Academic journal article Economic Quarterly - Federal Reserve Bank of Richmond

A Quantitative Study of the Role of Wealth Inequality on Asset Prices

Academic journal article Economic Quarterly - Federal Reserve Bank of Richmond

A Quantitative Study of the Role of Wealth Inequality on Asset Prices

Article excerpt

(ProQuest: ... denotes formulae omitted.)

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 p (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 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 estimatesmusing 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). …

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