A Parsimonious Macroeconomic Model for Asset Pricing: Habit Formation of Cross-sectional Heterogeneity?

In this paper we study asset prices in a parsimonious two-agent macroeconomic model with two key features: limited participation in the stock market and heterogeneity in the elasticity of intertemporal substitution in consumption. The parameter values for the model are taken from the business cycle literature, and in particular, are not calibrated to match financial statistics. The model generates a number of asset pricing phenomena that have been documented in the literature, including a high equity premium and a low risk-free rate; procyclical variation in the price-dividend ratio; countercyclical variation in the equity premium, in its volatility, and in the Sharpe ratio; and long- horizon predictability of returns with high R2 values. We also show that the similarity of our results to those from an external habit model is not a coincidence: the model has a reduced form representation that is similar to Campbell and Cochrane’s (1999) framework for asset pricing. However, the implications of the two models for macroeconomic questions and policy analyses are different.Limited stock market participation, the equity premium puzzle, incomplete markets, habit formation, elasticity of intertemporal substitution.

An Empirical Investigation of Labor Income Processes

In this paper we reassess the evidence on labor income risk. There are two leading views on the nature of the income process in the current literature. The first view, which we call the "Restricted Income Profiles" (RIP) process, holds that individuals are subject to large and very persistent shocks, while facing similar life-cycle income profiles. The alternative view, which we call the "Heterogeneous Income Profiles" (HIP) process, holds that individuals are subject to income shocks with modest persistence, while facing individual-specific income profiles.We first show that ignoring profile heterogeneity, when in fact it is present, introduces an upward bias into the estimates of persistence. Second, we estimate a parsimonious parameterization of the HIP process that is suitable for calibrating economic models. The estimated persistence is about 0.8 in the HIP process compared to about 0.99 in the RIP process. Moreover, the heterogeneity in income profiles is estimated to be substantial, explaining between 56 to 75 percent of income inequality at age 55. We also find that profile heterogeneity is substantially larger among higher educated individuals. Third, we discuss the source of identification -- in other words, the aspects of labor income data that allow one to distinguish between the HIP and RIP processes. Finally, we show that the main evidence against profile heterogeneity in the existing literature -- that the autocorrelations of income changes are small and negative -- is also replicated by the HIP process, suggesting that this evidence may have been misinterpreted.

Do Stockholders Share Risk More Effectively Than Non- stockholders?

This paper analyzes the extent of risk-sharing among stockholders and among nonstockholders. Wealthy households play a crucial role in many economic problems due to the substantial concentration of asset holdings in the U.S. data. Hence, to evaluate the empirical importance of market incompleteness, it is essential to determine if idiosyncratic shocks are important for the wealthy, who have access to better insurance opportunities, but also face different risks, than the average household. We study a model where each period households decide whether to participate in the stock market by paying a fixed cost. Due to this endogenous entry decision, the testable implications of perfect risk- sharing take the form of a sample selection model, which we estimate and test using a semi-parametric GMM estimator proposed by Kyriazidou (2001). Using data from PSID we strongly reject perfect risk-sharing among stockholders, but perhaps surprisingly, do not find evidence against it among non-stockholders. These results appear to be robust to several extensions we considered. These findings indicate that market incompleteness may be more important for the wealthy, and suggest further focus on risk factors that primarily affect this group, such as entrepreneurial income risk.Perfect risk-sharing, incomplete markets, semiparametric estimation, Generalized Method of Moments, limited stock market participation.

An Empirical Investigation of Labor Income Processes

Labor Income Risk, Profile Heterogeneity, Random Walk Model, Incomplete Markets, Idiosyncratic Shocks

Learning Your Earning: Are Labor Income Shocks Really Very Persistent?

The current literature offers two views on the nature of the income process. According to the first view, which we call the “restricted income profiles” (RIP) model (MaCurdy, 1982), individuals are subject to large and very persistent shocks, while facing similar life-cycle income profiles (conditional on a few characteristics). According to the alternative view, which we call the “heterogeneous income profiles” (HIP) model (Lillard and Weiss, 1979), individuals are subject to income shocks with modest persistence, while facing individual-specific income profiles. While labor income data does not seem to distinguish between the two hypotheses in a definitive way, the RIP model is overwhelmingly used to specify the income process in economic models, because it delivers implications consistent with certain features of consumption data. In this paper we study the consumption-savings behavior under the HIP model, which so far has not been investigated. In a life-cycle model, we assume that individuals enter the labor market with a prior belief about their individual-specific profile and learn over time in a Bayesian fashion. We find that learning is slow, and thus initial uncertainty affects decisions throughout the life-cycle allowing us to estimate the prior uncertainty from consumption behavior later in life. This procedure implies that 40 percent of variation in income growth rates is forecastable by individuals at time zero. The resulting model is consistent with several features of consumption data including (i) the substantial rise in within-cohort consumption inequality (Deaton and Paxson 1994), (ii) the non-concave shape of the age-inequality profile (which the RIP model is not consistent with), and (iii) the fact that consumption profiles are steeper for higher educated individuals (Carroll and Summers 1991). These results bring new evidence from consumption data on the nature of labor income risk.Labor income risk, Incomplete markets, Inequality, Consumption-savings decision, Kalman filter.

Reconciling Conflicting Evidence on the Elasticity of Intertemporal Substitution: A Macroeconomic Perspective

In this paper we reconcile two opposing views about the elasticity of intertemporal substitution in consumption (EIS). Empirical studies using aggregate consumption data typically find that the EIS is close to zero (Hall, 1988). Calibrated models designed to match growth and fluctuations facts typically require that the EIS be close to one (Lucas, 1990). This apparent contradiction is resolved when two kinds of heterogeneity are acknowledged: One, the majority of households do not participate in stock markets; and two, empirical evidence indicates that the EIS increases with wealth. We introduce these two features into a standard real business cycle model. First, limited participation creates substantial wealth inequality as in the U.S. data. Consequently, the properties of aggregates directly linked to wealth (e.g., investment and output) are mainly determined by the (high-EIS) stockholders. At the same time, since consumption is much more evenly distributed in the population, estimation from aggregate consumption uncovers the low EIS of the majority (i.e., the poor).The elasticity of intertemporal substitution, limited stock market participation, business cycle fluctuations, incomplete markets, wealth inequality.

A parsimonious macroeconomic model for asset pricing

I study asset prices in a two-agent macroeconomic model with two key features: limited stock market participation and heterogeneity in the elasticity of intertemporal substitution in consumption (EIS). The model is consistent with some prominent features of asset prices, such as a high equity premium; relatively smooth interest rates; procyclical stock prices; and countercyclical variation in the equity premium, its volatility, and in the Sharpe ratio. In this model, the risk-free asset market plays a central role by allowing non-stockholders (with low EIS) to smooth the fluctuations in their labor income. This process concentrates non-stockholders' labor income risk among a small group of stockholders, who then demand a high premium for bearing the aggregate equity risk. Furthermore, this mechanism is consistent with the very small share of aggregate wealth held by non-stockholders in the US data, which has proved problematic for previous models with limited participation. I show that this large wealth inequality is also important for the model's ability to generate a countercyclical equity premium. When it comes to business cycle performance the model's progress has been more limited: consumption is still too volatile compared to the data, whereas investment is still too smooth. These are important areas for potential improvement in this framework.Wealth ; Stock market

An empirical investigation of labor income processes

In this paper we reassess the evidence on labor income risk. There are two leading views on the nature of the income process in the current literature. The first view, which we call the "Restricted Income Profiles" RIP process, holds that individuals are subject to large and very persistent shocks, while facing similar life-cycle income profiles. The alternative view, which we call the "Heterogeneous Income Profiles" HIP process, holds that individuals are subject to income shocks with modest persistence, while facing individual-specific income profiles. We first show that ignoring profile heterogeneity, when in fact it is present, introduces an upward bias into the estimates of persistence. Second, we estimate a parsimonious parameterization of the HIP process that is suitable for calibrating economic models. The estimated persistence is about 0.8 in the HIP process compared to about 0.99 in the RIP process. Moreover, the heterogeneity in income profiles is estimated to be substantial, explaining between 56 to 75 percent of income inequality at age 55. We also find that profile heterogeneity is substantially larger among higher educated individuals. Third, we discuss the source of identification - in other words, the aspects of labor income data that allow one to distinguish between the HIP and RIP processes. Finally, we show that the main evidence against profile heterogeneity in the existing literature - that the autocorrelations of income changes are small and negative - is also replicated by the HIP process, suggesting that this evidence may have been misinterpreted.

A Parsimonious Macroeconomic Model for Asset Pricing: Habit Formation or Cross-sectional Heterogeneity?

In this paper we study the asset pricing implications of a parsimonious two-agent macroeconomic model with two key features: limited participation in the stock market and heterogeneity in the elasticity of intertemporal substitution. The parameter values for the model are taken from the real business cycle literature and are not calibrated to match any financial statistic. Yet, with a risk aversion of two, the model is able to explain a large number of asset pricing phenomena including all the facts matched by the external habit model of Campbell and Cochrane (1999). Examples in this list include a high equity premium and a low risk-free rate; a counter-cyclical risk premium, volatility and Sharpe ratio; predictable stock returns with coe?cients and R2 values of long-horizon regressions matching their empirical counterparts, among others. In addition the model generates a risk-free rate with low volatility (5.7 percent annually) and with high persistence. We also show that the similarity of our results to those from an external habit model is not a coincidence: the model has a reduced form representation which is extremely similar to Campbell and Cochrane’s framework for asset pricing. However, the macroeconomic implications of the two models are very different, favoring the limited participation model. Moreover, we show that policy analysis yields dramatically different conclusions in each framework.Limited stock market participation, asset pricing, the equity premium puzzle, incomplete markets, habit formation, elasticity of intertemporal substitution.

Does Stockholding Provide Perfect Risk Sharing?

This paper analyzes the extent of risk-sharing among stockholders. To provide a benchmark, we ask if stockholders are able to share risk more effectively than non-stockholders, where the latter serves as a control group. We study a dynamic structural model where each period households compare the benefits from stockholding with a per-period trading cost and decide whether to be in the stock market. Due to the endogenous entrym decision, the testable implications of perfect risk-sharing take the form of a sample selection model. To eliminate the selection bias, we implement a semiparametric estimation method (kernel-weighted GMM) recently proposed by Kyriazidou (2001). Using data from the Panel Study of Income Dynamics on U.S. households we find a surprising result: We strongly reject perfect risk-sharing for stockholders, but find no evidence against it among non-stockholders. Moreover, we also strongly reject risk-sharing for the whole population consistent with existing literature. We offer two explanations. First, if financial markets are incomplete, holding stocks may expose owners to extra risks more than it insures existing risks. Second, stockholders also own a large part of the entrepreneurial wealth which is largely uninsurable. Thus, stockholders not only have more assets for risk sharing but also have more risks to insure. These results suggest that these two groups face different economic environments and solve quite different optimization problems. Finally, we find significant heterogeneity in the risk aversion and leisure elasticities between the two groups. We conclude that the distinction between stockholders and non-stockholders is crucial in exploring many questions in macroeconomics and finance.Perfect risk-sharing, incomplete markets, semiparametric estimation, Generalized Method of Moments, limited stock market participation