Creative Destruction, Investment Volatility, and the Average Age of Capital

In this article, a new numerical procedure is used to compute the equilibrium of a vintage capital growth model with nonlinear utility, where the scrapping time is nonconstant. We show that equilibrium investment and output converge nonmonotonically to the balanced growth path due to replacement echoes. We find that the average age of capital is inversely related to output, which is consistent with recent micro evidence reinforcing the importance of the embodied question. We also find that an unanticipated permanent increase in the rate of embodied technological progress causes labor productivity to slowdown in the short run.     

Optimal regime switching and threshold effects

We consider a general control problem with two types of optimal regime switch. The first one concerns technological and/or institutional regimes indexed by a finite number of discrete parameter values, and the second features regimes relying on given threshold values for given state variables. We propose a general optimal control framework allowing to derive the first-order optimality conditions and in particular to characterize the geometry of the shadow prices at optimal switching times (if any). We apply this new optimal control material to address the problem of the optimal management of natural resources under ecological irreversibility, and with the possibility to switch to a backstop technology.     

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. Within this realistic framework, we first characterize long-term growth regimes driven by scarcity (induced-innovation) vs. long-term growth regimes driven by quota regulation (Porter-like innovation). More importantly, we study the interaction between scarcity and quota regulation. In particular, we show that there exists a threshold level for the growth rate of the resource price above which the Porter mechanism is killed while the scarcity-induced growth regime may emerge. Symmetrically, we also find that there must exist a threshold value for the environmental quota under which the growth regime induced by scarcity vanishes while the Porter-like growth regime may survive.     

Early Mortality Declines at the Dawn of Modern Growth*

We explore the hypothesis that demographic changes which began in the seventeenth and eighteenth centuries are at the root of the acceleration in growth rates at the dawn of the modern age. During this period, life tables for Geneva and Venice show a decline in adult mortality; French marriage registers reveal an important increase in literacy; historians measure an acceleration of economic growth. We develop an endogenous growth model with a realistic survival law in which rising longevity increases individual incentives to invest in education and fosters growth. We quantitatively estimate that the observed improvements in adult mortality account for 70% of the growth acceleration in the pre‐industrial age.     

History’s a curse: leapfrogging, growth breaks and growth reversals under international borrowing without commitment

A simple open-economy AK model with collateral constraints accounts for growth breaks and growth-reversal episodes, during which countries face abrupt changes in their growth rate that may lead to either growth miracles or growth disasters. Absent commitment to investment by the borrowing country, imperfect contract enforcement leads to an informational lag such that the debt contracted upon today depends upon the past stock of capital. The no-commitment delay originates a history effect by which the richer a country has been in the past, the more it can borrow today. For (arbitrarily) small delays, the history effect offsets the growth benefits from international borrowing and dampens growth, and it leads to both leapfrogging in long-run levels and growth breaks. When large enough, the history effect originates growth reversals and we connect the latter to leapfrogging. Finally, we argue that the model accords with the reported evidence on changes in the growth rate at break dates. We also provide examples showing that leapfrogging and growth reversals may coexist, so that currently poor but fast-growing countries experiencing sharp growth reversals may end up, in the long-run, significantly richer than currently rich but declining countries.     

How do epidemics induce behavioral changes?

This paper develops a theory of optimal fertility behavior under mortality shocks. In an OLG model, young adults determine their optimal fertility, labor supply and life-cycle consumption with both exogenous child and adult mortality risks. We show that a rise in adult mortality exerts an ambiguous effect on both net and total fertility in a general equilibrium framework, while child mortality shocks unambiguously lead to a rise in total fertility, leaving net fertility unchanged. We complement our theory with an empirical analysis using a sample of 39 Sub-Saharan African (SSA) countries over the 1980–2004 period, examining the overall effects of the child and adult mortality channels on both total and net fertility. We find child mortality to exert a robust, positive impact on total fertility but no impact on net fertility, whereas a rise in adult mortality is found to negatively influence both total and net fertility. Given the particular demographic profile of the HIV/AIDS epidemic (killing essentially young, active adults), we then conclude in favor of an unambiguous negative effect of the HIV/AIDS epidemic on net fertility in SSA.     

The Development Problem under Embodiment

This paper studies technology adoption in an optimal growth model with embodied technical change. The economy consists of the final good sector, the capital sector, and the technology sector which role is the imitation of exogenous innovations. Scarce labor resources are allocated to the technology and final good sectors. The final good is allocated to consumption and to the capital sector. The authors analytically characterize the long run optimal allocations. Using a calibrated version of the model, they find that an acceleration in the rate of embodied technical change should not be responded by an immediate and strong adoption effort. Instead, adoption labor should decrease in the short run, and the optimal technological gap is shown to increase either in the short or in the long run. The state of the institutions and policies around the technology sector is key in the design of the optimal adoption timing.     

Vintage capital and the dynamics of the AK model

This paper analyzes the equilibrium dynamics of an AK-type endogenous growth model with vintage capital. The inclusion of vintage capital leads to oscillatory dynamics governed by replacement echoes, which additionally influence the intercept of the balanced growth path. These features, which are in sharp contrast to those from the standard AK model, can contribute to explaining the short-run deviations observed between investment and growth rates time series. To characterize the optimal solutions of the model we develop analytical and numerical methods that should be of interest for the general resolution of endogenous growth models with vintage capital.     

A closer look at the relationship between life expectancy and economic growth

We first provide a nonparametric inference of the relationship between life expectancy and economic growth using historical data for 18 countries over the period 1820–2005. The obtained shape indicates convexity for low enough values of life expectancy and concavity for large enough values. We then study this relationship using a benchmark model combining "perpetual youth" and learning-by-investing. The generated relationship between life expectancy and economic growth is shown to be strictly increasing and concave. We finally examine two models departing from "perpetual youth" by assuming successively age-dependent earnings and age-dependent survival probabilities. With age-dependent earnings, the obtained relationship is hump-shaped, whereas age-dependent survival laws reproduce the convex–concave shape detected in prior empirical study.