Journal of Risk Model Validation

Statistical properties of the population stability index

Bilal Yurdakul and Joshua Naranjo

  • Population stability index is currently being used in the industry as a traffic light by employing 0.10, 0.25 as critical values. However, this use does not have any support or references in the academic world.
  • Population stability index has intimate relationship with KL Divergence, consequently has similar statistical properties.
  • Population stability index has an asymptotic distribution with expected value and variance depending on the number of bins and sample size of both base and target populations.
  • Under null hypothesis, both samples are coming from the same underlying distribution, PSI does not move easily away from 0.
  • Correct way of using PSI should consider sample sizes and number of bins.

The population stability index (PSI) is a widely used statistic that measures how much a variable has shifted over time. A high PSI may alert the business to a change in the characteristics of a population. This shift may require investigation and possibly a model update. PSI is commonly used among banks to measure the shift between model development data and current data. Banks may face additional risks if models are used without proper validation. The incorrect use of PSI may bring unexpected risks for these institutions. However, there are not many studies about the statistical properties of PSI. In practice, the following “rule of thumb” is used: PSI < 0.10 means a “little change”, 0.10 < PSI < 0.25 means a “moderate change”, and PSI > 0.25 means a “significant change, action required”. These benchmarks are used without reference to statistical type I or type II error rates. This paper aims to fill the gap by providing statistical properties of the PSI and some recommendations on its use.

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