CNRC Code ?0. CNRC Code 22. OP-13. jP-135. OP-135D. OP-91. OP-91D. OP-
913. OP-OB. OP-01B7. ASSTSECNAV MRA. DASN(M). USNA, Nimitz Library.
CRM 87-181 (Revised) / February 1988
RESEARCH MEMORANDUM
CD
RECRUITING EFFICIENCY AND ENLISTMENT OBJECTIVES: AN EMPIRICAL ANALYSIS Timothy W. Cooke
O3TIC ELECTE JUN 131988
A Division of
[,
V.*
Hudson Institute
-
_
CENTER FOR NAVAL ANALYSES 4401 Ford Avenue • Post Office Box 16268 • Alexandria, Virginia 22302-0268
I
"I2'--L•fON -' .•
10.8)
Total
Efficient (STAT = 0)
27
25
4
56
Low (STAT < 4.8)
14
10
17
41
High (STAT > 4.8)
15
8
44
67
Total
56
43
65
164
Contingency coefficient
e.464
X2 statistic = 44.
88a
a. The nuil hypothesis is that the contingency coefficient is zero. The x test statistic is used. It is compited as 2 SX
r Zi
k z
2
(Oo - Ei i
,
where 0. and Elg are, respectiiely, the observed and expected 1 number ofJobserva z ns in the ith row and Jth column, r is number of rows, and k the number of columns. Under the null hypothesis the expected frequencies for each cell is computed as the product of the two common marginal totals divided by the 2umber of observations. The null hypothesis is rejected if observed x is larger than expected for a given significance level.
-30-
II-|
remaining 65 observations with high inefficiency. (statistical) classification also has
The alternative
56 efficient observations,
although they are not the same ones. Of the 56 observations gauged ef'ficient with the DEft approach, 27 are also gauged efficient with the
statistical approach. Of the remaining 29 efficient in the DEft approach, 1A4 were classified with a low level ot Inefficiency In the statistical approach. For the 67 observations with high levels of inefficiency based on the statistical measure, 15 are labeled efficient with DEft, 414 of the 65 are Classified as having a high level of ir~efficiency with both approaches. In 19 of the 1614 cases (12 percent), the two methods disagree significantly with efficient performance by one
measure being labeled highly inefficient by the othier. Wh~en the DEft method classifies a district's performance as (highly) inefficient, it is unlikely that the statistical approach will find the district effi-
cient. This is not true to the same degree whei the statistical approach identifies a district as (highly) inefficient. The contingency coefficient given in table 8 is One measure of association between the two efficiency criteria of the table. The
coefficient is positive and significant. This suggests that the classifications based on the two measures are not independent and provides further evidence of the similarity In the way the two approaches gauge efficiency for the sample. CONSISTENCY OF CONTRACT OBJECTIVES With information on district goals or contract objectives, the DEA approach can be used to provide additional information to planners. By
comparing the contract objectives of similar districts, the consistency of the allocation of objectives across districts can be assessed. Typically, recruiting performance is evaluated on the basis Of goal attainment. Combining the relative measures of technical efficiency with observations of goal attainment provides additional information for more efficient allocation of contract objectives and resources across districts. This section and the next analyze three measures of perforrance. The Table 9 lists these measures for each district and fiscal year. first measure, labeled TE, is the DEA measure of technical efficiency. This measure is similar to the DEA measures discussed in the previous section in that the same output (total A- and CU-cell contracts) and set
?
1. This may be due to the "global" nature of the statistical measure, ~and the "local" nature of the flEA measure. DEA compares only similar districts; the statistical approach extrapolates across districts. 2. Data an contract objectives in 1981 were not available, and, therefore, 1981 is excluded from this analysis. Furthermore, since the data are not pooled across years, analysis of 1983 recruiting is included. -31-
T AB9LE TECHNICAL
~rPICENcy
(TE). COAL EFFICIENCY (CE). ANDOCOAL ATTAWNMET (CO'4AL)
1982 TE GE
*
1983
1984
RESULTS 1985
GOAL
TE
GE
COAL
TE
GE
GOAL
TE
GE
MOAL, s P
lei 102 103 104 119 161
6.6 96. 15.6 13.? 17 0 11.2
1.1 0.9 6.2 9.6 19.5 22.6
AT AT 60 AT AT AT
19.4 0.0 2.5 .3.6 2.2 8.1
6.6 0.0 6.8 1.6 9.5 11.2
AT AT AT AT AT AT
6.7 9.6 9.1 14.1 0.0 10.0
9.1 6.6 3.5 9.5 6.3 5.4
90 80 80 AT AT AT
10's 690 20.6 21.5 Is67 .34.4
4.3 9.9
4.4 9,f 6.4
K O G
.310 311 312
15.6 0.0 g.e 6.6 40.3 15'.46,16. 19.4 6.6
16.2 0.9 31.7 6.6 19.5
.0 9.0 6.0 0.6 ZA.4 t.0 9.0 9.0
1.3 9.0 0.0 9.9 16,5 6.0 0.9 06ý
AT AT AT AT AT AT 80 AT
0.0 0.6 O's 0.0 22.4 0.9 0.0 28.2
1.1 6.9 0.6 R.6 11.6 .0 6.0 9.2
AT AT AT BG 80 0.6 B 90 AT
0.6 0.0 6.9 0.a 24.1
14.6 6.6
AT AT AT AT AT AT AT AT
0. 0.0
1.!s 960 0.9 9.0 12.7 0.6 9.6 0.9
AT Fr AT AT AT BG go BC
36.5 6.4 .3.7 10.5 297 0.0
AT AT AT AT AT AT
19.3 0.0 0.0 9.7 3.0 6.6
24.0 0.0 16.5 14.6 21.4 0.0
AT AT AT AT AT AT
3.2 0.0 0.0 5.4 0.0 6.0
80G AT AT AT AT AT AT AT
9.9 6.6 6.0 6.1 6.2 9.0 6.0 0.0
0.0 3.9 6.6 5.3 10.2 6.6 6.8 9,9
AT AT AT AT AT AT AT AT
0.0 960 6.0 3.1 12.2 0,0 0.0 6.6
.31.
314 3116 348
466 409 417 418 4210 420.9 521 '424
6 4 9.6 o.0 16.3 21.1
0.0
00
0.'1 6.9 .0. 3. 0 2.6 6.6
AT 90 AT 80 AT 90
8.2 0.0 9.9 9.2 0.0 O.0
90. 6.0 6.9 960 26 6.6
GG K. 80 W 8M 80
0.6 3.2 9.6 G.6 7.3 6.6 6.6 6.6
ect AT 80 9o AT AT AT 9C
0.6 0.0 6.0 0.6 6. 0. 2.2 6l6
09. 9.6 0.0 .0. .6 .6 6. 3.6
80 AT 80 BC AT 9 8 AT
6.6 6.0 a,0
AT AT B0
6.0 6.6 90.
6.6 6.6 6.6
AT AT AT
5219 547 559
691 6.6 6.6
6.6 2.2 6.9 5.4 279 6.6 6.6 6.6
7310 7,11
6d, .0 00 6.6
6.6 669 6.0
AT AT AT
6.0 6.0 0.9
-0.0 0.6 6.6
AT AT AT
732 7331 734 '14f
6.6 06 445%7 0.6 9.9
08 .6 9.3 6 6 6.6
AT AT AT AT AT
9.7 8.9 16.4 6.9 6.0
11.3 0.6 6.3 6.6 6.0
AT AT AT AT AT
2.6 12.4 7.9 906 6.6
9.6 3.9 6.5 6.6 6.0
AT 9G 00G AT AT
6.6 164 8.9 6.6 6.6
6.6 6.6 6.6 9.6 6.6
00G 90 AT AT AT
.6
16.6 0.0 6.6 4.9 8 29.7
6. P 6 0 6.6 3.2 13.9
AT AT AT AT AT
11.6 0,9 6.6 6.3 8.4
6.6 6.6 6.8 6.6 e.g
AT AT AT AT AT
89.7 6.0 6.6 6.6 6.6
1.9 6.6 6.6 0.6 6.6
BC AT 80 AT AT
6.6 6.6 6.6 6.6 6.6
2.2 6.6 6.6 6.0 3.2
AT AT AT AT AT
.0, 3. R 529.6 520.0 563.8
747
*
2
837
8.3A R84
-32-
0.0 .0. 6.6
of inputs is specified. There is, however, one Important difference between the measures. The TE measures discussed in this section are computed for each year separately. The DRA measures In the previous section were computed for the pooled (by year) sample. Thus, the efficiency of a district was gauged relative to all other districts operating in the same year and in other years as well as to itself operating in a different year. The TE measures In table 9 gauge the performance of a district relative to only the performance or other, districts operating in that same year. The second performance measure listed in table 9, labeled GE, Is a DEA measure or goal efficiency. This measure differs from the TE measure in that the output specified is the active-duty contract objective. Thus, GE is the ratio of the maximum potential contract objective to the actual contract objective. The maximum potential contract objective is determined by the contract objectives of other similar districts. The third variable in table 9, labeled COAL, is a binary variable that compares actual production to the goal. If the district attained or exceeded the contract objective, then GOAL a AT. Otherwise, GOAL a BG. The contract objectives and recruiting resources (e.g., number of recruiters) are allocated among areas based on past production levels and the estimated relationship between past production levels, the level of resources, and indicators of the economic and demographic conditions. The net result should be that two districts operating in similar recruiting markets with the same number and type of recruiters should have similar contract objectives. Consistency of objectives depends on the appropriate appraisal of the recruiting environment. The ability to predict changes in the environment due to business cycle swings is also required. The goal efficiency measures (GE) in table 9 are used to examine the consistency of the allocation or the contract objectives across districts. The measure gauges a district's actual contract objective relative to the maximum potential contract objective determined by the other districts in that year. If the measure is 0.0, the district's objective is consistent in that It is at least as large as other similar districts' objectives. On the other hand, if the measure is greater than 0.0, the contract objective is low relative to the contract objectives of other districts operating in a similar recruiting environment with similar resources. Note that a value of 0.0 of the GE measure does not necessarily mean that the district's contract objective was set efficiently, only that relative to the other similar districts, that district's objective was the maximum objective specified. If each district's contract objective is determined solely by the characteristics of the recruiting environment included in the analysis, then the GE measure should be zero for all districts. An ordinary least squares regression of contract objectives on the five
-33-
-__ ......
characteristics of the environment for each fiscal year explained a minimum of 93 percent of the variation in the contract objectives. The .. fact that the variables used to compute GEeplainjnuofO-the-cross .... section variation in contract objectives suggests that the characterization-of the recruiting -environment -used- to-compute the -GE ie-as-ures-it
....
similar to that used to set contract objectives.
Tables 10 and 11 summarize the GE measures given in table 9. Table 10 gives the number of inefficient observations by fiscal year and, area. The most apparent change is the decrease in the number of districts whose goals were gauged inefficient between 1982 and 1985. In 1982, over half of the districts (22) had contract objectives that were low relative to similar districts operating that 'year. Three years later, most districts' contract objectives were "in line" with other similar districts; only 9 districts had lower goals relative to other districts in that year. In-each year, districts with inefficient goals were found within each area, although area 7 has the smallest proportion overall. Area 1 has the largest incidence of inconsistent (low) objec-
tives. TABLE 10 NUMBER OF OBSERVATIONS WITH INEFFICIENT CONTRACT OBJECTIVES BY YEAR AND AREA Area (number of obs.)
1982
1983
1984
1985
1
5
5
5
4
5
2
3
2
4 (6)
5
4
3
1
5
3
4
2
0
1
2
3
0
3
0
1
2
22
17
17
9
(6) 3 (8)
(8) 7
(8) 8
(5) Total
-34-
A __
-1
TABLE 11 DISTRICT ACTUAL AND EFFICIENT CONTRACT OBJECTIVES BY -YEAR ....... (Where Different)
1982
1983
1984
1985
District
Actual
Efficient
Actual
Efficient
101
2,809
2,857
2,226
103 104 119 161
2,988 3,678 2,896 2,596
3,173 4,031 3,461 3,183
2,312 3,003 2,246 2,100
310
1,951
2,267
1,759
312
2,081
2,741
314
2,124
2,538
315 316 348
2,471 1,878
2,590 2,141
406
2,184
2,981
409 417
2,963 2,662
3,153 2,760
1,849
2,154
418 420
2,858 2,245
3,158 2,912
2,219 1,657
2,543 2,012
2,261 1,843
2,329 1,891
524
2,255
2,305
1,883
1,956
1,697
1,751
527
1,984
2,091
1,538
1,620
528
2,050
2,622
1,872
2,063
1,610
1,719
1,560
1,736
--
542
--
732 733
--
--
.... --
734
1,954
2,136
836
3,646
3,668
839 840
2,576 3,368
2,658 3,836
2,555
2,875
Average [Average difference] No.
--
[320]
inefficient
Average TE
Actual
Efficient
Actual
Efficient
2,411
1,951
2,129
2, 132
2,224
2,465 3,051 2,459 2,335
2,352 2,678 2,023 1,893
2,434 2,932 2,150 1,995
2,996 2,138 2,066
3,128 2,348 2,198
1,782
1,680
1,698
1,711
1,737
--
--
1,707
1,989 --
--
--
--
1,569
1,742 ---.
--
......---
--
1,722
2,135 --
--
--
--
1,771
1,766 --
--
--
--
1,943
2,129 £187]
22
--
....
1,905
1,907
....
--
--
--
--...
.... 2,049
--
--
1,967
1,833
....
--...
--
1,344 1,586
1,473 1,648
.... ....
1,430
1,552
--
2,962
3,018
--
1,907
--
3,155
3,224
--
--.--
--
2,851
2,942
2,315
2,429
2,009
--
[114] 9
5.6
''
2,106
--...
--
5.3
-35-
..fw-n ltM nwat~t SSflm .t
---
..
-
17
10.0
1,953
--
1,536
4
--
1,733
1,407
-A
_
--
[102]
17
13.4
-
--
.
For the districts classified as having inefficient contract objec-. tives, table 11 lists the actual ob ective and the efficient or maximum objective determined by the method. Also included are the average of these variables and the average of their difference (maximum-contract objective minus actual contract objective). In 1982, the average difference is about 320 contracts. In 1985, when contract objectives were set more consistently across districts, the difference between the maximum and actual objectives for the 9 inefficient districts is, on average, 120 contracts.
1. Recall that the GE measure is one minus the ratio of the maximum objective to actual objective. -36-
--
EVALUATING OBJECTIVES
Despite the fact that efficient contract objectives are imperfectly known and goals are sometimes inconsistently set across districts, the achievement of contract objectives plays an important role in evaluating district performance. The ability to attain the contract objective depends on whether contract objectives Fire consistent with resources allocated to a district and recruiting conditions. A consistent allocation of contract objectives is obtained only if the market conditions facing each district are correctly evaluated. Districts not achieving their contract objective may nevertheless be as productive as similar districts that achieved their goal. Conversely, some districts that achieve their contract objectives may not
be as productive as similar districts that did not.
Using this informa-I
tion on the relation between performance and goal attainment may be valuable in allocating changes in district objectives. IF
To illustrate the use of comparing the two performance measures, the observations are divided into four groups based on goal performance and the technical efficiency measure. Table 12 gives the number of districts classified into each of four groups by year. In 1985, there are 2 districts with production above goal, but less production than other similar districts. They would have been candidates for goal increases. On the other hand, 1~4 districts were as productive as similar districts, but did not achieve goal. Their failure to meet goal is not associated with differences in productivity between them and those efficient districts that attained goal. The nine districts that were as productive and did not achieve their objectives deserve closer scrutiny.
-37-
TABLE 12 COMPARISON OF GOAL PERFORMANCE AND TECH~NICAL EFFICIENCY Number efficient
*Below
Number inefficient
Average inefficiency
1982 Attained goal (39) Below goal (2)
24 1
15 1
6.5 7.8
1983 Attained goal (40)
23
17
3.7
Below goal (1) 1984 Attained goal (22) goal (19)
1
0
0.0
16 11
6 8
3.2 4.1
1985 Attained goal (18) Below goal (23)
16 14l
2
1.8
9
5.8
-38-
I
CONCLUSIONS b
This research has examined the relative performance of different recruiting districts and the consistency of recruiting objectives during fiscal years 1981 through 1985. The results can be summarized as follow$: * The consistency of enlistment contract goals assigned to districts improved remarkably between FY '1982 and FY 1985. The number of districts with goals lower than similar districts (as defined by economic and demographic characteristics of the districts) fell by nearly 60 per-A cent. The average amount by which goals were lower fell by 64 percent. The only significant inconsistency is that area 1 districts are more likely to have lower goals than similar districts in other areas. This may reflect a relative difficulty of recruiting in the Northeast that is not captured in this analysis. 9 The improvement in consistency of goaling over this period is reflected in more similar performance among similar districts. Fiscal years 1984 and 1985 show an improvement in average technical efficiency of about 5 percentage points relative to 1981 and 1982. This may be associated in part with a desired shift in the qualityI composition of enlistment contracts between 1982 and 1984. * Districts in area 1 have been less effective in producing A- and CU-cell recruits than similar districts in other areas. * A cross-classification of districts by technical efficiency and goal attainment can be used to identify where goals should be redistributed, if necessary. Those districts achieving their objectives but not producing as many enlistments as similar districts should be considered for larger goals. On the other hand, districts performing as well as other similar districts but not achieving their objectives are candidates for smaller goals. Districts that are neither performing as well as other districts nor ach ieving their objectives deserve special attention. * Two different approaches to the measurement of Navy Recruiting District production potential, DEA and statistical, produced measurements that generally agree on the ranking of districts with respect to technically efficient production of A- and CU-cell enlistment contracts. .. 39-
When the DEA procedure classifies a district as (highly) inefficient, it is likely that the statistical approach will find a qualitatively similar result; however, when the statistical method identifies a district as technically inefficient, it is less likely that the DEA approach will concur. All analykis in this paper is based on a particular characterization of the recruiting environment. A number of potentially important factors have been omitted, including advertising and interservice competition, among others. Other research along these lines would examine the allocative efficiency of the recruit mix produced by different districts. Such analysis is complicated by the necessity to assign relative values to recruit types. Nevertheless, allocative efficiency may be more important than technical efficiency.
-40-
. 2
REFERENCES [1]
A. Charnes, W.W. Cooper, and R. Rhodes. "Measuring the Efficiency of Decision Making Units." European Journal of Operational Research vol. 2, no. 6, (1978): pp. 429-444
[2)
R. Fare, S. Grosskopf, and C.A. K. Lovell. The measurement of Efficiency of Production. Boston: Kluwer-Nijhof Publishing, Kluwer Academic Publishers, 1985
[3]
The University of Massachusetts, Department of Industrial Engineering and Operations Research, A Bibliography of Data Envelopment Analysis (1978-1986), mimeograph, by Lawrence M.
Seiford, Jan 1987 [4]
Dennis J. Aigner and Peter Schmidt, eds. "Specification and Estimation of Frontier Production, Profit and Cost Functions." Journal of Econometrics v. 13(1), (1980): pp. 1-138
[51
CNA Research Memorandum 86-110, Econometric Time Series Analysis of Navy Recruiting: 1977-1985, by Timothy W. Cooke, May 1986 (27860110)
[6]
CNA Study 1168, Enlisted Supply: Past, Present, and Future, by Lawrence Goldberg, Sep 1982 (07116801)
[71
CNA Study 1073, Recruiters, Quotas and the Number of Enlistments, by Christopher Jehn and William F. Shughart, USN, Dec 1976 (07107300)
[8)
United States Military Academy, Working Paper, Recruiting Goals, Enlistment Supply, and Enlistments in the U.S. Army, by Thomas V. Daula and D. Alton Smith, Dec 1984
£91
The RAND Cor-ration, R-3065-MIL, Recruiter Incentives and Enlistment Suppl"
)y J.N. Dertouzos, May 1985
[10]
CNA Report 121, Educational Quality Requirements for Marine Corps Enlisted Personnel, by Laurie J. May, Jul 1986
£111
U.S.
Army Research Institute for the Behavioral and Social WP 86-18, setting Battalion Recruiting Missions, by A. Nelson, C.E. Phillips, and E.J. Schmitz, Apr 1986
Sciences, MPPRG,
1. The number in parentheses is a CNA internal control number. -41-
[12] Arie Y. Lewin and Richard C. Morey. "Measuring the Relative Efficiency and Output Potential of Public Sector Organizations: An Application of' Data Envelopment Analysis." Journal of Policy and znformation systems 5(4) (1981): pp. 217-285 (13] Nancy M. Ostrove et al. youth Attitude Tradking Studyz Arlington, VA: Defense Manpower Data Center, Jun 1987
Pall 1986,
[14] The RiMJD Corporation, R-3353-FMP, The Enlistment Bonus Experiment, by J. Michael Polich, James N. Dertouzos, and S. James Press, Apr 1986
(151 CNA Research Memorandum 87-58, Indicators of Navy Recruiting Success, by Timothy W. Cooke and Robert F. Lookman,
May 1987
(16] CNA Research Memorandum 86-269, Indiviual Incentives In Navy-i Recruiting, by Timothy W. Cooke, Dec 1986 (17] D.J. Aigner, K. Lovell, and P. Schmidt. "Formulation and Estimation of Stochastic Frontier Production Functions Models." Journal of Econometrics 5(1): pp. 21-38 [18] James Jondrow et al. "On the Estimation of Technical Inefficiency in the Stochastic Frontier Production Function Model." Journal of Econometrics 19(2): pp. 233-238 (191 W.H. Greene.
LIZDEP Manual, mimeograph,
-42-
1986
-
-.
- -.
-
-
- -
-
-
-
0
J
APPENDIX A THE RECRUITING DATA SET
0'
N'
S
b
,
.-
.'.
S
0 if I.
S
I '... I
r.
A
.
9
APPENDIX A RECRUITING DATA SET This appendix contains the recruiting data set used. Tables A-1 through A-5 list all variables described in table 1 of~ the text by district and year (one table for each year 1981 through 1985). The variables are measured in the Units specified in the text. Note that data on contract goals for FY 1981 were not available, and the GOAL variable is set to aero for that year.
A-1
TABLE A-1 1981 RECRUITING DATA SET
DISTRICT ACCON 101
99
POP
UR
130730 i
URBPCT
.4
a7.9
PAY 110.9a 104.91
ATTN
GOAL
2698
00
127.14 111.29
4112 3150 3664
100.0 99.0
114.3a 109.64
2808 2763
0 0
9.4 7.8 5.8 6.1 9.0 6.4 6.2 7.0
67.3 83.2 82.3 68.5 87.3 54.1 69.8 92.3
115.43 119.82 137.00 120.74 118.90 125.86 123.30 123.30
2047 1771 2609 2233 2140 2887 1864 2926 8
0 0 0 0 0 0 0
95039 122708 121630 136218 107
8.3 6.4 9.4 87 a.6
79.4 88.1 82.5 6. 74.7
122.5a 111.74 99.4a 105.71 1.922
1957 3128 2805 2850
0 0 0 02
151
212367
12.2
83.3
95.90
4597
0
528 529 542 559
1427 1034 858 527 957 1271 1049 735
145 82 65 815 68 91 98 a2 62
203232 106395 93096 99729 151986 140208 92236 110485
8.4 8.6 9.0 5.6 5.8 5.8 9.5 7.7
92.0 58.2 45.8 58.7 60.3 42.2 63.5 68.6
92.94 102.24 107.55 116.64 108.37 107.55 100.19 97.44
2712 2195 1945 1840 1812 2135 1967 1633
0 0 0 0 0 0 0 0
725 730 731 732 733 734 746 747
762 683 661 678 774 714 508 758
71 60 68 65 68 71 63 67
90242 65835 98978 89490 102120 88943 64487 66408
5.3 6.2 4.9 4.7 5.5 8.0 6.6 8.6
68.9 56.1 81.3 86.5 53.3 69.7 80.5 31.2
93.04 110.52 94.88 97.84 107.35 102.55 102.24 124.32
1820 1629 1794 1769 1575 1675 1313 1644
0 0 0 0 0 0 0 0
1424
157
220985
6.3
98.1
101.04
3785
0
200242 120548 192504
6.1 7.8 7.6
a4.7 78.7 100.0
103 98
129011 137682
7.3 7.2
937 786 1475 A12 946 1281 623 692
75 60 119 81 79 V 62 2
73873 60774 110717 71923 93307 107254 67148 685703
406 409 417 418
1021 1419 1522 1563 18
67 91 95 101 7
422
2368
521 524 526
102 103 104
2054 1439 1571
155 104 136
119 161
1292 130a
310 311 312 313 314 315 316 348
836
a37 838 839 840
SThe
1444
RTR
1076 1820 1209 1342
94 183 91 119
127126 246403 123070 159766
8.1 7.4 8.5 6.9
61.4 91.6 70.3 88.8
99.73 99.32 98.82 109-79
2559 5570 2746 3755
0 0
0 0 0 0
contract goal data for FY81 were not available and
the value of GOAL is
zero for all distriots in that year.
A-2
TABLE A-2 1982 RECRUITING DATA SET PAY
ATTN
GOAL
87.8 84.6 76.6 100.0 100.0 99.0
117.55 111.12 134.67 117.88 121.15 116.13
2858 4352 2954 3974 2970 2666
2809 4131 2988 3678 2896 2596
12.3 9.5 7.2 7.3 11.3 8.4 7.8 8.3
67.4 63.3 82.3 68.7 57.3 54.2 69.9 92.2
122.35 126.68 145.21 127.98 126.03 133.40 130.69 130.69
2156 2124 2237 2547 2199 2899 2012 3229
1951 1908 2081 2254 2124 2471 1878 2818
93312 120527 118421 133425 107219 207353
10.1 7.7 12.2 11.1 12.0 14.5
79.4 88.0 82.3 74.6 68.8 83.1
131.29 119.69 106.56 113.23 122.64 102.73
2549 3006 3108 3056 2424 5105
2184 2963 2662 2858 2245 4660
120 76 61 68 77 85 77 61
198299 104283 91555 98007 149895 137470 90205 108540
10.3 9.8 10.7 6.9 7.3 7.3 11.0 10.1
92.0 58.1 45.7 58.6 60.4 42.3 63.5 68.5
99.56 109.51 115.20 124.94 116.08 115.20 107.33 104.37
3326 2473 1858 2036 2165 2778 2479 1895
3373 2255 1847 1984 2050 2706 2160 1742
860 827 767 805 870 ?49 666 1004
66 59 70 63 71 67 65 69
90520 65702 98438 89694 101323 87957 63405 65044
6.7 7.2 5.6 6.2 6.2 9.1 7.3 10.7
69.1 56.4 81.3 86.7 53.3 69.9 80.5 31.4
98.62 117.15 100.57 103.71 113.79 108.69 108.37 131.78
1885 1693 1824 1737 1940 1955 1640 1965
1771 1629 1719 1644 1806 1954 1558 1734
1561 1352 2161 1388 1503
126 92 153 89 116
217731 126627 245169 122049 160866
8.0 9.8 9.8 10.8 9.6
98.1 P1.4 91.5 70.4 88.7
104.80 103.45 103.03 102.51 113.88
3692 2917 5223 2917 365,1
3646 2736 4787 2576 3368
UR
DISTRICT ACCON
RTR
POP
101 102 103 104 119 161
1495 2096 1492 1776 1447 1351
102 151 100 140 95 88
128046 196209 117654 186740 125624 134106
7.0 7.8 8.9 8.0 8.7 8.1
310 311 312 313 314 315 316 348
1043 1009 1687 1196 993 1590 811 798
77 63 118 83 75 90 66 52
72964 59945 110802 71092 92370 105977 66174 65898
406 409 417 418 420 422
1378 1627 1895 1664 1281 2645
77 97 85 90 77 149
521 524 526 527 528 529 542 559
1494 1245 900 1021 1157 1328 1383 959
725 730 731 732 733 734 746 7-17 836 837 838 839 840
URBPCT
t-3
I•r!f
A1vu f.
•-.&
M•
IW, A °AI
o-
u Am•• a
•
MIN.-. W,.
w,.
•Nuam
-.
,ra
..-,•-
-
.
-..
-,
.A.
..
...
.
..
..
..
..
TABLE A-3 1983 RECRUITING DATA SIT
I
I•
____A-
ATTN
GOAL
118.81 109.47 132.87 116.13 119.38 114.41
2322 3401 2424 3237 2389 2187
2220
67.4 63.5 82.4 66.9 57.4 54.3 70.0 92.0
120.73 125.00 143.29 126.29 124.36 131.83 128.96 128.96
1815 1708 2678 1872 1736 2*34 1516 1854
1759 1638 2522 1838 1707 2177 1531 1815
11.6 7.1 13.8 11.9 16.2 15.1
79.5 87.9 82.3 74.6 68.6 83.0
129.83 118.36 108.38 111.98 121.28 101.59
1914 2437 2068 2357 1750 3743
1722 2360 1849 2219 1657 3652
193186 101735 89346 95815 147198 133920 87737 106116
11.8 11.9 13.9 8.1 8.6 8.0 11.4 11.5
92.0 58.0 45.6 58.7 60.5 42.5 63.6 68.5
98.46 108.30 113.93 123.56 114.79 113.93 106.14 103.22
3083 2012 1364 1568 1961 1829 1686 1605
2997 1883 1316 1538 1872 1762 1610 1591
69 62 68 70 83 75 66 66
90191 65245 98241 90324 99952 86267 62757 63003
7.2 8.9 5.9 9.9 9.5 11.9 9.1 12.4
69.1 56.6 81.4 86.8 53.5 70.0 80.6 31.6
97.31 115.59 99.23 102.33 112.28 107.25 106.93 130.03
1696 1468 1620 1685 1918 1818 1258 1583
1635 1440 1612 1560 1835 1766 1211 1508
1809 1544
131 92
213627 124907
9.5 10.7
98.0 61.4
103.07 101.73
3336 2276
3303 2199
2310 1520 1797
157 95 108
242555 120331 160734
10.5 11.1 10.7
91.5 70.6 88.7
101.32 100.81 112.00
3985 2429 2948
3694 2258 2818
DISTRICT ACCON
RTR
POP
UR
URBPCT
101 102 103 104 119 161
1460 2075 1724 1924 1632 1414
99 152 103 127 95 89
124990 191191 114852 180149 121712 130241
7.1 7.4 10.8 8.5 8.9 8.2
87.8 84.6 76.5 100.0 100.0 99.0
310 311 312 313 314 315 316 348
1262 1079 1767 1165 1123 1600 838 908
86 68 122 84 79 89 68 55
71611 58576 110184 69629 90592 104305 64658 65464
13.8 10.3 8.4 7.6 12.7 9.6 6.8 9.5
406 409 417 418 420 422
1303 1605 1655 1700 1363 2850
81 95 85 101 76 152
91153 117997 114658 129969 103920 201120
521 524 526 527 528 529 542 559
1925 1482 953 1018 1384 1307 1232 1151
138 84 64 70 87 83 72 64
725 730 731 732 733 734 746 747
1090 942 975 1063 1174 1057 760 1029
836 837 838 839 840
PAY
3301 2312 3003 2246 2100
TABLE A-4 1984 RECRUITING DATA SET DISTRICT ACCON 101 102 103
1214 1638 1421
RTR 87 124
POP.
UR
URBPCT
PAY
ATTN
GOA..
5.4 5.3 7.9
87.7 84.5 7,.2
-104 572
100 110
121869 186460 111220
114.89 108.60 131.62
173260
1888 1981 2745 2797 22-19 -- 2352
7.4
100.0
119 161
1395 1155
i11521
.83 79
118202 126156
2683
7-.2 6.2
100--..0 99.0
. 118.40 113.50
310 311 312
1138 1011 1648
77 68 112
313 314 315
69770 57488 109523
10.5 7.2 6.3
925 950 1312
72 71 88
67.8 63.8 82.3
68144 88301 102047
118.62 122.82 140.79
682 755
65 65
69.2 57.5 64.7
1680 1575 2462
316 348
6.0 9.3 6.9
1726 1594 2556
63734 64317
124.09 122.19 129.34
5.3 7.2
1677 1564 1992
70.8 91.8
1712 15692038
126.71 126.71
1295 1477
1534 1407
406 409
1248 1315
417
77 85
1434
88889 115488
76
79.5 87.9
126053 100575
104.46
1905 2111
90 75
82.3
1965 2064
1437 1360
10.3
128.70 117.33
418 420
110540
9.0 5.4 9.3 12.7
2074
2150
111.01 120.23
1934
422
74.6 68.4
145
194550
2137 1899
2261 1843
11.5
82.9
100.71
3278
3772
521
1649
129
187192
9.0
92.0
97.60
2753
3136
524 526 527 528 529 542 559
1136 894 852 1175 1093 992 906
71 64 62 80 67 61 56
99013 86885 93525 143650 130356 85315 103156
9.4 10.9 6.0 6.6 6.2 8.1 7.9
57.7 45.4 58.4 60.5 42.6 63.8 68.3
107.36 112.94 122.48 113.7P 112.64 105.21 102.32
1733 1483 1298 1852 1562 1506 1421
1697 1558 1387 1833 1502 1505 1451
725
836
730 731 732
62
89386
740 738 947
55 56 66
5.7
64377 97360 89349
69.6
95.61
76
113.58 97.50 100.55
1307
963
56.8 81.4 86.5
1352
733 -
7.0 4.3 7.7
943
7.7
1080 1123 1344
734
98414
1107 1040 1408
74
53.7
84422
110.32
1570
668 909
69.9
1586
746 747
9.9
57 65
62187 60968
105.38
7.6 9.9
1419
1430
80.7 31.7
105.07 127.76
1086 1501
1086 1450
836
1617
122
837
208158
1271
7.2
76
122812
97.9
102.94
8.4
2702
61.4
2962
101.61
1960
838 839 840
2089 1489 1758
145 92 106
238108 118641 159876
8.5 9.0 7.2
A-5
91.4 70.5 88.7
101.20 100.68 111.86
2678
2045&-.. 2023-.... 1914 1893
3411 2173 2868
1939
3678 2130 2844
-
..
TABLE A-5 1985 RECRUITING DATA SET DISTRICT ACCON
RTR
101 102 103 104 119 161
1096 1455 1.3221504 1210 932
88 118 -100 124 91 86
121018 184460 110106 168700 116868 123856
5.0 4.3 7.0 6.8 6.1 5.4
87.5 84.3 75.8-100.0 100.0 98.9
310 .311 312 313 314 315 316 348
1169 904 1796 662 979 1345 709 678
82 71 119, 77 75 90 66 62
67953 57603 109889 67410 .86133 100110 64913 62547
9.4 6.6 5.8 6.0 8.6 5.9 5.4 6.8
68.2 118.91 64.2 123.12 82.1 141.13 69.4 124.39 .. 57.5 -122.49 .5,2 129.65 71.7 127.02 91.5 127.02
406 409 417 418 420 422
1180 1185 1482 1390 1350 1848
81 86 82 91 78 140
87639 114471 107234 123044 98056 187817
7.9 4.8 9.4 8.3 10.9 10.3
79.4 87.9 82.3 74.5 68.2 82.8
521 524 526 527 528
1637 1264 906 873 1351
133 85 63 59 80
18.1772 97049 84566 92227 140802
8.6 8.8 10.1 5.4 6.0
128476
6.8
ý542 559
935 989
66 64
83747 100423
725 730 731 732 733 734 746 747
909 817 756 894 1042 961 690 1038
67' 61 64 63 79 71 58 70
836 837 838 839 840
1942 1327 1933 1504 1746
529
1180
72
139 83 164 92 114
POP
UR
URBPCT
PAY
ATTN
GOAL ..
114.02 107.78 130 ,63114.34 117.51 112.65
17M2 2409 2012544 1756 1566
2132 2982 . -2-565--2996 2138 2066
1791 1565 2884 1730 1741 2186 1411 1571
1711 1605 2864-... 1692 1733 2261 1565 1736
129.24 117.82 104.90 111.47 120.73 101.13
1700 1962 2199 2134 1953 2864
2188 2172 2284 2440 2049 3646
92.0 57.3 45.2 58.1 60.6
98.01 107.81 113.41 122.99 114.27
2727 2044 1519 1428 2083
3005 2022 1630 1509 2076
7.7 7.2
64,.1 68.2
105.65 102.75
1466 1628
1748 1602
89085 64087 97311 87568 97880 83305 62967 59640
5.7 7.3 4.8 8.0 7.4 10.6 7.8 9.6
70.2 57.1 81.5 86.1 53.9 69.8 80.8 31.8
95.84 113.85 97.74 100.79 110.59 105.64 105.32 128.07
1563 1320 1424 1484 1770 1790 1269 1696
1560 1282 1375 1506 1876 1762 1253 1687
203907 119835 234676 116966 159147
6.4 8.2 7.8 8.4 6.7
97.9 61.4 91.3 70.4 88.6
102.55 101.22 100.81 100.30 111.44
3210 2160 3738 2353 2852
3155 2153 3713 2332 2851
A-6
42.7
113.41
1709
1855
.
-
--
-
-
.-
wnwrnw.
-.
.
..
,
wn
1.,
7 an rn
r
an Err WrS
-. -.-
-.
-
0
.4
-
APPENDIX B DEA LINEAR PROGRAMMING PROBLEMS
*
77.
*1 I
4
"I
I Ii
S
S \ * 14
*
I
S p
.'
A4
APPENDIX B DEA LINEAR PROGRAMMING PROBLEMS This appendix provides a further description of the DEA approach to the measurement of productive efficiency. The piecewise linear reference technology specification and linear programming problem are included. The piecewise linear reference technology or frontier is constructed from the observed inputs and output of the recruiting districts in the sample. We assume that there are n inputs, denoted by x = (xl, x2, ... , xn), one output, denoted by y, 1 and1 k observations (or recruiting districts) of x and y, i.e., (x , y ), i = 1, ... , k.1 Denote the matrix of observed inputs by X, where X is of dimension (k, n), k observations and n inputs. Denote the k dimensional vector of observed outputs by Y. The construction of the piecewise linear techrology requires the following restrictions: (i)
(ii)
(iii)
yi > O, i
k Z i=1
1, ... , k, i.e., a positive output is produced by each activity (recruiting district)
> 0, j = 1,
n,
..
J
n = x >O, i = 1,
k,
i.e., each input is utilized by at least one activity i.e., each activity uses at least one input.
Finally, let z = [l1, ... , zk] be a (1 x k) row vector representing the intensity (or activity) parameters for each of the k observations. Following Fare, Grosskopf, and Lovell [2], the technology formed by the data (X and Y) can be written as: T =
y): z . Y = y >
.
X
=
k
zi = 1}
(B-1)
i=1
1. For this application, x would consist of the inputs and environmental variables given on the right-hand side of equation 1. The output y is ACCON, the total A- and CU-cell contracts. B-1
A
Computation of the degree of efficiency relative to the frontier is accomplished via linear programming (LP) techniques. The measu e og technical efficiency relative to T for a given observation (x6, y ) is defined as: DEA 0 = max to: (xO, 0y
0
(B-2)
)cT}
and is computed for that observation, l em:
DEA 0
s.t.
" __ -
maximize 8 0, z Y e ey 0
z z
.XX
0
I z E~z.-
1
(B-3)
i=1
0, zi
by solving the following LP prob-
, i
1,
...
,
k
.
B-2
S-APPENDIX
C DESCRIPTION AND LISTING OF DEA COMPARISON DISTRICTS
i.M ',i
L"'..
A-"
p
4,)F
.4
APPENDIX C DESCRIPTION AND LISTING OF DEA COMPARISON DISTRICTS The solution to the linear programming problem indicates to which distzicts on the reference frontier an inefficient observation is compared. The optimal basic variables, i.e., the zi 9 0 in the optimal solution of each LP problem, determines a "best practiae" subset of For recruiting districts to which the district's performance is gauged. each district, the efficient subset,*in which that district's efficiency is gauged, is given by the set of xi in the optimal basic solution. Tables C-1 through C-4 provide the computed efficiency measure and set of comparison observations for each district by year. The efficiency measure listed is the solution to the LP problem and gives the ratio of efficient to actual contracts rather than percent of actual contracts lost due to inefficiency as was presented in the text. The comparison For districts are identified by year of operation and district number. example, district 101 in 1981 is gauged inefficient with a computed efficiency meab're of 1.043. This district is gauged Inefficient relative to five "similar" districts. Only one district (102) was compared in FY 1981, one in 1984 (840), and three In 1985 (districts 312, 725, and 839). The comparison year-district observations are efficient observations (see table 3 of the text) that compose the facet of the efficient frontier~to which district 81-101 is compared. These districts that the z identify together generate the efficient facet or comparison group oý the reference technology to which the district is compared.
C-1
TABLE
C-i
DISTRICT COMPARISON DISTRICTS FOR 1981 MEASURES DISTRICT
DEA MEASURE
COMPARISON DISTRICTS (YEAR-DISTRICT) ----------------------------------------------
101 102 103 104 119 161
1.043 1.000 1.226 1.290 1.279 1.220
81-102 81-102 82-315 81-102 84-409 84-409
84-840
85-312
85-725
85-839
82-417 82-422 84-840 84-840
82-422 84-840 85-312 85-312
85-312 85-312 85-725 85-725
85-528
310 311 312 313 314 315 316 348
1.289 1 .000 1.179 1.100 1.455 1.057 1.307 1.000
82-417 81-311 81-102 85-311 82-315 82-315 81-348 81-348
82-542
84-311
85-310
84-731 85-312 82-417 82-417 84-311
85-312 85-313 84-311 85-315 84-316
85-725 85-315 84-529 85-828 84-730
85-725 85-725 85-529 84-731
406 409 417 418
82-348 8-1-409 81-417 81-102 82-417 81-422
82-417 84-840
84-311 85-312
85-527 85-725
85-839
81-529 84-529
82-417 85-315
85-312 85-527
85-528 85-528
422
1.189 1.008 1.000 1.085 1.221 1.000
521 524 526 527 528 529 542 559
1.000 1.098 1.000 1.233 1.384 1.000 1.000 1.183
81-521 81-526 81-526 81-529 81-102 81-529 81-542 84-529
81-529
81-542
81-725
85-837
84-529 81-529
84-731 84-731
85-315 85-528
85-527 85-725
85-72
84-559
84-725
84-837
725
1.000
81-725
730
1.000
81-730
731 732 733 734 746
1. 145 1.000 1.000 1.590 1.000
81-102 81-732 81-733 82-417 81-746
81-725
84-731
82-542
84-311
84-542
84-746
85-725
836 837 838 839 84C
1.244 1.177 1.000 1.181 1.334
81-521 81-422 81-838 81-422 81-102
81-725 81-529
85-836 81-725
85-837
84-837 84-840
85-725 85-312
85-837 85-725
420
747
1.000
85-839 85-839
81-747
C-2
85-839 85-839
85-74 85-83
85-839 85-725
TABLE
C-2
DISTRICT COMPARISON DISTRICTS FOR 1982 MEASURNS
DISTRICT
DEA MEASURE
COMPARISON DISTRICTS (YEAR-DISTRICT) -------------------------------------------------------
101 102 103 104 119 161
1.098 1.028 1.206 1.181 1.203 1.192
82-417 81-102 82-315 81-102 82-417 82-417
84-409 82-422 82-417 82-422 84-840 84-840
84-840 85-312 82-422 84-840 85-312 85-312
85-312 85-312 85-528 85-528
310 311 312 313 314 315 316 348
1.187 1.000 1.071 1.016 1.416 1.000 1.285 1.000
82-417 82-311 82-417 84-311 82-417 82-315 82-348 82-348
84-311
85-310
85-312
85-312 85-310 84-529
85-312 84-559
85-747 84-747
82-417
84-311
84-730
85-527
406 409 417 418 420 422
1.095 1.025 1.000 1.106 1.213 1.000
82-348 82-417 82-417 82-315 82-417 82-422
82-417 84-409
84-311 84-840
88-527 85-312
85-839
82-417 84-529
82-422 84-559
85-312 84-747
85-528
521 524 526 527 528 529 542 559
1.315 1.091 1.000 1.106 1.193 1.000 1.000 1.108
81-422 82-417 82-526 82-315 82-417 82-529 82-542 82-417
82-417 82-542
84-731 84-529
85-836 85-529
82-417 84-529
84-529 84-731
85-527 85-528
85-747
84-529
84-559
725 730 731 732 733 734 746 747
1.133 1.008 1.305 1.182 1.208 1.599 1.143 1.000
82-417 82-417 82-417 82-417 81-730 82-417 81-746 82-747
82-542 84-311 84-409 84-311 84-311 84-311 84-311
84-542 84-730 84-731 84-542 84-529 84-542 84-746
84-725 85-527 85-725 84-731 85-315 84-730 85-725
84-837 85-747 85-839 85-725 85-725 84-746
836 837 838 839 840
1.253 1.089 1.064 1.142 1.339
82-417 81-529 81-102 82-417 82-417
82-422 82-422 81-422 82-422 82-422
84-840 82-542 82-422 82-542 84-840
85-838 85-837
C-3
85-312
85-837 85-312
85-839
85-747
85-747
85-839 85-839
85-725
85-747
TABLE
C-3
DISTRICT COMPARISON DISTRICTS FOR 1984 MEASURES D:STRICT
DEA MEASURE
COMPARISON DISTRICTS (YEAR--DISTRICT)
101 102 103 104 119 161
1.090 1.012 1.206 1.151 1.035 1.141
84-409 81-102 82-315 81-102 82-417 82-417
84-731 85-102 82-417 82-422 84-409 84-409
85-102 85-312 84-409 84-840 85-527 84-731
85-528 88-528 85-312 88-312 85-528 85-527
310 311 312 313 314 315 316 348
1.043 1.000 1.056 1.000 1.328 1.073 1.000 1.299
82-417 84-311 82-417 84-311 82-417 82-315 84-316 82-348
82-542
84-311
85-310
84-409 84-316 84-529 84-311
85-312 84-731 84-730 84-529
85-527 85-312 85-527 85-315
82-417
84-311
85-527
406 409 417 418 420 422
1.126 1.000 1.079 1.180 1.090 1.068
82-417 84-409 82-417 81-102 82-417 81-102
84-311
85-312
85-527
84-542 81-529 84-559 81-422
84-559 82-417 84-730 82-422
84-725 85-312 84-747 85-839
521 524 526 527 528 529 542 559
1.154 1.047 1.037 1.129 1.178 1.000 1.000 1.000
81-422 81-526 81-526 82-315 82-315 84-529 84-542 84-559
81-725 82-542 82-542 82-417 82-417
85-725 84-529 84-529 84-311 82-422
85-836 84-542 85-526 84-529 85-528
84-837 85-747 85-527 85-529
725 730 731 732 733 734 746 747
1.000 1.000 1.000 1.086 1.222 1.249 1.000 1.000
84-725 84-730 84-731 82-417 82-417 82-542 84-746 84-747
84-542 85-315 84-746
84-725 85-529 85-725
84-746 85-725
85-747
636
1.128
1.000 1.010
82-417
84-731
84-840
85-836
837 838
81-422
82-422
85-8368
839 840
1.025 1.000
82-422
82-542
85-837
84-837 84-802 82-417 84-840
C-4
85-836 85-836 85-527 85-528
85-313 85-747 85-725
a5-741
84-731 85-528
85-83
85-839
88-32.
85-741
85-83$
TABLE
C-4
DISTRICT COMPARISON DISTRICTS FOR 1985 MEASURES DISTRICT
DEA MEASURE
COMPARISON DISTRICTS (YEAR-DISTRICT)
101 102 103 104 119 161
1.150 1.000 1.236 1.246 1.184 1.395
81-102 85-102 82-315 81-102 82-417 84-409
84-409
84-731
85-102
85-312
82-417 82-422 84-409 84-731
84-409 84-840 84-840 84-840
85-312 85-312 85-312 85-528
85-527
310 311 312 313 314 315 316 348
1.000 1.000 1.000 1.000 1.315 1.000 1.020 1.269
85-310 85-311 85-312 85-313 82-315 85-315 84-311 81-348
82-417
84-311
84-529
85-527
85-74
84-318 84-311
84-731 84-316
85-312 84--731
406
1.156
82-417
84-311
85-312
85-527
409 417 418
1.008
84-731 85-725 84-409
85-102 85-839 84-840
85-312
1.154
84-409 82-417 82-417
85-312
85-528
85-83
420 422
1.154 1.176
82-417 81-102
84-311 81-422
84-730 82-422
85-527 85-839
85-747
521
1.151
81-102
81-422
81-725
85-836
524
1.000
85-524
526 527 528 529 542 559
1.000 1.000 1.000 1.000 1.099 1.050
85-526 85-527 85-528 85-529 82-417 82-417
82-542 84-529
84-311 84-542
84-542 84-559
725 730
1.000 1.000
85-725 85-730
731
1.106
81-102
84-731
85-312
85-725
732 733
1.062 1.126
82-417 81-529
84-542 85-315
84-725 85-529
84-746 85-725
734
1.208
82-417
82-542
84-746
85-725
746 747
1.004 1.000
82-542 85-747
84-746
85-310
836 837 838 839 840
1.000 1.000 1.047 1.000 1.003
85-836 85-837 81-102 85-839 81-102
81-422
81-838
85-836
84-409
84-840
85-312
1.032
C-5
85-839 85-836
i
85-725 84-725
85-7 84-73
85-747
85-831
85-725
-
--
--
--.-
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l
ma-e~r n
APPENDIX D -.
PRODUCTION FUNCTION ESTIMATION RLULTS. FOR THE STATISTICAL APPROACH
NRA
Ie •
,.,-..Y"
APPENDIX D PIHODUCTION FUNCTION ESTIMATION RESULTS FOR THE STATISTICAL APPROACH
The statistical characteristics or the parametric, stochastic estimation and prediction of enlistment contracts are important for judging the confidence that may be placed in the predictions.
Table 0-1
presents the major statistics and parameter estimates associated with the linear specification. the two-stage procedure. sense.
The
R2
The fit
is 0.83 in the OLS first stag* of is thus reasonably good in an average
Maximum likelihood estimation of the parameters of the frontier
converged quickly with only the c~nstant term and population coefficient is 0.95, so that the standard X = changing. The estimate of deviation of inefficiency componenV is about the same as that of the random noise component.
Average technical inefficiency is estimated
from the formula in [17, p. 234].
It represents a loss of slightly less
than one percent of enlistment contracts.
The formulas in the text are
used to evaluate the most likely value (mode) of the inefficiency component for each observation based on the results of this regression. AN ALTERNATIVE STOCHASTIC PROCEDURE Schmidt (D-1] suggests using the results of a one-way fixed effects model of cross-section, time-series variation in observed production to impute stochastic measures of technical inefficiency.
In this approach,
the regression equation Is the same as equation 1 in the main text except for the inclusion of separate intercept terms for each of the districts. The estimation procedure is equivalent to OLS (as implemented in LIMDEP), but with district-specific fixed effects. These estimated fixed effects can be Interpreted as average differences in productivity, other things being equal,
assuming that the environmental variables have
the same effect on output in all districts and at all times.
D- 1
TABLE 0-1 SUiMMARY STATISTICS FOR STATISTICAL APPROACH (Dependent Variable: A- and CU-Cell Contraota)a Variable
Coefficient
t-ratto
-1,133.88
-5.35
1.00
POP
4.94
5.87
115.20
RTR
7.61
6.01
87.26
UR
54.33
7.69
7.87
625.96
4.18
1.13
79.90
0.67
0.73
0.95
1.88
--
CONSTANT
PAY URBPCT LAMBDA (X)
o2-
194.83
2a u
Mean oa
V
Average technical
inefficiency log-likelihood Mean of dependent variable Number of observations
a.
8.07 -1,079.7
1,208.8
1614
FY 1983 observations excluded from the sample.
D-2
vpriable
The results of a one-way fixed-effects estimation of the production relation are given in table D-2. Schmidt [D-1] suggests measuring technical inefficiency as the dtffcrence between the maximum estimated-
fixed effect and each-of -thie others.
'In--this -case, the- measurement of
technical inefficiency does -not depend on any---distributional;-- assumptions, regarding the skewness of the error term. Another advantage of this approach is the ready availability of standard statistical tests for the significance of the resulting technical inefficiency estimates. r4
The maximum fixed effect is about 220 recruits. The standard errors for the fixed effects are large (reflecting only-four observations per district). They range from &bout 270 to 350. Only 6 districts have estimated fixed effects below -200 recruits per year, and they are predominantly (4 of 6) in area 3. This is surprising, because the four area 3 districts (310-313) were generally judged efficient in the other approaches. Perhaps this is evidence that even though they are efficient relative to the best practice of other districts, these districts had significant excess capacity and could have been goaled higher. Districts 161 and 420 are Judged inefficient in all approaches, and closer inspection may yield fruitful analytical insights.
I
D-3
MUM.
..
.
TABLE D-2 FIXED EFFECTS MODEL FOR CONTRACTS (A-cell plus CU-cell) Analysis of Variance Source Within Between Total
Variation
D.F.
O.1192E÷08 0.132OE,08 0.2512E+08
123 40 163
,Mean
quare
Proportion
O.9688E+05O.3301E+06 O.1541E+06
o.474351 0.525649
F test for homogeneity across individuals F(4O,123) = 3.41
Significance = 0.000
Ordinary least squares estimates Dependent variable Number of observations Mean of dependent variable Std. dev. of dep. variable Std. error of regression R-squared Adjusted R-squared Variable
POP ONBOARD URATE RELMILPY URBPCT Sigma
Coefficient
1.56 1O.69 2916.24 118.91 -219.37 142.33
Contract 164.00 1208.81 392.57 142.33 0.90 0.87
Std. error
T-ratio (sig.lvl.)
0.95
1.63 (0.10)
--a192.5 .a 29.96 7.86
a 15.15 (0.00) -- a -7.32 (0.00) 18.11 (0.00)
a..LIMDEP did not produce reliable estimates of confidence for these parameters.
D-~4
-_
-A
A
TABLE D-2 (Continued) F test for homogeneity across individuals (Estimated coefficients) F(40,118) z 2.22 Significance = 0.001 Estimated individual effects District 101 102 .103 104 119 161
310 311 312 313 314 315 S316 ,348 406 409 417 418 420 422 521 524 526 527 528 529 542 559 725 730 731 732 733 734 746 747 836 837 838 839 84o
Coeffieient -91.00 -160.38 -178.63 -90.33 64.00 -339.65 -283.93 -254.79
Std. error 316.97 316.60 316.29 324.59 307.92 291.20 284.14 272.20 287.10 293.28 325.42 340.55 336.62 344.53 334.02 319.84 311.22 292.37 297.63 319.29 314.05 335.92 322.49 323.09 323.20 316.21 306.65 287.36 290.83 304.13 310.30 32.38 320.88 314.20 324.66 314.20 302.53 285ý04 289.71 303.92 298.71
-366.14 -463.52 -68.o5 -78.58 -79.70 7.0O0 218.40 -52.52 -34.84 -162.27 -251.62 -167.43 -82.13 39.79 -31.59 -180.28 102.88 -47.25 -143.45 -86.46 -152.05 -138.12 49.53 - 129.13 -70.34 - 147.85 -10.80 -86.92 -65.83 -61.60 --144.86 133.58 -7.55
D-5
T-ratio -0.29 -0.51 -0.56 -0.28 0.28 -1.17 -1.00 -0.94 -1.28 -1.58 -0.21 -0.23 -0.24 0.02 o.65 -0.16 -0.11 -0.56 -0.85 -0.52 -0.26 0.12 -0.10 -0.56 0.32 -0.15 -0.47 -0.30 -0.52 -0.45 0.16 -0.40 -0.22 -o.47 -0.03 -0.28 -0.22 -0.22 -0.50 -0.44 -0.03
REFERENCE [1D-]
Peter Schmidt. "Frontier Production Functions." Reviews vol. 4, no. 2 (1985-1986): pP. 312-315
RCnonmetzic
-D
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Recruiting Efficiency and Enlistment Objectives: An Empirical Analysis 12. PERSONAL AUTHOR(S)
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Enlistments, Linear Programming, Manpower, Military Requirements,
I-Naval Personnel, Navy Recruiting Districts, Recruiters, Recruiting, IRecruiting Quotas, Statistical Analysism
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19. ABSTRACT (Contrnue on reverne if nenssaay and de*ntify by bdagk number)
SWith increasing accession requirements and a more competitive recruiting environment, the size of the enlisted recruiting force has grown substantially. The Center for Naval Analyses was asked to provide analyticl sulport to Commander, Navy Recruiting Command (CNRC), concerning ways to improve the return on this recruiting investment by exaining the geographic allocation of recruiters, gfoals, and incentives. This reseec memorandum reports on the empi~rical analysis of three questions: (1) How do recruiting dist icts c€ompare in terms of pt production? (2)Ae ~orphic differences in enlistment goals consistent with measured differences in recruwtingswar ket condirLions? 3)Hwcan the results be used to better evaluate district recruit production.
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