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Hatchondo, Juan Carlos. "A Quantitative study of the role of wealth inequality on asset prices." Economic Quarterly. Federal Reserve Bank of Richmond. 2008. HighBeam Research. 24 Apr. 2018 <https://www.highbeam.com>.
Hatchondo, Juan Carlos. "A Quantitative study of the role of wealth inequality on asset prices." Economic Quarterly. 2008. HighBeam Research. (April 24, 2018). https://www.highbeam.com/doc/1G1-180927531.html
Hatchondo, Juan Carlos. "A Quantitative study of the role of wealth inequality on asset prices." Economic Quarterly. Federal Reserve Bank of Richmond. 2008. Retrieved April 24, 2018 from HighBeam Research: https://www.highbeam.com/doc/1G1-180927531.html
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There is an extensive body of work devoted to understanding the determinants of asset prices. The cornerstone formula behind most of these studies can be summarized in equation (1). The asset pricing equation states in recursive formulation that the current price of an asset equals the present discounted value of future payments delivered by the asset. Namely,
p([S.sub.t]) = E[m([S.sub.t],[S.sub.[t + 1])(x([S.sub.[t + 1]])+p([S.sub.[t + 1]])) | [S.sub.t], (1)
where [RHO] (s) denotes the current price of an asset in state s; x (s) denotes the payments delivered by the asset in state s; and m (s, s') denotes the stochastic discount factor from state s today to state s' tomorrow, that is, the function that is, the function that determines the equivalence between current period dollars in state s and next period dollars in state s'. It is apparent from equation (1) that the stochastic discount factor m plays a key role in explaining asset prices.
One strand of the literature estimates m using time series of asset prices, as well as other financial and macroeconomic variables. The estimation procedure is based on some arbitrary functional form linking the discount factor to the explanatory variables. Even though this strategy allows for a high degree of flexibility in order to find the stochastic discount factor that best fits the data, it does not provide a deep understanding of the forces that drive asset prices. In particular, this approach cannot explain what determines the shape of the estimated discount factor. This limitation becomes important once we want to understand how structural changes, like a modification in the tax code, may affect asset prices. The answer to this type of question requires that the stochastic discount factor is derived from the primitives of a model.
This is the strategy undertaken in the second strand of the literature.(1) The extra discipline imposed by this line of research has the additional benefit that it allows one to integrate the analysis of asset prices into the framework used for modern macroeconomic analysis.(2) On the other hand, the extra discipline imposes a cost: it limits the empirical performance of the model. The most notable discrepancy between the asset pricing model and the data was pointed out by Mehra and Prescott (1985). They calibrate a stylized version of the consumption-based asset pricing model to the U.S. economy and find that it is incapable of replicating the differential returns of stocks and bonds. The average yearly return on the Standard & Poor's 500 Index was 6.98 percent between 1889 and 1978, while the average return on 90-day government Treasury bills was 0.80 percent. Mehra and Prescott(1985) could explain an equity premium of, at most, 0.35 percent. The discrepancy, known as the equity premium puzzle, has motivated an extensive literature trying to understand why agents demand such a high premium for holding stocks.(3) The answer to this question has important implications in other areas. For example, most macroeconomic models conclude that the costs of business cycles are relatively low (see Lucas 2003), which suggests that agents do not care much about the risk of recessions. On the other hand, a high equity premium implies the opposite, which suggests that a macro model that delivers asset pricing behavior more aligned with the data may offer a different answer about the costs of business cycles.
The present article is placed in the second strand of the literature mentioned above. The objective here is to explore how robust the implications of the standard consumption-based asset pricing model are once we allow for preferences that do not aggregate individual behavior into a representative agent setup.
Mehra and Prescott (1985) consider an environment with complete markets and preferences that display a linear coefficient of absolute risk tolerance (ART) or hyperbolic absolute risk aversion (HARA).(4) This justifies the use of a representative-agent model. Several authors have explored how the presence of heterogenous agents could enrich the asset pricing implications of the standard model and, therefore, help explain the anomalies observed in the data. Constantinides and Duffle (1996), Heaton and Lucas (1996), and Krusell and Smith (1997) are prominent examples of this literature. These articles maintain the HARA assumption, but abandon the complete markets setup. The lack of complete markets introduces a role for the wealth distribution in the determination of asset prices.
An alternative departure from the basic model that also introduces a role for the wealth distribution is to abandon the assumption of a linear ART. This is the avenue taken in Gollier (2001). He studies explicitly the role that the curvature of the ART plays in a model with wealth inequality. He shows in a two-period setup that when the ART is concave, the equity premium in an unequal economy is larger than the equity premium obtained in an egalitarian economy. The aim of the present article is to quantify the analytical results provided in Gollier's article. Preferences with habit formation constitute another example of preferences with a nonlinear ART. Constantinides (1990) and Campbell and Cochrane (1999) are prominent examples of asset pricing models with habit formation. As in Gollier (2001), these preferences also introduce a role for the wealth distribution, but this channel is shut down in these articles by assuming homogeneous agents.
The present article considers a canonical Lucas tree model with complete markets. There is a single risky asset in the economy, namely a tree. This asset pays either high or low dividends. The probability distribution governing the dividend process is commonly known. Agents also trade a risk-free bond. Each agent receives in every period an exogenous endowment of goods, which can be interpreted as labor income. The endowment varies across agents. For simplicity, it is assumed that a fraction of the population receives a higher endowment in every period, that is, there is income inequality. Agents are also initially endowed with claims to the tree, which are unevenly distributed across agents. The last two features imply that wealth is unequally distributed. Agents share a utility function with a piecewise linear ART.
The exercise conducted in this article compares the equilibrium asset prices in an economy that features an unequal distribution of wealth with an egalitarian economy, that is, an economy that displays the same aggregate resources as the unequal economy, but in which there is no wealth heterogeneity. For a concave specification of the ART, this article finds evidence suggesting that the role played by the distribution of wealth on asset prices may be non-negligible. The unequal economy displays an equity premium between 24 and 47 basis points larger than the egalitarian economy. This is still far below the premium of 489 basis points observed in the data.(5) The risk-free rate in the unequal economy is between 11 and 20 basis points lower than in the egalitarian economy.
The rest of the article is organized as follows. Section 1 discusses the assumption of a concave ART. Section 2 introduces the model. Section 3 outlines how the model is calibrated. Section 4 presents the results, defining the equilibrium concept and describing how the model is solved. Finally, Section 5 presents the conclusions.
1. PREFERENCES
It is assumed that agents' preferences with respect to random payoffs satisfy the continuity and independence axioms and, therefore, can be represented by a von Neumann-Morgenstern expected utility formulation. The utility function is denoted by u (c). The utility function is increasing and concave in c. The concavity of u (c) implies that agents dislike risk, that is, agents are willing to pay a premium to eliminate consumption volatility. The two most common measures of the degree of risk aversion are the coefficient of absolute risk aversion and the coefficient of relative risk aversion. The coefficient of absolute risk aversion measures the magnitude of the premium (up to a constant of proportionality) that agents are willing to pay at a given consumption level c, in order to avoid a "small" gamble with zero mean and payoff levels unrelated to c. …
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