1 / 11

AEB 6184 – Review and Frontier Models

AEB 6184 – Review and Frontier Models. Elluminate - 10. Review of the Production Function. Kumbhakar , S.C. and C.A. Knox Lovell. 2000. Stochastic Frontier Analysis .

olympe
Télécharger la présentation

AEB 6184 – Review and Frontier Models

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.

E N D

Presentation Transcript

  1. AEB 6184 – Review and Frontier Models Elluminate - 10

  2. Review of the Production Function • Kumbhakar, S.C. and C.A. Knox Lovell. 2000. Stochastic Frontier Analysis. • Definition 2.1: The graph of the production technology, GR={(y,x): x can produce y}, describes the set of feasible input-output vectors. [pp.18-19]. • Definition 2.2: The input sets of production technology, L(y)={x:(y,x)  GR}, describe the sets of input vectors that are feasible for each output y R+M.[p. 21 see Shephard p 13 – Level sets]. • Definition 2.3: The output sets of production technology P(x) = {y:(y,x)  GR}, describe the sets of output vectors that are feasible for each input vector x  R+n. [p. 22]

  3. Definition 2.4: The input isoquantsIsoL(y) = {x: x L(y), λx  L(x), λ < 1} describe the sets of input vectors capable of producing each output vector y but which, when radially contracted, became incapable of producing output vector y. [p. 23] • Definition 2.5: The input efficiency subsetsEffL(y) = {x: x L(y), x’ ≤ x→ x’  L(y)} describe the sets of input vectors capable of producing each output vector y but which, when contracted in any dimension, become incapable of producing the output vector y. [p.23] • Definition 2.9: A production frontier is a function f(x) = max[y: y P(x)} = max[y: x  L(y)]. [p. 26, see Shephard pp. 20-23].

  4. Bridging to New Materials • We will be developing the dual relationships using three different approaches: • Diewert – Generalized Leontief • Shephard – Distance Functions • Lau – Conjugate Duality • A first step is to define the distance functions – Starting with Kumbhakar and Lovell. • Definition 2.10: An input distance function is a function DI(y,x) = max[λ: x/λ L(y)]. [p. 28]

  5. Input Distance Functions x/λ x/λ

  6. Distance Functions • From Kumbhakar and Lovell’s perspective, the value of the distance function is a measure of inefficiency. • If λ>1 then the current vector is inefficient. • From Shephard’s viewpoint, λ defines the efficient frontier. • As noted in Kumbhakar and Lovell • Definition 2.12: A cost function is a function c(y,w) = minx[w’x: x L(y)] = minx[w’x: DI(y,x)≥1]. [p.33]. • We will start developing this dual function in more detail in future lectures.

  7. Cost Function • The dominant theme in duality is that under some assumptions cost minimizing or profit maximizing behavior retains the information in the production function. • We start with a simple quadratic cost function

  8. Optimality • First we define optimality from the level of output • Next, looking ahead, we define the optimal levels of input using Shephard’s lemma

  9. Sample Draw (Without Error)

  10. Least Squares Estimates of Production Function • Representing the technology as a quadratic production function • Estimates

  11. Problem Set

More Related