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# Re: st: Inefficiency measures greater than one for frontier commands

 From Aljar Meesters To statalist@hsphsun2.harvard.edu Subject Re: st: Inefficiency measures greater than one for frontier commands Date Tue, 23 Apr 2013 23:24:30 +0200

```Your understanding about - predict var, te - is correct. Your
conceptual question needs some elaboration. A score of one indeed
represents a fully efficient bank, you can call this 100% efficient.
If you find a score of say 1.2 you can say that that particular bank
makes 20% more costs than a fully efficient bank would make. I think
you can say that the bank is 20% inefficient. Although opinions on
this may differ, it is at least clear what the 20% means. If you
prefer to have a score between zero and one (one is fully efficient),
you can calculate a new score by one over the old score, yet, in this
case there is no clear interpretation, as far as I know. So, if you
find that bank Y has a score of 0.8 after the rescaling and call this
bank 80% efficient, I don't know what this 80% exactly means. However,
you do find cost efficiencies in the literature that are scaled
between zero and one, so, it is not uncommon.  As a side note, if you
rescale the efficiency score by one over the old score, you will
ignore Jensen's inequality (E[f(x)] != f(E[x])). Whether you find this
problematic or not is up to you.
Best,

Aljar

2013/4/23 Reut Levi <rlevi2@student.gsu.edu>:
> Thank you!
>
> To clarify and make sure I understand.  The syntax: predict VariableName, te would give me inefficiency scores that range from 1 to infinity (for cost functions), right?
>
> In addition, here is a conceptual question. The frontier represents 100% efficiency. According to the inefficiency scores described above, banks that receive a score of one are 100% present efficient. Therefore, scores above 1 would represent banks that are operating above the cost frontier and therefore less efficient.  Now, how can I interpret those inefficiency scores above one? Is there an accepted way to normalize them to range from 0 to 100%, so I will be able to make a statement such as "bank Y is X% efficient/inefficient"?
>
> Thank you for your help and inputs,
> Reut
>
>
>
> ________________________________________
> From: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] on behalf of Federico Belotti [f.belotti@gmail.com]
> Sent: Tuesday, April 23, 2013 12:55 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: Inefficiency measures greater than one for frontier commands
>
> If you are using the -xtfrontier- command the syntax is
>
> predict te, te
>
> In this way you obtain an estimate of efficiency scores through the Jondrow et al. (1982) formula.
>
> Federico
>
> On Apr 23, 2013, at 5:35 PM, Reut Levi wrote:
>
>> Thank you Federico!
>>
>> Do you happen to know if there is a way to predict efficiency scores in STATA, instead of inefficiency scores?
>> If there is, can you please specify the command syntax?
>> If there isn't, how should I go about converting the inefficiency scores predicted to represent efficiency levels?
>>
>> Thank you very much,
>> Reut
>>
>> ________________________________________
>> From: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] on behalf of Federico Belotti [f.belotti@gmail.com]
>> Sent: Monday, April 22, 2013 5:54 AM
>> To: statalist@hsphsun2.harvard.edu
>> Subject: Re: st: Inefficiency measures greater than one for frontier commands
>>
>> Dear Reut,
>>
>> in the stochastic frontier framework, "inefficiency" scores ranges from 0 to infinity, while "efficiency" scores are restricted between 0 and 1 by construction since
>>
>> TE = exp{-E[su|e]}  following  Jondrow et al., 1982,
>>  or,
>> TE = E{exp(s*u)|e}  following Battese and Coelli, 1988,
>>
>> where s = 1 (s = -1) in the cost frontier (production frontier) case.
>>
>> Hope this helps.
>> Federico
>>
>> On Apr 21, 2013, at 2:28 AM, Reut Levi wrote:
>>
>>> Dear Statalist members,
>>>
>>> I am using the xtfrontier command to estimate inefficiency levels for the U.S banking industry. My data comprised of information from the FFIEC Call Report for the year 2012. It is a large data set with over 29,000 observations. I broke it down by asset size in order to reduce the number of observation and also because the literature suggests that asset size peer group will produce more appropriate inefficiency measures. After breaking down the dataset, the average number of banks in each peer group data set is 650, with observations for 4 quarters, totaling in 2700 data points. All of my variable are in natural logs.
>>>
>>> I am using the xtfrontier command with the options ti and cost. I then predict the inefficiency measures using predict with the option u, but some of my inefficiency predications are greater than one. How is it possible? The manual says that the inefficiency measures are restricted to be between 0 and 1. Am I doing something wrong? Or what could explain those measures greater than 1?
>>>
>>> I am relatively new to STATA so please take it into consideration in your response.
>>> Thank you very much,
>>> Reut
>>>
>>>
>>> *
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>>
>> --
>> Federico Belotti, PhD
>> Research Fellow
>> Centre for Economics and International Studies
>> University of Rome Tor Vergata
>> tel/fax: +39 06 7259 5627
>> e-mail: federico.belotti@uniroma2.it
>> web: http://www.econometrics.it
>>
>>
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>>
>>
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>
> --
> Federico Belotti, PhD
> Research Fellow
> Centre for Economics and International Studies
> University of Rome Tor Vergata
> tel/fax: +39 06 7259 5627
> e-mail: federico.belotti@uniroma2.it
> web: http://www.econometrics.it
>
>
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>
>
>
> *
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```