To show that any equilibrium growth path that can be supported using unrestricted national age-dependent lump-sum tax and transfer schemes can also be attained using restricted lump-sum transfer policies with deficit-finance, let a particular path for the capital stock of each country and consumption of every household be supported by the unfunded social security schemes,
for all t ≥ 1. Let overbars indicate the transfers and public debt for an age-independent lump-sum fiscal policy for each country. Note that
Note that bt and
To assure that the same path for capital accumulation and consumption of households is followed, the budget set for every generation in each country must be unchanged. This requires that
In the home country, the unfunded social security scheme increases the present value of lifetime resources of the generation born at time t by
From the home country public sector budget identity, we have
Adding this to its foreign counterpart and using equations (A2a), (A2b), and (11), it is apparent that the sawtooth pattern in each country’s public debt is reflected in a similar pattern in the world stock of public debt. This raises the important question of how to formulate the proper solvency constraint for the government.
The conventional solvency constraint is the requirement the discounted public debt, δT–1
This can be rewritten using equation (A2a) as
The natural solvency condition for the home country government now is that the limit of the sequence of discounted public debt every two periods, δt+2T+1
Buiter and Kletzer (1990a) propose the following modification to the usual formulation of the public sector solvency constraint: the sequence of discounted public sector debt need not converge if it possesses a convergent subsequence that converges to a limit less than or equal to zero.
What this means is that public sector debt may have to zigzag explosively if a restricted lump-sum transfer scheme is to achieve a national social welfare command optimum or support a Pareto efficient growth path. The public sector will be solvent under such a tax and transfer plan financed by a sequence of deficits and surpluses ever growing in absolute value if the length of each “fiscal year” can be chosen. That is, periods (in sequence) can be grouped together, so that the budget for each string of periods discounted remains bounded as the horizon goes to infinity.
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The author is an Associate Professor of Economics at Yale University. This paper was prepared while the author was a Visiting Scholar in the Fiscal Affairs Department in April of 1990. The author has benefited from several discussions with A. Lans Bovenberg, Adrienne Cheasty, Daniel Hewitt, George Kopits and Mark Lutz, on the issues of this paper.