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

We present two new stylized facts regarding the setting of deposit rates by US banks. First, deposit-rate pass-through is greater at highly leveraged banks: they overshoot the average bank both when policy tightens and when financial stress forces rates downward. Second, large banks (once we control for other bank characteristics) display state-dependent pass-through: they under-react to policy rate hikes but over-react to rate cuts, pushing their deposit rates further below the average in both cases. 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.

Bank Heterogeneity, Deposits, Deep Habits, and the Pass-through of Interest Rates

Positive feedback in the climate system, e.g. the capacity of oceans to absorb carbon declines with global warming, does not affect the optimal carbon price under certainty very much. However, when we allow for uncertainty in the economy and the climate system, including tipping points, positive feedback loops significantly increase the optimal carbon price. We show that the effect is stronger when tail risks increase the probability of tipping at higher temperatures. We allow for extensions to incorporate Burke et al. (2015)’s specification of more convex damages and a positive effect of global warming on the risk of negative jumps in the capital stock, which further increase the social cost of carbon.

Carbon pricing under uncertainty: role of positive feedback

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.

Gustavo Mellior

Publications

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

Higher education funding, welfare and inequality in equilibrium

Working papers

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

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

Transitional dynamics of a debt limit tightening in a Aiyagari economy

Works in progress

Bankruptcy, information and welfare - Joint work with Katsuyuki Shibayama

Other contributions

Credit Crunch