Currently, studying heterogeneous agents (HA) is a very promising area. The empirical evidence suggests that heterogeneity is relevant and could provide answers related to the welfare questions -crucial in macroeconomics. Additionally, many fundamental macro questions cannot be addressed without touching on the issue of heterogeneity. There are many exciting HA models; however, one of the most important heterogeneous agents models is the Huggett model. Its importance lies in analyzing market equilibria considering two types of heterogeneity and the policy recommendations that could be given after analyzing the equilibrium.
The Huggett model, in general terms, aims to analyze how the movement of the idiosyncratic income can affect the equilibrium in both the goods and bond markets. A crucial assumption is that the bonds are not risky, hence its rate is the risk-free rate. Most importantly, agents are heterogeneous in two aspects: different income and wealth but similar preferences.
A crucial question is how to model income. There are at least two ways to do that. First, as a Poisson process, allowing the income to take two values. Second, as a diffusion process, allowing that the income to take many values. In particular, in this post, I will explain the case in which the income process follows a two-stage Poisson process: yt ∈ { y1 , y2 } with y1 < y2 . The income jumps from state 1 to state 2 with intensity λ1 and vice versa with intensity λ2 .
The next question is how the agent chooses his consumption optimally. In this model, each agent faces a dynamic and stochastic optimization problem. They maximize the lifetime present value utility function subject to the dynamic of individual wealth, the borrowing constraint, and the income process. When the agent solves his optimization problem, he takes as given the evolution of the equilibrium of the interest rate. Why? The underlying assumption is that the agent is a price-taker.
The next step is to set up and solve the equilibrium of this economy. The equilibrium is represented by a system of partial differential equations (PDEs). To solve this PDEs system, we need first to solve the Hamilton-Jacobi-Bellman equation (HJB) given an interest rate, and then to solve the Fokker-Planck equation (KFPE), and hence the equilibrium in the bond market.
Finally, we update the value of the interest rate and start the loop again until we find the equilibrium interest rate. From these equations, we can find the consumption and savings policy functions and the stationary distribution of wealth.
The great importance of this model also lies in the policy recommendations that can be given. For instance, economic policies should increase the probability of moving from income 1 (poor) to income 2 (rich). This is really relevant because it would develop efforts that would increase the probability of having a higher income, thus improving in some way the welfare of the households.
As we can see, the Hugget model is a powerful heterogeneous agents model that helps us draw important economic conclusions and policy recommendations.
I hope this topic has been informative and precise for you! See you in the next post. It is going to be about the numerical methods of the Huggett model -a fascinating topic as well-.
Annie.
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