Testing Fiscal Sustainability via Strong Convergence of Gaussian Random Variables |
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Authors: | Frederik Herzberg Angélique Herzberg |
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Affiliation: | 1. Department of Mathematics , University of California , Berkeley , California , USA fherzberg@uni-bielefeld.de;3. Wirtschaftswissenschaftliche Fakult?t , Heinrich-Heine-Universit?t , Düsseldorf , Germany |
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Abstract: | We prove, via the Borel-Cantelli lemma, that for every sequence of Gaussian random variables the combination of convergence in expectation and decreasing variances at fractional-polynomial rate implies strong convergence. This result has an important consequence for macroeconomic stochastic infinite-horizon models: The almost sure transversality condition (i.e., fiscal sustainability with probability one) is satisfied if (a) the discounted levels of net liabilities are Gaussian-distributed with fractional-polynomially decaying variances and (b) their means converge to zero. If (a) holds but (b) fails, the transversality condition will be almost surely violated. Hence, (a) and (b) constitute a test for almost sure fiscal sustainability. |
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Keywords: | Almost sure convergence Borel-Cantelli lemma Fiscal sustainability Gaussian random variables Stochastic infinite-horizon models Transversality condition |
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