Revision

**a9ad709c106fcaa6c21d03edad7c83fa02a3fbf0**authored by Javier Barbero on**14 September 2022, 17:40:23 UTC**, committed by GitHub on**14 September 2022, 17:40:23 UTC****1 parent**63f7300

malmquist.jl

```
"""
MalmquistDEAModel
An data structure representing a malmquist productivity DEA model.
"""
struct MalmquistDEAModel <: AbstractProductivityDEAModel
n::Int64
m::Int64
s::Int64
periods::Int64
orient::Symbol
rts::Symbol
refperiod::Symbol
dmunames::Union{Vector{AbstractString},Nothing}
Prod::Matrix
EC::Matrix
TC::Matrix
end
"""
malmquist(X, Y)
Compute the Malmquist productivity index using data envelopment analysis for inputs X and outputs Y.
# Optional Arguments
- `orient=:Input`: chooses between input oriented radial model `:Input` or output oriented radial model `:Output`.
- `refperiod=:Geomean`: chooses reference period for technological change: `:Base`, `:Comparison` or `:Geomean`.
- `rts=:CRS`: chooses constant returns to scale. For variable returns to scale choose `:VRS`.
- `names`: a vector of strings with the names of the decision making units.
"""
function malmquist(X::Array{Float64,3}, Y::Array{Float64,3};
orient::Symbol = :Input, rts::Symbol = :CRS, refperiod::Symbol = :Geomean,
names::Union{Vector{<: AbstractString},Nothing} = nothing,
optimizer::Union{DEAOptimizer,Nothing} = nothing)::MalmquistDEAModel
# Check parameters
nx, m, Tx = size(X)
ny, s, Ty = size(Y)
if nx != ny
throw(DimensionMismatch("number of rows in X and Y ($nx, $ny) are not equal"));
end
if Tx != Ty
throw(DimensionMismatch("number of time periods in X and Y ($Tx, $Ty) are not equal"));
end
# Default optimizer
if optimizer === nothing
optimizer = DEAOptimizer(GLPK.Optimizer)
end
# Compute efficiency for each DMU
n = nx
T = Tx
Prod = zeros(n, T - 1)
EC = zeros(n, T - 1)
TC = zeros(n, T - 1)
# For each time period
for t = 1:T - 1
# Compute efficiency in t
efft = efficiency(dea(X[:, :, t], Y[:, :, t], orient = orient, rts = rts, slack = false, optimizer = optimizer))
# Compute efficiency in t + 1
efft1 = efficiency(dea(X[:, :, t + 1], Y[:, :, t + 1], orient = orient, rts = rts, slack = false, optimizer = optimizer))
# Compute efficiency in t +1, with reference t
efft1_reft = efficiency(dea(X[:, :, t + 1], Y[:, :, t + 1], orient = orient, rts = rts, slack = false,
Xref = X[:, :, t], Yref = Y[:, :, t],
optimizer = optimizer))
# Compute efficiency in t, with reference t + 1
efft_reft1 = efficiency(dea(X[:, :, t], Y[:, :, t], orient = orient, rts = rts, slack = false,
Xref = X[:, :, t + 1], Yref = Y[:, :, t + 1],
optimizer = optimizer))
# Inver if output oriented
if orient == :Output
efft .= 1 ./ efft
efft1 .= 1 ./ efft1
efft1_reft .= 1 ./ efft1_reft
efft_reft1 .= 1 ./ efft_reft1
end
# Technical Efficiency Change
EC[:, t] .= efft1 ./ efft
# Technological Change
if refperiod == :Base
TC[:, t] .= efft1_reft ./ efft1
elseif refperiod == :Comparison
TC[:, t] .= efft ./ efft_reft1
elseif refperiod == :Geomean
TC[:, t] .= sqrt.( (efft ./ efft_reft1) .* (efft1_reft ./ efft1) )
else
throw(ArgumentError("`refperiod` must be :Base, :Comparison or :Geomean"));
end
# Mamlmquist Index
Prod[:, t] .= EC[:, t] .* TC[:, t]
end
return MalmquistDEAModel(n, m, s, T, orient, rts, refperiod, names, Prod, EC, TC)
end
function Base.show(io::IO, x::MalmquistDEAModel)
compact = get(io, :compact, false)
n = nobs(x)
m = ninputs(x)
s = noutputs(x)
dmunames = names(x)
periods = nperiods(x)
Prod = prodchange(x, :Prod)
EC = prodchange(x, :EC)
TC = prodchange(x, :TC)
if !compact
print(io, "Mamlmquist DEA Model \n")
print(io, "DMUs = ", n)
print(io, "; Inputs = ", m)
print(io, "; Outputs = ", s)
print(io, "; Time periods = ", periods)
print(io, "\n")
print(io, "Orientation = ", string(x.orient))
print(io, "; Returns to Scale = ", string(x.rts))
print(io, "\n")
print(io, "Referene period = ", string(x.refperiod))
print(io, "\n")
if periods == 2
show(io, CoefTable(hcat(Prod, EC, TC), ["M", "EC", "TC"], dmunames))
end
if periods > 2
show(io, CoefTable(hcat(Prod, EC, TC),
vcat(["M$i" for i in 1:2], ["EC$i" for i in 1:2], ["TC$i" for i in 1:2 ]),
dmunames))
end
print(io, "\n")
print(io, "M = Malmquist Productivity Index \n")
print(io, "EC = Efficiency Change \n")
print(io, "TC = Technological Change")
end
end
```

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