Precautionary saving and partially observed income

I propose an intertemporal precautionary saving model in which the agent's labor income is subject to (possibly correlated) shocks with different degrees of persistence and volatility. However, he only observes his total income, not individual components. I show that partial observability of individual components of income gives rise to additional precautionary saving due to estimation risk, the error associated with estimating individual components of income. This additional precautionary saving is higher, when estimation risk is greater. Compared with a precautionary agent who is otherwise identical, but ignores estimation risk, the rational agent consumes less at the beginning of his life, but consumes more later, because of larger wealth accumulated from savings for estimation risk. The utility cost of ignoring estimation risk is also quantified in closed form.     

Portfolio choice and mortality-contingent claims: The general HARA case

We solve a portfolio choice problem that includes mortality-contingent claims and labor income under general HARA preferences. Our contribution beyond existing literature is to (i) focus on the covariance between shocks to human capital and financial capital, to (ii) model the utility of a family with basic needs and (iii) include life insurance and pension annuity claims in one unified life-cycle model. Our solution employs a “similarity reduction” mapping which reduces the two-dimensional HJB equation into one dimension. This allows for the implementation of a quick numerical scheme. And, when shocks to human capital and financial capital are perfectly correlated, a closed-form expression is obtained as a special case.     

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.     

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].     

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.     

Correlation Risk and Optimal Portfolio Choice

We develop a new framework for multivariate intertemporal portfolio choice that allows us to derive optimal portfolio implications for economies in which the degree of correlation across industries, countries, or asset classes is stochastic. Optimal portfolios include distinct hedging components against both stochastic volatility and correlation risk. We find that the hedging demand is typically larger than in univariate models, and it includes an economically significant covariance hedging component, which tends to increase with the persistence of variance–covariance shocks, the strength of leverage effects, the dimension of the investment opportunity set, and the presence of portfolio constraints.     

Uninsurable risk and financial market puzzles

We compare the empirical performances of three risk-sharing arrangements involving idiosyncratic skill shocks: (a) where individuals are unable to directly insure their consumption against individual-specific shocks, (b) where agents strike long-term insurance contract with financial intermediaries involving a truth revelation constraint as in Kocherlakota and Pistaferri (2009), (c) full risk sharing. Based on the widely accepted assumption of cross-sectional log-normality of individual consumption levels, we work out closed form expressions of the pricing kernels for (a) and (b). We put these three models to test four financial market anomalies, namely the equity premium, currency premium, risk-free rate, and consumption-real exchange rate puzzles simultaneously in an integrated framework. We find that the pricing kernel associated with (a) outperforms the other two models in terms of the produced estimates of the agent’s preference parameters and the model ability to predict the equity and currency premia, the risk-free rate, and the log growth in the exchange rate. However, the predictive ability is still far from satisfactory for all three models under scrutiny.     

Asset allocation and location over the life cycle with investment-linked survival-contingent payouts

This paper shows how survival-contingent investment-linked payouts can enhance investor wellbeing in the context of a portfolio choice model which integrates uninsurable labor income and asymmetric mortality expectations. In exchange for illiquidity, these products provide the consumer with access to mutual-fund style portfolio choice, as well as the survival credit generated from pooling mortality risk. Our model generates optimal asset location patterns indicating how much to hold in liquid versus illiquid survival-contingent payouts over the lifetime, and also asset allocation paths, showing how to invest in stocks versus bonds. We show that the investor who moves her money out of liquid saving into survival-contingent assets gradually from middle age to retirement and beyond, will enhance her welfare by as much as 50%. The results are robust to the introduction of uninsurable consumption shocks in housing expenses, income flows during the worklife and retirement, sudden changes in health status, and medical expenses.     

Risk Aversion Revisited

In order to supply additional empirical evidence of the effect of wealth on relative risk aversion, this study investigates households' demand for risky assets, using analysis of covariance techniques applied to the asset holdings of Canadian individual households. The extent and pattern of life-cycle effects are also examined. Results generally point to decreasing relative risk aversion when housing is either excluded from the definition of wealth or treated as a riskless asset. The investor's life-cycle plays a prominent role in portfolio selection behavior, with risk aversion increasing uniformly with age. Tax differentials do not seem to be an important element in investment decisions with respect to risk. When the sample and wealth definitions are censored in order to approximate those of previous empirical studies, their findings on relative risk aversion are generally corroborated.     

Income hedging and portfolio decisions

We examine whether the decision to participate in the stock market and other related portfolio decisions are influenced by income hedging motives. Economic theory predicts that the market participation propensity should increase as the correlation between income growth and stock market returns decreases. Surprisingly, empirical studies find limited support for the income hedging motive. Using a rich, unique Dutch data set and the National Longitudinal Survey of the Youth (NLSY) from the United States, we show that when the income-return correlation is low, individuals exhibit a greater propensity to participate in the market and allocate a larger proportion of their wealth to risky assets. Even when the income risk is high, individuals exhibit a higher propensity to participate in the market when the hedging potential is high. These findings suggest that income hedging is an important determinant of stock market participation and asset allocation decisions.     

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.     

Health status and portfolio choice: Is their relationship economically relevant?

Recent empirical work on individual portfolio choice focuses on the role of the individual's health in making financial decisions. The key idea is that, through precautionary saving or reducing investors' time horizon, health issues make people choose safer financial portfolios. This paper questions the empirical relevance of the link between health and portfolio choice, measured as stockownership and overall fraction of risky securities held. We handle with caution the findings from previous papers and ask whether data from the first wave of the Survey of Health, Aging and Retirement in Europe (SHARE) are able to clarify some of our doubts. We find that only poor self-reported health negatively impacts the portfolio choice, while other health measures (chronic conditions, limitations in daily activities of life, mental health) are irrelevant for investment decisions.     

Labor-dependent capital income taxation

Capital taxation which is negatively correlated with labor supply is proposed. This paper uses a life-cycle model of heterogeneous agents that face idiosyncratic productivity shocks and shows that the tax scheme provides a strong work incentive when households possess large assets and high productivity later in the life-cycle, when they otherwise would work less. The system also adds to the saving motive of prime-age households and raises aggregate capital. The increased economic activities expand the tax base and the revenue neutral reform results in a lower average tax rate. The negative cross-dependence generates a sizable welfare gain in the long-run relative to the tax system that treats labor and capital income separately as a tax base. The reform, however, can hurt the elderly during the transition with a high marginal tax on their capital income.     

Equity fund ownership and the cross-regional diversification of household risk

We explore the link between portfolio home bias and consumption risk sharing among Italian regions using household-level information on consumption, income and portfolio holdings. Since equity funds are typically diversified at the national or international level, we use data on equity fund ownership to proxy for regional home bias. Cross-regional patterns of equity fund ownership are qualitatively consistent with simple portfolio theory: regions with more asymmetric business cycles are more diversified because they have higher fund participation rates (the extensive margin of diversification) and higher average holdings of equity funds (diversification’s intensive margin). Also, fund holdings increase with the exposure of non-tradable income components (such as labor or entrepreneurial income) to regional shocks. Finally, interregional consumption risk sharing increases with fund holdings and this effect seems strongest when participation is widespread. Increased equity market participation could substantially improve interregional risk sharing.     

Real option component of cash holdings,business cycle,and stock returns

Corporate managers tend to preserve cash with an expectation of a worse economy while spend cash to exercise growth opportunities with a favorable economic condition. Using three empirical proxies (book-to-market ratio, idiosyncratic volatility and return on asset) in the literature, we extract a real option component of corporate cash holdings, serving both functions of precautionary saving and exercising growth options. Our empirical results show this component, in aggregate, increases when the real GDP declines and decreases when GDP inflates. Also, stocks with returns declining more to a shock to the aggregate real option component of cash holdings earn higher future returns. Moreover, stock returns of firms with higher cash holdings positively comove with the shock to the aggregate real option component, suggesting investors prefer to hold firms with higher cash holdings when the economy is deteriorating.     

Reinforcement Learning and Savings Behavior

We show that individual investors over‐extrapolate from their personal experience when making savings decisions. Investors who experience particularly rewarding outcomes from 401(k) saving—a high average and/or low variance return—increase their 401(k) savings rate more than investors who have less rewarding experiences. This finding is not driven by aggregate time‐series shocks, income effects, rational learning about investing skill, investor fixed effects, or time‐varying investor‐level heterogeneity that is correlated with portfolio allocations to stock, bond, and cash asset classes. We discuss implications for the equity premium puzzle and interventions aimed at improving household financial outcomes.     

Investment,consumption, and hedging under incomplete markets

Entrepreneurs often face undiversifiable idiosyncratic risks from their business investments. We extend the standard real options approach to an incomplete markets environment and analyze the joint decisions of business investments, consumption/savings, and portfolio selection. For a lump-sum investment payoff and an agent with a sufficiently strong precautionary savings motive, an increase in volatility can accelerate investment, contrary to the standard real options analysis. When the agent can trade the market portfolio to partially hedge against investment risk, the systematic volatility is compensated via the standard CAPM argument, and the idiosyncratic volatility generates a private equity premium. Finally, when the investment payoff is a series of flows, the agent's idiosyncratic risk exposure alters both the implied option value and the implied project value, causing a reversal of the results in the lump-sum payoff case.     

Divisia Monetary Aggregates,the Great Ratios,and Classical Money Demand Functions

King et al. ( 1991 ) evaluate the empirical relevance of a class of real business cycle models with permanent productivity shocks by analyzing the stochastic trend properties of postwar U.S. macroeconomic data. They find a common stochastic trend in a three‐variable system that includes output, consumption, and investment, but the explanatory power of the common trend drops significantly when they add money balances and the nominal interest rate. In this paper, we revisit the cointegration tests in the spirit of King et al., using improved monetary aggregates whose construction has been stimulated by the Barnett critique. We show that previous rejections of the balanced growth hypothesis and classical money demand functions can be attributed to mismeasurement of the monetary aggregates.     

中国收入等级不同的城镇居民预防性储蓄动机研究

将流动性约束条件纳入Dynan(1993)模型对其进行扩展,构建出包含流动性约束、不确定性、实际利率变量的新预防性储蓄模型。理论与实证结果表明:该模型更能体现我国收入等级不同城镇居民的储蓄行为特征;在不确定性存在条件下,新引入的流动性约束变量会对面临流动性约束不同居民的储蓄行为产生不同程度、甚至不同方向的影响,其影响程度随居民面临流动性约束的不同而变化。同时发现转轨时期仍然偏紧的流动性约束和日益增强的不确定性是抑制我国消费需求增长,加大居民预防性储蓄动机的根源。