Testing Fiscal Sustainability via Strong Convergence of Gaussian Random Variables

Herzberg F, Herzberg A (2013)
Communication in Statistics- Theory and Methods 42(18): 3235-3242.

Journal Article | Published | English

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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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Herzberg F, Herzberg A. Testing Fiscal Sustainability via Strong Convergence of Gaussian Random Variables. Communication in Statistics- Theory and Methods. 2013;42(18):3235-3242.
Herzberg, F., & Herzberg, A. (2013). Testing Fiscal Sustainability via Strong Convergence of Gaussian Random Variables. Communication in Statistics- Theory and Methods, 42(18), 3235-3242.
Herzberg, F., and Herzberg, A. (2013). Testing Fiscal Sustainability via Strong Convergence of Gaussian Random Variables. Communication in Statistics- Theory and Methods 42, 3235-3242.
Herzberg, F., & Herzberg, A., 2013. Testing Fiscal Sustainability via Strong Convergence of Gaussian Random Variables. Communication in Statistics- Theory and Methods, 42(18), p 3235-3242.
F. Herzberg and A. Herzberg, “Testing Fiscal Sustainability via Strong Convergence of Gaussian Random Variables”, Communication in Statistics- Theory and Methods, vol. 42, 2013, pp. 3235-3242.
Herzberg, F., Herzberg, A.: Testing Fiscal Sustainability via Strong Convergence of Gaussian Random Variables. Communication in Statistics- Theory and Methods. 42, 3235-3242 (2013).
Herzberg, Frederik, and Herzberg, Angelique. “Testing Fiscal Sustainability via Strong Convergence of Gaussian Random Variables”. Communication in Statistics- Theory and Methods 42.18 (2013): 3235-3242.
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