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We characterize the optimal linear tax on capital in an Overlapping Generations model with two period lived households facing uninsurable idiosyncratic labor income risk. The Ramsey government internalizes the general equilibrium feedback of private precautionary saving. For logarithmic utility our full analytical solution of the Ramsey problem shows that the optimal aggregate saving rate is independent of income risk. The optimal time-invariant tax on capital is increasing in income risk. Its sign depends on the extent of risk and on the Pareto weight of future generations. If the Ramsey tax rate that maximizes steady state utility is positive, then implementing this tax rate permanently generates a Pareto-improving transition even if the initial equilibrium is dynamically efficient. We generalize our results to Epstein-Zin-Weil utility and show that the optimal steady state saving rate is increasing in income risk if and only if the intertemporal elasticity of substitution is smaller than 1.
Recent models with liquidity constraints and impatience emphasize that consumers use savings to buffer income fluctuations. When wealth is below an optimal target, consumers try to increase their buffer stock of wealth by saving more. When it is above target, they increase consumption. This important implication of the buffer stock model of saving has not been subject to direct empirical testing. We derive from the model an appropriate theoretical restriction and test it using data on working-age individuals drawn from the 2002 and 2004 Italian Surveys of Household Income and Wealth. One of the most appealing features of the survey is that it has data on the amount of wealth held for precautionary purposes, which we interpret as target wealth in a buffer stock model. The test results do not support buffer stock behavior, even among population groups that are more likely, a priori, to display such behavior. The saving behavior of young households is instead consistent with models in which impatience, relative to prudence, is not as high as in buffer stock models. JEL Classification: D91
We present a tractable model of the effects of nonfinancial risk on intertemporal choice. Our purpose is to provide a simple framework that can be adopted in fields like representative-agent macroeconomics, corporate finance, or political economy, where most modelers have chosen not to incorporate serious nonfinancial risk because available methods were too complex to yield transparent insights. Our model produces an intuitive analytical formula for target assets, and we show how to analyze transition dynamics using a familiar Ramsey-style phase diagram. Despite its starkness, our model captures most of the key implications of nonfinancial risk for intertemporal choice.
The budget constraint requires that, eventually, consumption must adjust fully to any permanent shock to income. Intuition suggests that, knowing this, optimizing agents will fully adjust their spending immediately upon experiencing a permanent shock. However, this paper shows that if consumers are impatient and are subject to transitory as well as permanent shocks, the optimal marginal propensity to consume out of permanent shocks (the MPCP) is strictly less than 1, because buffer stock savers have a target wealth-to-permanent-income ratio; a positive shock to permanent income moves the ratio below its target, temporarily boosting saving. Keywords: Risk, Uncertainty, Consumption, Precautionary Saving, Buffer Stock Saving, Permanent Income Hypothesis.
This paper introduces a method for solving numerical dynamic stochastic optimization problems that avoids rootfinding operations. The idea is applicable to many microeconomic and macroeconomic problems, including life cycle, buffer-stock, and stochastic growth problems. Software is provided. Klassifikation: C6, D9, E2 . July 28, 2005.
"Buffer-stock" models of saving are now standard in the consumption literature. This paper builds theoretical foundations for rigorous understanding of the main features of such models, including the existence of a target wealth ratio and the proposition that aggregate consumption growth equals aggregate income growth in a small open economy populated by buffer stock savers. JEL Classification: D81, D91, E21 Keywords: Precautionary Saving, Buffer Stock Saving, Marginal Propensity to Consume, Permanent Income Hypothesis