BufferStockTheory-Add-Refs.bib

@article{bewleyPIH,
  author =        {Bewley, Truman},
  journal =       {Journal of Economic Theory},
  pages =         {252--292},
  title =         {The Permanent Income Hypothesis: A Theoretical
                   Formulation},
  volume =        {16},
  year =          {1977},
}

@inproceedings{carroll_et_al-proc-scipy-2018,
  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},
  booktitle =     {{P}roceedings of the 17th {P}ython in {S}cience
                   {C}onference},
  editor =        {{F}atih {A}kici and {D}avid {L}ippa and
                   {D}illon {N}iederhut and {M} {P}acer},
  pages =         {25 - 30},
  title =         {{T}he {E}con-{A}{R}{K} and {H}{A}{R}{K}: {O}pen
                   {S}ource {T}ools for {C}omputational {E}conomics},
  year =          {2018},
  doi =           {10.25080/Majora-4af1f417-004},
}

@article{CarrollKimballPSPW,
  author =        {Carroll, Christopher D. and Kimball, Miles S.},
  journal =       {Palgrave Dictionary of Economics and Finance, 2nd
                   Ed.},
  note =
  {\url{https://www.econ2.jhu.edu/people/ccarroll/papers/PalgravePrecautionary.pdf}},
  title =         {Precautionary Saving and Precautionary Wealth},
  year =          {2007},
  url =           {https://www.econ2.jhu.edu/people/ccarroll/papers/
                  PalgravePrecautionary.pdf},
}

@article{kimball:standardra,
  author =        {Kimball, Miles S.},
  journal =       {Econometrica},
  month =         may,
  number =        {3},
  pages =         {589--611},
  title =         {Standard Risk Aversion},
  volume =        {61},
  year =          {1993},
}

@article{deatonLiqConstr,
  author =        {Deaton, Angus S.},
  journal =       {Econometrica},
  note =          {\url{https://www.jstor.org/stable/2938366}},
  pages =         {1221-1248},
  title =         {Saving and Liquidity Constraints},
  volume =        {59},
  year =          {1991},
  url =           {http://www.jstor.org/stable/2938366},
}

@article{kmpHandbook,
  author =        {Krueger, Dirk and Mitman, Kurt and Perri, Fabrizio},
  journal =       {Handbook of Macroeconomics},
  pages =         {843--921},
  publisher =     {Elsevier},
  title =         {Macroeconomics and Household Heterogeneity},
  volume =        {2},
  year =          {2016},
  abstract =      {The goal of this chapter is to study how, and by how
                   much, household income, wealth, and preference
                   heterogeneity amplify and propagate a macroeconomic
                   shock. We focus on the U.S. Great Recession of
                   2007-2009 and proceed in two steps. First, using data
                   from the Panel Study of Income Dynamics, we document
                   the patterns of household income, consumption and
                   wealth inequality before and during the Great
                   Recession. We then investigate how households in
                   different segments of the wealth distribution were
                   affected by income declines, and how they changed
                   their expenditures differentially during the
                   aggregate downturn. Motivated by this evidence, we
                   study several variants of a standard heterogeneous
                   household model with aggregate shocks and an
                   endogenous cross-sectional wealth distribution. Our
                   key finding is that wealth inequality can
                   significantly amplify the impact of an aggregate
                   shock, and it does so if the distribution features a
                   sufficiently large fraction of households with very
                   little net worth that sharply increase their saving
                   (i.e. they are not hand-to mouth) as the recession
                   hits. We document that both these features are
                   observed in the PSID. We also investigate the role
                   that social insurance policies, such as unemployment
                   insurance, play in shaping the cross-sectional income
                   and wealth distribution, and through it, the dynamics
                   of business cycles.},
  doi =           {10.3386/w22319},
  url =           {http://www.nber.org/papers/w22319},
}

@article{carrollBSLCPIH,
  author =        {Carroll, Christopher D.},
  journal =       {Quarterly Journal of Economics},
  number =        {1},
  pages =         {1--56},
  title =         {Buffer Stock Saving and the Life Cycle/Permanent
                   Income Hypothesis},
  volume =        {CXII},
  year =          {1997},
}

@book{fisherInterestTheory,
  address =       {New York},
  author =        {Fisher, Irving},
  publisher =     {MacMillan},
  title =         {The Theory of Interest},
  year =          {1930},
}

@book{friedmanATheory,
  author =        {Friedman, Milton A.},
  publisher =     {Princeton University Press},
  title =         {A Theory of the Consumption Function},
  year =          {1957},
}

@article{muthOptimal,
  author =        {Muth, John F.},
  journal =       {Journal of the American Statistical Association},
  number =        {290},
  pages =         {299--306},
  title =         {Optimal Properties of Exponentially Weighted
                   Forecasts},
  volume =        {55},
  year =          {1960},
}

@article{zeldesStochastic,
  author =        {Zeldes, Stephen P.},
  journal =       {Quarterly Journal of Economics},
  month =         {May},
  number =        {2},
  pages =         {275--298},
  title =         {Optimal Consumption with Stochastic Income:
                   {D}eviations from Certainty Equivalence},
  volume =        {104},
  year =          {1989},
}

@article{gpLifeCycle,
  author =        {Gourinchas, Pierre-Olivier and Parker, Jonathan},
  journal =       {Econometrica},
  number =        {1},
  pages =         {47--89},
  title =         {Consumption Over the Life Cycle},
  volume =        {70},
  year =          {2002},
}

@article{Cagetti,
  author =        {Marco Cagetti},
  journal =       {Journal of Business and Economic Statistics},
  number =        {3},
  pages =         {339--353},
  title =         {Wealth Ac{\-}cumulation Over the Life Cycle and
                   Pre{\-}cau{\-}tion{\-}ary Savings},
  volume =        {21},
  year =          {2003},
}

@article{macurdyTimeseries,
  author =        {MaCurdy, Thomas},
  journal =       {Journal of Econometrics},
  number =        {1},
  pages =         {83--114},
  title =         {The Use of Time Series Processes to Model the Error
                   Structure of Earnings in a Longitudinal Data
                   Analysis},
  volume =        {18},
  year =          {1982},
}

@article{acCovariance,
  author =        {Abowd, John M. and Card, David},
  journal =       {Econometrica},
  pages =         {411--445},
  title =         {On the Covariance Structure of Earnings and Hours
                   Changes},
  volume =        {57},
  year =          {1989},
}

@article{csNature,
  author =        {Carroll, Christopher D. and Samwick, Andrew A.},
  journal =       {Journal of Monetary Economics},
  number =        {1},
  pages =         {41--71},
  title =         {The {N}ature of {P}recautionary {W}ealth},
  volume =        {40},
  year =          {1997},
  url =           {https://www.econ2.jhu.edu/people/ccarroll/papers/
                   nature.pdf},
}

@article{jpCins,
  author =        {Jappelli, Tullio and Pistaferri, Luigi},
  journal =       {Econometric Society World Congress 2000 Contributed
                   Paper Number 0118},
  month =         {August},
  title =         {Intertemporal Choice and Consumption Mobility},
  year =          {2000},
  url =           {http://fmwww.bc.edu/RePEc/es2000/0118.pdf},
}

@techreport{dhmImproving,
  author =        {Daly, Moira and Hryshko, Dmytro and
                   Manovskii, Iourii},
  institution =   {National Bureau of Economic Research},
  title =         {Improving the measurement of earnings dynamics},
  year =          {2016},
}

@article{dmHowMuch,
  author =        {Hryshko, Dmytro and Manovskii, Iourii},
  journal =       {Manuscript, University of Alerta},
  month =         {August},
  title =         {How much consumption insurance in the US?},
  year =          {2020},
  url =           {http://www.artsrn.ualberta.ca/econweb/hryshko/Papers/
                   HryshkoManovskii-how-much-aug25-2020.pdf},
}

@article{blanchardFinite,
  author =        {Blanchard, Olivier J.},
  journal =       {Journal of Political Economy},
  month =         {April},
  number =        {2},
  pages =         {223--247},
  title =         {Debt, Deficits, and Finite Horizons},
  volume =        {93},
  year =          {1985},
}

@article{mstIncFluct,
  author =        {Ma, Qingyin and Stachurski, John and
                   Toda, Alexis Akira},
  journal =       {Journal of Economic Theory},
  publisher =     {Elsevier},
  title =         {The income fluctuation problem and the evolution of
                   wealth},
  volume =        {187},
  year =          {2020},
}

@article{maUnboundedDP,
  author =        {Ma, Qingyin and Stachurski, John and
                   Toda, Alexis Akira},
  journal =       {Journal of Mathematical Economics},
  pages =         {102652},
  title =         {Unbounded dynamic programming via the Q-transform},
  volume =        {100},
  year =          {2022},
}

@book{stachurski2022,
  author =        {Stachurski, J.},
  publisher =     {MIT Press},
  title =         {Economic Dynamics, second edition: Theory and
                   Computation},
  year =          {2022},
  url =           {https://books.google.com/books?id=2rJaEAAAQBAJ},
}

@article{szeidlInvariant,
  author =        {Szeidl, Adam},
  journal =       {Manuscript, Central European University},
  note =          {Available at
  \url{http://www.personal.ceu.hu/staff/Adam_Szeidl/papers/invariant_revision.pdf}},
  title =         {Sta{\-}ble In{\-}vari{\-}ant Distribution in
                   Buffer-Stock Sav{\-}ing and Sto{\-}chastic Growth
                   Models},
  year =          {2013},
}

@article{harmenbergInvariant,
  author =        {Karl Harmenberg},
  journal =       {Journal of Economic Dynamics and Control},
  pages =         {104185},
  title =         {Agg{\-}re{\-}gat{\-}ing hetero{\-}gen{\-}eous-agent
                   mod{\-}els with per{\-}manent in{\-}come shocks},
  volume =        {129},
  year =          {2021},
  abstract =      {I introduce a method for simulating aggregate
                   dynamics of heterogeneous-agent models where log
                   permanent income follows a random walk. The idea is
                   to simulate the model using a counterfactual
                   permanent-income-neutral measure which incorporates
                   the effect that permanent income shocks have on
                   macroeconomic aggregates. With the
                   permanent-income-neutral measure, one does not need
                   to keep track of the permanent-income distribution.
                   The permanent-income-neutral measure is both useful
                   for the analytical characterization of aggregate
                   consumption-savings behavior and for simulating
                   numerical models. Furthermore, it is trivial to
                   implement with a few lines of code.},
  doi =           {https://doi.org/10.1016/j.jedc.2021.104185},
  issn =          {0165-1889},
  url =           {https://www.sciencedirect.com/science/article/pii/
                   S0165188921001202},
}

@article{schmitt2003closing,
  author =        {Schmitt-Groh{\'e}, Stephanie and Uribe, Mart{\i}n},
  journal =       {Journal of international Economics},
  number =        {1},
  pages =         {163--185},
  publisher =     {Elsevier},
  title =         {Closing small open economy models},
  volume =        {61},
  year =          {2003},
}

@article{kimballPrecautionarySaving,
  author =        {Kimball, Miles S.},
  journal =       {Econometrica},
  pages =         {53--73},
  title =         {Precautionary Saving in the Small and in the Large},
  volume =        {58},
  year =          {1990},
}

@article{ckConcavity,
  author =        {Carroll, Christo{\-}pher D. and
                   Kim{\-}ball, Miles S.},
  journal =       {Econometrica},
  note =
  {\url{https://www.econ2.jhu.edu/people/ccarroll/concavity.pdf}},
  number =        {4},
  pages =         {981--992},
  title =         {On the {C}on{\-}cav{\-}ity of the {C}onsumption
                   {F}unction},
  volume =        {64},
  year =          {1996},
  url =           {https://www.econ2.jhu.edu/people/ccarroll/concavity.pdf},
}

@article{lightPrecautionarySaving,
  author =        {Light, Bar},
  journal =       {Review of Economic Dynamics},
  pages =         {138-147},
  title =         {Precautionary Saving in a Markovian Earnings
                   Environment},
  volume =        {29},
  year =          {2018},
}

@article{chkLiqConstr,
  author =        {Carroll, Christopher D. and Martin Holm and
                   Miles S. Kimball},
  journal =
  {\href{https://www.econ2.jhu.edu/people/ccarroll/papers/LiqConstr}{Manuscript,
  Johns Hopkins University}},
  note =
  {\url{https://www.econ2.jhu.edu/people/ccarroll/papers/LiqConstr}},
  title =         {Liquidity Constraints and Precautionary Saving},
  year =          {2019},
  url =           {https://www.econ2.jhu.edu/people/ccarroll/papers/LiqConstr},
}

@article{maSavingRateRich,
  author =        {Ma, Qingyin and Toda, Alexis Akira},
  journal =       {Journal of Economic Theory},
  pages =         {105193},
  title =         {A Theory of the Saving Rate of the Rich},
  volume =        {192},
  year =          {2021},
}

@article{imrohorogluBusinessCycles,
  author =        {Imrohoro\u{g}lu, Ayşe},
  journal =       {Journal of Political Economy},
  pages =         {1364--1383},
  title =         {Cost of Business Cycles with Indivisibilities and
                   Liquidity Constraints},
  volume =        {97},
  year =          {1989},
}

@article{huggettRiskFreeRate,
  author =        {Huggett, Mark},
  journal =       {Journal of Economic Dynamics and Control},
  pages =         {953-969},
  title =         {The risk-free rate in heterogeneous-agent
                   incomplete-insurance economies},
  volume =        {17},
  year =          {1993},
}

@article{aiyagari:ge,
  author =        {Aiyagari, S. Rao},
  journal =       {Quarterly Journal of Economics},
  pages =         {659--684},
  title =         {Uninsured Idiosyncratic Risk and Aggregate Saving},
  volume =        {109},
  year =          {1994},
}

@article{carrollBrookings,
  author =        {Carroll, Christopher D.},
  journal =       {Brookings Papers on Economic Activity},
  note =
  {\url{https://www.econ2.jhu.edu/people/ccarroll/BufferStockBPEA.pdf}},
  number =        {2},
  pages =         {61--156},
  title =         {The Buffer-Stock Theory of Saving: Some Macroeconomic
                   Evidence},
  volume =        {1992},
  year =          {1992},
  url =           {https://www.econ2.jhu.edu/people/ccarroll/
                   BufferStockBPEA.pdf},
}

@book{slpMethods,
  author =        {Stokey, Nancy L. and Lucas, Robert E. and
                   Edward C. Prescott},
  publisher =     {Harvard University Press},
  title =         {Recursive Methods in Economic Dynamics},
  year =          {1989},
}

@article{seIncFluct,
  author =        {Schechtman, Jack and Escudero, Vera},
  journal =       {Journal of Economic Theory},
  pages =         {151--166},
  title =         {Some results on `An Income Fluctuation Problem'},
  volume =        {16},
  year =          {1977},
}

@article{scheinkman&weiss:borrowing,
  author =        {Scheinkman, Jos\'e and Weiss, Laurence},
  journal =       {Econometrica},
  number =        {1},
  pages =         {23--46},
  title =         {Borrowing Constraints and Aggregate Economic
                   Activity},
  volume =        {54},
  year =          {1986},
}

@article{claridaErgodic,
  author =        {Clarida, Richard H.},
  journal =       {International Economic Review},
  pages =         {339--351},
  title =         {Consumption, Liquidity Constraints, and Asset
                   Accumulation in the Face of Random Fluctuations in
                   Income},
  volume =        {XXVIII},
  year =          {1987},
}

@article{cwcUnderUncert,
  author =        {Chamberlain, Gary and Wilson, Charles A.},
  journal =       {Review of Economic Dynamics},
  number =        {3},
  pages =         {365--395},
  title =         {Optimal Intertemporal Consumption Under Uncertainty},
  volume =        {3},
  year =          {2000},
}

@article{tocheUrisk,
  author =        {Toche, Patrick},
  journal =       {Economics Letters},
  number =        {2},
  pages =         {267--272},
  title =         {A Tractable Model of Pre{\-}cau{\-}tion{\-}ary
                   Sav{\-}ing in Con{\-}tin{\-}uous Time},
  volume =        {87},
  year =          {2005},
}

@article{asHomogeneous,
  author =        {Alvarez, Fernando and Stokey, Nancy L},
  journal =       {Journal of economic theory},
  number =        {1},
  pages =         {167--189},
  publisher =     {Elsevier},
  title =         {Dynamic programming with homogeneous functions},
  volume =        {82},
  year =          {1998},
}

@article{mnUnique,
  author =        {Janusz Matkowski and Andrzej S. Nowak},
  journal =       {Economic Theory},
  pages =         {455--474},
  title =         {On Discounted Dynamic Programming With Unbounded
                   Returns},
  volume =        {46},
  year =          {2011},
}

@article{yaoNote,
  author =        {Jiaxiong Yao},
  journal =       {Manuscript, Johns Hopkins University},
  title =         {The Theoretical Foundations of Buffer Stock Saving: A
                   Note},
  year =          {2012},
}

@article{mvExistence,
  author =        {Martins-da-Rocha, V Filipe and Vailakis, Yiannis},
  journal =       {Econometrica},
  number =        {3},
  pages =         {1127--1141},
  publisher =     {Wiley Online Library},
  title =         {Existence and uniqueness of a fixed point for local
                   contractions},
  volume =        {78},
  year =          {2010},
}

@article{rrExistence,
  author =        {Rinc{\'o}n-Zapatero, Juan Pablo and
                   Rodr{\'\i}guez-Palmero, Carlos},
  journal =       {Econometrica},
  number =        {5},
  pages =         {1519--1555},
  publisher =     {Wiley Online Library},
  title =         {Existence and uniqueness of solutions to the Bellman
                   equation in the unbounded case},
  volume =        {71},
  year =          {2003},
}

@article{lsIncFluct,
  author =        {Li, Huiyu and Stachurski, John},
  journal =       {Journal of Economic Dynamics and Control},
  pages =         {353--365},
  publisher =     {Elsevier},
  title =         {Solving the income fluctuation problem with unbounded
                   rewards},
  volume =        {45},
  year =          {2014},
}

@article{jboydWeighted,
  author =        {Boyd, John H.},
  journal =       {Journal of Economic Theory},
  month =         {April},
  number =        {2},
  pages =         {326--345},
  title =         {Recursive Utility and the Ramsey Problem},
  volume =        {50},
  year =          {1990},
}

@article{duranDiscounting,
  author =        {Dur{\'a}n, Jorge},
  journal =       {Economic Theory},
  number =        {2},
  pages =         {395--413},
  publisher =     {Springer},
  title =         {Discounting long run average growth in stochastic
                   dynamic programs},
  volume =        {22},
  year =          {2003},
}

@article{Feinberg2012,
  author =        {Feinberg, Eugene A and Kasyanov, Pavlo O and
                   Zadoianchuk, Nina V},
  journal =       {Mathematics of Operations Research},
  pages =         {591--607},
  title =         {{Average Cost Markov Decision Processes with Weakly
                   Continuous Transition Probabilities}},
  volume =        {37},
  year =          {2012},
  doi =           {10.1287/moor.1120.0555},
}

@article{Shanker2017a,
  author =        {Shanker, Akshay},
  journal =       {SSRN Working Paper 3011662},
  title =         {{Existence of Recursive Constrained Optima in the
                   Heterogenous Agent Neoclassical Growth Model}},
  year =          {2017},
  url =           {https://papers.ssrn.com/sol3/papers.cfm?
                  abstract_id=3011662},
}

@article{benhabibWealth,
  author =        {Benhabib, Jess and Bisin, Alberto and Zhu, Shenghao},
  journal =       {Journal of Economic Theory},
  note =          {Available at
                   \url{https://www.nber.org/papers/w20157.pdf}},
  pages =         {489--515},
  publisher =     {Elsevier},
  title =         {The wealth distribution in Bewley economies with
                   capital income risk},
  volume =        {159},
  year =          {2015},
  url =           {https://www.sciencedirect.com/science/article/pii/
                   S0022053115001362},
}

@misc{maTodaRich,
  author =        {Qingyin Ma and Alexis Akira Toda},
  journal =       {arXiv},
  title =         {A Theory of the Saving Rate of the Rich},
  year =          {2020},
}

@article{sargstach2023,
  author =        {Sargent,Thomas J and Stachurski, John},
  journal =       {arXiv:2308.02148 [math.OC]},
  note =          {Optimization and Control (math.OC)},
  title =         {Completely Abstract Dynamic Programming},
  year =          {2023},
}

@article{wolf2021play,
  author =        {Wolf, Martin and Shanker, Akshay},
  journal =       {CEPR Discussion Papers},
  publisher =     {C.E.P.R. Discussion Papers},
  title =         {Play for the Rich and Work for the Poor? The Optimal
                   Distribution of Saving and Work in the Heterogeneous
                   Agents Neoclassical G},
  volume =        {16479},
  year =          {2021},
}

@article{BufferStockTheoryQESubmit,
  author =        {Christopher D. Carroll},
  journal =       {Quantitative Economics},
  title =         {Theoretical Foundations of Buffer Stock Saving},
  year =          {2019, Submitted},
  doi =           {https://zenodo.org/badge/latestdoi/304124725},
  url =           {https://econ-ark.github.io/BufferStockTheory},
}

@article{Sun2009,
  author =        {Sun, Yeneng and Zhang, Yongchao},
  journal =       {Journal of Economic Theory},
  pages =         {432--443},
  publisher =     {Elsevier Inc.},
  title =         {{Individual Risk and Lebesgue Extension Without
                   Aggregate Uncertainty}},
  volume =        {144},
  year =          {2009},
}

@article{Cao2020,
  author =        {Dan Cao},
  journal =       {Journal of Economic Theory},
  pages =         {104978},
  title =         {Recursive equilibrium in Krusell and Smith (1998)},
  volume =        {186},
  year =          {2020},
  issn =          {0022-0531},
}

@article{cstwMPC,
  author =        {Christopher D. Carroll and Jiri Sla{\-}calek and
                   Kiichi To{\-}ku{\-}o{\-}ka and Matt{\-}hew N. White},
  journal =       {Quantitative Economics},
  month =         {November},
  note =          {At
  \url{https://www.econ2.jhu.edu/people/ccarroll/papers/cstwMPC}},
  pages =         {977-1020},
  title =         {The Dis{\-}tri{\-}bu{\-}tion of Wealth and the
                   Mar{\-}gi{\-}nal Pro{\-}pen{\-}si{\-}ty to
                   Con{\-}sume},
  volume =        {8},
  year =          {2017},
  doi =           {10.3982/QE694},
  url =           {http://onlinelibrary.wiley.com/doi/10.3982/QE694/pdf},
}

@article{yaari1965uncertain,
  author =        {Yaari, Menahem E},
  journal =       {The Review of Economic Studies},
  number =        {2},
  pages =         {137--150},
  publisher =     {JSTOR},
  title =         {Uncertain lifetime, life insurance, and the theory of
                   the consumer},
  volume =        {32},
  year =          {1965},
}

@article{modiglianiWealth,
  author =        {Modigliani, Franco},
  journal =       {Social Research},
  pages =         {160--217},
  title =         {The Life Cycle Hypothesis, the Demand for Wealth, and
                   the Supply of Capital},
  volume =        {33},
  year =          {1966},
}

@book{hendricksBequests,
  author =        {Hendricks, Lutz},
  journal =       {Manuscript, University of Arizona},
  publisher =     {University of Arizona},
  title =         {Bequests and Retirement Wealth in the United States},
  year =          {2001},
  url =           {https://lhendricks.org/Research/wps/bequdata_paper.pdf},
}

@article{hendricksSmallBequests,
  author =        {Lutz Hendricks},
  journal =       {Lecture Notes, Economics 821, University of North
                   Carolina},
  title =         {Wealth Distribution and Bequests},
  year =          {2016},
  url =           {https://lhendricks.org/econ821/wealth/wealth_bequ_sl.pdf},
}

@book{riehl2017category,
  author =        {Riehl, Emily},
  publisher =     {Courier Dover Publications},
  title =         {Category theory in context},
  year =          {2017},
}

@book{hlermaSDS1995,
  address =       {New York, NY},
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@article{StachurskiToda2019JET,
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@book{Aliprantis2005,
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@book{Rockafellar1972,
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@article{rinconZapatero2024,
author = {Rinc{\'{o}}n-Zapatero, Juan Pablo},
file = {:Users/akshayshanker/Dropbox/Research/Non-convex dynamic programming/Literature/ZapatertoTE2024.pdf:pdf},
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@book{bertsekas2012dynamic,
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}