The method of endogenous gridpoints for solving dynamic stochastic optimization problems

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

Precautionary saving and the marginal propensity to consume out of permanent income

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

Death to the Log-Linearized Consumption euler Equation! (And Very Poor Health to the Second-Order Approximation)

This paper shows that standard empirical methods for estimating log-linearized consumption Euler equations cannot successfully uncover structural parameters like the coefficient of relative risk aversion from a dataset of simulated consumers behaving exactly according to the standard model Furthermore consumption growth for simulated consumers is very highly statistically related to predictable income growth -- and thus standard 'excess sensitivity' tests would reject the hypothesis that consumers are behaving according to the standard model Results are not much better for the second-order approximation to the Euler equation The paper concludes that empirical estimation of consumption Euler equations should be abandoned and discusses some alternative empirical strategies that are not subject to the problems of Euler equation estimation

Solving Dynamic Stochastic Optimization Problems Using the Method of Endogenous Gridpoints

Numerical Optimization; Dynamic Programming; Precautionary Saving

Precautionary Saving and the Marginal Propensity to Consume out of Permanent Income

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.

The Method of Endogenous Gridpoints for Solving Dynamic Stochastic Optimization Problems

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.

'Risky Habits' and the Marginal Propensity to Consume Out of Permanent Income, or, How Much Would a Permanent Tax Cut Boost Japanese Consumption?

Papers in variety of disparate literatures have recently suggested that habit formation in consumption may explain several empirical puzzles, ranging from the level and cyclical variability of the equity premium (Abel (1990,1999); Constantinides (1990); Jermann (1998); Campbell and Cochrane (1999)) to the excess smoothness' of aggregate consumption (Fuhrer (2000)) to the apparent fact that increases in economic growth cause subsequent increases in aggregate saving rates (Carroll and Weil (1994); Bosworth (1993); Attanasio, Picci, and Scorcu (2000); Rodrik (1999); Loayza, Schmidt-Hebbel, and Serv‚n (2000)). This paper examines an implication of these models that has mostly been overlooked: Habits strong enough to solve these puzzles imply an immediate marginal propensity to consume out of permanent shocks of much less than one. When the model is calibrated to roughly match the rise in the Japanese saving rate over the postwar period, it implies that the immediate MPC out of permanent tax cuts may be as low as 30 percent, suggesting that calls for permanent income tax cut as a quick means of stimulating aggregate demand in Japan may be misguided.

Portfolios of the Rich

Recent research has shown that rich' households save at much higher rates than others (see Carroll (2000); Dynan, Skinner, and Zeldes (1996); Gentry and Hubbard (1998); Huggett (1996); Quadrini (1999)). This paper documents another large difference between the rich and the rest of the population: portfolios of the rich are heavily skewed toward risky assets, particularly investments in their own privately held businesses. The paper explores three possible explanations of these facts. First, perhaps there is exogenous variation in risk tolerance, so that highly risk tolerant house-holds engage in high-risk, high-return activities, and the risk-lovers who are lucky constitute the rich. A second possibility is that capital market imperfections a la Gentry and Hubbard (1998)and Quadrini (1999) require entrepreneurial activities to be largely self-financed, and these same imperfections imply that entreprenurial investment will yield high average returns. The final possibility is that wealth enters households' utility functions directly as a luxury good as in Carroll (2000) (one interpretation is that this reflects the utility of anticipated bequests), implying that risk aversion declines as wealth rises. The paper concludes that the overall pattern of facts suggests both Carroll-style utility and Gentry/Hubbard-Quadrini style capital market imperfections are important.

Why Do the Rich Save So Much?

This paper considers several alternative explanations for the fact that households with higher levels of lifetime income have higher lifetime saving rates (Dynan Skinner and Zeldes (1996); Lillard and Karoly (1997)) The paper argues that the saving behavior or the richest households cannot be explained by models in which the only purpose of wealth accumulation is to finance their own future consumption or even consumption of heirs The paper concludes that the simplest model that explains the relevant facts is one in which either consumers regard the accumulation of wealth as an end in itself or unspent wealth yields a flow of services (such as power or social status) which have the same practical effect on behavior as if wealth were intrinsically desirable

A tractable model of precautionary reserves, net foreign assets, or sovereign wealth funds

We model the motives for residents of a country to hold foreign assets, including the precautionary motive that has been omitted from much previous literature as intractable. Our model captures many of the principal insights from the existing specialized literature on the precautionary motive, deriving a convenient formula for the economy’s target value of assets. The target is the level of assets that balances impatience, prudence, risk, intertemporal substitution, and the rate of return. We use the model to shed light on two topical questions: The “upstream” flows of capital from developing countries to advanced countries, and the long-run impact of resorbing global financial imbalance