2026working paper
Behnaz Minooei Fard, Willi Semmler, Tato Khundadze
SSRN
Critical mineral markets exhibit nonlinear price responses, constrained supply adjustment, and substantial asymmetries between dominant and emerging producers. This paper develops a dynamic two-player model of strategic critical-mineral extraction involving China and the rest of the world (ROW). The model combines discovered-reserve dynamics with a reduced-form nonlinear cubic price function and is solved using a Nash–Model Predictive Control framework with finite decision horizons. Three scenarios examine the effects of changes in the ROW’s marginal extraction cost and production support. The simulations show that reducing the ROW’s marginal cost substantially increases its extraction and profitability. Continued production support strengthens this effect, but also raises aggregate extraction and accelerates reserve depletion. When support is removed, the ROW remains viable and profitable, although its extraction and profits are lower than in the supported case. Longer decision horizons induce earlier extraction restraint and preserve a larger stock of discovered reserves. The reported solutions remain within the downward-sloping region of the nonlinear price function and should therefore be interpreted as regime-specific Nash–MPC equilibria. The results highlight a policy trade-off between supply diversification and long-run resource conservation.
2026published
Herbert Dawid, Philipp Harting, Michael Neugart
Labour Economics
Online digital labor platforms are increasingly important as tools for matching employers and workers. They reduce labor market frictions and provide the opportunity for remote work, but concerns have been raised about whether workers receive adequate incomes. We study how the use of machine-learning based algorithms for the determination of wage offers affects workers’ wages on online labor platforms by setting up a simulation framework and analyzing outcomes under different assumptions about platform and algorithm design. Firms use reinforcement-learning to update posted wages on the platform, and heterogeneous workers send applications based on the posted information. We show that, if firms use a deep Q-network (DQN), a state-of-the-art machine learning algorithm, collusive wages emerge when the number of competitors is small, and no experience replay is used. Our findings are robust across many features of the model, including the design of the online labor platform.
2026working paper
Tato Khundadze, Willi Semmler
Frontiers in Artificial Intelligence · AI for Human Learning and Behavior Change
The resilience of economic systems depends mainly on coordination among key stakeholders during macroeconomic or external shocks, while a lack of coordination can lead to financial and economic crises. The paper builds on the experience of global and regional shocks, such as the Eurozone crises of 2009–2012 and the economic disruption resulting from COVID-19, starting in 2020. The paper demonstrates the importance of cooperation in monetary and fiscal policies during emergencies to address macroeconomic non-resilience, particularly focusing on public debt management. The Euro area is chosen as the sample for testing the models presented in the paper, given that its resilience is heavily dependent on cooperation among different actors within the region. The shocks affecting nations within the European Union are asymmetric, and the responses to these shocks require coordination, considering heterogeneous economic structures, levels of economic development, and policies. We develop a macroeconomic modeling framework to simulate fiscal and monetary policy interactions under a cooperative regime. The approach builds on earlier nonlinear control models and incorporates modern reinforcement learning techniques. Specifically, we implement the Soft Actor-Critic algorithm to optimize policy responses across key variables including inflation, interest rates, output gaps, public debt, and government net lending. We demonstrate that the Soft Actor-Critic algorithm provides comparable or, in some cases, better solutions to multi-objective macroeconomic optimization problems, in comparison to Nonlinear Model Predictive Control (NMPC) algorithm.
2025published
Helmut Maurer, Willi Semmler
Central European Journal of Operations Research
In this paper, we propose a multi-objective control framework to address climate change, climate risks, and the transition to a low-carbon economy. Extending our previous collaborative work in Atolia et al. (Mathematical Control and Related Fields, 13:583–604, 2023), we build on a Nordhaus-type DICE model to incorporate optimal macroeconomic policies such as mitigation, adaptation, and climate-related infrastructure investment, with a focus on the dynamics of decarbonization.
Based on a finite-horizon model that includes the threats of climate disasters arising from CO₂ emissions and temperature increases, we study preventive measures such as adaptation aimed at reducing disaster impacts. Our optimal control problem includes a dynamical system with a multi-dimensional state vector representing private capital, green capital, public capital, the stock of brown energy in the ground, carbon emissions, and temperature.
The objective function captures preferences over consumption while also accounting for atmospheric CO₂, climate-risk events, and mitigation and adaptation policies. Given the multiple objectives involved in climate policy, the control vector includes mitigation, adaptation, and infrastructure investment decisions. The optimal control problem is studied under various state constraints.
In two scenarios, we compute the Pareto front for a bi-objective control problem. Optimization over the Pareto front provides suitable weights for the two objectives. In particular, we explore the role of CO₂ constraints, as suggested by the Kyoto Protocol, and temperature constraints, as proposed in the Copenhagen and Paris agreements.
2026working paper
Tato Khundadze
SSRN
This paper introduces scientific machine learning methods to macroeconomic model discovery, focusing on Sparse Identification of Nonlinear Dynamics (SINDy), Universal Differential Equations (UDEs), and a hybrid UDE-SINDy pipeline in which a neural network embedded within a differential equation learns unknown dynamics that are subsequently distilled into interpretable symbolic equations via sparse regression. The Goodwin growth cycle, a canonical predator-prey formulation of distributional conflict between labour and capital, serves as the testing ground throughout. We survey the relevant methodology, implement each approach in a unified computational framework, and benchmark them on problems calibrated to macroeconomic scales, where data are scarce, noisy, and nonstationary. On stationary synthetic Goodwin data, the hybrid pipeline recovers the bilinear interaction coefficients to four significant figures, with the vu term emerging as the sole active component of the sparse representation. On nonstationary synthetic data, consisting of a four-regime piecewise system with forced oscillations, abrupt parameter shifts, and transition damping, both direct SINDy and UDE-SINDy recover the predator-prey structure with correct structural identification. These experiments establish that the methods can operate under conditions characteristic of macroeconomic time series. When the validated pipeline is applied to 77 years of U.S. quarterly data (1948:Q1-2025:Q3) on employment, capacity utilisation, and the labour share, neither method recovers the vu interaction at any regularisation strength. Direct SINDy returns dense polynomial models; the UDE-SINDy pipeline finds near-zero neural network corrections and no dominant interaction term. The result is consistent across both methods and both empirical specifications, classical (v, u) and structuralist (TCU, u). The Lotka-Volterra functional form that defines the Goodwin model is not present in the data. Several caveats apply, including the restriction to secondorder polynomial libraries and the treatment of the system as a two-dimensional autonomous ODE. The methods developed here are not specific to the Goodwin model and can be applied to other macroeconomic dynamical systems for which candidate functional forms can be specified.
2004published
Alfred Greiner, Jens Rubart, Willi Semmler
Journal of Macroeconomics
In recent literature skill-biased technical change has been viewed as a major cause for wage inequality. Some modelling and presentation of stylized facts have been undertaken for US time series data. A preliminary study of wage inequality in a model with knowledge as input in an aggregate production function has been presented by Riddell and Romer [General Purpose Technologies and Economic Growth, 1998, MIT Press]. Although some important forces determining wage inequality are widely accepted we know little about the quantitative impact of each source and differences across countries. We present a growth model of the Romer type with innovation-based technical change and two skill groups where the growth of knowledge, the relative supply of the two skill groups, externalities and substitution effects among the two groups are the driving forces for wage inequality. We undertake estimates for US time series data and contrast those estimates with results from some European countries. In particular, we compare parameter estimations for US and German time series data. The paper concludes that there is less wage inequality across skills in Europe in contrast to the US on the macroeconomic level. But, considering disaggregated data we observe some increases in inequality for Germany, too. Although our model reveals important variables for the explanation of wage inequality there may, however, also be other factors, such as trade unions, which have impacted the wage spread.
2025published
Pu Chen, Willi Semmler
Studies in Nonlinear Dynamics & Econometrics
In this paper, we develop a Markov switching method to quantify the relative contributions of cost-push and demand-pull to current inflationary pressures. This approach aids in studying whether the inflation is short-lived or more persistent. We apply this method to Australian data and identify three episodes in the last 25 years when the inflation rate exceeded 4 %. All three episodes were primarily driven by cost-push factors. Our results reveal that monetary policy is more effective in controlling demand-pull inflation but less so in controlling cost-push inflation. This observation explains why the episodes of relatively higher inflation were predominantly driven by cost-push factors. Furthermore, we contrast our findings with US inflation drivers.
2025working paper
Tato Khundadze, Willi Semmler
SSRN
Deep Reinforcement Learning is actively used in modern financial literature. However, there is a major gap regarding the inclusion of investor preferences for sustainable and green investments. This paper applies a DRL framework that brings those preferences into dynamic portfolio management with sustainability constraints. We employ the Soft Actor-Critic (SAC) and Proximal Policy Optimization algorithm to design a continuous-time investment model that allocates wealth between fossil-based, green and risk-free assets. The model aims to optimize a utility function derived from both consumption and green innovation, and our agents are trained to navigate stochastic return dynamics, transition costs, and the behavioral effects of investor short-termism. When benchmarked against Nonlinear Model Predictive Control (NMPC) investor, the DRL agent achieves both comparable long-run wealth and greener portfolio allocations under the realistic uncertainty. The paper incorporates the regime-switching process, which affects the investor's diversification strategy. The paper shows how the Deep Reinforcement Learning agents can successfully learn the strategy of diversification during the turbulent financial regimes.