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Economics 

Computational economics is an interdisciplinary research discipline that combines methods in computational science and economics to solve complex economic problems.^{[1]} This subject encompasses computational modeling of economic systems. Some of these areas are unique, while others established areas of economics by allowing robust data analytics and solutions of problems that would be arduous to research without computers and associated numerical methods.^{[2]}
Computational methods have been applied in various fields of economics research, including but not limiting to:
Econometrics: Nonparametric approaches, semiparametric approaches, and machine learning.
Dynamic systems modeling: Optimization, dynamic stochastic general equilibrium modeling, and agentbased modeling.^{[3]}
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Transcription
History
Computational economics developed concurrently with the mathematization of the field. During the early 20th century, pioneers such as Jan Tinbergen and Ragnar Frisch advanced the computerization of economics and the growth of econometrics. As a result of advancements in Econometrics, regression models, hypothesis testing, and other computational statistical methods became widely adopted in economic research. On the theoretical front, complex macroeconomic models, including the real business cycle (RBC) model and dynamic stochastic general equilibrium (DSGE) models have propelled the development and application of numerical solution methods that rely heavily on computation. In the 21st century, the development of computational algorithms created new means for computational methods to interact with economic research. Innovative approaches such as machine learning models and agentbased modeling have been actively explored in different areas of economic research, offering economists an expanded toolkit that frequently differs in character from traditional methods.
Applications
Agent based modelling
Computational economics uses computerbased economic modeling to solve analytically and statistically formulated economic problems. A research program, to that end, is agentbased computational economics (ACE), the computational study of economic processes, including whole economies, as dynamic systems of interacting agents.^{[4]} As such, it is an economic adaptation of the complex adaptive systems paradigm.^{[5]} Here the "agent" refers to "computational objects modeled as interacting according to rules," not real people.^{[3]} Agents can represent social, biological, and/or physical entities. The theoretical assumption of mathematical optimization by agents in equilibrium is replaced by the less restrictive postulate of agents with bounded rationality adapting to market forces,^{[6]} including gametheoretical contexts.^{[7]} Starting from initial conditions determined by the modeler, an ACE model develops forward through time driven solely by agent interactions. The scientific objective of the method is to test theoretical findings against realworld data in ways that permit empirically supported theories to cumulate over time.^{[8]}
Machine learning in computational economics
Machine learning models present a method to resolve vast, complex, unstructured data sets. Various machine learning methods such as the kernel method and random forest have been developed and utilized in datamining and statistical analysis. These models provide superior classification, predictive capabilities, flexibility compared to traditional statistical models, such as that of the STAR method. Other methods, such as causal machine learning and causal tree, provide distinct advantages, including inference testing.
There are notable advantages and disadvantages of utilizing machine learning tools in economic research. In economics, a model is selected and analyzed at once. The economic research would select a model based on principle, then test/analyze the model with data, followed by crossvalidation with other models. On the other hand, machine learning models have built in "tuning" effects. As the model conducts empirical analysis, it crossvalidates, estimates, and compares various models concurrently. This process may yield more robust estimates than those of the traditional ones.
Traditional economics partially normalize the data based on existing principles, while machine learning presents a more positive/empirical approach to model fitting. Although Machine Learning excels at classification, predication and evaluating goodness of fit, many models lack the capacity for statistical inference, which are of greater interest to economic researchers. Machine learning models' limitations means that economists utilizing machine learning would need to develop strategies for robust, statistical causal inference, a core focus of modern empirical research. For example, economics researchers might hope to identify confounders, confidence intervals, and other parameters that are not wellspecified in Machine Learning algorithms.^{[9]}
Machine learning may effectively enable the development of more complicated heterogeneous economic models. Traditionally, heterogeneous models required extensive computational work. Since heterogeneity could be differences in tastes, beliefs, abilities, skills or constraints, optimizing a heterogeneous model is a lot more tedious than the homogeneous approach (representative agent).^{[10]} The development of reinforced learning and deep learning may significantly reduce the complexity of heterogeneous analysis, creating models that better reflect agents' behaviors in the economy.^{[11]}
The adoption and implementation of neural networks, deep learning in the field of computational economics may reduce the redundant work of data cleaning and data analytics, significantly lowering the time and cost of large scale data analytics and enabling researchers to collect, analyze data on a great scale.^{[12]} This would encourage economic researchers to explore new modeling methods. In addition, reduced emphasis on data analysis would enable researchers to focus more on subject matters such as causal inference, confounding variables, and realism of the model. Under the proper guidance, machine learning models may accelerate the process of developing accurate, applicable economics through large scale empirical data analysis and computation.^{[13]}
Dynamic stochastic general equilibrium (DSGE) model
Dynamic modeling methods are frequently adopted in macroeconomic research to simulate economic fluctuations and test for the effects of policy changes. The DSGE one class of dynamic models relying heavily on computational techniques and solutions. DSGE models utilize microfounded economic principles to capture characteristics of the real world economy in an environment with intertemporal uncertainty. Given their inherent complexity, DSGE models are in general analytically intractable, and are usually implemented numerically using computer software. One major advantage of DSGE models is that they facilitate the estimation of agents' dynamic choices with flexibility. However, many scholars have criticized DSGE models for their reliance on reducedform assumptions that are largely unrealistic.
Computational tools and programming languages
Utilizing computational tools in economic research has been the norm and foundation for a long time. Computational tools for economics include a variety of computer software that facilitate the execution of various matrix operations (e.g. matrix inversion) and the solution of systems of linear and nonlinear equations. Various programming languages are utilized in economic research for the purpose of data analytics and modeling. Typical programming languages used in computational economics research include C++, MATLAB, Julia, Python, R and Stata.
Among these programming languages, C++ as a compiled language performs the fastest, while Python as an interpreted language is the slowest. MATLAB, Julia, and R achieve a balance between performance and interpretability. As an early statistical analytics software, Stata was the most conventional programming language option. Economists embraced Stata as one of the most popular statistical analytics programs due to its breadth, accuracy, flexibility, and repeatability.
Journals
The following journals specialise in computational economics: ACM Transactions on Economics and Computation,^{[14]} Computational Economics,^{[1]} Journal of Applied Econometrics,^{[15]} Journal of Economic Dynamics and Control^{[16]} and the Journal of Economic Interaction and Coordination.^{[17]}
References
 ^ ^{a} ^{b} Computational Economics. ""About This Journal" and "Aims and Scope."
 ^ • Hans M. Amman, David A. Kendrick, and John Rust, ed., 1996. Handbook of Computational Economics, v. 1, Elsevier. Description Archived 20110715 at the Wayback Machine & chapterpreview links. Archived 20200406 at the Wayback Machine • Kenneth L. Judd, 1998. Numerical Methods in Economics, MIT Press. Links to description Archived 20120211 at the Wayback Machine and chapter previews.
 ^ ^{a} ^{b} Scott E. Page, 2008. "agentbased models," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract.
 ^ • Scott E. Page, 2008. "agentbased models," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract. • Leigh Tesfatsion, 2006. "AgentBased Computational Economics: A Constructive Approach to Economic Theory," ch. 16, Handbook of Computational Economics, v. 2, [pp. 831880]. doi:10.1016/S15740021(05)020162. • Kenneth L. Judd, 2006. "Computationally Intensive Analyses in Economics," Handbook of Computational Economics, v. 2, ch. 17, pp. 881 893. Prepub PDF. • L. Tesfatsion and K. Judd, ed., 2006. Handbook of Computational Economics, v. 2, AgentBased Computational Economics, Elsevier. Description Archived 20120306 at the Wayback Machine & and chapterpreview links. • Thomas J. Sargent, 1994. Bounded Rationality in Macroeconomics, Oxford. Description and chapterpreview 1stpage links.
 ^ • W. Brian Arthur, 1994. "Inductive Reasoning and Bounded Rationality," American Economic Review, 84(2), pp. 406411 Archived 20130521 at the Wayback Machine. • Leigh Tesfatsion, 2003. "Agentbased Computational Economics: Modeling Economies as Complex Adaptive Systems," Information Sciences, 149(4), pp. 262268 Archived April 26, 2012, at the Wayback Machine. • _____, 2002. "AgentBased Computational Economics: Growing Economies from the Bottom Up," Artificial Life, 8(1), pp.5582. Abstract and prepub PDF Archived 20130514 at the Wayback Machine.
 ^ • W. Brian Arthur, 1994. "Inductive Reasoning and Bounded Rationality," American Economic Review, 84(2), pp. 406411 Archived 20130521 at the Wayback Machine. • John H. Holland and John H. Miller (1991). "Artificial Adaptive Agents in Economic Theory," American Economic Review, 81(2), pp. 365370 Archived 20110105 at the Wayback Machine. • Thomas C. Schelling, 1978 [2006]. Micromotives and Macrobehavior, Norton. Description Archived 20171102 at the Wayback Machine, preview. • Thomas J. Sargent, 1994. Bounded Rationality in Macroeconomics, Oxford. Description and chapterpreview 1stpage links.
 ^ • Joseph Y. Halpern, 2008. "computer science and game theory," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract. • Yoav Shoham, 2008. "Computer Science and Game Theory," Communications of the ACM, 51(8), pp. 7579 Archived 20120426 at the Wayback Machine. • Alvin E. Roth, 2002. "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," Econometrica, 70(4), pp. 1341–1378 Archived 20040414 at the Wayback Machine.
 ^ Leigh Tesfatsion, 2006. "AgentBased Computational Economics: A Constructive Approach to Economic Theory," ch. 16, Handbook of Computational Economics, v. 2, sect. 5, p. 865 [pp. 831880]. doi:10.1016/S15740021(05)020162.
 ^ Athey, Susan (2019), "The Impact of Machine Learning on Economics", The Economics of Artificial Intelligence, University of Chicago Press, pp. 507–552, doi:10.7208/chicago/9780226613475.003.0021, ISBN 9780226613338, S2CID 67460253, retrieved 20220505
 ^ Jesus, Browning, Martin Carro (2006). Heterogeneity and microeconometrics modelling. CAM, Centre for Applied Microeconometrics. OCLC 1225293761.
{{cite book}}
: CS1 maint: multiple names: authors list (link)  ^ Charpentier, Arthur; Élie, Romuald; Remlinger, Carl (20210423). "Reinforcement Learning in Economics and Finance". Computational Economics. arXiv:2003.10014. doi:10.1007/s10614021101194. ISSN 15729974. S2CID 214612371.
 ^ Farrell, Max H.; Liang, Tengyuan; Misra, Sanjog (2021). "Deep Neural Networks for Estimation and Inference". Econometrica. 89 (1): 181–213. doi:10.3982/ecta16901. ISSN 00129682. S2CID 203696381.
 ^ "Deep learning for individual heterogeneity: an automatic inference framework". 20210727. doi:10.47004/wp.cem.2021.2921. S2CID 236428783.
{{cite journal}}
: Cite journal requiresjournal=
(help)  ^ "ACM Teac".
 ^ "Journal of Applied Econometrics". Wiley Online Library. 2011. doi:10.1002/(ISSN)10991255. Retrieved October 31, 2011.
 ^ Journal of Economic Dynamics and Control, including Aims & scope link. For a muchcited overview and issue, see: • Leigh Tesfatsion, 2001. "Introduction to the Special Issue on Agentbased Computational Economics," Journal of Economic Dynamics & Control, pp. 281293. • [Special issue], 2001. Journal of Economic Dynamics and Control, Agentbased Computational Economics (ACE). 25(34), pp. 281654. Abstract/outline links^{[permanent dead link]}.
 ^ "Journal of Economic Interaction and Coordination". springer.com. 2011. Retrieved October 31, 2011.
External links
 Society for Computational Economics
 Journal of Economic Dynamics and Control Archived 20210505 at the Wayback Machine  publishes articles on computational economics
 AgentBased Computational Economics  maintained by Leigh Tesfatsion
 The Use of AgentBased Models in Regional Science  a study on agentbased models to simulate urban agglomeration
 Computational Economics with Python  a series of lectures
 Computational Finance and Economic Agents Archived 20181215 at the Wayback Machine
 Journal of Economic Interaction and Coordination  official journal of the Association of Economic Science with Heterogeneous Interacting Agents
 Chair of Economic Policy, University of Bamberg (Germany)
 Repository of publicdomain computational solutions