Equilibrium holdings distributions in durable asset markets

The stock of durable goods can be represented by its holdings distribution, defined as the joint distribution of age and physical condition of the population of durable goods. This paper derives the holdings distribution which arises under stationary conditions when durable goods deteriorate according to a Markov process. We show that given the scrappage and utilization decisions of consumers, the holdings distribution F(x) is an equilibrium distribution of an associated regenerative Markov process. Using a basic result from the theory of regenerative stochastic processes, we characterize F(x) as the ratio of the expected number of periods the durable's condition is better than x to the expected lifetime of the asset. Using data from the 1977 National Transportation Survey we illustrate these results by estimating a simple two-parameter model of automobile deterioration and comparing the implied distribution of automobile holdings to the actual distribution.