QUALITATIVE VARIABLES

• Qualitative variables are nominal scale variables which have no particular numerical values.

• We can “quantify” them by creating the so-called dummy variables, which take values of 0 and 1

  • 0 indicates the absence of an attribute
  • 1 indicates the presence of the attribute

• For example, a variable denoting gender can be quantified as female = 1 and male = 0 or vice versa.

Dummy variables are also called indicator variables, categorical variables, and qualitative variables. Examples: gender, race, color, religion, nationality, geographical region, party affiliation, and political upheavals

DUMMY VARIABLE TRAP

• If an intercept is included in the model and if a qualitative variable has m categories, then introduce only (m – 1) dummy variables.

  • For example, gender has only two categories; hence we introduce only one dummy variable for gender.
  • This is because if a female gets a value of 1, ipso facto a male gets a value of zero.

• If we consider self-reported health as a choice among excellent, good, and poor, we can have at most two dummy variables to represent the three categories.

• If we do not follow this rule, we will fall into what is called the dummy variable trap, the situation of perfect collinearity.

REFERENCE CATEGORY

• The category that gets the value of 0 is called the reference, benchmark, or comparison category.

• All comparisons are made in relation to the reference category.

• If there are several dummy variables, you must keep track of the reference category; otherwise, it will be difficult to interpret the results.

POINTS TO KEEP IN MIND

• If there is an intercept in the regression model, the number of dummy variables must be one less than the number of classifications of each qualitative variable.

• If you drop the (common) intercept from the model, you can have as many dummy variables as the number of categories of the dummy variable.

• The coefficient of a dummy variable must always be interpreted in relation to the reference category.

• Dummy variables can interact with quantitative regressors as well as with qualitative regressors. If a model has several qualitative variables with several categories, introduction of dummies for all the combinations can consume a large number of degrees of freedom.

INTERPRETATION OF DUMMY VARIABLES

• Dummy coefficients are often called differential intercept dummies, for they show the differences in the intercept values of the category that gets the value of 1 as compared to the reference category.

• The common intercept value refers to all those categories that take a value of 0.

• If we have: Yi = B1 + B2 Fi where Y = wage and F = female dummy variable

• Then, on average, females earn a wage of (B1 + B2) and males earn a wage of B1. (Note that B2 can be negative.)

• Thus females earn a wage that is B2 higher than males.

• Since wages tend to be skewed to the right, we might instead model the wage function as: lnYi = B1 + B2 Fi

• In this case, females earn exp(B2 – 1)*100% more than males on average.

• On average, male wages are equal to exp(B1), and female wages are equal to exp(B1+B2).

Data on Teachers Evaluation and Beauty

TeachingRatings <- read_excel("C:/Users/hp/Dropbox/Applied Econometrics SBP/Stock and Watson Data sets/TeachingRatings.xls")
sample_n(TeachingRatings, size=5)

TeachingRatings1<-TeachingRatings %>% mutate(male=(1-female), advanced=(1-intro))
set.seed(12345)
sample_data<-sample_n(TeachingRatings1, size=20)

sample_data

Dummy Variable

lm_dummy<-lm(course_eval~beauty+female,data = sample_data)

lm_saturated<-lm(course_eval~beauty+female+male,data = sample_data)

lm_nointercept<-lm(course_eval~beauty+female+male+0,data = sample_data)


huxreg("One Less Dummy"=lm_dummy,"Constant+Dummies"=lm_saturated, "full dummies without constant"=lm_nointercept) %>% set_caption("Teaching Evaluation as function of Beauty")