APPENDIX A

SUPPLY METHODOLOGY 1

Two approaches determining the supply pool of qualified and available men, followed by a mathematical discussion, are illustrated below. Specific sources are given in Tables 3-5 and 3-6.

Approach One

Table A-1 and the discussion which follows show how figures in Table 3–5 are derived.

TABLE A-1.-MALES QUALIFIED AND AVAILABLE FOR MILITARY SERVICE, FISCAL YEARS 1960-79

Qualified and available males data (line 9) are computed by adding or subtracting the following categories from the total male population (line 1):

Institutionalized (line 2): 1.5 percent of line 1. 1.5 percent represents an average of the total male institutionalized population derived by the authors from 1960 and 1970 census statistics.

Full-time students (line 3): 46.5 percent 2 of the noninstitutionalized population (line 1-line 2). 46.5 percent is derived from 1971 data by dividing full-time students (5.17) by total population (11.11).

First and second year college dropouts (line 4): 7.1 percent of line 3. 7.1 percent is derived as follows: 50 percent of all men who enter college leave before graduating. Of these, 50 percent (or 25 percent of all first year students) leave during the first year and 25 percent (or 12.5 percent of all second year students) leave during the second year. 0.263 from a total of 1.051 million men left during the first year (0.25) (1.051); 0.103 from a total of 0.826 million left during the second year (0.125) (0.826).3 Total first and second year dropouts (0.263+0.103) or (0.366) divided by full-time students (5.1) is 7.1 percent.

Full-time students adjusted (line 5): Line 3-line 4.

Unqualified (line 6): 31.7 percent of line 1-(lines 2+5). 31.7 percent, the percentage of unqualified males during 1958-60 was considered by the authors in consultation with Bernard D. Karpinos to be most representative for the general population.

1 Developed with the assistance of Arnold M. Kuzmack, Brookings Institution.

2 This percentage applies to fiscal 1971-79 figures. Data for fiscal 1960 and 1965, line 3; Office for Special Studies. Assistant Chief of Staff, Studies and Analysis Headquarters, "CY 1960-CY 1980 Demographic Data for Males of the United States (17-22 year olds) (Saber Volunteer)" (U.S. Air Force, October 1971; processed), p. 17a.

3 Data from Department of Health, Education, and Welfare, Office of Education, National Center for Educational Statistics (April, 1973).

Active military duty (line 7) and Ex-military who are not full-time students (line 8): taken directly from specific sources.

Qualified and available (line 9): Line 1-(lines 2+5+6+7+8).

Exclusions reduce total male population for fiscal 1975-79 from 12.65 million to 3.82 million qualified and available.

Table 3-6 shows the age spread for the 3.82 million qualified and available. Table A-2 shows how these figures were derived. Sequences of calculation and categories are the same as those used in Table A-1. The breakdown for full-time students (5.79) is spread on the basis of percentages in U.S. Bureau of the Census, Current Population Reports, Series P-20, No. 241, "Social and Economic Characteristics of Students; October 1971" (1972) p.48: 33 percent for 17-year-olds; 22 percent for 18-year-olds; 16 percent for 19-year-olds; 11 percent for 20-year-olds; 10 percent for 21-year-olds; 8 percent for 22-year-olds.

TABLE A-2.-MALES QUALIFIED AND AVAILABLE FOR MILITARY SERVICE, BY AGE (17- TO 22-YEAR OLDS), FISCAL YEARS 1975-79

Table A-3 shows how the figure 1.087 referred to on page 42 is derived. Estimates are based on 1974 data for 17-year-olds and following that group through 1979.

TABLE A-3.—17-YEAR-OLDS IN FISCAL 1974 LIKELY TO BE QUALIFIED AND AVAILABLE FOR MILITARY SERVICE AT SOMETIME BEFORE REACHING AGE 23 [Manpower in millions]

Total male population (line A): from Table A-2, line 1. Institutionalized (line B): 1.5 percent of A. 1.5 percent is derived as in Table A-1, line 3.

College enrollment (line C): 38.7 percent of line A-line B. 38.7, the percentage who will enroll in college was obtained from the Department of Health, Education, and Welfare, Department of Education, National Center for Educational Statistics (April, 1973).

First and second year college dropouts (line D): 37.5 percent of line C. 50 percent of all men entering college (or 25 percent of all first year students) leave during the first year and 25 percent (or 12.5 percent of all second year students) leave during the second year.

Unqualified (line E): 31.7 percent of (line A-line B-line C+line D). 31.7 percent is from the same source as that mentioned in Table A-1, line 6. Qualified and available (line F): Line A-line B-line C+line D-line E.

61

MATHEMATICAL DISCUSSION

Equivalence of Supply Pools

The following discussion demonstrates that the two approaches determining the supply of qualified and available males are mathematically equivalent: Let A(a, t) = available and qualified population of age a in year t, including those who have already enlisted and those who are full-time students but will become available in later years.

P=probability that a member of this population will volunteer at some time.

Pa=probability that a man will volunteer at age a, given that he will volunteer at some age. This takes into account the number of potential volunteers who volunteer after finishing school or who cannot volunteer because they volunteered earlier.

N(t)= number of volunteers in year t.

Assuming that mortality is negligible: A(a, t)=A(a+1, t+1) = . . .

If N(t) represents a required level of accessions, then the proportion of the qualified and available population that must volunteer to meet requirements is

In the steady-state, with N(t) unchanging and with all the cohort sizes the same, since Σpa=1:

N
P=
A

To see the equivalence between this formulation and that shown in Table A-3, let.

Sa probability that someone, who has not volunteered previously, is in school at age a but will be qualified and available.

The number actually in the pool of a given age a reflects the number in school and the number who previously volunteered and is:

a

A(1-Sa) (1-P Σ Pi)

i=17

The proportion of this group that will volunteer in a given year is the conditional probability that an individual will volunteer at age a, given that he is out of school and has not volunteered previously. By the rules of conditional probability, this is:

Thus, the number of volunteers of age a in a given year is APpa, the same number as derived above.

UB 323.B56

All-volunteer armed ford 104001

3323 $6

APPENDIX B

THE RESULTS OF LINEAR AND MULTIPLE REGRESSION
ANALYSES OF VOLUNTEERISM IN RELATION TO UN-
EMPLOYMENT RATES, MEDIAN INCOMES, AND RACIAL
COMPOSITION FOR THE FIFTY STATES AND THE DIS-
TRICT OF COLUMBIA

Data used in the linear and multiple regression analyses are presented in
Figure 19.

The Results of the Linear Regression Analysis

The analysis shows the relationship between volunteerism and unemployment rates. The variables used are: dependent variable (y)=true volunteer rates; independent variable (x)=unemployment rates.

The results of the analysis are shown by age in the following three equations: 1. 18 year olds: The linear relationship is y=0.0611x+2.535

with standard error of estimate 0.91; coefficient of correlation=0.29.

2. 19 year olds: The linear relationship is y=0.046x+3.254

with standard error of estimate 1.02; coefficient of correlation=0.19.

3. 20 year olds: The linear relationship is y=-0.008x+2.452

with standard error of estimate 1.05; coefficient of correlation=0.03.

Results of the Multiple Regression Analysis

The analysis shows the relationship of volunteerism to unemployment rates, median incomes, and racial composition. The variables used are: dependent variable (y)=true volunteer rates; independent variables (x's)=unemployment rates, median incomes, and racial composition.

The results of the analysis are shown for the following three combinations of variables:

1. True volunteer and unemployment rates for 18-year-olds; median incomes for 14- to 19-year-olds; racial composition for all ages. The statistical analysis is— Regression statistics: R-squared (uncorrected)=0.16; R-squared (corrected)= 0.11; standard error=0.89; mean for dependent variable=3.41.

2. True volunteer and unemployment rates for 19-year-olds; median incomes for 14- to 19-year-olds; racial composition for all ages. The statistical analysis is-Regression statistics: R-squared (uncorrected)=0.19; R-squared (corrected) = 0.14; standard error=0.96; mean for dependent variable=3.83.