Aggregation of producer durables with exogenous technical change and endogenous useful lives

Abstract

The received theory of aggregation of producer durables has been erected on certain fundamental hypotheses. One of them is that producer durables deteriorate exponentially, which implies that their replacement is proportional to the corresponding capital stocks. However the proportionality hypothesis conflicts with most of the available theoretical and empirical evidence. So an effort to relax it is long overdue. To this end the present paper investigates the conditions for aggregation in a two-sector vintage capital model with exogenous technological change and endogenous useful lives. In the model aggregation is achieved by adapting the procedure first suggested by Haavelmo [11]. From the simulations of the solution with data from the United States in the post-war period it is found that the conventional approach to aggregation may be responsible for significant biases in the measurement of capital stocks.