Some applications include: time series data • changes in government economic policy (regime changes) • seasonality cross-section data. A labour force survey may record individual characteristics such as: • gender (male / female) • educational achievement (high school / university) • marital status (married / single)
2 Econ 326 - Chapter 7 Example A survey of professors at ABC University has data for: i y annual salary for professor i i x years of teaching experience for professor i A research question is: Is there a salary differential between male professors and female professors ? This differential is known as the ‘gender wage gap’. Define the dummy variable : = female if male if 0 1 D i for i = 1, 2, . . . , N This is the ‘gender dummy’ variable. In general, a dummy variable is an artificial variable that assigns arbitrary codes to different groups. The use of 0-1 codes suggests that the name binary variable or indicator variable may be a more descriptive name than dummy variable . The term ‘dummy variable’ is widely used in econometrics work and so is the term used here.
3 Econ 326 - Chapter 7 The gender dummy variable can be included in the salary determination equation to get the linear regression equation: i i 2 i i e x D y + β + δ + β = 1 The equation has a differential intercept: 1 β is the intercept for the female professor δ + β 1 is the intercept for the male professor δ is the salary differential between male and female professors. The use of dummy variables as explanatory variables does not affect any of the statistical properties of the least squares (OLS) estimator. Estimation and hypothesis testing can proceed as before.
4 Econ 326 - Chapter 7 The figure below shows that, with δ > 0, the intercept dummy variable gives different, but parallel, regression lines for male professors and female professors. The vertical distance between the two lines is the amount δ . annual salary years of teaching experience female professor male professor
5 Econ 326 - Chapter 7 The parameters 1 β , 2 β and δ can be estimated by the least squares principle. Is there a ‘gender wage gap’ ? To test the claim that male professors earn more than female professors with the identical teaching experience consider: 0 : H 0 = δ against 0 : H 1 > δ This is a one-tail test. The test statistic is the t-statistic for a test of significance that is reported as a standard part of least squares (OLS) estimation output. If the coefficient on the gender dummy variable is positive then the p-value for this one-tail test is obtained by dividing the p-value for a two-tail test by 2. For a significance level of 0.05, if the p-value is less than 0.05 then the null hypothesis is rejected in favour of the alternative that male professors have higher salaries than female professors.
6 Econ 326 - Chapter 7 Another way to proceed is to define the gender dummy variable as: = male if female if 0 1 F i The dummy variable F can replace the dummy variable D in the salary determination equation.
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