Guvenen's two-agent production economy (Econometrica, 2009) explains a high, countercyclical equity premium together with a smooth risk-free rate through limited stock market participation combined with heterogeneity in the elasticity of intertemporal substitution (EIS): non-stockholders with low EIS use the riskless bond market to insure their labor income risk, which concentrates aggregate risk on a small group of wealthy stockholders who demand a high premium. The model achieves its stationary two-group wealth distribution by assuming the economy has no long-run growth, and it assumes the EIS partition (stockholders 0.3, non-stockholders 0.1) exogenously; the paper explicitly leaves the extension to long-run growth with a stationary wealth distribution under preference heterogeneity -- for example via benchmark consumption levels or nonhomothetic preferences -- as an important open area. Later work shows that stationary wealth distributions with preference heterogeneity, Pareto tails, and realistic asset prices are achievable in overlapping-generation economies (Gârleanu-Panageas 2015; Gomez 2025), and heterogeneous EIS across households is now empirically documented (Calvet et al. 2021). What remains open is the extension in the original framework itself: a growing production economy with limited participation and EIS heterogeneity whose de-trended equilibrium (equilibrium variables normalized by the economy's growth trend) admits a stationary, non-degenerate wealth distribution, together with a determination of whether the bond-market risk-concentration mechanism and its asset-pricing successes survive.

Background

A central fact of consumption-based asset pricing is the equity premium puzzle: US equity returns have exceeded safe interest rates by roughly 4-6 percent per year on average, far more than a standard representative-agent model can rationalize without implausible risk aversion, while the risk-free (sure, one-period) interest rate has been low and smooth. Standard power utility forces the coefficient of relative risk aversion (RRA, the willingness to substitute consumption across states of nature) to be the reciprocal of the elasticity of intertemporal substitution (EIS, the percent change in planned consumption growth induced by a one-percent change in the expected return on saving). Epstein-Zin preferences break this link by specifying RRA and EIS as separate parameters, which is what makes preference heterogeneity along the EIS dimension possible at all. Limited stock market participation is a robust household-finance fact: only about 20 percent of US households held stocks over 1962-1992 (the calibration window Guvenen adopts), stockholders are much wealthier than non-stockholders, and the top 20 percent of households have consistently owned more than 98 percent of stocks, with stockholders owning about 82 percent of net worth in the 1980s-1990s.

Guvenen (2009) studies a production economy with capital accumulation subject to investment adjustment costs (costs that make rapid changes in the capital stock expensive, so the price of capital can exceed its replacement cost and equities are levered claims on capital) and a representative firm, populated by two infinitely-lived agent types -- stockholders (about 20 percent of the population, EIS 0.3) and non-stockholders (EIS 0.1) -- both with Epstein-Zin preferences. Non-stockholders cannot hold equity but can trade a riskless bond. Because their labor income fluctuates with the aggregate economy, they use the bond market to smooth consumption; in equilibrium their aggregate labor income risk is transferred to and concentrated on the small stockholder group, which demands a high equity premium as compensation. The relatively high EIS of stockholders on the other side of the bond market keeps the interest rate smooth, and the wealth inequality between the groups makes the premium and the Sharpe ratio (expected excess return divided by its volatility) countercyclical. The paper's own robustness experiments show the assumed EIS partition is load-bearing: raising non-stockholders' EIS from 0.1 to 0.3 collapses the equity premium from 5.5 percent to 2.44 percent and the Sharpe ratio from 0.25 to 0.16.

Two acknowledged gaps motivate the open problem. First, the model is stationary in levels -- it has no long-run growth -- precisely because obtaining a stationary wealth distribution with heterogeneous preferences in a growing economy is difficult: absent some rebalancing device, the wealth share of one type drifts toward zero or one, so the two-type invariant distribution (the long-run distribution of the state to which the economy converges) degenerates. Chan and Kogan (2002) generate a stationary wealth distribution in a growing endowment economy with "benchmark consumption levels": utility uti=(cti−aCt)1−ρ/(1−ρ)u^i_t=(c^i_t-aC_t)^{1-\rho}/(1-\rho) depends on consumption relative to an aggregate benchmark CtC_t, so the effective EIS rises with a household's relative consumption and wealth. Browning and Crossley (2000) supply the consumption-theory basis for such nonhomotheticity (the marginal propensity to spend depends on the consumption level, so "luxuries are easier to postpone"). Guvenen's footnote 6 sketches exactly this device as a microfoundation for the EIS partition -- identical utility functions with benchmark levels make the EIS rise with wealth, so the wealthier stockholder group endogenously has the higher EIS -- and reports a supplemental-appendix calibration that reproduces the model's asset-pricing results in the no-growth economy; what the paper does not do is introduce long-run growth, calling this "an important area for extension of this model." Second, the EIS partition is assumed rather than derived, although later empirical work documents genuine EIS heterogeneity across households (Calvet et al. 2021).

A parallel literature has meanwhile made the joint dynamics of wealth distributions and asset prices stationary in growing economies by a different device: overlapping generations (OLG), in which finitely-lived agents are continually replaced by newborns. Gârleanu and Panageas (2015) construct an OLG economy with heterogeneous Epstein-Zin preferences that delivers a non-degenerate stationary wealth distribution and asset-pricing implications; Gomez (2025) studies a growing economy in which levered "entrepreneurs" (EIS 1) and low-EIS households coexist, the normalized wealth distribution is stationary with a Pareto tail (an upper tail decaying like a power of wealth), and the model is calibrated jointly to the risk-free rate, stock returns, and top wealth shares over the twentieth century, with an explicit feedback loop between asset prices and top wealth inequality. These are endowment-style economies in which stationarity comes from demographic turnover rather than from the benchmark-level preference device, participation-type is assigned at birth, and the bond-market risk-concentration mechanism at the heart of Guvenen's equity premium is absent.

Problem Statement

Extend the limited-participation, EIS-heterogeneity production economy of Guvenen (2009) to an economy with long-run growth, and settle whether its asset-pricing mechanism survives. Specifically: (i) construct the model inside the same framework -- a growing production economy with capital accumulation and investment adjustment costs, a riskless bond, and two agent groups distinguished by their access to the stock market (stockholders, about 20 percent of the population, and non-stockholders, who cannot hold equity and can trade only the bond), so that the two features generating the bond-market risk-concentration mechanism are retained -- with long-run growth produced by an explicitly stated source, with equilibrium variables normalized by the resulting deterministic trend, and with a stationarity device for the de-trended wealth distribution that is itself stated explicitly. Any device adopted must be embedded in the limited-participation production economy, keeping non-stockholders' exclusion from equity and their use of the bond market intact. The EIS partition may be retained as exogenous at Guvenen's benchmark values (stockholders 0.3, non-stockholders 0.1) or microfounded through a stated device; the choice made, and the EIS values it implies, should be specified. (ii) Establish that the de-trended equilibrium (equilibrium variables expressed relative to the economy's growth trend) admits a stationary, non-degenerate wealth distribution across the two groups: an invariant probability measure over the ergodic set of de-trended equilibrium distributions, as in the source's equilibrium definition, under which neither group's wealth share collapses to a boundary, i.e. the ergodic bounds of each group's de-trended wealth share lie strictly inside (0,1)(0,1); and characterize that distribution -- analytically, or through its simulated support, moments and tail behaviour as the construction permits, with uniqueness or ergodicity reported where they are established. (iii) Evaluate quantitatively, against Guvenen's benchmark calibration and the corresponding data moments reported in the source, whether the extended model retains the original model's central implications: the average equity premium and its cyclicality, the Sharpe ratio, the level and smoothness of the risk-free rate, the group net-worth shares (the source reports stockholders owning 82 percent of net worth in the 1980s-1990s data and 86-92 percent across its own model versions), and the business-cycle statistics, reporting the moments of the extended model together with their deviations from the no-growth benchmark. The scientific question to answer is whether the bond-market risk-concentration mechanism -- non-stockholders with low EIS insuring labor income risk in the bond market and thereby concentrating aggregate risk on wealthy stockholders -- remains a viable explanation of the equity premium once the framework is made consistent with long-run growth and a stationary wealth distribution, or whether the devices that growth-compatible stationarity requires destroy it. Either outcome, established for the model actually constructed, answers this question.

References

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