For example suppose instead the following regression

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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).
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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: H. Ozan ERUYGUR e-mail: [email protected] 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, when we are interested in detecting and estimating the magnitudes of shifts in relationships associated with categorical or quantitative variables, we can employ intercept dummy variables. Note that the intercept dummy leaves the slope of the relation between Y and X unchanged. A more general possibility is that the relationship between Y and X is completely different for different part of sample data (groups or periods). Dummy variables can also be used to study these more general differences.
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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: H. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 12 B. Intercept Dummy Example Consider the following model; Y t = 0 + 1 X t + 2 D t + t , where Y t = Personal consumption expenditure in year t, X t = Disposable income in year t, D t = 1 during the war years, 1942, 1943, 1944, 1945 0 in other years. We expect 2 to be negative, so that in the war time the intercept ( 0 + 2 ) will be lower than peace time intercept ( 0 ), which will result in lower average consumption. In peace time Y t = 0 + 1 X t + t . One of the first published uses of dummy variables in economic literature was to show the difference between consumption in war years and peace times during 1930-1949 time period. This period included the time period 1942-1945 associated with World War II. Because of rationing and controls during the war, one might hypothesizes that the average propensity to consume was lower during the war years.
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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: H. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 13 C. More Than Two Dummy Variables In examples presented above we assumed that there was only two possible categories (characteristics) for each observation. For example, we assumed the head of household is either male or female, each year is either a war year or not. Thus when we had two categories we used one dummy variable to present the impact of two characteristics on the dependent variable (# of dummy variable = # of categories 1).
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