QuantEcon
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diff --git a/‎lectures/imp_sample.md‎
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@@ -203,7 +203,8 @@ @article{Epstein_Zin1989
   volume    = {57},
   number    = {4},
   pages     = {937--969},
-  year      = {1989}
+  year      = {1989},
+  doi       = {10.2307/1913778}
 }
 
 @article{Epstein_Zin1991,
@@ -213,7 +214,8 @@ @article{Epstein_Zin1991
   volume    = {99},
   number    = {2},
   pages     = {263--286},
-  year      = {1991}
+  year      = {1991},
+  doi       = {10.1086/261750}
 }
 
 @article{Duffie_Epstein1992a,
@@ -292,7 +294,8 @@ @article{Kreps_Porteus1978
   volume    = {46},
   number    = {1},
   pages     = {185--200},
-  year      = {1978}
+  year      = {1978},
+  doi       = {10.2307/1913656}
 }
 
 @article{Lucas_Stokey1984,
@@ -302,7 +305,8 @@ @article{Lucas_Stokey1984
   volume    = {32},
   number    = {1},
   pages     = {139--171},
-  year      = {1984}
+  year      = {1984},
+  doi       = {10.1016/0022-0531(84)90079-6}
 }
 
 @book{Karlin_Taylor1981,
@@ -2133,17 +2137,6 @@ @book{Lucas1987
   publisher = {Oxford Blackwell}
 }
 
-@article{Hans_Scheink_2009,
-  author  = {Lars Peter Hansen and Jose A. Scheinkman},
-  title   = {Long-Term Risk: An Operator Approach},
-  journal = {Econometrica},
-  year    = {2009},
-  volume  = {77},
-  number  = {1},
-  pages   = {177-234},
-  month   = {01}
-}
-
 @book{Whittle1963,
   title     = {Prediction and regulation by linear least-square methods},
   author    = {Whittle, Peter},
@@ -2841,6 +2834,53 @@ @article{MarcetMarimon1994
   year    = {2019}
 }
 
+@article{MarcetSargent1989jet,
+  author    = {Marcet, Albert and Sargent, Thomas J.},
+  title     = {Convergence of Least Squares Learning Mechanisms in
+               Self-Referential Linear Stochastic Models},
+  journal   = {Journal of Economic Theory},
+  year      = {1989},
+  volume    = {48},
+  number    = {2},
+  pages     = {337--368},
+  publisher = {Elsevier},
+  doi       = {10.1016/0022-0531(89)90032-X}
+}
+
+@article{Ljung1977,
+  author  = {Ljung, Lennart},
+  title   = {Analysis of Recursive Stochastic Algorithms},
+  journal = {IEEE Transactions on Automatic Control},
+  year    = {1977},
+  volume  = {22},
+  number  = {4},
+  pages   = {551--575},
+  doi     = {10.1109/TAC.1977.1101561}
+}
+
+@article{Evans1985,
+  author  = {Evans, George W.},
+  title   = {Expectational Stability and the Multiple Equilibria Problem
+             in Linear Rational Expectations Models},
+  journal = {Quarterly Journal of Economics},
+  year    = {1985},
+  volume  = {100},
+  number  = {4},
+  pages   = {1217--1233},
+  doi     = {10.2307/1885681}
+}
+
+@article{FourgeaudGourieroux1986,
+  author  = {Fourgeaud, Claude and Gourieroux, Christian and Pradel, Jacqueline},
+  title   = {Learning Procedures and Convergence to Rationality},
+  journal = {Econometrica},
+  year    = {1986},
+  volume  = {54},
+  number  = {4},
+  pages   = {845--868},
+  doi     = {10.2307/1912839}
+}
+
 @article{MarcetSargent1989,
   author    = {Marcet, Albert and Sargent, Thomas J},
   journal   = {Journal of Political Economy},
@@ -3063,29 +3103,26 @@ @article{Schelling1969
 }
 
 @article{Bansal_Yaron_2004,
-  author   = {Ravi Bansal and Amir Yaron},
-  title    = {{Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles}},
-  journal  = {Journal of Finance},
-  year     = 2004,
-  volume   = {59},
-  number   = {4},
-  pages    = {1481-1509},
-  month    = {08},
-  keywords = {},
-  doi      = {},
-  abstract = { We model consumption and dividend growth rates as containing (1) a small long-run predictable component, and (2) fluctuating economic uncertainty (consumption volatility). These dynamics, for which we provide empirical support, in conjunction with Epstein and Zin's (1989) preferences, can explain key asset markets phenomena. In our economy, financial markets dislike economic uncertainty and better long-run growth prospects raise equity prices. The model can justify the equity premium, the risk-free rate, and the volatility of the market return, risk-free rate, and the price-dividend ratio. As in the data, dividend yields predict returns and the volatility of returns is time-varying. Copyright 2004 by The American Finance Association.},
-  url      = {https://ideas.repec.org/a/bla/jfinan/v59y2004i4p1481-1509.html}
+  author  = {Bansal, Ravi and Yaron, Amir},
+  title   = {Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles},
+  journal = {Journal of Finance},
+  year    = {2004},
+  volume  = {59},
+  number  = {4},
+  pages   = {1481--1509},
+  doi     = {10.1111/j.1540-6261.2004.00670.x}
 }
 
 @article{hansen2008consumption,
-  title     = {Consumption strikes back? Measuring long-run risk},
-  author    = {Hansen, Lars Peter and Heaton, John C and Li, Nan},
-  journal   = {Journal of Political economy},
+  title     = {Consumption Strikes Back? Measuring Long-Run Risk},
+  author    = {Hansen, Lars Peter and Heaton, John C. and Li, Nan},
+  journal   = {Journal of Political Economy},
   volume    = {116},
   number    = {2},
   pages     = {260--302},
   year      = {2008},
-  publisher = {The University of Chicago Press}
+  publisher = {The University of Chicago Press},
+  doi       = {10.1086/588200}
 }
 
 @article{Hansen_2007,
@@ -3166,7 +3203,9 @@ @article{Townsend1983
   title   = {Forecasting the Forecasts of Others},
   journal = {Journal of Political Economy},
   volume  = {91},
-  pages   = {546-588}
+  number  = {4},
+  pages   = {546--588},
+  doi     = {10.1086/261166}
 }
 
 @article{tobin1992old,
@@ -3859,3 +3898,179 @@ @article{grossman1976
   pages   = {573--585},
   year    = {1976}
 }
+
+@incollection{BrayKreps1987,
+  author    = {Bray, Margaret M. and Kreps, David M.},
+  title     = {Rational Learning and Rational Expectations},
+  booktitle = {Arrow and the Ascent of Modern Economic Theory},
+  editor    = {Feiwel, George R.},
+  publisher = {Palgrave Macmillan},
+  address   = {London},
+  year      = {1987},
+  pages     = {597--625},
+  doi       = {10.1007/978-1-349-07239-2_19}
+}
+
+@article{Bray1982,
+  author  = {Bray, Margaret M.},
+  title   = {Learning, Estimation, and the Stability of Rational Expectations},
+  journal = {Journal of Economic Theory},
+  year    = {1982},
+  volume  = {26},
+  number  = {2},
+  pages   = {318--339},
+  doi     = {10.1016/0022-0531(82)90007-2}
+}
+
+@article{BraySavin1986,
+  author  = {Bray, Margaret M. and Savin, N. E.},
+  title   = {Rational Expectations Equilibria, Learning and Model Specification},
+  journal = {Econometrica},
+  year    = {1986},
+  volume  = {54},
+  number  = {5},
+  pages   = {1129--1160},
+  doi     = {10.2307/1912325}
+}
+
+@article{Radner1979,
+  author  = {Radner, Roy},
+  title   = {Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices},
+  journal = {Econometrica},
+  year    = {1979},
+  volume  = {47},
+  number  = {3},
+  pages   = {655--678},
+  doi     = {10.2307/1910413}
+}
+
+@article{Jordan1982,
+  author  = {Jordan, James S.},
+  title   = {The Generic Existence of Rational Expectations Equilibrium in the Higher Dimensional Case},
+  journal = {Journal of Economic Theory},
+  year    = {1982},
+  volume  = {26},
+  number  = {2},
+  pages   = {224--243},
+  doi     = {10.1016/0022-0531(82)90002-3}
+}
+
+@article{Jordan1982b,
+  author  = {Jordan, James S.},
+  title   = {Admissible Market Data Structures: A Complete Characterization},
+  journal = {Journal of Economic Theory},
+  year    = {1982},
+  volume  = {28},
+  number  = {1},
+  pages   = {19--31},
+  doi     = {10.1016/0022-0531(82)90089-8}
+}
+
+@article{Admati1985,
+  author  = {Admati, Anat R.},
+  title   = {A Noisy Rational Expectations Equilibrium for Multi-Asset Securities Markets},
+  journal = {Econometrica},
+  year    = {1985},
+  volume  = {53},
+  number  = {3},
+  pages   = {629--657},
+  doi     = {10.2307/1911659}
+}
+
+@article{GrossmanStiglitz1980,
+  author  = {Grossman, Sanford J. and Stiglitz, Joseph E.},
+  title   = {On the Impossibility of Informationally Efficient Markets},
+  journal = {American Economic Review},
+  year    = {1980},
+  volume  = {70},
+  number  = {3},
+  pages   = {393--408},
+  doi     = {10.2307/1805228}
+}
+
+@article{AndersonSonnenschein1982,
+  author  = {Anderson, Robert M. and Sonnenschein, Hugo},
+  title   = {On the Existence of Rational Expectations Equilibrium},
+  journal = {Journal of Economic Theory},
+  year    = {1982},
+  volume  = {26},
+  number  = {2},
+  pages   = {261--278},
+  doi     = {10.1016/0022-0531(82)90004-7}
+}
+
+@article{BlumeEasley1982,
+  author  = {Blume, Lawrence E. and Easley, David},
+  title   = {Learning to be Rational},
+  journal = {Journal of Economic Theory},
+  year    = {1982},
+  volume  = {26},
+  number  = {2},
+  pages   = {340--351},
+  doi     = {10.1016/0022-0531(82)90008-4}
+}
+
+@article{Frydman1982,
+  author  = {Frydman, Roman},
+  title   = {Towards an Understanding of Market Processes: Individual Expectations, Learning, and Convergence to Rational Expectations Equilibrium},
+  journal = {American Economic Review},
+  year    = {1982},
+  volume  = {72},
+  number  = {4},
+  pages   = {652--668}
+}
+
+@article{Grossman1981,
+  author  = {Grossman, Sanford J.},
+  title   = {An Introduction to the Theory of Rational Expectations under Asymmetric Information},
+  journal = {Review of Economic Studies},
+  year    = {1981},
+  volume  = {48},
+  number  = {4},
+  pages   = {541--559},
+  doi     = {10.2307/2297195}
+}
+
+@techreport{ArrowGreen1973,
+  author      = {Arrow, Kenneth J. and Green, Jerry R.},
+  title       = {Notes on Expectations Equilibria in Bayesian Settings},
+  year        = {1973},
+  type        = {Working Paper},
+  number      = {33},
+  institution = {Institute for Mathematical Studies in the Social Sciences, Stanford University}
+}
+
+@article{Kreps1977,
+  author  = {Kreps, David M.},
+  title   = {A Note on Fulfilled Expectations Equilibria},
+  journal = {Journal of Economic Theory},
+  year    = {1977},
+  volume  = {14},
+  number  = {1},
+  pages   = {32--43},
+  doi     = {10.1016/0022-0531(77)90083-7}
+}
+
+@article{Breeden1979,
+  author    = {Breeden, Douglas T.},
+  title     = {An Intertemporal Asset Pricing Model with Stochastic
+               Consumption and Investment Opportunities},
+  journal   = {Journal of Financial Economics},
+  year      = {1979},
+  volume    = {7},
+  number    = {3},
+  pages     = {265--296},
+  doi       = {10.1016/0304-405X(79)90016-3}
+}
+
+@book{Nummelin_1984,
+  author    = {Nummelin, Esa},
+  title     = {General Irreducible {Markov} Chains and Non-Negative
+               Operators},
+  series    = {Cambridge Tracts in Mathematics},
+  number    = {83},
+  publisher = {Cambridge University Press},
+  address   = {Cambridge},
+  year      = {1984},
+  doi       = {10.1017/CBO9780511526237}
+}
@@ -142,8 +142,11 @@ parts:
   - file: ge_arrow
   - file: harrison_kreps
   - file: morris_learn
+  - file: rational_learning_re
+  - file: ls_learning
   - file: affine_risk_prices
   - file: ross_recovery
+  - file: long_run_risk_operator
   - file: misspecified_recovery
 - caption: Data and Empirics
   numbered: true
 
@@ -264,13 +264,12 @@ We next study the bias and efficiency of the Monte Carlo and importance sampling
 The code  below produces distributions of estimates using both Monte Carlo and importance sampling methods.
 
 ```{code-cell} ipython3
-@jit(parallel=True)
 def simulate(p_a, p_b, q_a, q_b, N_simu, T=1):
 
     μ_L_p = np.empty(N_simu)
     μ_L_q = np.empty(N_simu)
 
-    for i in prange(N_simu):
+    for i in range(N_simu):
         μ_L_p[i] = estimate(p_a, p_b, p_a, p_b, T=T)
         μ_L_q[i] = estimate(p_a, p_b, q_a, q_b, T=T)