Considering annual data for data envelopment analysis will give effective result by eliminating the too much of variance. Annualising the overhead cost is better than direct cost. 

To  make it comparable maybe you can subtract 6-2013 labour costs to 12-2013 labour costs so that your 12.2013 data only reflects the second semester. This way all 6 month periods would be comparable, unless you have significant seazonality effects like higher labour costs for turism companies during holiday season. 

But I am curious to Know how you are going to include the variable time in DEA. Usually labour cost would be a DEA input and you would have data on this variable for different  DMU's (decision making units like companies for example) and not for different periods of time.

But maybe you plan do perfom one DEA analysis for each moment in time to see how the companies performance evolves? Is that it? Just curious.

Kind regards.

Fernando.

Considering the annual data will give effective results in DEA. It is better to take annual financial report. 

Thank you for answers. @Fernando : I'm calculating DEA separately for every 6-months of data for companies (Efficiency of companies) and comparing the results.

The "Labor Costs" was an example. Suppose that we have these variables : "Current account", "Total Assets", "Total Liabilities", "Total income(Revenue)", "Non-interest income", "Interest income", "Physical capital", "Fixed deposits", "Saving deposits". We should use your subtract method in all above variables?  These companies are financial institutions.

The subtraction would only make sense for the cumulative variables, such that their value after one year is about twice the value after 6 months. But if the variable is cumulative in all companies you don't even have to subtract anything because DEA performance evaluations are relative (between companies).

Good luck.

Fernando

@Fernando. Thank You for your answer. But there is a problem here. Suppose that we have an income variable type. Value of this variable in 6-2013 is 120000$ but value of this variable in 12-2013 is 100000$ ( 20000$ lost in second 6-months of year) so the value for second 6-months here is -20000$. Is this true? We can have negative value using your proposed method?

It should be okay if you are computing exactly the same way for the other companies and always comparing the same periods.

You just have to be careful if drawing conclusions for all periods together in the end:

Imagine you compute DEA for several periods and for all but one of them a certain company always performs best. You could think of averaging its performance across the several DEA computations and so it would be the best performing company overall. But this could be a mistake, because in just one DEA computation the company could have lost more money than all the other profits together.

Could be an interesting problem (maybe prone to research-like novelty, but I am not aware of the literature on this) how to aggregate the DEA results for all time periods, supposing you want to do that. Maybe one way was to add all values of all periods for each variable and calculate one only aggregate historical DEA performance for each company. Another could be something like taking an average between the worst DEA efficiency, the best DEA efficency, and the average DEA efficiency of each company, to make average performance sensitive to potentially dramatic scenarios.

Kind regards.

Fernando  

@Fernando. Thank you again for your detailed answer. There isn't any problem in comparing companies in same cutting time in your method? Suppose that finally we want draw a line plot which x-axis is time and y-axis is DEA score of companies in that cutting time. For example we draw line plot 5 companies in this plot. Is this correct?

The best thing is checking in the literature whether this is ok.

DEA applications can be fertile in taking more information from data than one should or could. Efficiency scores are questioned by some people, they are just relative, they have no meaning as absolute values, so one can not loose sight of the context. The fact that a company is efficient or not  (eficiency score 1 or not) is more widely accepted as something rigorous that you can use than the efficiency scores, so that could be a better alternative if possible. 

Also, if companies lack the power to make the decisions they are evaluated for (in DEA) concerning some variables, for example for political constraints, then DEA analysis with those variables might be an abuse.

Anyway, provided we keep this sort of things in mind and preferably try to check the literature for similar cases, if you plot the values of all the companies for each point in time (to keep the context in sight, because the absolute value can be bad but the relative position good), I guess maybe you can draw your plot.

King regards.

Fernando 

@Fernando. Thank you again for your detailed answers.

Dear Eghbal Rahimikia

Greetings,

I think annual data more effective,

Best Regards

 Dear Eghbal Rahimikia,

Annual data is right choice for DEA Analysis.