Estimation of a Markov Model of Loan Seasoning with Aggregated Performance Data

Robert B. Avery and Michael Gordy - Federal Reserve Board

The performance of a portfolio of bank loans is widely understood to depend not only on the quality of the constituent loans, but also on macroeconomic conditions. Much less is known on the possible dependence of the performance of a loan portfolio on its age structure. Bank regulators have long been concerned with the possibility that rapid growth in lending, which increases the concentration of new loans, could temporarily lower the measured delinquency ratio of a loan portfolio below the "steady state" delinquency ratio commensurate with its underlying quality. This would be the case, in particular, if the delinquency hazard is systematically lower early in the life of a loan. More generally, the hazard rate for delinquency may vary nonlinearly with loan age. We will refer to the passage of a loan through its lifecycle as loan seasoning.

Despite its relevance to bankers and regulators, information on loan seasoning is anecdotal, at best, for Commerical and Industrial (C & I) loans, which form the main category of lending to business. One important obstacle to estimation of a hazard model for C & I loans is that there are no available cohort performance data. This paper develops and implements a method of hazard estimation which makes use of a sparse information set. We specify a Markov model in which the probability of transitting from a "performing" state to a "delinquent" state is conditioned on loan age and macro variables. Estimation requires bank level time-series data on new loan issuance and on bank level aggregate (i.e., aggregatedacross cohorts) stocks of performing and delinquent loans.

We find a robust and economically significant pattern of loan seasoning, as well as intuitively plausible macroeconomic effects, in transitions to delinquency. The estimated model is used to generate a variety of impulse-response simulations of bank performance following periods of rapid expansion or contraction in lending.

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