Couplings and convergence of Markov Chain Monte Carlo methods

Andreas EBERLE

University of Bonn

Couplings and convergence of Markov Chain Monte Carlo methods

Summary:

In this mini-course we introduce different couplings on continuous state spaces and apply them to quantify contraction and convergence properties of Markov Chain Monte Carlo methods in Wasserstein distances. In the first lecture, we start by introducing several variants of reflection couplings for diffusion processes. These couplings are applied to prove contractivity with explicit rates both for overdamped and for second order Langevin dynamics. In the second lecture, I will explain several ways to carry over the couplings to Markov chains. As a consequence, we derive error bounds for MCMC methods with explicit dependence on the dimension of the state space. Finally, in the last lecture, a related approach will be applied to quantify the convergence to equilibrium for Hamiltonian Monte Carlo.

Topics in Behavioral Political Economy

Spring 2020
Allan DRAZEN
University of Maryland

Abstract
This course will focus on integrating recent strands of behavioral economics into models of political economy. The area is sufficiently new that there is not even agreement about what it includes. We will look at both the basis for behavioral approaches and at specific questions and topics, using theoretical models and results from laboratory experiments. The course will look at some or all of the following subjects, focusing on voter and politician behavior: general modeling of non-selfish preferences; bounded rationality; cognitive biases and context effects; overconfidence; aspiration-based adaptive rules; political participation and voter turnout; polarization; and experimental evidence.

READINGS: We may add (or subtract) from this list.

1. Overview and Basic Issues
– Wilson, R. (2010) “The Contribution of Behavioral Economics to Political Science,” Annual Review of Political Science 14): 201-223.
– Bendor, J., D. Diermeier, D. Siegel & M. Ting (2011), A Behavioral Theory of Elections, Princeton: Princeton University Press. (BDST), chapter 1. [BDST] – Schnellenbach, J. and C. Schubert (2015), Behavioral Political Economy: A Survey,” European Journal of Political Economy 40 (2015) 395–417..

2. Other Regarding Behavior
– Fehr, E. and K. Schmidt (2005), “The Economics of Fairness, Reciprocity and Altruism – Experimental Evidence and New Theories,” in Handbook on the Economics of Giving, Reciprocity and Altruism.
– Rabin, M. (1993), “Incorporating Fairness into Game Theory and Economics,” American Economic Review 83, 1281-1302.
– Falk, A. and U. Fischbacher (2006), “A Theory of Reciprocity,” Games and Economic Behavior 54 (2), 293-315.
– Dana, J., R. Weber, and J. Kuang (2007), “Exploiting Moral Wiggle Room: Experiments Demonstrating an Illusory Preference for Fairness,” Economic Theory 33, 67–80.
– Lazear, E., U. Malmendier, and R. Weber (2012), “Sorting in Experiments with Application to Social Preferences,” American Economic Journal: Applied Economics 4(1), 136–163.
– Malmendier,U., V. te Velde, and R. Weber (2014), “Rethinking Reciprocity,” Annual Review of Economics 6, 849–74.
– Van der Weele, J. et al. (2014), “Resisting Moral Wiggle Room: How Robust Is Reciprocal Behavior?,” American Economic Journal: Microeconomics 6(3), 256–264.
– Benabou, R. and J. Tirole. 2006. “Incentives and Prosocial Behavior,” American Economic Review 96 (5): 1652–78.

3. Aspirations
– Cherepanov, V., T. Feddersen and A. Sandroni, (2013) “Revealed Preferences and Aspirations in Warm Glow Theory,” Economic Theory 54(3), 501-535.
– Saito, K. (2015), “Impure Altruism and Impure Selfishness,” Journal of Economic Theory 158(A), 336-70.
BDST, ch. 2.

4. Identity
– Akerlof, G. and R. Kranton (2000), “Economics of Identity,” Quarterly Journal of Economics 115, 715-753.
– Shayo, M. (2009), “A Model of Social Identity with an Application to Political Economy: Nation, Class, and Redistribution,” American Political Science Review 103(2), 147-174.
– Gennaioli, N. and G. Tabellini (2019), “Identity, Beliefs, and Political Conflict,” CESifo Working Paper, No. 7707, Center for Economic Studies and Ifo Institute, Munich.

5. Voter Turnout
– Levine, D. and T. Palfrey (2007), “The Paradox of Voter Participation? A Laboratory Study.” American Political Science Review 101 (1): 143-158.
– Coate, S. and M. Conlin (2004), “A Group Rule-Utilitarian Approach to Voter Turnout: Theory and Evidence,” American Economic Review 94, 1476-150.
– Feddersen, T., Sandroni, A (2006), “A Theory of Participation in Elections,” American Economic Review 96, 1271-92.
– Levine, D. and A. Mattozzi (2017), “Voter Turnout with Peer Punishment”, working paper.
BDST, ch. 4.
– Ali, S. N. and C. Lin (2013), “Why People Vote: Ethical Motives and Social Incentives,” American Economic Journal: Microeconomics 5(2): 73–98.
– Goeree, J. and C. Holt (2005), “An Explanation of Anomalous Behavior in Models of Political Participation,” American Political Science Review, 99(2), 201-213.

6. Beliefs and Polarization
a. Prospect Theory – Loss Aversion and Status Quo Bias
– Mercer, J. (2005), “Prospect Theory and Political Science,” Annual Review of Political Science 8, 1-21. (Link)
– Quattrone, G. and A. Tversky (1998), “Contrasting Rational and Psychological Analyses of Political Choice,” American Political Science Review 82(3), 719-736.
– Chong, D., and J. Druckman (2007), “Framing Theory,” Annual Review of Political Science 10, 103-126.
b. Rational Polarization
– Gerber, A. and D. Green (1999), “Misperceptions About Perceptual Bias,” Annual Review of Political Science 2, 189-210.
– Dixit, A. and J. Weibull (2007), “Political Polarization,” Proceedings of the National Academy of Sciences 104(18), 7351-7356.
– Andreoni, J., and T. Mylovanov. (2012), “Diverging Opinions,” American Economic Journal: Microeconomics 4 (1): 209–32.
– Benabou, R. (2008), “Ideology,” Journal of the European Economic Association 6(2/3), 321-352.
c. Confirmation Bias, Correlation Neglect, and Overconfidence
– Rabin, M., and J. Schrag (1999), “First Impressions Matter: A Model of Confirmatory Bias,” Quarterly Journal of Economics 114 (1), 37–82.
– Ortoleva, P. and E. Snowberg (2015), “Overconfidence in Political Behavior,” American Economic Review 105(7), 504-35. : 3071–3083.

7. Voter Choice
– Lodge, M., K M. McGraw, and P. Stroh (1989), “An Impression-Driven Model of Candidate Evaluation,” American Political Science Review, 83(2), 399–419.
– Druckman, J. N. (2004), “Political Preference Formation: Competition, Deliberation, and the (Ir)Relevance of Framing Effects,” American Political Science Review 98 (4): 671-686.
– Glaeser, E. and G. Ponzetto (2017), “Fundamental Errors in the Voting Booth,” NBER Working Paper 23683.
– Callander, S. and C. Wilson (2008), “Context-Dependent Voting and Political Ambiguity,” Journal of Public Economics 92, 565–581.
BDST, chapter 5.
– Nunnari, S and J. Zapal (2018), “A Model of Focusing in Political Choice,” working paper.

8. Politician Reactions
– BDST, chapter 3.
– Tomz, M. and P. Van Houweling (2008), “Candidate Positioning and Voter Choice,” American Political Science Review 102 (3), 303-318.
– Matějka, F. and G. Tabellini (2019), “Electoral Competition with Rationally Inattentive Voters,” working paper.
– Diermeier, D. and C. Li (2017), “Electoral Control with Behavioral Voters,” The Journal of Politics 2017 79:3, 890-902.
– Krupnikov, Y. (2011), “When Does Negativity Demobilize? Tracing the Conditional Effect of Negative Campaigning on Voter Turnout,” American Journal of Political Science 55(4), 797-813.
– Drazen, A. and E. Yucel, (in progress) “Voter Alienation, Policy Extremism and Negative Advertising,” working paper.

9. Behavioral Politicians
– Marcus George E. (2000), “Emotions in Politics,” Annual Review of Political Science, 3: 221-250.
– Drazen, A. and E. Ozbay (2019), “‘Does ‘Being Chosen to Lead’ Induce Non-Selfish Behavior? Experimental Evidence on Reciprocity,” Journal of Public Economics 174, 13-21.
– Corazzini, L., S. Kube, M. A. Maréchal, and A. Nicolò (2014), “Elections and Deceptions: An Experimental Study on the Behavioral Effects of Democracy,” American Journal of Political Science, 58(3), 579–592.
– Dalmia, P., A. Drazen, and E. Ozbay (2019), “Reelection versus Reciprocity,” working paper.
– Van Winden, F. (2015), “Political Economy with Affect: On the Role of Emotions and Relationships in Political Economics,” European Journal of Political Economy 40, 298–311.

MATERIALS
– Behavioral Political Economy’s 2020 reading list.
– Wilson, R. (2010), The Contribution of Behavioral Economics to Political Science.
– Bendor, J., D. Diermeier, D. Siegel & M. Ting (2011), A Behavioral Theory of Elections.
– Schnellenbach, J. and C. Schubert (2015), Behavioral Political Economy: A Survey.
– Fehr, E. and K. Schmidt (2005), The Economics of Fairness, Reciprocity and Altruism – Experimental Evidence and New Theories.
– Rabin, M. (1993), Incorporating Fairness into Game Theory and Economics.
– Falk, A. and U. Fischbacher (2006), A Theory of Reciprocity.
– Dana, J., R. Weber, and J. Kuang (2007), Exploiting Moral Wiggle Room: Experiments Demonstrating an Illusory Preference for Fairness.
– Lazear, E., U. Malmendier, and R. Weber (2012), Sorting in Experiments with Application to Social Preferences.
– Malmendier,U., V. te Velde, and R. Weber (2014), Rethinking Reciprocity.
– Benabou, R. and J. Tirole. (2006), Incentives and Prosocial Behavior.
– Cherepanov, V., T. Feddersen and A. Sandroni (2013), Revealed Preferences and Aspirations in Warm Glow Theory.
– Saito, K. (2015), Impure Altruism and Impure Selfishness.
– Akerlof, G. and R. Kranton (2000), Economics of Identity.
– Shayo, M. (2009), A Model of Social Identity with an Application to Political Economy: Nation, Class, and Redistribution.
– Gennaioli, N. and G. Tabellini (2019), Identity, Beliefs, and Political Conflict.
– Van der Weele, J. et al. (2014), Resisting Moral Wiggle Room: How Robust Is Reciprocal Behavior?.
– Levine, D. and T. Palfrey (2007), The Paradox of Voter Participation? A Laboratory Study.
– Coate, S. and M. Conlin (2004), A Group Rule-Utilitarian Approach to Voter Turnout: Theory and Evidence.
– Feddersen, T., Sandroni, A (2006), A Theory of Participation in Elections.
– Levine, D. and A. Mattozzi (2017), Voter Turnout with Peer Punishment.
– Ali, S. N. and C. Lin (2013), Why People Vote: Ethical Motives and Social Incentives.
– Goeree, J. and C. Holt (2005), An Explanation of Anomalous Behavior in Models of Political Participation.
– Gerber, A. and D. Green (1999), Misperceptions About Perceptual Bias.
– Dixit, A. and J. Weibull (2007), Political Polarization.
– Andreoni, J., and T. Mylovanov. (2012), Diverging Opinions.
– Benabou, R. (2008), Ideology.
– Rabin, M., and J. Schrag (1999), First Impressions Matter: A Model of Confirmatory Bias.
– Ortoleva, P. and E. Snowberg (2015), Overconfidence in Political Behavior.
– Lodge, M., K M. McGraw, and P. Stroh (1989), An Impression-Driven Model of Candidate Evaluation.
– Druckman, J. N. (2004), Political Preference Formation: Competition, Deliberation, and the (Ir)Relevance of Framing Effects.
– Glaeser, E. and G. Ponzetto (2017), Fundamental Errors in the Voting Booth.
– Callander, S. and C. Wilson (2008), Context-Dependent Voting and Political Ambiguity.
– Tomz, M. and P. Van Houweling (2008), Candidate Positioning and Voter Choice.
– Matějka, F. and G. Tabellini (2019), Electoral Competition with Rationally Inattentive Voters.
– Diermeier, D. and C. Li (2017), Electoral Control with Behavioral Voters.
– Drazen, A. and E. Yucel, (in progress) Voter Alienation, Policy Extremism and Negative Advertising.
– Marcus George E. (2000), Emotions in Politics.
– Drazen, A. and E. Ozbay (2019), ‘Does ‘Being Chosen to Lead’ Induce Non-Selfish Behavior? Experimental Evidence on Reciprocity.
– Corazzini, L., S. Kube, M. A. Maréchal, and A. Nicolò (2014), Elections and Deceptions: An Experimental Study on the Behavioral Effects of Democracy.
– Dalmia, P., A. Drazen, and E. Ozbay (2019), Reelection versus Reciprocity.
– Van Winden, F. (2015), Political Economy with Affect: On the Role of Emotions and Relationships in Political Economics.