Aggregate Demand and Supply

This paper is part of a broader project that provides a microfoundation to the General Theory of J.M. Keynes. I call this project 'old Keynesian economics' to distinguish it from new-Keynesian economics, a theory that is based on the idea that to make sense of Keynes we must assume that prices are sticky. I describe a multi-good model in which I interpret the definitions of aggregate demand and supply found in the General Theory through the lens of a search theory of the labor market. I argue that Keynes' aggregate supply curve can be interpreted as the aggregate of a set of first order conditions for the optimal choice of labor and, using this interpretation, I reintroduce a diagram that was central to the textbook teaching of Keynesian economics in the immediate post-war period.

Shooting the Auctioneer

Unemployment Real Business Cycles

A sunspot-based theory of unconventional monetary policy

This paper is about the effectiveness of qualitative easing, a form of unconventional monetary policy that changes the risk composition of the central bank balance sheet. We construct a general equilibrium model where agents have rational expectations, and there is a complete set of financial securities, but where some agents are unable to participate in financial markets. We show that a change in the risk composition of the central bank’s balance sheet affects equilibrium asset prices and economic activity. We prove that, in our model, a policy in which the central bank stabilizes non-fundamental fluctuations in the stock market is self-financing and leads to a Pareto efficient outcome

Graptemys barbouri

Number of Pages: 2Integrative BiologyGeological Science

Higher Spin Alternating Sign Matrices

We define a higher spin alternating sign matrix to be an integer-entry square matrix in which, for a nonnegative integer r, all complete row and column sums are r, and all partial row and column sums extending from each end of the row or column are nonnegative. Such matrices correspond to configurations of spin r/2 statistical mechanical vertex models with domain-wall boundary conditions. The case r=1 gives standard alternating sign matrices, while the case in which all matrix entries are nonnegative gives semimagic squares. We show that the higher spin alternating sign matrices of size n are the integer points of the r-th dilate of an integral convex polytope of dimension (n-1)^2 whose vertices are the standard alternating sign matrices of size n. It then follows that, for fixed n, these matrices are enumerated by an Ehrhart polynomial in r.Comment: 41 pages; v2: minor change

Solutions of the boundary Yang-Baxter equation for ADE models

We present the general diagonal and, in some cases, non-diagonal solutions of the boundary Yang-Baxter equation for a number of related interaction-round-a-face models, including the standard and dilute A_L, D_L and E_{6,7,8} models.Comment: 32 pages. Sections 7.2 and 9.2 revise

On the indeterminacy of determinacy and indeterminacy

A number of authors have attempted to test whether the U.S. economy is in a determinate or an indeterminate equilibrium. We argue that to answer this question, one must impose a priori restrictions on lag length that cannot be tested. We provide examples of two economic models. Model 1 displays an indeterminate equilibrium, driven by sunspots. Model 2 displays a determinate equilibrium driven by fundamentals. Given assumptions about the shock distribution of model 2, it is possible to find a distribution of sunspot shocks that drive model 1 such that the two models are observationally equivalent. JEL Classification: C39, C62, D51Identification, indeterminacy

On the Indeterminacy of New-Keynesian Economics

We study identification in a class of three-equation monetary models. We argue that these models are typically not identified. For any given exactly identified model, we provide an algorithm that generates a class of equivalent models that have the same reduced form. We use our algorithm to provide four examples of the consequences of lack of identification. In our first two examples we show that it is not possible to tell whether the policy rule or the Phillips curve is forward or backward looking. In example 3 we establish an equivalence between a class of models proposed by Benhabib and Farmer and the standard new-Keynesian model. This result is disturbing since equilibria in the Benhabib-Farmer model are typically indeterminate for a class of policy rules that generate determinate outcomes in the new-Keynesian model. In example 4, we show that there is an equivalence between determinate and indeterminate models even if one knows the structural equations of the modelIndeterminacy, identification

On the indeterminacy of new-Keynesian economics

We study identiÞcation in a class of three-equation monetary models. We argue that these models are typically not identiÞed. For any given exactly identiÞed model, we provide an algorithm that generates a class of equivalent models that have the same reduced form. We use our algorithm to provide four examples of the consequences of lack of identiÞcation. In our Þrst two examples we show that it is not possible to tell whether the policy rule or the Phillips curve is forward or backward looking. In example 3 we establish an equivalence between a class of models proposed by Benhabib and Farmer [1] and the standard new-Keynesian model. This result is disturbing since equilibria in the Benhabib-Farmer model are typically indeterminate for a class of policy rules that generate determinate outcomes in the new-Keynesian model. In example 4, we show that there is an equivalence between determinate and indeterminate models even if one knows the structural equations of the model. JEL Classification: C39, C62, D51, E52, E58IdentiÞcation, indeterminacy, new-Keynesian model, transparency

Shooting the Auctioneer

Most dynamic stochastic general equilibrium models of the macroeconomy assume that labor is traded in a spot market. Two exceptions by David Andolfatto and Monika Merz combine a two-sided search model with a one-sector real business cycle model. These hybrid models are successful, in some dimensions, but they cannot account for observed volatility in unemployment and vacancies. Following suggestions by Robert Hall and Robert Shimer, this paper shows that a relatively standard DSGE model with sticky wages can account for these facts. Using a second-order approximation to the policy function we simulate moments of an artificial economy with and without sticky wages and we document the dependence of unemployment and vacancy volatility on two key parameters; the disutility of effort and the degree of wage stickiness. We compute the welfare costs of the sticky wage equilibrium and find them to be small.