INDIVISIBLE LABOR, LOTTERIES AND IDIOSYNCRATIC PRODUCTIVITY SHOCKS

This paper extends the indivisible-labor model by Hansen (1985) and Rogerson (1988) to include multiple consumers who differ in initial wealth and whose labor productivities are subject to idiosyncratic shocks. In the presence of idiosyncratic uncertainty, the optimal allocations for the individual employment probabilities are at corners: agents work with probability one (zero) when their productivities are high (low). As in Hansen (1985), each agent in our indivisible-labor economy behaves as if her labor choice was divisible and her utility function was linear in hours worked. However, the quasi-linearity of the social preferences, established in Hansen (1985) for the homogeneous-agent case, does not survive after the introduction of idiosyncratic shocks.indivisible labor, lotteries, idiosyncratic shocks, neoclassical growth model

QUASI-LINEAR PREFERENCES IN THE MACROECONOMY: INDETERMINACY, HETEROGENEITY ANDTHE REPRESENTATIVE CONSUMER

We use aggregation theory to investigate the link between one-consumer and multi-consumer economies under a quasi-linear class of preferences. Our study is carried out in the context of the neoclassical growth model. The quasi-linear preferences considered are additive in consumption and leisure and linear in leisure. We first show that in a homogeneous agents economy, the individual hours worked are not uniquely determined. We then demonstrate that the indeterminacy can be resolved by introducing heterogeneity. For example, idiosyncratic shocks to productivities or imperfect substitutability of labor restore the uniqueness of equilibrium. As a special case, our analysis includes the indivisible labor model by Hansen (1985).Quasi-linear preferences

INDETERMINACY IN A LOG-LINEARIZED NEOCLASSICAL ROWTH MODEL WITH QUASI-GEOMETRIC DISCOUNTING

This paper studies the properties of solutions to a log-linearized version of the neoclassical growth model with quasi-geometric discounting. We show that after the log-linearization, the model has indeterminacy and multiplicity of equilibria even though the original non-linear model has a unique interior solution. Specifically, in both the deterministic and stochastic cases, the log-linearized model has a continuum of steady states. In the deterministic case, there is a unique log-linear policy function leading to each steady state, while in the stochastic case, there is a continuum of log-linear policy functions, associated with each steady state. Hence, the standard log-linearization method cannot be applied for solving models with quasi-geometric discounting.quasi-geometric (quasi-hyperbolic) discounting, time inconsistency, neoclassical growth model

CAPITAL-SKILL COMPLEMENTARITY AND STEADY-STATE GROWTH

We construct a general-equilibrium version of Krusell, Ohanian, Ríos-Rulland Violante’s (2000) model with capital-skill complementarity. To account forgrowth patterns observed in the data, we assume several sources of growthsimultaneously, specifically, exogenous growth of skilled and unskilled labor,equipment-specific technological progress, skilled and unskilled labor-augmentingtechnological progress and Hicks-neutral technological progress. We deriverestrictions that make our model consistent with steady-state growth. A calibratedversion of our model is able to account for the key growth patterns in the U.S. data,including those for capital equipment and structures, skilled and unskilled laborand output, but it fails to explain the long-run behavior of the skill premium.capital-skill complementarity, steady state growth, skill premium, growth model.

HETEROGENEITY IN THE DEGREE OF QUASI-GEOMETRIC DISCOUNTING: THE DISTRIBUTIONAL IMPLICATIONS

This paper modifies the standard one-sector growth model with uninsurable idiosyncratic risk and liquidity constraints to include multiple types of quasi-geometric consumers. For a calibrated version of the model, we show that a modest difference between the quasi-geometric discounting parameters of types can lead to large differences in their marginal propensities to consume. Unlike the standard one-sector growth model, the model with heterogeneous quasi-geometric consumers can generate realistic degrees of wealth inequality.Time inconsistency, quasi-geometric discounting, hyperbolic discounting

SOLVING THE NEOCLASSICAL GROWTH MODEL WITH QUASI-GEOMETRIC DISCOUNTING: NON-LINEAR EULER-EQUATION MODELS

The neoclassical growth model with quasi-geometric discounting is shown by Krusell and Smith (2000) to have multiple solutions. As a result, value-iterative methods fail to converge. The set of equilibria is however reduced if we restrict our attention to the interior (satisfying the Euler equation) solution. We study the performance of the grid-based and the simulation-based Euler-equation methods in the given context. We find that both methods converge to an interior solution in a wide range of parameter values, not only in the ''test'' model with the closed-form solution but also in more general settings, including those with uncertainty.quasi-geometric (hyperbolic) discounting, time-inconsistency,

SOLVING NONLINEAR DYNAMIC STOCHASTIC MODELS: AN ALGORITHM COMPUTING VALUE FUNCTIONS BY SIMULATIONS

This paper presents an algorithm for solving nonlinear dynamic stochastic models that computes value function by simulations. We argue that the proposed algorithm can be a useful alternative to the existing methods in some applications.Nonlinear stochastic models; Value function; Parameterized expectations; Monte Carlo simulations; Numerical solutions

- DIFFERENTIAL RESPONSES OF LABOR SUPPLY ACROSS PRODUCTIVITY GROUPS

There is a substantial amount of microeconomic evidence documenting diferential responses oflabor supply across productivity groups. In partic-ular, more productive individuals: (i) enjoy ahigher employment rate, (ii) have a lower volatility of employment and (iii) spend less time workingat home. This paper constructs a real business cycle model with permanent heterogeneity inindividual productivity. We calibrate the model with five productivity groups to match keyaggregate features of the U.S. economy. We find that the model delivers most of the properties ofthe data.Ex-ante heterogeneity, Indivisible labor, Home production

PREFERENCE SHOCKS FROM AGGREGATION: TIME SERIES DATA EVIDENCE

We investigate the impact of preference shocks on the aggregate dynamics of the U.S. economy in the context of a neoclassical growth model derived from aggregation. The aggregation result we use is as follows: if markets are complete and if agents have identical preferences of the addilog type, then the heterogeneous-agent economy where agents are subject to idiosyncratic productivity shocks behaves as if there was a representative consumer who faces shocks to preferences and technology. We estimate the parameters in the aggregation-based model from the aggregate time-series data and compute the numerical solution. We find that the preference shocks play an important role in the aggregate labor-market fluctuations.neoclassical growth model, heterogenous agents, aggregation, business cycles, preference shock

THE NEOCLASSICAL GROWTH MODEL WITH HETEROGENOUS QUASI-GEOMETRIC CONSUMERS

This paper studies how the assumption of quasi-geometric (quasi-hyperbolic) discounting affects the individual consumption-savings behavior in the context of the standard one-sector neoclassical growth model with heterogeneous agents. The agents are subject to idiosyncratic shocks and face borrowing constraints. We confine attention to an interior Markov recursive equilibrium. The consequence of quasi-geometric discounting is that the effective discount factor of an agent is not a constant, but an endogenous variable which depends on the agent's current state. We show, both analytically and by simulation, that this feature of the model can significantly affect its distributional implications.time inconsistency, quasi-geometric discounting, quasi-hyperbolic discounting, idiosyncratic shocks, wealth inequality.