## _wp1640

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### Model parameter values and calibrations
- Discount factor: 0.995 (Iwata (2013))
- Relative size of the domestic economy: 0.5
- Within-country substitutability (ρ): 11 (Basu and Fernald (1997))
- Cross-country substitutability (ρ): 1.5 (Dong (2012))
- Frisch elasticity of labor supply (ν): 0.7 (Keane and Rogerson (2012) and Chetty et al (2013))
- Calvo parameter (γ): 0.5 (Bils and Klenow (2004))
- Home bias parameter (α): 1.68 (World Bank (2015) & Coenen (2013))
- Home bias parameter (α*): 0.32 (World Bank (2015) & Coenen (2013))
- Risk premium in UIP (ψ): 0.004 (Bergin (2006))
- Interest rate smoothing (μ1): 0.79 (Clarida et al. (2000))
- Interest rate smoothing (μ2): 1.5 (Coefficient for inflation in the monetary policy rule; Taylor (1993))
- Persistency of public spending shocks (CI ρρ,): 0.75 (Iwata (2013))
- Size of public spending shocks (CI εε,): 1
- Weight of public consumption (υ): 0.4 (Song et al. (2012))
- Depreciation rate of public infrastructure (λ): 0.025 (Bom and Lighhart (2014))
- Parameter (φ): [value not provided in the source excerpt]

### Multiplier definitions and welfare methodology
- Cumulative multiplier (CM): cumulative change of output over cumulative change of public spending over a horizon (as in Gechert and Rannenberg (2014)).
- Net present value fiscal multiplier (NPVM): sum of output over a certain time horizon discounted at the steady state interest rate and divided by government spending discounted in the same way; the analysis uses 2,000 periods.
- Welfare multiplier methodology: follows Sims and Wolff (2013) and Schmitt-Grohe and Uribe (2007). The welfare multiplier is the consumption-equivalent one-period change in the present discounted value of flow utility for a one dollar change in government spending, computed as the NPV of the welfare impact expressed as a percentage of initial consumption and divided by the discounted government spending.

### Output and welfare multipliers — public consumption (key findings)
- A one percent increase in domestic public consumption increases domestic output (demand and wealth effects), but initial domestic trade balance deteriorates and then improves (hump-shaped).
- Cumulative output multipliers of public consumption are in the 0.4-0.5 range (consistent with Gechert and Rannenberg (2014)).
- Empirical multipliers and welfare:
  - Domestic welfare multiplier for public consumption: -0.30 (domestic households willing to pay 0.3 dollars to avoid one dollar rise in public consumption).
  - World welfare multiplier for a public consumption shock: -0.28.
- Comparative and robustness notes:
  - Sims and Wolff (2013) report welfare multipliers ranging between -8.6 and 35 depending on steady-state government spending; their output multiplier is 1.2.
  - Increasing the utility weight on public consumption (υ) from benchmark 0.4 to υ = 1 yields a welfare multiplier just above zero; υ = 1.5 yields welfare multiplier = 0.25.
  - Rendhal (2015): long-duration fiscal expansion welfare multiplier = 0.65; temporary expansions can be between -0.4 and -0.2.

- Selected figures (Table 2, public consumption)
  - Consumption:
    - CM, 4 PRs = 0.44
    - CM, 8 PRs = 0.41
    - CM, 12 PRs = 0.41
    - CM, 16 PRs = 0.41
    - CM, 20 PRs = 0.42
    - NPV of output multiplier = 0.46
    - Welfare multiplier = -0.30
    - World welfare multiplier = -0.28
  - Investment (for comparison):
    - CM, 4 PRs = 0.58
    - CM, 8 PRs = 0.79
    - CM, 12 PRs = 1.0
    - CM, 16 PRs = 1.3
    - CM, 20 PRs = 1.5
    - NPV of output multiplier = 3.2
    - Welfare multiplier = 0.77
    - World welfare multiplier = 0.91

### Public infrastructure investment — output and welfare effects
- Two channels: temporary demand effect and a supply-side effect (higher infrastructure stock raises productive capacity).
- Short-term consumption typically falls due to higher taxes needed to finance investment; medium-term output rises because of expanded productive capacity.
- Output multipliers rise with horizon as infrastructure stock increases productive capacity.
- Cumulative output multipliers (Table 3) — comparison:
  - IMF (2014):
    - CM, 4 PRs = 0.5
    - CM, 8 PRs = 0.7
    - CM, 12 PRs = 1
    - CM, 16 PRs = 1.3
    - CM, 20 PRs = 1.5
  - Our model:
    - CM, 4 PRs = 0.6
    - CM, 8 PRs = 0.8
    - CM, 12 PRs = 1
    - CM, 16 PRs = 1.3
    - CM, 20 PRs = 1.5

- Long-run and NPV effects:
  - NPV of output multiplier for public infrastructure investment (benchmark): 3.2 (much higher than cumulative multipliers because spending returns to zero after about four years while productive capacity and output remain elevated).
  - Bom and Lighhart (2014) theoretical long-run multiplier = 2.3 for permanent increase.
  - Leduc and Wilson (2013) estimate output returns to pre-shock level after ten years.

- Welfare multipliers (benchmark and spillovers):
  - Domestic welfare multiplier for a public infrastructure investment shock (benchmark): 0.77 (households willing to pay 0.77 dollars for a one dollar increase in public infrastructure investment).
  - World welfare multiplier: 0.91 (domestic plus foreign welfare effects).
  - Welfare spillovers: positive after some time because improvement in foreign terms of trade raises foreign consumption more than foreign output and labor supply.

### Sensitivity to the output elasticity of public infrastructure (ϕ) and other parameters
- Results are sensitive to output elasticity of public capital (ϕ). Selected cases (Table 4):
  - ϕ = 0.02:
    - CM, 16 periods = 0.62
    - CM, 20 periods = 0.68
    - NPV of output multiplier = 1.1
    - Welfare multiplier = -0.19
    - World welfare multiplier = -0.14
  - ϕ = 0.03:
    - CM, 16 periods = 0.73
    - CM, 20 periods = 0.82
    - NPV of output multiplier = 1.5
    - Welfare multiplier = -0.042
    - World welfare multiplier = 0.021
  - ϕ = 0.083 (benchmark):
    - CM, 16 periods = 1.3
    - CM, 20 periods = 1.5
    - NPV of output multiplier = 3.2
    - Welfare multiplier = 0.77
    - World welfare multiplier = 0.91
  - ϕ = 0.131:
    - CM, 16 periods = 1.8
    - CM, 20 periods = 2.2
    - NPV of output multiplier = 4.8
    - Welfare multiplier = 1.5
    - World welfare multiplier = 1.7

- Interpretations from sensitivity analysis:
  - When ϕ = 0.03 welfare multiplier is close to zero (-0.042).
  - Matching IMF (2014) low-efficiency multipliers (0.6 and 0.7 after 4 and 5 years) corresponds roughly to ϕ = 0.02 (welfare multiplier = -0.19).
  - High-efficiency case matching IMF (2014) multipliers (2.1 and 2.3 after 4 and 5 years) corresponds roughly to ϕ = 0.131 (welfare multiplier = 1.5).
  - Bom and Ligthart (2014) show welfare effects turn negative when ϕ < 3 percent; in this model welfare multiplier is positive when ϕ is slightly higher than 3 percent.

- Sensitivity to within-country substitutability and labor supply elasticity:
  - Within-country substitutability examples: setting it to 6 (21) implying a 20 (5) percent markup over marginal costs:
    - When ϕ = 0.083, domestic welfare multiplier = 0.79 (if substitutability = 6) and = 0.76 (if substitutability = 21).
    - Conclusion: welfare multipliers are not very sensitive to changes in within-country substitutability.
  - Footnote: welfare multipliers are not responsive to changes in the Frisch elasticity of labor supply.

### Policy implications and conclusions
- Main conclusion: public infrastructure investment can yield sizable positive welfare multipliers when public capital is sufficiently productive.
- Improving productivity/efficiency of public spending is crucial to capture benefits:
  - For low elasticity of public infrastructure, increases in public investment can be welfare-detrimental (negative welfare multiplier).
  - For high efficiency, public investment can yield very large welfare gains (e.g., welfare multiplier = 1.5 when ϕ = 0.131).
- Policy recommendation: strengthen public investment management—planning, allocation, and implementation—to enhance productivity of public investment and ensure positive welfare multipliers.
- Additional implication: a global infrastructure push is timely—expected to increase output, reduce public debt-to-GDP ratio (per IMF (2014)), and yield sizable welfare benefits.

*Source: _wp1640 - 0.083 Output elasticity of public infrastructure (PDF chapter content provided).*

### 0.995 Discount factor Iwata (2013)

### 0.995 Discount factor Iwata (2013)

### Model parameter values and calibrations
- Discount factor: 0.995 (Īwata (2013))
- Relative size of the domestic economy: 0.5
- Within-country substitutability (ρ): 11 (Basu and Fernald (1997))
- Cross-country substitutability (ρ): 1.5 (Dong (2012))
- Frisch elasticity of labor supply (ν): 0.7 (Keane and Rogerson (2012) and Chetty et al (2013))
- Calvo parameter (γ): 0.5 (Bils and Klenow (2004))
- Home bias parameter (α): 1.68 (World Bank (2015) & Coenen (2013))
- Home bias parameter (α*): 0.32 (World Bank (2015) & Coenen (2013))
- Risk premium in UIP (ψ): 0.004 (Bergin (2006))
- Interest rate smoothing (μ1): 0.79 (Clarida et al. (2000))
- Interest rate smoothing (μ2): 1.5 (Coefficient for inflation in the monetary policy rule; Taylor (1993))
- Persistency of public spending shocks (CI ρρ,): 0.75 (Iwata (2013))
- Size of public spending shocks (CI εε,): 1
- Weight of public consumption (υ): 0.4 (Song et al. (2012))
- Depreciation rate of public infrastructure (λ): 0.025 (Bom and Lighhart (2014))
- Parameter (φ): [value not provided in the source excerpt]

### Key statistics and model primitives
- All numeric values preserved exactly as reported in the source excerpt.
- Parameter set combines micro estimates (e.g., Frisch elasticity, Calvo parameter) and macro calibrations (e.g., discount factor, home bias).
- Public finance parameters: persistency 0.75, shock size 1, public consumption weight 0.4, infrastructure depreciation 0.025.

*Source: _wp1640 - 0.995 Discount factor Iwata (2013), PDF chapter/section (source content excerpt).*

### 0.083 Output elasticity of public

### 0.083 Output elasticity of public infrastructure

### Methodology and multiplier definitions
- Cumulative multiplier (CM): cumulative change of output over cumulative change of public spending over a horizon (as in Gechert and Rannenberg (2014)).
- Net present value fiscal multiplier (NPVM): sum of output over a certain time horizon discounted at the steady state interest rate and divided by government spending discounted in the same way; the analysis uses 2,000 periods.
- Welfare multiplier methodology: follows Sims and Wolff (2013) and Schmitt-Grohe and Uribe (2007). The welfare multiplier is the consumption-equivalent one-period change in the present discounted value of flow utility for a one dollar change in government spending, computed as the NPV of the welfare impact expressed as a percentage of initial consumption and divided by the discounted government spending.

### Output and welfare multipliers — public consumption (key findings)
- A one percent increase in domestic public consumption increases domestic output (demand and wealth effects), but initial domestic trade balance deteriorates and then improves (hump-shaped).
- Cumulative output multipliers of public consumption are in the 0.4-0.5 range (consistent with Gechert and Rannenberg (2014)).
- Welfare effects:
  - Domestic welfare multiplier for public consumption: -0.30 (domestic households willing to pay 0.3 dollars to avoid one dollar rise in public consumption).
  - World welfare multiplier for a public consumption shock: -0.28.
- Comparative and robustness notes:
  - Sims and Wolff (2013) report welfare multipliers ranging between -8.6 and 35 depending on steady-state government spending; their output multiplier is 1.2.
  - In the model: increasing the utility weight on public consumption (υ) from benchmark 0.4 to υ = 1 yields a welfare multiplier just above zero; υ = 1.5 yields welfare multiplier = 0.25.
  - Rendhal (2015): long-duration fiscal expansion welfare multiplier = 0.65; temporary expansions can be between -0.4 and -0.2, close to the benchmark negative result here.

- Table 2 (selected figures)
  - Consumption: CM, 4 PRs = 0.44; CM, 8 PRs = 0.41; CM, 12 PRs = 0.41; CM, 16 PRs = 0.41; CM, 20 PRs = 0.42; NPV of output multiplier = 0.46; Welfare multiplier = -0.30; World welfare multiplier = -0.28.
  - Investment (for comparison): CM, 4 PRs = 0.58; CM, 8 PRs = 0.79; CM, 12 PRs = 1.0; CM, 16 PRs = 1.3; CM, 20 PRs = 1.5; NPV of output multiplier = 3.2; Welfare multiplier = 0.77; World welfare multiplier = 0.91.

### Public infrastructure investment — output and welfare effects
- Two channels: temporary demand effect and a supply-side effect (higher infrastructure stock raises productive capacity).
- Short-term consumption typically falls due to higher taxes needed to finance investment; medium-term output rises because of expanded productive capacity.
- Output multipliers rise with horizon as infrastructure stock increases productive capacity.

- Table 3 (cumulative output multipliers, CM by PRs)
  - IMF (2014): CM, 4 PRs = 0.5; CM, 8 PRs = 0.7; CM, 12 PRs = 1; CM, 16 PRs = 1.3; CM, 20 PRs = 1.5.
  - Our model: CM, 4 PRs = 0.6; CM, 8 PRs = 0.8; CM, 12 PRs = 1; CM, 16 PRs = 1.3; CM, 20 PRs = 1.5.

- Long-run and NPV effects
  - NPV of output multiplier for public infrastructure investment (benchmark): 3.2 (much higher than cumulative multipliers because spending returns to zero after about four years while productive capacity and output remain elevated).
  - Comparison: Bom and Lighhart (2014) theoretical long-run multiplier = 2.3 for permanent increase; Leduc and Wilson (2013) estimate output returns to pre-shock level after ten years.

- Welfare multipliers (benchmark and spillovers)
  - Domestic welfare multiplier for a public infrastructure investment shock (benchmark): 0.77 (households willing to pay 0.77 dollars for a one dollar increase in public infrastructure investment).
  - World welfare multiplier: 0.91 (domestic plus foreign welfare effects).
  - Intuition: productivity gains from infrastructure allow higher consumption without increased labor supply, improving welfare.
  - Welfare spillovers: positive after some time because improvement in foreign terms of trade raises foreign consumption more than foreign output and labor supply.

### Sensitivity to the output elasticity of public infrastructure (ϕ) and other parameters
- Results are sensitive to output elasticity of public capital (ϕ). Selected cases in Table 4:

  - Output elasticity of public capital ϕ = 0.02:
    - CM, 16 periods = 0.62
    - CM, 20 periods = 0.68
    - NPV of output multiplier = 1.1
    - Welfare multiplier = -0.19
    - World welfare multiplier = -0.14

  - Output elasticity of public capital ϕ = 0.03:
    - CM, 16 periods = 0.73
    - CM, 20 periods = 0.82
    - NPV of output multiplier = 1.5
    - Welfare multiplier = -0.042
    - World welfare multiplier = 0.021

  - Output elasticity of public capital ϕ = 0.083 (benchmark):
    - CM, 16 periods = 1.3
    - CM, 20 periods = 1.5
    - NPV of output multiplier = 3.2
    - Welfare multiplier = 0.77
    - World welfare multiplier = 0.91

  - Output elasticity of public capital ϕ = 0.131:
    - CM, 16 periods = 1.8
    - CM, 20 periods = 2.2
    - NPV of output multiplier = 4.8
    - Welfare multiplier = 1.5
    - World welfare multiplier = 1.7

- Interpretation:
  - When ϕ = 0.03 welfare multiplier is close to zero (-0.042).
  - Matching IMF (2014) low-efficiency multipliers (0.6 and 0.7 after 4 and 5 years) corresponds roughly to ϕ = 0.02 (welfare multiplier = -0.19).
  - High-efficiency case matching IMF (2014) multipliers (2.1 and 2.3 after 4 and 5 years) corresponds roughly to ϕ = 0.131 (welfare multiplier = 1.5).
  - Bom and Ligthart (2014) show welfare effects turn negative when ϕ < 3 percent; in this model welfare multiplier is positive when ϕ is slightly higher than 3 percent.

- Sensitivity to within-country substitutability and labor supply elasticity:
  - Within-country substitutability examples: setting it to 6 (21) implying a 20 (5) percent markup over marginal costs:
    - When ϕ = 0.083, domestic welfare multiplier = 0.79 (if substitutability = 6) and = 0.76 (if substitutability = 21).
    - Conclusion: welfare multipliers are not very sensitive to changes in within-country substitutability.
  - Footnote: welfare multipliers are not responsive to changes in the Frisch elasticity of labor supply.

### Policy implications and conclusions
- Main conclusion: public infrastructure investment can yield sizable positive welfare multipliers when public capital is sufficiently productive.
- Improving productivity/efficiency of public spending is crucial to capture benefits:
  - For low elasticity of public infrastructure, increases in public investment can be welfare-detrimental (negative welfare multiplier).
  - For high efficiency, public investment can yield very large welfare gains (e.g., welfare multiplier = 1.5 when ϕ = 0.131).
- Policy recommendation: strengthen public investment management—planning, allocation, and implementation—to enhance productivity of public investment and ensure positive welfare multipliers.
- Additional implication: a global infrastructure push is timely—expected to increase output, reduce public debt-to-GDP ratio (per IMF (2014)), and yield sizable welfare benefits.

*Source: _wp1640 - 0.083 Output elasticity of public infrastructure (PDF chapter content provided).*

### REFERENCES

### _wp1640 - REFERENCES

### References
- Basu, P. and R. Kollman 2013, Productive government purchases and the real exchange rate. The Manchester School 81, 461–469.  
- Basu, S. and J. G. Fernald, 1997. Returns to scale in U.S. production: Estimates and implications. Journal of Political Economy 105, 249–283.  
- Bergin, P. R, 2006. How well can the new open economy macroeconomics explain the exchange rate and current account? Journal of International Money and Finance 25, 675–701.  
- Bils, M. and P. Klenow 2004. Some evidence on the importance of sticky prices. Journal of Political Economy 112, 947–985.  
- Bom, P.R.D and J. E. Ligthart R, 2013. What have we learned from three decades of research on the productivity of public capital. Journal of Economic Surveys 28, 889–916.  
- Bom, P.R.D and J. E. Ligthart, 2014. Public infrastructure investment, output dynamics, and balanced budget fiscal rules. Journal of Economic Dynamics & Control 40, 334–354.  
- Calvo, G. A., 1983. Staggered prices in a utility maximizing framework. Journal of Monetary Economics 12, 383–398.  
- Clarida, Richard, Jordi Galí, and Mark Gertler, 2000. Monetary policy rules and macroeconomic stability: Evidence and some theory. Quarterly Journal of Economics, Vol. 115, No. 1, pp. 147-180.  
- Chetty, R., A. Guren, D. Manoli and A. Weber, 2013. Does indivisible labor explain the difference between micro and macro elasticities? A meta-analysis of extensive margin elasticities. NBER Macroeconomics Annual 2012 27, 1–56.  
- Coenen, G., C. J. Erceg, C. Freedman, D. Furceri, M. Kumhof, R. Lalonde, D. Laxton, J. Lindé, A. Mourougane, D. Muir, S. Mursula, C. de Resende, J. Roberts, W. Roeger, S. Snudden, M. Trabandt, and J. In’t Veld 2012. Effects of fiscal stimulus in structural models. American Economic Journal: Macroeconomics 4, 22–68.  
- Coenen, G., Straub, R. and M.Trabandt 2013. Gauging the effects of fiscal stimulus packages in the euro area. Journal of Economic Dynamics & Control 37, 367–386.  
- Dong, W. 2012. The role of expenditure switching in the global imbalance adjustment. Journal of International Economics 86, 237–251.  
- Gechert, S. and A. Rannenberg 2014. Are fiscal multipliers regime-dependent? A meta regression analysis, IMK Working Paper 139.  
- IMF 2014. World economic outlook: Legacies, clouds, uncertainties. IMF, Washington, DC.  
- IIMF 2015. Making public investment more efficient. IMF, Washington, DC.  
- Iwata, Y, 2013. Two fiscal policy puzzles revisited: New evidence and an explanation. Journal of International Money and Finance 33, 188–207.  
- Keane, M. and R. Rogersson, 2012. Micro and macro labor supply elasticities: A reassessment of conventional wisdom. Journal of Economic Literature 50, 464–476.  
- Klein, P., 2000. Using the generalized Schur form to solve a multivariate linear rational expectations model. Journal of Economic Dynamics and Control 24, 1405–1223.  
- Leduc, S. and D. Wilson 2013, Roads to prosperity or bridges to nowhere? Theory and evidence on the impact of public infrastructure investment. NBER Macroeconomics Annual 27, 89–142.  
- Mankiw, G. and M. Weinzierl, An exploration of optimal stabilization policy. Brookings Papers on Economic Activity 42, 209–272.  
- McCallum, B., 2001, Software for RE analysis. Computer software available at http://wpweb2.tepper.cmu.edu/faculty/mccallum/research.html  
- Obstfeld, M. and K. Rogoff 1995. The intertemporal approach to the current account. In G. Grossman and K. Rogoff (eds.) Handbook of International Economics. North-Holland Publishing Company, Amsterdam.  
- Rendahl, P. 2015. Fiscal policy in an unemployment crisis. Mimeo, University of Cambridge.  
- Schmitt-Grohe, S. and M. Uribe, 2003. Closing small open economy models. Journal of International Economics 61, 163–185.  
- Schmitt-Grohe, S. and M. Uribe, 2007. Optimal simple and implementable monetary and fiscal rules. Journal of Monetary Economics 54, 1702–1725.  
- Sims, E. and J. Wolff, 2014. The output and welfare effects of government spending shocks over the business cycle. NBER Working Paper No 19749.  
- Song, Z., K. Storesletten and F. Zilibotti 2012. Rotten parents and disciplined children: A politico-economic theory of public expenditure and debt. Econometrica 80, 2785–2803.  
- Taylor, J. B. 1993. Discretion versus policy rules in practice. Carnegie-Rochester Conference Series on Public Policy 39, 195–214.  
- Uhlig, H., 2010. Some fiscal calculus. American Economic Review 100, 30–34.  
- World Bank, 2015. Data available online at http://data.worldbank.org/ (accessed 12.3.2015).

*Source: _wp1640 - REFERENCES.*

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