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PUBLG100A Introduction To Quantitative Research Methods

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Question:

An important question in economics is whether female ‘role models’ help to reduce the gendergap in career progression within organisations. To investigate this idea, we collect data on 1500 employees who applied for promotion within their firm. We will focus on the following variables: 
• promotion – 1 if the employee was promoted following their application, 0 otherwise
• female employee – 1 if the employee is female, 0 otherwise
• female manager – 1 if the employee’s manager is female, 0 otherwise
• employee quality – A variable measuring the “quality” of the employee based on their performance evaluations over the past year (the variable is measured from 0 to 10, with higher values indicating higher quality employees).

To test the ‘role model’ effect, we specify a logistic regression with promotion as the dependent variable, and female employee, female manager and employee quality as independent variables. We also include the interaction between female employee and female manager.The equation for the model we estimate is:
= α + β1 ∗ employee qualityi +
β2 ∗ female employeei +
β3 ∗ female manageri +
β4 ∗ (female employeei
∗ female manageri

the probability that Y = 1 (i.e. the employee was promoted) for observation i. The estimates from the logistic regression are shown in table 1.
 
1. What is the null hypothesis for the interaction term β4
2. Which coefficients are significantly different from zero at the 95% confidence level
3. Describe the effect of employee quality on promotion using the concept of an odds-ratio
4. Describe the effects of being a female employee on promotion using odds-ratios
5. Calculate the predicted probability of promotion for the following types of respondent:
• A female employee, with an employment quality of 6, working with a male manager
• A male employee, with an employment quality of 6, working with a male manager.
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