The Dynamics of Car Sales: A Discrete Choice Approach

Mankiw [1982] explores the Permanent Income Hypothesis implication that durable expenditures follow an ARMA(1,1) representation. He finds that durable expenditures are represented by an AR(1) process which implies that the rate of depreciation of durables, under the PIH model, is 100%. This finding presents a puzzle. Our paper builds on earlier work which attempts to explain this puzzle by considering the aggregation of the discrete dynamic choices of heterogeneous households. We implement this approach by estimating a dynamic discrete choice model of car replacement. We find that through aggregation we can explain both the AR and MA components of Mankiw's results. Further we find that our model is able to match a VAR representation of car sales, prices and income. We find that most of the variation in car sales is due to shocks which influence the replacement probability.