Technological Progress, Obsolescence and Depreciation

Abstract

We construct a vintage capital model à la Whelan (2002) with both exogenous embodied and disembodied technical progress, and variable utilization of each vintage. The lifetime of capital goods is endogenous and it relies on the associated maintenance costs. We study the properties of the balanced growth paths. First, we show that the lifetime of capital is an increasing (resp. decreasing) function of the rate of disembodied (resp. embodied) technical progress. Second, we show that both the use-related depreciation rate and the scrapping rate increase when embodied technical progress accelerates. However, the latter drops when disembodied technical progress accelerates while the former remains unaffected. A key feature of our model is that the age-related depreciation rate does depend on the obsolescence rate in sharp contrast to the neoclassical model.

Optimal pattern of technology adoptions under embodiment: A multi‐stage optimal control approach

“…The welfare cost of this drop in the consumption level is referred to as obsolescence costs and they are shown to be non‐negligible (see 4–6). In addition to these obsolescence costs inherent to embodiment, switching to a newer technology induces an accelerated erosion effect on physical capital (see 7, 8) and a slow adjustment process for reaching the best productivity level of the new technology. This posits a trade‐off between the improvement in the efficiency of investment, referred to as growth rate advantage and the adjustment cost of technology adoption together with obsolescence inherent to embodiment.…”

Role of Endogenous Vintage Specific Depreciation in the Optimal Behavior of Firms

“…However, these papers, assuming a homogenous stock of capital goods, could not explore the linkages between investment and maintenance expenditures directed towards each available vintage and, hence, provide answers to the questions (ii)–(iv). Boucekkine, Rio, and Martinez (2005), concerned with the economic performances at the aggregate level, analyze question (iii) and determine that an increase in embodied technical progress increases the depreciation rate, which in turn reduces the operating lifetime of capital goods. As the analysis does not allow for the possibility to invest in older capital goods, the trade‐off between investing in new versus the existing capital goods and the maintenance of these goods have not been taken into consideration.…”

“…Embodied technological progress is both quantitatively and qualitatively one of the most important features of investment dynamics (see Greenwood et al 1997). As mentioned in Boucekkine, del Rio, and Martinez (2005), a technological acceleration induces two opposite effects: an incentive to reduce maintenance and scrap earlier to profit from the increased efficiency of new vintages but also as an incentive to increase maintenance and delay scrapping due to a drop in the profitability of investment. The above proposition resolves this trade‐off analytically so that the maintenance appears to be a substitute of technological growth.…”

Vintage capital and the diffusion of clean technologies

“…However in our model, an increase in γ raises the equilibrium interest rate by , which diminishes the marginal return from investing. As in Boucekkine et al (1998), and more recently in Boucekkine et al (2009), this negative effect is more than compensated by the positive one as long as the interest burden is bounded over the lifetime of machines, for example when γ T ≤ 1 (see the Appendix). Hereafter, we shall assume that we are only considering the parameterizations such that the latter property holds 9…”