ECON301_Handout_11_1213_02

# Example household consumption the dependent variable

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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.

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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. For example, suppose instead, the following regression line is formed: Y i = 0 + 1 X 1i + 2 D i + i , where, D i = 1, if the i th observation on X is a female D i = 0, otherwise (the head of household is male).
ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: H. Ozan ERUYGUR e-mail: Lecture Notes 11 If the head of the i th household is male, D i =0 and equation reduces to Y i = 0 + 1 X 1i + i If the head of household is female, then D i =1 and the regression is Y i = ( 0 + 2 ) + 1 X 1i + i The parameter 2 measures the shift in equation due to incorporating the sex of the head of the household. In both regressions the slopes are the same (same marginal propensity to consume) but female- headed households have higher intercept. In this case the slope is a more accurate measure of the responsiveness of consumption (Y) to their disposable income (X) compared to the slope measured by the flatter dotted line regression. Thus,

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example household consumption the dependent variable cannot...

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