# 10. Bibliography

> [1]

> Milton Abramowitz and Irene A. Stegun, (1965). Handbook of mathematical functions. Dover Publications, New York.

> [2]

> Stéphane Adjemian, Matthieu Darracq Parriès, and Stéphane Moyen, (2008). Towards a monetary policy evaluation framework. Working Paper Series 942, European Central Bank.

> [3]

> Stéphane Adjemian and Michel Juillard, (2025). Stochastic extended path. Journal of Economic Dynamics and Control, pages 105227. doi:10.1016/j.jedc.2025.105227.

> [4]

> Stéphane Adjemian and Michel Juillard, (2025). Stochastic extended path. Dynare Working Papers 84, CEPREMAP. URL: https://ideas.repec.org/p/cpm/dynare/084.html, doi:None.

> [5]

> Mark Aguiar and Gita Gopinath, (2007). Emerging market business cycles: the cycle is the trend. Journal of Political Economy, 115:69–102. doi:10.1086/511283.

> [6]

> Gianni Amisano and Oreste Tristani, (2010). Euro area inflation persistence in an estimated nonlinear DSGE model. Journal of Economic Dynamics and Control, 34(10):1837–1858. doi:10.1016/j.jedc.2010.05.001.

> [7]

> Martin M. Andreasen, Jesús Fernández-Villaverde, and Juan F. Rubio-Ramírez, (2018). The pruned state-space system for non-linear DSGE models: theory and empirical applications. Review of Economic Studies, 85(1):1–49. doi:10.1093/restud/rdx037.

> [8]

> Donald W. K. Andrews, (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica, 59(3):817–858. doi:10.2307/2938229.

> [9]

> Michal Andrle and Miroslav Plašil, (2018). Econometrics with system priors. Economics Letters, 172:134–137. doi:10.1016/j.econlet.2018.08.038.

> [10]

> Ienkaran Arasaratnam and Simon Haykin, (2009). Cubature Kalman Filters. IEEE Transactions on Automatic Control, 54(6):1254–1269. doi:10.1109/tac.2009.2019800.

> [11]

> Adrien Auclert, Bence Bardóczy, Matthew Rognlie, and Ludwig Straub, (2021). Using the Sequence‐Space Jacobian to solve and estimate heterogeneous‐agent models. Econometrica, 89(5):2375–2408. doi:10.3982/ecta17434.

> [12]

> David K. Backus, Patrick J. Kehoe, and Finn E. Kydland, (1992). International real business cycles. Journal of Political Economy, 100(4):745–75. doi:10.1086/261838.

> [13]

> Marianne Baxter and Robert G. King, (1999). Measuring business cycles: approximate band-pass filters for economic time series. Review of Economics and Statistics, 81(4):575–593. doi:10.1162/003465399558454.

> [14]

> Anmol Bhandari, Thomas Bourany, David Evans, and Mikhail Golosov, (2023). A perturbational approach for approximating heterogeneous agent models. NBER Working Papers 31744, National Bureau of Economic Research, Inc.

> [15]

> Dario A. Bini, Guy Latouche, and Beatrice Meini, (2002). Solving matrix polynomial equations arising in queueing problems. Linear Algebra and its Applications, 340(1–3):225–244. doi:10.1016/s0024-3795(01)00426-8.

> [16]

> Gregor Boehl, (2022). Dime mcmc: a swiss army knife for bayesian inference. SSRN Electronic Journal. doi:10.2139/ssrn.4250395.

> [17]

> Benjamin Born and Johannes Pfeifer, (2014). Policy risk and the business cycle. Journal of Monetary Economics, 68:68–85. doi:10.1016/j.jmoneco.2014.07.012.

> [18]

> Raouf Boucekkine, (1995). An alternative methodology for solving nonlinear forward-looking models. Journal of Economic Dynamics and Control, 19(4):711–734. doi:10.1016/0165-1889(94)00800-w.

> [19]

> Flint Brayton, Morris Davis, and Peter Tulip Tulip, (2000). Polynomial adjustment costs in FRB/US. Technical Report, Board of Governors of the Federal Reserve System (U.S.).

> [20]

> Flint Brayton and Peter Tinsley, (1996). A guide to FRB/US: a macroeconomic model of the United States. Finance and Economics Discussion Series 96-42, Board of Governors of the Federal Reserve System (U.S.). URL: https://EconPapers.repec.org/RePEc:fip:fedgfe:96-42.

> [21]

> Stephen P. Brooks and Andrew Gelman, (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4):434–455. doi:10.1080/10618600.1998.10474787.

> [22]

> Margarida F. Cardoso, Romualdo L. Salcedo, and S. Feyo de Azevedo, (1996). The simplex-simulated annealing approach to continuous non-linear optimization. Computers & Chemical Engineering, 20(9):1065–1080. doi:10.1016/0098-1354(95)00221-9.

> [23]

> Béatrice Cherrier, Aurélien Saïdi, and Francesco Sergi, (2023). “write your model almost as you would on paper and Dynare will take care of the rest!” a history of the dynare software. OEconomia, 13–3:801–848. doi:10.4000/oeconomia.16123.

> [24]

> Siddhartha Chib and Srikanth Ramamurthy, (2010). Tailored randomized block MCMC methods with application to DSGE models. Journal of Econometrics, 155(1):19–38. doi:10.1016/j.jeconom.2009.08.003.

> [25]

> Lawrence J. Christiano, Martin Eichenbaum, and Charles L. Evans, (2005). Nominal rigidities and the dynamic effects of a shock to monetary policy. Journal of Political Economy, 113(1):1–45. doi:10.1086/426038.

> [26]

> Lawrence J. Christiano, Roberto Motto, and Massimo Rostagno, (2007). Notes on Ramsey-optimal monetary policy. Available at http://faculty.wcas.northwestern.edu/ lchrist/d16/d1606/ramsey.pdf.

> [27]

> Lawrence J. Christiano, Mathias Trabandt, and Karl Walentin, (2010). DSGE models for monetary policy analysis. In Benjamin M. Friedman and Michael Woodford, editors, Handbook of Monetary Economics, volume 3, chapter 7, pages 285–367. Elsevier. doi:10.1016/B978-0-444-53238-1.00007-7.

> [28]

> Lawrence J. Christiano, Mathias Trabandt, and Karl Walentin, (2011). Introducing financial frictions and unemployment into a small open economy model. Journal of Economic Dynamics and Control, 35(12):1999–2041. doi:10.1016/j.jedc.2011.09.005.

> [29]

> Kai Christoffel, Günter Coenen, and Anders Warne, (2011). Forecasting with DSGE models. In Michael P. Clements and David F. Hendry, editors, The Oxford Handbook of Economic Forecasting, pages 89–128. Oxford University Press. doi:10.1093/oxfordhb/9780195398649.013.0005.

> [30]

> Fabrice Collard, (2001). Stochastic simulations with DYNARE. a practical guide. Technical Report, GREMAQ, University of Toulouse.

> [31]

> Fabrice Collard and Michel Juillard, (2001). A higher-order Taylor expansion approach to simulation of stochastic forward-looking models with an application to a nonlinear Phillips curve model. Computational Economics, 17(2-3):125–139. doi:10.1023/A:1011624124377.

> [32]

> Fabrice Collard and Michel Juillard, (2001). Accuracy of stochastic perturbation methods: the case of asset pricing models. Journal of Economic Dynamics and Control, 25(6-7):979–999. doi:10.1016/s0165-1889(00)00064-6.

> [33]

> Angelo Corana, Maurizio Marchesi, Claudio Martini, and Sandro Ridella, (1987). Minimizing multimodal functions of continuous variables with the \textquotedblleft simulated annealing\textquotedblright algorithm. ACM Transactions on Mathematical Software, 13(3):262–280. doi:10.1145/29380.29864.

> [34]

> Pablo Cuba-Borda, Luca Guerrieri, Matteo Iacoviello, and Molin Zhong, (2019). Likelihood evaluation of models with occasionally binding constraints. Journal of Applied Econometrics, 34(7):1073–1085. doi:10.1002/jae.2729.

> [35]

> Richard Dennis, (2007). Optimal policy in rational expectations models: new solution algorithms. Macroeconomic Dynamics, 11(1):31–55. doi:10.1017/s1365100507050341.

> [36]

> Darrell Duffie and Kenneth J. Singleton, (1993). Simulated moments estimation of Markov models of asset prices. Econometrica, 61(4):929. doi:10.2307/2951768.

> [37]

> James Durbin and Siem J. Koopman, (2012). Time series analysis by state space methods. Oxford University Press, Oxford, second revised edition edition.

> [38]

> Ray C. Fair and John B. Taylor, (1983). Solution and maximum likelihood estimation of dynamic nonlinear rational expectations models. Econometrica, 51(4):1169. doi:10.2307/1912057.

> [39]

> Jesús Fernández-Villaverde, (2010). The econometrics of DSGE models. SERIEs, 1(1-2):3–49. doi:10.1007/s13209-009-0014-7.

> [40]

> Jesús Fernández-Villaverde and Juan F. Rubio-Ramírez, (2005). Estimating dynamic equilibrium economies: linear versus nonlinear likelihood. Journal of Applied Econometrics, 20(7):891–910. doi:10.1002/jae.814.

> [41]

> Jesús Fernández-Villaverde and Juan Francisco Rubio-Ramírez, (2004). Comparing dynamic equilibrium models to data: a Bayesian approach. Journal of Econometrics, 123(1):153–187. doi:10.1016/j.jeconom.2003.10.031.

> [42]

> Michael C. Ferris and Todd S. Munson, (1999). Interfaces to PATH 3.0: design, implementation and usage. Computational Optimization and Applications, 12(1–3):207–227. doi:10.1023/a:1008636318275.

> [43]

> Jordi Galí, (2015). Monetary policy, inflation and the business cycle. Princeton University Press, Princeton, 2 edition.

> [44]

> John Geweke, (1992). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In José M. Bernardo, James O. Berger, A. Philip Dawid, and Adrian F. M. Smith, editors, Bayesian Statistics, volume 4, pages 169–194. Clarendon Press, Oxford. doi:10.1093/oso/9780198522669.003.0010.

> [45]

> John Geweke, (1999). Using simulation methods for Bayesian econometric models: inference, development, and communication. Econometric Reviews, 18(1):1–73. doi:10.1080/07474939908800428.

> [46]

> Paolo Giordani, Michael Pitt Pitt, and Robert Kohn, (2011). Bayesian inference for time series state space models. In John Geweke, Gary Koop, and Herman van Dijk, editors, The Oxford Handbook of Bayesian Econometrics, chapter 3, pages 60–124. Oxford University Press, Oxford. doi:10.1093/oxfordhb/9780199559084.013.0004.

> [47]

> Massimo Giovannini, Philipp Pfeiffer, and Marco Ratto, (2021). Efficient and robust inference of models with occasionally binding constraints. JRC Working Papers in Economics and Finance 2021-03, Joint Research Centre, European Commission. URL: https://ideas.repec.org/p/jrs/wpaper/202103.html.

> [48]

> William L. Goffe, Gary D. Ferrier, and John Rogers, (1994). Global optimization of statistical functions with simulated annealing. Journal of Econometrics, 60(1/2):65–100. doi:10.1016/0304-4076(94)90038-8.

> [49]

> N. J. Gordon, D. J. Salmond, and A. F. M. Smith, (1993). Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proceedings F - Radar and Signal Processing, 140(2):107–113. doi:10.1049/ip-f-2.1993.0015.

> [50]

> Luca Guerrieri and Matteo Iacoviello, (2015). OccBin: a toolkit for solving dynamic models with occasionally binding constraints easily. Journal of Monetary Economics, 70(C):22–38. doi:10.1016/j.jmoneco.2014.08.005.

> [51]

> Gaygysyz Guljanov, Willi Mutschler, and Mark Trede, (forthcoming). Pruned skewed kalman filter and smoother with application to dsge models. Journal of Economic Dynamics and Control.

> [52]

> Lars Peter Hansen, (1982). Large sample properties of generalized method of moments estimators. Econometrica, 50(4):1029–1054. doi:10.2307/1912775.

> [53]

> Nikolaus Hansen and Stefan Kern, (2004). Evaluating the CMA Evolution Strategy on multimodal test functions, pages 282–291. Springer, Berlin, 2004. doi:10.1007/978-3-540-30217-9_29.

> [54]

> Andrew C. Harvey and Garry D. A. PHILLIPS, (1979). Maximum likelihood estimation of regression models with autoregressive-moving average disturbances. Biometrika, 66(1):49–58. doi:10.1093/biomet/66.1.49.

> [55]

> Edward Herbst, (2015). Using the 'Chandrasekhar Recursions' for likelihood evaluation of DSGE models. Computational Economics, 45(4):693–705. doi:10.1007/s10614-014-9430-2.

> [56]

> Edward Herbst and Frank Schorfheide, (2014). Sequential Monte Carlo sampling for DSGE models. Journal of Applied Econometrics, 29(7):1073–1098. doi:10.1002/jae.2397.

> [57]

> Robert J. Hodrick and Edward C. Prescott, (1997). Post-war U.S. business cycles: an empirical investigation. Journal of Money, Credit and Banking, 29(1):1–16. doi:10.2307/2953682.

> [58]

> Edward L. Ionides, (2003). Inference and filtering for partially observed diffusion processes via Sequential Monte Carlo. Statistics Department Technical Report 405, University of Michigan.

> [59]

> Peter N. Ireland, (2004). A method for taking models to the data. Journal of Economic Dynamics and Control, 28(6):1205–1226. doi:10.1016/s0165-1889(03)00080-0.

> [60]

> Nikolay Iskrev, (2010). Local identification in DSGE models. Journal of Monetary Economics, 57:189–202. doi:10.1016/j.jmoneco.2009.12.007.

> [61]

> Kenneth Judd, (1996). Approximation, perturbation, and projection methods in economic analysis. In Hans Amman, David Kendrick, and John Rust, editors, Handbook of Computational Economics, volume 1, chapter 12, pages 511–585. North Holland Press. doi:10.1016/S1574-0021(96)01014-3.

> [62]

> Michel Juillard, (1996). Dynare: a program for the resolution and simulation of dynamic models with forward variables through the use of a relaxation algorithm. CEPREMAP Working Papers (Couverture Orange) 9602, CEPREMAP. URL: https://ideas.repec.org/p/cpm/cepmap/9602.html.

> [63]

> Simon J. Julier and Jeffrey K. Uhlmann, (1997). A new extension of the Kalman filter to nonlinear systems. In The 11th International Symposium on Aerospace/Defence Sensing, Simulation and Controls, 182–193. Orlando, 1997. doi:10.1117/12.280797.

> [64]

> Christian Kanzow and Stefania Petra, (2004). On a semismooth least squares formulation of complementarity problems with gap reduction. Optimization Methods and Software, 19(5):507–525. doi:10.1080/10556780410001683096.

> [65]

> Jinill Kim, Sunghyun Kim, Ernst Schaumburg, and Christopher A. Sims, (2008). Calculating and using second-order accurate solutions of discrete time dynamic equilibrium models. Journal of Economic Dynamics and Control, 32:3397–3414. 11. doi:10.1016/j.jedc.2008.02.003.

> [66]

> Ivana Komunjer and Serena Ng, (2011). Dynamic identification of dynamic stochastic general equilibrium models. Econometrica, 79(6):1995–2032. doi:10.3982/ecta8916.

> [67]

> Gary Koop, (2003). Bayesian econometrics. John Wiley & Sons, Chichester.

> [68]

> Siem J. Koopman and James Durbin, (2000). Fast filtering and smoothing for multivariate state space models. Journal of Time Series Analysis, 21(3):281–296. doi:10.1111/1467-9892.00186.

> [69]

> Siem J. Koopman and James Durbin, (2003). Filtering and smoothing of state vector for diffuse state-space models. Journal of Time Series Analysis, 24(1):85–98. doi:10.1111/1467-9892.00294.

> [70]

> Jayesh H. Kotecha and Petar M. Djuric, (2003). Gaussian particle filtering. IEEE Transactions on Signal Processing, 51(10):2592–2601. doi:10.1109/tsp.2003.816758.

> [71]

> Jayesh H. Kotecha and Petar M. Djuric, (2003). Gaussian sum particle filtering. IEEE Transactions on Signal Processing, 51(10):2602–2612. doi:10.1109/tsp.2003.816754.

> [72]

> Per Krusell and Anthony A. Smith, Jr., (1998). Income and wealth heterogeneity in the macroeconomy. Journal of Political Economy, 106(5):867–896. doi:10.1086/250034.

> [73]

> Alexei V. Kuntsevich and Franz Kappel, (1997). SolvOpt - the solver for local nonlinear optimization problems (version 1.1, Matlab, C, FORTRAN). Technical Report, University of Graz.

> [74]

> Laffargue, (1990). Résolution d’un modèle macroéconomique avec anticipations rationnelles. Annales d’Économie et de Statistique, pages 97. doi:10.2307/20075774.

> [75]

> Jane Liu and Mike West, (2001). Combined parameter and state estimation in simulation-based filtering, chapter 10, pages 197–223. Springer, New York, 2001. doi:10.1007/978-1-4757-3437-9_10.

> [76]

> Lawrence M. Murray, Emlyn M. Jones, and John Parslow, (2013). On disturbance state-space models and the particle marginal Metropolis-Hastings sampler. SIAM/ASA Journal on Uncertainty Quantification, 1(1):494–521. doi:10.1137/130915376.

> [77]

> Willi Mutschler, (2015). Identification of DSGE models—the effect of higher-order approximation and pruning. Journal of Economic Dynamics and Control, 56:34–54. doi:10.1016/j.jedc.2015.04.007.

> [78]

> Willi Mutschler, (2018). Higher-order statistics for DSGE models. Econometrics and Statistics, 6:44–56. doi:10.1016/j.ecosta.2016.10.005.

> [79]

> Marco Del Negro and Frank Schorfheide, (2004). Priors from general equilibrium models for VARS. International Economic Review, 45(2):643–673. doi:10.1111/j.1468-2354.2004.00139.x.

> [80]

> Joseph G. Pearlman, Paul D. Currie, and Peter W. Levine, (1986). Rational expectations models with partial information. Economic Modelling, 3:90–105. doi:10.1016/0264-9993(86)90001-5.

> [81]

> Johannes Pfeifer, (2013). A guide to specifying observation equations for the estimation of DSGE models. Technical Report, Universität der Bundeswehr München. URL: https://drive.google.com/file/d/1r89OU5OE3CBa6tOlj6l3hNVWEaRH5Anv/view?usp=sharing.

> [82]

> Johannes Pfeifer, (2014). An introduction to graphs in Dynare. Technical Report, Universität der Bundeswehr München.

> [83]

> Michael K. Pitt and Neil Shephard, (1999). Filtering via simulation: auxiliary particle filters. Journal of the American Statistical Association, 94(446):590–599. doi:10.1080/01621459.1999.10474153.

> [84]

> Christophe Planas, Marco Ratto, and Alessandro Rossi, (2015). Slice sampling in Bayesian estimation of DSGE models. Technical Report, European Commission, Joint Research Centre.

> [85]

> Zhongjun Qu and Denis Tkachenko, (2012). Identification and frequency domain quasi-maximum likelihood estimation of linearized dynamic stochastic general equilibrium models: QML estimation of linearized DSGE models. Quantitative Economics, 3(1):95–132. doi:10.3982/qe126.

> [86]

> Pau Rabanal and Juan F. Rubio-Ramírez, (2005). Comparing New Keynesian models of the business cycle: a Bayesian approach. Journal of Monetary Economics, 52(6):1151–1166. doi:10.1016/j.jmoneco.2005.08.008.

> [87]

> Adrian E. Raftery and Steven Lewis, (1992). How many iterations in the Gibbs sampler? In José M. Bernardo, James O. Berger, A. Philip Dawid, and Adrian F. M. Smith, editors, Bayesian Statistics, volume 4, pages 763–773. Clarendon Press, Oxford.

> [88]

> Marco Ratto, (2008). Analysing DSGE models with global sensitivity analysis. Computational Economics, 31(2):115–139.

> [89]

> Marco Ratto and Nikolay Iskrev, (2011). Algorithms for identification analysis under the Dynare environment: final version of the software. Technical Report, Joint Research Centre, European Commission.

> [90]

> K. Geert Rouwenhorst, (1995). Asset pricing implications of equilibrium business cycle models. In Thomas F. Cooley, editor, Frontiers of Business Cycle Research, pages 294–330. Princeton University Press, Princeton, NJ.

> [91]

> Francisco J. Ruge-Murcia, (2012). Estimating nonlinear DSGE models by the simulated method of moments: with an application to business cycles. Journal of Economic Dynamics and Control, 36(6):914–938. doi:10.1016/j.jedc.2012.01.008.

> [92]

> Stephanie Schmitt-Grohé and Martin Uríbe, (2004). Solving dynamic general equilibrium models using a second-order approximation to the policy function. Journal of Economic Dynamics and Control, 28(4):755–775. doi:10.1016/s0165-1889(03)00043-5.

> [93]

> Robert B. Schnabel and Elizabeth Eskow, (1990). A new modified Cholesky factorization. SIAM Journal on Scientific and Statistical Computing, 11(6):1136–1158. doi:10.1137/0911064.

> [94]

> Frank Schorfheide, (2000). Loss function-based evaluation of DSGE models. Journal of Applied Econometrics, 15(6):645–670. doi:10.1002/jae.582.

> [95]

> Christopher A. Sims, Daniel F. Waggoner, and Tao Zha, (2008). Methods for inference in large multiple-equation Markov-switching models. Journal of Econometrics, 146(2):255–274. doi:10.1016/j.jeconom.2008.08.023.

> [96]

> Martin Sköld and Gareth O. Roberts, (2003). Density estimation for the Metropolis–Hastings algorithm. Scandinavian Journal of Statistics, 30(4):699–718. doi:10.1111/1467-9469.00359.

> [97]

> Frank Smets and Rafael Wouters, (2003). An estimated dynamic stochastic general equilibrium model of the euro area. Journal of the European Economic Association, 1(5):1123–1175. doi:10.1162/154247603770383415.

> [98]

> James H. Stock and Mark W. Watson, (1999). Forecasting inflation. Journal of Monetary Economics, 44(2):293–335. doi:10.1016/S0304-3932(99)00027-6.

> [99]

> Cajo J. F. Ter Braak, (2006). A Markov Chain Monte Carlo version of the genetic algorithm Differential Evolution: easy Bayesian computing for real parameter spaces. Statistics and Computing, 16(3):239–249. doi:10.1007/s11222-006-8769-1.

> [100]

> Harald Uhlig, (2001). A toolkit for analysing nonlinear dynamic stochastic models easily. In Ramon Marimon and Andrew Scott, editors, Computational Methods for the Study of Dynamic Economies, pages 30–61. Oxford University Press, Oxford. doi:10.1093/0199248273.003.0003.

> [101]

> Sébastien Villemot, (2011). Solving rational expectations models at first order: what Dynare does. Dynare Working Papers 2, CEPREMAP. URL: https://ideas.repec.org/p/cpm/dynare/002.html.

> [102]

> Daniel F. Waggoner, Hongwei Wu, and Tao Zha, (2016). Striated Metropolis–Hastings sampler for high-dimensional models. Journal of Econometrics, 192(2):406–420. doi:10.1016/j.jeconom.2016.02.007.

> [103]

> Eric A. Wan and Rudolph van der Merwe, (2001). The unscented Kalman filter. In Haykin. Simon, editor, Kalman Filtering and Neural Networks, chapter 7, pages 221–280. John Wiley & Sons, New York. doi:10.1002/0471221546.ch7.

> [104]

> U.S. Census Bureau, (2020). X-13 ARIMA-SEATS Reference Manual, Version 1.1. Technical Report, Center for Statistical Research and Methodology, U.S. Census Bureau. URL: https://www.census.gov/data/software/x13as.html.