One attribute of consumer loans which is thought to play a role in consumer takeup is the maturity, defined as the number of months over which the loan must be paid back. A longer maturity, for a fixed loan size and interest rate, means that the monthly repayment required is lower.

In the experiment, the firm sent out letters to potential borrowers offering a loan of a specified amount and interest rate, for which they were invited to apply at the local branch. For a selected subset of these letters, sent to a group of 3096 low or medium risk customers, the offer also included a suggested maturity of either 4 months, 8 months, or 12 months, for which they were invited but not obligated to apply. The maturity length suggestion was assigned randomly within this group, independent of any other loan or customer attributes.

To see the extent to which consumers might be responding to the suggestion, we can compare the number in each group who ended up taking out a loan with 12 month maturity, which we measure by a variable term12mon which equals 1 if a 12 month maturity loan was actually taken out and 0 otherwise. Among these customers, 1565 received a suggested maturity of 4 months, among whom 27 took out a 12 month loan, 785 received a suggested maturity of 6 months, among whom 8 took out a 12 month loan, and 746 received a suggested maturity of 12 months, among whom 26 took out a 12 month loan.

(a) Use the above numbers to provide an estimate of the average treatment effect among low or medium risk customers of this bank of receiving a suggested maturity of 12 months instead of a suggested maturity of 4 months on the probability of taking out a 12 month loan.

Explain why this estimate can be interpreted as a causal effect.

(b) For a variety of promotion attributes, the authors run a balance test, regressing the randomized offer attribute on pre-offer characteristics of individuals who received an offer, such as gender, marital status, age, education level, rural location, number of children, and gross income. Consider such a regression in which termshown12, a variable equal to 1 if the customer was shown a 12 month maturity and 0 otherwise, is regressed on these attributes for customers in the sample receiving a randomized maturity length.

Given that the suggestions are assigned randomly, should we be surprised if one finds that a joint hypothesis test of the hypothesis that all of the coefficients on these predictors are 0 rejects this null? Why or why not?