Rare Disasters & Asset Prices

The core of the research employs a representative-consumer model incorporating Epstein-Zin-Weil (EZW) preferences and independent and identically distributed (i.i.d.) shocks. This framework includes the critical element of 'rare disasters,' which are infrequent but significantly impactful economic downturns. The model's success lies in its ability to align with key asset-pricing observations, particularly when the coefficient of relative risk aversion is set between 3 and 4. This range accurately reflects observed equity premia and risk-free real interest rates. A crucial aspect is the intertemporal elasticity of substitution (IES), which, when greater than one, leads to predictions consistent with market behavior: increased uncertainty decreases the price-dividend ratio for equity, while a rise in expected growth increases it. The model's capacity to match major asset pricing characteristics positions it as a suitable tool for analyzing the welfare implications of aggregate consumption uncertainty.

The study contrasts its findings with those derived from models using simpler power utility functions. While the EZW model shares similarities with the power utility model in its basic asset-pricing conditions, crucial differences emerge. The EZW model incorporates consumption into asset-pricing formulas using an exponent involving the coefficient of relative risk aversion rather than the IES. Furthermore, the effective rate of time preference (ρ*) differs from the standard rate (ρ) when the coefficient of relative risk aversion deviates from the reciprocal of the IES. This effective rate is influenced by several factors including the standard rate, IES, coefficient of relative risk aversion, and parameters representing expected growth and uncertainty. The EZW model, employing i.i.d. shocks, is as straightforward as the power utility model but accurately captures a broader array of asset-pricing facts, successfully explaining the equity premium and risk-free rate with a coefficient of relative risk aversion of 3-4, unlike its power utility counterpart. In an AK model with endogenous saving, and IES above one, increased uncertainty leads to lower savings.

The research addresses the limitations of previous models, such as Lucas's model, which struggles to accurately predict the high equity premium and low risk-free rate. This failure, noted by Atkeson and Phelan (1994), highlights a lack of consideration for essential aspects of consumption uncertainty. This deficiency compromises the accuracy of welfare effect estimations. The study adopts the Atkeson-Phelan principle, suggesting that analyses of consumption uncertainty should be conducted using models that closely replicate how asset markets price this uncertainty. The incorporation of rare economic disasters, similar to Rietz (1988), is crucial for aligning the model with real-world asset pricing facts. The model demonstrates that changes in consumption uncertainty, reflecting shifts in disaster probabilities, have significant welfare implications. The study shows a willingness to sacrifice as much as 20% of annual GDP to eliminate the risk of macroeconomic disasters, while the impact of standard economic fluctuations is much less severe (approximately 1.5% of GDP).

The paper explores the implications of the model with respect to the impact of various parameters such as the mean growth rate (g*), the coefficient of relative risk aversion (γ), and the intertemporal elasticity of substitution (IES, represented by θ). The model predicts a negative relationship between uncertainty and the price-dividend ratio when IES is above 1, contrasting with predictions from models using power utility. The model's calibration involves choosing parameters to generate plausible risk-free real interest rates, and the study highlights the difficulty of separately identifying the rate of time preference (ρ) and the IES from asset price data alone. The calibration involves data from various sources, including data on asset returns and consumer price indexes from Global Financial Data (discussed in Taylor, 2005) and uses macroeconomic estimates of the IES (Hall, 1988) in conjunction with the observed real rate of return on government bills across 11 OECD countries from 1880-2005 (averaging 0.010 per year). The parameters are then adjusted to generate a plausible risk-free interest rate within the model, while maintaining consistency with observed equity premia.

The study's primary focus is on quantifying the welfare costs associated with different types of economic uncertainty. It contrasts the welfare impact of 'normal' economic fluctuations with that of rare, large-scale macroeconomic disasters. The model reveals a stark difference: the welfare cost of disaster risk is dramatically higher. Specifically, the simulations indicate that society would be willing to accept a 20% annual reduction in real GDP to eliminate the possibility of major economic collapses. This contrasts sharply with the much smaller, though still significant, welfare cost of around 1.5% of GDP associated with typical economic fluctuations. This disparity underscores the disproportionate impact of rare, catastrophic events on overall societal well-being. The magnitude of GDP contractions during these disasters historically ranged from 15% to over 60%.

The research emphasizes the importance of using models that accurately reflect asset market pricing when analyzing welfare effects from consumption uncertainty. This aligns with the Atkeson-Phelan principle, which argues that accurate assessment of welfare costs requires models capable of replicating observed asset prices. The authors highlight that previous models, like Lucas's model, fail to adequately capture the high equity premium and low risk-free rate observed in real-world markets, leading to unreliable welfare cost estimates. The inclusion of 'rare disasters,' as suggested by Rietz (1988), proves critical in addressing this issue and achieving a closer match with real market data. The improved accuracy of the model, stemming from its ability to replicate observed asset market behavior, strengthens the confidence in its welfare cost calculations. The model's success in matching asset pricing facts significantly enhances the reliability of its conclusions about welfare impacts of various economic uncertainties.

The paper further explores the sensitivity of welfare cost estimates to variations in key parameters. The impact of changes in the intertemporal elasticity of substitution (θ) and the coefficient of relative risk aversion (γ) on the welfare gains from eliminating uncertainty are analyzed. While changes in θ influence the effective rate of time preference (ρ*), the study maintains ρ* at its baseline value to isolate the effects of θ and γ. Results show that decreases in the coefficient of relative risk aversion reduce the welfare benefits from eliminating uncertainty. These effects are more significant than those from altering θ. For instance, holding θ constant at 0.50, the welfare gain from eliminating normal economic fluctuations drops from 1.65% of output at γ=4 to 0.74% at γ=1, while the corresponding reduction for disaster risk falls from 24% to 4.6%. This analysis emphasizes the substantial influence of risk aversion on the welfare implications of uncertainty, particularly with respect to the significant costs associated with disaster risk.

This section extends the model by incorporating endogenous saving and investment, moving beyond the simpler endowment economy framework. The chosen approach utilizes a tractable AK model, building upon the work presented in Barro (2006, section VIII). In contrast to the endowment economy where agents passively accept changes in uncertainty, the AK model allows agents to actively adjust their saving and investment behavior in response to shifts in economic uncertainty. This adjustment mechanism has a potential impact on the overall welfare costs, particularly for large changes in the model's parameters. The model's calibration maintains consistency with the baseline parameters from the endowment economy model, including a coefficient of relative risk aversion (γ) of 4 and an intertemporal elasticity of substitution (IES) reciprocal (θ) of 0.5. Matching the expected growth rate between the two models is crucial for a consistent comparison of welfare effects.

The study compares the welfare costs of uncertainty in the endogenous saving model to those in the endowment economy. A key finding is that the welfare costs are identical in both models when the gross saving ratio (ν) remains constant at its initial value (0.075). In this scenario, the endogenous-saving model effectively behaves like an endowment economy. This finding holds true for both the welfare costs from eliminating typical economic fluctuations (σ=0) and those from eliminating disaster risk (p=0). Specifically, the compensating proportionate reduction in GDP for setting σ=0 is 1.65%, and for setting p=0, it's 32.5%. When θ equals 1, the saving ratio becomes independent of both σ and p, resulting in identical outcomes for fixed and variable ν scenarios. A modified formula for calculating welfare costs (which incorporates the investment ratio) is presented, adjusting for the endogenous saving aspect of the model.

A new formula, modifying the original one, is used for welfare cost calculations in the context of endogenous saving. This modified equation explicitly incorporates the investment ratio (ν) alongside the price-dividend ratios (V and V*) which are determined using the model's parameters and expected growth rate. This modification reflects the fact that, unlike the endowment economy, the endogenous saving model allows agents to react to changes in uncertainty by adjusting their saving and investment behavior. This adjustment can alter the welfare effects calculated, particularly when the saving ratio is allowed to vary. The variables V and V* represent price-dividend ratios but incorporate expected growth rate adjustments that reflect the model's endogenous nature. The variables ν and ν* represent investment ratios in initial and hypothetical states respectively. The modified welfare calculation emphasizes the importance of considering the dynamic interaction between saving behavior and the welfare impacts of uncertainty in such economies.

The concluding observations emphasize the contrasting welfare implications of different types of economic uncertainty. The parameter σ, representing the magnitude of typical business fluctuations, is analyzed in relation to the post-World War II period in OECD countries, which was relatively tranquil. A reduction in σ, therefore, represents a marginal improvement to already mild business cycles. The welfare gains from such a reduction are modest (around 1.5% of GDP annually), highlighting that the benefit of reducing already-low fluctuations is comparatively limited. In stark contrast, parameters p and b represent major economic disasters, such as those experienced during World Wars I and II and the Great Depression. These parameters represent larger-scale risks, including events like the Asian financial crisis or the Argentine exchange-rate crisis. Reducing p (probability) lowers the chance of such events, while reducing b (size) lessens their potential impact. The study finds the welfare benefits of mitigating these major economic disasters are far more substantial than the benefits of smoothing ordinary business cycles.

The research explores how various macroeconomic stabilization policies, particularly monetary policy, can affect both typical business fluctuations (σ) and the probability/magnitude of major economic disasters (p and b). The successful management of inflation in OECD countries since the mid-1980s is cited as an example, potentially contributing to milder fluctuations and stronger economic growth. However, the role of central banks in either exacerbating or mitigating major crises is also discussed, referencing examples like the Federal Reserve's role in the Great Depression. The study acknowledges that while some policies might reduce σ, their impact on p and b remains an open question. Furthermore, it proposes the potential for an indirect benefit from reducing σ; that is, mitigating smaller economic downturns might reduce the probability of these turning into larger-scale disasters. This highlights the significant potential rewards of effective stabilization policies and warrants further investigation.

The conclusion extends the discussion to the influence of governmental institutions and policies on disaster probabilities and sizes. The formation of the European Union and the adoption of the euro are used as examples, noting their effects on business fluctuations and growth, but also emphasizing the underlying political motivation—to prevent another large-scale conflict (reducing the probability of war, represented by p). The paper concludes by highlighting that eliminating all uncertainty related to large economic crises or similar events (such as large-scale natural disasters and epidemics) yields substantial welfare gains, approximately 15 times larger than the gains from mitigating typical economic fluctuations. The analysis focuses on utility losses from reduced consumption but acknowledges that incorporating direct utility losses from mortality and health would further amplify these significant welfare effects. The research emphasizes the need for further investigation into the ways monetary authorities and government institutions can actively mitigate the probability and severity of major economic collapses.