Empirically estimated flexible functional forms frequently fail to satisfy the appropriate theoretical curvature conditions. Lau and Gallant and Golub have worked out methods for imposing the appropriate curvature conditions locally, but those local techniques frequently fail to yield...

The paper considers alternative approaches to providing consistent multilateral indexes of real output, real input, real consumption or productivity across many regions, countries or industries at one point in time. The recommended approaches are based on aggregating up various bilateral indexes...