Iv some illustrations econ 301 introduction to

Info icon This preview shows pages 6–11. Sign up to view the full content.

View Full Document Right Arrow Icon
IV. Some Illustrations
Image of page 6

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: H. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 7 V. Model Parametrizations Consider the following equations; Y t = B 01 + B 11 X t1 + B 21 X t2 + u t t T 1 (1 st Subsample) Y t = B 02 + B 12 X t1 + B 22 X t2 + u t t T 2 (2 nd Subsample) Let us now define dummy variables for these two sub periods; 1 if t T 1 D t1 = 0 otherwise while
Image of page 7
ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: H. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 8 1 if t T 2 D t2 = 0 otherwise 1 st Parametrization : We are combining two models by using dummy variables; Y t = B 01 D t1 +B 11 D t1 X t1 +B 21 D t1 X t2 +B 02 D t2 +B 12 D t2 X t1 +B 22 D t2 X t2 2 nd Parametrization 1 : D t1 + D t2 = 1 D t1 = 1 - D t2 , putting this in the model above we get; Y t = B 01 (1-D t2 )+ B 11 (1-D t2 )X t1 + B 21 (1-D t2 )X t2 + B 02 D t2 + B 12 D t2 X t1 + B 22 D t2 X t2 and we obtain Y t = B 01 +B 11 X t1 + B 21 X t2 + (B 02 - B 01 ) D t2 + (B 12 - B 11 )D t2 X t1 + (B 22 - B 21 )D t2 X t2 + u t 1.subsample is base 02 12 22 ( D t1 = 1 - D t2 ) Intercept Slope Slope dummy dummy dummy 1 We are using (p -1) Dummy variables (p number of subsamples, or categories ) in the 2 nd parametrization..
Image of page 8

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: H. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 9 A. An Example Model Frequently researchers need to include qualitative variables in their regressions to explain variations in the dependent variable. For example household consumption (the dependent variable) cannot be explained entirely by disposable income of the household. Some other variables such as sex and race of the family head may affect the level of consumption expenditure. But variables such as sex and race cannot be quantified. How can we include them in a regression? Dummy variables can be used to account for qualitative characteristics and categorical variables that are not measurable except by a signal of whether the characteristic is absent or present. A dummy variable is a variable, which is assigned the value 1 when the characteristic is present in the observation, and is assigned the value zero otherwise. For example if D is a dummy variable representing the sex of the head of the household, then it could be assigned the value 1 if the head of household is female and 0 if the head of household is male. Suppose families headed by men tend to have higher incomes than families headed by a woman. Also, suppose that female-headed families have a higher average propensity to consume than families headed by males. In such case the sample data available to researcher might be comprised of two clusters as shown in the following figure.
Image of page 9
ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: H. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 10 If the sex of the household is ignored, then researcher runs a regression of the form: Y i = 0 + 1 X 1i + i The regression line for this equation is estimated and presented by the flatter regression line shown above with dotted line. If sample data is divided into two part by sex (i.e., if sex is taken into account), and separate regression lines are run, a better estimate of the true slope is found.
Image of page 10

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern