TFP Toolbox

Total Factor Productivity Toolbox is a new package for MATLAB that includes functions to calculate the main Total Factor Productivity indices and their decompositions, based on Shephard’s distance functions and using Data Envelopment Analysis programming techniques. The package includes code for the standard Malmquist, Moorsteen- Bjurek, price weighted and share weighted TFP indices, allowing for the choice of orientation (input or output), reference period (base, comparison, geometric mean), returns to scale (variable or constant) and specific decompositions (aggregate or identifying scale effects as well as input and output mix effects). Classic definitions of TFP corresponding to the Laspeyres, Paasche, Fisher or Törnqvist formulations can be also calculated as particular cases.

$$\check{M}_{o}^{t}(\boldsymbol{x}^1,\boldsymbol{y}^1,\boldsymbol{x}^0,\boldsymbol{y}^0) \equiv \frac{\check{D}_{o}^{t}(\boldsymbol{x}^1,\boldsymbol{y}^1)}{\check{D}_{o}^{t}(\boldsymbol{x}^0,\boldsymbol{y}^0)}$$