<p>There is a scientific tradition of decades that occupies itself with the measurement/estimation of the productivity/efficiency of firms. The three strands of the literature are <strong>Data Envelopment Analysis</strong> (DEA), <strong>Discriminant Analysis</strong> (DA), and <strong>Stochastic Frontier Analysis</strong> (SFA).  </p>

<p>I am familiar with the third one. Stochastic Frontier Analysis starts with the observation that firms do <em>not</em> operate all the time on their <em>efficiency frontier</em>, i.e at maximum efficiency, either due to unanticipated shocks, or because, while competitive market forces may push firms to be efficient, they nevertheless are not that strong or that perfect in their effects in order to make firms to be <em>fully</em> efficient, as it is usually assumed in theoretical models. Therefore, inefficiencies due to organizational problems and the like, may persist. </p>

<p><strong>"Efficiency"</strong> in the context of SFA, has many facets: output-oriented technical efficiency, input-oriented technical efficiency, cost-efficiency, revenue efficiency, profit efficiency. All have been developed in the literature. One can choose the approach  or approaches most suited to the purpose at hand, and to data availability. </p>

<p>To consider the case of <strong>output-oriented technical efficiency</strong>, SFA modifies/augments the production function of a firm as</p>

<p>$$Q = F(\mathbf x) + u -v$$</p>

<p>Where $u$ is a zero-mean normal random variable and $u$ is a non-negative random variable (usually specified as a half-normal or as an exponential r.v.). The $v$ component captures the inefficiency (measured in terms of output), while the $u$ component captures stochastic disturbances that may affect production (either positively or negatively).  $F(\mathbf x)$ represents the full-efficiency level of output.</p>

<p>Econometrically, this is estimated by using Maximum Likelihood (the least-squares method cannot decompose the error term in its two components), on a data set that contains data on output, and on quantities of input factors (in other words, no more than the usual data set required to estimate a production function).<br>
The estimation procedure itself will provide of course estimates that are averages over the data set. If one wants to rank the firms present in the sample, one can implement the approach developed in <a href="http://www.sciencedirect.com/science/article/pii/0304407682900045" rel="nofollow">Jondrow, J., Knox Lovell, C. A., Materov, I. S., &amp; Schmidt, P. (1982). On the estimation of technical inefficiency in the stochastic frontier production function model. Journal of econometrics, 19(2), 233-238.</a>  </p>

<p>A comprehensive book on Stochastic Frontier Analysis is <a href="http://books.google.gr/books/about/Stochastic_Frontier_Analysis.html?id=wrKDztxLWZ8C&amp;redir_esc=y" rel="nofollow">Kumbhakar, S. C., &amp; Lovell, C. K. (2003). Stochastic frontier analysis. Cambridge University Press.</a></p>

CC BY-SA 3.0
2014-11-25T09:55:57.307Z
2014-11-25T21:04:45.620Z
2014-11-25T21:04:45.620Z
Alecos Papadopoulos
<p>I want to rank firms based on a metric, let's call it productivity.
Theoretically, this firm productivity measure may be well defined. Empirically, however, data that account for all dimensions of productivity are generally unavailable.
On the other hand, typically available data (e.g. output/worker) does not suffice to rank firms across industries/sectors because sector-specific differences, for instance in production technology, need to be taken into account. </p>

<p>What empirical approach would be both feasible in the light of data availability and non-trivial with respect to the theoretical understanding of firm productivity?</p>

CC BY-SA 3.0
2014-11-25T16:35:05.243Z
Thank you @EnergyNumbers. I rewrote the question and hope that it is more answerable now. I agree that Alecos' answer is very helpful and I shall accept it.
bsecon
CC BY-SA 3.0
2014-11-25T17:47:52.640Z
This sounds like asking all questions about a whole research project. I think it would be more appropriate to ask specific subparts of this in a single question, as it gives less of the impression you want someone else to "do all the work for you"
FooBar
CC BY-SA 3.0
2014-11-24T22:03:46.020Z
This seems far too broad and opinionated to have a good empirical answer. I would be willing to reconsider my close vote if this were broken out more and far less sweeping.
Jason Nichols
CC BY-SA 3.0
2014-11-24T22:20:53.843Z
A very rough remark based on a *vague* recollection from my undergrad years is that it might be worth looking-up Farrell Efficiency.
Ubiquitous
CC BY-SA 3.0
2014-11-24T22:34:51.037Z
Are you familiar with/aware of, the Stochastic Frontier Analysis field?
Alecos Papadopoulos
CC BY-SA 3.0
2014-11-25T07:49:48.970Z
Thank you for your comments. I understand the concerns and will edit my question to address them and make it more specific. @Ubiquitous: Many thanks for the hint. I shall look-up Farrell Efficiency.
bsecon
CC BY-SA 3.0
2014-11-25T08:02:36.460Z
@AlecosPapadopoulos: Yes, I am aware of Stochastic Frontier Analysis. The method could be very useful in the context of my question but I want to learn more about the available data first. Thank you for your hint!
bsecon
CC BY-SA 3.0
2014-11-25T10:39:16.680Z
I agree with @GuidoJorg that this needs rewriting to be more answerable, though Alecos has done a pretty good job. For future readers and answerers, a tighter, more focussed question will be helpful. Putting a question on hold isn't of itself a sign that we don't want it: it's a pause to give the asker chance to edit it into shape, so that it can be reopened.
410 gone
<firm><productivity><ranking>
Empirical ranking of firms based on productivity
bsecon
# Empirical ranking of firms based on productivity

(Asked by: username_0 on 2014-11-24)

I want to rank firms based on a metric, let's call it productivity.
Theoretically, this firm productivity measure may be well defined. Empirically, however, data that account for all dimensions of productivity are generally unavailable.
On the other hand, typically available data (e.g. output/worker) does not suffice to rank firms across industries/sectors because sector-specific differences, for instance in production technology, need to be taken into account.

What empirical approach would be both feasible in the light of data availability and non-trivial with respect to the theoretical understanding of firm productivity?

**Tags:** firm, productivity, ranking

> **Comments:**
> **username_2**: This seems far too broad and opinionated to have a good empirical answer. I would be willing to reconsider my close vote if this were broken out more and far less sweeping.  
> **username_3**: A very rough remark based on a *vague* recollection from my undergrad years is that it might be worth looking-up Farrell Efficiency.  
> **username_4**: Are you familiar with/aware of, the Stochastic Frontier Analysis field?  
> **username_0**: Thank you for your comments. I understand the concerns and will edit my question to address them and make it more specific. @username_3: Many thanks for the hint. I shall look-up Farrell Efficiency.  
> **username_0**: @AlecosPapadopoulos: Yes, I am aware of Stochastic Frontier Analysis. The method could be very useful in the context of my question but I want to learn more about the available data first. Thank you for your hint!  
> **username_5**: I agree with @GuidoJorg that this needs rewriting to be more answerable, though Alecos has done a pretty good job. For future readers and answerers, a tighter, more focussed question will be helpful. Putting a question on hold isn't of itself a sign that we don't want it: it's a pause to give the asker chance to edit it into shape, so that it can be reopened.  
> **username_0**: Thank you @EnergyNumbers. I rewrote the question and hope that it is more answerable now. I agree that Alecos' answer is very helpful and I shall accept it.  
> **username_1**: This sounds like asking all questions about a whole research project. I think it would be more appropriate to ask specific subparts of this in a single question, as it gives less of the impression you want someone else to "do all the work for you"  

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## 1 answers

### Answer by username_4 on 2014-11-25. Score: 7 | Accepted answer

There is a scientific tradition of decades that occupies itself with the measurement/estimation of the productivity/efficiency of firms. The three strands of the literature are **Data Envelopment Analysis** (DEA), **Discriminant Analysis** (DA), and **Stochastic Frontier Analysis** (SFA).

I am familiar with the third one. Stochastic Frontier Analysis starts with the observation that firms do *not* operate all the time on their *efficiency frontier*, i.e at maximum efficiency, either due to unanticipated shocks, or because, while competitive market forces may push firms to be efficient, they nevertheless are not that strong or that perfect in their effects in order to make firms to be *fully* efficient, as it is usually assumed in theoretical models. Therefore, inefficiencies due to organizational problems and the like, may persist.

**"Efficiency"** in the context of SFA, has many facets: output-oriented technical efficiency, input-oriented technical efficiency, cost-efficiency, revenue efficiency, profit efficiency. All have been developed in the literature. One can choose the approach or approaches most suited to the purpose at hand, and to data availability.

To consider the case of **output-oriented technical efficiency**, SFA modifies/augments the production function of a firm as

$$Q = F(\mathbf x) + u -v$$

Where $u$ is a zero-mean normal random variable and $u$ is a non-negative random variable (usually specified as a half-normal or as an exponential r.v.). The $v$ component captures the inefficiency (measured in terms of output), while the $u$ component captures stochastic disturbances that may affect production (either positively or negatively). $F(\mathbf x)$ represents the full-efficiency level of output.

Econometrically, this is estimated by using Maximum Likelihood (the least-squares method cannot decompose the error term in its two components), on a data set that contains data on output, and on quantities of input factors (in other words, no more than the usual data set required to estimate a production function).  
The estimation procedure itself will provide of course estimates that are averages over the data set. If one wants to rank the firms present in the sample, one can implement the approach developed in [Jondrow, J., Knox Lovell, C. A., Materov, I. S., & Schmidt, P. (1982). On the estimation of technical inefficiency in the stochastic frontier production function model. Journal of econometrics, 19(2), 233-238.](http://www.sciencedirect.com/science/article/pii/0304407682900045)

A comprehensive book on Stochastic Frontier Analysis is [Kumbhakar, S. C., & Lovell, C. K. (2003). Stochastic frontier analysis. Cambridge University Press.](http://books.google.gr/books/about/Stochastic_Frontier_Analysis.html?id=wrKDztxLWZ8C&redir_esc=y)


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