Speaker A
Hi. Welcome back to the course of plate production analysis using MATLAB. It's a 12-week course and we are somewhat at the end of this 10th week.
This tutorial summarizes key concepts of performance evaluation using parametric and non-parametric approaches in MATLAB, focusing on efficiency and productivity analysis.
Key Takeaways
- Efficiency and productivity are key performance measures covered in the course.
- Parametric methods require specifying functional forms and estimating regression coefficients for efficiency calculation.
- SFA involves modeling composite error terms and likelihood functions to estimate inefficiency.
- Non-parametric methods like DEA provide simpler frameworks for efficiency estimation, especially in single input-output cases.
- MATLAB implementation is essential for handling complex multi-input/output efficiency and productivity analyses.
What the video covers
- The video revisits the entire course content on plate production analysis using MATLAB, focusing on efficiency and productivity as performance measures.
- It explains parametric approaches including COLS, CMADI, and OLS, with emphasis on estimating efficiency using regression techniques like Cobb-Douglas functions.
- Stochastic Frontier Analysis (SFA) is discussed, detailing the estimation steps, error term assumptions, and differences between Coelli 1992 and Coelli 1995 models.
- Non-parametric approaches such as Data Envelopment Analysis (DEA) and Free Disposal Hull (FDH) are explained, with examples of output-oriented VRS efficiency estimation.
- The tutorial highlights the complexity of multi-input and multi-output efficiency estimation and the use of MATLAB code for practical implementation.
- It covers the use of super efficiency and Malmquist productivity index within DEA frameworks, including challenges like infeasibility issues.
- The video stresses the importance of understanding theoretical and econometric concepts underlying parametric, non-parametric, and semi-parametric methods.
- Practical exam-oriented problems are discussed, encouraging students to apply learned concepts to estimate firm efficiencies using given data sets.
- The session also outlines how productivity components can be analyzed and interpreted using MATLAB and DEA-based methods.
- Overall, the tutorial serves as a comprehensive review and exam preparation guide for performance evaluation in production analysis.
Chapters
- 00:00Introduction and Course Overview
- 01:11Performance Evaluation: Efficiency and Productivity
- 03:29Parametric Approach: Efficiency Estimation Using Regression
- 04:39Corrected OLS and Cobb-Douglas Functional Form
- 05:42Stochastic Frontier Analysis (SFA) Estimation Steps
- 08:34Choosing Between Stochastic and Deterministic Frontier Models
- 10:16Non-Parametric Approach: DEA and Output-Oriented VRS Efficiency
- 11:44Complexity of Multi-Input/Output Efficiency Estimation
- 13:16MATLAB Implementation for DEA Efficiency Estimation
- 16:01Super Efficiency and Malmquist Productivity Index Overview
Full Transcript — Download SRT & Markdown
Speaker A
So, in this session, I would like to revisit the entire concept that we covered in a very short manner.
Speaker A
Also, approach these problems from an exam point of view or from a learning outcome point of view.
Speaker A
So, this session learning journey so far, key concept and highlight, it's going to be more of a tutorial.
Speaker A
Where we are covering the entire concept that we have covered under the framework of efficiency analysis and the productivity analysis and see it from an exam point of view.
Speaker A
So, you remember this course is basically performance evaluation. And as I mentioned in the very beginning, we have efficiency and productivity as measures of performance. Unfortunately, we were not able to capture effectiveness as a component of our performance evaluation.
Speaker A
So, in the first instance, in efficiency, we followed the parametric approach. We have COLS or CMADI and OLS S of A. These are the concepts we covered under the parametric approach. These are basically the parametric approach and parallel to that we had
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non-parametric approach. It's basically the DEA or FDH. Okay? From an exam point of view, say we have parametric approach.
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If I give you a simple input-output data, say one input one output case, say we have Y X and say I give you a simple data set of six observations.
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A B C D E F. So, it's basically a framework where you can use a simple input simple output function, say Y is basically a function of X.
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And given that I may ask you estimate, say efficiency of firm C given the actual value that we are having. These are the actual values, say.
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You should be able to estimate the efficiency of firm C using the concept that we have covered.
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Particularly, if I ask you to estimate the same using corrected OLS, how are you going to proceed?
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So, corrected OLS is a framework where you'll have to specify the functional form. In order to make this case simple, we can estimate a Cobb-Douglas form. So, we can estimate Y equal to beta zero plus beta one X plus
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U. And this beta zero and beta one you should be able to estimate by using beta one equal to sum of YI XI divided by sum of XI squared where XI is basically XI minus X bar.
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And YI is basically capital YI minus Y bar. This is something you should be very familiar with in the econometrics point of view or any regression fitting point of view.
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Once you have beta hat, we can use the beta hat and beta zero hat is basically Y bar minus beta one hat X bar.
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Okay? Now, once you have these coefficients estimated using simple formula, what you can do, you can get a predicted value Y hat.
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Okay? Once you have Y hat as a predicted value, Y minus Y hat will give you U hat.
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Okay? Once you have U hat, you can get maximum value of U hat. Then you can adjust the intercept such a way that it is shifted following the formula we have.
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So, this was the regression function. This was the COLS. And then using the formula for getting the new U star, we can estimate U star and we can take the exponential of that and get an idea of inefficiency or estimate efficiency of
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firm C. This is doable. I would encourage all of you to go through this.
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I'm not going to ask you to approach this problem from a MOLS point of view because MOLS involve an explicit assumption about the inefficiency term and based on that you may have to get the expected value which is going to be
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computationally involving so and so. Talking about SFA, if I give you data and estimating SFA without having access to MATLAB is going to be complicated.
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But from an exam point of view, you can be familiar with each and every step involved in estimation of SFA. Say SFA steps involved in estimation of efficiency following SFA involves first case you have to estimate the
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model using OLS Y as a function of X using OLS, right? Then here basically these OLS estimates are not reliable in the context of an econometric point of view. So then we need to assume a functional form for our
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composite error term. Basically, composite error term is basically VI minus UI and based on the functional form that you are imposing for UI, you get a distribution for a joint distribution for our epsilon, right?
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Given that then based on that you can specify, we can estimate, we can based on that you can specify your likelihood function and once you have the likelihood function being estimated then we can get the predicted values of epsilon and then
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using our formula that is basically UI, we can get expected value of UI given epsilon, right? So the first step we are following and you can revisit the entire procedure that we followed.
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And here alternatively you should be aware of the lambda and all the gamma that we just defined in the context of stochastic frontier analysis and its importance and see how particular values of lambda you can use
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in determining whether to go for a stochastic frontier analysis or for a deterministic frontier analysis like COLS or MOLES, okay?
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Then within SFA we have two alternative models basically Coelli 1992 and Coelli 1995. So the main difference between these two are basically this one is purely based on Y and X values and here additionally we have
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plus Z variables being included, the determinants of inefficiency also into the model when you are estimating stochastic frontier analysis using Coelli 1995. Moving ahead if I give you the same data A B C D E F G say input output data or output
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data for a cross section. Okay. You have real values over here. And if I ask you to approach this efficiency estimation from a non-parametric point of view, it's going to be even easier than as compared to our parametric approach. Say, if I ask
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you to estimate the efficiency of firm D under output-oriented VRS, what you need to do, you have to plot this observation.
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And then see say D is coming here. Then you can just plot it and get a case for how far D is deviating from its potential output.
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It's basically YD YD star and it is going to be the convex combination of these two observations or this observation in this case and you can get a YD divided by YD star as the technical efficiency of firm
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D under. So, you can use this formula to get efficiency of firm D under output-oriented VRS. Okay.
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Even scale efficiency you can estimate manually. But the moment we go beyond one input, one output, even two input, one output, you can conceptualize using an isoquant. Doable.
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Even two output, one input you can estimate by using a production possibility set or production possibility frontier. That's also doable.
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But if we go beyond the single input or output or two output, one input or two inputs, one output case, it is going to be complicated. So, from an estimation point of view, it will be difficult. But from an exam
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point of view, I can ask you to come up with a MATLAB code given the function that we were using and estimate the provide me the code in the live script or the space provided for providing the
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answer from a MATLAB estimation point of view. So, there you need to say here, if I want to do it with multiple input, multiple output, I need to say MATLAB example.
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Say giving you the data with Y X1 X2, right? And asking you to estimate efficiency of firm D efficiency of firm D output-oriented VRS. So, we are asking you to estimate the model.
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So, using the DEA package that we are having. For that first stage, you will have to define our Y. Y will remain data.Y or whatever.
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We can keep it as data.Y. X you need to define as matrix of data data.Y Sorry data.X1 and data.
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X2. Okay. Now, we have the data for all the matrices for estimating efficiency. So, you can estimate DEA as a model.
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It is going to be DEA package index X Y then orientation will become output-oriented, comma RTS basically VRS.
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This index is something you can type in and e
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So, once we have this DEA, no, that's not the end of the story. Uh, FD basically FD _D_ output oriented_VRS is going to be DEA DEA dot F is doable.
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Not necessarily you need to execute, but unless it's otherwise requested, so you can estimate this but from a MATLAB index point of view.
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Going beyond we have super efficiency and free disposability hull. So, uh, you should be aware of super efficiency or free disposal hull.
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So, you should be aware of the application of these two approaches particularly as an extension of conventional DEA model or then uh, uh compare it and we should be aware of the classical issue that we encounter when you are using a super
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efficiency model or the context that you can use 3D possibility heart. And even the same data which I gave over here, you should be able to estimate uh using graphical method or uh by using simple formula. If I ask you to estimate
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CCR model, you should be able to estimate this from a simple ratio format. If I ask you estimate the super efficiency using a graphical approach, the same logic remains, but uh the frontier that you are estimating should not include the particular observation
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that is D in the reference set. And you then you estimate the uh super efficiency. Here in this case, the super even if whether it is super efficiency or DEA, it is not going to change the efficiency score of firm D,
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which is lying on a point which is away from the frontier, but if it was an observation, say here, we name it as B.
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And for that, if you estimate the super efficiency model by using a graphical approach, your frontier is going to be something like this, and your actual output will lay above the potential output, which will give you a super efficiency score.
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So, be prepared for such uh question. FDH is also very simple. Uh we need to identify uh whether in the first instance you'll be given the data.
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And using the data, you can approach the problem from Initially, you can approach the data set from a input point of view. We can see whether any firms are dominating a particular observation for you to your estimating the FDH efficiency, then that will
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become a new set. And within that new set, you can see whether any firms are dominating the particular firm from a output point of view. Then you take the ratios accordingly whether input oriented or output oriented, then taking
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the minimum of that ratios, input ratios or output ratio maximum output ratio, then you can get the value of theta or fee that we are expecting you to be from a estimation point of view using MDH.
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And moving ahead, we have productivity analysis. So, we have productivity analysis. So, for productivity analysis, basically the the back end, we have most of the case we have a production function estimation or fitting of production frontier using a
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non-parametric approach. So, from an exam point of view, be very clear about the relationship or the difference between uh efficiency and productivity.
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You should have a very clear understanding about the the transition that we had within the context of efficiency estimation to the productivity estimation.
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From an exam point of view, you should be aware of uh the non-parametric approaches.
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Approach, basically we followed Malmquist productivity index. Within that, we have three variant that we discussed FGLR, FGNZ, and Ray and Desli.
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So, be very clear about the difference between these three models. And once you are aware of these uh three models and the underlying principles, FGLR is completely based on CR FGNZ uses VRS for the technical efficiency change, but for uh
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technological change it still uses uh CRS and it has additional component as compared to FGLR that is basically the scale efficiency. And moving ahead we have Ray and the scale decomposition which is completely based on uh VRS and
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so on and so and once you have a clear understanding of difference between all the interconnection between these three uh variations of Malmquist productivity index decomposition, you should be able to answer any questions based on that.
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So, then we have parametric approaches which is basically an extension of our parametric approach for estimating efficiency, but additionally we have uh components when it comes to the productivity analysis.
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Now, from an exam point of view you should be aware of endogeneity as an issue based on which we motivated ourselves for having an additional model or a new model that is basically the semi-parametric approach after parametric.
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We have semi-parametric approach that we discussed in the last session. And within semi-parametric we have Levenson and Petrina and earlier Olesen and Peaks.
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So, you should be aware of the comparison or the difference between Levenson and Petrina and Olesen and Peaks.
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Or from a parametric approach you should be clear about how we estimate production function, how we proceed in the estimation of productivity in a parametric framework. And uh this course we have already covered how semi-parametric approach deviates from
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uh parametric or non-parametric approaches and what are the uh econometric or theoretical concept that or theoretical issue that semi-parametric approach covers from a estimation point of view.
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Over and above we had uh topics like super efficiency. Right? Which we have already discussed.
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At some point I have mentioned you uh this can be connected with our productivity analysis also, particularly the Malmquist productivity analysis or Malmquist productivity index.
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Where uh this uh Malmquist productivity index involves estimation of say uh distance function of input-output bundle XT YT against a frontier for period T minus one. This is something we have already conceptualized.
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So basically this comes with the same technicality of super efficiency estimation, particularly in the case of ray industry decomposition.
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Having said that the super efficiency being plugged in or integrated with a estimation of Malmquist productivity index by estimating a distance function of or cross distance function it comes with the infeasibility issue.
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The source of infeasibility we have already discussed. For example, from an output-oriented manner if the input of any observation that you are estimating efficiency minimum of uh the from an output-oriented manner, if the input is input of K is less than the minimum of
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R J's in J's where K is not included in the J. Then we'll be getting an infeasible solution.
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In an output-oriented manner, similarly, we'll have a case of input-oriented, particularly considering the output.
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So, this interconnection you should be aware of. And then, in case of Malmquist productivity index, and the two ray industry decomposition when we are getting infeasible solution, we were giving a case that the productivity scores, so particularly the
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components of productivity scores, we were replacing with the uh nan. Okay? Uh so, alternative ways that I check understanding of my students from a uh conceptual point of view, I used to give a set of uh component out of which they can choose
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some a a con- concepts and create a or establish a relationship between them. So, for example, we can use the same uh concept. The question can be like uh compare or connect any pairs of concept given.
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So, for that I can ask A, B, C, D, E. Say, one concept can be super efficiency.
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Other concept can be DEA. The third concept can be SFA. Uh Uh, fourth concept can be infeasibility.
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And the fifth concept can be Malmquist productivity index. So, this gives you a very wide range of uh, answer that you can think of, but the interconnection sometime it may go beyond pairs and ask you to keep three concepts, any three concepts
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and uh, establish a relationship. So here the much expected uh, item uh, I can see it's basically combination of say B and C.
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It's a very straightforward. Anyone went through the entire course will be able to do that.
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Very easily. B being DEA, that is basically a non-parametric approach and SFA is basically a parametric approach. That is a very straightforward comparison that you can establish.
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Continuing our last slide, you can establish a relation between connection between A and D.
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Basically, infeasibility is a particular case of uh outcome. In case of super efficiency and you can explain how infeasibility arises in the case of super efficiency estimation from output or input oriented men.
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One more example, we can have a connection between uh say B and E. Well, you remember that Malmquist productivity index is basically a DEA based productivity estimation and decomposition.
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Okay? So, these are the possibilities that you can think and these questions, for example, this compare and connect any pairs will particularly evaluate your understanding. And if I go beyond that and keep three concepts, ask you to pick
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any three concepts and compare or connect them, it is going to be even uh rigorous or even depth depthful in the in an exam point of view.
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So then we have concepts like uh energy efficiency, environmental efficiency, which is also being covered as a part of this course and you should be aware of the motivation for such modified models or extension of conventional production function.
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So, to summarize, in this session, we were revisiting all our India concepts of uh applied production analysis covered so far from an exam some point of view.
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Uh from a knowledge point of view or a understanding point of view, you should have two compartments for the concept that we covered so far.
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One is basically the compartment consists of our efficiency tools and the compartment consists of our productivity tools. And honestly speaking, these two compartments are not in a very watertight uh framework.
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Some concepts we learned in the efficiency are overlapping with our productivity estimation and even our product efficiency estimation, we started with the productivity concept, so on and so forth.
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So, you should be aware of this interconnection. Before that, you should be aware of which concept comes under which theoretical framework.
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Then we saw one simple example that I can give you uh from a numerical estimation point of view and using the data how to estimate uh productivity and the complicated case you can consider the steps involved in the production
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function and estimation of productivity or efficiency using parametric approaches. We had earlier models like Coelli 1992 Coelli 1995. We have FGNZ, FGLR and the industry as the theoretical models and Evenson and Battese and Olsen and Peaks so and so and we very clearly have a
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good motivation or theoretical underpinning to this model. And also from a MATLAB point of view, you should be aware of the syntax that we generally follow. And if I ask you estimate an output-oriented VRS uh using a particular case, you should be
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uh able to replicate or provide the syntax that we used in our practical sessions.
Speaker A
So, that's all for uh this review. We can have further details when we are having a live session on uh the tutorial or live session on how to approach this concepts from an exam point of view. Thank you.
Topics:performance evaluationefficiency analysisproductivity analysisparametric approachnon-parametric approachstochastic frontier analysisData Envelopment AnalysisMalmquist productivity indexMATLAB tutorialproduction analysis
