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@article{MALIAR202176,
title = {Deep learning for solving dynamic economic models.},
journal = {Journal of Monetary Economics},
volume = {122},
pages = {76-101},
year = {2021},
issn = {0304-3932},
doi = {https://doi.org/10.1016/j.jmoneco.2021.07.004},
url = {https://www.sciencedirect.com/science/article/pii/S0304393221000799},
author = {Lilia Maliar and Serguei Maliar and Pablo Winant},
keywords = {Artificial intelligence, Machine learning, Deep learning, Neural network, Stochastic gradient, Dynamic models, Model reduction, Dynamic programming, Bellman equation, Euler equation, Value functio},
abstract = {We introduce a unified deep learning method that solves dynamic economic models by casting them into nonlinear regression equations. We derive such equations for three fundamental objects of economic dynamics – lifetime reward functions, Bellman equations and Euler equations. We estimate the decision functions on simulated data using a stochastic gradient descent method. We introduce an all-in-one integration operator that facilitates approximation of high-dimensional integrals. We use neural networks to perform model reduction and to handle multicollinearity. Our deep learning method is tractable in large-scale problems, e.g., Krusell and Smith (1998). We provide a TensorFlow code that accommodates a variety of applications.}
}

@article{KrusellSmith,
author = {Krusell, Per and Smith, Jr., Anthony A.},
title = {Income and Wealth Heterogeneity in the Macroeconomy},
journal = {Journal of Political Economy},
volume = {106},
number = {5},
pages = {867-896},
year = {1998},
doi = {10.1086/250034},
abstract = { How do movements in the distribution of income and wealth affect the macroeconomy? We analyze this question using a calibrated version of the stochastic growth model with partially uninsurable idiosyncratic risk and movements in aggregate productivity. Our main finding is that, in the stationary stochastic equilibrium, the behavior of the macroeconomic aggregates can be almost perfectly described using only the mean of the wealth distribution. This result is robust to substantial changes in both parameter values and model specification. Our benchmark model, whose only difference from the representative‐agent framework is the existence of uninsurable idiosyncratic risk, displays far less cross‐sectional dispersion and skewness in wealth than U.S. data. However, an extension that relies on a small amount of heterogeneity in thrift does succeed in replicating the key features of the wealth data. Furthermore, this extension features aggregate time series that depart significantly from permanent income behavior. }
}

@article{cAndCwithStickyE,
Author = {Carroll, Christopher D. and Crawley, Edmund and Slacalek, Jiri and Tokuoka, Kiichi and White, Matthew N.},
Title = {Sticky Expectations and Consumption Dynamics},
Journal = {American Economic Journal: Macroeconomics},
Volume = {12},
Number = {3},
Year = {2020},
Month = {July},
Pages = {40–76},
DOI = {10.1257/mac.20180286},
URL = {https://www.aeaweb.org/articles?id=10.1257/mac.20180286}
}

@periodical{JEDCspecial,
editor = {Den Haan, Wouter},
year = {2010},
title = {Journal of Economic Dynamics and Control},
issuetitle = {Computational Suite of Models with Heterogeneous Agents: Incomplete Markets and Aggregate Uncertainty},
volume = {34},
number = {1},
url = {https://www.sciencedirect.com/journal/journal-of-economic-dynamics-and-control/vol/34/issue/1},
}

@article{FiveGuys,
author = {Ahn, SeHyoun and Kaplan, Greg and Moll, Benjamin and Winberry, Thomas and Wolf, Christian},
title = {When Inequality Matters for Macro and Macro Matters for Inequality},
journal = {NBER Macroeconomics Annual},
volume = {32},
number = {},
pages = {1-75},
year = {2018},
doi = {10.1086/696046},
,
abstract = { We develop an efficient and easy to use computational method for solving a wide class of general equilibrium heterogeneous agent models with aggregate shocks together with an open source suite of codes that implement our algorithms in an easy to use toolbox. Our method extends standard linearization techniques and is designed to work in cases when inequality matters for the dynamics of macroeconomic aggregates. We present two applications that analyze a two asset incomplete markets model parameterized to match the distribution of income, wealth, and marginal propensities to consume. First, we show that our model is consistent with two key features of aggregate consumption dynamics that are difficult to match with representative agent models: (1) the sensitivity of aggregate consumption to predictable changes in aggregate income, and (2) the relative smoothness of aggregate consumption. Second, we extend the model to feature capital-skill complementarity and show how factor-specific productivity shocks shape dynamics of income and consumption inequality. }
}

@misc{Reiter2010,
number = {258},
address = {Wien},
title = {Approximate and Almost-Exact Aggregation in Dynamic Stochastic Heterogeneous-Agent Models},
year = {2010},
series = {Economics Series},
publisher = {Institut f{\"u}r H{\"o}here Studien},
editor = {Robert M. Kunst and Walter Fisher and Klaus Ritzberger},
month = {October},
keywords = {'Heterogeneous agents' 'Aggregation' 'Model reduction'},
isbn = {1605-7996},
author = {Reiter, Michael},
url = {https://irihs.ihs.ac.at/id/eprint/2021/},
abstract = {Abstract: The paper presents a new method to solve DSGE models with a great number of heterogeneous agents. Using tools from systems and control theory, it is shown how to reduce the dimension of the state and the policy vector so that the reduced model approximates the original model with high precision. The method is illustrated with a stochastic growth model with incomplete markets similar to Krusell and Smith (1998), and with a model of heterogeneous firms with state-dependent pricing. For versions of those models that are nonlinear in individual variables, but linearized in aggregate variables, approximations with 50 to 200 state variables deliver solutions that are precise up to machine precision. The paper also shows how to reduce the state vector even further, with a very small reduction in precision.;}
}

@article{CarrollEGM,
title = {The method of endogenous gridpoints for solving dynamic stochastic optimization problems},
journal = {Economics Letters},
volume = {91},
number = {3},
pages = {312-320},
year = {2006},
issn = {0165-1765},
doi = {https://doi.org/10.1016/j.econlet.2005.09.013},
url = {https://www.sciencedirect.com/science/article/pii/S0165176505003368},
author = {Christopher D. Carroll},
keywords = {Dynamic optimization, Precautionary saving, Stochastic growth model, Endogenous gridpoints, Liquidity constraints},
abstract = {This paper introduces a solution method for numerical dynamic stochastic optimization problems that avoids rootfinding operations. The idea is applicable to many microeconomic and macroeconomic problems, including life cycle, buffer-stock, and stochastic growth problems. Software is provided.}
}

@article{CarrollBuffer,
author = {Carroll, Christopher D.},
title = "{Buffer-Stock Saving and the Life Cycle/Permanent Income Hypothesis*}",
journal = {The Quarterly Journal of Economics},
volume = {112},
number = {1},
pages = {1-55},
year = {1997},
month = {02},
abstract = "{This paper argues that the typical household's saving is better described by a “buffer-stock” version than by the traditional version of the Life Cycle/Permanent Income Hypothesis (LC/PIH) model. Buffer-stock behavior emerges if consumers with important income uncertainty are sufficiently impatient. In the traditional model, consumption growth is determined solely by tastes. In contrast, buffer-stock consumers set average consumption growth equal to average labor income growth, regardless of tastes. The model can explain three empirical puzzles: the “consumption/income parallel” documented by Carroll and Summers; the “consumption/income divergence” first documented in the 1930s; and the stability of the household age/wealth profile over time despite the unpredictability of idiosyncratic wealth changes.}",
issn = {0033-5533},
doi = {10.1162/003355397555109},
url = {https://doi.org/10.1162/003355397555109},
eprint = {https://academic.oup.com/qje/article-pdf/112/1/1/5291627/112-1-1.pdf},
}

@InProceedings{HARK,
author = { {C}hristopher {D}. {C}arroll and {A}lexander {M}. {K}aufman and {J}acqueline {L}. {K}azil and {N}athan {M}. {P}almer and {M}atthew {N}. {W}hite },
title = { {T}he {E}con-{A}{R}{K} and {H}{A}{R}{K}: {O}pen {S}ource {T}ools for {C}omputational {E}conomics },
booktitle = { {P}roceedings of the 17th {P}ython in {S}cience {C}onference },
pages = { 25 - 30 },
year = { 2018 },
editor = { {F}atih {A}kici and {D}avid {L}ippa and {D}illon {N}iederhut and {M} {P}acer },
doi = { 10.25080/Majora-4af1f417-004 }
}
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