Question

Applications : The Logit Model )

Suppose that you've been hired to work as an analyst at a credit card department of a major bank.

Your job is to analyse the historical card sales data, and to make recommendations to the management team.

Suppose that in the past, your bank has been offering a choice of five credit cards, each with different level of annual interest and fees. Using the historical sales data, you estimated the following Logit model (using WLS):

P(Yi = 1/X2i,X3i) = 1 / 1 + exp(−(β1 + β2X2i + β3X3i + ui))

where Yi = 1 indicates that an individual subscribed for card i, X2i is the annual interest (in %) for card i, and X3i are the annual fees (in $) for card i, i = 1,...,5. That is, there are n = 5 observations in this grouped sample. The WLS estimates of model coefficients are shown in Table 1.

Coefficient Estimate St. Error P-value

  

β1 0.199 0.065. 0.003

β2 -0.036 0.093 0.001

β3 -0.001 0.002. 0.756

a) In percentage terms, approximately by how much would the odds of signing up change as a result of a one percent increase in annual interest?

(B) With 95% confidence, in percent terms, by at least how much would the odds of signing up change as a result of a one percent increase in annual interest?

C) How would the probability of signing up a person for a credit card with 15% annual interest and $75 annual fees change is you were to increase interest by 1%, to 16% per year, leaving the annual fees unchanged?

D) Suppose that your bank is considering offering a brand new credit card with an annual interest rate of 12% and no annual fee. Describe how using your model and estimates you could test the hypothesis that on average, 60 out of every 100 individuals to whom this card will be offered will subscribe for this card.

Answer 1