درآمد چرخه زندگی، اثرات اندازه گروهی و تامین اجتماعی: یک اکتشاف کمی

One of the features of the large overlapping generations model pioneered by Auerbach and Kotlikoff (1987) Dynamic Fiscal Policy is that individuals with different experience levels are perfect substitutes in production. This paper replaces this assumption with a labor market characterized by imperfect substitutability between less and more experienced workers. By comparing the quantitative properties of both cases in a calibrated model for Spain, it is found that in the model economy with imperfect substitution, the effects of aging on the financial viability of the pension system are less severe than in the standard model economy with perfect substitution.

The purpose of this paper is to examine the relationship between the aging of the population and the future prospects of the social security system in Spain. Although this topic has received much attention over the last 10 years mainly due to the sharp expected increase in the share of retired individuals over the working population (see Fig. 1), the existing studies have abstracted from the interaction between the age composition of the population and the life-cycle profile of earnings. Since the pattern of pension benefits and contributions are strongly age dependent, this assumption can have important effects on the evolution of the percentage of GDP spent on pensions. For this reason in this paper I study the following question: How do the properties of the standard large overlapping generations model compare to the properties of a model that accounts for the existence of cohort size effects? I study this issue by calibrating a computable overlapping generations model to match some key features of the Spanish economy in 1995. Then I use the demographic projections for this economy that match those from Eurostat Demographic Statistics 1996 and analyze what should be the adjustment in the tax rate needed to keep balanced the pension system in several model economies that have different assumptions about the degree of substitution of workers with different levels of work experience.This paper is not new in addressing the effects of the aging process upon the social security systems. The potential economic effects caused by the individuals that belong to the baby-boom generation as they enter retirement has motivated an increasing concern about the sustainability of the pension systems in developed countries. In this sense, the recent research effort on social security has mainly concentrated on the efficiency of the current pay-as-you-go pension system (e.g. Imrohoroglu et al. (1995) and Boldrin et al. (1999)), the design of a feasible reform to a funded system (e.g. Huang et al. (1997)) and the fiscal adjustments that prevents from privatization (De Nardi et al. (1999) and Montero (2000) for the Spanish economy). These studies are characterized by the perfect substitutability of workers with different levels of work experience, namely they abstract from the possible effect that an increase in the number of older workers relative to the number of young less experienced workers could have on the relative labor earnings of these workers. In sharp contrast with this assumption, there are many empirical studies for the US economy (e.g. Berger, 1985, Freeman, 1979, Katz and Murphy, 1992, Murphy and Welch, 1992 and Welch, 1979) that have found that the age-earnings profile of workers appears to be significantly affected by the age composition of the workforce. In words of Freeman (1979), “apparently because younger and older male workers are imperfect substitutes in production, changes in the number of young male workers relative to older male workers substantially influence the ratio of the earnings of younger men to the earnings of older men”. For the specific case of the Spanish economy the lack of data on wages by age has not allowed researchers to test these effects although there is some empirical evidence ( Eguia and Echevarria (2004)) concerning the relative higher unemployment rate experienced by those individuals that belong to the baby-boom generation. In this sense, it is worth noting that in highly regulated labor markets one should expect the adjustment of the labor market to be done through a change in quantities (employment) instead of prices (wages) following a change in the relative supply of workers with different levels of work experience. Since both cases imply that the individuals of the baby-boom generation have on average lower labor earnings than individuals belonging to more scarce cohorts, we think that the assumption of perfect competitive labor markets with imperfect substitutability between young and old workers is a good starting point to tackle the question at hand. Despite the potential implications of these cohort size effects for a variety of macroeconomic issues, there are not many studies that have attempted to introduce these effects in macroeconomic models. Some exemptions are the seminal work of Lam (1989) that studied the effects of changes in age structure on life-cycle wage profiles in stable populations. And more recently, Kremer and Thomson (1998) have studied the implications of the imperfect substitution between young and old workers for the speed of convergence of per capita output between countries and find that the existence of imperfect substitutability creates a kind of adjustment cost in human capital because total output depends positively on each generation generation's human capital but negatively on the change in human capital between generations. Although we think that the assumption of perfect substitution between young and old workers may be useful depending on the question at hand, in the context of an aging population to legitimately abstract from the interaction between the age structure of the population and the life-cycle profile of labor earnings, the consequences of the aging of the baby-boom generation should be quantitatively similar in a model economy that abstracts from cohort size effects an one that it does not. In this paper I address this question by studying the effects of demographic projections from 1995 to 2050 on the finances of the social security system. I compare the equilibrium allocations in two model economies that only differ from each other in the degree of substitution of workers with different experience levels. Results indicate that there are quantitatively relevant differences between both economies. For instance it is found that if the rule used to compute pension benefits is left untouched, in the standard model the percentage of GDP spent on pensions will increase from 7.1% in 1995 to 17.1% in 2040. In contrast, in the model economy with cohort size effects this percentage will increase from 7.1% in 1995 to 12.8% in 2040. Similarly, under the perfect substitution case the social security tax rate has to be increased from 11.8% in 1995 to 30.5% in 2045 while with imperfect substitutability across age groups the tax rate should be increased from 11.8% in 1995 to 23.7% in 2045. The mechanism that accounts for such difference is the lower pension benefits of individuals belonging to the baby-boom generation in the model economy with cohort size effects. This is so due to the fall in the experience premium and the reduction of labor effort before retirement displayed by the members of the baby-boom generation as part of the intertemporal reallocation of hours worked in response to the fall in relative wages. The rest of the paper is organized as follows. Section 2 describes the main features of the model economies I investigate and its calibration to be a realistic description of the Spanish economy in 1995. Section 3 presents the main results of the paper. Section 4 studies the sensitivity of the results to different modelling strategies and finally Section 5 concludes.

This paper has extended the standard large overlapping generations model to allow for the interaction between changes in the age composition of the workforce and the shape of life-cycle earnings. We have found that the effect of aging on the sustainability of the social security system depends critically on the degree of substitution of labor at different ages. In particular, for the empirically plausible parameter space used in this paper we find that the adjustment of the tax rate needed to left untouched the pension system in Spain is less severe in a model that accounts for the existence of cohort size effects than in a model that it does not. However, despite the potential implications of the present paper for the political discussion about the desirability and the magnitude of the reform of the existing pay-as-you-go systems in developed countries, one should bear in mind that in the present analysis it is crucial to have a good estimation of the degree of substitution between young and old workers. And for this to be the case, more empirical research is needed for countries other than the US.