How to read this lecture...

Code should execute sequentially if run in a Jupyter notebook

References

[Abr88] Dilip Abreu. On the theory of infinitely repeated games with discounting. Econometrica, 56:383–396, 1988.

[APS90] Dilip Abreu, David Pearce, and Ennio Stacchetti. Toward a theory of discounted repeated games with imperfect monitoring. Econometrica, 58(5):1041–1063, September 1990.

[AJR01] Daron Acemoglu, Simon Johnson, and James A Robinson. The colonial origins of comparative development: an empirical investigation. The American Economic Review, 91(5):1369–1401, 2001.

[Aiy94] S Rao Aiyagari. Uninsured Idiosyncratic Risk and Aggregate Saving. The Quarterly Journal of Economics, 109(3):659–684, 1994.

[AMSSeppala02] S Rao Aiyagari, Albert Marcet, Thomas J Sargent, and Juha Seppälä. Optimal taxation without state-contingent debt. Journal of Political Economy, 110(6):1220–1254, 2002.

[AM05] D. B. O. Anderson and J. B. Moore. Optimal Filtering. Dover Publications, 2005.

[AHMS96] E. W. Anderson, L. P. Hansen, E. R. McGrattan, and T. J. Sargent. Mechanics of Forming and Estimating Dynamic Linear Economies. In Handbook of Computational Economics. Elsevier, vol 1 edition, 1996.

[Are08] Cristina Arellano. Default risk and income fluctuations in emerging economies. The American Economic Review, pages 690–712, 2008.

[AP91] Papoulis Athanasios and S Unnikrishna Pillai. Probability, random variables, and stochastic processes. Mc-Graw Hill, 1991.

[AP11] Orazio P Attanasio and Nicola Pavoni. Risk sharing in private information models with asset accumulation: explaining the excess smoothness of consumption. Econometrica, 79(4):1027–1068, 2011.

[BY04] Ravi Bansal and Amir Yaron. Risks for the long run: a potential resolution of asset pricing puzzles. The journal of Finance, 59(4):1481–1509, 2004.

[Bar79] Robert J Barro. On the Determination of the Public Debt. Journal of Political Economy, 87(5):940–971, 1979.

[Bar99] Robert J Barro. Determinants of democracy. Journal of Political economy, 107(S6):S158–S183, 1999.

[BM03] Robert J Barro and Rachel McCleary. Religion and economic growth. Technical Report, National Bureau of Economic Research, 2003.

[BBZ15] Jess Benhabib, Alberto Bisin, and Shenghao Zhu. The wealth distribution in bewley economies with capital income risk. Journal of Economic Theory, 159:489–515, 2015.

[BS79] L M Benveniste and J A Scheinkman. On the Differentiability of the Value Function in Dynamic Models of Economics. Econometrica, 47(3):727–732, 1979.

[Ber75] Dmitri Bertsekas. Dynamic Programming and Stochastic Control. Academic Press, New York, 1975.

[Bew77] Truman Bewley. The permanent income hypothesis: a theoretical formulation. Journal of Economic Theory, 16(2):252–292, 1977.

[Bew86] Truman F Bewley. Stationary monetary equilibrium with a continuum of independently fluctuating consumers. In Werner Hildenbran and Andreu Mas-Colell, editors, Contributions to Mathematical Economics in Honor of Gerard Debreu, pages 27–102. North-Holland, Amsterdam, 1986.

[BEGS17] Anmol Bhandari, David Evans, Mikhail Golosov, and Thomas J. Sargent. Fiscal Policy and Debt Management with Incomplete Markets. The Quarterly Journal of Economics, 132(2):617–663, 2017.

[Bis06] C. M. Bishop. Pattern Recognition and Machine Learning. Springer, 2006.

[BL92] Fischer Black and Robert Litterman. Global portfolio optimization. Financial analysts journal, 48(5):28–43, 1992.

[Cag56] Philip Cagan. The monetary dynamics of hyperinflation. In Milton Friedman, editor, Studies in the Quantity Theory of Money, pages 25–117. University of Chicago Press, Chicago, 1956.

[Cal78] Guillermo A. Calvo. On the time consistency of optimal policy in a monetary economy. Econometrica, 46(6):1411–1428, 1978.

[Car01] Christopher D Carroll. A Theory of the Consumption Function, with and without Liquidity Constraints. Journal of Economic Perspectives, 15(3):23–45, 2001.

[Car06] Christopher D Carroll. The method of endogenous gridpoints for solving dynamic stochastic optimization problems. Economics Letters, 91(3):312–320, 2006.

[Cas65] David Cass. Optimum growth in an aggregative model of capital accumulation. Review of Economic Studies, 32(3):233–240, 1965.

[Cha98] Roberto Chang. Credible monetary policy in an infinite horizon model: recursive approaches. Journal of Economic Theory, 81(2):431–461, 1998.

[CK90] Varadarajan V Chari and Patrick J Kehoe. Sustainable plans. Journal of Political Economy, pages 783–802, 1990.

[Coa37] Ronald Harry Coase. The nature of the firm. economica, 4(16):386–405, 1937.

[Col90] Wilbur John Coleman. Solving the Stochastic Growth Model by Policy-Function Iteration. Journal of Business & Economic Statistics, 8(1):27–29, 1990.

[CC08] J. D. Cryer and K-S. Chan. Time Series Analysis. Springer, 2nd edition edition, 2008.

[DFH06] Steven J Davis, R Jason Faberman, and John Haltiwanger. The flow approach to labor markets: new data sources, micro-macro links and the recent downturn. Journal of Economic Perspectives, 2006.

[Dea91] Angus Deaton. Saving and Liquidity Constraints. Econometrica, 59(5):1221–1248, 1991.

[DP94] Angus Deaton and Christina Paxson. Intertemporal Choice and Inequality. Journal of Political Economy, 102(3):437–467, 1994.

[DH10] Wouter J Den Haan. Comparison of solutions to the incomplete markets model with aggregate uncertainty. Journal of Economic Dynamics and Control, 34(1):4–27, 2010.

[DJ92] Raymond J Deneckere and Kenneth L Judd. Cyclical and chaotic behavior in a dynamic equilibrium model, with implications for fiscal policy. Cycles and chaos in economic equilibrium, pages 308–329, 1992.

[Dic75] J Dickey. Bayesian alternatives to the f-test and least-squares estimate in the normal linear model. In S.E. Fienberg and A. Zellner, editors, Studies in Bayesian econometrics and statistics, pages 515–554. North-Holland, Amsterdam, 1975.

[DVGC99] JBR Do Val, JC Geromel, and OLV Costa. Solutions for the linear-quadratic control problem of markov jump linear systems. Journal of Optimization Theory and Applications, 103(2):283–311, 1999.

[DS10] Ulrich Doraszelski and Mark Satterthwaite. Computable markov-perfect industry dynamics. The RAND Journal of Economics, 41(2):215–243, 2010.

[DLP13] Y E Du, Ehud Lehrer, and A D Y Pauzner. Competitive economy as a ranking device over networks. submitted, 2013.

[Dud02] R M Dudley. Real Analysis and Probability. Cambridge Studies in Advanced Mathematics. Cambridge University Press, 2002.

[EG87] Robert F Engle and Clive W J Granger. Co-integration and Error Correction: Representation, Estimation, and Testing. Econometrica, 55(2):251–276, 1987.

[EP95] Richard Ericson and Ariel Pakes. Markov-perfect industry dynamics: a framework for empirical work. The Review of Economic Studies, 62(1):53–82, 1995.

[EH01] G W Evans and S Honkapohja. Learning and Expectations in Macroeconomics. Frontiers of Economic Research. Princeton University Press, 2001.

[FSTD15] Pablo Fajgelbaum, Edouard Schaal, and Mathieu Taschereau-Dumouchel. Uncertainty traps. Technical Report, National Bureau of Economic Research, 2015.

[Fri56] M. Friedman. A Theory of the Consumption Function. Princeton University Press, 1956.

[FF98] Milton Friedman and Rose D Friedman. Two Lucky People. University of Chicago Press, 1998.

[Gal89] David Gale. The theory of linear economic models. University of Chicago press, 1989.

[Gal37] Albert Gallatin. Report on the finances*, november, 1807. In Reports of the Secretary of the Treasury of the United States, Vol 1*. Government printing office, Washington, DC, 1837.

[Hal78] Robert E Hall. Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence. Journal of Political Economy, 86(6):971–987, 1978.

[HM82] Robert E Hall and Frederic S Mishkin. The Sensitivity of Consumption to Transitory Income: Estimates from Panel Data on Households. National Bureau of Economic Research Working Paper Series, 1982.

[HTW67] Michael J Hamburger, Gerald L Thompson, and Roman L Weil. Computation of expansion rates for the generalized von neumann model of an expanding economy. Econometrica, Journal of the Econometric Society, pages 542–547, 1967.

[Ham05] James D Hamilton. What’s real about the business cycle? Federal Reserve Bank of St. Louis Review, pages 435–452, 2005.

[HS08a] L P Hansen and T J Sargent. Robustness. Princeton University Press, 2008.

[HS13a] L P Hansen and T J Sargent. Recursive Models of Dynamic Linear Economies. The Gorman Lectures in Economics. Princeton University Press, 2013.

[Han07] Lars Peter Hansen. Beliefs, doubts and learning: valuing macroeconomic risk. American Economic Review, 97(2):1–30, 2007.

[HHL08] Lars Peter Hansen, John C Heaton, and Nan Li. Consumption strikes back? measuring long-run risk. Journal of Political economy, 116(2):260–302, 2008.

[HR87] Lars Peter Hansen and Scott F Richard. The Role of Conditioning Information in Deducing Testable. Econometrica, 55(3):587–613, May 1987.

[HS80] Lars Peter Hansen and Thomas J Sargent. Formulating and estimating dynamic linear rational expectations models. Journal of Economic Dynamics and control, 2:7–46, 1980.

[HS00] Lars Peter Hansen and Thomas J Sargent. Wanting robustness in macroeconomics. Manuscript, Department of Economics, Stanford University., 2000.

[HS08b] Lars Peter Hansen and Thomas J Sargent. Robustness. Princeton university press, 2008.

[HS01] Lars Peter Hansen and Thomas J. Sargent. Robust control and model uncertainty. American Economic Review, 91(2):60–66, 2001.

[HS13b] Lars Peter Hansen and Thomas J. Sargent. Recursive Linear Models of Dynamic Economics. Princeton University Press, Princeton, New Jersey, 2013.

[HS09] Lars Peter Hansen and José A Scheinkman. Long-term risk: an operator approach. Econometrica, 77(1):177–234, 2009.

[HK78] J. Michael Harrison and David M. Kreps. Speculative investor behavior in a stock market with heterogeneous expectations. The Quarterly Journal of Economics, 92(2):323–336, 1978.

[HK79] J. Michael Harrison and David M. Kreps. Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20(3):381–408, June 1979.

[HL96] John Heaton and Deborah J Lucas. Evaluating the effects of incomplete markets on risk sharing and asset pricing. Journal of Political Economy, pages 443–487, 1996.

[HK85] Elhanan Helpman and Paul Krugman. Market structure and international trade. MIT Press Cambridge, 1985.

[HLL96] O Hernandez-Lerma and J B Lasserre. Discrete-Time Markov Control Processes: Basic Optimality Criteria. Number Vol 1 in Applications of Mathematics Stochastic Modelling and Applied Probability. Springer, 1996.

[HP92] Hugo A Hopenhayn and Edward C Prescott. Stochastic Monotonicity and Stationary Distributions for Dynamic Economies. Econometrica, 60(6):1387–1406, 1992.

[HR93] Hugo A Hopenhayn and Richard Rogerson. Job Turnover and Policy Evaluation: A General Equilibrium Analysis. Journal of Political Economy, 101(5):915–938, 1993.

[Hug93] Mark Huggett. The risk-free rate in heterogeneous-agent incomplete-insurance economies. Journal of Economic Dynamics and Control, 17(5-6):953–969, 1993.

[Haggstrom02] Olle Häggström. Finite Markov chains and algorithmic applications. Volume 52. Cambridge University Press, 2002.

[Janich94] K Jänich. Linear Algebra. Springer Undergraduate Texts in Mathematics and Technology. Springer, 1994.

[JYC88] Robert J. Shiller John Y. Campbell. The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors. Review of Financial Studies, 1(3):195–228, 1988.

[Jov79] Boyan Jovanovic. Firm-specific capital and turnover. Journal of Political Economy, 87(6):1246–1260, 1979.

[Jud90] K L Judd. Cournot versus bertrand: a dynamic resolution. Technical Report, Hoover Institution, Stanford University, 1990.

[Jud85] Kenneth L Judd. On the performance of patents. Econometrica, pages 567–585, 1985.

[JYC03] Kenneth L. Judd, Sevin Yeltekin, and James Conklin. Computing Supergame Equilibria. Econometrica, 71(4):1239–1254, 07 2003. URL: https://ideas.repec.org/a/ecm/emetrp/v71y2003i4p1239-1254.html, doi:.

[Kam12] Takashi Kamihigashi. Elementary results on solutions to the bellman equation of dynamic programming: existence, uniqueness, and convergence. Technical Report, Kobe University, 2012.

[KMT56] John G Kemeny, Oskar Morgenstern, and Gerald L Thompson. A generalization of the von neumann model of an expanding economy. Econometrica, Journal of the Econometric Society, pages 115–135, 1956.

[KNS18] Tomoo Kikuchi, Kazuo Nishimura, and John Stachurski. Span of control, transaction costs, and the structure of production chains. Theoretical Economics, 13(2):729–760, 2018.

[Koo65] Tjalling C. Koopmans. On the concept of optimal economic growth. In Tjalling C. Koopmans, editor, The Economic Approach to Development Planning, pages 225–287. Chicago, 1965.

[Kre88] David M. Kreps. Notes on the Theory of Choice. Westview Press, Boulder, Colorado, 1988.

[Kuh13] Moritz Kuhn. Recursive Equilibria In An Aiyagari-Style Economy With Permanent Income Shocks. International Economic Review, 54:807–835, 2013.

[KP80] Finn E Kydland and Edward C Prescott. Dynamic optimal taxation, rational expectations and optimal control. Journal of Economic Dynamics and Control, 2:79–91, 1980.

[LM94] A Lasota and M C MacKey. Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics. Applied Mathematical Sciences. Springer-Verlag, 1994.

[Lea78] Edward E Leamer. Specification searches: Ad hoc inference with nonexperimental data. Volume 53. John Wiley & Sons Incorporated, 1978.

[LL01] Martin Lettau and Sydney Ludvigson. Consumption, Aggregate Wealth, and Expected Stock Returns. Journal of Finance, 56(3):815–849, 06 2001.

[LL04] Martin Lettau and Sydney C. Ludvigson. Understanding Trend and Cycle in Asset Values: Reevaluating the Wealth Effect on Consumption. American Economic Review, 94(1):276–299, March 2004.

[LM80] David Levhari and Leonard J Mirman. The great fish war: an example using a dynamic cournot-nash solution. The Bell Journal of Economics, pages 322–334, 1980.

[LS18] L Ljungqvist and T J Sargent. Recursive Macroeconomic Theory. MIT Press, 4 edition, 2018.

[Luc78] Robert E Lucas, Jr. Asset prices in an exchange economy. Econometrica: Journal of the Econometric Society, 46(6):1429–1445, 1978.

[LP71] Robert E Lucas, Jr. and Edward C Prescott. Investment under uncertainty. Econometrica: Journal of the Econometric Society, pages 659–681, 1971.

[LS83] Robert E Lucas, Jr. and Nancy L Stokey. Optimal Fiscal and Monetary Policy in an Economy without Capital. Journal of monetary Economics, 12(3):55–93, 1983.

[LJ03] Robert E Lucas Jr. Macroeconomic priorities. American economic review, 93(1):1–14, 2003.

[MS89] Albert Marcet and Thomas J Sargent. Convergence of Least-Squares Learning in Environments with Hidden State Variables and Private Information. Journal of Political Economy, 97(6):1306–1322, 1989.

[MdRV10] V Filipe Martins-da-Rocha and Yiannis Vailakis. Existence and Uniqueness of a Fixed Point for Local Contractions. Econometrica, 78(3):1127–1141, 2010.

[MCWG95] A Mas-Colell, M D Whinston, and J R Green. Microeconomic Theory. Volume 1. Oxford University Press, 1995.

[McC70] J J McCall. Economics of Information and Job Search. The Quarterly Journal of Economics, 84(1):113–126, 1970.

[MT09] S P Meyn and R L Tweedie. Markov Chains and Stochastic Stability. Cambridge University Press, 2009.

[MF02] Mario J Miranda and P L Fackler. Applied Computational Economics and Finance. Cambridge: MIT Press, 2002.

[MB54] F. Modigliani and R. Brumberg. Utility analysis and the consumption function: An interpretation of cross-section data. In K.K Kurihara, editor, Post-Keynesian Economics. 1954.

[Mut60] John F Muth. Optimal properties of exponentially weighted forecasts. Journal of the american statistical association, 55(290):299–306, 1960.

[Nea99] Derek Neal. The Complexity of Job Mobility among Young Men. Journal of Labor Economics, 17(2):237–261, 1999.

[Neu28] J v Neumann. Zur theorie der gesellschaftsspiele. Mathematische annalen, 100(1):295–320, 1928.

[Orf88] Sophocles J Orfanidis. Optimum Signal Processing: An Introduction. McGraw Hill Publishing, New York, New York, 1988.

[Par99] Jonathan A Parker. The Reaction of Household Consumption to Predictable Changes in Social Security Taxes. American Economic Review, 89(4):959–973, 1999.

[Put05] Martin L Puterman. Markov decision processes: discrete stochastic dynamic programming. John Wiley & Sons, 2005.

[PalS13] Jenő Pál and John Stachurski. Fitted value function iteration with probability one contractions. Journal of Economic Dynamics and Control, 37(1):251–264, 2013.

[Rab02] Guillaume Rabault. When do borrowing constraints bind? Some new results on the income fluctuation problem. Journal of Economic Dynamics and Control, 26(2):217–245, 2002.

[Ram27] F. P. Ramsey. A Contribution to the theory of taxation. Economic Journal, 37(145):47–61, 1927.

[Ref96] Kevin L Reffett. Production-based asset pricing in monetary economies with transactions costs. Economica, pages 427–443, 1996.

[Rei09] Michael Reiter. Solving heterogeneous-agent models by projection and perturbation. Journal of Economic Dynamics and Control, 33(3):649–665, 2009.

[Rom05] Steven Roman. Advanced linear algebra. Volume 3. Springer, 2005.

[RMS94] Sherwin Rosen, Kevin M Murphy, and Jose A Scheinkman. Cattle cycles. Journal of Political Economy, 102(3):468–492, 1994.

[Roz67] Y. A. Rozanov. Stationary Random Processes. Holden-Day, San Francisco, 1967.

[Rus96] John Rust. Numerical dynamic programming in economics. Handbook of computational economics, 1:619–729, 1996.

[Rya12] Stephen P Ryan. The costs of environmental regulation in a concentrated industry. Econometrica, 80(3):1019–1061, 2012.

[RR04] Jaewoo Ryoo and Sherwin Rosen. The engineering labor market. Journal of political economy, 112(S1):S110–S140, 2004.

[Sam39] Paul A. Samuelson. Interactions between the multiplier analysis and the principle of acceleration. Review of Economic Studies, 21(2):75–78, 1939.

[SHR91] Thomas Sargent, Lars Peter Hansen, and Will Roberts. Observable implications of present value budget balance. In Rational Expectations Econometrics. Westview Press, 1991.

[Sar77] Thomas J Sargent. The Demand for Money During Hyperinflations under Rational Expectations: I. International Economic Review, 18(1):59–82, February 1977.

[Sar87] Thomas J Sargent. Macroeconomic Theory. Academic Press, New York, 2nd edition, 1987.

[SE77] Jack Schechtman and Vera L S Escudero. Some results on an income fluctuation problem. Journal of Economic Theory, 16(2):151–166, 1977.

[Sch14] Jose A. Scheinkman. Speculation, Trading, and Bubbles. Columbia University Press, New York, 2014.

[Sch69] Thomas C Schelling. Models of Segregation. American Economic Review, 59(2):488–493, 1969.

[Shi95] A N Shiriaev. Probability. Graduate texts in mathematics. Springer. Springer, 2nd edition, 1995.

[SLP89] N L Stokey, R E Lucas, and E C Prescott. Recursive Methods in Economic Dynamics. Harvard University Press, 1989.

[Sto89] Nancy L Stokey. Reputation and time consistency. The American Economic Review, pages 134–139, 1989.

[Sto91] Nancy L. Stokey. Credible public policy. Journal of Economic Dynamics and Control, 15(4):627–656, October 1991.

[STY04] Kjetil Storesletten, Christopher I Telmer, and Amir Yaron. Consumption and risk sharing over the life cycle. Journal of Monetary Economics, 51(3):609–633, 2004.

[Sun96] R K Sundaram. A First Course in Optimization Theory. Cambridge University Press, 1996.

[SW09] Lars E.O. Svensson and Noah Williams. Optimal Monetary Policy under Uncertainty in DSGE Models: A Markov Jump-Linear-Quadratic Approach. In Klaus Schmidt-Hebbel, Carl E. Walsh, Norman Loayza (Series Editor), and Klaus Schmidt-Hebbel (Series, editors, Monetary Policy under Uncertainty and Learning, volume 13 of Central Banking, Analysis, and Economic Policies Book Series, chapter 3, pages 077–114. Central Bank of Chile, edition, March 2009.

[SW+08] Lars EO Svensson, Noah Williams, and others. Optimal monetary policy under uncertainty: a markov jump-linear-quadratic approach. Federal Reserve Bank of St. Louis Review, 90(4):275–293, 2008.

[Tal00] Thomas D Tallarini. Risk-sensitive real business cycles. Journal of Monetary Economics, 45(3):507–532, June 2000.

[Tau86] George Tauchen. Finite state markov-chain approximations to univariate and vector autoregressions. Economics Letters, 20(2):177–181, 1986.

[Tre16] Daniel Treisman. Russia’s billionaires. The American Economic Review, 106(5):236–241, 2016.

[VL11] Ngo Van Long. Dynamic games in the economics of natural resources: a survey. Dynamic Games and Applications, 1(1):115–148, 2011.

[VN37] John Von Neumann. Uber ein okonomsiches gleichungssystem und eine verallgemeinering des browerschen fixpunktsatzes. In Erge. Math. Kolloq., volume 8, 73–83. 1937.

[Wal47] Abraham Wald. Sequential Analysis. John Wiley and Sons, New York, 1947.

[Whi63] Peter Whittle. Prediction and regulation by linear least-square methods. English Univ. Press, 1963.

[Whi83] Peter Whittle. Prediction and Regulation by Linear Least Squares Methods. University of Minnesota Press, Minneapolis, Minnesota, 2nd edition, 1983.

[Woo15] Jeffrey M Wooldridge. Introductory econometrics: A modern approach. Nelson Education, 2015.

[YS05] G Alastair Young and Richard L Smith. Essentials of statistical inference. Cambridge University Press, 2005.