## The Nature Of Dummy Variables

In regression analysis the dependent variable, or regressand, is frequently influenced not only by ratio scale variables (e.g., income, output, prices, costs, height, temperature) but also by variables that are essentially qualitative, or nominal scale, in nature, such as sex, race, color, religion, nationality, geographical region, political upheavals, and party affiliation. For example, holding all other factors constant, female workers are found to earn less than their male counterparts or nonwhite workers are found to earn less than whites.2 This pattern may result from sex or racial discrimination, but whatever the reason, qualitative variables such as sex and race seem to

1We will discuss ordinal scale variables in Chap. 15.

2For a review of the evidence on this subject, see Bruce E. Kaufman and Julie L. Hotchkiss, The Economics of Labor Market, 5th ed., Dryden Press, New York, 2000.

298 PART ONE: SINGLE-EQUATION REGRESSION MODELS

influence the regressand and clearly should be included among the explanatory variables, or the regressors.

Since such variables usually indicate the presence or absence of a "quality" or an attribute, such as male or female, black or white, Catholic or non-Catholic, Democrat or Republican, they are essentially nominal scale variables. One way we could "quantify" such attributes is by constructing artificial variables that take on values of 1 or 0, 1 indicating the presence (or possession) of that attribute and 0 indicating the absence of that attribute. For example 1 may indicate that a person is a female and 0 may designate a male; or 1 may indicate that a person is a college graduate, and 0 that the person is not, and so on. Variables that assume such 0 and 1 values are called dummy variables.3 Such variables are thus essentially a device to classify data into mutually exclusive categories such as male or female.

Dummy variables can be incorporated in regression models just as easily as quantitative variables. As a matter of fact, a regression model may contain regressors that are all exclusively dummy, or qualitative, in nature. Such models are called Analysis of Variance (ANOVA) models.4

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