We present a qualitative and quantitative analysis of the standard growth model modified to include precautionary saving motives and liquidity constraints. We address the impact on the aggregate saving rate, the importance of asset trading to individuals, and the relative inequality of wealth and income distributions.

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Uninsured Idiosyncratic Risk and Aggregate Saving

How do movements in the distribution of income and wealth affect the macroeconomy? We analyze this question using a calibrated version of the stochastic growth model with partially uninsurable idiosyncratic risk and movements in aggregate productivity. Our main finding is that, in the stationary stochastic equilibrium, the behavior of the macroeconomic aggregates can be almost perfectly described using only the mean of the wealth distribution. This result is robust to substantial changes in both parameter values and model specification. Our benchmark model, whose only difference from the representative‐agent framework is the existence of uninsurable idiosyncratic risk, displays far less cross‐sectional dispersion and skewness in wealth than U.S. data. However, an extension that relies on a small amount of heterogeneity in thrift does succeed in replicating the key features of the wealth data. Furthermore, this extension features aggregate time series that depart significantly from permanent income behavior.

/pdf/income-and-wealth-heterogeneity-in-the-macroeconomy-1p1dd3prlk.pdf

Income and Wealth Heterogeneity in the Macroeconomy

The theory of precautionary saving is shown in this paper to be isomorphic to the Arrow-Pratt theory of risk aversion, making possible the application of a large body of knowledge about risk aversion to precautionary saving, and more generally, to the theory of optimal choice under risk In particular, a measure of the strength of precautionary saving motive analogous to the Arrow-Pratt measure of risk aversion is used to establish a number of new propositions about precautionary saving, and to give a new interpretation of the Oreze-Modigliani substitution effect

Precautionary Saving in the Small and in the Large

Recursive methods offer a powerful approach in dynamic macroeconomics. This book contains both an introduction to recursive tools, including standard applications such as asset pricing, and advanced material, including analyses of reputational mechanisms and contract design. The tools are presented with enough technical sophistication to get the reader started working on practical problems. When numerical simulations are called for, the book provides suggestions for how to proceed, as well as references for further reading. The applications cover many substantive issues in macroeconomics, such as equilibrium asset prices, market incompleteness, wealth distribution, fiscal-monetary theories of inflation, government debt, optimal labour and capital taxation, time consistency and credible government policies, optimal social insurance, economic growth and labour market dynamics.

Recursive Macroeconomic Theory

This paper presents economic models of child development that capture the essence of recent findings
from the empirical literature on skill formation. The goal of this essay is to provide a theoretical framework
for interpreting the evidence from a vast empirical literature, for guiding the next generation of empirical
studies, and for formulating policy. Central to our analysis is the concept that childhood has more than one
stage. We formalize the concepts of self-productivity and complementarity of human capital investments
and use them to explain the evidence on skill formation. Together, they explain why skill begets skill
through a multiplier process. Skill formation is a life cycle process. It starts in the womb and goes on
throughout life. Families play a role in this process that is far more important than the role of schools.
There are multiple skills and multiple abilities that are important for adult success. Abilities are both
inherited and created, and the traditional debate about nature versus nurture is scientiÞcally obsolete.
Human capital investment exhibits both self-productivity and complementarity. Skill attainment at one
stage of the life cycle raises skill attainment at later stages of the life cycle (self-productivity). Early
investment facilitates the productivity of later investment (complementarity). Early investments are not
productive if they are not followed up by later investments (another aspect of complementarity). This
complementarity explains why there is no equity-efficiency trade-off for early investment. The returns to
investing early in the life cycle are high. Remediation of inadequate early investments is difficult and very
costly as a consequence of both self-productivity and complementarity.

/pdf/interpreting-the-evidence-on-life-cycle-skill-formation-3nqqp9sew6.pdf

Interpreting the evidence on life cycle skill formation

The risk-free rate in heterogeneous-agent incomplete-insurance economies

the average real return to stocks in the United States has been about six percent per year higher than that on Treasury bills. At the same time, the average real return on Treasury bills has been about one percent per year. In this paper, I discuss and assess various theoretical attempts to explain these two different empirical phenomena: the large "equity premium" and the low "risk free rate." I show that while there are several plausible explanations for the low level of Treasury returns, the large equity premium is still largely a mystery to economists. In order to understand why the sample means of the equity premium and the risk free rate represent "puzzles," it is useful to review the basics of modern asset pricing theory. It is well known that the real returns paid by different financial securities may differ considerably, even when averaged over long periods of time. Financial economists typically explain these differences in average returns by attributing them to differences in the degree to which a security's return covaries with the typical investor's consumption. If this covariance is high, selling off the security would greatly reduce the variance of the typical investor's consumption stream; in equilibrium, the investor must be deterred from reducing his risk in this fashion by the security's paying a high average return. There is a crucial problem in making this qualitative explanation of cross-sectional differences in asset returns operational: what exactly is "the typical investor's consumption"? The famous Capital Asset Pricing Model represents one answer to this question: it assumes that the typical investor's consumption stream is perfectly correlated with the return to the stock market. This allows financial analysts to measure the risk of a financial security by its covariance with the return to the stock market (that is, a scaled version of its "beta"). More recently, Douglas Breeden (1979) and Robert Lucas (1978) described so-called "representative" agent models of asset returns in which per capita consumption is perfectly correlated with the consumption stream of the typical investor. (See also

/pdf/the-equity-premium-it-s-still-a-puzzle-2ms6nm9jlw.pdf

The Equity Premium: It's Still a Puzzle

http://drphilipshaw.com/Huggett%201996.pdf

Wealth distribution in life-cycle economies

Is lifetime inequality mainly due to differences across people established early in life or to differences in luck experienced over the working lifetime? We answer this question within a model that features idiosyncratic shocks to human capital , estimated directly from data, as well as heterogeneity in ability to learn, initial human capital, and initial wealth. We find that, as of age 23, differences in initial conditions account for more of the variation in lifetime earnings, lifetime wealth, and lifetime utility than do differences in shocks received over the working lifetime. ( JEL D31, D91, J24, J31) To what degree is lifetime inequality due to differences across people established early in life as opposed to differences in luck experienced over the working lifetime? Among the individual differences established early in life, which ones are the most important? A convincing answer to these questions is of fundamental importance. First, and most simply, an answer serves to contrast the potential importance of the myriad policies directed at modifying or at providing insurance for initial conditions (e.g., public education) against those directed at shocks over the working lifetime (e.g., unemployment insurance). Second, a discussion of lifetime inequality cannot go too far before discussing which specific type of initial condition is the most critical for determining how one fares in life. Third, a useful framework for answering these questions should also be central in the analysis of a wide range of policies considered in macroeconomics, public finance, and labor economics. We view lifetime inequality through the lens of a risky human capital model. Agents differ in terms of three initial conditions: initial human capital, learning ability, and financial wealth. Initial human capital can be viewed as controlling the intercept of an agent's mean earnings profile, whereas learning ability acts to rotate

/pdf/sources-of-lifetime-inequality-2pcncinuc8.pdf

Sources of Lifetime Inequality

https://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=1426&context=economicsresrpt

Mark Huggett

Papers

The risk-free rate in heterogeneous-agent incomplete-insurance economies

The Equity Premium: It's Still a Puzzle

Wealth distribution in life-cycle economies

Sources of Lifetime Inequality

On the Distributional Effects of Social Security Reform