page_title: Dummy variable (statistics)
section_title: Incorporating a dummy independent
hierarchical_section_title: Dummy variable (statistics) / Incorporating a dummy independent
caption_attribution_description: English: The wage lines for males and females are parallel to each other because 'education' is kept constant across both gender categories. The female wage line is lower than the male wage line because δ0&lt;0, which means that females are earning a lower wage than men, for a given education level.
context_page_description: In statistics and econometrics, particularly in regression analysis, a dummy variable is one that takes only the value 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome. They can be thought of as numeric stand-ins for qualitative facts in a regression model, sorting data into mutually exclusive categories.
  A dummy independent variable which for some observation has a value of 0 will cause that variable's coefficient to have no role in influencing the dependent variable, while when the dummy takes on a value 1 its coefficient acts to alter the intercept. For example, suppose membership in a group is one of the qualitative variables relevant to a regression. If group membership is arbitrarily assigned the value of 1, then all others would get the value 0. Then the intercept would be the constant term for non-members but would be the constant term plus the coefficient of the membership dummy in the case of group members.
  Dummy variables are used frequently in time series analysis with regime switching, seasonal analysis and qualitative data applications.
context_section_description: Dummy variables are incorporated in the same way as quantitative variables are included (as explanatory variables) in regression models. For example, if we consider a Mincer-type regression model of wage determination, wherein wages are dependent on gender (qualitative) and years of education (quantitative):
  where  is the error term. In the model, female = 1 when the person is a female and female = 0 when the person is male.  can be interpreted as the difference in wages between females and males, holding education constant. Thus, δ₀ helps to determine whether there is a discrimination in wages between males and females. For example, if δ₀>0 (positive coefficient), then women earn a higher wage than men (keeping other factors constant). The coefficients attached to the dummy variables are called differential intercept coefficients. The model can be depicted graphically as an intercept shift between females and males. In the figure, the case δ₀<0 is shown (wherein men earn a higher wage than women).
  Dummy variables may be extended to more complex cases. For example, seasonal effects may be captured by creating dummy variables for each of the seasons:  if the observation is for summer, and equals zero otherwise;  if and only if autumn, otherwise equals zero;  if and only if winter, otherwise equals zero; and  if and only if spring, otherwise equals zero. In the panel data, fixed effects estimator dummies are created for each of the units in cross-sectional data (e.g. firms or countries) or periods in a pooled time-series. However in such regressions either the constant term has to be removed or one of the dummies has to be removed, with its associated category becoming the base category against which the others are assessed in order to avoid the dummy variable trap:
  The constant term in all regression equations is a coefficient multiplied by a regressor equal to one. When the regression is expressed as a matrix equation, the matrix of regressors then consists of a column of ones (the constant term), vectors of zeros and ones (the dummies), and possibly other regressors. If one includes both male and female dummies, say, the sum of these vectors is a vector of ones, since every observation is categorized as either male or female. This sum is thus equal to the constant term's regressor, the first vector of ones. As result, the regression equation will be unsolvable, even by the typical pseudoinverse method. In other words: if both the vector-of-ones (constant term) regressor and an exhaustive set of dummies are present, perfect multicollinearity occurs, and the system of equations formed by the regression does not have a unique solution. This is referred to as the dummy variable trap. The trap can be avoided by removing either the constant term or one of the offending dummies. The removed dummy then becomes the base category against which the other categories are compared.
caption: Figure 1 : Graph showing wage = α0 + δ0female + α1education + U, δ0 < 0.
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