Vintage capital growth theory: Three breakthroughs

Vintage capital growth models have been at the heart of growth theory in the 60s. This research line collapsed in the late 60s with the so-called embodiment controversy and the technical sophisitication of the vintage models. This paper analyzes the astonishing revival of this literature in the 90s. In particular, it outlines three methodological breakthroughs explaining this resurgence: a growth accounting revolution, taking advantage of the availability of new time series, an optimal control revolution allowing to safely study vintage capital optimal growth models, and a vintage human capital revolution, along with the rise of economic demography, accounting for the vintage structure of human capital similarly to physical capital age structuring. The related literature is surveyed.Vintage capital, embodied technical progress, growth accounting, optimal control, endogenous growth, vintage human capital, demography.

Vintage capital theory: Three breakthroughs

Vintage capital growth models have been at the heart of growth theory in the 60s. This research line collapsed in the late 60s with the so-called embodiment controversy and the technical sophisitication of the vintage models. This paper analyzes the astonishing revival of this literature in the 90s. In particular, it outlines three methodological breakthroughs explaining this resurgence: a growth accounting revolution, taking advantage of the availability of new time series, an optimal control revolution allowing to safely study vintage capital optimal growth models, and a vintage human capital revolution, along with the rise of economic demography, accounting for the vintage structure of human capital similarly to physical capital age structuring. The related literature is surveyed.Vintage capital; embodied technical progress; growth accounting; optimal control; endogenous growth; vintage human capital; demography.

Scarcity, regulation and endogenous technical progress

This paper studies to which extent a firm using a scarce resource input and facing environmental regulation, can still manage to have a sustainable growth of output and profits. The firm has a vintage capital technology with two complementary factors, capital and a resource input subject to quota, the latter being increasingly scarce through an exogenously rising price. The firm can scrap obsolete capital and invest in adoptive and/or innovative R&D resource-saving activities. We show that there exists a threshold level for the growth rate of the resource price above which the firm will collapse. Below this threshold, two important properties are found. In the long-run, a sustainable growth is possible at a growth rate which is independent of the resource price. In the short-run, not only will the firms respond to increasing resource price by increasing R&D on average, but they will also reduce capital expenditures and speed up the scrapping of older capital goods. Finally, we identify optimal intensive Vs extensive transitional growth regimes depending on the history of the firms.Vintage capital, technological progress, dynamic optimization, Sustainability, scarcity, environmental regulation

Optimal firm behavior under environmental constraints

The paper examines the Porter and induced-innovation hypotheses in a firm model where: (i) the firm has a vintage capital technology with two complementary factors, energy and capital ; (ii) scrapping is endogenous; (iii) technological progress is energy-saving and endogenous through purposive R&D investment; (iv) the innovation rate increases with R&D investment and decreases with complexity; (v) the firm is subject to emission quotas which put an upper bound on its energy consumption at any date; (vi) energy and capital prices are exogenous. Balanced growth paths are first characterized, and a comparative static analysis is performed to study a kind of long-term Porter and induced-innovation hypotheses. In particular, it is shown that tighter emission quotas do not prevent firms to grow in the long-run, thanks to endogenous innovation, but they have an inverse effect on the growth rate of profits. Some short-term dynamics are also produced, particularly, to analyze the role of initial conditions and energy prices in optimal firm behavior subject to environmental regulation. Among numerous results, we show that (i) firms which are historically “small” polluters find it optimal to massively pollute in the short run: during the transition, new and clean machines will co-exist with old and dirty machines in the productive sectors, implying an unambiguously dirty transition; (ii) higher energy prices induce a shorter lifetime for capital goods but they depress investment in both new capital and R&D, featuring a kind of reverse Hicksian mechanism.matching problem, von Neumann-Morgenstern stable sets, farsighted stability

Optimal firm behavior under environmental constraints

The paper examines the Porter and induced-innovation hypotheses in a firm model where : (i) the firm has a vintage capital technology with two complementary factors, energy and capital; (ii) scrapping is endogenous; (iii) technological progress is energy-saving and endogenous trough purposive R&D investment; (iv) the innovation rate increases with R&D investment and decreases with complexity; (v) the firm is subject to emission quotas which put an upper bound on its energy consumption at any date; (vi) energy and capital prices are exogenous. Balanced growth paths are first characterized, and a comparative static analysis is performed to study a kind of long-term Porter and induced-innovation hypotheses. In particular, it is shown that tighter emission quotas do not prevent firms to grow in the long-run, thanks to endogenous innovation, but they have an inverse effect on the growth rate of profits. Some short-term dynamics are also produced, particularly, to analyze the role of initial conditions and energy prices in optimal firm behavior subject to environmental regulation. Among numerous results, we show that (i) firms which are historically “small” polluters find it optimal to massively pollute in the short run : during the transition, new and clean machines will co-exist with old and dirty machines in the productive sectors, implying an unambiguously dirty transition; (ii) higher energy prices induce a shorter lifetime for capital goods but they depress investment in both new capital and R&D, featuring a kind of reverse Hicksian mechanism.matching problem, von Neumann-Morgenstern stable sets, farsighted stability

Optimal Firm Behavior under Environmental Constraints

The paper examines the Porter and induced-innovation hypotheses in a firm model where: (i) the firm has a vintage capital technology with two complementary factors, energy and capital ; (ii) scrapping is endogenous; (iii) technological progress is energy-saving and endogenous through purposive R&D investment; (iv) the innovation rate increases with R&D investment and decreases with complexity; (v) the firm is subject to emission quotas which put an upper bound on its energy consumption at any date; (vi) energy and capital prices are exogenous. Balanced growth paths are first characterized, and a comparative static analysis is performed to study a kind of long-term Porter and induced-innovation hypotheses. In particular, it is shown that tighter emission quotas do not prevent firms to grow in the long-run, thanks to endogenous innovation, but they have an inverse effect on the growth rate of profits. Some short-term dynamics are also produced, particularly, to analyze the role of initial conditions and energy prices in optimal firm behaviour subject to environmental regulation. Among numerous results, we show that (i) firms which are historically “small” polluters find it optimal to massively pollute in the short run: during the transition, new and clean machines will co-exist with old and dirty machines in the productive sectors, implying an unambiguously dirty transition; (ii) higher energy prices induce a shorter lifetime for capital goods but they depress investment in both new capital and R&D, featuring a kind of reverse Hicksian mechanism.Vintage capital, R&D, Emission quotas, Porter hypothesis, Induced innovation hypothesis, Optimization

Vintage capital growth theory : three breakthroughs

Vintage capital growth models have been at the heart of growth theory in the 60s. This research line collapsed in the late 60s with the so-called embodiment controversy and the technical sophisitication of the vintage models. This paper analyzes the astonishing revival of this literature in the 90s. In particular, it outlines three methodological breakthroughs explaining this resurgence: a growth accounting revolution, taking advantage of the availability of new time series, an optimal control revolution allowing to safely study vintage capital optimal growth models, and a vintage human capital revolution, along with the rise of economic demography, accounting for the vintage structure of human capital similarly to physical capital age structuring. The related literature is surveyed

Concavity in a vintage capital model with nonlinear utility

An optimization problem in an economic vintage capital model with nonlinear utility is investigated. It is described by non-linear Volterra integral equations with an unknown in the limits of integration. The concavity of the problem is proven, the condition for an extremum is established, and their relevance to applications is demonstrated. © 2005 Elsevier Ltd. All rights reserved