Regime change

1. Regime change Ec 517 October 2, 2017

2. Dynamics of complementarity and learning • Boom and busts in business cycles • Switch of political regimes • Eastern Europe • Arab world • Two structural properties • Strategic complementarity implies that the marginal agents are in the tail of the distribution • The observation of the tail of the distribution provides little information on the entire distribution

3. Interactions with externalities and complexity • Boom and busts in business cycles • Financial crises • Switch of political regimes or general opinion • Eastern Europe • Herding behavior

4. Structural models of interactions • “Canonical” model • Minimalist, abstract • Interactions are caused by externalities • Two types of externalities • Payoff externality (coordination) • Information externality Imperfect observation of the state Learning from others’ actions (social learning, informational cascades, herding)

5. Coordination • Positive externality: strategic complementarity • The action of others increases my incentive to act • Bank runs • Speculative attacks against a fixed exchange regime • Change of political regime, etc…

6. Stylized model • Large number of individuals, each chooses, 0-1 action with an individual cost • Gross payoff of action: mass of actions • Net payoff • Distribution of individuals with costs • Each individual knows his own c and has an estimate of the others’ costs • If agents with cost small than c* invests, and F is the cdf, the payoff is F(c*)-c • Under perfect information, Nash equilibrium is F(c*)=c*

7. Stylized model • Large number of individuals, each chooses, 0-1 action with an individual cost • Gross payoff of action: mass of actions • Net payoff • Distribution of individual costs

8. Static equilibrium • Strategy • Equilibrium • With sufficient strat. compl., Multiple equilibria

9. Problem of the “choice” of equilibrium • Global games (Carlsson and Van Damme, Morris & Shin) • (very) Small uncertainty on the structure of the economy • No common knowledge

10. Evolution (dynamics), learning • Global games (Carlsson and Van Damme, Morris & Shin) • (very) Small uncertainty on the structure of the economy • No common knowledge

11. Imperfect information • Individuals have a strategy • They observe only • Impact of the shift of the c.d.f • Aggregate activity shows the tail of the distribution • Property inherent to strategic complementarity

12. Model of regime choice • Kuran: “Public lies private truths”. • Continuum of people, total mass normalized to one. • Y is the mass of people choosing action 0 (speak against) • Mass that supports the regime is 1-Y • Individual is defined by his preference for the regime • Payoff of individual with parameter c : • The difference between the payoffs is

13. Representation Two (stable) equilibria L1 and H1 The structure (cdf) evolves randomly and slowly

14. Evolution of the structure of costs • The distribution of costs is “placed” by a parameter that evolves by a random walk (with regression to the mean) Unique equilibrium with low activity Multiple equilibria (under perfect information) Unique equilibrium with high activity T=60

15. Evolution of beliefs and actions • Individuals form their beliefs from • Their private information (cost c) • The history of aggregate activities (mass of total actions in each past period) • Individuals have a monotone strategy (invest in period t iff the own cost is smaller than ct* (can be proven to be iteratively dominant under the structure of information) • Unique equilibrium

16. Under imperfect information • On the left, the true state of nature and the public belief (from history) • On the right, the payoff of agent with cost c if every agent (uncertain mass) with cost lower than c chooses to invest

46. Delays • Assumption: individuals can delay • Delay has a cost • But with delay, more information • Tradeoff • Impact of the cost of delay (equivalent to longer period) • Does a lower cost (shorter period) facilitate coordination ?

47. Impact of the cost of delay • No under the following argument: • Because of strategic complementarity, the marginal agent is in the tail of the distribution. • Little information • If more agents act, more information that reduces the incentive to act: more incentive to delay • Waiting for information reduces information • Under some plausible assumption, delay prevents an equilibrium with high activity (work with Lucia Esposito).

48. Social learning • Definition for economists: learning for the observation of what others • Do • Say • Learning about what? • State of nature that affects the payoff of the observed and me (possibly in different ways.

49. Rational (Bayesian) learning • Requirements • Common knowledge on • The prior distribution of the states of nature • The mechanical properties of the private signals • The payoff functions of the others (how they take action as a function of the information: the common prior and their private signal) • What is not known is the private information (signal) of others. • One’s action is a signal (noisy) on one’s private information

50. General properties • Because learning is rational (Bayesian), the beliefs (probability distributions about the state) converge (in probability). • Consequence of the Martingale Convergence Theorem • But beliefs may not converge to the truth • More “pathologies” in social learning when individuals are selfishly rational.