. - CEMAC application: oil production projected to decline from about 380 million barrels a year in 2012 to about 100 million barrels in 2030; simulations use a non-linear perfect foresight solution and constant oil price to avoid linearization errors for large deviations. *Source: IMF — _wp12274 - 3. Traded Good Sector (excerpts provided).* ### 1. The Baseline Scenario ### 1. The Baseline Scenario ### Baseline calibration — saving in a SWF - Saving in a SWF: accumulation of windfall (by equation (25)) increases the fund steadily, reaching 132 percent of GDP in the new steady state. - Interest income from the SWF enters the regular budget each period and is mainly distributed to households as transfers. - Consumption and welfare effects: - In the new steady state, consumption is 5.2 percent higher relative to the path without the windfall. - Higher consumption produces a small negative influence on labor inputs (wealth effect), causing non-oil GDP to experience a small decline in the new steady state. - Public capital does not increase because public investment stays constant at the initial steady state level. - Distributional/behavioral note: - Given the calibration of a low Frisch labor elasticity (0.1), negative labor responses on non-resource output are suppressed. - Welfare measurement: - Welfare is measured by the average consumption change each period—in percent of consumption of the initial steady state—required to equate present-value welfare in a path with a windfall to that in a path without. The horizon computed is from 2012 to 2040. ### All-investing approach (invest all windfall in public capital) - Public capital dynamics: - Public capital builds up and at the peak (in 2025) public capital is 26 percent higher relative to the path without the windfall. - Output and consumption: - Higher public capital raises the marginal product of private inputs, resulting in higher non-oil GDP and higher private consumption. - Peak consumption (in 2026) is 4.3 percent above the path without the windfall and slightly higher than consumption with saving in a SWF (4.1 percent). - Welfare comparison: - Welfare is higher under all-investing by 1.0 percent of initial steady-state consumption each period (relative to saving in a SWF). - Alternative use of interest income: - Results are similar when the interest income is used to lower the consumption tax rate. --- ### 2. Absorptive Capacity ### Role of absorptive capacity constraints - Baseline assumption: - Investment efficiency falls from 0.5 to 0.35 when expenditure levels are above 60 percent of the initial steady-state level (binding absorptive capacity). - Implication under binding constraints (baseline, column one of Figure 1): - Despite much more public investment, households only enjoy slightly more consumption with all-investing than with saving in a SWF. - Peak consumption with binding constraints: 4.3 percent above no-windfall path (see All-investing above). ### Non-binding absorptive capacity scenario (scenario 2) - Assumption: - Investment efficiency does not fall: ϕ = 0.5 ∀t. - Outcomes relative to baseline: - Public capital under all-investing rises much higher with the same amount of investment expenditures. - Peak consumption in scenario 2 is 8.4 percent higher than under the path without a windfall (versus 4.3 percent with binding constraints). - Between saving in a SWF and all-investing in scenario 2, on average households enjoy more utility each period relative to saving in a SWF, equal to 3 percent of consumption in the initial steady state. ### Public investment multiplier (present-value, cumulative non-oil output multiplier) - Definition (following Mountford and Uhlig (2009)): - Cumulative multiplier at the end of year k is defined as ∑_{i=0}^k (∏_{j=0}^i R_{t+j}^{-1}) ΔY^{NO}_{t+i} / ∑_{i=0}^k (∏_{j=0}^i R_{t+j}^{-1}) Δp g_{t+i} G I_{t+i}, where ΔY^{NO}_{t+i} and Δp g_{t+i} G I_{t+i} are level changes in non-resource GDP and public investment relative to pre-windfall values, and discount factors are products of domestic real rates R_{t+j} constructed from model-implied interest rates along a transition path. - Empirical values: - Baseline with all-investing: cumulative non-oil output multiplier is 0.41 at the end of 2040. - Scenario 2 (non-binding constraints): multiplier increases to 0.64 at the end of 2040. - Interpretation: - Multipliers are generally low (much smaller than 1), mainly attributed to investment inefficiencies and potential absorptive capacity constraints. - The model assumes investment efficiency does not improve over time; building implementation capacity (“investing in investing”) could allow investment efficiency to change with capacity-building expenditures. --- ### 3. Return to Public Capital ### Parameterization and baseline return - Public capital elasticity: α_G = 0.1 in the first two scenarios, implying a net annual return of 13.4 percent. ### Scenario 3: Low return - Assumption: - α_G = 0.05, implying an annual return of 2.7 percent. - Outcomes: - Households are better off saving in a SWF and consuming the interest income. - By the end of 2040, private consumption under saving in a SWF is 4.7 percent above the path without the windfall, while it is only 0.8 percent with all-investing. - Cumulative non-resource output multiplier in 2040: 0.28 when α_G = 0.05. ### Scenario 4: High return - Assumption: - α_G = 0.20, implying an annual return of 35 percent (noted as much higher than the median return (24 percent) of World Bank projects in 2008). - Outcomes: - Households enjoy more consumption before 2035 with all-investing than with saving in a SWF. - Welfare with all-investing on average is 3.2 percent higher than with saving in a SWF. - Cumulative non-resource output multiplier in 2040: 0.67 when α_G = 0.2. - If absorptive capacity constraints are also relaxed (ϕ = 0.5 ∀t, scenario not shown), the multiplier is further increased to 1.12. ### Policy insight - Sensitivity: - Economic outcomes are highly sensitive to returns to public capital. - When public capital is not sufficiently productive, saving a windfall in an external fund (SWF) can be preferable. - When public investment is productive and absorptive capacity allows effective deployment, all-investing can yield higher consumption and welfare. --- ### 4. Sustaining Public Capital ### Financing and maintenance concern - Issue: - When a resource revenue horizon is short, sustaining public capital built with a windfall may be difficult in the long run. - Politicians often prefer new projects over allocating budget for operating and maintaining existing capital. - Implication: - The financing issue of sustaining public capital under a short revenue horizon can undermine long-lasting development gains from investing a windfall. ### Sustainable investing approach - Introduction: - The text introduces the sustainable investing approach as an alternative designed to ensure long lasting development gains from investing a windfall (details of the approach are discussed subsequently in the original source). *Source: IMF Working Paper — "1. The Baseline Scenario" (extracted content).* ### 1. The Cost of Fiscal Adjustments ### 1. The Cost of Fiscal Adjustments ### All-investing approach: fiscal adjustments needed to sustain capital - With the all-investing approach, fiscal adjustments (cutting government spending or raising non-resource taxes) are required to maintain sufficient investment to replenish depreciated capital after a windfall ends. - Figure 2 (four scenarios with all-investing) assumes transfers to households (solid lines) or the consumption tax rate (dotted-dashed lines) are adjusted to sustain public capital. - Key quantitative outcomes (baseline / first column): - Transfers to GDP ratio must be lowered to0.9percent of GDP in the new steady state, from2.7percent in the initial steady state. - If financed by taxes, the consumption tax rate must be raised to0.21in the new steady state, from0.18originally. - Welfare outcomes (Rows (1) to (3) in Table 2): - Households on average enjoy slightly higher welfare when capital is sustained under the baseline and scenario 4. - When public capital is less productive (scenario 3), households are slightly better off if capital is not sustained. - In scenario 2 (higher investment with non-binding absorptive capacity constraints), transfers as a share of GDP must be lowered to−0.01, equivalent to a lump-sum tax of 1 percent of GDP; alternatively the consumption tax rate must be raised to0.24in the new steady state. - Political economy and feasibility: - Large fiscal adjustments implied in some scenarios may not be feasible in practice; given political economy constraints, public capital stocks built with windfalls are likely to depreciate over time. ### Endogenous depreciation of public capital - Model specification: the depreciation rate of public capital rises when investment is lower than the cost required to replenish capital at a steady-state depreciation rate (equation (20)). - Under all-investing, the depreciation rate rises after 2020 to about10percent. - Comparison with fixed depreciation: - Figure 3 presents same four scenarios with a fixed steady-state depreciation rate of8percent. - With fixed depreciation, public capital declines more slowly; non-oil GDP and private consumption are both higher with all-investing across scenarios. - Removing endogenous depreciation overturns earlier result that sustaining capital through fiscal adjustment yields higher welfare in more optimistic scenarios 1 and 4 (compare row (4) to row (1) in Table 2). - Interpretation: - Endogenous depreciation penalizes volatile public investment trajectories relative to strategies that preserve capital once built. - Strategies resulting in volatile capital stocks are less efficient in the model and believed to be so in practice. ### The sustainable investing approach: design and results - Concept: - Combine saving abroad and domestic investment to choose a sustainable scaling-up magnitude given windfall size and fiscal/structural characteristics. - After windfall exhaustion, interest income from external savings and additional non-resource revenue jointly finance recurrent costs to maintain capital. - Investment rule (formalization): - GIt = (1 − e−γt) GIns s + e−γt GI0 . (34) - When γ= 0, GI t = GI0 ∀t; when γ→∞, public investment jumps immediately to the new steady-state level. - For simulations: choose GI0 > GIns s (front-loaded investment), and γ= 0.15 to yield gradual declining investment path settling at sustainable level. - Consumption tax rate is used as fiscal adjustment instrument in simulations (results similar under transfers adjustment). - Baseline case (first column): - GI0 = 1.6×GI and GIns s = 1.26×GI. - Under the 0.5 saving rate, the resource fund eventually climbs to64 percent of GDP. - Public capital is26percent permanently higher relative to the path without a windfall. - Private consumption is raised by4.7percent in the new steady state. - During transition, government can lower the consumption tax rate, boosting private consumption during the windfall period. - Investment efficiency: during first 12 years, ϑ stays at a constant level of0.5with sustainable investing, relative to0.35under all-investing. - Sustainable investing with 1.26×GI scaling-up and φ= 0.5 removes need for fiscal adjustments after windfall exhaustion; consumption tax returns to initial steady-state level. - Welfare: households enjoy on average more periodic utility—equivalent to1.1percent of initial steady-state consumption—under sustainable investing than with all-investing. - Higher scaling-up case (second column): - Long-run investment is40percent higher than initial steady-state level. - Public capital is38percent above the no-windfall path (vs 26percent). - Interest income from sovereign wealth fund insufficient to support higher investment; consumption tax must be raised to about0.2to sustain capital. - Despite higher public capital and non-resource GDP, consumption is lower due to higher consumption tax; periodic utility is on average0.5percent lower compared to the 26percent scaling-up case. - Lower saving-rate case (third column): - φ= 0.2 with scaling-up at26percent yields a smaller resource fund. - During windfall, more windfall is allocated to reduce consumption tax, producing a consumption boom; after windfall, smaller fund yields less interest income. - Consumption tax must be raised to about0.2to sustain capital; in the new steady state private consumption is1.7percent lower than under the φ= 0.5 case. - Calibration note: - GI nss = 1.26GI and φ= 0.5 in the preferred first case are pinned down after a sequence of simulations to find a magnitude that does not require fiscal adjustment in the long run. - Caveats: - Results conditioned on assumptions about return to public capital, absorptive capacity constraints, etc. - If investment projects are less productive or absorptive costs are higher, fiscal adjustments would be larger and more difficult to implement. - Initial planning of an investment scaling-up must account for future financing needs to sustain capital. ### Development without the windfall (Lucas paradox implications) - Closed capital account is part of the explanation why public investment scaling-up cannot occur absent a resource windfall; foreign capital does not flow easily to finance development in the model. - Foreign direct investment often focuses on natural resource extraction in practice. - Two emphasized distortions preventing domestically financed scaling-up: - Financing constraint and closed capital account implies countries would need to reduce private consumption and investment to finance scaling up. - Weak and distortionary domestic tax system (low effective tax rates and ineffectiveness of income tax). - Figure 5 comparisons (scaling-up without windfall vs with windfall): - Front-loaded scaling-up without windfall requires consumption tax to jump from0.18to almost0.27immediately, implying substantial fall in private consumption. - Gradual scaling-up without windfall reduces immediate fall in private consumption, but consumption increase in new steady state is minimal. - Without a windfall, welfare is higher if scaling up is not undertaken. - With a windfall, welfare is generally higher under either scaling up approach (all-investing or sustainable investing) than with full saving of the windfall (saving in a SWF). - Interpretation: - Resource windfall relaxes financing constraint and effectively provides a new tax technology (high ability to extract rents). ### Investing volatile resource revenue (Angola application) — sustainable investing for volatility management - Context: - Angola: long-lasting oil reserve, potential future findings, high oil production in initial steady state. - Revenue volatility introduced by fluctuating oil prices mimicking historical dynamics. - Equilibrium solved by log-linearization and Sims’s (2001) method for rational expectations models. - Stabilization fund and policy rule: - With long revenue horizon and high fiscal dependence on resource revenue, the resource fund acts as a stabilization fund to smooth government spending. - Savings rule revised to allow depositing and withdrawing (equation (28)): surplus revenues (TO∗t − TO∗) − (p g t G t s t − p g G s) are saved; fund drawn down when revenue shortfall. - Non-negative constraint imposed on path of F∗t; if buffer insufficient, investment spending is cut to maintain non-negative balance. - Simulation design for volatility comparison: - Compare standard deviations of key variables under sustainable investing vs spend-as-you-go. - Standard deviations in Table 3 are averages of 100 simulations using different draws of price shock sequences {εpot} from estimated distribution. - Oil production quantity projection from International Monetary Fund (2012d) taken as given; production shocks {εyot} injected to hit projected path. - For simplicity, same oil production path used across simulations. - Spend-as-you-go specification: - Similar to all-investing earlier but assumes60percent of additional revenues goes to investment and the rest40percent goes to government consumption. - Sustainable investing path for Angola (simulation assumption beginning point): - Public investment specified to gradually increase from8.7percent of GDP (the actual level in 2011) to15percent in ... [content ends here in supplied excerpt] *Source: _wp12274 - 1. The Cost of Fiscal Adjustments* ### 2022. Given a high government consumption to GDP ratio in 2011 of19.5percent, we ### _wp12274 - 2022. Given a high government consumption to GDP ratio in 2011 of19.5percent, we ### Fiscal rules, spend-as-you-go versus sustainable investing - Simulation setup: - Government consumption fixed at18percent of GDP throughout the simulation horizon. - Labor and consumption tax rates set at their initial steady-state levels. - Transfers experience small fluctuations to clear the government budget constraint. - Comparative volatility results (average standard deviations, percent deviations from trend, 2011–2025, based on 100 simulations): - public investment: Spend-as-You-Go =16.2; Sustainable Investing =7.4 - non-resource GDP: Spend-as-You-Go =1.2; Sustainable Investing =0.7 - private consumption: Spend-as-You-Go =1.0; Sustainable Investing =0.6 - real exchange rate: Spend-as-You-Go =2.2; Sustainable Investing =1.4 - Key mechanisms: - Spend-as-you-go generates about60−70 percent more volatility across key macro variables than sustainable investing. - Sustainable investing de-links periodic government spending from resource revenue flows via a stabilization fund, shielding the domestic economy from volatile resource revenues. - When large negative revenue shocks hit, the stabilization fund may not have sufficient balance to support a pre-determined investment level, forcing investment expenditures to dip even under sustainable investing. ### Allocation between investing and external saving (stabilization fund sizing) - Trade-off described: - A more aggressive scaling-up leads to faster build-up of public capital and potentially higher economic growth, but leaves less in a stabilization fund and increases vulnerability to negative shocks. - A more conservative scaling-up creates a larger buffer, allowing realized investment to follow pre-determined paths more closely and reducing depreciation pressures. - Angola application — two investment paths compared: - Conservative scaling-up (public investment and government consumption as assumed earlier). - Aggressive scaling-up: public investment quickly rises from9.2percent in 2011 to20percent in 2016 and stays at this level for the simulation horizon. - Simulation outcomes (Angola, end-2025 averages and bands): - Stabilization fund (mean end-2025): - Aggressive path =1.1 percent of GDP - Conservative path =37.1 percent of GDP - Mean realized scaling-up magnitude from 2016 to 2025 under aggressive path =15 percent (deviates from pre-determined 20 percent). - Average depreciation rate (95-percent upper bound): - Conservative path =0.08 - Aggressive path =0.10 - Public capital accumulation above the no-windfall path at end-2025: - Aggressive path =40percent - Conservative path =31percent - Tail risk (one- and two-standard-deviation lower bands for public capital in 2025): - Aggressive path: one-standard-deviation lower band =7.3 percent; two-standard-deviation lower band =−27.0 percent - Conservative path: one-standard-deviation lower band =24.8 percent; two-standard-deviation lower band =−4.0 percent - Non-oil GDP one-standard-deviation interval in 2025 (above no-windfall path): - Aggressive path =5.0 to 22.0 percent - Conservative path =7.5 to 15.0 percent - Households’ average consumption: similar magnitudes under aggressive and conservative paths on average. ### Depreciation channel and robustness checks - Endogenous depreciation channel: - Bad revenue outcomes imply investment below replacement rates → increase in depreciation rates → amplifies negative shock effects on capital stock and output. - High upper band for depreciation under aggressive scaling-up contributes to much worse lower bands for public capital and GDP. - Fixed-depreciation robustness (constant δG at initial 7 percent): - Lower bands of public capital are much less negative than with endogenous depreciation. - Performance of non-oil GDP and consumption in lower bands is much improved when depreciation is fixed at the initial7 percent. ### Policy implications and recommendations - Sustainable investing approach: - Combines investment with a resource fund to grapple with exhaustibility and volatility of natural resource revenues. - Enables scaling up public investment while maintaining macroeconomic stability by de-linking spending from volatile revenue flows. - Cautions on scaling-up design: - Scaling up too much and too fast (aggressive path) can: - Subject the economy to more instability. - Lower investment efficiency. - Risk higher depreciation rates. - Increase likelihood of boom-bust cycles. - Not guarantee superior growth outcomes versus a more conservative path. - Practical considerations: - The size of a scaling-up plan should be jointly considered with an economy’s ability to finance future recurrent costs to sustain public capital and with the distorting effects of fiscal adjustments. - In implementation, public investment is most likely to be cut when adjustment is needed, rather than immediate increases in tax rates or reductions in government consumption or transfers. ### Extensions and further research avenues - Model extensions suggested in the source: - Extend analysis to other types of investment (health, education) that build human capital and improve productivity. - Develop fuller rule-based optimal policy analysis within the complex model. - Adapt the model to short-run policy issues by introducing nominal rigidities. - Study interaction of natural resource revenues with fiscal rules that allow accumulation of commercial debt as developing economies access international bond markets. ### Key baseline calibration values (selected, as reported) - Public investment in 2011 (Angola): 9.2 percent - Public investment target (aggressive path from 2016): 20 percent - Stabilization fund (initial states, selected): - F* / GDP (CEMAC) =0.01 - F* / GDP (Angola) =0.02 - Depreciation rate for public capital (δG): - CEMAC =0.08 - Angola =0.07 - Annual real return to a resource fund (r*) =0.027 - Oil GDP/GDP (Y_O GDP): - CEMAC =0.09 - Angola =0.475 - Effective labor tax rates (τl): - CEMAC =0.08 - Angola =0.1 - Effective consumption tax rates (τc): - CEMAC =0.18 - Angola =0.1 *Source: IMF working paper content unit _wp12274 (PDF chapter/section).* ### REFERENCES ### _wp12274 - REFERENCES ### Major thematic clusters in the references - Absorptive capacity, public investment efficiency, and public capital - Adler, J. 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Owssowski, J. Daniel, and S. Barnett, 2001, Stabilizing and Saving Funds for Non-Renewable Resources: Experience and Fiscal Policy Implications (Washington, D.C.: International Monetary Fund). IMF Occasional Paper No. 205. - van der Ploeg, Frederick, and Anthony J. Venables, 2011, “Harnessing Windfall Revenues: Optimal Policies for Resource-Rich Developing Economies,” The Economic Journal, Vol. 121, No. 551, pp. 1-30. - Venables, Anthony J., 2010, “Resource Rents; When to Spend and How to Save,” International Tax and Public Finance, Vol. 17, pp. 340-356. - Gelb, Alan H., 1988, Oil Windfalls: Blessing or Curse? (Oxford University Press). - Takizawa, Hajime, Edward H. Gardner, and Kenichi Ueda, 2004, “Are Developing Countries Better Off Spending Their Oil Wealth Upfront?” IMF Working Paper WP/04/141. - Gros, Daniel, and Thomas Mayer, 2012, A Soverign Wealth Fund to Lift Germany’s Curse of Excess Savings). CEPS Policy Brief No. 280, August 28, Centre for European Policy Studies. - Den Bremer, Ton S. Van, and Frederick van der Ploeg, 2012, “How to Spend a Windfall: Dealing with Volatility and Capital Scarcity.” OxCarre Research Paper 85. - Multiple manuscripts and working papers on harnessing oil revenues (Ghana, Angola, CEMAC region), fiscal regimes for extractive industries, and the design and implementation of fiscal frameworks. - Macroeconomic modeling, fiscal policy effects, and investment dynamics - Baxter, Marianne, and Robert G. King, 1993, “Fiscal Policy in General Equilibrium,” American Economic Review, Vol. 86, No. 3, pp. 1154-1174. - Mountford, Andrew, and Harald Uhlig, 2009, “What Are the Effects of Fiscal Policy Shocks?,” Journal of Applied Econometrics, Vol. 24, No. 6, pp. 960-992. - Sims, Christopher A., 2001, “Solving Linear Rational Expectations Models,” Journal of Computational Economics, Vol. 20, No. 1-2, pp. 1-20. - Stockman, Alan C., and Linda L. Tesar, 1995, “Tastes and Technology in a Two-Country Model of the Business Cycle: Explaining International Comovements,” American Economic Review, Vol. 85, No. 1, pp. 168-185. - Burstein, Ariel, Martin Eichenbaum, and Sergio Rebelo, 2005, “Large Devaluations and the Real Exchange Rate,” Journal of Political Economy, Vol. 113, No. 4, pp. 742-784. - Greenwood, Jeremy, Zvi Hercowitz, and Gregory W. Huffman, 1988, “Investment, Capacity Utilization, and the Real Business Cycle,” American Economic Review, Vol. 78, No. 3, pp. 402-417. - Horvath, Michael, 2000, “Sectoral Schoks and Aggregate Fluctuations,” Journal of Monetary Economics, Vol. 45, No. 1, pp. 69-106. - Kraay, Aart, 2012, “How Large is the Government Spending Multiplier? Evidence from World Bank Lending,” Quarterly Journal of Economics, Vol. 127, No. 2. - Debt, aid, and international financial staff guidance - International Development Association and International Monetary Fund, 2011, Heavily Indebted Poor Countries (HIPC) Initiative and Multilateral Debt Relief Initiative (MDRI)–Status of Implementations and Proposals for the Future of the HIPC Initiative. - International Monetary Fund, 2009, Debt Limits in Fund-Supported Programs: Proposed New Guidelines, Vol. SM/09/215. - Berg, Andrew, Jan Gottschalk, Rafael Portillo, and Luis-Felipe Zanna, 2010, “The Macroeconomics of Medium-Term Aid Scaling-Up Scenarios.” IMF Working Paper WP/10/160, International Monetary Fund. - International Bank for Reconstruction and Development and the World Bank, 2010, Cost-Benefit Analysis in World Bank Projects (Washington, D.C.: The International Bank for Reconstruction and Development / The World Bank). - Empirical country and regional studies relevant to policy application - Caceres, Carlos, Marcos Poplawksi-Ribeiro, and Darlena Tartari, 2011, “Inflation Dynamics in the CEMAC Region.” IMF Working Paper WP/11/232, International Monetary Fund. - Baker, Carol, and Mpumelelo Nxumalo, forthcoming, “Assessing Reserve Adequacy of the Oil-rich CEMAC Region: What Can We Learn from the 2008-09 Oil Price Shock?” IMF Working Paper, International Monetary Fund. - Dagher, Jihad, Jan Gottschalk, and Rafael Portillo, forthcoming, “Oil Windfalls in Ghana: A DSGE Approach,” Journal of African Economies. - Richmond, Christine J., Irene Yackovlev, and Shu-Chun S. Yang, 2012, “Investing Volatile Oil Revenue in Capital-Scarce Economies: an Application to Angola.” Manuscript, International Monetary Fund. - Takizawa et al. (2004), van der Ploeg et al. (2012), and others addressing country-specific policy application and modeling. - Resource curse, Dutch disease, and political economy of natural resources - Sachs, Jeffrey D., and Andrew M. Warner, 1999, “The Big Push, Natural Resource Booms and Growth,” Journal of Development Economics, Vol. 59, No. 1, pp. 43-76. - Sachs, Jeffrey D., and Andrew M. Warner, 2001, “The Curse of Natural Resources,” European Economic Review, Vol. 45, pp. 827-838. - Manzano, Osmel, and Roberto Rigobon, “Resource Curse or Debt Overhang,” 2007, in Daniel Lederman, and William F. Maloney, eds., Natural Resources: Neither Curse nor Destiny, (Washington, D.C.: the World Bank). - van Wijnbergen, Sweder, 1984, “The ‘Dutch Disease’: A Disease After All?,” The Economic Journal, Vol. 94, No. 1, pp. 41-55. - van der Ploeg, Rick, 2010, “Aggressive Oil Extraction and Precautionary Saving: Coping with Volatility,” Journal of Public Economics, Vol. 94, pp. 421-433. - van der Ploeg, Frederick, 2011, “Natural Resources: Curse or Blessing?,” Journal of Economic Literature, Vol. 49, No. 2, pp. 366-420. ### Methodological and data sources cited - Empirical and modeling techniques - Sims, Christopher A., 2001, “Solving Linear Rational Expectations Models,” Journal of Computational Economics, Vol. 20, No. 1-2, pp. 1-20. - Baxter and King (1993); Mountford and Uhlig (2009); Greenwood et al. (1988) for general equilibrium and business cycle analysis. - Kraay, Aart, 2012, for empirical identification of government spending multipliers. - Databases, handbooks, and institutional guidance - International Bank for Reconstruction and Development and the World Bank, 2010, Cost-Benefit Analysis in World Bank Projects. - UNCTAD, 2012, World Investment Report: Towards a New Generation of Investment Policies (Geneva: United Nations). *References list as provided in _wp12274 - REFERENCES* --- _Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12274.pdf_