The role of expectations in economic fluctuations and the efficacy of monetary policy

We show diverse beliefs is an important propagation mechanism of fluctuations, money non neutrality and efficacy of monetary policy. Since expectations affect demand, our theory shows economic fluctuations are mostly driven by varying demand not supply shocks. Using a competitive model with flexible prices in which agents hold Rational Belief (see Kurz (1994)) we show that (i) our economy replicates well the empirical record of fluctuations in the U.S. (ii) Under monetary rules without discretion, monetary policy has a strong stabilization effect and an aggressive anti-inflationary policy can reduce inflation volatility to zero. (iii) The statistical Phillips Curve changes substantially with policy instruments and activist policy rules render it vertical. (iv) Although prices are flexible, money shocks result in less than proportional changes in inflation hence the aggregate price level appears "sticky" with respect to money shocks. (v) Discretion in monetary policy adds a random element to policy and increases volatility. The impact of discretion on the efficacy of policy depends upon the structure of market beliefs about future discretionary decisions. We study two rationalizable beliefs. In one case, market beliefs weaken the effect of policy and in the second, beliefs bolster policy outcomes and discretion could be a desirable attribute of the policy rule. Since the central bank does not know any more than the private sector, real social gain from discretion arise only in extraordinary cases. Hence, the weight of the argument leads us to conclude that bank´s policy should be transparent and abandon discretion except for rare and unusual circumstances. (vi) An implication of our model suggests the current effective policy is only mildly activist and aims mostly to target inflation

Interval minors of complete bipartite graphs

Interval minors of bipartite graphs were recently introduced by Jacob Fox in the study of Stanley-Wilf limits. We investigate the maximum number of edges in $K_{r,s}$-interval minor free bipartite graphs. We determine exact values when $r=2$ and describe the extremal graphs. For $r=3$, lower and upper bounds are given and the structure of $K_{3,s}$-interval minor free graphs is studied

Beyond Ohba's Conjecture: A bound on the choice number of kk-chromatic graphs with nn vertices

Let $\text{ch}(G)$ denote the choice number of a graph $G$ (also called "list chromatic number" or "choosability" of $G$). Noel, Reed, and Wu proved the conjecture of Ohba that $\text{ch}(G)=\chi(G)$ when $|V(G)|\le 2\chi(G)+1$. We extend this to a general upper bound: $\text{ch}(G)\le \max\{\chi(G),\lceil({|V(G)|+\chi(G)-1})/{3}\rceil\}$. Our result is sharp for $|V(G)|\le 3\chi(G)$ using Ohba's examples, and it improves the best-known upper bound for $\text{ch}(K_{4,\dots,4})$.Comment: 14 page

The Role of Expectations in Economic Fluctuations and the Efficacy of Monetary Policy

We show diverse beliefs is an important propagation mechanism of fluctuations, money non neutrality and efficacy of monetary policy. Since expectations affect demand, our theory shows economic fluctuations are mostly driven by varying demand not supply shocks. Using a competitive model with flexible prices in which agents hold Rational Belief (see Kurz (1994)) we show that (i) our economy replicates well the empirical record of fluctuations in the U.S. (ii) Under monetary rules without discretion, monetary policy has a strong stabilization effect and an aggressive anti-inflationary policy can reduce inflation volatility to zero. (iii) The statistical Phillips Curve changes substantially with policy instruments and activist policy rules render it vertical. (iv) Although prices are flexible, money shocks result in less than proportional changes in inflation hence the aggregate price level appears “sticky” with respect to money shocks. (v) Discretion in monetary policy adds a random element to policy and increases volatility. The impact of discretion on the efficacy of policy depends upon the structure of market beliefs about future discretionary decisions. We study two rationalizable beliefs. In one case, market beliefs weaken the effect of policy and in the second, beliefs bolster policy outcomes and discretion could be a desirable attribute of the policy rule. Since the central bank does not know any more than the private sector, real social gain from discretion arise only in extraordinary cases. Hence, the weight of the argument leads us to conclude that bank’s policy should be transparent and abandon discretion except for rare and unusual circumstances. (vi) An implication of our model suggests the current effective policy is only mildly activist and aims mostly to target inflation.Monetary policy rules, Money non neutrality, Business cycles, Market volatility, Propagation mechanism, Capacity utilization, Heterogenous beliefs, Over confidence, Rational Belief, Optimism, Pessimism, Non stationarity, Empirical distribution

Large Supports are required for Well-Supported Nash Equilibria

We prove that for any constant $k$ and any $\epsilon<1$, there exist bimatrix win-lose games for which every $\epsilon$-WSNE requires supports of cardinality greater than $k$. To do this, we provide a graph-theoretic characterization of win-lose games that possess $\epsilon$-WSNE with constant cardinality supports. We then apply a result in additive number theory of Haight to construct win-lose games that do not satisfy the requirements of the characterization. These constructions disprove graph theoretic conjectures of Daskalakis, Mehta and Papadimitriou, and Myers