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a sample be chosen for which the data could be obtained.

The specifics regarding the sampling process are

described in Appendix A-2.

The number of employees for which education data

was obtained determined the number of observations avail

able for the correlation analysis. Thus, the correlation

was performed using data representing 817 of the Department's 27/

10,700 employees, a 7.6 percent sample.

The breakdown

of the data by race, sex, and professional/nonprofessional status is shown by the table on the following page.

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See Appendix A2 for a discussion of the validity of the sample (that is, the degree to which it is representative of DOL employees),

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Dummy variables are often used to study the affects of variables that do not vary continuously over a range of values. For example, such variables can be used to represent the yes/no status as regards membership in certain classification groupings, like white or black or nonblack minority, male or female, etc. They are always used to give values with respect to a specified base group. In this case, employees with a high school diploma comprise the base group. The various dummy variables show the average increase or decrease in annual salary, due to other levels of educational degree attainment, as compared against those with high school diplomas. A value of $2,000 (Continued on page77 ).

Distribution of the Input Data for the Correlation Analysis by Race, Sex, and Professional/Nonprofessional Status

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Various forms of the independent variables were used

One re

in order to find the forms giving the best fit. gression fit is better than another if the choice and form of the independent variables results in more of the variation of the dependent variable being explained. Of course, the criterion of reasonableness must always be applied. Variables cannot be manipulated just to obtain the best fit. They must be chosen because they correspond to a particular theory or model which has been hypothesized to describe reality. The correlation is, then, a test of

the various models. A brief discussion of the various

forms of the independent variables used in this analysis

follows:

Education. It was hypothesized that salary increased linearly with increases in the number of years of completed education. Also, it was believed that extra salary

benefits might result from the attainment of various degrees. In other words, if it were found that each year of additional education was worth, on the average, another $500 annually in salary, it might also be true that, for example, the salary gain from 15 years of education to

16 years of education, when a bachelor's degree is normally earned, is really $500 plus an additional $2,000 for the

degree. This type of affect was studied by using dummy variables for a bachelor's degree, an advanced degree, a

two-year certificate, and no high school diploma; the base group was employees with a high school diploma.

Age and experience.

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Several forms were tried for

these two factors in that they are highly correlated (a correlation coefficient of .726 for our data) and neither

was, believed to have a linear affect on salary. Years of government service was represented both as actual years and as the natural logarithm of actual years. The natural log function increases at a decreasing rate, so that the salary differential for each additional year of government service is less at higher levels of service than at lower levels. This, on the average, is what one would expect. The factor of age was represented variously by the following forms: (1) age in years, (2) the natural logarithm of years of age, and (3) the quadratic form of age (i.e., years of age plus years of age squared). When age-squared

28/ (Continued from page 74) . for the "degree"

variable would mean that, on the average, it is worth $2,000 in annual salary to have a bachelor's degree rather than a high school diploma.

has a negative sign, the quadratic form of age function increases at a decreasing rate, similar to the natural logarithmic function. This quadratic form has been used successfully in several previous studies attempting to

approximate the age-earnings profile.29,

It has been

shown to fit the Census age-earnings data. In attempting to find what would best represent the combined affects of age and experience, several combinations of the above forms for age and experience were tried. In Albert Rees and George Schultz's study of the Chicago Labor Market, a good fit was obtained using the natural logarithm of years 30/ of service and the quadratic form of age.

Geographic location and organizational unit. Dummy variables, similar to those used to represent educational degrees attained, were used to represent geographic location and organizational unit. Individual dummy variables were used for each of the eight regional administrative offices

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Albert Rees and George P. Schultz, Workers and Wages in an Urban Labor Market (Chicago: University of Chicago Press, 1970), pp. 148-149.

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