Question 1 (20 pts.) The gender gap in promotions An important awtion in economi

Question

Question 1 (20 pts.) The gender gap in promotions An important awtion in economics is whether Semale 'sole models help to reduce the grader gop in career peoon within orgmisations. To inestigate this idea, we couect data on 1500 employees who applied for proot ion within their firm. We will Socus on the Sollowing variables promotion 1 if the employee was promsoted Sollowing their pplication,therwise * fenale esployee if theeuwpkyve female, 0 otherwise esployee quality-A varialde measuring the "quairy othe employee based on their perfunnitice evaluation over the past ytur(thr varialsle mnMured from 0 to 10, with higher values indicating higher quality employees To teet the "role model effect, we specify a lit ir regresion with promotion as the dpen- dest variable, and fenale esployee, fesale sanager and esployee quality as independeurt ariabes We abo inclule the intrraction between fenale eaployee anad female sanager The equation for the model we estimate i kg* (1r,r) . o +A+"ployee quality, .tenale omployee. + -female manager,+ (female eaployee,.female manager.) where s, is the probability that Y-1 ( the employee ws promoted) for okeervation& The est males from the logiic rgssion aee shown in talbi 1 Table 1: Logstic regression for employee promot ion Promotio Eamgployee Quality Frmak Employee Female Manage Frmak Eployee Female Manage Constant (0036) (0.276) (0.470) 1 500 Liarlsbood em 2017 I. What is the null hypot hesis foe the internction teem A 2, whicbcoeffirints are signifiantly diferent from·zero at the 95% conseme level? 3. Ihrnle the effotof eaployee qualityProaatsonusithwconcept cdmodderdb 4. Dirrile the effretsof being fesa1e opleyee on promotion u odbratios . Coleulate the predieted probability of peomotion for the folowing types of eespondent * A kinde employee, with an employment quality of 6, working with mak manager * A-ale employee, withpkoymett qualityof6, working wit a male manager

Explanation / Answer

Part 1.

Null hypothesis: There is no relation b/w promotion and gender of employee or manager or employee quality

Alternative hypothesis: There is a relation b/w promotion and gender of employee or manager or employee quality

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Part 2.

To find estimates that are significantly different to zero (0) @ 95% confidence interval, calculate Z-statistic

Z-stat_coeff = (estimate_coeff - 0)/(std_dev_coeff)

1. Emp. Quality: 0.326/0.036 = 9.0556 (Significantly different)

2. Female employee: -1.318/0.204 = -6.461 (Significantly different)

3. Female manager: 0.085/0.276 = 0.308 (NOT Significantly different)

4. Female employee, Female manager: 0.983/0.47 = 2.0915 (Significantly different)

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Part 3. and Part 4.

Let's say there are n independent variables: (X1, X2, ..., Xn). The exponential function of the regression coefficients (e^bn) is the odds ratio associated with a one-unit increase in the exposure/independent_variable Xn.

Employee quality: 0.326 increase in odds-ratio given a one-unit increase in Employee quality

Female employee: 1.338 decrease in odds-ratio if employee is a Female

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Part 5)

Case a): Female, 6, Male manager

Case b): Male, 6 Male manager

emp q man emp*man constant Case a 1 6 0 0 1 Case b 0 6 0 0 1 Beta -1.338 0.326 0.085 0.983 0.977 Equation result Exponential Value of pi Case a 1.595 4.92832907 0.8313184 [Ans. 5 a] Case b 2.933 18.7838977 0.9494538 [Ans. 5 b]

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