# Jan Žemlička

# Ph.D. candidate at UZH BF and SFI

About

Hi! I am a Ph.D. candidate at the Department of Banking and Finance at the University of Zürich and the Swiss Finance Institute working under the guidance of Felix Kübler. Previously, I was a student of Marek Kapička at CERGE-EI, and spent Fall 2022 as a visiting scholar at UPenn Economics under the supervision of Jesús Fernandéz-Villaverde.My research interests lie in macrofinance, monetary economics, and development of computational methods for solving models originating in those fields.You can find my CV attached here.

**RESEARCH**

Economics-Inspired Neural Networks with Stabilizing Homotopies

with *Marlon Azinovic*

Contemporary deep learning based solution methods used to compute approximate equilibria of high-dimensional dynamic stochastic economic models are often faced with two pain points. The first problem is that the loss function typically encodes a diverse set of equilibrium conditions, such as market clearing and households' or firms' optimality conditions. Hence the training algorithm trades off errors between those - potentially very different - equilibrium conditions. This renders the interpretation of the remaining errors challenging. The second problem is that portfolio choice in models with multiple assets is only pinned down for low errors in the corresponding equilibrium conditions. In the beginning of training, this can lead to fluctuating policies for different assets, which hampers the training process. To alleviate these issues, we propose two complementary innovations. First, we introduce Market Clearing Layers, a neural network architecture that automatically enforces all the market clearing conditions and borrowing constraints in the economy. Encoding economic constraints into the neural network architecture reduces the number of terms in the loss function and enhances the interpretability of the remaining equilibrium errors. Furthermore, we present a homotopy algorithm for solving portfolio choice problems with multiple assets, which ameliorates numerical instabilities arising in the context of deep learning. To illustrate our method we solve an overlapping generations model with two permanent risk aversion types, three distinct assets, and aggregate shocks.**Presented** at: Reading Group, UPenn (2022); CERGE-EI, Prague (2023); Advances in Computational Economics and Finance, UZH (2023); CEF Conference, Nice (2023); DSE Conference,* Lausanne (2023); EEA-ESEM Conference, Barcelona (2023).*: Presented by coauthor

Average Inflation Targeting in a Behavioral Heterogeneous Agent New Keynesian Model

with *František Mašek*

We analyze the optimal window length in the average inflation targeting rule within a Behavioral THANK model of Pfäuti and Seyrich (2022). The central bank faces an occasionally binding effective lower bound (ELB) or persistent supply shocks and can also use quantitative easing when we merge Pfäuti and Seyrich (2022) with Sims et al. (2020). We show that the optimal averaging period is infinitely long in the case of a conventional degree of myopia. However, finite yet long-lasting window lengths dominate for a higher cognitive discounting. We solve the model locally and globally to disentangle the effects of uncertainty about hitting the ELB in the future, leading to a downward inflation bias in the case of the global solution. Given the solution technique, the welfare loss difference is considerably decreasing in the degree of history dependence.

Stabilizing Ergodic Set Simulation in Deep Equilibrium Nets Training

PRELIMINARY

I propose a new approach for approximating the ergodic set of dynamic macroeconomic models in deep learning solution methods: the Convergent Cloud Method. Instead of tracking a small number of state particles for a very large number of periods, my method obtains training data by simulating the transition of a large cloud of states toward the ergodic set of the model. The key advantage of my procedure is stability gain: empirically, I show that my procedure is substantially less likely to diverge relative to long simulation procedures. Beyond that, my method bypasses the need for a sophisticated initial guess and features a massively parallel structure, which allows for more than 60 percent speed-up on modern deep learning hardware.

GET IN TOUCH

Center for Economic Research and Graduate Education – Economics Institute

Politických vězňů 7

111 21 Prague 1

Czech Republic[email protected]