شکل گیری سرمایه انسانی و عملکرد اقتصاد کلان در یک اقتصاد باز کوچک قدیمی

We study the effects of stylized demographic and fiscal shocks on the macroeconomic performance of an industrialized small open economy. We construct an overlapping-generations model which incorporates a realistic description of the mortality process. Agents engage in educational activities at the start of life and thus create human capital to be used later on in life for production purposes. Simple and intuitive expressions are derived which demonstrate the key economic and demographic mechanisms that are operating in the model. The engine of growth during the demographic transition is an intergenerational externality in the production of human capital. In a calibrated version of our model, we find that the effects of increased longevity on human capital formation are small whereas the reduction in fertility has a rather strong effect.

The western world is ageing rapidly. Since the postwar period, the ageing process can be attributed both to increased longevity and reduced fertility (Lee, 2003). For example, in the Netherlands, life expectancy at birth rose from 71.5 years in 1950 to 78.5 years in 2000, whilst the annual (crude) birth rate fell from 2.3% to 1.3% of the population. Because infant mortality stayed relatively constant during that period (at 0.8% of the population), the increase in longevity must be attributed to reduced adult mortality (Vaupel, 1997). A similar demographic pattern can be observed for most OECD countries. The objective of this paper is to investigate the effects on the macroeconomic performance of a small open economy of demographic shocks of the type and magnitude mentioned above. It must be stressed from the outset that we restrict attention to the study of advanced industrial economies of small size having access to well-functioning markets including the world capital market. Our study is thus intended as a contribution to the field of open-economy macroeconomics.1 We formulate a simple analytical growth model in which finitely lived agents accumulate both physical and human capital. Our analysis makes use of modeling insights from two main bodies of literature. First, in order to allow for demographic shocks, we employ the generalized Blanchard-Yaari overlapping-generations model reported in our earlier paper (Heijdra and Romp, 2008a). In this model disconnected generations are born at each instant and individual agents face a positive and age-dependent probability of death at each moment in time. By making the mortality rate age-dependent, the model can be used to investigate changes in adult mortality.2 The second building block of our analysis concerns the engine of growth during the demographic transition and possibly also in the long run. Following Lucas (1988), we assume that the purposeful accumulation of human capital forms the core mechanism leading to economic growth. More specifically, like Bils and Klenow (2000), Kalemli-Ozcan et al. (2000), de la Croix and Licandro (1999) and Boucekkine et al. (2002) we assume that individual agents accumulate human capital by engaging in full-time educational activities at the start of life. The start-up education period is chosen optimally by each individual and labor market entry is assumed to be irreversible. Depending on the parameter setting, the human capital production function (or training function) may include an intergenerational external effect of the ‘shoulders of giants’ variety, as first proposed in an overlapping generations context by Azariadis and Azariadis and Drazen (1990). With an operative externality, an individual's training function depends positively on the economy-wide stock of human capital per worker in that individual's birth period. In our model, the strength of the intergenerational spillover is regulated by a single non-negative parameter, φφ. Unfortunately, there is no consensus regarding the appropriate magnitude of this φφ. For example, Kalemli-Ozcan et al. (2000) abstract from the intergenerational spillover altogether and thus set φ=0φ=0. In contrast, Bils and Klenow (2000) set 0<φ<10<φ<1, and thus assume that the externality is operative but subject to diminishing returns. Finally, de la Croix and Licandro (1999), Boucekkine et al. (2002), Echevarría (2004) and Echevarría and Iza (2006) consider the knife-edge case with φ=1φ=1. In our theoretical model, we generalize the existing literature by allowing the spillover parameter to take on any value between zero and unity (0⩽φ⩽10⩽φ⩽1). Our paper is structured as follows. In Section 2 we present the model and analytically demonstrate its main properties. A unique solution for the optimal schooling period is derived which depends on fiscal parameters and on the mortality process. For a given initial level of per capita human capital, the model implies a unique time path for all macroeconomic variables. Depending on the strength of the intergenerational external effect, the model either displays exogenous growth (0⩽φ<10⩽φ<1) and ultimate convergence to constant per capita variables, or endogenous growth (φ=1φ=1) and convergence to a constant growth rate. Our model, and indeed the closely related one by Boucekkine et al. (2002), is analytically tractable because the interest rate is held constant, making the system block recursive. Boucekkine et al. achieve constancy of the interest rate by assuming that the felicity function is linear, i.e. that the intertemporal substitution elasticity is infinite. Apart from its empirical implausibility, this assumption has the unattractive implication that individual consumption profiles are indeterminate. In contrast, we attain tractability by assuming a small open economy facing a constant world interest rate. This allows us to postulate a concave felicity function, which gives rise to well-defined consumption profiles, both individually and in the aggregate. Our model thus fully determines unique transition paths for all macroeconomic variables of interest, including the current account of the balance of payments. In Section 3 we investigate the effects of once-off demographic changes on the population growth rate, both at impact, during transition, and in the long run. We estimate the Gompertz–Makeham (G–M) mortality process, employing data for the Dutch cohorts born in the period 1920–2000, and use it to illustrate the rather complicated (cyclical) adjustment path resulting from once-off demographic changes. Especially for the cohort-specific mortality shock, convergence toward the new steady state is extremely slow. Indeed, due to the vintage nature of the population, more than a century passes until the new demographic steady state is reached. In Section 4 we study the determinants of the optimal schooling decision in detail. An increase in the educational subsidy or the labor income tax leads to an increase in the length of the educational period. Similarly, a reduction in adult mortality also prompts agents to increase the schooling period. In the absence of retirement, such a shock lengthens the post-school period and increases the pecuniary benefits of schooling. In contrast, a reduction in child mortality has no effect on the optimal schooling period. Such a shock increases the probability of surviving the schooling period, but has no effect on the length of the working period. Finally, a baby bust also leaves the optimal schooling period unchanged because it has no effect on the individual's optimization problem. Unlike Boucekkine et al. (2002), who use a specific functional form for the mortality process, we reach our analytical conclusions using a general specification for the mortality process. Section 5 deals with the exogenous growth model, which, on the basis of the empirical evidence, we consider to be the most relevant one. Indeed, using the recent empirical study by de la Fuente and Doménech (2006), we argue that a plausible value for the intergenerational externality parameter, φφ, lies between 0.27 and 0.40, i.e. nowhere in the vicinity of the knife-edge case considered by Boucekkine et al. (2002) and others. The factual evidence points firmly in the direction of positive but strongly diminishing returns to the intergenerational external effect.3 In Section 5 we also study the (impact, transitional, and long-run) effects of fiscal and demographic changes on per capita human capital and the other macroeconomic variables. A positive fiscal impulse leads to an increase in the per capita stock of human capital but leaves the steady-state growth rate of the macro-variables in level terms unchanged (and equal to the steady-state population growth rate). Furthermore, a reduction in the birth rate and an increase in longevity (due to reduced adult mortality) both increase the steady-state per capita human capital stock but have opposite effects on the population growth rate. Using a plausible calibration of the model, we demonstrate that the effects of the baby bust on human capital and the labor force participation rate are quantitatively significant. In stark contrast, even a rather large longevity shock hardly affects these variables at all. The effect is much larger for the baby bust because the drop in the population growth rate reduces required human capital investment (i.e. human capital investment that is needed to endow each newborn worker with the same amount of this type of capital). In contrast, for the longevity boost, the schooling effect increases human capital per worker but the slight increase in the population growth rate decreases it somewhat, rendering the total effect small. In our numerical analysis we extend the literature in that we are able to compute the transitional dynamics also for shocks affecting the optimal schooling period (such as the fiscal and longevity shocks). In contrast, Boucekkine et al. (2002, pp. 363–365), only show the adjustment path in the (endogenous) growth rate following a drop in the birth rate. Such a shock leaves the optimal schooling period unchanged, so that all transitional dynamics is entirely attributable to changes in the growth rate of the population. In our model we find that, for all shocks considered, the transitional adjustment is rather slow and often non-monotonic. In Section 6 we present some concluding thoughts and give some suggestions for future research. A brief appendix contains the key mathematical derivations.

We have studied how fiscal incentives and demographic shocks affect the macroeconomic performance of a small open economy populated by disconnected generations of finitely lived agents facing age-dependent mortality and constant factor prices. Among other things, the paper highlights the crucial role played by the strength of the intergenerational external effect in the training function faced by individual agents. Provided this external effect is non-zero, as the empirical evidence suggests, the vintage nature of the model gives rise to very slow and rather complicated dynamic adjustment. This feature of the model may help explain why robust empirical results linking education and growth have been so hard to come by. Provided the intergenerational externality parameter is below the knife-edge value of unity, the stock of per capita human capital settles at a constant level in the long run. In the long run, growth in consumption, investment, output, employment, and human and physical capital is entirely due to population growth, just as in the celebrated Solow–Swan model. Fiscal incentives and demographic shocks, though causing permanent level effects, thus produce temporary (but long-lasting) growth effects in per capita terms. The model's main message is found in its transitional dynamics, not in its long-run effects. Of the demographic shocks considered, only the baby bust features a quantitatively significant effect on human capital and the participation rate. Throughout our paper we compare and contrast our findings with those of Boucekkine et al. (2002). We have chosen their paper as a point of departure for two reasons. First, it is by far the most sophisticated treatment in our specific area of interest, i.e. demography-based macroeconomics. Second, it is the paper most closely associated with ours and thus shares a lot of common features. Although we are able to generalize their analysis in several directions, there is one dimension in which the analysis of Boucekkine et al. (2002) is more general than ours: their model simultaneously explains both the schooling decision and the retirement decision. We have decided to study these two decisions in separate papers. The current paper focuses on the education decision made early on in life, and ignores the retirement decision. Our companion paper, Heijdra and Romp (2007) ignores the education decision and focuses on the retirement decision that agents make at the onset of old-age. There is both a practical and a fundamental reason why we think it is fruitful to study schooling and retirement in isolation. First, by zooming in on one decision at a time, simple and intuitive analytical insights are much easier to come by. A more detailed simultaneous treatment can always be implemented in the context of a Computable General Equilibrium (CGE) model. Second, and more fundamentally, it allows us to expand the model in other, potentially more interesting, directions. In the current paper, for example, we chose to introduce a system of taxes and educational subsidies which impinges directly on the education decision. In Heijdra and Romp (2007), we ignore schooling and instead endogenize the agent's retirement decision in the presence of a stylized public pension system which includes realistic institutional features such as an early entitlement age (EEA) and a statutory retirement age.