Polynomial inequalities for non-commuting operators

We prove an inequality for polynomials applied in a symmetric way to non-commuting operators

Are home prices the next "bubble"?

The strong rise in home prices since the mid-1990s has raised concerns over a possible bubble in the housing market and the effect of a sharp price decline on the U.S. economy. This article assesses two measures frequently cited to support a bubble-the rising price-to-income ratio and the declining rent-to-price ratio-and finds the measures to be flawed and the conclusions drawn from them unpersuasive. In particular, the measures do not fully account for the effects of declining nominal mortgage interest rates and fail to use appropriate home price indexes. The authors also estimate a structural model of the housing market and find that aggregate prices are not inconsistent with long-run demand fundamentals. Accordingly, they conclude that market fundamentals are strong enough to explain the recent path of home prices and that no bubble exists. Nevertheless, weakening fundamentals could have an impact on home values on the east and west coasts, where the new housing supply appears to be relatively inelastic. However, prices in these regions have typically been volatile, and previous declines have not had a sizable negative effect on the overall economy.Housing - Prices ; Housing - Finance ; Business cycles

Monetary policy transmission to residential investment

Paper for a conference sponsored by the Federal Reserve Bank of New York entitled Financial Innovation and Monetary TransmissionMonetary policy ; Housing - Finance ; Mortgages

HST imaging and Keck Spectroscopy of z~6 I-band Drop-Out Galaxies in the ACS GOODS Fields

We measure the surface density of i'-band dropout galaxies at z~6 through wide field HST/ACS imaging and ultra-deep Keck/DEIMOS spectroscopy. Using deep HST/ACS SDSS-i' (F775W) and SDSS-z' (F850LP) imaging from GOODS-N (200 arcmin^2), we identify 9 i'-drops satisfying an (i'-z')_AB>1.5 selection criterion to a depth of z'_AB=25.6 (corresponding to L*_UV at z~3-4). We use HK' imaging data to improve the fidelity of our sample, discriminating against lower redshift red galaxies and cool Galactic stars. Three i'-drops are consistent with M/L/T dwarf stars. We present ultra-deep Keck/DEIMOS spectroscopy of 10 objects from our combined GOODS-N and GOODS-S i'-drop sample. We detect Lyman-alpha emission at z=5.83 from one object in the GOODS-S field, which lies only 8arcmin away (i.e. 3Mpc/h_70) from the z=5.78 object already confirmed by Bunker et al. (2003). One possible Lyman-alpha emitter at z=6.24 is found in the GOODS-N field (although identification of this spatially-offset emission line is ambiguous). Using the rest-frame UV continuum from our 6 candidate z~6 galaxies from the GOODS-N field, we determine a lower limit to the unobscured volume-averaged global star formation rate at z~6 of (5.4+/-2.2)x10^-4 h_70 M_sun/yr/Mpc^3. We find that the cosmic star formation density in galaxies with unobscured star formation rates 15M_sun/yr/h_70^2 falls by a factor of 8 between z~3 and z~6. Hence the luminosity function of LBGs must evolve in this redshift interval: a constant integrated star formation density at $z>3$ requires a much steeper faint-end slope, or a brighter characteristic luminosity. This result is in agreement with our previous measurement from the Chandra Deep Field South (Stanway et al. 2003), indicating that cosmic variance is not a dominant source of uncertainty.Comment: to appear in ApJ; replaced with accepted versio