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Re: st: Bootstrapping Malmquist Poductivity Index

From   Nick Cox <>
Subject   Re: st: Bootstrapping Malmquist Poductivity Index
Date   Sat, 1 Dec 2012 12:08:24 +0000

On a second reading I can make more sense of this, namely this interpretation:

(a) The Malmquist index is in effect data here. It was calculated
upstream but that is not material to the present exercise.

(b) The interest is in geometric means. The null case is a value of 1.

It might be easier to work on a log scale and work with the mean of
the logs. Then Yaseen can bootstrap -summarize- results. But big
problems remain.

1. By lumping different panels together for the same year the
assumption is that they are independent. What economic or statistical
sense does this make?

2. By testing separately for each year, the assumption is that
separate years are independent. The same question applies, but with
added strength. All time series structure (trend, business cycles,
autocorrelation) is being ignored.

I have raised similar concerns in  a general way as issues of
dependence structure in my two previous replies. I am not an economist
and am pontificating here merely from general knowledge.


On Fri, Nov 30, 2012 at 5:03 PM, Nick Cox <> wrote:
> I can add almost nothing useful to what I said before.
> Nothing is said here about what program you are using to calculate
> Malmquist index, what the original data are, what saved results you
> expect to -bootstrap-, how the panel structure is
> relevant, etc.
> In fact, as you present things, the Malmquist index looks like data,
> not a parameter being estimated.
> However, what is now clear is that your Malmquist index is a time
> series varying between panels and over time. Default -bootstrap-
> procedures do not apply to such set-ups, or to put it more positively
> you cannot progress without taking that dependence structure into
> consideration.
> Nick
> On Fri, Nov 30, 2012 at 4:47 PM, Yaseen Ghulam <> wrote:
>> Thanks a lot for the response.
>> My fault if problem was not explained clearly or not in detail.
>> My example data of unbalanced panel structure is such as:
>> panelid   year              malmquist index
>> 1          2007                1.05
>> 1          2008               1.03
>> 1                    2009                1.01
>> 1                    2010                0.96
>> 1                    2011                0.98
>> 2                    2008               1.02
>> 2                    2009              1.07
>> 2                   2010               1.00
>> 2                   2011               0.99
>> .
>> .
>> .
>> .
>> 26                2007          0.92
>> 26               2008                 0.96
>> 26               2010                1.01
>> 26               2011                 0.98
>> I would like to:
>> 1. Bootstrap malmquist index with let say 1000 replications and then calculate geometric mean, standard error and confidence interval of malmquist index for each year i.e. 2007, 2008, 2009, 2010 and 2011.
>> 2. By using bootstrap standard error, I would like to carry out a test where null hypothesis is that geometric mean is equal to unity (no change in productivity) for each year.
>> I hope it is clear now. st0193 is very good but I am using different estimator to calculate malmquist index.
>>>>> Nick Cox  30/11/12 3:49 PM >>>
>> It is unclear quite what you are doing. The -summarize- example does
>> not seem closely related to what you describe (although note that it
>> clearly refers to the median, and has nothing to do with the mean).
>> The allusion to DEA may or may not be an allusion to
>> st0193 from
>>     SJ10-2 st0193.  Data Envelopment Analysis / Data Envelopment Analysis / by
>>     Ji, Yong-Bae, Korea National Defense University, / Republic of Korea /
>>     Lee, Choonjoo, Korea National Defense University, / Republic of Korea /
>>     Support:,, /
>> Either way, you are asked to be precise about what commands you are
>> using and (if they are user-written) to explain where they come from.
>> What you need is a program that emits the geometric mean as an e-class
>> result or an r-class result. If you are producing one geometric mean
>> for all panels that is one parameter; if there is a separate geometric
>> mean for each panel that is several parameters.
>> However, there will be some dependence structure either way that may
>> be problematic for -bootstrap-, but as everything depends on the
>> details of what you are doing it is difficult to give further precise
>> advice.
>> Nick
>> On Fri, Nov 30, 2012 at 1:03 PM, Yaseen Ghulam  wrote:
>>>  I have calculated malmquist productivity index using DEA. I want to bootstrap the index in Stata. I have unbalanced panel (14 firms and 26 years). I have seen a general command like
>>> webuse auto
>>> bootstrap r(p50), reps(1000) seed(1234): summarize mpg, detail
>>> I believe above command calculates standard error for median or mean by using 1000 replications. I am interested in calculating standard error of geometric mean by taking into account panel structure of the data (which above command probably does not) and then test whether geometric mean is significantly different than unity or not.

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