Raouf Boucekkine

Vintage Human Capital, Demographic Trends and Endogenous Growth

We study how economic growth is affected by demographics in an overlapping generations model with a realistic survival law. Individuals optimally chose the dates at which they leave school to enter the labor market and at which they retire. Endogenous growth arises thanks to the accumulation of generation-specific human capital. Favorable shifts in the survival probabilities always induce longer schooling and later retirement but have an ambiguous effect on growth. The relationship between the growth of population and per-capita growth is hump-shaped. Increases in longevity can be responsible for a switch from a no-growth regime to a sustained growth regime and for a positive relationship between fertility and growth to vanish.

An alternative methodology for solving nonlinear forward-looking models

This paper presents a new methodology for solving nonlinear deterministic forward-looking models. Based on a relaxation algorithm described by Laffargue (1990), the methodology is theoretically founded on a general multivariate linear model. Then, a complete experimental scheme is provided in the nonlinear case, including solution time horizon selection and saddlepoint path testing strategies. The proposed experiment is mathematically robust and it does not require any expert knowledge in numerical analysis. It is especially adapted to the simulation exercises conducted on medium scale economic models.

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.

Special Functions for the Study of Economic Dynamics: The Case of the Lucas-Uzawa Model

The special functions are intensively used in mathematical physics to solve differential systems. We argue that their use should be most useful in economic dynamics, notably in the assessment of the transition dynamics of endogenous growth models. We illustrate our argument on the Lucas-Uzawa model, which we solve by the means of Gaussian hypergeometric functions. We show how the use of Gaussian hypergeometric functions allows for an explicit representation of the equilibrium dynamics of the variables in level. In contrast to the preexisting approaches, our method is global and does not rely on dimension reduction.

Differential-difference equations in economics: On the numerical solution of vintage capital growth models

In this papel, we examine techniques for the analytical and numerical solution of statedependent differential-difference equations. Such equations occur in the continuous time modelling of vintage capital growth models, which form a particularly important class of models in modern economic growth theory. The theoretical treatment of non-statedependent differential-difference equations in economics has already been discussed by Benhabib and Rustichini (1991). In general, though, the state-dependence of a model prevents its analytical solution in all but the simplest of cases. We review a numerical method for solving state-dependent models, using sorne simple examples to illustrate our discussion. In addition, we analyse the Solow vintage capital growth model. We conclude by mentioning a crucial unresolved issue related to this topic.

Embodied technological change learning-by-doing and the productivity slowdown

The productivity slowdown faced by the US economy since the first oil shock has been associated with a rise in the decline rate of the relative price of equipment and a reduction in the rate of disembodied technical change. We build up a growth model in which learning-by-doing is the engine of both embodied and disembodied technological progress. A change in the relative efficiency of learning-by-doing from the consumption to the investment sector is shown to imply a technological reassignment consistent with the above mentioned evidence. This result derives from the interaction between the obsolescence costs inherent to embodiment and the learning-by-doing engine.

MODELLING VINTAGE STRUCTURES WITH DDEs: PRINCIPLES AND APPLICATIONS*

A comprehensive study of the linkages between demographic and economic variables should not only account for vintage specificity but also incorporate the relevant economic and demographic decisions in a complete optimal control set-up. In this paper, a methodological set-up allowing to reach these objectives is described. In this framework, time is continuous but agents take discrete timing decisions. The mixture of continuous and discrete time yields differential-difference equations (DDEs). This paper shows clearly that the approach allows for a relatively complete and rigorous analytical exploration in some special cases (mainly linear or quasi linear models), and for an easy computational appraisal in the general case.

BRIDGING THE GAP BETWEEN GROWTH THEORY AND THE NEW ECONOMIC GEOGRAPHY: THE SPATIAL RAMSEY MODEL

We study a Ramsey problem in infinite and continuous time and space. The problem is discounted both temporally and spatially. Capital flows to locations with higher marginal return. We show that the problem amounts to optimal control of parabolic partial differential equations (PDEs). We rely on the existing related mathematical literature to derive the Pontryagin conditions. Using explicit representations of the solutions to the PDEs, we first show that the resulting dynamic system gives rise to an ill-posed problem in the sense of Hadamard. We then turn to the spatial Ramsey problem with linear utility. The obtained properties are significantly different from those of the nonspatial linear Ramsey model due to the spatial dynamics induced by capital mobility.

Energy saving technical progress and optimal capital stock: the role of embodiment

We study optimal capital accumulation at the firm level when technical progress is energy saving. Energy and capital are complementary. First we solve a benchmark case with disembodied technical progress. Then, we turn to the model with embodiment. We characterize the optimal replacement of obsolete capital, and the optimal capital stock. The latter is shown to be lower under embodiment compared to the benchmark case. Moreover, we demonstrate that a rising energy price has two opposite effects on the optimal capital stock under embodiment: the traditional direct negative effects, but also an indirect positive effect via the optimal scrapping rule. Nevertheless, the optimal capital stock is shown to remain a decreasing function of the energy cost.

Imbalance Effects in the Lucas Model: An Analytical Exploration

In this note, we extend Xie (JET, 1994) to solve analytically the Lucas model with a weak externality in a specific parametric case. In particular, we characterize the shape of imbalance effects in this model. Our results are mostly consistent with the findings of the related computational literature. Among other analytical findings, we prove that, while U-shaped imbalance effects are not apparent in the Lucas model for the growth rate of output per capita, the level of such a variable may exhibit this shape.