A Multiplier Approach to Understanding the Macro Implications of Household Finance

Abstract

Our paper examines the impact of heterogeneous trading technologies for households on asset prices and the distribution of wealth. We distinguish between passive traders who hold fixed portfolios of stocks and bonds, and active traders who adjust their portfolios to changes in expected returns. To solve the model, we derive an optimal consumption sharing rule that does not depend on the trading technology, and we derive an aggregation result for state prices. This allows us to solve for equilibrium prices and allocations without having to search for market-clearing prices in each asset market separately. We show that the fraction of total wealth held by active traders, not the fraction held by all participants, is critical for asset prices, because only these traders respond to variation in state prices and hence absorb the residual aggregate risk created by non-participants. We calibrate the heterogeneity in trading technologies to match the equity premium and the risk-free rate. The calibrated model reproduces the skewness and kurtosis of the wealth distribution in the data. In contrast to existing models with heterogeneous agents, our model matches the high volatility of returns and the low volatility of the risk-free rate.

Dynamic Competitive Economies with Complete Markets and Collateral Constraints

“…Judd et al (2003) show how to use this approach to compute equilibria in Lucas-style models with complete markets (and without collateral constraints). Chien and Lustig (2010) (see also Chien et al (2011)) consider a Markov equilibrium notion that features individual multipliers -interpretable as the inverse of our consumption weights -as the endogenous state variable in a model analogous to ours, though for a slightly different economy with a continuum of agents. The state, then, consists of the current shock and all agents' current Negishi weights, (s, λ).…”

Implementing the Modified Golden Rule? Optimal Ramsey Capital Taxation with Incomplete Markets Revisited

“…This approach of modeling incomplete markets is pioneered by Aiyagari, Marcet, Sargent, and Seppala (2002), who named the additional constraints for incomplete markets as measurability conditions. The later work by Chien, Cole, and Lustig (2011) extends this approach to heterogeneous-agent models in the context of asset pricing. The advantage of this time zero setting allows us to trace the evolution of stochastic agent types over time through the Lagrangian multipliers associated with these additional constraints.…”

Risk premiums and macroeconomic dynamics in a heterogeneous agent model

“…Alternatively, when the economy consists of shareholders as well as workers, our setup is very close to that of Danthine and Donaldson (2002). With all three agents present, our model has the ‡avor of agent heterogeneity as analyzed in Chien et al (2007). In our production economy, we incorporate the labor decision for shareholders and bondholders in all versions to maintain comparability over di¤erent models.…”

“…This means that workers will supply labor up to the point where their marginal rate of substitution between labor and consumption is equal to the spot wage, the second condition in (8). 7 Finally, following Danthine and Donaldson (2002), we consider to be a time-varying process, driven by exogenous shocks to the bargaining power. We will refer to these shocks as distribution risk where:…”