Hostname: page-component-669899f699-7tmb6 Total loading time: 0 Render date: 2025-05-06T15:18:15.000Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear quadratic approximation of rationally inattentive control problems

Published online by Cambridge University Press:  08 November 2023

Jianjun Miao  and
Bo Zhang
Jianjun Miao*
Affiliation:
Department of Economics, Boston University, Boston, MA, USA
Bo Zhang
Affiliation:
Institute of Chinese Financial Studies, Southwestern University of Finance and Economics, Chengdu, China
*
Corresponding author: Jianjun Miao; Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper proposes a linear quadratic approximation approach to dynamic nonlinear rationally inattentive control problems with multiple states and multiple controls. An efficient toolbox to implement this approach is provided. Applying this toolbox to five economic examples demonstrates that rational inattention can help explain the comovement puzzle in the macroeconomics literature.

Keywords

Rational inattentioninformation theorytracking problemoptimal controlentropynumerical methods
Type
Articles
Information
Macroeconomic Dynamics , Volume 28 , Issue 6 , September 2024 , pp. 1371 - 1393
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

†

We are grateful to two anonymous referees and an associate editor for helpful comments. Bo Zhang is grateful to the support by the Guanghua Talent Project of Southwestern University of Finance and Economics.

References

Afrouzi, H. and Yang, C. (2021) Dynamic Rational Inattention and the Phillips Curve. Working Paper, Columbia University.10.2139/ssrn.3770462CrossRefGoogle Scholar
Angeletos, G.-M. and Lian, C. (2017) Incomplete information in macroeconomics: Accommodating frictions in oordination. In: Angeletos, G.-M. and Lian, C. (eds.), Handbook of Macroeconomics, vol. 2, pp. 1065–1240. Amsterdam: North Holland.Google Scholar
Angeletos, G.-M. and Lian, C. (2022) Confidence and the propagation of demand shocks. Review of Economic Studies 89(3), 1085–1119.10.1093/restud/rdab064CrossRefGoogle Scholar
Beaudry, P. and Portier, F. (2004) An exploration into Pigou’s theory of cycles. Journal of Monetary Economics 51(6), 1183–1216.10.1016/j.jmoneco.2003.10.003CrossRefGoogle Scholar
Benigno, P. and Woodford, M. (2012) Linear-quadratic approximation of optimal policy problems. Journal of Economic Theory 147(1), 1–42.10.1016/j.jet.2011.10.012CrossRefGoogle Scholar
Bernanke, B. (1985) Adjustment costs, durable, and aggregate consumption. Journal of Monetary Economics 15(1), 41–68.10.1016/0304-3932(85)90052-2CrossRefGoogle Scholar
Caplin, A., Dean, M. and Leahy, J. (2019) Rational inattention, optimal consideration sets, and stochastic choice. Review of Economic Studies 86(3), 1061–1094.10.1093/restud/rdy037CrossRefGoogle Scholar
Cover, T. M. and Thomas, J. A. (2006) Elements of Information Theory, 2nd ed. New York: John Wiley & Sons, Inc.Google Scholar
Fulton, C. (2022) Choosing what to pay attention to. Theoretical Economics 17(1), 153–184.10.3982/TE3850CrossRefGoogle Scholar
Hébert, B. and La’O, J. (2021) Information Acquisition, Efficiency, and Non-fundamental Volatility. Working Paper, Columbia University and Stanford University.10.3386/w26771CrossRefGoogle Scholar
Jaimovich, N. and Rebelo, S. (2009) Can news about the future drive the business cycle? American Economic Review 99(4), 1097–1118.10.1257/aer.99.4.1097CrossRefGoogle Scholar
Judd, K. L. (1998) Numerical Methods in Economics. Cambridge, MA: The MIT Press.Google Scholar
Kacperczyk, M., Van Nieuwerburgh, S. and Veldkamp, L. (2016) A rational theory of mutual funds’ attention allocation. Econometrica 84(2), 571–626.10.3982/ECTA11412CrossRefGoogle Scholar
Kim, J. and Kim, S. (2003) Spurious welfare reversals in international business cycle models. Journal of International Economics 60(2), 471–500.10.1016/S0022-1996(02)00047-8CrossRefGoogle Scholar
Kydland, F. E. and Prescott, E. C. (1982) Time to build and aggregate fluctuations. Econometrica 50(6), 1345–1370.10.2307/1913386CrossRefGoogle Scholar
Kőszegi, B. and Matějka, F. (2020) Choice simplification: A theory of mental budgeting and naive diversification. Quarterly Journal of Economics 135(2), 1153–1207.10.1093/qje/qjz043CrossRefGoogle Scholar
Levine, P., Pearlman, J. and Pierse, R. (2008) Linear-quadratic approximation, external habit, and targeting rules. Journal of Economic Dynamics and Control 32(10), 3315–3349.10.1016/j.jedc.2008.02.001CrossRefGoogle Scholar
Luo, Y. (2008) Consumption dynamics under information processing constraints. Review of Economic Dynamics 11(2), 366–385.10.1016/j.red.2007.07.003CrossRefGoogle Scholar
Luo, Y., Nie, J. and Young, E. R. (2015) Slow information diffusion and the inertial behavior of durable consumption. Journal of the European Economic Association 13(5), 805–840.10.1111/jeea.12125CrossRefGoogle Scholar
Magill, M. J. P. (1977) Some new results on the local stability of the process of capital accumulation. Journal of Economic Theory 15(1), 174–210.10.1016/0022-0531(77)90075-8CrossRefGoogle Scholar
Matějka, F. and McKay, A. (2015) Rational inattention to discrete choices: A new foundation for the multinomial logit model. American Economic Review 105(1), 272–298.10.1257/aer.20130047CrossRefGoogle Scholar
Maćkowiak, B., Matějka, F. and Wiederholt, M. (2018) Dynamic rational inattention: Analytical results. Journal of Economic Theory 176, 650–692.10.1016/j.jet.2018.05.001CrossRefGoogle Scholar
Maćkowiak, B., Matějka, F. and Wiederholt, M. (2020) Rational Inattention: A Review. Working Paper, Sciences Po., CEPR DP1540.Google Scholar
Maćkowiak, B. and Wiederholt, M. (2009) Optimal sticky prices under rational inattention. American Economic Review 99(3), 769–803.10.1257/aer.99.3.769CrossRefGoogle Scholar
Maćkowiak, B. and Wiederholt, M. (2015) Business cycle dynamics under rational inattention. Review of Economic Studies 82(4), 1502–1532.10.1093/restud/rdv027CrossRefGoogle Scholar
Maćkowiak, B. and Wiederholt, M. (2020) Rational Inattention and the Business Cycle Effects of Productivity and News Shocks. Working Paper, European Central Bank and Sciences Po.Google Scholar
Miao, J. and Su, D. (2023) Asset market equilibrium under rational inattention. Economc Theory 75(1), 1–30.10.1007/s00199-021-01396-zCrossRefGoogle Scholar
Miao, J. and Wu, J. (2021) A Matlab Toolbox to Solve Dynamic Multivariate Rational Inattention Problems in the LQG Framework. Working Paper, Boston University.Google Scholar
Miao, J., Wu, J. and Young, E. R. (2022) Multivariate rational inattention. Econometrica 2(2), 907–945.10.3982/ECTA18086CrossRefGoogle Scholar
Miao, J. and Xing, H. (in press) Dynamic discrete choice under rational inattention. Economic Theory.Google Scholar
Mondria, J. (2010) Portfolio choice, attention allocation, and price comovement. Journal of Economic Theory 145(5), 1837–1864.10.1016/j.jet.2010.03.001CrossRefGoogle Scholar
Peng, L. (2005) Learning with information capacity constraints. Journal of Financial and Quantitative Analysis 40(2), 307–329.10.1017/S0022109000002325CrossRefGoogle Scholar
Peng, L. and Xiong, W. (2006) Investor attention, overconfidence and category learning. Journal of Financial Economics 80(3), 563–602.10.1016/j.jfineco.2005.05.003CrossRefGoogle Scholar
Schmitt-Grohé, S. and Uribe, M. (2003) Closing small open economy models. Journal of Monetary Economics 61, 163–185.Google Scholar
Sims, C. A. (1998). Stickiness. Carnegie-Rochester Conference Series on Public Policy 49, 317–356.10.1016/S0167-2231(99)00013-5CrossRefGoogle Scholar
Sims, C. A. (2003) Implications of rational inattention. Journal of Monetary Economics 50(3), 665–690.10.1016/S0304-3932(03)00029-1CrossRefGoogle Scholar
Sims, C. A. (2006) Rational inattention: Beyond the linear-quadratic case. American Economic Review 96(2), 158–163.10.1257/000282806777212431CrossRefGoogle Scholar
Sims, C. A. (2011) Rational inattention and monetary economics. In: B. M. Friedman and M. Woodford (eds.), Handbook of Monetary Economics, vol. 3A. Amsterdam: North-Holland.Google Scholar
Steiner, J., Stewart, C. and Matějka, F. (2017) Rational inattention dynamics: Inertia and delay in decision-making. Econometrica 85(2), 521–553.10.3982/ECTA13636CrossRefGoogle Scholar
Tanaka, T., Kim, K. K., Parrio, P. A. and Mitter, S. K. (2017) Semidefinite programming approach to Gaussian sequential rate-distortion trade-offs. IEEE Transactions on Automatic Control 62(4), 1896–1910.10.1109/TAC.2016.2601148CrossRefGoogle Scholar
Woodford, M. (2009) Information-constrained state-dependent pricing. Journal of Monetary Economics 56, S100–S124.10.1016/j.jmoneco.2009.06.014CrossRefGoogle Scholar
Zorn, P. (2018) Investment Under Rational Inattention: Evidence from US Sectoral Data. Working Paper, University of Munich.Google Scholar