Dea (demerjian 2012 methodology)

[Asmara Rani]

Hello, I need to calculate please firm efficiency using DEA (Data Envelopment Analysis) measure (following Demerjian et al., 2012). In fact, I have a panel data of 350 companies over 11 years (from 2013 to 2022). According to Demerjian et al., (2012), the DEA measure requires companies to be sorted by groups of industry using the classification of Fama and French, (currently, I have already grouped the firms by industry and they are classified from 1 to 48 according to the FF industry classification). According to the authors, to calculate the efficiency score, the companies should be sorted by industry groups, and then for each group, we will calculate the efficiency score for each company using the DEA measure. Actually, I didn't know how to do this in stata, how could I run the DEA command for each group of companies (belonging to the same industry) during the period 2013 to 2022 ? thanks in advance,

[Choonjoo Lee]

Dear Asmara,

Yes, the analysis is feasible in Stata.
Although some time has passed, if you still need help with the implementation, please feel free to ask to me. I can send you the relevant files and explain how to replicate the analysis in the paper using the DEA commands in Stata.

The current `deas` package includes `dea_sw2007`. In Stata 16 or later, the complete package can be installed directly from SourceForge as follows:

net install deas, from("https://svn.code.sf.net/p/deas/code/trunk") all replace
which dea
which dea_sw2007

Regarding Demerjian(2012), there are, however, two different versions of the MA Score methodology that should not be mixed.
The dataset associated with Demerjian, Lev, and McVay (2012) was generated in February 2011 and covers fiscal years 1980 through 2009. In the original paper, the years are pooled and one output-oriented, variable-returns-to-scale DEA frontier is estimated within each Fama-French industry. The paper requires at least 100 observations per industry because the model has seven inputs. Thus, estimating your 350 firms separately in each of 48 industries and each year would generally create very small reference sets and would not reproduce the original measure.

The authors released an updated dataset through fiscal year 2024 on September 2, 2025. Its official description reports two important methodological changes: both stages are now estimated by year rather than by Fama-French industry, and, beginning with the 2022 update, the second stage is estimated by OLS rather than Tobit, following Banker and Park (2021). Therefore, you should decide whether your purpose is a strict replication of the 2012 article or an application of the authors' current method.

For stage 1, the output is sales. The seven inputs are COGS, adjusted SG&A, beginning net PPE, beginning capitalized operating leases, beginning capitalized R&D, beginning goodwill, and beginning other acquired intangibles. The accompanying do-file loops over FF48 industries and saves one firm-year efficiency score in a Stata dataset that can be merged into the second-stage analysis.

The CSV files supplied by the MA-score authors contain already-computed firm-efficiency and managerial-ability scores, not the underlying seven DEA inputs. I converted the 2024 release (247,520 firm-years covering 1980-2024) to a clean Stata panel file, so it can be merged and used immediately for an updated application. A new calculation on your own firms requires the underlying accounting variables listed in the do-file.

There are also distinct choices for stage 2. To reproduce the original Demerjian et al. (2012) score, estimate the industry-specific two-limit Tobit with year fixed effects and define managerial ability as the residual after removing firm size, market share, positive free cash flow, firm age, business-segment concentration, and foreign-currency activity. To follow the current release methodology, estimate the stages by year and use OLS in stage 2.

For substantive inference about variables associated with efficiency, some methodological caution is required. Simar and Wilson (2007) explain why conventional DEA-then-OLS or DEA-then-Tobit inference is generally invalid: estimated DEA scores are bounded and mutually dependent. Their Algorithm 2 uses truncated regression with a double bootstrap designed for valid inference in this setting. I would therefore recommend reading Badunenko and Tauchmann (2019), “Simar and Wilson two-stage efficiency analysis for Stata,” The Stata Journal 19(4): 950-988. Rather than saying this is literally the only possible second-stage technique, the careful claim is that it is the preferred established procedure when the objective is valid inference on environmental or determinant variables. This is conceptually different from constructing the published DLM managerial-ability residual.

Best regards,
Choonjoo