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2014 | OriginalPaper | Buchkapitel

10. Convergence in a Three-Factor Dynamic Model: Finite Versus Infinite Lives

verfasst von : Partha Sen

Erschienen in: Trade, Globalization and Development

Verlag: Springer India

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Abstract

In two-sector dynamic trade models with infinitely-lived agents in the presence of factor–price-equalization, convergence of aggregate capital-labor ratios and incomes does not occur. The Euler equation implies equal growth rate of consumption in all trading economies. With finite lives capital-labor ratios do get equalized. In a dynamic specific factors model, we show that factor–price-equalization occurs only in the long run with infinitely lived agents. With finite lives, even in the steady state there is no factor price equalization.

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Vorheriges Kapitel Catching Up in Terms of Product Quality

Nächstes Kapitel Some Reflections on the Recent Financial Crisis

The world economy, of course, is a closed economy and hence a decline in the return to capital accompanies any accumulation of capital.

In this we are following Sen and Shimomura (2012). Eaton (1987, 1988) used specific factors in an overlapping generations framework.

In a previous paper, capital was mobile between sectors. The presentation in this paper corresponds to a model of industrialization, where as capital is accumulated, industry grows and sucks out labor from agriculture.

Hence the description of this model as “a model of perpetual youth”.

It would be straightforward, if tedious, to extend the analysis to the case of the instantaneous utility function being of the CRRA variety but with an intertemporal consumption elasticity different from unity (as in Buiter (1988)).

Solving the differential equation in (18) (similarly for (19)) and imposing transversality conditions, we find that the price of land is given by the present discounted value of the marginal product of land, where the (time-varying) discount factor is the return to capital.

$$ q(t) = \int\limits_{t}^{\infty } {e^{{ - \int_{t}^{s} {[\alpha k^{\alpha - 1} (\nu ) - \delta z(\nu )]{\text{d}}v} }} } p\left( s \right)\beta m^{\beta - 1} \left( s \right){\text{d}}s $$

The specific factors L and M could be thought of as two kinds of labor. The interpretation that suits the analysis in Sect. 2 is to think of L as labor and M as some endowment of fruits. In Sect. 3.2, we introduce the valuation of the trees that bear these fruits (as in Eaton (1987), (1988)). In the earlier dynamic specific factors models, the capitals in the sectors were specific in the short run, while labor was mobile across sectors (Neary (1978)). In the long run, capital was also mobile across sectors, and the model collapsed into the familiar Heckscher-Ohlin model.

Where there is no chance of confusion, we do not explicitly write the time index.

Constant growth rates for L and M can easily be incorporated, as can exogenous technical progress.

Atkeson, A., & Kehoe, P. J. (2000). “Paths of development for early- and late-boomers in a dynamic heckscher-ohlin model.” Research Staff Report No. 256, Federal Reserve Bank of Minneapolis.

Bajona, C., & Kehoe, T. J. (2006). “Demographics in Dynamic Heckscher-Ohlin Models: Overlapping generations versus infinitely lived consumer.” Research Staff Report No. 377, Federal Reserve Bank of Minneapolis.

Bajona, C., & Kehoe, T. J. (2010). Trade, growth, and convergence in a Dynamic Heckscher-Ohlin Model. Review of Economic Dynamics, 13, 487–513.CrossRef

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Blanchard, O.-J. (1985). Deficits, Debt and Finite Horizons, Journal of Political Economy, 93, 223-247.

Buiter, W. H. (1988). Death, birth, productivity growth and debt neutrality. Economic Journal, 98, 279–293.CrossRef

Chen, Z. (1992). Long-run Equilibria in a Dynamic Heckscher-Ohlin Model. Canadian Journal of Economics, 23, 923–943.CrossRef

Eaton, J. (1987). A dynamic specific-factors model of international trade. Review of Economic Studies, 54, 325–338.CrossRef

Eaton, J. (1988). Foreign-owned land. American Economic Review, 78, 76–88.

Joseph, F., & Shiells, C. R. (2008). “Dynamic factor price equalization and international convergence.” Johannes Kepler University of Linz, Working Paper No. 0820.

Neary, P. (1978). Short-run capital specificity and the Pure Theory of International Trade. Economic Journal, 88, 488–512.CrossRef

Sanyal, K. K., & Jones, R. W. (1982). The theory of trade in middle products. The American Economic Review, 72, 16–3.

Sen, P. (2012a). “Capital accumulation and convergence in a small open economy”, Review of International Economics (forthcoming).

Sen, P. (2012b). Finite lives and convergence in a Two-Country Heckscher-Ohlin Model. Mimeo: Delhi School of Economics.

Sen, P., & Shimomura, K. (2012). Convergence in a Two-Country Dynamic Trade Model. Mimeo: Delhi School of Economics.

Ventura, J. (1997). Growth and interdependence. Quarterly Journal of Economics, 112, 57–84.CrossRef

Titel: Convergence in a Three-Factor Dynamic Model: Finite Versus Infinite Lives
verfasst von: Partha Sen
Verlag: Springer India
Buch: Trade, Globalization and Development
Print ISBN: 978-81-322-1150-1

Electronic ISBN: 978-81-322-1151-8

Copyright-Jahr: 2014
DOI: https://doi.org/10.1007/978-81-322-1151-8_10

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