Saving and Growth: A Reinterpretation

We examine the relationship between income growth and saving using both cross-country and household data. At the aggregate level, we find that growth Granger causes saving, but that saving does not Granger cause growth. Using household data, we find that households with predictably higher income growth save more than households with predictably low growth. We argue that standard Permanent Income models of consumption cannot explain these findings, but that a model of consumption with habit formation may. The positive effect of growth on saving implies that previous estimates of the effect of saving on growth may be overstated.

Historical Perspectives on the Monetary Transmission Mechanism

This paper examines changes over time in the importance of the lending channel in the transmission of monetary shocks to the real economy. We first use a simple extension of the Bernanke-Blinder model to isolate the observable factors that affect the strength of the lending channel. We then show that based on changes in the structure of banks assets, reserve requirements, and the composition of external firm finance, the lending channel should have been stronger before 1929 than during the post-World War II period, especially the first half of this period. Finally, we demonstrate that conventional indicators of the importance of the lending channel, such as the spread between the loan rate and the bond rate and the correlation between loans and output, do not show the predicted decline in the importance of lending over time. From this we conclude that either the traditional indicators are not useful measures of the strength of the lending channel or that the lending channel has not been quantitatively important in any era.

Star Formation and Feedback in Dwarf Galaxies

We examine the star formation history and stellar feedback effects of dwarf galaxies under the influence of extragalactic ultraviolet radiation. We consider the dynamical evolution of gas in dwarf galaxies using a one-dimensional, spherically symmetric, Lagrangian numerical scheme to compute the effects of radiative transfer and photoionization. We include a physically-motivated star formation recipe and consider the effects of feedback. Our results indicate that star formation in the severe environment of dwarf galaxies is a difficult and inefficient process. For intermediate mass systems, such as the dSphs around the Galaxy, star formation can proceed with in early cosmic epochs despite the intense background UV flux. Triggering processes such as merger events, collisions, and tidal disturbance can lead to density enhancements, reducing the recombination timescale, allowing gas to cool and star formation to proceed. However, the star formation and gas retention efficiency may vary widely in galaxies with similar dark matter potentials, because they depend on many factors, such as the baryonic fraction, external perturbation, IMF, and background UV intensity. We suggest that the presence of very old stars in these dwarf galaxies indicates that their initial baryonic to dark matter content was comparable to the cosmic value. This constraint suggests that the initial density fluctuation of baryonic matter may be correlated with that of the dark matter. For the more massive dwarf elliptical galaxies, the star formation efficiency and gas retention rate is much higher. Their mass to light ratio is regulated by star formation feedback, and is expected to be nearly independent of their absolute luminosity. The results of our theoretical models reproduce the observed $M/L-M_v$ correlation.Comment: 35 pages, 13 figure

Roche Lobe Overflow from Dwarf Stellar Systems

We use both analytical analyses and numerical simulations to examine the evolution of residual gas within tidally-limited dwarf galaxies and globular clusters. If the gas sound speed exceeds about 10% of the central velocity dispersion, as is the case for ionized gas within small stellar systems, the gas shall have significant density at the tidal radius, and the gas may be lost on timescales as short as a few times the sound crossing time of the system. In colder systems, the density at the tidal radius is much lower, greatly reducing the mass loss rate, and the system may retain its gas for a Hubble time. The tidally removed gas shall follow an orbit close to that of the original host system, forming an extended stream of ionized, gaseous debris. Tidal mass loss severely limits the ability of dwarf systems to continuously form stars. The ordinary gas content in many dwarf galaxies is fully ionized during high red-shift epochs, possibly preventing star formation in some systems, leading to the formation of starless, dark-matter concentrations. In either the field or in the center of galaxy clusters, ionized gas may be retained by dwarf galaxies, even though its sound speed may be comparable to or even exceed the velocity dispersion. These processes may help to explain some observed differences among dwarf galaxy types, as well as observations of the haloes of massive galaxies.Comment: 28 pages, LaTeX, AASTex macro

Global Star Formation Rates in Disk Galaxies and Circumnuclear Starbursts from Cloud Collisions

We invoke star formation triggered by cloud-cloud collisions to explain global star formation rates of disk galaxies and circumnuclear starbursts. Previous theories based on the growth rate of gravitational perturbations ignore the dynamically important presence of magnetic fields. Theories based on triggering by spiral density waves fail to explain star formation in systems without such waves. Furthermore, observations suggest gas and stellar disk instabilities are decoupled. Following Gammie, Ostriker & Jog (1991), the cloud collision rate is set by the shear velocity of encounters with initial impact parameters of a few tidal radii, due to differential rotation in the disk. This, together with the effective confinement of cloud orbits to a two dimensional plane, enhances the collision rate above that for particles in a three dimensional box. We predict Sigma_{SFR}(R) proportional to Sigma_{gas} Omega (1-0.7 beta). For constant circular velocity (beta = 0), this is in agreement with recent observations (Kennicutt 1998). We predict a B-band Tully-Fisher relation: L_{B} proportional to v_{circ}^{7/3}, also consistent with observations. As additional tests, we predict enhanced star formation in regions with relatively high shear rates, and lower star formation efficiencies in clouds of higher mass.Comment: 27 pages including 3 figures and 2 tables. Accepted to ApJ. Expanded statistical analysis of cloud SF efficiency test. Stylistic changes. Data for figures available electronically at http://astro.berkeley.edu/~jt/disksfr.htm

An Exact Black Hole Entropy Bound

We show that a Rademacher expansion can be used to establish an exact bound for the entropy of black holes within a conformal field theory framework. This convergent expansion includes all subleading corrections to the Bekenstein-Hawking term.Comment: 6 pages, Latex, v2 minor re-wording, additional reference, to appear in Phyical Review D (title changed in journal

On logical hierarchies within FO^2-definable languages

We consider the class of languages defined in the 2-variable fragment of the first-order logic of the linear order. Many interesting characterizations of this class are known, as well as the fact that restricting the number of quantifier alternations yields an infinite hierarchy whose levels are varieties of languages (and hence admit an algebraic characterization). Using this algebraic approach, we show that the quantifier alternation hierarchy inside FO^{2}[<] is decidable within one unit. For this purpose, we relate each level of the hierarchy with decidable varieties of languages, which can be defined in terms of iterated deterministic and co-deterministic products. A crucial notion in this process is that of condensed rankers, a refinement of the rankers of Weis and Immerman and the turtle languages of Schwentick, Th\'erien and Vollmer.Comment: arXiv admin note: text overlap with arXiv:0904.289