ECON301_Handout_11_1213_02

# Iv some illustrations econ 301 introduction to

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IV. Some Illustrations

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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: H. Ozan ERUYGUR e-mail: 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
ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: H. Ozan ERUYGUR e-mail: 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..

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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: H. Ozan ERUYGUR e-mail: 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.
ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: H. Ozan ERUYGUR e-mail: 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.

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