We introduce bankruptcy choice to the heterogeneous agent in continuous time (HACT) framework developed in Achdou et al. (2022). We demonstrate that real-options-like problems such as the decision to declare bankruptcy can be efficiently solved using the ``value-matching'' condition only (unlike alternative methods that require both value matching and ``smooth pasting''). Moreover, we show that under certain conditions, smooth-pasting may not hold. Given this, we recommend (and demonstrate the use of) linear complementarity problem (LCP) solvers for real-option like problems, especially in settings where control variables depend on the slope of the value function. We show that this approach is more flexible and computationally efficient than other popular solution methods. In particular, it is less prone to errors in settings that have corner solutions.

Economic Letters, 2024

Solving HACT models with bankruptcy choice

This paper analyses theoretically and quantitatively the effect that different higher education funding policies have on welfare (on aggregate and at the individual level) and wealth inequality. A heterogeneous agent model in continuous time, which has uninsurable income risk and endogenous educational choice is used to evaluate five different higher education financing schemes. Educational investments can be self financed, supported by government guaranteed student loans – that may come with or without income contingent support – or be covered by the public sector. When educational costs are small, differences in outcomes amongst systems are negligible. On the other hand, when these costs rise to realistic levels we see that there can be large gains in welfare and significant drops in inequality by moving to a system with more public sector support. This support can come in the form of tuition subsidies and/or income contingent student loans. However, as the cost of education and the share of debtors in society gets larger, it is preferable to increase public support in the form of tuition subsidies. The reason is that there is a pecuniary externality of debt that gets magnified when student loans become excessive. While I identify large steady state welfare gains from more public sector ﬁnancing, I show that the transition costs can be large enough to justify the status quo.

Journal of Comparative Economics, 2025 (forthcoming). Awarded the Peter Sinclair prize for best paper at the 2020 Money Macro Finance PhD Conference

Higher education funding, welfare and inequality in equilibrium

List

This article develops a simple method for computing the transitional dynamics of a debt limit tightening in heterogeneous agent in continuous time (HACT) models. The method is implemented for three different types of permanent debt limit contractions. The results show that contractions that are announced in advance or that are gradual are the best at mitigating welfare losses, although they slow transitions. Additionally, this paper extends on Obiols (2011) by computing the welfare loses of a debt limit tightening. The results indicate that comparing steady state welfare due to different debt limits is misleading; the transition costs must be taken into account. Furthermore, the article illustrates how the findings in Obiols (2011) still hold when we use Epstein-Duffie preferences.

Transitional dynamics of a debt limit tightening in a Aiyagari economy

We present two new stylized facts regarding the setting of deposit rates by US banks. First, during periods of financial stress, more highly leveraged banks are slower to pass-through a falling federal funds rate to deposit customers. Second, during cyclical downturns, larger banks (once we control for other bank characteristics are faster to pass-through a falling federal funds rate to deposit customers. To explain these two stylized facts, we develop a continuous-time general equilibrium heterogenous bank model, in which banks face an occasionally binding leverage constraint, have monopolistic power in the market for household deposits, and importantly, households have deep habits with regard to their demand for banking services.

Gustavo Mellior

Publications

Solving HACT models with bankruptcy choice - Joint work with Katsuyuki Shibayama

Higher education funding, welfare and inequality in equilibrium

Working papers

Transitional dynamics of a debt limit tightening in a Aiyagari economy

Bank Heterogeneity, Deposits, Deep Habits, and the Pass-through of Interest Rates - Joint work with Oliver de Groot

Works in progress

Carbon pricing under uncertainty: role of positive feedback - Joint work with Rick van der Ploeg

Bankruptcy, information and welfare - Joint work with Katsuyuki Shibayama

Other contributions

Credit Crunch