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The author wishes to thank Tony Atkinson and Michael Keen for their advice and comments.
The public good can be seen as a publicly provided private good, so that scale effects are ignored.
The generation born at time t is subject to capital income taxes on returns maturing when old, that is at time t + 1. Other forms of taxation are, of course, preferable to these taxes which distort investment and saving decisions. In this setting, a tax on labor income, for example, is non-distortionary as labor is inelastically supplied. However, this is equivalent to levying a lump-sum tax, and the purpose of the analysis is to explore decentralized government behavior in the absence of lump-sum taxation. In addition, it is worth noting that in a setting with large countries, national governments may want to use distortionary taxes even if first-best tools are available.
For simplicity, we assume that there is no population growth and normalize total population to be equal to one. This allows us to concentrate on the single representative member of each generation.
For alternative assumptions about the role of public goods, see for example Azariadis (1993).
It is also assumed, for convenience, that the function Fi (⋅) satisfies the Inada conditions with respect to the stock of domestic capital
For discussion of international spillovers of knowledge, see for example Bertola (1993), and Grossman and Helpman (1994).
For empirical evidence of international spillovers of R&D spending, and references to the literature, see also Bernstein and Mohnen (1998), and Leahy and Neary (1999).
For discussion of the equivalence between government debt policy and differential lump-sum taxation in overlapping generations models, see for example Diamond (1973, p. 222) and Atkinson and Sandmo (1980, p. 533).
For an explicit calculation of the ratio αt+1 and the rate Rt+1 in the case of Cobb-Douglas production functions, see Appendix I.
For discussion of the existence and uniqueness of equilibria in overlapping generations models, and reference to the literature, see Blanchard and Fisher (1989), and Azariadis (1993). For applications to models with open economies and to models with endogenous growth, see also Buiter (1981), and Buiter and Kletzer (1992).
In this case, the net return to capital in each country may be written as
It may be noticed that in this model with perfect capital mobility there are no transitional dynamics, and the economy is always at its balanced growth path. However, as noted in previous sections, the existence and uniqueness of a balanced accumulation path with positive economic growth are not guaranteed. In what follows, we assume that a unique equilibrium for any given set of tax rates exists, and Appendix I provides an example with Cobb-Douglas utility and production functions where a unique equilibrium exists indeed.
We may notice that, in this model, changes in domestic taxes have strong international effects. Specifically, changes in one country’s taxes has as strong an effect on domestic growth as on foreign growth. This undesirable feature of this model derives from the fact that the model has no transitional dynamics and perfect mobility of capital. Introducing these dynamics an imperfect capital mobility would lead to country differentiated effects. However, the purpose of the analysis is to examine the effects of domestic tax policies along the balanced growth path, and the absence of transitional dynamics greatly simplifies this task.
It is worth noting that for a steady state to exist, preferences must be homothetic; see for example Buiter and Kletzer (1992).
For a simplified version of this model with Cobb-Douglas utility and production functions, see appendix I. In this example, conditions on the parameters of the model can be found such that a positive long-run growth rate for the economy indeed exists (see Appendix I).
A large volume of empirical work which seeks to determine the effects of capital taxation on personal savings and economic growth exists which suggests the possibility of low elasticity of substitution. For discussion of this evidence, and references to the literature, see for example Atkinson and Stiglitz (1980), (Hall, 1988), Uhlig and Yanagawa (1996), and Bernheim (2002).
For example, the term in the bracket is maximized at α = 1. From the definition of α, it then follows that, the growth rate is maximum when σ1* = σ2*. These may be either taxes (positive) or subsidies (negative), depending of the exact parameterization of the model.
This result holds, for example, under the assumption that μ* = 0.5 and s (1 – ε) (L)1+ϑ >
Specifically, in these models, the Euler equation predicts a stable long-run positive relation between the net interest rate and economic growth; thus increases in taxation reduce the stock of domestic capital and also decrease the rate of growth.
For discussion of the infinite-lived agent model, and references to the literature, see for example Blanchard and Fischer (1989). For specific applications to the case of open economies, see also Lejour and Verbon (1998).
There will, however, be adjustments along the dynamics between stationary states as world savings adjust to new tax rates.