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Mehra Prescott ModelEdit

The Mehra–Prescott model, introduced by Rajnish Mehra and Edward Prescott in 1985, is a foundational framework in asset pricing that links stock returns to the economics of consumption. In its core, the model asks: why do stocks, on average, yield such high returns relative to safe bonds? The answer it offers is that financial markets price risk through the marginal utility of consumption, and that solving for prices in a simple, consumption-based economy implies a large premium on risky assets unless investors exhibit a significant aversion to risk. The paper is a standard reference in discussions of the so-called Equity premium puzzle and has shaped how economists think about the relationship between consumption, risk, and asset prices. The model is frequently cited as a benchmark for thinking about risk sharing, intertemporal consumption choice, and the behavior of financial markets in the face of economic uncertainty.

In the Mehra–Prescott setup, a single representative agent consumes a stream of goods that is subject to random growth. The agent can invest in a risk-free asset or in a single risky security that pays out dividends tied to consumption. Prices are determined by an Euler equation that links desired consumption growth to the stochastic payoff of assets through the agent’s marginal utility. A key feature is the use of a constant relative risk aversion (CRRA) utility function, which makes the agent’s willingness to bear risk depend on how consumption responds to shocks. The model’s mathematics show that to reconcile observed stock returns with plausible consumption volatility, the coefficient of relative risk aversion must be relatively large. In the canonical implementations, this implies a notable risk price attached to the market portfolio, which helps explain why the equity premium—the excess return on stocks over bonds—appears so large in historical data. See Consumption-based asset pricing for the broader framework in which these ideas sit, and CRRA for the utility specification often used in the model.

Model structure

  • Assumptions and primitives

    • A representative agent with CRRA utility allocates consumption across time and states of the world. The relevant utility is often described in terms of a coefficient of relative risk aversion, commonly denoted by gamma.
    • The economy features a risk-free asset and a single risky asset (the Lucas tree) whose payoff is stochastically tied to aggregate consumption. See Lucas tree for the archetype used in many asset-pricing models.
    • The consumption process is driven by a stochastic growth process, typically modeled in a way that makes consumption growth uncertain but otherwise well-behaved.

  • Prices and risk premia

    • Prices are determined by the intertemporal Euler equation, which equates the marginal rate of substitution across periods to the expected payoff of held assets.
    • The price of risk—the premium investors demand to hold the risky asset—emerges from how much risk the asset adds to the household’s consumption stream. In this framework, higher perceived risk in consumption or greater measured risk aversion translates into higher required returns on the stock market.

  • What the model explains

    • The premium on equities relative to risk-free bonds can be explained by plausible levels of risk aversion and by the stochastic nature of consumption, without invoking more exotic behavioral biases.
    • The framework links macroeconomic uncertainty to financial prices, reinforcing the view that asset prices reflect fundamental real economic risks rather than merely investor psychology.

  • Key references and links

Implications and significance

  • The model is one of the first to show how macroeconomic risk translates into financial returns within a tractable, quantitative framework. It provides a clear link between the volatility of consumption and the risk premia that investors require.
  • It reinforces the idea that financial markets are a mechanism for sharing consumption risk over time and across states of the world. In this sense, the Mehra–Prescott model sits at the crossroads of macroeconomics and finance, illustrating how macro shocks can imprint themselves on observable prices.
  • The framework has influenced a wide range of extensions, including models with habit formation, rare disaster risks, and heterogeneous agents, each attempting to capture aspects of real-world data that the original setup could not fully explain.

Controversies and debates

  • Realism of assumptions

    • Critics point out that the model relies on a single representative agent, complete markets, and a simple two-asset economy. In reality, households are heterogeneous, markets are imperfect, and financial innovations create a richer set of investment opportunities. Critics argue these simplifications limit the applicability of the conclusions to real-world economies.
    • The assumption of a fixed coefficient of relative risk aversion across individuals and over time is also controversial. In practice, risk preferences may vary with wealth, experience, and macro conditions, which can affect risk premia in ways the original model cannot capture.

  • Empirical fit and alternatives

    • The original Mehra–Prescott result suggested fairly large risk aversion levels to reproduce the observed equity premium. Some critics have argued that such large parameters are implausible once one accounts for a fuller set of risk factors, frictions, and investor heterogeneity.
    • Competing explanations for the equity premium puzzle emphasize different mechanisms. Habit formation models (see Habit formation model) suggest that consumers’ past consumption affects current utility and can inflate risk premia without requiring extreme risk aversion. Rare disasters or "tail risk" models (see Rare disasters) attribute the large premia to low-probability, high-impact events that are not well captured by standard diffusion processes.
    • Cross-country and time-series evidence has shown that the magnitude of premia can vary with data choices and model specification. This has led to a broad literature testing the robustness of the equity premium puzzle and exploring how much of the premium is due to macroeconomic risk versus other channels.

  • Woke criticisms and responses

    • Some critics frame asset-pricing puzzles in terms of fairness, inequality, or social considerations, arguing that financial markets distort or miss broader economic purposes. Proponents of the Mehra–Prescott approach tend to view such critiques as outside the model’s scope: the framework is a tool for understanding how risk and consumption interact to determine prices, not a normative blueprint for social policy. From a defense-in-advantage perspective, these criticisms are often seen as outside the core scientific question and sometimes as ideological overreach that distracts from empirical testing and theoretical clarity.

  • Implications for policy and practice

    • The model underscores the importance of risk management, diversification, and long-horizon investing. If consumption risk matters for asset prices, then financial innovations and prudent macroeconomic policy that stabilizes consumption can influence risk premia and overall welfare.
    • Critics of overreliance on stylized models argue for incorporating heterogeneity, market frictions, and a broader set of risk factors to better capture real-world investor behavior and asset prices.

See also