Lifespan and Output

I. INTRODUCTION This paper presents a finite-life model of human capital acquisition. Time is continuous and individuals have lifespan T. Technological progress has two components, an ease-of-learning parameter and a knowledge frontier. The first reflects the rate of knowledge acquisition for a given amount of learning time, and the second reflects the limit on what can be learned. We obtain three main results. The first is that as lifespan increases, output per person-hour rises. The increase is nearly linear for short lifespans, but diminishes at higher lifespans as the knowledge frontier becomes binding. An increase in lifespan causes individuals to opt for more pre-work learning, higher skill levels at the beginning of the working phase, and, for sufficiently long lifespans, more learning during the work-phase. Thus, an increase in lifespan raises the skill level and thereby the total human capital and labor supply of a country, and consequently its per capita capital stock and output levels.(1) The data are consistent with a lifespan impact on output that is positive and diminishes as lifespan increases.(2) The second result concerns the technology adoption behavior of working individuals. We find that workers will only adopt new technology after they begin working if they have sufficiently long lifespans so that reaching the knowledge frontier is in their interest. When lifespans are short, individuals begin to work before they reach the knowledge frontier and never attempt to learn anything after that point. This aspect of optimal behavior is important because if there is a surge in worldwide technological progress, current workers will not adopt the new knowledge in a country characterized by short lifespans. Rates of transition will therefore be slower for short-lifespan countries. The final result is that when lifespans differ among countries, international differences in output per person can persist even in the presence of perfect markets. Goods can trade freely. Capital can move across borders without any borrowing or lending impediments. The only restriction is that individuals cannot migrate freely. The per capita differences persist because countries that differ in skill levels, real wages and per capita output levels will nevertheless have similar per skill-unit wages. Human capital accumulation has received renewed attention in the growth literature.(3) Prominent examples are Jones, Manuelli and Rossi [1993] and Caballe and Santos [1993]. These authors study models in which individuals have infinite lifespans, which contrasts with ours where lifespans are finite. The finite-life behavior of our model reflects the earlier work of Ryder, Stafford, and Stephan [1976] and has been reviewed in Blinder and Weiss [1976]. In particular, these authors describe a four-stage sequence (learning, work and learning, learning only and retirement) that is also central to our analysis. O'Neill [1995] studies the role of the returns to human capital accumulation in explaining transitional growth rates. Parente and Prescott [1994] study the acquisition of knowledge and also assume an exogenously decreasing cost of knowledge acquisition, although in their model firms, not individuals, engage in the acquisition of knowledge. Moreover, our paper assumes two forms of technology, a knowledge frontier and an ease of acquiring it, whereas Parente and Prescott only have the second. The present paper builds on Swanson, Kopecky, and Tucker [1997], who study the business cycle effects of different adoption rates at different ages. In this paper we focus on the lifespan effects of a similar model. The paper is organized as follows. Section II describes the nature of the correlations of lifespan with both current output and future growth. Section III develops the finite lifetime model. Section IV characterizes the behavior of the model and compares it with the evidence provided in section II. …