Birkhoff's Theorem in Higher Derivative Theories of Gravity

In this paper we present a class of higher derivative theories of gravity which admit Birkhoff's theorem. In particular, we explicitly show that in this class of theories, although generically the field equations are of fourth order, under spherical (plane or hyperbolic) symmetry, all the field equations reduce to second order and have exactly the same or similar structure to those of Lovelock theories, depending on the spacetime dimensions and the order of the Lagrangian.Comment: 7 pages, no figures. v1: This version received an Honorable Mention from the Gravity Research Foundation - 2011 Awards for Essays on Gravitation. v2: Expanded version. To appear in CQ

Dynamic Factor Demands Under Rational Expectations

This paper presents a dynamic model of the industrial demands for structures, equipment, and blue- and white-collar labor. Our approach is consistent with producers holding rational expectations and optimizing dynamically in the presence of adjustment costs, yet it permits generality of functional form regarding the technology. We represent the technology by atranslog input requirement function that specifies the amount of blue-collar labor (a flexible factor) the firm must hire to produce a level of output given its quantities of three quasi-fixed factors that are subject to adjustment costs: non-production (white-collar) workers, equipment, and structures.A complete description of the production structure is obtained by simultaneously estimating the input requirement function and three stochastic Euler equations.We apply an instrumental variable technique to estimate these equations using aggregate data for U.S. manufacturing. We find that as a fraction of total expenditures, adjustment costs are small in total hut large on the margin,and that they differ considerably across quasi-fixed factors. We also present short- and long-run elasticities of factor demands.

The Excess Co-Movement of Commodity Prices

This paper tests and confirms the existence of a puzzling phenomenon - the prices of largely unrelated raw commodities have a persistent tendency to move together. We show that this comovement of prices is well in excess of anything that can be explained by the common effects of past, current, or expected future values of macroeconomic variables such as inflation, industrial production, interest rates, and exchange rates. These results are a rejection of the standard competitive model of commodity price formation with storage.

The Phase-Space Density Profiles of Cold Dark Matter Halos

We examine the coarse-grained phase-space density profiles of a set of recent, high-resolution simulations of galaxy-sized Cold Dark Matter (CDM) halos. Over two and a half decades in radius the phase-space density closely follows a power-law, $\rho/\sigma^3 \propto r^{-\alpha}$, with $\alpha = 1.875$. This behaviour matches the self-similar solution obtained by Bertschinger for secondary infall in a uniformly expanding universe. On the other hand, the density profile corresponding to Bertschinger's solution (a power-law of slope $r^{2\alpha-6}$) differs significantly from the density profiles of CDM halos. We show that isotropic mass distributions with power-law phase-space density profiles form a one-parameter family of structures controlled by $\kappa$, the ratio of the velocity dispersion to the peak circular velocity. For $\kappa=\alpha=1.875$ one recovers the power-law solution $\rho \propto r^{2\alpha-6}$. For $\kappa$ larger than some critical value, $\kappa_{cr}$, solutions become non-physical, leading to negative densities near the center. The critical solution, $\kappa =\kappa_{cr}$, has the narrowest phase-space density distribution compatible with the power-law phase-space density stratification constraint. Over three decades in radius the critical solution is indistinguishable from an NFW profile. Our results thus suggest that the NFW profile is the result of a hierarchical assembly process that preserves the phase-space stratification of Bertschinger's infall model but which ``mixes'' the system maximally, perhaps as a result of repeated merging.Comment: 16 pages, 4 figures; submitted to The Astrophysical Journa