Recursive Contracts

Recursive methods have become a basic tool for the study of dynamic economic models, especially within macroeconomics. The advantage of recursive methods is its ability to summarise the optimal decisions of agents as a function of a small number of “state variables”. This is important in allowing the feasible solution of complex economic models, and has proved to be one of the most important advances in 20th century economics.

However, there is a wide class of interesting economic models in which the assumptions required to allow the application of recursive methods are not satisfied. Without a way of simply characterising the solution to these problems they are not computable. The CEP’s Albert Marcet, and Ramon Marimon provide in this paper the tool needed to simply characterise the solution to such models. In fact, their method has proved so popular that google scholar already reports that the paper has been cited over 350 times.

Among the many applications of their method is the study of optimal government policy. The reason that many optimal policy problems can’t be solved using recursive methods is that agents’ decisions today will depend on what they expect the government to do tomorrow. This means that future choices of the government affect the feasible set of actions the government can take today. This actually violates a key assumption of recursive theory, but these problems can be solved using Marcet & Marimon’s Recursive Contracts approach.

As examples in this field, Aiyagari et al. (2002) applied Marcet & Marimon’s method to solve for the government’s optimal labour tax rules when asset markets are incomplete (this being the incomplete markets counterpart to the famous optimal tax problem of Lucas & Stokey (1983)). Debortoli & Nunes (2010) also apply their methods to the problem of “loose commitment”: what happens when a government cannot completely commit to fulfil their promises, and can only partially commit?

This touches on a key contribution of their method: it allows the study of models that are time inconsistent. Many macroeconomic policy problems are time inconsistent, in the sense that the promises made by the government today would not be fulfilled tomorrow if the government were allowed to reoptimise. Marcet & Marimon allows us to study what the government would do in a time inconsistent model if it could actually somehow commit to carry out their promises. Other authors have previously studied what the government would do if it could not commit, and thus Marcet & Marimon allow us to study the other extreme, full commitment, as well as intermediate cases, as demonstrated by Debortoli & Nunes.

Further Reading:

"Recursive Contracts "[Link to paper] (Albert Marcet, Ramon Marimon) Paper No CEPDP1055 June 2011