Economic Dynamics Newsletter

Amir Yaron on Lifetime Inequality and Long Run Risks and Asset Pricing

My research is at the intersection of macroeconomics and finance. An ongoing challenge in macroeconomics and finance is to identify the important sources of risks that individuals and firms face and how these in turn affect allocations and prices. These risks might include, for example, aggregate productivity shocks, uninsurable individual labor risk, and/or financial frictions faced by both individuals and firms. My research identifies and measures a subset of these risks, and analyzes how they map into observable quantities such as consumption and prices.I would like to describe two research programs which at first may appear somewhat remote, but at least from my perspective, do ultimately have a common intersection point. The first area departs from the representative agent paradigm and analyzes issues such as consumption behavior, portfolio choices, risk sharing, inequality and equilibrium prices in environments where agents face uninsurable idiosyncratic labor market risk. Most of this research has been with Chris Telmer and Kjetil Storesletten. In this research line there are two interrelated questions: (i) what are the properties of idiosyncratic earnings shocks and (ii) what are their quantitative ramifications for allocations, risk sharing, inequality, and ultimately asset pricing? Since Kjetil described most of it in his newsletter contribution, I will proceed to discuss some recent work with Mark Huggett and Gustavo Ventura that tries to embed these risks within models of human capital. The second area focuses on my recent work with Ravi Bansal on aggregate models that feature Long Run Risks for understanding the sources of fluctuations of asset prices.

Human Capital and Lifetime Inequality

Much of my current research in this area is channeled to endogenize, to some degree, idiosyncratic earnings risks. Currently, the common approach to modern versions of the life-cycle, permanent-income hypothesis, is to specify earnings and wages as exogenous random processes. This approach has dominated the literature on consumption, savings, and wealth distribution as well the literature on social security and income tax reform.Our research program asks to what extent differences in individual conditions at the start of economic life contribute to the dynamics of earnings inequality over the life cycle. In this context, we revisit issues regarding the quantitative importance of earnings shocks during agents’ working years for lifetime inequality and welfare. That is, we ask to what degree is lifetime inequality due to differences across people established early in life as opposed to differences in luck experienced over the lifetime? Among initial conditions, individual differences established early in life, which ones are the most important?

Answers to these questions should shed light on several important issues. This analysis can provide quantitative information on the relative importance of the many policies directed at modifying or at providing insurance for initial conditions (e.g. public education) against those directed at shocks over the lifetime (e.g., unemployment insurance programs). A discussion of lifetime inequality cannot proceed far without discussing which type of initial condition is the most critical for determining how one fares in life. Finally, 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. In particular, many of the current policy analyses are done with an exogenous earnings or wage processes. These policy experiments do not change, by construction, the earnings process and thus changes are mainly operative through various risk sharing channels. However, when human capital is endogenous, such policy experiments can alter the incentives to acquire human capital and therefore change the earnings profiles themselves, and potentially result in large welfare gains/losses.

In Huggett, Ventura and Yaron (2006), we first take an extreme view, abstract from idiosyncratic risk altogether, and ask whether the process for endogenous accumulation of human capital can induce sufficient transition dynamics over the life-cycle to allow such a model to match salient features of the earnings distribution. We focus on the age profiles for the mean, Gini and skewness of earnings. Surprisingly, the richness of these dynamics can accommodate many features of the earnings distribution. We show that a benchmark human capital model (the Ben-Porath (1967) model) in which agents are different in learning ability and initial human capital can replicate these earning properties. The distributions for initial human capital and ability to learn have the property that learning ability must substantively differ across agents and that learning ability and initial human capital are positively correlated.

The model implies, however, that over time both individual earnings levels and growth rates are strongly positively autocorrelated. Evidence from US data shows that earnings growth rates are negatively correlated. This, in conjunction with related evidence on consumption inequality as in Storesletten, Telmer and Yaron (2004) and Deaton and Paxson (1994), suggests an important role for persistent idiosyncratic shocks. Moreover, based on the human capital view, observed earnings fluctuations are a mixture of exogenous shocks and investment in human capital–making inference regarding earnings shocks difficult.

To address these issues in Huggett, Ventura and Yaron (2007), we extend the human capital model to include idiosyncratic shocks to human capital. In order to identify the shocks empirically, we exploit the fact that toward the end of (working) life agents no longer invest in human capital and thus first differences in wages will reveal the shock process. Given this process and observed initial conditions for wealth, we solve for the best (joint log-normal) distribution for learning ability and initial human capital that allows the model to fit various earnings facts. The model suggests that most (around 60 to 70%) of the variation in life time utility (or wealth) are attributable to initial conditions as opposed to shocks. Among initial conditions, variation in initial human capital is substantially more important than variation in learning ability or initial wealth for determining how an agent fares in life.

In the model there are two offsetting forces which together account for the increase in earnings dispersion. One force is that agents differ in learning ability. Agents with higher learning ability have steeper mean earnings profiles than low ability agents, other things equal. This mechanism is supported by the literature, see Card (1999), on the shape of the mean age-earnings profiles by years of education. It is also supported by the work of Lillard and Weiss (1979), Baker (1997) and closely related to the recent work of Guvenen (2007). These authors estimate a statistical model of earnings and find important permanent differences in individual earnings growth rates. The other force is that agents differ in idiosyncratic human capital shocks received over the lifetime.

Future work entails important analysis both in terms of data and models. One important issue stems from the fact that some of the known stylized facts have ‘changed’. For example, the quantitative magnitude of the rise in consumption inequality, found say in Deaton and Paxson (1994) and which is so important for interpreting the role of shocks and market insurance, seems to have diminished with the recent samples. These results seem to also be more sensitive to whether one treats the data using cohort or time effects. There are several important efforts trying to address these issues by contemplating various structural changes, data collection issues, etc. (see Heathcote, Storesletten and Violante (2004) and Attanasio, Battistin and Ichimura (2004)). These are important measurement issues as they clearly affect our inference and modeling choices.

We are currently working on several extensions and applications of our framework. In particular, we are investigating issues related to taxation and social insurance in the presence of human capital acquisition and idiosyncratic risk. The analysis should reveal whether the explicit consideration of human capital accumulation is quantitatively important for some policy experiment and whether the conclusions are different from those that arise using exogenous wage or earnings framework. To get a better handle on the shocks to human capital it would be interesting to link our framework more directly to the literature on unemployment durations–the latter presumably affects the degree to which human capital depreciates. This can be a fruitful ground for better understanding the mapping from job loss duration and shocks to human capital. Another potentially important area is distinguishing between general human capital and schooling. We plan to extend our framework to allow for discrete schooling choice early in life. This extension can be important for differentiating the effects of skilled and unskilled exposure to these human capital shocks. Finally, in the background, many models assume agents (and their employer) know their ability type. It can be potentially interesting to extend our framework to allow for learning. Recent work by Guvenen and Smith (2007) seems to indicate that this can be an interesting channel for quantitatively interpreting the data.

Long Run Risks

A fundamental question both macro and finance academics seek to understand is what causes asset prices to fluctuate and what risks warrant significant risk premia? In general, fluctuations in asset prices can be attributed either to changes in costs of capital or to changes in expected cash flows. However, the conventional wisdom about cash flows, be it consumption growth or dividends growth, is that for all practical purposes they are i.i.d. This view leaves fluctuations in expected cash flows no role in explaining asset prices. As a result, much attention in this literature has focused on changes in the costs of capital. In general equilibrium, such changes are often accommodated by fluctuations in risk preferences.In Bansal and Yaron (2004), we challenge this view by refocusing attention to cash flows. We model consumption and dividend growth rates as containing (i) a small persistent expected growth rate component, and (ii) fluctuating volatility–which captures time-varying economic uncertainty and in the presence of the Epstein and Zin (1989) preferences leads to fluctuations in costs of capital/expected returns. We show that this specification for consumption and dividends is consistent with observed annual consumption and dividend data. Our model captures the intuition that financial markets dislike economic uncertainty, and fluctuating growth prospects are important for asset valuations. Shocks to expected growth alter expectations about future economic growth not only for short horizons but also for the very long run. Agents demand large equity risk premia as they fear that a reduction in economic growth prospects or a rise in economic uncertainty will lower equilibrium consumption, wealth and asset prices. This is distinct from habits-based models in which almost all asset price fluctuations are attributable to time variation in risk premium due to altering risk aversion. Hence, in these models fluctuations in corporate profits (or dividends) do not play a significant role in determining asset prices.

The Long Run Risks model relies on generalized recursive preferences (e.g., Kreps and Porteus (1978), Epstein and Zin (1989), Weil (1989)), which provide a separate role for relative risk aversion and the intertemporal elasticity of substitution (IES). In this framework, a restriction on preferences arises if agents are to explicitly fear (in the sense of lowering prices) adverse movements in expected growth and economic volatility. The restriction is that the IES be greater than one and that agents prefer early resolution of uncertainty (the risk aversion be larger than the reciprocal of the IES). Risk premia in this model are determined by three distinct sources of risk: transient, long-run, and volatility (economic uncertainty) risks, whereas in the standard time separable CRRA preferences the latter two risks simply have zero market prices of risk.

We use econometric techniques to show that the cash flow process, which contains in addition to an i.i.d component a small persistent component, is essentially indistinguishable in finite samples from a pure i.i.d process. Nonetheless, this process results in profoundly different asset pricing implications. Although, the innovations in expected cash flows are relatively small, it is their long-lasting feature that requires risk compensation and leads to large reaction in the price-dividend ratio and ex-post equity return and, consequently, the risk-premium on the asset. We show that risks related to varying growth prospects and fluctuating economic uncertainty can indeed quantitatively justify the observed equity premium, the level of the risk free rate, and the ex-post volatilities of the market return, risk free rate and the price-dividend ratio. The model implies time varying risk premia and, as in the data, that market return volatility is stochastic.

The Long Run Risks framework has already received quite a bit of attention and has been a useful framework for thinking about asset pricing. There is an extensive ongoing body of research examining various extensions to other assets markets. For example, to further evaluate the empirical implications of long-run risks model, Bansal, Dittmar and Lundblad (2005) measure cash-flows of different portfolios (value, growth, size, etc.) and show that differences in magnitude of the long-run response of cash-flows to consumption shocks can empirically account for differences in expected returns across assets. They show how to use cointegration to measure long-run consumption risks in cash flows, and document, that this goes quite a long way in explaining differences in mean returns. There is an ongoing discussion on understanding the precision of various approaches to measuring the long-run cash flow responses to consumption shocks, see for example Hansen, Heaton and Li (2005).

In a more recent work, Bansal, Kiku and Yaron (2007), we focus directly on a relatively rich menu of asset returns and show how to estimate the long-run risks model using the more standard Euler equation-GMM based approach such as in Hansen and Singleton (1982). The difficulty in applying the standard GMM techniques is that the intertemporal marginal rate of substitution contains the unobservable return on wealth. We circumvent this by exploiting the dynamics of aggregate consumption growth and the model’s Euler restrictions to solve for the unobserved return on the claim over the future consumption stream. We show that quantitatively the long-run risks model can successfully account for the market, value, and size sorted returns. Although we initially find low estimates of the IES and large risk aversion coefficients, we show via simulations that finite sample and time-averaging effects (the latter emanating from averaged annual data but monthly decision interval) lead to a downward bias in the IES estimate and a upward bias of the risk aversion coefficient–reconciling many of the previous findings in this literature. After accounting for these effects, the model generates many of the appropriate asset pricing results at reasonable values of risk aversion and IES. The empirical evidence in this paper highlights, again, the importance of low-frequency movements and time-varying uncertainty in economic growth for understanding risk-return trade-offs in financial markets.

One of the important channels of the Long-Run Risks model is the role of time variation in cash flow volatility. There is ample evidence of time variation in market returns at least at high frequency and also to some extent over business cycles. A question that naturally arises is whether there is a detectable component for these effects in consumption, dividends and earnings, the data that researchers in this area often use. In Bansal, Khatchatrian and Yaron (2005), we provide extensive empirical evidence supporting this channel of fluctuating economic uncertainty. We use data from the U.S. and several other countries to show that economic uncertainty (measured by consumption and earnings volatility) sharply predicts and is predicted by price-dividend and price-earnings ratios. Our evidence shows that a rise in economic uncertainty leads to a fall in asset prices, and that high valuation ratios predict low subsequent economic uncertainty. This latter finding is consistent with a long-lasting uncertainty channel, but is inconsistent with the standard formulation in which consumption growth is i.i.d and homoskedastic.

Views regarding the sources of variation of asset markets are often shaped via a decomposition of the variation of the price-dividend ratio. Interpreting this decomposition is intimately related to whether one views asset market fluctuations as driven by variation in discount rates or by changes in expected cash flows. This view turns out to depend on the type of cash flow one chooses to focus on. For example, in Bansal, Khatchatrian and Yaron (2005) we show that there is a strong positive relation between aggregate earnings growth and asset prices. This evidence suggests that broadening the notion of cash flows provides a different view about the sources of asset price fluctuations, and that the focus on dividends (which are somewhat less predictable) may have led researchers to dismiss the cash flow channel prematurely. Furthermore, in Bansal and Yaron (2006), we show that the price-dividend ratio decomposition critically hinges on whether one analyzes price and dividend per share or total dividend and total market capitalization. Broadly, the difference between these two cash flow measures captures equity investment from the non financial corporate sector to the corporate sector via issuances, and payments by the non-financial corporate sector to the private sector via repurchases. While there is no theoretical reason to impose cointegration between dividend per-share and consumption or output, macroeconomic restrictions suggest that total payouts ought to be cointegrated with consumption. This is indeed the case in the data, and estimation which imposes this restriction for aggregate payouts seems to support a view in which about 50% of the variation in valuation ratios are attributable to expected growth and the remaining to discount rates. Furthermore, a variant of the Long Run Risk model that imposes this cointegration restriction generates comparable results. These issues highlight the importance of examining and modeling cash flow dynamics. For example, models focusing on production, which typically impose cointegation, have the difficult task of endogenously generating the joint dynamics of consumption and dividends–features that are so critical for the purpose of asset pricing evaluations. Related issues arise when thinking about how cash flows of firms, sectors, portfolios and aggregate quantities relate. Future research will clearly have to explore these dimensions of the data and models will need to address them in a more consistent manner.

Long Run Risks is an exciting area and there are now several researchers and papers that use features of the Long Run Risks framework or extend it to address various issues and markets. These include research on foreign exchange markets, the term structure of interest rates, credit spreads, derivative markets, the recent rise in the stock market and the great moderation, cost of business cycles, cointegration and portfolio choice, the value premium, production economies with long run risks, heterogeneous agents, robust control and learning, inflation risk premia, and housing. I believe these lines of research will remain fruitful and contribute toward our understanding of economic risks.

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