Endogenous versus exogenous efficiency units of labour for the quantitative study of social security: two examples

Abstract

This paper explores the role of endogenous versus exogenous efficiency units of labour for the quantitative evaluation of the impact of pay-as-you-go Social Security on labour supply. Pension response to a population growth rate change is also studied. Two dynamic general equilibrium models are used: one with human capital accumulation through learning-by-doing, and a second with exogenous efficiency units of labour. The main differences in the results are the following: (a) the shift in the working time-age profile induced by the elimination of Social Security considerably differs in both models. The increase in average hours worked is 4% higher under human capital accumulation than in the alternative model; and (b) the pension falls by a similar percentage in both models when the population growth rate is set to zero. This occurs because the capital–labour ratio changes less under learning-by-doing than with exogenous efficiency units of labour.

Acknowledgements

I am deeply indebted to Víctor Ríos for his help and suggestions. I am also grateful to Fernando Perera for his comments.

Notes

 Human capital technology does not permit the introduction of either exogenous or endogenous growth.

 hn is a parameter introduced here to rescale hours worked just to avoid dealing with large numbers in computation. See Imai (2001) for the justification of the functional form.

 The non-linear least squares method (Levenberg–Marquardt) used here permits systems with more unknowns than equations to be solved. The value for b ₁ in Imai (2001) results too high to replicate the targets, this is why the parameter is calibrated.

 These are the observations constructed by Cooley and Prescott (1995), but do not reflect government data.

 The sample is composed of 20–64 year olds, both sex family heads. Only individuals who belong to the employment status categories ‘currently working’ and ‘retired’ are included in the sample. The hourly wage is computed as annual labour income divided by annual hours worked. Data are collapsed in means by age.

 Data, codes and results are available upon request via e-mail.