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This paper was prepared for a special issue of Revista de Análisis Economico on Economic Growth, edited by Bill Easterly. I am grateful to Richard Agénor, Carlos Asilis, Bill Easterly, and an anonymous referee for valuable comments, and Catherine Fleck for editorial assistance. The views expressed in this paper do not necessarily represent those of the International Monetary Fund
De Gregorio (1992) presents a more general model where both human and physical capital are the engines of growth, which shows that liquidity constraints reduce human capital accumulation, although their effects on growth are ambiguous. However, this paper rules out the possibilities of multiple equilibria. In addition, De Gregorio (1992) presents empirical evidence showing that liquidity constraints have a negative effect on human capital accumulation. For empirical evidence on liquidity constraints, savings and growth, see Jappelli and Pagano (1992).
See also Tsiddon (1992) for a model of growth with multiple equilibria stemming from imperfect information.
Normally, two-period overlapping generations models consider one young and one old generation. In this paper, however, it is mote appropriate to think about young and middle-aged people, since both generations are able to work and there is no retirement.
Depreciation of individuals’ human capital would imply a negative value of ϵ, but, without loss of generality, I assume that ϵ is non-negative.
Formally, δ = (1/Ht) (∂Ht+1j/∂hj). For short, δ will be called marginal efficiency of education. Finally, for reasons that will be clear later, δ is also the marginal private return on education.
Note from equation (4) that education is provided free of charge. Therefore, when specifying liquidity constraints later in the paper, these refer to the inability to borrow to finance consumption, not education.
If utility is assumed to include altruistic behavior the results would be basically the same, since the choice of h is independent of the choice of consumption, and hence of utility.
Note that h may take any value in [0,1] when δ=1+r. I will not discuss further this case, and to simplify the presentation I will assume that h reaches its minimum when δ=1+r.
The model could be extended to a third period, which would correspond to retirement, without altering any of the results. In these circumstances, middle-aged individuals would save rather than borrow, and again (8) would not be binding. However, the extension to a third period is useful when physical capital accumulation is included (De Gregorio (1992)).
A condition for optimization is that λ and μ must be greater than, or equal to, zero. When δ≤1+r, μ is equal to zero, that is, liquidity constraints are not binding.
It is plausible that there may be some economies of congestion, which are ignored in this analysis.
One could roughly think of education as being produced with an “0-ring” technology (see Kremer (1991)), by which a large number of similarly skilled students increases the efficiency of education.
As should be clear by now, a problem with specifying δ as a function of H rather than h is that in the presence of positive exogenous growth (equal to ϵ) it is not possible for an economy to be “stuck” in the low growth equilibrium. Sooner or later δ will be such that h=h* is the optimal solution.
In the case of 2(a) I assume that δ(h) is convex and that the slope conditions which ensure that the equilibrium (δ1, h1) is stable hold. In addition, in the case drawn in 2(b), if the value of δ that makes h*=0 is less than δ(0), there will be only two equilibria.