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[music] [music] Hi. Welcome back to the course of play production analysis using MATLAB. Following our discussion on efficiency analysis using both and extensions thereof.
Introduction to total factor productivity and Solow residual, explaining productivity vs efficiency and growth accounting framework.
Key Takeaways
- Productivity is distinct from efficiency and is a critical driver of economic growth.
- Total factor productivity measures output relative to a composite of multiple inputs over time.
- The Solow residual captures productivity changes unexplained by input variations, often linked to technology.
- Productivity analysis helps identify why some firms or units perform better than others.
- Growth accounting frameworks provide a theoretical basis for decomposing output growth into input and productivity effects.
What the video covers
- The video introduces productivity analysis in the context of performance evaluation, distinguishing it from efficiency and effectiveness.
- It explains productivity as an engine of growth, emphasizing technological change as a key driver.
- The difference between single factor productivity and total factor productivity (multi-factor productivity) is discussed.
- The Solow residual and growth accounting framework are introduced to explain unexplained output growth beyond input changes.
- The video references seminal works by Solow and literature by Sickles and Zelenyuk on productivity measurement.
- It highlights the economic relevance of productivity analysis for understanding firm and economy-level growth.
- The concept of composite input and output indices in a multi-input/output framework is explained.
- The video discusses how productivity changes can be decomposed and analyzed over time using panel data.
- It clarifies that productivity improvements can be due to technological advances or other factors not captured by input increases.
- The video sets the stage for further detailed discussion on parametric and semi-parametric methods for productivity estimation.
Chapters
- 00:00Introduction and course overview
- 01:12What is productivity and its economic relevance
- 02:21References and motivation for productivity analysis
- 03:59Productivity as an engine of growth
- 05:12Sources of productivity differences among firms
- 06:23Difference between efficiency and productivity
- 07:53Single factor productivity examples
- 09:07Multi-factor productivity and composite indices
- 09:54Interpreting productivity changes over time
- 10:49Growth accounting framework and Solow residual
Full Transcript — Download SRT & Markdown
Speaker A
Now, we start our discussion on productivity analysis. As I mentioned, the overall framework of performance evaluation of decision-making unit is being divided into three components.
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Efficiency, productivity, and effectiveness. Due to some reason that we have already explained, particularly the objective nature of effectiveness, we are not covering the components of effectiveness as a performance measurement unit.
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Applied framework. Now, moving ahead, we discuss the productivity aspect of a play production analysis.
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Where in the first instance, we are going to see what is productivity? How it is different from efficiency as a measure of performance, the economic relevance of productivity also we will see and then we are going to discuss one
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Important topic that is basically total factor productivity. Some literature uses multi-factor productivity and total factor productivity interchangeably.
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Then we see the very classic work on productivity analysis of total factor productivity by Solow. Not the complete story, but simply the theoretical underpinnings of measuring performance from a productivity point of view proposed by Solow and popularized in the
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Growth accounting frame. So these are the references I'm referring to: Solow Nobel-winning literature. This is the main one of the main contributions he had in the field of economic growth and growth accounting, technical change in aggregate production
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Function. Also, we'll be referring to measurement of productivity and efficiency by Sickles and Zelenyuk. So before going into the technicalities of our productivity analysis, we see why productivity analysis.
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Going ahead, we see given these limited resources and increased need for goods or services in a country or in a state or even in a firm-level context, for having more output, getting more input usage might not be very feasible
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Because our resources are limited. Having said that, one of the main objectives or one of the most popular or feasible channels through which you can increase the output for a given level of input is basically increasing productivity.
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So productivity is being considered as an engine of growth. It's not the trade only that can create growth for a country as well as, uh, we can have productivity also as a... We can consider productivity also as a
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Engine of growth. So, when there is an improvement in productivity mainly happening due to technological change, uh, what we can see, we can see keeping the same amount of input, you can produce more output.
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Okay? So, productivity can be defined as an engine of growth. Uh, so productivity analysis will help us to identify the sources of growth.
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So, once you have a growth being observed, we can see how much growth has been, uh, happened because of the productivity change.
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Also, we can see by using the results of productivity analysis, we can see why some firms or DMUs perform better in terms of production as compared to the other. So, otherwise we can say that by doing a productivity
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Analysis, we can see the sources of productivity itself. What we can do, we can regress the productivity scores that we are getting for each observation or DMUs and see what makes differences in the productivity among firms.
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So, that is what we are talking about economic relevance. Moving ahead, we see how efficiency is different from productivity.
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These are two pillars of performance evaluation, particularly the economic performance. So, efficiency as we know, we will have a maximum output or minimum input.
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This is basically considered as potential outcome in general. Either one of that based on the orientation that you're thinking.
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And efficiency as a measure of performance says how much each DMU is deviating from their potential output or inputs.
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But as against, uh, efficiency, productivity unit output. That means for each unit of input that we are using to see how much output you're getting. So, we define it as Q by X if you are having a single one input one output case.
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So in, uh, single one input one output case, we can say single factor productivity. It's a very rarely used approach. Say labor productivity or energy productivity or capital productivity. So, single factor productivity is basically output by input for a unit.
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How much you are producing? This input can be replaced by labor or capital or, uh, even energy.
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Okay? That will tell us how much each labor is producing in terms of their production process. So, that will tell the labor productivity or capital productivity or energy productivity.
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But, in reality, we will have multiple inputs or multiple outputs. So, we need to go for a multi-factor productivity or alternatively we call it as total factor productivity.
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It is basically TF. Total factor productivity. So here what we are interested we are considering more of a time framework or a panel framework. At least you have two time periods.
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And you can see that your output is changing. So, we can say QY as the output quantity index. So, that tells, uh, how much percentage output has improved. So, it is basically change in output. We can, in a very direct sense,
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We can say that alternatively we have change in input. So, this is basically not one, uh, input. Here we will be creating inputs.
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So, this is basically a composite input and composite output we are talking about. So, this is basically a multiple input multiple output framework.
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And the ratio of this output quantity index to input quantity index tells us whether productivity has improved. What is the logic here?
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If output has changed more than proportionately than change in input, that means there is something unexplained in the framework.
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That gives us a hint that productivity of factors has changed during the period under consideration.
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So, that is basically the difference between productivity and efficiency and the single factor productivity and multi-factor productivity or total factor productivity. We'll be discussing further in detail.
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So, now let's quickly see the growth accounting approach and Solow residual. So, in a very simple notational manner, your output has changed.
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Say it's composite output or aggregate output. This has changed because of change in input or composite change in composite input plus some unexplained.
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So, I'll keep it as U not in a very direct sense. Okay? So, in this case, uh, not the U from the regression model or whatever. This is something being unexplained. So, there is a change in or a proportionate change in output
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Which is not being explained by, uh, input change. We can call it as a productivity change. This is basically... This will capture the residual.
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Or that will basically... This will mainly happen because of productivity. See, it can be, uh, reduction also.
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Sometimes our productivity can get deteriorated. So now the main question: why would productivity keep changing over period?
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So, the sources of, uh, productivity change is basically, uh, discussed in growth accounting framework. So, we face a growth in output or growth in economy or growth in aggregate output of the economy. So, growth accounting in a very layman's
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Perspective searches for the sources of, uh, what I would say growth mostly happening because of the productivity change.
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So, the roots of theoretical literature based on productivity analysis are going to the Solow 1957 paper as I mentioned. So, you can see if you open that paper, he follows more of a this framework follows more of a one
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Input one output. So, here you can see we have this as the, uh, f of x c f of x zero then see here you can see f of x one. So, if you consider this potential output, say
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This is basically x zero y zero say y one x one. So, you can see as compared to, uh, zero period input has changed, of course, but output has changed more than proportionate to the change in input.
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So, why is happening? The technology itself has changed.
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Solow's framework. Go to next. So, for Solow's framework, uh we can have Q T of firm K is basically the aggregate output.
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This aggregate output is basically uh produced by using X T K basically set of inputs X 1 T K X 1 T 2 T K up to X N capital N T K we have N inputs that we are considering.
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And basically uh from a very uh production point of view Q T K is can be defined as uh C psi K T X T K Okay?
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So, this is like a the functional form or functional relationship between uh output, aggregate output, and the inputs being put.
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This can be decomposed to A T K psi K X T K. So, here now the psi we are defining as a factor independent of time. And now we have A T K that is particularly for the time
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uh period T. And here, this will be the portion of our uh change in output, which is being explained by change in input. But, this portion is basically the ATK is basically a portion of uh change in output, which is not being
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explained by or independent of uh input bundle. So, this can This is basically called the solo procedural or total factor productivity in the empirical literature.
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Okay? Uh so, moving ahead, what I mentioned, we have something called productivity chain. In this course, in the upcoming sessions, we'll be estimating productivity change from uh multiple perspective.
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So, we'll be having uh simple methods like uh non-frontier approaches or I would say price weighted or share weighted measures.
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So, here what we'll be doing, we'll be using uh inputs, outputs, their corresponding prices, uh that is input prices and output prices. And that input prices and output prices will help you to uh create a composite output and
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composite input or output quantity index or input quantity index. And that weight weight will be assigned based on either based on the price of this thing or it can be based on the overall share of uh each inputs or output in the total
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revenue or total cost. So, here we'll be having two indexer in basically two indices. One is Tornqvist.
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Another one is Fisher. Moving ahead, we'll be having frontier-based approaches. So, very first frontier-based approach we can think of is basically the Malmquist productivity index.
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And also we can see the uh parametric approach which is also going to be more or more or less based on a frontier where instead of going for a non-parametric uh this is basically a non-parametric approach, we'll be following a
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parametric approach in estimating the frontier and see how well it has been shifted. Then we will have a set of uh semi-parametric approaches to see the productivity change.
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And this course is not going to be simply uh talking about productivity change. We also see the sources of productivity change.
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From an applied pro- production point of view, productivity may change because of technological change.
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It can happen because of technical efficiency change or scale change. Sometime the recent literature say that sometime you are uh productivity may change because of the input composition.
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Input or output composition, change in input or output composition can also result in uh productivity change.
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So, just to summarize, we are moving with a new measure of performance. So, we'll be using productivity as a measure of performance in this context. It is going to be more of an absolute measure in some sense. Uh instead of taking the
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potential output or potential input, we'll be considering what is what was the firm doing in the last year and what they are doing in the present year.
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And uh we also saw uh the difference between efficiency and productivity. In fact, they are interconnected when we were discussing the DEA basic DEA model. We have already seen this. Uh DEA measures were defined from it.
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Uh productivity in the packet. Okay. Uh then we saw single factor productivity, simple ratio, and then the growth accounting framework which take considered multi-factor productivity and works uh the roots are basically to the solo residual which is basically the
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proportional change in output which is not being explained by uh change in input or it is something termed as solo residual in the literature. And moving ahead, we will see how to estimate Donquist index, Fisher's index, and Malmquist index and
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the parametric and semi-parametric indices in the latest case. Thank you. [music] [music]
Topics:total factor productivitySolow residualgrowth accountingproductivity analysisefficiency vs productivityeconomic growthmulti-factor productivitytechnological changeperformance evaluationproduction function
