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on Computational Economics |
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Issue of 2021‒03‒01
fifteen papers chosen by |
| By: | Jean-Fran\c{c}ois Chassagneux; Junchao Chen; Noufel Frikha; Chao Zhou |
| Abstract: | Relying on the classical connection between Backward Stochastic Differential Equations (BSDEs) and non-linear parabolic partial differential equations (PDEs), we propose a new probabilistic learning scheme for solving high-dimensional semi-linear parabolic PDEs. This scheme is inspired by the approach coming from machine learning and developed using deep neural networks in Han and al. [32]. Our algorithm is based on a Picard iteration scheme in which a sequence of linear-quadratic optimisation problem is solved by means of stochastic gradient descent (SGD) algorithm. In the framework of a linear specification of the approximation space, we manage to prove a convergence result for our scheme, under some smallness condition. In practice, in order to be able to treat high-dimensional examples, we employ sparse grid approximation spaces. In the case of periodic coefficients and using pre-wavelet basis functions, we obtain an upper bound on the global complexity of our method. It shows in particular that the curse of dimensionality is tamed in the sense that in order to achieve a root mean squared error of order ${\epsilon}$, for a prescribed precision ${\epsilon}$, the complexity of the Picard algorithm grows polynomially in ${\epsilon}^{-1}$ up to some logarithmic factor $ |log({\epsilon})| $ which grows linearly with respect to the PDE dimension. Various numerical results are presented to validate the performance of our method and to compare them with some recent machine learning schemes proposed in Han and al. [20] and Hur\'e and al. [37]. |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2102.12051&r=all |
| By: | Alexandre Carbonneau; Fr\'ed\'eric Godin |
| Abstract: | This paper studies the equal risk pricing (ERP) framework for the valuation of European financial derivatives. This option pricing approach is consistent with global trading strategies by setting the premium as the value such that the residual hedging risk of the long and short positions in the option are equal under optimal hedging. The ERP setup of Marzban et al. (2020) is considered where residual hedging risk is quantified with convex risk measures. The main objective of this paper is to assess through extensive numerical experiments the impact of including options as hedging instruments within the ERP framework. The reinforcement learning procedure developed in Carbonneau and Godin (2020), which relies on the deep hedging algorithm of Buehler et al. (2019b), is applied to numerically solve the global hedging problems by representing trading policies with neural networks. Among other findings, numerical results indicate that in the presence of jump risk, hedging long-term puts with shorter-term options entails a significant decrease of both equal risk prices and market incompleteness as compared to trading only the stock. Monte Carlo experiments demonstrate the potential of ERP as a fair valuation approach providing prices consistent with observable market prices. Analyses exhibit the ability of ERP to span a large interval of prices through the choice of convex risk measures which is close to encompass the variance-optimal premium. |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2102.12694&r=all |
| By: | Emiliano Álvarez (Universidad de la República; Universidad Nacional del Sur); Marcelo Álvez (Banco Central del Uruguay; Universidad de la República); Juan Gabriel Brida (Universidad de la República) |
| Abstract: | In this work, an agent-based stock-flow consistent model (AB-SFC) is applied to analyze economic growth differences when establishing different types of taxes on personal income, proportional and progressive. Different combinations of threshold and rate are tested. There are no significant differences in economic performance in the presence of one tax scheme or the other. This tax design, which only distinguishes two sections of income, is not able to reduce the inequality generated throughout the income distribution. The tax design seems to offset the inequality in the lower section of income distribution through tax exemption for low-income households, but not the one generated in the section of higher income. An additional policy is necessary to offset the differences generated in the range of higher-income individuals. In this exercise, there is no evidence of a deterioration of economic growth in the presence of a progressive income tax, instead of a proportional one. |
| Keywords: | agent-based model, inequality, economic growth, income tax distortion, computational modeling |
| JEL: | O33 D63 O49 H23 C63 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:bku:doctra:2020008&r=all |
| By: | Tengyuan Liang (University of Chicago - Booth School of Business); Pragya Sur (Harvard University - Department of Statistics) |
| Abstract: | This paper establishes a precise high-dimensional asymptotic theory for boosting on separable data, taking statistical and computational perspectives. We consider the setting where the number of features (weak learners) p scales with the sample size n, in an over-parametrized regime. Under a broad class of statistical models, we provide an exact analysis of the generalization error of boosting, when the algorithm interpolates the training data and maximizes the empirical L1-margin. The relation between the boosting test error and the optimal Bayes error is pinned down explicitly. In turn, these precise characterizations resolve several open questions raised in [15, 81] surrounding boosting. On the computational front, we provide a sharp analysis of the stopping time when boosting approximately maximizes the empirical L1 margin. Furthermore, we discover that the larger the overparametrization ratio p/n, the smaller the proportion of active features (with zero initialization), and the faster the optimization reaches interpolation. At the heart of our theory lies an in-depth study of the maximum L1-margin, which can be accurately described by a new system of non-linear equations; we analyze this margin and the properties of this system, using Gaussian comparison techniques and a novel uniform deviation argument. Variants of AdaBoost corresponding to general Lq geometry, for q > 1, are also presented, together with an exact analysis of the high-dimensional generalization and optimization behavior of a class of these algorithms. |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:bfi:wpaper:2020-152&r=all |
| By: | Ivan Jericevich; Dharmesh Sing; Tim Gebbie |
| Abstract: | We deploy and demonstrate the CoinTossX low-latency, high-throughput, open-source matching engine with orders sent using the Julia and Python languages. We show how this can be deployed for small-scale local desk-top testing and discuss a larger scale, but local hosting, with multiple traded instruments managed concurrently and managed by multiple clients. We then demonstrate a cloud based deployment using Microsoft Azure, with large-scale industrial and simulation research use cases in mind. The system is exposed and interacted with via sockets using UDP SBE message protocols and can be monitored using a simple web browser interface using HTTP. We give examples showing how orders can be be sent to the system and market data feeds monitored using the Julia and Python languages. The system is developed in Java with orders submitted as binary encodings (SBE) via UDP protocols using the Aeron Media Driver as the low-latency, high throughput message transport. The system separates the order-generation and simulation environments e.g. agent-based model simulation, from the matching of orders, data-feeds and various modularised components of the order-book system. This ensures a more natural and realistic asynchronicity between events generating orders, and the events associated with order-book dynamics and market data-feeds. We promote the use of Julia as the preferred order submission and simulation environment. |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2102.10925&r=all |
| By: | Luisa Roa; Andr\'es Rodr\'iguez-Rey; Alejandro Correa-Bahnsen; Carlos Valencia |
| Abstract: | The presence of Super-Apps have changed the way we think about the interactions between users and commerce. It then comes as no surprise that it is also redefining the way banking is done. The paper investigates how different interactions between users within a Super-App provide a new source of information to predict borrower behavior. To this end, two experiments with different graph-based methodologies are proposed, the first uses graph based features as input in a classification model and the second uses graph neural networks. Our results show that variables of centrality, behavior of neighboring users and transactionality of a user constituted new forms of knowledge that enhance statistical and financial performance of credit risk models. Furthermore, opportunities are identified for Super-Apps to redefine the definition of credit risk by contemplating all the environment that their platforms entail, leading to a more inclusive financial system. |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2102.09974&r=all |
| By: | Tetsuya Kaji (University of Chicago - Booth School of Business); Elena Manresa (New York University - Department of Economics); Guillaume Pouliot (University of Chicago - Harris School of Public Policy) |
| Abstract: | We propose a new simulation-based estimation method, adversarial estimation, for structural models. The estimator is formulated as the solution to a minimax problem between a generator (which generates synthetic observations using the structural model) and a discriminator (which classifies if an observation is synthetic). The discriminator maximizes the accuracy of its classification while the generator minimizes it. We show that, with a sufficiently rich discriminator, the adversarial estimator attains parametric efficiency under correct specification and the parametric rate under misspecification. We advocate the use of a neural network as a discriminator that can exploit adaptivity properties and attain fast rates of convergence. We apply our method to the elderly’s saving decision model and show that including gender and health profiles in the discriminator uncovers the bequest motive as an important source of saving across the wealth distribution, not only for the rich. |
| Keywords: | Structural estimation, generative adversarial networks, neural networks, simulated method of moments, indirect inference, efficient estimation |
| JEL: | C13 C45 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:bfi:wpaper:2020-144&r=all |
| By: | Brotherhood, L.; Cavalcanti, T.; Da Mata, D.; Santos, C. |
| Abstract: | This paper studies the role of slums in shaping the economic and health dynamics of pandemics. Using data from millions of mobile phones in Brazil, an event-study analysis shows that residents of overcrowded slums engaged in less social distancing after the outbreak of Covid-19. We develop a choice-theoretic equilibrium model in which poorer agents live in high-density slums and others do not. The model is calibrated to Rio de Janeiro. Slum dwellers account for a disproportionately high number of infections and deaths. In a counterfactual scenario without slums, deaths increase in non-slum neighborhoods. Policy simulations indicate that: reallocating medical resources cuts deaths and raises output and the welfare of both groups; mild lockdowns favor slum individuals by mitigating the demand for hospital beds whereas strict confinements mostly delay the evolution of the pandemic; and cash transfers benefit slum residents in detriment of others, highlighting important distributional effects. |
| Keywords: | Covid-19, slums, health, social distancing, public policies |
| JEL: | E17 I10 I18 D62 O18 C63 |
| Date: | 2020–08–06 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:2076&r=all |
| By: | Bernardo Alves Furtado |
| Abstract: | Policymakers decide on alternative policies facing restricted budgets and uncertain, ever-changing future. Designing housing policies is further difficult giving the heterogeneous characteristics of properties themselves and the intricacy of housing markets and the spatial context of cities. We propose PolicySpace2 (PS2) as an adapted and extended version of the open source PolicySpace agent-based model. PS2 is a computer simulation that relies on empirically detailed spatial data to model real estate, along with labor, credit and goods and services markets. Interaction among workers, firms, a bank, households and municipalities follow the literature benchmarks to integrate economic, spatial and transport literature. PS2 is applied to a comparison among three competing municipal housing policies aimed at alleviating poverty: (a) property acquisition and distribution, (b) rental vouchers and (c) monetary aid. Within the model context, the monetary aid, that is, a smaller amounts of help for a larger number of households, makes the economy perform better in terms of production, consumption, reduction of inequality and maintenance of financial duties. PS2 as such is also a framework that may be further adapted to a number of related research questions. |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2102.11929&r=all |
| By: | Tengyuan Liang (University of Chicago - Booth School of Business); Hai Tran-Bach (University of Chicago - Department of Statistics) |
| Abstract: | We utilize a connection between compositional kernels and branching processes via Mehler’s formula to study deep neural networks. This new probabilistic insight provides us a novel perspective on the mathematical role of activation functions in compositional neural networks. We study the unscaled and rescaled limits of the compositional kernels and explore the different phases of the limiting behavior, as the compositional depth increases. We investigate the memorization capacity of the compositional kernels and neural networks by characterizing the interplay among compositional depth, sample size, dimensionality, and non-linearity of the activation. Explicit formulas on the eigenvalues of the compositional kernel are provided, which quantify the complexity of the corresponding reproducing kernel Hilbert space. On the methodological front, we propose a new random features algorithm, which compresses the compositional layers by devising a new activation function. |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:bfi:wpaper:2020-151&r=all |
| By: | Elena Miola (Ministry of Economy and Finance); Marco Manzo (Ministry of Economy and Finance) |
| Abstract: | The paper presents a static tax-benefit microsimulation model developed by combining the IT-SILC 2016 dataset, a survey on Italian incomes and living conditions, and administrative tax return micro data in the same year. The dataset derives from the exact matching of survey and administrative data. The microsimulation model reproduces in detail the features of Italian personal income tax and benefit system and is aimed at evaluating tax revenue and fiscal policies distributive impact. Redistribution analysis is carried out by using concentration, progressivity and redistribution indices for individual taxpayers and equivalent households. Inequality issues are analysed further through the computation of decile and quintile distribution of household gross and disposable income, by using the tax-benefit microsimulation model. |
| Keywords: | tax-benefit microsimulation model, personal income taxation, redistribution, inequality |
| JEL: | D31 H20 H24 |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:ahg:wpaper:wp2021-10&r=all |
| By: | Xiuqin Xu; Ying Chen |
| Abstract: | Volatility for financial assets returns can be used to gauge the risk for financial market. We propose a deep stochastic volatility model (DSVM) based on the framework of deep latent variable models. It uses flexible deep learning models to automatically detect the dependence of the future volatility on past returns, past volatilities and the stochastic noise, and thus provides a flexible volatility model without the need to manually select features. We develop a scalable inference and learning algorithm based on variational inference. In real data analysis, the DSVM outperforms several popular alternative volatility models. In addition, the predicted volatility of the DSVM provides a more reliable risk measure that can better reflex the risk in the financial market, reaching more quickly to a higher level when the market becomes more risky and to a lower level when the market is more stable, compared with the commonly used GARCH type model with a huge data set on the U.S. stock market. |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2102.12658&r=all |
| By: | Tengyuan Liang (University of Chicago - Booth School of Business) |
| Abstract: | This paper studies the rates of convergence for learning distributions implicitly with the adversarial framework and Generative Adversarial Networks (GAN), which subsume Wasserstein, Sobolev, MMD GAN, and Generalized/Simulated Method of Moments (GMM/SMM) as special cases. We study a wide range of parametric and nonparametric target distributions, under a host of objective evaluation metrics. We investigate how to obtain a good statistical guarantee for GANs through the lens of regularization. On the nonparametric end, we derive the optimal minimax rates for distribution estimation under the adversarial framework. On the parametric end, we establish a theory for general neural network classes (including deep leaky ReLU networks), that characterizes the interplay on the choice of generator and discriminator pair. We discover and isolate a new notion of regularization, called the generator-discriminator-pair regularization, that sheds light on the advantage of GANs compared to classical parametric and nonparametric approaches for explicit distribution estimation. We develop novel oracle inequalities as the main technical tools for analyzing GANs, which is of independent interest. |
| Keywords: | Generative adversarial networks, implicit distribution estimation, simulated method of moments, oracle inequality, neural network learning, mini- max problem, pair regularization |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:bfi:wpaper:2020-154&r=all |
| By: | Zhen Zeng; Tucker Balch; Manuela Veloso |
| Abstract: | Time series forecasting is essential for decision making in many domains. In this work, we address the challenge of predicting prices evolution among multiple potentially interacting financial assets. A solution to this problem has obvious importance for governments, banks, and investors. Statistical methods such as Auto Regressive Integrated Moving Average (ARIMA) are widely applied to these problems. In this paper, we propose to approach economic time series forecasting of multiple financial assets in a novel way via video prediction. Given past prices of multiple potentially interacting financial assets, we aim to predict the prices evolution in the future. Instead of treating the snapshot of prices at each time point as a vector, we spatially layout these prices in 2D as an image, such that we can harness the power of CNNs in learning a latent representation for these financial assets. Thus, the history of these prices becomes a sequence of images, and our goal becomes predicting future images. We build on a state-of-the-art video prediction method for forecasting future images. Our experiments involve the prediction task of the price evolution of nine financial assets traded in U.S. stock markets. The proposed method outperforms baselines including ARIMA, Prophet, and variations of the proposed method, demonstrating the benefits of harnessing the power of CNNs in the problem of economic time series forecasting. |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2102.12061&r=all |
| By: | Saïd Assar (TIM - Département Technologies, Information & Management - IMT - Institut Mines-Télécom [Paris] - IMT-BS - Institut Mines-Télécom Business School, LITEM - Laboratoire en Innovation, Technologies, Economie et Management (EA 7363) - UEVE - Université d'Évry-Val-d'Essonne - Université Paris-Saclay - IMT-BS - Institut Mines-Télécom Business School); Christine Balagué (CONNECT - Consommateur Connecté dans la Société Numérique - DEFI - Département Droit, Economie et Finances - TEM - Télécom Ecole de Management - IMT - Institut Mines-Télécom [Paris] - IMT-BS - Institut Mines-Télécom Business School - MMS - Département Management, Marketing et Stratégie - TEM - Télécom Ecole de Management - IMT - Institut Mines-Télécom [Paris] - IMT-BS - Institut Mines-Télécom Business School - IMT-BS - Institut Mines-Télécom Business School, MMS - Département Management, Marketing et Stratégie - TEM - Télécom Ecole de Management - IMT - Institut Mines-Télécom [Paris] - IMT-BS - Institut Mines-Télécom Business School, LITEM - Laboratoire en Innovation, Technologies, Economie et Management (EA 7363) - UEVE - Université d'Évry-Val-d'Essonne - Université Paris-Saclay - IMT-BS - Institut Mines-Télécom Business School); Loréa Baïada-Hirèche (MMS - Département Management, Marketing et Stratégie - TEM - Télécom Ecole de Management - IMT - Institut Mines-Télécom [Paris] - IMT-BS - Institut Mines-Télécom Business School, LITEM - Laboratoire en Innovation, Technologies, Economie et Management (EA 7363) - UEVE - Université d'Évry-Val-d'Essonne - Université Paris-Saclay - IMT-BS - Institut Mines-Télécom Business School) |
| Date: | 2020–12–16 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03123998&r=all |