1 / 23

หลักสูตรอบรม การวัดประสิทธิภาพและผลิตภาพของการผลิตสินค้าเกษตร ด้วยแบบจำลอง DEA

หลักสูตรอบรม การวัดประสิทธิภาพและผลิตภาพของการผลิตสินค้าเกษตร ด้วยแบบจำลอง DEA. ผศ. ดร. ศุภวัจน์ รุ่งสุริยะวิบูลย์ คณะเศรษฐศาสตร์ มหาวิทยาลัยเชียงใหม่. Lecture 4: ขอบเขตเนื้อหา. Metafrontier การวิเคราะห์ Metafrontier ด้วยแบบจำลอง DEA การวิเคราะห์ Metafrontier ด้วยแบบจำลอง SFA.

leonard-acevedo
Download Presentation

หลักสูตรอบรม การวัดประสิทธิภาพและผลิตภาพของการผลิตสินค้าเกษตร ด้วยแบบจำลอง DEA

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. หลักสูตรอบรมการวัดประสิทธิภาพและผลิตภาพของการผลิตสินค้าเกษตรด้วยแบบจำลอง DEA ผศ. ดร. ศุภวัจน์ รุ่งสุริยะวิบูลย์ คณะเศรษฐศาสตร์ มหาวิทยาลัยเชียงใหม่

  2. Lecture 4: ขอบเขตเนื้อหา • Metafrontier • การวิเคราะห์ Metafrontier ด้วยแบบจำลอง DEA • การวิเคราะห์ Metafrontier ด้วยแบบจำลอง SFA

  3. Metafrontier • When all producers in different groups of a given industry have a potential access to the same technology but each producer may choose to operate on a different part of their technologies depending on circumstances such as the natural endowments, relative prices of inputs and the economic environment, then the assessment of producer’s efficiency and productivity can be measured using a metafrontier concept. • Hayami and Ruttan (1970) initially proposed a metaproduction function which is defined as the envelope of commonly conceived neoclassical production functions. Thus, it is a common underlying production function that is used to represent the input-output relationship of a given industry.

  4. Metafrontier • Consider there are two different groups of technologies, namely A and B. • Let points A1, A2, A3 and A4 indicate the input-output bundles of four producers in group A. These points are used to construct a frontier for production technology in group A or TA. • Similarly, points B1, B2, B3 and B4 show the input-output bundles of four producers in group B. These points are used to construct a frontier for production technology in group or TB. • If each group of producers has potential access to the same technology, the grand frontier which envelops the two group-specific frontiers can be represented by line AoA1A2B2B3Bo. • This line is referred as a metafrontier function or T*.

  5. y T* Bo B3 B2 A4 A2 TA B4 A3 A1 B1 TB x Ao Metafrontier A1

  6. Metafrontier • The metafrontier function can be measuring using both nonparametric and parametric approaches. • The metafrontier function using DEA constructs piece-wise linear convex production technology by enveloping all observed data from each group-specific technology. It does not require specified functional form for each group-specific technology. • The metafrontier function using SFA constructs a smooth production technology by tangenting a specified functional form of production functions from each group-specific technology. The metafrontier using SFA is a smooth function and not a segmented envelope of each group-specific technology.

  7. y y T* Bo B3 B3 B2 B2 A4 A4 A2 A2 TA A3 B4 A3 B4 A1 A1 A1 B1 B1 TB x x x Ao Ao T* TA TB Metafrontier SFA DEA

  8. y T * B3 B4** A3** A4** B2 6.8 5.6 A4 A3*** A2 B4 B1** T A 3.1 A3 B1 A1 T B B4* Bo x A3* Boo Aoo A4* Ao Decomposition of TE under metatechnology

  9. Decomposition of TE under metatechnology • The metatechnology (T*) which is constructed from the two production technologies, TA and TB, is represented by line AoA1A2B2B3Boo. The boundary of the metaechnology represents a metafrontier. • Consider the production technology T A where point A1, A2 and A4 lie on the frontier but point A3 lies below the frontier. TEoAof the point A1, A2 and A4= 1 TEoA of the point A3= A3*A3/ A3*A3***. • When the metafrontier (T*) is considered, TEo*of the point A1, A2= 1 TEo* of the point A3= A3*A3/ A3*A3** TEo*of the point A4= A4*A4/ A4*A4**.

  10. Decomposition of TE under metatechnology • Similarly, consider the production technology TB where point B1, B2 and B3 lie on the frontier but point B3 lies below the frontier. TEoB of the point B1, B2 and B3= 1 TEoB of the point B4= B4*B4/ B4*B4** • When the metafrontier (T *) is considered, TEo* of the point B2, B3 and B4 is still the same as TEoB TEo* of the point B1= BoB1/ BoB1** • When the TEo is measured relative to the group-specific technology and metatechnology, it can occur a gap between the two technologies used as a reference. This gap is called a technology gapwhich is defined as the ratio of the distance function using an observed data based on the metotechnology T* to the group-specific technology Tk.

  11. Metafrontier • Using the output orientation, the technology gap ratio can be defined as or it can be written as • The metafrontier (T*) can be decomposed into the product of the TE measured with respect to the k-th group technology (T k) and the technology gap ratio.

  12. Metafrontier • For example, consider point A3 in the figure, TE with respect to T A can be measured by the ratio of the distances between A3*A3 to A3*A3***. • The TEoA = 3.1/5.6 = 0.554 implying that all outputs could be possibly produced by 45% more from the given inputs by using TA as a reference. • The TE with respect to T* can be measured by the ratio of the distances between A3*A3 to A3*A3**. The TEo* = 3.1/6.8 = 0.456 implying that all outputs could be possibly produced by 54% more from the given inputs by using T* as a reference. • Therefore, TGRok = 0.456/0.554 = 0.823 implying that the possible output for the TA is 82.3 percent of that represented by the metafrontier (T*).

  13. DEA Approach to Metafrontier • First, calculate the group-specific technology • If the group k consists of data on Ik producers, the linear programming (LP) problem that is solved for the i-th producer in the k-th group at the t-th time period is given as follows. st where θk ≥1. The inverse of θk is used to define an output-oriented TE scores of the i-th producer in the k-th group at the t-th time period or TEko,it(x, y). 0 ≤ TEko,it(x, y) ≤ 1.

  14. DEA Approach to Metafrontier • Second, calculate the metafrontier technology • The metafrontier is constructed based on the pooled data of all producers in all groups. The LP problem that is solved for the i-th producer at time period t is given as follows. st where θ*≥1. The inverse of θ* is used to define an output-oriented TE scores of the i-th producer at the t-th time period using the metafrontier as a reference or TE*o,it(x, y). 0 ≤TE*o,it(x, y) ≤ 1 and TE*o,it(x, y)≤TEko,it(x, y).

  15. SFA Approach to Metafrontier • First, the stochastic production frontier for each group is estimated and compared with that for all producers.Then, a statistical test is performed to examine whether all producers in different groups have potential access to the same technology. • If the group k consists of data on producers, the stochastic production frontier model for thei-th producer at time period t based on the group-specific data and the pooled data is given as follows. where c = k refers to the stochastic group-specific production frontier model when the data for thei-th producer in the k-th group at the t-th time period are used, and c = p refers to the stochastic pooled production frontier model when the data for all producers in all groups for all time periods are used.

  16. SFA Approach to Metafrontier • Following Battese and Coelli (1992), the stochastic group-specific and pooled production frontier models, taking the log-quadratic translog functional form under a non-neutral TC assumption can be written as follows. • An estimate of output-orientated TE for the i-th producer at the t-th time period is given by

  17. Tests of Hypotheses • If the stochastic frontiers across groups do not differ, then the stochastic pooled frontier function can be used as a grand technology for each group. A test based on the hypothesis that all producers in different groups have potential access to the same technology can be conducted using the likelihood ratio (LR) test. Ho: All producers in different groups have potential access to the same technology Ha: All producers in different groups do not have potential access to the same technology • The test statistic is calculated as where L(H0) and L(Ha) are the value of the likelihood function under the null and alternative hypothesis.

  18. SFA Approach to Metafrontier • The second step will involve estimating the metafrontier function. The parameter estimates of the metafrontier function are estimated by solving the following LP problem. such that where ßk s are the estimated coefficients obtained from the stochastic group-specific frontiers ß*s are parameters of the metafrontier function to be estimated.

  19. SFA Approach to Metafrontier • Once the ß* parameters of the metafrontier function are estimated, the decomposition of TE under the metafrontier can be calculated. • The technology gap for the i-th producer in the k-th group at the t-th time period can be obtained by • Then, a measure of the output-oriented TE relative to the metafrontier, TE*o(x, y). can be obtained using equation

  20. Exercise • Panel data of conventional and organic farms • 28 Farms: 14 farms are conventional farms and 14 farms are organic farms • 15 periods from 1991 to 2005 • 1 output: The gross output value of farming aggregates physical output from seven grain crops and twelve economic crops. • 6 inputs: capital, labor, chemical fertilizer, pesticide, plastic film and irrigation

  21. Estimated Parameters

  22. Estimated Parameters (continued)

  23. Average TE and TGR

More Related