I have panel data from 2002-2016 on approximately 5000 firms. I would like to run a proportional hazards model to estimate the likelihood that the firm is sold (DV) due to regulatory violations (IV). Many of the firms in the sample existed prior to 2002, however, the agency responsible for collecting this data started doing so in 1997. Therefore, firms that existed prior to 1997 are coded as 1/1/1901 which isn't accurate. The issue is that when setting the time variable, I would like to set it to the actual age of the firm and not when it enters the sample (2002). Given that I cannot observe the actual date the firm was created, how can I control for the unobserved & potentially different longevities the companies?
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