Table 1.
Open in new tab

Crowding Out in the Simplified Model

Benchmark Model
τ*|$\bar{\tau }$|
R = 0.10R = 0.20R = 0.30R = 0.10R = 0.20R = 0.30
ρ = 0.06α = 0.402.662.662.660.120.460.75
α = 0.502.142.142.140.150.500.77
ρ = 0.10α = 0.402.652.652.65–0.250.51
α = 0.502.132.132.13–0.290.54
CICSR when τ = 0.25CICSR when τ = 0.50
R = 0.10R = 0.20R = 0.30R = 0.10R = 0.20R = 0.30
ρ = 0.06α = 0.40−0.80−1.33−1.87−0.57−0.95−1.34
α = 0.50−0.85−1.42−1.98−0.60−1.00−1.40
ρ = 0.10α = 0.40−0.60−1.00−1.41−0.43−0.72−1.01
α = 0.50−0.64−1.06−1.49−0.45−0.76−1.06
Open Private Capital Account
ξ*
τ = 0.25τ = 0.50τ = 0.75τ = 1
ρ = 0.06α = 0.4061.047.136.929.0
α = 0.5061.246.535.326.4
ρ = 0.10α = 0.4033.626.220.616.2
α = 0.5033.625.819.714.7
CICSR when τ = 0.25 and α = 0.40CICSR when τ = 0.50 and α = 0.40
R = 0.10R = 0.20R = 0.30R = 0.10R = 0.20R = 0.30
ρ = 0.06α = 0.40−0.78−1.29−1.81−0.55−0.92−1.29
α = 0.50−0.68−1.14−1.59−0.48−0.79−1.11
ρ = 0.10α = 0.40−0.57−0.95−1.33−0.40−0.67−0.94
α = 0.50−0.45−0.75−1.05−0.31−0.51−0.72
Benchmark Model
τ*|$\bar{\tau }$|
R = 0.10R = 0.20R = 0.30R = 0.10R = 0.20R = 0.30
ρ = 0.06α = 0.402.662.662.660.120.460.75
α = 0.502.142.142.140.150.500.77
ρ = 0.10α = 0.402.652.652.65–0.250.51
α = 0.502.132.132.13–0.290.54
CICSR when τ = 0.25CICSR when τ = 0.50
R = 0.10R = 0.20R = 0.30R = 0.10R = 0.20R = 0.30
ρ = 0.06α = 0.40−0.80−1.33−1.87−0.57−0.95−1.34
α = 0.50−0.85−1.42−1.98−0.60−1.00−1.40
ρ = 0.10α = 0.40−0.60−1.00−1.41−0.43−0.72−1.01
α = 0.50−0.64−1.06−1.49−0.45−0.76−1.06
Open Private Capital Account
ξ*
τ = 0.25τ = 0.50τ = 0.75τ = 1
ρ = 0.06α = 0.4061.047.136.929.0
α = 0.5061.246.535.326.4
ρ = 0.10α = 0.4033.626.220.616.2
α = 0.5033.625.819.714.7
CICSR when τ = 0.25 and α = 0.40CICSR when τ = 0.50 and α = 0.40
R = 0.10R = 0.20R = 0.30R = 0.10R = 0.20R = 0.30
ρ = 0.06α = 0.40−0.78−1.29−1.81−0.55−0.92−1.29
α = 0.50−0.68−1.14−1.59−0.48−0.79−1.11
ρ = 0.10α = 0.40−0.57−0.95−1.33−0.40−0.67−0.94
α = 0.50−0.45−0.75−1.05−0.31−0.51−0.72

Source: Authors’ calculations based on solutions from Mathematica programs.

Note: The depreciation rate and the ratio of infrastructure investment to GDP equal 5 percent in all runs. ρ is the pure time preference rate; α is the income share of private capital; R is the return on infrastructure (net of depreciation); τ* (⁠|${\rm {\bar{\tau }}}$| d) is the value of the intertemporal elasticity of substitution below which private (total) investment decreases at t = 0 CICSR is the crowding-in coefficient for private investment in the short run (t = 0); and ξ* is the value of elasticity of capital flows (measured as a percentage of GDP, with respect to the interest rate differential) below which private investment decreases. (ξ* is independent of the return on infrastructure.)

Table 1.
Open in new tab

Crowding Out in the Simplified Model

Benchmark Model
τ*|$\bar{\tau }$|
R = 0.10R = 0.20R = 0.30R = 0.10R = 0.20R = 0.30
ρ = 0.06α = 0.402.662.662.660.120.460.75
α = 0.502.142.142.140.150.500.77
ρ = 0.10α = 0.402.652.652.65–0.250.51
α = 0.502.132.132.13–0.290.54
CICSR when τ = 0.25CICSR when τ = 0.50
R = 0.10R = 0.20R = 0.30R = 0.10R = 0.20R = 0.30
ρ = 0.06α = 0.40−0.80−1.33−1.87−0.57−0.95−1.34
α = 0.50−0.85−1.42−1.98−0.60−1.00−1.40
ρ = 0.10α = 0.40−0.60−1.00−1.41−0.43−0.72−1.01
α = 0.50−0.64−1.06−1.49−0.45−0.76−1.06
Open Private Capital Account
ξ*
τ = 0.25τ = 0.50τ = 0.75τ = 1
ρ = 0.06α = 0.4061.047.136.929.0
α = 0.5061.246.535.326.4
ρ = 0.10α = 0.4033.626.220.616.2
α = 0.5033.625.819.714.7
CICSR when τ = 0.25 and α = 0.40CICSR when τ = 0.50 and α = 0.40
R = 0.10R = 0.20R = 0.30R = 0.10R = 0.20R = 0.30
ρ = 0.06α = 0.40−0.78−1.29−1.81−0.55−0.92−1.29
α = 0.50−0.68−1.14−1.59−0.48−0.79−1.11
ρ = 0.10α = 0.40−0.57−0.95−1.33−0.40−0.67−0.94
α = 0.50−0.45−0.75−1.05−0.31−0.51−0.72
Benchmark Model
τ*|$\bar{\tau }$|
R = 0.10R = 0.20R = 0.30R = 0.10R = 0.20R = 0.30
ρ = 0.06α = 0.402.662.662.660.120.460.75
α = 0.502.142.142.140.150.500.77
ρ = 0.10α = 0.402.652.652.65–0.250.51
α = 0.502.132.132.13–0.290.54
CICSR when τ = 0.25CICSR when τ = 0.50
R = 0.10R = 0.20R = 0.30R = 0.10R = 0.20R = 0.30
ρ = 0.06α = 0.40−0.80−1.33−1.87−0.57−0.95−1.34
α = 0.50−0.85−1.42−1.98−0.60−1.00−1.40
ρ = 0.10α = 0.40−0.60−1.00−1.41−0.43−0.72−1.01
α = 0.50−0.64−1.06−1.49−0.45−0.76−1.06
Open Private Capital Account
ξ*
τ = 0.25τ = 0.50τ = 0.75τ = 1
ρ = 0.06α = 0.4061.047.136.929.0
α = 0.5061.246.535.326.4
ρ = 0.10α = 0.4033.626.220.616.2
α = 0.5033.625.819.714.7
CICSR when τ = 0.25 and α = 0.40CICSR when τ = 0.50 and α = 0.40
R = 0.10R = 0.20R = 0.30R = 0.10R = 0.20R = 0.30
ρ = 0.06α = 0.40−0.78−1.29−1.81−0.55−0.92−1.29
α = 0.50−0.68−1.14−1.59−0.48−0.79−1.11
ρ = 0.10α = 0.40−0.57−0.95−1.33−0.40−0.67−0.94
α = 0.50−0.45−0.75−1.05−0.31−0.51−0.72

Source: Authors’ calculations based on solutions from Mathematica programs.

Note: The depreciation rate and the ratio of infrastructure investment to GDP equal 5 percent in all runs. ρ is the pure time preference rate; α is the income share of private capital; R is the return on infrastructure (net of depreciation); τ* (⁠|${\rm {\bar{\tau }}}$| d) is the value of the intertemporal elasticity of substitution below which private (total) investment decreases at t = 0 CICSR is the crowding-in coefficient for private investment in the short run (t = 0); and ξ* is the value of elasticity of capital flows (measured as a percentage of GDP, with respect to the interest rate differential) below which private investment decreases. (ξ* is independent of the return on infrastructure.)

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