Suppose doing DEA for N DMUs，each has S input variables，and the panel data set has T periods（Year_1 - Year_T, in order to assess the efficiency yearly and malmquist index). I plan to do PCA on S inputs to reduce the variable dI mentions before loading to DEA.
As the PCA, there are two options:（1）do the PCA on all T period data all together (W*S matrix ，W=N*T）to get the principal component for all periods （2）do PCA one by one on each year data （each is N*S matrix）to get the principal component.
My question is，which option is applicable for PCA-DEA ?
Are you proposing to do your DEA with single year frontiers or as panel data? Refer to Tulkens and Vanden Eeckaut (1995) in EJOR.
DEA is a single time frontier estimate, therefore I think it is more appropriate using PCA and DEA year by year. Of course you can apply DEA on aggregate data, if you want so, but this can reduce the accuracy of your technical efficiency score, unless your data meets very restrictive structure.
DEA for a single year is suitable for a dynamic analysis which allows capturing the changes over times.
DEA undertaken on a year-by-year basis (i.e single year frontiers) does not allow for measurement of efficiency changes through time.
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