arXiv subjects

Simon Scheidegger

Publications and source records attributed to Simon Scheidegger.

15 recordsLinked to original sources

arXiv2026

Equilibrium World Models

We introduce \emph{Equilibrium World Models} (EWMs), a deep-learning method for globally solving dynamic stochastic models that feature rare disasters, binding constraints, and counterfactual states. Standard unsupervised neural-network-based solvers impose equilibrium conditions only on states generated by their own simulated policy. Their solutions can therefore be self-confirming: accurate on the simulated path, but untested off it, sensitive to initialization, and costly when expectations must be recomputed at each step. EWMs change the computational representation, not the economics. They enforce the model's exact equilibrium conditions on a broader, model-generated distribution of ordinary, rare, stressed, and counterfactual states. They carry the continuation with a learned surrogate, but certify the resulting policy strictly against the true equilibrium conditions. We provide an error decomposition, an off-path residual bound, and a convergence result linking self-confirming solutions to rational-expectations equilibria. We demonstrate EWMs through a sequence of test cases that isolate the main pathologies of classical deep-learning solvers and then scale them to richer economies. In a rare-disaster Brock--Mirman laboratory, coverage reduces disaster-region residuals by an order of magnitude. In a high-dimensional international real-business-cycle model, classical deep-learning solvers fail from all random starts, whereas EWMs converge from nearly all and evaluate continuations up to two orders of magnitude less often. When actions move transition measures, EWMs use action-conditioned continuations to recover the relevant policy margin. In a heterogeneous-agent economy with aggregate risk, EWMs compress the numerical representation of the wealth distribution by at least 25x while imposing exact full-distribution rational-expectations conditions.

econ.GN↗

arXiv2026

Deep Learning for Solving and Estimating Dynamic Models in Economics and Finance

This script offers an implementation-oriented introduction to deep learning methods for solving and estimating high-dimensional dynamic stochastic models in economics and finance. Its starting point is the curse of dimensionality: heterogeneous-agent economies, overlapping-generations models with aggregate risk, continuous-time models with occasionally binding constraints, climate-economy models, and macro-finance environments with many assets and frictions generate state and parameter spaces that strain classical tensor-product grid methods. The exposition is organized around four complementary methodologies. Deep Equilibrium Nets embed discrete-time equilibrium conditions into neural-network loss functions. Physics-Informed Neural Networks approximate continuous-time Hamilton--Jacobi--Bellman, Kolmogorov forward, and related partial differential equations. Deep surrogate models provide fast, differentiable approximations to expensive structural models, while Gaussian processes add a probabilistic layer that quantifies approximation uncertainty; together they support estimation, sensitivity analysis, and constrained policy design. Gaussian-process-based dynamic programming, combined with active learning and dimension reduction, extends value-function iteration to very large continuous state spaces. Applications span representative-agent and international real business cycle models, overlapping-generations and heterogeneous-agent economies, continuous-time macro-finance, structural estimation by simulated method of moments, and climate economics under uncertainty. Companion notebooks in TensorFlow and PyTorch invite hands-on experimentation. These notes are a deliberately subjective and inevitably incomplete snapshot of a rapidly evolving field, aimed at equipping PhD students and researchers to engage with this frontier hands-on.

econ.GN↗

arXiv2025

Using Machine Learning to Compute Constrained Optimal Carbon Tax Rules

We develop a computational framework for deriving Pareto-improving and constrained optimal carbon tax rules in a stochastic overlapping generations (OLG) model with climate change. By integrating Deep Equilibrium Networks for fast policy evaluation and Gaussian process surrogate modeling with Bayesian active learning, the framework systematically locates optimal carbon tax schedules for heterogeneous agents exposed to climate risk. We apply our method to a 12-period OLG model in which exogenous shocks affect the carbon intensity of energy production, as well as the damage function. Constrained optimal carbon taxes consist of tax rates that are simple functions of observables and revenue-sharing rules that guarantee that the introduction of the taxes is Pareto improving. This reveals that a straightforward policy is highly effective: a Pareto-improving linear tax on cumulative emissions alone yields a 0.42% aggregate welfare gain in consumption-equivalent terms while adding further complexity to the tax provides only a marginal increase to 0.45%. The application demonstrates that the proposed approach produces scalable tools for macro-policy design in complex stochastic settings. Beyond climate economics, the framework offers a template for systematically analyzing welfare-improving policies in various heterogeneous-agent problems.

econ.GN↗

arXiv2025

Narrowline Laser Cooling and Spectroscopy of Molecules via Stark States

The electronic energy level structure of yttrium monoxide (YO) provides a long-lived, low-lying $^{2}\Delta$ state ideal for high-precision molecular spectroscopy, narrowline laser cooling at the single photon-recoil limit, and studying dipolar physics with unprecedented interaction strength. High-resolution laser spectroscopy of ultracold laser-cooled YO molecules is used to study the Stark effect in the A$^{\prime}\,^{2}\Delta_{3/2}\,J=3/2$ state. An immediate onset of the linear Stark effect is observed in the presence of weak applied electric fields due to the near degenerate $\Lambda$-doublet and the large electric dipole moment. By applying a small electric field the Stark insensitive state is spectroscopically isolated and the absolute transition frequency to the X$\,^2\Sigma^+$ electronic ground state is determined with a fractional frequency uncertainty of 9 $\times$ 10$^{-12}$. This electric field control is necessary to implement a quasi-closed photon cycling scheme that preserves parity. With this scheme the first narrowline laser cooling of a molecules is demonstrated, reducing the temperature of sub-Doppler cooled YO in two dimensions.

physics.atom-ph↗

arXiv2025

Scalable Global Solution Techniques for High-Dimensional Models in Dynare

For over three decades, Dynare has been a cornerstone of dynamic stochastic modeling in economics, relying primarily on perturbation-based local solution methods. However, these techniques often falter in high-dimensional, non-linear models that demand more comprehensive approaches. This paper demonstrates that global solutions of economic models with substantial heterogeneity and frictions can be computed accurately and swiftly by augmenting Dynare with adaptive sparse grids (SGs) and high-dimensional model representation (HDMR). SGs mitigate the curse of dimensionality, as the number of grid points grows significantly slower than in traditional tensor-product Cartesian grids. Additionally, adaptivity focuses grid refinement on regions with steep gradients or non-differentiabilities, enhancing computational efficiency. Complementing SGs, HDMR tackles large state spaces by approximating policy functions with a hierarchical expansion of low-dimensional terms. Using a time iteration algorithm, we benchmark our approach on an international real business cycle model. Our results show that both SGs and HDMR alleviate the curse of dimensionality, enabling accurate solutions for at least 100-dimensional models on standard hardware in relatively short times. This advancement extends Dynare's capabilities beyond perturbation approaches, establishing a versatile platform for sophisticated non-linear models and paving the way for integrating the most recent global solution methods, such as those from machine learning.

econ.GN↗

arXiv2025

A Dynamic Model of Private Asset Allocation

We build a state-of-the-art dynamic model of private asset allocation that considers five key features of private asset markets: (1) the illiquid nature of private assets, (2) timing lags between capital commitments, capital calls, and eventual distributions, (3) time-varying business cycle conditions, (4) serial correlation in observed private asset returns, and (5) regulatory constraints on certain institutional investors' portfolio choices. We use cutting-edge machine learning methods to quantify the optimal investment policies over the life cycle of a fund. Moreover, our model offers regulators a tool for precisely quantifying the trade-offs when setting risk-based capital charges.

q-fin.PM↗

arXiv2024

Building Interpretable Climate Emulators for Economics

We introduce a framework for developing efficient and interpretable climate emulators (CEs) for economic models of climate change. The paper makes two main contributions. First, we propose a general framework for constructing carbon-cycle emulators (CCEs) for macroeconomic models. The framework is implemented as a generalized linear multi-reservoir (box) model that conserves key physical quantities and can be customized for specific applications. We consider three versions of the CCE, which we evaluate within a simple representative agent economic model: (i) a three-box setting comparable to DICE-2016, (ii) a four-box extension, and (iii) a four-box version that explicitly captures land-use change. While the three-box model reproduces benchmark results well and the fourth reservoir adds little, incorporating the impact of land-use change on the carbon storage capacity of the terrestrial biosphere substantially alters atmospheric carbon stocks, temperature trajectories, and the optimal mitigation path. Second, we investigate pattern-scaling techniques that transform global-mean temperature projections from CEs into spatially heterogeneous warming fields. We show how regional baseline climates, non-uniform warming, and the associated uncertainties propagate into economic damages.

econ.EM↗

arXiv2023

Metrology of Rydberg states of the hydrogen atom

We present a method to precisly measure the frequencies of transitions to high-$n$ Rydberg states of the hydrogen atom which are not subject to uncontrolled systematic shifts caused by stray electric fields. The method consists in recording Stark spectra of the field-insensitive $k=0$ Stark states and the field-sensitive $k=\pm2$ Stark states, which are used to calibrate the electric field strength. We illustrate this method with measurements of transitions from the $2\,\text{s}(f=0\text{ and } 1)$ hyperfine levels in the presence of intentionally applied electric fields with strengths in the range between $0.4$ and $1.6\,$Vcm$^{-1}$. The slightly field-dependent $k=0$ level energies are corrected with a precisely calculated shift to obtain the corresponding Bohr energies $\left(-cR_{\mathrm{H}}/n^2\right)$. The energy difference between $n=20$ and $n=24$ obtained with our method agrees with Bohr's formula within the $10\,$kHz experimental uncertainty. We also determined the hyperfine splitting of the $2\,\text{s}$ state by taking the difference between transition frequencies from the $2\,\text{s}(f=0 \text{ and }1)$ levels to the $n=20,k=0$ Stark states. Our results demonstrate the possibility of carrying out precision measurements in high-$n$ hydrogenic quantum states.

physics.atom-ph↗

arXiv2023

Imaging-assisted single-photon Doppler-free laser spectroscopy and the ionization energy of metastable triplet helium

Skimmed supersonic beams provide intense, cold, collision-free samples of atoms and molecules are one of the most widely used tools in atomic and molecular laser spectroscopy. High-resolution optical spectra are typically recorded in a perpendicular arrangement of laser and supersonic beams to minimize Doppler broadening. Typical Doppler widths are nevertheless limited to tens of MHz by the residual transverse-velocity distribution in the gas-expansion cones. We present an imaging method to overcome this limitation which exploits the correlation between the positions of the atoms and molecules in the supersonic expansion and their transverse velocities - and thus their Doppler shifts. With the example of spectra of $(1\mathrm{s})(n\mathrm{p})\,^3\mathrm{P}_{0-2}\leftarrow (1\mathrm{s})(2\mathrm{s})\,^3\mathrm{S}_1$ transitions to high Rydberg states of metastable triplet He, we demonstrate the suppression of the residual Doppler broadening and a reduction of the full linewidths at half maximum to only about 1 MHz in the UV. Using a retro-reflection arrangement for the laser beam and a cross-correlation method, we determine Doppler-free spectra without any signal loss from the selection, by imaging, of atoms within ultranarrow transverse-velocity classes. As an illustration, we determine the ionization energy of triplet metastable He and confirm the significant discrepancy between recent experimental (Clausen et al., Phys. Rev. Lett. 127 093001 (2021)) and high-level theoretical (Patk\'os et al., Phys. Rev. A 103 042809 (2021)) values of this quantity.

physics.atom-ph↗

arXiv2022

High-Dimensional Dynamic Stochastic Model Representation

We propose a scalable method for computing global solutions of nonlinear, high-dimensional dynamic stochastic economic models. First, within a time iteration framework, we approximate economic policy functions using an adaptive, high-dimensional model representation scheme, combined with adaptive sparse grids to address the ubiquitous challenge of the curse of dimensionality. Moreover, the adaptivity within the individual component functions increases sparsity since grid points are added only where they are most needed, that is, in regions with steep gradients or at nondifferentiabilities. Second, we introduce a performant vectorization scheme for the interpolation compute kernel. Third, the algorithm is hybrid parallelized, leveraging both distributed- and shared-memory architectures. We observe significant speedups over the state-of-the-art techniques, and almost ideal strong scaling up to at least $1,000$ compute nodes of a Cray XC$50$ system at the Swiss National Supercomputing Center. Finally, to demonstrate our method's broad applicability, we compute global solutions to two variates of a high-dimensional international real business cycle model up to $300$ continuous state variables. In addition, we highlight a complementary advantage of the framework, which allows for a priori analysis of the model complexity.

econ.GN↗

arXiv2021

Uniformly Self-Justified Equilibria

We consider dynamic stochastic economies with heterogeneous agents and introduce the concept of uniformly self-justified equilibria (USJE) -- temporary equilibria for which forecasts are best uniform approximations to a selection of the equilibrium correspondence. In a USJE, individuals' forecasting functions for the next period's endogenous variables are assumed to lie in a compact, finite-dimensional set of functions, and the forecasts constitute the best approximation within this set. We show that USJE always exist and develop a simple algorithm to compute them. Therefore, they are more tractable than rational expectations equilibria that do not always exist. As an application, we discuss a stochastic overlapping generations exchange economy and provide numerical examples to illustrate the concept of USJE and the computational method.

econ.TH↗

arXiv2021

Detecting Edgeworth Cycles

We develop and test algorithms to detect "Edgeworth cycles," which are asymmetric price movements that have caused antitrust concerns in many countries. We formalize four existing methods and propose six new methods based on spectral analysis and machine learning. We evaluate their accuracy in station-level gasoline-price data from Western Australia, New South Wales, and Germany. Most methods achieve high accuracy in the first two, but only a few can detect the nuanced cycles in the third. Results suggest whether researchers find a positive or negative statistical relationship between cycles and markups, and hence their implications for competition policy, crucially depends on the choice of methods. We conclude with a set of practical recommendations.

physics.soc-ph↗

arXiv2021

The climate in climate economics

To analyze climate change mitigation strategies, economists rely on simplified climate models - climate emulators. We propose a generic and transparent calibration and evaluation strategy for these climate emulators that is based on Coupled Model Intercomparison Project, Phase 5 (CMIP5). We demonstrate that the appropriate choice of the free model parameters can be of key relevance for the predicted social cost of carbon. We propose to use four different test cases: two tests to separately calibrate and evaluate the carbon cycle and temperature response, a test to quantify the transient climate response, and a final test to evaluate the performance for scenarios close to those arising from economic models. We re-calibrate the climate part of the widely used DICE-2016: the multi-model mean as well as extreme, but still permissible climate sensitivities and carbon cycle responses. We demonstrate that the functional form of the climate emulator of the DICE-2016 model is fit for purpose, despite its simplicity, but its carbon cycle and temperature equations are miscalibrated. We examine the importance of the calibration for the social cost of carbon in the context of a partial equilibrium setting where interest rates are exogenous, as well as the simple general equilibrium setting from DICE-2016. We find that the model uncertainty from different consistent calibrations of the climate system can change the social cost of carbon by a factor of four if one assumes a quadratic damage function. When calibrated to the multi-model mean, our model predicts similar values for the social cost of carbon as the original DICE-2016, but with a strongly reduced sensitivity to the discount rate and about one degree less long-term warming. The social cost of carbon in DICE-2016 is oversensitive to the discount rate, leading to extreme comparative statics responses to changes in preferences.

econ.GN↗

arXiv2021

SI-traceable frequency dissemination at 1572.06 nm in a stabilized fiber network with ring topology

Frequency dissemination in phase-stabilized optical fiber networks for metrological frequency comparisons and precision measurements are promising candidates to overcome the limitations imposed by satellite techniques. However, network constraints restrict the availability of dedicated channels in the commonly-used C-band. Here, we demonstrate the dissemination of an SI-traceable ultrastable optical frequency in the L-band over a 456 km fiber network with ring topology, in which telecommunication data traffic occupies the full C-band. We characterize the optical phase noise and evaluate a link instability of $4.7\cdot 10^{-16}$ at 1 s and $3.8\cdot 10^{-19}$ at 2000 s integration time, and a link accuracy of $2\cdot 10^{-18}$, which is comparable to existing metrology networks in the C-band. We demonstrate the application of the disseminated frequency by establishing the SI-traceability of a laser in a remote laboratory. Finally, we show that our metrological frequency does not interfere with data traffic in the telecommunication channels. Our approach combines an unconventional spectral choice in the telecommunication L-band with established frequency-stabilization techniques, providing a novel, cost-effective solution for ultrastable frequency-comparison and dissemination, and may contribute to a foundation of a world-wide metrological network.

physics.ins-det↗

arXiv2021

Deep Structural Estimation: With an Application to Option Pricing

We propose a novel structural estimation framework in which we train a surrogate of an economic model with deep neural networks. Our methodology alleviates the curse of dimensionality and speeds up the evaluation and parameter estimation by orders of magnitudes, which significantly enhances one's ability to conduct analyses that require frequent parameter re-estimation. As an empirical application, we compare two popular option pricing models (the Heston and the Bates model with double-exponential jumps) against a non-parametric random forest model. We document that: a) the Bates model produces better out-of-sample pricing on average, but both structural models fail to outperform random forest for large areas of the volatility surface; b) random forest is more competitive at short horizons (e.g., 1-day), for short-dated options (with less than 7 days to maturity), and on days with poor liquidity; c) both structural models outperform random forest in out-of-sample delta hedging; d) the Heston model's relative performance has deteriorated significantly after the 2008 financial crisis.

econ.EM↗