The Malmquist index

The Malmquist Productivity Index

The Malmquist index introduced by Caves, Christensen and Diewert(1982) measures the change in productivity of the observation under evaluation by comparing its relative performance with respect to reference technologies corresponding to two different time periods.

Following Fare, Grosskopf, Norris and Zhang (1994) productivity change can be decomposed into efficiency change and technical change under the assumption of a constant returns to scale techncology.

In this example we compute the Malmquist productivity index:

using DataEnvelopmentAnalysis

X = Array{Float64,3}(undef, 5, 1, 2);
X[:, :, 1] = [2; 3; 5; 4; 4];
X[:, :, 2] = [1; 2; 4; 3; 4];

Y = Array{Float64,3}(undef, 5, 1, 2);
Y[:, :, 1] = [1; 4; 6; 3; 5];
Y[:, :, 2] = [1; 4; 6; 3; 3];

malmquist(X, Y)

Mamlmquist DEA Model 
DMUs = 5; Inputs = 1; Outputs = 1; Time periods = 2
Orientation = Input; Returns to Scale = CRS
Referene period = Geomean
─────────────────────────
         M        EC   TC
─────────────────────────
1  2.0      1.33333   1.5
2  1.5      1.0       1.5
3  1.25     0.833333  1.5
4  1.33333  0.888889  1.5
5  0.6      0.4       1.5
─────────────────────────
M  = Malmquist Productivity Index 
EC = Efficiency Change 
TC = Technological Change

malmquist Function Documentation

malmquist(X, Y)