Explanation of computation of the risk set at each time period. This explanation won’t be needed until a few slides ahead, but I put it here because the visual image helps us understand the idea. At time 1 (one year) the number of accounts in the risk set is the number in all 18 bars added together. Imagine stacking all the bars on top of the 456 accounts that are uncensored and that closed after 1 year. The “hazard probability’ of experiencing the event of importance (closing) is 456/total of all bars or 456/3941. At each time period up until period 7 (these accounts have been open 7 years) we compute the “hazard probability” the same way, by dividing the number of accounts that close that year (red bar) by all the sum of all the remaining bars…the red and yellow bars for that time period (here it is year 7) plus all those to the right of that time period. The odd thing that happens, however, when we go from period 7 to period 8 is the censored cases from period 7 seem to suddenly disappear from the numerator of the hazard probability coefficient. Why? Because these accounts are no longer in the risk set. But they didn’t drop out of the risk set because of closed accounts, they dropped out of the risk set because they were part of a later cohort that was only studied for 7 years.
You can see on this graph that hazard probability gets smaller as people keep the account open longer. In other words, the risk of closing an account is about 12% after the first year, but drops to about 1% after 12 years.
Median lifetime survivor probability can be found by drawing a horizontal line across the graph at .5 survivor probability. When you hit the survivor function, drop a line straight down the duration of accounts at this point (6.6) is the median lifetime survivor probability of accounts for this sample. In other words, half of the accounts will “survive” this long. And this includes the information about the censored accounts (the ones that are still open at the time when we stopped gathering our observations.)
Core deposits sensitivity and survival analysis
Sensitivity and Survival
Sept. 13, 2010
Research question 1a
• Question 1a.
How can we visually summarize account duration?
Research question 1b
• Question 1b. How can we predict the length of time a
person will keep a core account open (account duration)?
We cannot simply compute an average of account
durations because we do not know how far into the future
current accounts will “survive.” Simple means will
produce a negatively biased estimate.
• Perhaps we can revise our question to read, “What is the
probability a person will keep an account open for a
specific period of time?” This new question allows us to
use survival analysis, hazard probabilities, and risk
functions to get a detailed picture of account duration.
Question 1b (continued)
• Can we create a model using time and other
indictors (e.g. interest rate or change in the interest
rate on the account) as predictors of account
duration? This is a more sophisticated question for
another time…food for thought for now…
• 1c – How can we summarize typical account
duration with a single index? Remember means and
other simple average indices will not do the trick
because we do not know how long accounts will stay
What is the best statistical tool for
answering each question?
• Question 1a – to visually summarize duration use a
histogram of the frequency of duration for censored
and uncensored accounts. I’ll show you how to do
• Question 1b - To predict duration, use survival
• Question 1c – for a single index, we can use median
lifetime survival probability…more on this…
Background for Study
• 1. Use a multi-cohort analysis such as accounts
opened between 1972 and 1977 and studied until
• 2. Measure duration of each account.
• 3. Predict length of time until a given event, in this
case, closing of the account.
• 4. Some people will not close the account within the
time period of observation. These people (accounts)
are considered to be censored.
Research Question 2
for Next Time…
• Question 2. How can we predict core deposit interest
• A. from prime interest rate?
• B. from market interest rate?
• 1. Can we predict core deposit interest rate from 3 month
LIBOR (one index of market interest rate)?
• 2. from lagged LIBOR indices?
• 3. Are there other market interest rate indices we want to
include to predict core deposit interest rate?