potential customers ratings depend B u s i n e s s F i n a n c e
Your firm just launched a new product and has solicited a large number of potential customers to rate its effectiveness between 0 and 100. You are particularly interested in how an individual’s rating of the new depends on his/her age. To estimate this effect, you divide the potential customers into age groups: under 25, 26 – 40, 41 – 55, and over 55. You then assume the following data-generating process:
Ratingi = α + β1Age25i + β2Age2640i + β3Age4155i + β4Age55i +Ui
Here, each Age variable is a dichotomous variable that equals 1 if individual i belong to that age group and 0 otherwise.
- Create the dichotomous variables: Age25, Age22640, Age4155, Age55.
- Why are you unable to estimate the effect of each age group as listed?
- Estimate and interpret the effect of changing age groups on the Rating.
You’ve decided to expand your analysis from Problem 1, and he would like to learn how potential customers ratings depend on both age and income. To perform this analysis, you decided to treat both Age and Income as continuous, rather than categorical variables. Consequently, you assume the following data-generating process:
Ratingi = α + β1Agei +β2Incomei +Ui
- Regress Rating on Age and Income, and comment on the significance of each independent variable.
- Provide evidence that there is imperfect multicollinearity in your regression results and discuss the consequences.
- How might you remedy the imperfect multicollinearity that exists in this dataset?
Your firm is attempting to determine the effect of sensitivity training on employee behavior. To do so, it has collected data for each employee on the number of times he/she has been reprimanded for insensitive behavior in the past year (Reprimandsi) and whether that employee receives sensitivity training the prior year (Trainingi). When regressing Reprimands on Training, the estimated effective training is an average reduction in Reprimands of 0.21.
- Argue why Training is likely endogenous in this regression.
- What is the likely sign of the bias in your estimated effect of Training on Reprimands?