Quantitative vs Qualitative factors
Introduction to Econometrics
Ekki Syamsulhakim Undergraduate Program Department of Economics
factors
- In previous chapters, the dependent and independent variables in our multiple regression models have had quantitative meaning.
- Just a few examples include hourly wage rate, years of education, college grade point average, amount
factors
- In empirical work, we must also incorporate qualitative factors into regression models.
- The gender or race of an individual, the industry of a frm (manufacturing, retail, etc.), and the region in the
United States where a city is located
Variables
- Most of this chapter is dedicated to qualitative independent variables.
• Qualitative factors often come in the form of
binary information:- – a person is female or male;
- – a person does or does not own a personal computer;
- – a frm ofers a certain kind of employee pension plan or it does not;
Dummy Variable
- In all of these examples, the relevant information can be captured by defning a binary variable or a zero-one variable.
• In econometrics, binary variables are most
commonly called dummy variables, although this name is not especially descriptive.- In defning a dummy variable, we must
Naming Dummy Variable
- The variable name (for dummy variables) indicates the event with the value one
- For example, in a study of individual wage determination, we might defne female to be a binary variable taking on the value
one for females and the value zero for males.
- The same information is captured by
Naming Dummy Variable
- Either of these is better than using gender
because this name does not make it clear
when the dummy variable is one: - – does gender = 1 correspond to male or female?
• Further, we defne a binary variable married
to equal one if a person is married and zero
• Suppose in the wage example that we have
chosen the name female to indicate gender.
Variable
- just add it as an independent variable in the equation
- We use as the parameter on female in order to highlight the interpretation of the parameters multiplying dummy variables;
- – later, we will use whatever notation is most
of dummy variable
• In model (7.1), only two observed factors
- afect wage: gender and education.
- Since female =1 when the person is
female, and female=0 when the person
is male, the parameter has the following interpretation: - – is the diference in hourly wage between females and males, given the same amount
of dummy variable
- Thus, the coefcient determines
whether there is discrimination against
women- – if , then, for
the same level of other factors ,
women earn less than men on average.
- In (7.1), we have chosen males to be
the base group or benchmark group, that is, the group against which of dummy variable
Graphical Analysis- The situation can be depicted graphic
as an intercept shift between males and females.
- In Figure 7.1, the case is shown, so that men earn a fxed amount more per hour than women.
- The diference does not depend on the amount of education, and this explains
Example: wage1.xlsx
Dummy Variable Trap
• You may wonder why we do not also include in
(7.1) a dummy variable, say male, which is one for males and zero for females.- – The reason is that this would be redundant.
- In (7.1), the intercept for males is , and the intercept for females is
- Since there are just two groups, we only need two diferent intercepts.
- – This means that, in addition to we need to use
Dummy Variable Trap
- Using two dummy variables would introduce perfect collinearity because female+male =1, which means that male is a perfect linear function of female.
- Including dummy variables for both genders is the simplest example of the so-called dummy variable trap , which arises when too many dummy variables
Interpretation Dummy Vrbl Continues…
- Interpreting Coefcients on Dummy Explanatory Variables When the Dependent Variable Is log(y)
- Using Dummy Variables For Multiple
Categories
- Incorporating Ordinal Information by Using Dummy Variables
When the Dependent Variable Is
log(y)
When the Dependent Variable Is
log(y)
For Multiple Categories
- We can use several dummy independent variables in the same equation.
- For example, we could add the dummy variable married to equation (7.9).
- The coefcient on married gives the
(approximate) proportional diferential in wages between those who are and are not married, holding gender, educ, exper,
For Multiple Categories
For Multiple Categories
- Assuming the coefcient of married is statistically signifcant, then:
“Misal terdapat 2 orang yang memiliki
pendidikan, pengalaman, masa kerja tetap,
dan jenis kelamin yang sama, namun salah
satu sudah menikah dan yang lainnya
belum , maka tingkat upah orang yang
menikah tersebut lebih tinggi rata-rata
categories
- Instead of using year of schooling, we use dummy variables:
- – primschd = 1 if the individual fnishes primary school and 0 otherwise
- – secondschd = 1 if the individual fnishes secondary school and 0 otherwise
- – Univd = 1 if the individual fnishes
categories
- Consider 2 individuals having identical experience, tenure, gender, and marital status, but 1 individual has fnished university and the other has fnished primary school , the person who
- Ordinal variable: a variable which value representing rank
- Ordinal variable can be something like:
- – Subjective well being (4=very happy;
3=happy; 2=not happy; 1=very sad)
- – etc
by Using Dummy Variables
- Hamermesh and Biddle (1993) used measures of physical attractiveness in a wage equation.
Omar Barkan vs Kiwil
by Using Dummy Variables
- Hamermesh and Biddle (1993) used measures of physical attractiveness in a wage equation.
by Using Dummy Variables
• Because there are so few people at the two
extremes, the authors put people into one of three groups for the regression analysis: average, below average, and above
average, where the base group is average.
- Using data from the 1977 Quality of Employment Survey, after controlling for the usual productivity characteristics,
Variables
- We can recast the previous model (the model where female and married appear separately) by adding an interaction term between female and married
• This allows the marriage premium to
depend on gender
…previously…
…with interaction femmar…
Variables
- Setting female=0 and married=0 corresponds to the group single men , which is the base group. The intercept of single men is 0.321
• We can fnd the intercept for married
men by setting female=0 and married=1
Variables
- We can fnd the intercept for single
women by setting female=1 and married=0 single women of
- – This gives an intercept 0.321 – 0.11 =0.210.
- – The (log) wage differfencfe between
single men and married men is 0.210 –
Variables
- We can fnd the intercept for
married women by setting female=1 and married=1
- – This gives an intercept of married women : 0.321 – 0.11 + 0.213 – 0.301
= 0.321 – 0.198 = 0.123
wage differfencfe between single men and married women is
- – The (log)
of interaction dummy term
Differencee table
FEMALE MALE
SINGLE - 0.11
(base) MARRIE
- -0.198 0.213
D
of interaction dummy term
“Misal terdapat 2 orang yang memiliki
pendidikan, pengalaman, masa kerja
tetap, namun salah satu adalah pria
yang belum menikah dan yang lainnya
wanita menikah , maka tingkat upah
wanita menikah tersebut lebih rendah
rata-rata sebesar 17.96%