1 / 25

Efficiency Measurement

William Greene Stern School of Business New York University. Efficiency Measurement. Session 4. Functional Form and Efficiency Measurement. Single Output Stochastic Frontier.

Télécharger la présentation

Efficiency Measurement

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.


Presentation Transcript

  1. William Greene Stern School of Business New York University Efficiency Measurement

  2. Session 4 Functional Form and Efficiency Measurement

  3. Single Output Stochastic Frontier ui > 0, but vi may take any value. A symmetric distribution, such as the normal distribution, is usually assumed for vi. Thus, the stochastic frontier is +’xi+vi and, as before,ui represents the inefficiency.

  4. The Normal-Half Normal Model

  5. Estimating ui • No direct estimate of ui • Data permit estimation of yi – β’xi. Can this be used? • εi = yi – β’xi= vi – ui • Indirect estimate of ui, using E[ui|vi – ui] = E[ui|yi,xi] • vi – ui is estimable with ei = yi – b’xi.

  6. Fundamental Tool - JLMS We can insert our maximum likelihood estimates of all parameters. Note: This estimates E[u|vi – ui], not ui.

  7. Multiple Output Frontier • The formal theory of production departs from the transformation function that links the vector of outputs, y to the vector of inputs, x; T(y,x) = 0. • As it stands, some further assumptions are obviously needed to produce the framework for an empirical model. By assuming homothetic separability, the function may be written in the form A(y) = f(x).

  8. Multiple Output Production Function Inefficiency in this setting reflects the failure of the firm to achieve the maximum aggregate output attainable. Note that the model does not address the economic question of whether the chosen output mix is optimal with respect to the output prices and input costs. That would require a profit function approach. Berger (1993) and Adams et al. (1999) apply the method to a panel of U.S. banks – 798 banks, ten years.

  9. Duality Between Production and Cost

  10. Implied Cost Frontier Function

  11. Stochastic Cost Frontier

  12. Cobb-Douglas Cost Frontier

  13. Translog Cost Frontier

  14. Restricted Translog Cost Function

  15. Cost Application to C&G Data

  16. Estimates of Economic Efficiency

  17. Duality – Production vs. Cost

  18. Multiple Output Cost Frontier

  19. Banking Application

  20. Economic Efficiency

  21. Allocative Inefficiency and Economic Inefficiency Technical inefficiency: Off the isoquant. Allocative inefficiency: Wrong input mix.

  22. Cost Structure – Demand System

  23. Cost Frontier Model

  24. The Greene Problem • Factor shares are derived from the cost function by differentiation. • Where does ek come from? • Any nonzero value of ek, which can be positive or negative, must translate into higher costs. Thus, u must be a function of e1,…,eK such that ∂u/∂ek > 0 • Noone had derived a complete, internally consistent equation system  the Greene problem. • Solution: Kumbhakar in several papers. (E.g., JE 1997) • Very complicated – near to impractical • Apparently of relatively limited interest to practitioners

  25. A Less Direct Solution(Sauer,Frohberg JPA, 27,1, 2/07) • Symmetric generalized McFadden cost function – quadratic in levels • System of demands, xw/y = * + v, E[v]=0. • Average input demand functions are estimated to avoid the ‘Greene problem.’ Corrected wrt a group of firms in the sample. • Not directly a demand system • Errors are decoupled from cost by the ‘averaging.’ • Application to rural water suppliers in Germany

More Related