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Add inv and derivativeinv to some utility functions #225

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Add inv and derivativeinv to some utility functions #225

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4 changes: 2 additions & 2 deletions src/QuantEcon.jl
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Original file line number Diff line number Diff line change
@@ -1,6 +1,6 @@
module QuantEcon

import Base: show, isapprox
import Base: show, isapprox, inv
import Statistics: mean, std, var
using Markdown
using FFTW
Expand Down Expand Up @@ -58,7 +58,7 @@ export

# modeltools
AbstractUtility, LogUtility, CRRAUtility, CFEUtility, EllipticalUtility,
derivative,
derivative, derivativeinv, inv,

# gth_solve
gth_solve,
Expand Down
25 changes: 20 additions & 5 deletions src/modeltools/utility.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -9,7 +9,7 @@ abstract type AbstractUtility end
@doc doc"""
Type used to evaluate log utility. Log utility takes the form

u(c) = \log(c)
u(c) = ξ log(c)

Additionally, this code assumes that if c < 1e-10 then

Expand All @@ -26,8 +26,12 @@ LogUtility() = LogUtility(1.0)
c > 1e-10 ? u.ξ*log(c) : u.ξ*(log(1e-10) + 1e10*(c - 1e-10))
derivative(u::LogUtility, c::Float64) =
c > 1e-10 ? u.ξ / c : u.ξ*1e10
inv(u::LogUtility, x::Float64) =
exp.(x / u.ξ)
derivativeinv(u::LogUtility, x::Float64) = u.ξ / x

"""

@doc doc"""
Type used to evaluate CRRA utility. CRRA utility takes the form

u(c) = ξ c^(1 - γ) / (1 - γ)
Expand All @@ -53,17 +57,21 @@ end
c > 1e-10 ?
u.ξ * (c^(1.0 - u.γ) - 1.0) / (1.0 - u.γ) :
u.ξ * ((1e-10^(1.0 - u.γ) - 1.0) / (1.0 - u.γ) + 1e-10^(-u.γ)*(c - 1e-10))
inv(u::CRRAUtility, x::Float64) = (((1 - u.γ)*x) / u.ξ + 1)^(1 / (1 - u.γ))
derivative(u::CRRAUtility, c::Float64) =
c > 1e-10 ? u.ξ * c^(-u.γ) : u.ξ*1e-10^(-u.γ)
derivativeinv(u::CRRAUtility, x::Float64) = (u.ξ / x)^(1.0 / u.γ)


# Labor Utility

"""
@doc doc"""
Type used to evaluate constant Frisch elasticity (CFE) utility. CFE
utility takes the form

v(l) = ξ l^(1 + 1/ϕ) / (1 + 1/ϕ)
v(l) = -ξ l^(1 + 1/ϕ) / (1 + 1/ϕ)

where l is hours worked

Additionally, this code assumes that if l < 1e-10 then

Expand All @@ -88,12 +96,18 @@ end
-u.ξ * (1e-10^(1.0 + 1.0/u.ϕ)/(1.0 + 1.0/u.ϕ) + 1e-10^(1.0/u.ϕ) * (l - 1e-10))
derivative(u::CFEUtility, l::Float64) =
l > 1e-10 ? -u.ξ * l^(1.0/u.ϕ) : -u.ξ * 1e-10^(1.0/u.ϕ)
inv(u::CFEUtility, x::Float64) =
((1 + 1.0/u.ϕ)*x / -u.ξ)^(1.0 / (1.0 + 1.0/u.ϕ))
derivativeinv(u::CFEUtility, x) =
(x / -u.ξ)^u.ϕ


"""
@doc doc"""
Type used to evaluate elliptical utility function. Elliptical utility takes form

v(l) = b (1 - l^μ)^(1 / μ)

where l is hours worked
"""
struct EllipticalUtility <: AbstractUtility
b::Float64
Expand All @@ -107,3 +121,4 @@ EllipticalUtility(;b=0.5223, μ=2.2926) = EllipticalUtility(b, μ)
u.b * (1.0 - l^u.μ)^(1.0 / u.μ)
derivative(u::EllipticalUtility, l::Float64) =
-u.b * (1.0 - l^u.μ)^(1.0/u.μ - 1.0) * l^(u.μ - 1.0)

56 changes: 47 additions & 9 deletions test/test_modeltool.jl
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Original file line number Diff line number Diff line change
@@ -1,53 +1,92 @@
@testset "Testing modeltools.jl" begin

@testset "Log Utility" begin
# Test log utility
# Test log utility
u = LogUtility(2.0)

# Test levels
@test isapprox(u(1.0), 0.0)
@test isapprox(2.0*log(2.5), u(2.5))
@test isapprox(u.(ones(5)), zeros(5))
@test u(2.0) > u(1.0) # Ensure it is increasing
@test isapprox(derivative(u, 1.0), 2.0)
@test isapprox(derivative(u, 2.0), 1.0)

# Test "extrapolation evaluations"
@test isapprox(u(0.5e-10), u(1e-10) + derivative(u, 1e-10)*(0.5e-10 - 1e-10))
@test u(-0.5) < u(-0.1) # Make sure it doesn't fail with negative values

@test isapprox(LogUtility().ξ, 1.0) # Test default constructor
# Test derivatives
@test isapprox(derivative(u, 1.0), 2.0)
@test isapprox(derivative(u, 2.0), 1.0)
@test isapprox(derivative(u, 1.0), (u(1.0 + 1e-4) - u(1.0))/1e-4; atol=1e-3)

# Test extrapolation derivatives
@test isapprox(derivative(u, 0.0), u.ξ*1e10)

# Test inverse of level
@test isapprox(u(inv(u, 1.0)), 1.0)
@test isapprox(u(inv(u, 2.0)), 2.0)

# Test inverse of derivative
@test isapprox(derivative(u, derivativeinv(u, 1.0)), 1.0)
@test isapprox(derivative(u, derivativeinv(u, 2.0)), 2.0)

@test isapprox(LogUtility().ξ, 1.0) # Test default constructor
end

@testset "CRRA Utility" begin
# Test CRRA utility
u = CRRAUtility(2.0)

# Test levels
@test isapprox(u(1.0), 0.0)
@test isapprox((2.5^(-1.0) - 1.0) / (-1.0), u(2.5))
@test isapprox(u.(ones(5)), zeros(5))
@test u(5.0) > u(3.0) # Ensure it is increasing
@test isapprox(derivative(u, 1.0), 1.0)
@test isapprox(derivative(u, 2.0), 0.25)

# Test "extrapolation evaluations"
@test isapprox(u(0.5e-10), u(1e-10) + derivative(u, 1e-10)*(0.5e-10 - 1e-10))
@test u(-0.5) < u(-0.1) # Make sure it doesn't fail with negative values

# Test derivatives
@test isapprox(derivative(u, 1.0), 1.0)
@test isapprox(derivative(u, 2.0), 0.25)

# Test inverse of level
@test isapprox(u(inv(u, 1.0)), 1.0)
@test isapprox(u(inv(u, 0.5)), 0.5)

# Test inverse of derivative
@test isapprox(derivative(u, derivativeinv(u, 1.0)), 1.0)
@test isapprox(derivative(u, derivativeinv(u, 2.0)), 2.0)

@test_throws ErrorException CRRAUtility(1.0) # Test error throwing at γ=1.0
end

@testset "CFE Utility" begin
# Test CFE Utility
v = CFEUtility(2.0)

# Test levels
@test isapprox(v(1.0), -2.0/3.0)
@test isapprox(v(0.5), -v.ξ * 0.5^(1.0 + 1.0/v.ϕ) / (1.0 + 1.0/v.ϕ))
@test v(0.5) > v(0.85) # Ensure it is decreasing
@test isapprox(derivative(v, 0.25), -0.5)
@test isapprox(derivative(v, 1.0), -1.0)

# Test "extrapolation evaluations"
@test isapprox(v(0.5e-10), v(1e-10) + derivative(v, 1e-10)*(0.5e-10 - 1e-10))
@test v(-0.5) > v(-0.1) # Make sure it doesn't fail with negative values

# Test derivatives
@test isapprox(derivative(v, 0.25), -0.5)
@test isapprox(derivative(v, 1.0), -1.0)

# Test inverse of level
@test isapprox(v(inv(v, -0.05)), -0.05)
@test isapprox(v(inv(v, -0.25)), -0.25)

# Test inverse of derivative
@test isapprox(derivative(v, derivativeinv(v, -0.5)), -0.5)
@test isapprox(derivative(v, derivativeinv(v, -0.25)), -0.25)

@test_throws ErrorException CRRAUtility(1.0) # Test error throwing at ϕ=1.0
end

Expand All @@ -63,7 +102,6 @@
# Test default values
@test isapprox(EllipticalUtility().b, 0.5223)
@test isapprox(EllipticalUtility().μ, 2.2926)

end

end
Expand Down