Michael J. Harper (1982) "The Measurement of Productive Capital Stock, Capital Wealth, and Capital Services"

In order to construct measures of multifactor productivity, the Bureau of Labor Statistics has investigated a number of issues. This paper discusses several related to the vintage aggregation of capital: a primary step in the measurement of capital input. Unless a capital good's efficiency declines geometrically, its price as it ages will follow a different schedule than its efficiency. The price schedule can be calculated if we assume an efficiency schedule, a discount rate, and the vintage aggregation conditions. Capital services are proportional to a "productive stock" constructed from a perpetual inventory calculation using the age/efficiency schedule. The wealth represented by all assets is consistently estimated by doing a similar calculation using the corresponding age/price schedule. Attempts in the literature to establish that age/efficiency schedules are geometric by studying used asset prices fall short of doing so, because very different age/efficiency schedules can generate very similar age/price profiles. Arguments which rationalize the use of the geometric assumption even when efficiency does not decay geometrically lack merit. All things considered, there is little evidence regarding which age/efficiency pattern is correct, but mounting evidence that the vintage aggregation conditions are badly violated.