Abstract
In the paper by Acemoglu and Zilibotti (1997) and in the contributions by St. Paul (1992) and Obstfeld (1994) it was assumed that agents were merely constrained by the number of intermediate sectors (Acemoglu and Zilibotti) or by the degree of international financial integration (St. Paul, Obstfeld). Given these constraints, a well-functioning financial system allowed them to realize their optimal investment plans.
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Notes
There is also an aggregate component of risk that affects all individuals in the economy. However, the key results in Greenwood and Jovanovic–s paper are driven by the financial sector–s ability to pool idiosyncratic risks.
We thus use the classical overlapping generations (OLG) framework that goes back to Samuelson (1958) and Diamond (1965).
For the CIES (constant intertemporal elasticity of substitution) utility function the intertemporal elasticity of substitution is the inverse of the Arrow-Pratt measure of relative risk-aversion. Weil (1990) uses a more general functional form that allows to disentangle agents’ attitudes towards risk and their desire to smooth consumption, and demonstrates that the reaction of an individual to changes in the distribution of future returns is determined by the intertemporal elasticity of substitution rather than by the measure of relative risk aversion.
Besley (1995) quotes jewelry, land and livestock as assets that are held outside the formal financial sector and that provide their owners with a relatively safe return.
In the paper of Greenwood and Jovanovic (1990) individuals face identical fixed costs but differ in their initial wealth endowments. In the present model where agents have finite time horizons and leave no bequests, the setup of Greenwood and Jovanovic would lead to an immediate disappearance of the heterogeneity.
Of course, both infrastructure and the quality of the financial system depend on the level of development. However, it would complicate the model without changing the results if v was a function of income.
Since the net return on productive investment is greater than zero in both states of nature, individuals who enter the financial sector would want to borrow additional resources to invest in productive capital. However, due to the assumption that lending is associated with the same fixed cost as productive investment, neither borrowing nor lending takes place in equilibrium. The reason is that all individuals who entered the financial sector would have the same investment portfolio and would want to borrow. Hence, the only source of credit would be those agents who chose primitive saving. However, the latter would have no incentive to lend, since this would imply entering the financial sector, and as soon as an agent has incurred the fixed cost x, she has the same optimal portfolio as all the other agents in the financial sector.
In what follows, the superscripts n, c and o will refer to “non-entry”, “closed economy” and “open economy”, respectively.
If σ = 1, the instant utility function is logarithmic and the saving rate, β /(1+β), does not depend on expected returns. It is therefore independent of an individual–s decision to enter the financial sector. However, it would not be correct to analyze this case by simply substituting σ = 1 into all equations. Apparently, L’Hô pita’s rule could not be applied in (3.10) and (3.11), and neither Vn nor Vc would be defined. Instead, to analyze the logarithmic case, one has to start from the logarithmic utility function and then derive the agents’ saving and investment decisions and the utility levels for entry and non-entry.
Ogaki et al. (1996) estimate the intertemporal elasticity of substitution for a sample of industrialized and developing countries. Their point estimates range from 0.05 to 0.64 and increase in countries’ per-capita incomes.
See Barro and Sala-i-Martin (1995:142).
I owe this representation to Acemoglu and Zilibotti (1995).
This assumption implies that returns on productive investment are also negatively correlated across countries. The low correlations between returns in developing and industrialized countries were discussed in Chapter 2. Of course, these correlations are not only driven by supply shocks but also by random changes in demand, government policy, etc. Appendix 3.B presents a simple model that shows that the model–s equations can also be interpreted as the description of two small open economies that are subject to terms-of-trade fluctuations.
In what follows we will add the superscripts H and F whenever it is necessary to distinguish domestic parameters from their counterparts in F. All qualitative results that were derived for country H in the previous section also hold for country F. However, if π < 0.5 it is easy to show that 56-1, while the relationship between the saving rates sc, H and sc, F depends on the intertemporal elasticity of substitution.
The fact that both risk and expected returns may change is an important difference to the model of Devereux and Smith (1994) where the elimination of investment barriers merely amounts to a (mean-preserving) change in risk.
It is easy to see why the intertemporal elasticity of substitution does not affect this result: since the elimination of investment barriers removes a constraint but leaves agents free to invest all their savings at home, it is generally the case that 56-1. This implies (3.18), and therefore 56-2. The same result holds for country F where 56-3
If π = 0.5, the two lines coincide. Recall that, in this case, it is optimal for agents to invest 50 percent of their savings abroad. As a consequence, they have diversified all country-specific risk, and the aggregate capital stock follows a deterministic growth path.
Note that 56-3 for the benchmark model: since π = 0.5, both countries are characterized by the same distribution of shocks in autarky. Therefore the thresholds do not differ between countries.
For the parameter values of our numerical example, only a fraction of the young generation in H and F enters the financial sector at 56-4.
Note that, by assuming (exogenous) specialization and non-substitutability in consumption and production we are abstracting from the interaction between goods and asset markets and its effects on the factor allocation and the pattern of trade. For more sophisticated analyses of this issue, see Newbery and Stiglitz (1984), Pomery (1984), and, more recently, Feeney (1994).
For ease of exposition we neglect fixed costs of entering the financial sector, which could be easily taken into account-however, at the cost of an additional fixed-proportions assumption.
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Harms, P. (2000). Stochastic Growth, Poverty Traps, and International Investment. In: International Investment, Political Risk, and Growth. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4521-7_3
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DOI: https://doi.org/10.1007/978-1-4615-4521-7_3
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