## _wp09154 — References (Introduction through Discussion) (excerpt)

## Source details

**Canonical URL:** [_wp09154 — References (Introduction through Discussion) (excerpt)](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09154.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09154.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09154.pdf.json)

---

### Key findings from literature and empirical regularities
- Public infrastructure in power, transport, and telecommunications facilitates access to productive opportunities and enhances growth; differences in infrastructure endowments are linked to large output and productivity differences across countries.
- Empirical magnitudes of the contribution of public infrastructure to output and growth vary considerably across studies due to differences in econometric methodology, measurement of physical capital, and level of data aggregation.
- Industry, regional, and sectoral studies generally report lower elasticities of public infrastructure capital to growth than macro-level studies.
- Studies using public investment flows (or their cumulative assets) often find ambiguous and negligible growth effects, particularly for low-income countries.
- Poor infrastructure provision and ineffective use of public capital reduce firm-level productive investments and help explain differential growth performance across regions.
- Weak institutions matter: empirical studies suggest growth effects of infrastructure depend on institutional strength.
- Aggregate regression reported: coef  = -.2320644, se = .04979987, t = -4.66 (Higher Infrastructure Quality values denote poorer infrastructure quality; higher Control of Corruption values denote better control of corruption.)

### Core contributions of the paper (model overview)
- Presents a framework reconciling contradictory empirical results on public infrastructure and growth by explicitly modeling interaction between inefficient/corrupt bureaucracies and provision of public investment services.
- Introduces corruption and bureaucratic oversight into a specialization-based endogenous growth setting (extension of Romer (1987) with infrastructure as in Glomm and Ravikumar (1994)).
- Public investment reduces costs of producing intermediate inputs, fostering specialization; corruption reduces the productivity of public expenditures and undermines specialization and capital accumulation.
- Government oversight is less effective when corruption is entrenched; lower oversight and higher corruption reduce the effectiveness of government spending and lead to much lower growth than in absence of specialization.
- Multiple, frequency-dependent equilibria arise from strategic interactions in bureaucratic decision-making, producing different incidences of corruption, quality of public infrastructure, and growth.

### Model environment — structure and key mechanisms
- Time: discrete, overlapping generations with two-period lived agents; households either work in production or as bureaucrats chosen by lottery. A measure m of public works projects is in operation, each managed by one official (m denotes public sector workforce share).
- Final goods produced competitively by combining a range of intermediate goods n_t using CES-like aggregator with parameter σ (σ ∈ [0,1], inverse of elasticity of substitution).
- Key relationships reproduced from the model:
  - Y_t = [∫_0^{n_t} x_{it}^{(σ−1)/σ} di]^{σ/(σ−1)}.
  - In symmetric equilibrium: x_{it} = x_t ∀i,t and Y_t = n_t^{1/(1−σ)} x_t.
  - Demand for i-th intermediate good: x_{it} = Y_t p_{it}^{−1/σ}.
- Intermediate goods producers: monopolistic competition, fixed cost φ, CRS technology x_{it} = A g_t θ k_i^α l_i^{1−α}; effective productivity g_t depends on technology A and aggregate public capital G_t scaled by output Y_t: g_t ≡ G_t / Y_t.
- Free entry and profit dissipation conditions lead to expressions:
  - p_i x_i σ = φ, x_t = (φ / n_t^{σ/(σ−1)}), and Y_t = n_t φ^{−σ}.
- Wages proportional to range of intermediate goods: w_t = λ n_t with λ defined by parameters m, σ, φ.

### Government, bureaucrats, and corruption mechanics
- Government budget: balanced; fraction μ of tax revenue T_t goes to public capital projects, remainder 1−μ to monitoring/auditing.
- Each project receives q_t funds; leakages imply project yields quality-adjusted public capital G_{jt} = q_{jt} ε_{jt} with ε ∈ [0,1] and same efficiency index across projects; aggregate G_t = ∫_0^m q_{jt} ε_{jt} dj.
- Corruption model for a project with diversion v ∈ [0,1]:
  - quality = q(1−v) with prob. π(v)
  - quality = q(1−v) δ_L with prob. 1−π(v)
  - δ_H and δ_L with δ_H>δ_L, and π′(v)>0.
- Government audits when project is low quality; audit success probability denoted φ (function of average theft v and enforcement e). Example functional form: φ(v,e) = 1 − v^θ e^β with specified properties.
- Bureaucrat expected end-of-period income: [1 − φ(v,e)](w + v q). First order condition defines optimal theft v = V(φ, w/q), decreasing in φ and w/q.
- Equilibrium theft v may admit multiple equilibria (including zero); illustration with feasible corruption equilibria v_L and v_H (and zero), where the intermediate solution is unstable—resulting equilibria include 0 and v_H in the example.

### General equilibrium and steady-state implications
- Given equilibrium corruption v ∈ {0, v_H} (or other feasible levels), fraction (1−v)π of projects are good quality; average quality-adjusted public capital:
  - G_t = m n_t λ μ τ [ (1−v) π δ_H + (1 − (1−v) π) δ_L ].
- Defining g_t ≡ G_t / Y_t leads to relationships: Y_t = g_t γ [π δ_H + (1−π) δ_L] (stylized representation).
- Quality-adjusted public capital g takes distinct values g_H and g_L depending on corruption equilibrium; explicit expressions provided in the paper text.
- Reduced-form aggregate technology (stylized): Y_t = n_t^{1/(1−σ)} g_t^{1/(1−σ)} K_t^{(1−α)/(1−2σ)}.
- Effective elasticity of output to public investment exceeds the direct firm-level elasticity θ and increases in σ (model statement: effective elasticity exceeds θ and increases in σ).
- Asset market clearing yields dynamic condition for K_t; parameter restriction for unique asymptotically stable steady-state: α(1−σ)/(1−2σ) < 1 (text notes σ < 1 / 2 implied by the restriction).
- Steady-state output per worker expressed (text, equation (29)):
  - y(v) = M(v) g^{1/(1−σ)}, where M is defined with parameters and corruption enters via g and Γ(v).
- Corruption lowers quality of public investment g, discourages specialization, and lowers steady-state output per worker. Corruption also affects bureaucrats’ savings flow Γ(v) with ambiguous net effect on capital accumulation; the paper focuses on the public investment quality channel and abstracts from ambiguous savings-channel effects.

### Micro vs. macro estimates of public capital productivity
- Micro-level estimates of the direct productivity effect of public capital: range reported 0.06 to 0.20.
- Industry-level evidence (manufacturing-focused) example: Pineda and Rodriguez (2006) (Venezuela): a 1 percent increase in the allocation to public expenditures generates an increase in productivity of the manufacturing sector of between 0.2 and 0.35.
- Macro estimates can be larger than micro estimates because of economy-wide mechanisms (specialization, complementarities) that magnify direct effects.

### Magnification effect, σ and θ, and illustrative elasticities (Table 1 excerpts)
- Public capital contributes directly to firm productivity with parameter θ; endogenous specialization amplifies aggregate impact when σ > 0.
- Acemoglu and Ventura (2002) estimate the elasticity of substitution among intermediate goods at 2.6, implying a point elasticity of 0.38 for the related expression reported in the paper.
- Table 1 entries (effective output elasticity of public capital) for combinations of σ and θ:
  - θ = 0.05: 0.06, 0.07, 0.09, 0.15 (for σ = 0.1, 0.2, 0.3, 0.4)
  - θ = 0.10: 0.11, 0.13, 0.18, 0.30
  - θ = 0.15: 0.17, 0.20, 0.26, 0.45
  - θ = 0.20: 0.23, 0.27, 0.35, 0.60
- Example interpretation: a conservative micro-elasticity θ = 0.10 implies a macro elasticity of about 0.30 in presence of significant complementarities.

### Evidence on externalities and sectoral magnification
- Hulten et al. (2006) (Indian states, 1972–1992): growth of road and electricity-generating capacity accounted for nearly half the growth of the productivity residual of India's registered manufacturing — indicating substantial externality effects from state infrastructure to manufacturing productivity.

### Accounting for income gaps: quality-adjusted public capital and steady-state output
- Embedding the technology in an OLG economy yields a steady-state output per worker with a public capital elasticity; when specialization is endogenous (σ > 0) the steady-state elasticity of public capital on income is higher.
- Two equilibria can exist:
  - Zero corruption/inefficiency: all public outlays converted into productive capital.
  - Positive theft/leakages: lower quality public capital stock.
- Cross-country estimates of public capital quality and implied quality ratios:
  - Hulten (1996): defines effective public capital e = g^ε. In his dataset (middle- and low-income countries, 1970-1990):
    - Public capital as share of GDP: top-third richest middle-income = 12.4 percent versus bottom-third = 8.6 percent for similar categories in low-income countries.
    - Average efficiency index: top third = 0.65; low income = 0.45.
    - Ratio of quality-adjusted public capital in rich versus poor countries ≈ 1.45.
  - Calderon and Serven (2004) dataset yields a reported ratio of quality-adjusted capital stock of around 3.28.

### Table 3 — steady-state predictions for output gaps (selected reproduced entries)
- Assuming quality-adjusted public capital ratios RP = 1.5, 2, 3 and α = 0.3, reported steady-state output gap predictions (rows correspond to θ levels and blocks in the source) include:
  - Quality ratio = 1.5:
    - σ = 0.10: 1.04; σ = 0.25: 1.06; σ = 0.40: 1.84
  - Quality ratio = 2:
    - σ = 0.10: 1.06; σ = 0.25: 1.10; σ = 0.40: 2.83
  - Quality ratio = 3:
    - σ = 0.10: 1.10; σ = 0.25: 1.16; σ = 0.40: 5.20
  - (Second block)
  - Quality ratio = 1.5:
    - σ = 0.10: 1.07; σ = 0.25: 1.12; σ = 0.40: 3.38
  - Quality ratio = 2:
    - σ = 0.10: 1.12; σ = 0.25: 1.21; σ = 0.40: 8.00
  - Quality ratio = 3:
    - σ = 0.10: 1.21; σ = 0.25: 1.35; σ = 0.40: 27.00
  - (Third block)
  - Quality ratio = 1.5:
    - σ = 0.10: 1.11; σ = 0.25: 1.18; σ = 0.40: 6.20
  - Quality ratio = 2:
    - σ = 0.10: 1.19; σ = 0.25: 1.33; σ = 0.40: 22.63
  - Quality ratio = 3:
    - σ = 0.10: 1.32; σ = 0.25: 1.57; σ = 0.40: 140.30
- Interpretation: small differences in quality-adjusted public investment can yield very large steady-state output gaps when σ and θ are moderate to large; differences in public investment quality produce larger gaps when specialization is endogenous.

### Policy implications and conclusions
- Public investment fosters specialization and enhances private capital productivity, generating direct and indirect growth effects.
- The growth impact of public investment depends critically on the quality and efficiency of public capital; inefficiencies and weak oversight reduce returns and magnify income gaps.
- Multiple corruption equilibria (rather than technology differences alone) can explain observed differences in public capital quality across rich and poor countries.
- Policy priority: in low-income countries with weak institutions and pressing infrastructure needs, improving monitoring and bureaucratic oversight is crucial to ensure public investment spending is not wasted — simply increasing public spending on infrastructure can be highly inefficient without improved oversight.

*Source: Excerpt from the paper (Introduction through Discussion) in _wp09154 - References.*

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

### References (excerpt) — Introduction and Model Summary

### Key findings from literature and empirical regularities
- Public infrastructure in power, transport, and telecommunications facilitates access to productive opportunities and enhances growth; differences in infrastructure endowments are linked to large output and productivity differences across countries.
- Empirical magnitudes of the contribution of public infrastructure to output and growth vary considerably across studies due to differences in econometric methodology, measurement of physical capital, and level of data aggregation (references to Straub, 2007, 2008; Romp and de Haan, 2007).
- Industry, regional, and sectoral studies generally report lower elasticities of public infrastructure capital to growth than macro-level studies.
- Studies using public investment flows (or their cumulative assets) often find ambiguous and negligible growth effects, particularly for low-income countries (Easterly and Rebelo, 1993; Pritchett, 2000), likely because investment spending may be a poor proxy for accumulation of productive assets.
- Poor infrastructure provision and ineffective use of public capital reduce firm-level productive investments (Reinnikka and Svensson, 2002) and help explain differential growth performance across regions (Hulten, 1996; Calderon and Serven, 2007).
- Weak institutions matter: empirical studies suggest growth effects of infrastructure depend on institutional strength (Esfahani and Ramirez, 2003; Dal Bo and Rossi, 2007).
- Figure 1 (aggregate data) shows a negative correlation between an index of Infrastructure Quality and an index of Control of Corruption; regression reported: coef  = -.2320644, se = .04979987, t = -4.66. (Higher Infrastructure Quality values denote poorer infrastructure quality; higher Control of Corruption values denote better control of corruption.)

### Core contributions of the paper (model overview)
- Presents a simple framework reconciling contradictory empirical results on public infrastructure and growth by explicitly modeling interaction between inefficient/corrupt bureaucracies and provision of public investment services.
- Introduces corruption and bureaucratic oversight into a specialization-based endogenous growth setting (extension of Romer (1987) with infrastructure as in Glomm and Ravikumar (1994)).
- Public investment reduces costs of producing intermediate inputs, fostering specialization; corruption reduces the productivity of public expenditures and undermines specialization and capital accumulation.
- Government oversight is less effective when corruption is entrenched; lower oversight and higher corruption reduce the effectiveness of government spending and lead to much lower growth than in absence of specialization.
- Multiple, frequency-dependent equilibria arise from strategic interactions in bureaucratic decision-making, producing different incidences of corruption, quality of public infrastructure, and growth.

### Model environment — structure and key mechanisms
- Time is discrete, overlapping generations with two-period lived agents; households either work in production or as bureaucrats chosen by lottery. A measure m of public works projects is in operation, each managed by one official (m denotes public sector workforce share).
- Final goods produced competitively by combining a range of intermediate goods nt using CES-like aggregator with parameter σ (σ ∈ [0,1], inverse of elasticity of substitution). Key relationships:
  - Yt = [∫0^nt xit^(σ−1)/σ di]^(σ/(σ−1)) (equation (1))
  - In symmetric equilibrium, xit = xt ∀i,t, and Yt = nt^(1/(1−σ)) xt (equation (2))
  - Demand for i-th intermediate good: xit = Yt p_it^(−1/σ) (equation (3))
- Intermediate goods producers are monopolistically competitive with fixed cost φ and CRS technology x_it = A g_t θ k_i^α l_i^(1−α) (equation (4)); effective productivity gt depends on technology A and aggregate public capital Gt scaled by output Yt: gt ≡ Gt / Yt.
- Free entry implies profits dissipated: p_i x_i σ = φ (equation (7)), leading to (equation (9)) xt = (φ / n_t^(σ/(σ−1))) and (equation (10)) Yt = n_t φ^(−σ).
- Wages proportional to range of intermediate goods: w_t = λ n_t (equation (12)) with λ defined in terms of parameters m, σ, φ.

### Government, bureaucrats, and corruption mechanics
- Government runs balanced budget: fraction μ of tax revenue Tt goes to public capital projects, remainder 1−μ to monitoring/auditing.
- Each project receives q_t funds; leakages and corruption imply project yields quality-adjusted public capital G_jt = q_jt ε_jt with ε ∈ [0,1] and same efficiency index across projects (equation (14)); aggregate public capital Gt = ∫_0^m q_jt ε_jt dj (equation (15)).
- Bureaucrats are offered market wage w; corruption allows diversion of v q of project funds where v ∈ [0,1]; project quality realized probabilistically:
  - quality = q(1−v) with prob. π(v)
  - quality = q(1−v) δ_L with prob. 1−π(v)
  where δ_H and δ_L with δ_H>δ_L, π′(v)>0 (equation (20) and surrounding text).
- Government audits when project is low quality; audit success probability denoted φ (function of average theft v and enforcement e). Functional form example: φ(v,e) = 1 − v^θ e^β with properties specified (equation (23) as an example).
- Bureaucrat expected end-of-period income: [1 − φ(v,e)](w + v q). First order condition defines optimal theft v = V(φ, w/q) decreasing in φ and w/q.
- Equilibrium vandalism v may admit multiple equilibria (including zero); illustration identifies two feasible corruption equilibria v_L and v_H (and zero), with the intermediate one unstable—hence equilibria are 0 and v_H in the example.

### General equilibrium and steady-state implications
- Given equilibrium corruption v ∈ {0, v_H} (or other feasible levels), fraction (1−v)π of projects are good quality; average quality-adjusted public capital:
  - G_t = m n_t λ μ τ [ (1−v) π δ_H + (1 − (1−v) π) δ_L ] (equation (24) representation)
  - Defining g_t ≡ G_t / Y_t leads to Y_t = g_t γ [π δ_H + (1−π) δ_L] relationships (equation (25) stylized).
- Quality-adjusted public capital g takes two values g_H and g_L depending on corruption equilibrium; explicit expressions provided in text.
- Range of intermediate goods expressed in terms of capital stock K_t via (26); reduced-form aggregate technology yields Y_t = n_t^((1)/(1−σ)) g_t^((1)/(1−σ)) K_t^((1−α)/(1−2σ)) (equation (27) stylized).
- Effective elasticity of output to public investment is (1)/(1−σ) × θ (text states combined effect captured by effective elasticity (1) / (1 − 2σ) θ σ σ−−? — preserve model statement that effective elasticity exceeds θ and increases in σ).
- Asset market clearing (equation (28)) yields dynamic equilibrium condition for K_t; parameter restriction for unique asymptotically stable steady-state: α(1−σ)/(1−2σ) < 1, equivalent to 1 / (2 α / (α − σ))? (text states inequality and notes σ<1 / 2 implied by the restriction).
- Steady-state expressions:
  - Steady-state capital K* given implicitly in text (expression in terms of Γ and parameters).
  - Steady-state output per worker:
    - y = M(v) g^( (1) / (1−σ) ) K^( (1−α) / (1−2σ) ) — text presents (29) specifically:
      - y(v) = M(v) g^( (1) / (1−σ) ) where M is defined with parameters and corruption enters via g and Γ(v).
  - Corruption lowers quality of public investment g, discourages specialization, and lowers steady-state output per worker. Corruption also affects bureaucrats’ savings flow Γ(v) with ambiguous net effect on capital accumulation; the paper focuses on public investment quality channel and abstracts from ambiguous savings-channel effects.

### Policy implications and discussion
- Public investment is more efficient in developed countries relative to poorer countries because corruption, bureaucratic oversight quality, and public infrastructure quality are jointly determined in equilibrium.
- The quality of monitoring and bureaucratic oversight is key to realizing investment returns; scaling up public investment without improvements in screening, monitoring, and oversight can fail to produce expected growth benefits.
- Model provides a mechanism to reconcile larger macro-level elasticities of public capital with smaller micro/sectoral estimates via specialization and entry effects: productive public investment increases profits in intermediate goods industries and eases entry of new varieties, amplifying aggregate-level effects relative to micro-level impacts.
- Empirical context: early aggregate estimates reported output elasticities of public capital ranging from 0.31 to 0.54; more recent national-level evidence suggests elasticities about 0.20 to 0.30 and possibly lower at regional level (text cites Aschauer (1989) and subsequent literature).

*Source: Excerpt from the paper (Introduction through Discussion) in _wp09154 - References.*

### 0.06 to 0.20 (Straub, 2008; Romp and de Haan, 2007). Studies at the industry level are

### _wp09154 - 0.06 to 0.20 (Straub, 2008; Romp and de Haan, 2007). Studies at the industry level are

### Micro vs. macro estimates of public capital productivity
- Micro-level estimates of the direct productivity effect of public capital are relatively small; cited range: 0.06 to 0.20.
- Industry-level evidence (manufacturing-focused) often finds significant productive effects:
  - Pineda and Rodriguez (2006) (Venezuela): a 1 percent increase in the allocation to public expenditures generates an increase in productivity of the manufacturing sector of between 0.2 and 0.35.
- Macro estimates can be larger than micro estimates because of economy-wide mechanisms (specialization, complementarities) that magnify direct effects.

### Model of public capital, specialization, and magnification effects
- Public capital is modeled as directly contributing to firm productivity; endogenous specialization amplifies the aggregate impact of public capital relative to a fixed-range-of-goods specification.
- Even if the direct firm-level productivity effect (θ) is small, quality-adjusted public investment can magnify macro-effects via its impact on intermediate goods specialization.
- The magnification effect increases with the complementarity of intermediate goods (σ).
  - Acemoglu and Ventura (2002) estimate the elasticity of substitution among intermediate goods at 2.6, implying a point elasticity of 0.38 for the related expression reported in the paper.
- Empirical evidence on σ is scarce; θ has some empirical guidance, σ does not.

### Table 1 (effective output elasticity of public capital) — selected illustrative values
- Table 1 demonstrates combinations of θ (direct firm output elasticity w.r.t. public capital) and σ (complementarity of intermediate goods). Selected matrix entries reported in the text:
  - For σ = 0.1, 0.2, 0.3, 0.4 and θ = 0.05, 0.10, 0.15, 0.20 the table entries are (organized by θ rows):
    - θ = 0.05: 0.06, 0.07, 0.09, 0.15
    - θ = 0.10: 0.11, 0.13, 0.18, 0.30
    - θ = 0.15: 0.17, 0.20, 0.26, 0.45
    - θ = 0.20: 0.23, 0.27, 0.35, 0.60
- Example interpretation: a conservative micro-elasticity θ = 0.10 implies a macro elasticity of about 0.30 in the presence of significant complementarities, consistent with some macro studies.

### Evidence on externalities and sectoral magnification
- Hulten et al. (2006) (Indian states, 1972–1992): growth of road and electricity-generating capacity accounted for nearly half the growth of the productivity residual of India's registered manufacturing — indicating substantial externality effects from state infrastructure to manufacturing productivity.

### Accounting for income gaps: quality-adjusted public capital and steady-state output
- Embedding the simpler technology in an OLG economy yields a steady-state output per worker with a public capital elasticity; when specialization is endogenous (σ > 0) the steady-state elasticity of public capital on income is higher.
- Two equilibria in corruption and public capital quality can exist:
  - One equilibrium: zero corruption/inefficiency, all public outlays converted into productive capital.
  - Other equilibrium: positive theft/leakages, lower quality public capital stock.
- Interpreting the two equilibria as pertaining to rich (R) and poor (P) countries differing only in corruption (hence quality of public investment), the model asks how much quality differences explain observed income gaps.

### Cross-country estimates of public capital quality and implied quality ratios
- Hulten (1996): defines effective public capital e = g^ε, where ε measures average public capital effectiveness.
  - In his dataset (middle- and low-income countries, 1970-1990):
    - Public capital as share of GDP: top-third richest middle-income = 12.4 percent versus bottom-third = 8.6 percent for similar categories in low-income countries.
    - Average efficiency index: top third = 0.65; low income = 0.45.
    - This yields a ratio of quality-adjusted public capital in rich versus poor countries of about 1.45.
- Calderon and Serven (2004): compile infrastructure quality stocks across low- and high-income countries.
  - Using their dataset the authors report a ratio of quality-adjusted capital stock of around 3.3 percent (reported in text as around 3.3 percent; Table 2 in the source reports 3.28).

### Table 3 — steady-state predictions for output gaps
- Assuming a range for quality-adjusted public capital of 1.5 to 3 and α = 0.3, steady-state output gap predictions (ratios /RP yy) are reported for combinations of σ and θ. The table entries reproduced from the text (quality-adjusted public capital ratios 1.5, 2, 3; columns are σ = 0.10, 0.25, 0.40; rows correspond to θ = 0.05, 0.10, 0.15):

  - For quality ratio = 1.5:
    - σ = 0.10: 1.04
    - σ = 0.25: 1.06
    - σ = 0.40: 1.84

  - For quality ratio = 2:
    - σ = 0.10: 1.06
    - σ = 0.25: 1.10
    - σ = 0.40: 2.83

  - For quality ratio = 3:
    - σ = 0.10: 1.10
    - σ = 0.25: 1.16
    - σ = 0.40: 5.20

  - (Second block)
  - For quality ratio = 1.5:
    - σ = 0.10: 1.07
    - σ = 0.25: 1.12
    - σ = 0.40: 3.38

  - For quality ratio = 2:
    - σ = 0.10: 1.12
    - σ = 0.25: 1.21
    - σ = 0.40: 8.00

  - For quality ratio = 3:
    - σ = 0.10: 1.21
    - σ = 0.25: 1.35
    - σ = 0.40: 27.00

  - (Third block)
  - For quality ratio = 1.5:
    - σ = 0.10: 1.11
    - σ = 0.25: 1.18
    - σ = 0.40: 6.20

  - For quality ratio = 2:
    - σ = 0.10: 1.19
    - σ = 0.25: 1.33
    - σ = 0.40: 22.63

  - For quality ratio = 3:
    - σ = 0.10: 1.32
    - σ = 0.25: 1.57
    - σ = 0.40: 140.30

- Interpretation: small differences in quality-adjusted public investment can yield large steady-state output gaps when σ and θ are moderate to large; differences in public investment quality produce larger gaps when specialization is endogenous.

### Policy implications and conclusions
- Public investment fosters specialization and enhances private capital productivity, generating direct and indirect growth effects.
- The growth impact of public investment depends critically on the quality and efficiency of public capital; inefficiencies and weak oversight reduce returns and magnify income gaps.
- Multiple corruption equilibria (rather than technology differences alone) can explain observed differences in public capital quality across rich and poor countries.
- Policy priority: in low-income countries with weak institutions and pressing infrastructure needs, improving monitoring and bureaucratic oversight is crucial to ensure public investment spending is not wasted — simply increasing public spending on infrastructure can be highly inefficient without improved oversight.

*Source: _wp09154 (excerpt).*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09154.pdf_