Asset Prices under Habit Formation and Catching up with the Joneses

The paper introduces a utility function that nests three classes of preferences within a single functional form: time-separable utility, “catching up with the Joneses” utility in which the consumer cares about consumption relative to the lagged cross-sectional average level of consumption, and habit formation in which the benchmark is the consumer’s own past consumption. The device is a preference parameter equal to a geometric average of the consumer’s own lagged consumption and lagged aggregate consumption per capita, weighted by a parameter D, raised to a power; setting that power to zero recovers time separability, a positive power with D equal to zero gives the relative consumption model, and a positive power with D equal to one gives habit formation. Period utility is isoelastic in the ratio of consumption to that benchmark, so when the power is zero the curvature parameter is simply the coefficient of relative risk aversion. Abel embeds this in a Lucas (1978) exchange economy where all output is consumed in the period it is produced and all consumers are identical, so that individual and aggregate consumption both equal output and the benchmark’s growth is a power of output growth. Assuming gross consumption growth is i.i.d., he obtains explicit closed-form solutions for the price-dividend ratio on a claim to risky capital, the price of a one-period riskless bill and the price of a consol, and hence for unconditional expected returns. The target is Mehra and Prescott’s (1985) finding that over 1889 to 1978 in the United States the average annual real return on short-term bills was 0.80 percent and on stocks 6.98 percent – an equity premium of 618 basis points – which their time-separable isoelastic model could not raise above 35 basis points while keeping the expected riskless rate at or below 4 percent per year. Calibrating with a discount factor of 0.99, a mean gross consumption growth of 1.018 and a standard deviation of 0.036 (Mehra and Prescott’s moments, though imposed here as i.i.d. rather than their two-point Markov process with a serial correlation of -0.14), Abel reports that under time-separable preferences the equity premium “does not come anywhere close to the 600 point historical average” as the curvature parameter rises from 0.5 to 10, because the expected riskless rate rises along with the expected stock return. Under relative consumption preferences with a curvature of 6 the equity premium is 463 basis points and the unconditional riskless rate 2.07 percent – much closer to the historical averages – but the paper immediately flags a failure: “the conditional expected rates of return (not reported in the table) vary too much,” with the standard deviation of the conditional expected bill return reaching 17.87 percent, which Abel describes as “an unrealistic implication of the model” that “poses a challenge for future research.” Under habit formation expected returns on the two long-lived assets are extremely sensitive to the curvature parameter: at exactly logarithmic utility the returns coincide with the other two cases, but at a curvature of 1.14 the expected returns on both stocks and consols exceed 35 percent. Whether the growth rate is lognormal or two-point makes no substantial difference to expected returns at the parameter values reported.

Running Primary Deficits Forever in a Dynamically Efficient Economy: Feasibility and Optimality

Research Question

The paper addresses two questions about government debt rollover. First, a positive question: what is the maximum ratio of government bonds to capital that can be sustained forever without any primary budget surpluses? Second, a normative question: among sustainable bond-capital ratios along a balanced growth path, which one maximizes the welfare (steady-state utility) of consumers? The analysis is motivated by Blanchard’s (2019) AEA presidential address and the fiscal responses to the COVID-19 pandemic.

Andrew B. Abel | Macro Paper Warehouse

Asset Prices under Habit Formation and Catching up with the Joneses

Running Primary Deficits Forever in a Dynamically Efficient Economy: Feasibility and Optimality

Research Question