Nyu – Leonard N. Stern School of Business Operations in Financial Service – B60. 2315. 030



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Simple DEA Analysis


A small DEA analysis was attempted using output variables of number of checks processed and dollar amount of checks processed and input variables of dollars spent for fee-based services by the Federal Reserve and number of employees employed for fee-based services. Additionally, instead of processing facilities, the DEA compares processes across years. This will measure the relative efficiency of 2004 (the first year that Check 21 instituted the use of substitute checks) against years prior to the enactment of Check 21. The data used for the DEA is derived from Federal Reserve Annual Reports 2001- 2004. Unfortunately, the Federal Reserve only started breaking down expenses and employees by functional group in their 2001 report, so there are a very limited number of data points.9 Further, though substitute check processing was used throughout 2004, Check 21 did not become active until October of the year; therefore, 2004 is more of a hybrid, introductory year. However, despite this characteristic, the results of the DEA do show some distinct efficiency results for 2004.





Outputs




Inputs

Year

Number Checks Processed

Dollar Value of Checks Processed

Expenses - Fee Services

Employees - fee based services

2001

16905

14853072

924769

5436

2002

16587

15033298

931189

5165

2003

15806

15431625

930975

4754

2004

13904

14287740

835239

4381

A simple efficiency frontier can be drawn using Dollar value of checks process versus the Expenses for Fee Base Services:





This graph shows that the efficient frontier for these two variables has been improving since 2003 when electronic presentment through checks started to be used on a large scale. The costs are higher for 2003 than other years, possibly indicating that learning curve and error effects. Further, the Federal Reserve instituted a check processing restructuring initiative in 2003 which reduced the number of Federal Reserve check processing locations from forty-five to thirty-two. However, this may also simply be an effect of the higher number of dollars processed during the year.


A DEA analysis was performed using both input variables and both output variables to find the relative efficiency of the years processes. Due to the small number of points and the relatively high number of degrees of freedom for the number of data points, it is not surprising that each year had an idiosyncratic maximum efficiency linear combinations. Thus, all data points (years) had 100% efficiency under their optimized model. This process was performed using a simple Microsoft Excel maximization program:





Relative Efficiency Using Other Data Points’ Model (Year)

2001

2002

2003

2004

Data Points of

Optimized

Efficiency Model (Year)

2001

1.00

0.997689

0.935347

0.837812

2002

0.974746

1.00

0.965906

0.892470

2003

0.929470

0.990788

1.00

0.995319

2004

0.911214

0.959516

0.954561

1.00



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