Optimal consumption and asset allocation with unknown income growth

Recent empirical evidence supports the view that the income process has an individual-specific growth rate component [Baker, M., 1997. Growth-rate heterogeneity and the covariance structure of life-cycle earnings. Journal of Labor Economics 15, 338-375; Guvenen, F., 2007b. Learning your earning: Are labor income shocks really very persistent? American Economic Review 97, 687-712; Huggett, M., Ventura, G., Yaron, A., 2007. Sources of life-cycle inequality. Working paper, University of Pennsylvania]. Moreover, the individual-specific growth component may be stochastic. Motivated by these empirical observations, I study an individual's optimal consumption-saving and portfolio choice problem when he does not observe his income growth. As in standard income fluctuation problems, the individual cannot fully insure himself against income shocks. In addition to the standard income-risk-induced precautionary saving demand, the individual also has learning-induced precautionary saving demand, which is greater when belief is more uncertain. With constant unobserved income growth, changes in belief are not predictable. However, with stationary stochastic income growth, belief is no longer a martingale. Mean reversion of belief reduces hedging demand on average and in turn mitigates the impact of estimation risk on consumption-saving and portfolio decisions.     

Precautionary Saving of Chinese and U.S. Households

We employ a model of precautionary saving to study why household saving rates are high in China and low in the United States. The use of recursive preferences gives a convenient decomposition of saving into precautionary and nonprecautionary components. Over 80% of China's saving rate and nearly all U.S. saving arises from the precautionary motive. The difference between U.S. and Chinese household income growth rates is vastly more important than income risk for explaining the saving rates. The key mechanism is that precautionary savers have target wealth‐to‐income ratios, and rapid income growth necessitates high saving rates to maintain the ratio.     

Precautionary Saving and Consumption Smoothing across Time and Possibilities

This paper examines how aversion to risk and aversion to intertemporal substitution determine the strength of the precautionary saving motive in a two-period model with Selden/Kreps–Porteus preferences. For small risks, we derive a measure of the strength of the precautionary saving motive that generalizes the concept of "prudence" introduced by Kimball (1990b) . For large risks, we show that decreasing absolute risk aversion guarantees that the precautionary saving motive is stronger than risk aversion, regardless of the elasticity of intertemporal substitution. Holding risk preferences fixed, the extent to which the precautionary saving motive is stronger than risk aversion increases with the elasticity of intertemporal substitution. We derive sufficient conditions for a change in risk preferences alone to increase the strength of the precautionary saving motive and for the strength of the precautionary saving motive to decline with wealth. Within the class of constant elasticity of intertemporal substitution, constant-relative risk aversion utility functions, these conditions are also necessary.     

Generalizing the permanent-income hypothesis: Revisiting Friedman's conjecture on consumption

Friedman's contribution to the consumption literature goes well beyond the seminal permanent-income hypothesis. He conjectured that the marginal propensity to consume out of financial wealth shall be larger than out of “human wealth”, the present discounted value of future labor income. I present an explicitly solved model to deliver this widely noted consumption property by specifying that the conditional variance of changes in income increases with its level. A larger realization of income not only implies a higher level of human wealth, but also signals a riskier stream of future labor income, inducing a higher precautionary saving, and thus giving rise to Friedman's conjecture. Appropriately adjusting human wealth for income risk, I show that Friedman's conjecture may be formulated as a “generalized” permanent income hypothesis. I further show that Friedman's conjecture captures the first-order effect of stochastic precautionary savings. Finally, I propose a natural decomposition of the optimal saving rule to formalize various motives for holding wealth as emphasized in [Friedman, M., 1957. A Theory of the Consumption Function. Princeton University Press, Princeton].     

Comparative precautionary saving under higher-order risk and recursive utility

Measuring and comparing the precautionary saving motive rest almost exclusively on the expected utility framework, and only focus on income risk or coefficients of the Arrow–Pratt type. We generalize the standard approach by characterizing comparative precautionary saving under recursive utility for increases in income risk and increases in risk on the saving return, including higher-order risk effects. We express the comparisons in terms of precautionary premia. In addition, we define a new class of preference coefficients, and derive the associated conditions to predict a stronger precautionary motive. The coefficients provide a detailed picture of the preferences sustaining precautionary saving and could be useful in applications.     

Precautionary Saving and Endogenous Labor Supply with and without Intertemporal Expected Utility

We analyze precautionary saving behavior in a framework with labor and nonlabor income risks, an endogenous supply of labor, and a representation of preferences that disentangles attitudes toward risk, attitudes toward intertemporal substitution, and ordinal preferences for consumption and leisure. This preference structure allows us to disentangle and to describe in an intuitive way the different forces that determine precautionary saving “in the small” and “in the large.”     

Domestic or global imbalances? Rising income risk and the fall in the US current account

When default leads to exclusion from financial markets, the implied loss of consumption smoothing opportunities is more costly when income volatility is high. A rise in income risk thus makes default less attractive, allowing creditors to relax borrowing limits. I show how, in an open economy, this endogenous financial deepening may reduce aggregate foreign assets in response to a rise in individual income risk, against the precautionary savings intuition. Conditions for this depend on whether default constrains complete or uncontingent contracts. The post-1980 rise in US household income risk strongly reduces foreign assets when domestic markets are complete or world interest rates low.     

Changes in risk and the demand for saving

How does risk affect saving? Empirical work typically examines the effects of detectible differences in risk within the data. How these differences affect saving in theoretical models depends on the metric one uses for risk. For labor-income risk, second-degree increases in risk require prudence to induce increased saving demand. However, prudence is not necessary for first-degree risk increases and not sufficient for higher-degree risk increases. For increases in interest-rate risk, a precautionary effect and a substitution effect need to be compared. This paper provides necessary and sufficient conditions on preferences for an Nth-degree change in risk to increase saving.     

Buffer stock saving in retirement accounts

We use a dynamic programming model to explore the possibility and extent of precautionary saving in tax-sheltered accounts such as the 401(k). The main policy experiment examines the behavior of saving for different levels of unemployment insurance (UI), which is a perfect substitute for precautionary saving against job loss. Our results indicate that increasing the generosity of UI crowds out 401(k) contributions made by younger workers, who save primarily for precautionary reasons. At the aggregate level, we find that 401(k)s increase national saving and that the magnitude of the effect depends on the generosity of UI.     

The Time‐Varying Volatility of Earnings and Aggregate Consumption Growth

Time‐varying specifications for the conditional variance of earnings of U.S. households are estimated with micro data over the period 1968–92. The cross‐sectional mean of the estimated time‐varying uncertainty of individual households has a significant impact on aggregate consumption growth. As such, aggregate precautionary savings may be more important than what is suggested by the results of estimating standard regression equations for aggregate consumption growth that incorporate only lagged income growth and the real interest rate. The estimation of a buffer stock consumption model with time‐varying earnings uncertainty suggests that the precautionary savings motive is cyclical and has become less important in the 1980s.     

Housing returns,precautionary savings and consumption: Micro evidence from China

We investigate how changes in home prices affect consumption in China via a wealth channel. Examining a panel of 7955 households via fixed effects and instrumental variable methods, we find a marginal propensity to consume out of housing wealth (home-price MPC) that is concentrated on goods consumed for pleasure rather than necessity. This trend is driven by the value of second homes rather than that of primary residences, suggesting a wealth channel. We further examine whether returns on housing investment, including rental income and home appreciation, fund the wealth channel; however, we find little supporting evidence. In contrast, a reduction in health risk increases the home-price MPC, but a reduction in income risk that also relieves precautionary saving motives does not. Our results are robust to alternative data, common-factor progress, expenditure shocks and bequest motives. We contribute by examining second homes, which carry little of the dual nature of housing that primary residences do, to identify a controversial wealth channel, and by studying the relative effects of health and income risks on the wealth channel.     

Taxing Internationally Mobile Individuals—A Case of Countervailing Incentives

With internationally mobile labour and the abolition of national border controls, the individual may not only have private information about his skill level (adverse selection), but also about the length of time he resides and works in the home country (moral hazard) and about his foreign income. To reduce domestic income taxes, the individual has an incentive to understate his domestic utility and to exaggerate the utility he could obtain by spending additional time abroad. Under the reasonable assumption that these are positively correlated, incentives are countervailing. The optimal government policy may be implemented by a tax schedule containing negative, zero, and positive marginal income tax rates.     

Idiosyncratic production risk, growth and the business cycle

We introduce a neoclassical growth economy with idiosyncratic production risk and incomplete markets. Each agent is an entrepreneur operating her own technology with her own capital stock. The general equilibrium is characterized by a closed-form recursion in the CARA-normal case. Incomplete markets introduce a risk premium on private equity, which reduces the demand for investment. As compared to complete markets, the steady state can thus have both a lower capital stock due to investment risk, and a lower interest rate due to precautionary savings. Furthermore, the anticipation of high real interest rates in the future feeds back into high risk premia and low investment in the present, thus slowing down convergence to the steady state. Our results highlight the importance of private risk premia for capital accumulation and business cycles.     

An equilibrium model of wealth distribution

I present an explicitly solved equilibrium model for the distribution of wealth and income in an incomplete-markets economy. I first propose a self-insurance model with an inter-temporally dependent preference [Uzawa, H. 1968. Time preference, the consumption function, and optimal asset holdings. In: Wolfe, J.N. (Ed.), Value, Capital, and Growth: Papers in Honour of Sir John Hicks. Edinburgh University Press, Edinburgh, pp. 485-504]. I then derive an analytical consumption rule which captures stochastic precautionary saving motive and generates stationary wealth accumulation. Finally, I provide a complete characterization for the equilibrium cross-sectional distribution of wealth and income in closed form by developing a recursive formulation for the moments of the distribution of wealth and income. Using this recursive formulation, I show that income persistence and the degree of wealth mean reversion are the main determinants of wealth-income correlation and relative dispersions of wealth to income, such as skewness and kurtosis ratios between wealth and income.     

Incomplete markets, labor supply and capital accumulation

Endogenous labor supply decisions are introduced in an equilibrium model of limited insurance against idiosyncratic shocks. Unlike in the standard case with exogenous labor (e.g. [Aiyagari, S.R., 1994. Uninsured idiosyncratic risk and aggregate saving. Quarterly Journal of Economics 109, 659-684; Huggett, M., 1997. The one-sector growth model with idiosyncratic shocks: steady states and dynamics. Journal of Monetary Economics 39, 385-403]), labor supply is likely to be lower than under complete markets. This is due to an ex post wealth effect on labor supply (rich productive agents work fewer hours) that runs counter the precautionary savings motive. As a result, equilibrium savings and output may be lower under incomplete markets. It is also found that long-run savings remain finite even when the interest rate equals the inverse of the discount factor.     

Precautionary Effort: A New Look

While the concept of precautionary saving is well documented, that of precautionary effort has received relatively limited attention. In this note, we set up a two period model in order to analyze the conditions under which the introduction (or deterioration) of an independent background risk increases effort.     

Specific knowledge and performance measurement

I examine optimal incentives and performance measurement in a model where an agent has specific knowledge (in the sense of Jensen and Meckling) about the consequences of his actions for the principal. Contracts can be based both on “input” measures related to the agent's actions and an “output” measure related to the principal's payoff. Whereas input‐based pay minimizes income risk, only output‐based pay encourages the agent to use his knowledge efficiently. In general, it is optimal to use both kinds of performance measures. The results help to explain some empirical puzzles and lead to several new predictions.     

城镇居民预防性储蓄动机强度的再认识

国内需求的萎靡不振已成当前经济学界的一个热点问题,而城镇居民储蓄的高速增长与此紧密相连,预防性储蓄强度在居民储蓄行为中起着重要作用.本文基于理性消费者最大化其一生效用的假设,推导出衡量居民预防性储蓄动机强度的新公式.随后,用30个省际地区1985-2010年的年度数据进行实证分析,结果显示,1998年前后城镇居民存在着明显的预防性储蓄强度的结构变化,这种转变对于政府决策具有重要意义.     

Voluntary Contributions to Personal Pension Plans: Evidence from the British Household Panel Survey

In this paper, we use data from the British Household Panel Survey (BHPS) for the years 1992 to 1998 to study the determinants of saving in the form of voluntary contributions to personal pension plans (PPPs). We first estimate a probit model with selection for the probability of making these voluntary contributions. We then estimate a random‐effects tobit regression for the amounts contributed and compare the results with those of a similar regression for conventional saving. Our findings suggest that voluntary contributions to PPPs are made essentially for retirement purposes, whereas conventional saving is undertaken for precautionary motives. The former type of saving is thus unlikely to offset the latter completely.