Finite Lifetimes, Borrowing Constraints, and Short-Run Fiscal Policy

Recent developments in public finance in the analysis of dynamic government debt policies have emphasized effects on the distribution of real resources across generations. At the same time, macroeconomists have emphasized the importance of the length of the time horizon over which agents optimize their decisions about consumption for judging the effects of fiscal policy on aggregate demand. Much of the discussion of these issues has focused on whether linkages among generations are sufficient to give consumers infinite horizons. To the extent that horizons are finite, debt burdens can be shifted to future generations, and substitutions of debt for taxes have real effects. This paper argues that, as a matter of quantitative significance, theoretical and empirical emphasis on the importance of finite horizons for the analysis of many fiscal policies is misplaced. Studies of the role of finite horizons in determining the effects of short-run fiscal policies on consumption have been conducted largely under the assumption of perfect capital markets. We show that while the marginal propensity to consume (MPC) out of temporary tax changes is nonzero in finite- horizon models, it is not very large. We demonstrate that the MPC is, however, quite sensitive to the importance of restrictions on borrowing in the economy. The clear implication is that shifting emphasis from the length of the planning horizon to the structure of capital markets is an important step for empirical research.

Social Security and Individual Welfare: Precautionary Saving, LiquidityConstraints, and the Payroll Tax

Recent advances in the examination of efficiency gains from dynamic tax reforms have used simulation models to isolate intragenerational and/or intergenerational effects. Important considerations having to do with uncertainty or capital market imperfections are frequently missing from such a framework. In this paper, we focus on the welfare gains from introducing social security retirement annuities, given lifetime uncertainty and borrowing restrictions.Our principal findings are four. First, given the considerations mentioned above, "precautionary saving" exceeds life-cycle saving (that would have taken place in the absence of lifetime uncertainty), lending further support to the notion that the perfect-certainty version of the life-cycle model provides an inadequate explanation of observed saving behavior. Second, the introduction of an actuarially fair social security system leads to a significant partial equilibrium increase in lifetime consumption and welfare, accompanied by a reduction in the capital stock.The increase in lifetime welfare is reduced, however,and in many cases eliminated, when borrowing restrictions are imposed.Third, extending the model to general equilibrium, we find that the partial equilibrium gains in lifetime welfare from participation in social security are offset by the interaction of higher steady-state interest rates and binding liquidity constraints. Finally, replacing the proportional payroll tax with a progressive tax (essentially a linear tax with an exemption), we show that age-specific tax schemes can restore much of the potential gain from introducing social security.

Liquidity Constraints, Fiscal Policy, and Consumption

macroeconomics, liquidity constraints, fiscal policy, and consumption

Scattering and absorption of ultracold atoms by nanotubes

We investigate theoretically how cold atoms, including Bose-Einstein condensates, are scattered from, or absorbed by nanotubes with a view to analysing recent experiments. In particular we consider the role of potential strength, quantum reflection, atomic interactions and tube vibrations on atom loss rates. Lifshitz theory calculations deliver a significantly stronger scattering potential than that found in experiment and we discuss possible reasons for this. We find that the scattering potential for dielectric tubes can be calculated to a good approximation using a modified pairwise summation approach, which is efficient and easily extendable to arbitrary geometries. Quantum reflection of atoms from a nanotube may become a significant factor at low temperatures, especially for non-metallic tubes. Interatomic interactions are shown to increase the rate at which atoms are lost to the nanotube and lead to non-trivial dynamics. Thermal nanotube vibrations do not significantly increase loss rates or reduce condensate fractions, but lower frequency oscillations can dramatically heat the cloud.Comment: 7 pages, 4 figure

Emergence of overwintered larvae of eye-spotted bud moth, Spilonota ocellana (Lepidoptera: Tortricidae) in relation to temperature and apple tree phenology at Summerland, British Columbia

We recorded daily appearance of overwintered larvae of eye-spotted bud moth (ESBM), Spilonota ocellana (Denis & Schiffermüller) in spring 1992, 1994, and 1996 in an unsprayed apple orchard at Summerland, British Columbia, to relate larval emergence to degree-day (DD) accumulation and apple phenology. In all years the first larva was found between mid-March and early April, and none appeared after late April. Median emergence of larvae occurred when McIntosh apple trees were at early, tight-cluster stage of fruit-bud development. Larval head capsule measurements showed that ESBM usually overwinter as fifth and sixth instars, with a small proportion (≤6%) as fourth instar larvae. In the laboratory we monitored emergence of non-diapausing overwintered larvae from apple branches incubated at 8.8, 9.4, 12.9, 15.0, 18.0, and 20.9ºC. A least-squares linear regression described emergence over this temperature range relatively accurately (r2 = 0.57, P < 0.05) and a base temperature for emergence (Tb = 1.0ºC ± 0.6) was extrapolated from this regression. Regression analysis indicated median emergence should require 154.6 ± 6.7 DD above 1ºC (DD 1ºC). Using daily airtemperature maxima and minima and 1 March to start accumulating DD1ºC, the error between predicted and observed days to median emergence in the field was -6.7 ± 3.1 d; the regression model predicted early in every case. Using observed larval appearance on apples (1992, 1994, & 1996) and an iterative process, we determined that a combination of 6ºC as the Tb and 1 January as a date to start accumulating DD6ºC, minimized the coefficient of variation for the three-year mean DD 6ºC accumulations (82.7 ± 3.5 DD 6ºC) required for 50% of the larvae to appear in the field. While this latter DD index described observed emergence of larvae accurately, and its use may help improve management of ESBM, it should be validated using independent data before growers use it routinely

Addition theorems for spin spherical harmonics. II Results

Based on the results of part I, we obtain the general form of the addition theorem for spin spherical harmonics and give explicit results in the cases involving one spin-$s'$ and one spin-$s$ spherical harmonics with $s',s=1/2$, 1, 3/2, and $|s'-s|=0$, 1. We obtain also a fully general addition theorem for one scalar and one tensor spherical harmonic of arbitrary rank. A variety of bilocal sums of ordinary and spin spherical harmonics are given in explicit form, including a general explicit expression for bilocal spherical harmonics

Zeros of 6j Symbols:Atoms:Nuclei and Bosons

The same 6j symbols that explains the absence of a certain atomic state in LS coupling also explain the absence of certain states for a system of bosons and also for certain nuclear states in jj coupling

Analytic Treatment of Positronium Spin Splittings in Light-Front QED

We study the QED bound-state problem in a light-front hamiltonian approach. Starting with a bare cutoff QED Hamiltonian, $H_{_{B}}$, with matrix elements between free states of drastically different energies removed, we perform a similarity transformation that removes the matrix elements between free states with energy differences between the bare cutoff, $\Lambda$, and effective cutoff, \lam (\lam < \Lam). This generates effective interactions in the renormalized Hamiltonian, $H_{_{R}}$. These effective interactions are derived to order $\alpha$ in this work, with $\alpha \ll 1$. $H_{_{R}}$ is renormalized by requiring it to satisfy coupling coherence. A nonrelativistic limit of the theory is taken, and the resulting Hamiltonian is studied using bound-state perturbation theory (BSPT). The effective cutoff, \lam^2, is fixed, and the limit, 0 \longleftarrow m^2 \alpha^2\ll \lam^2 \ll m^2 \alpha \longrightarrow \infty, is taken. This upper bound on \lam^2 places the effects of low-energy (energy transfer below \lam) emission in the effective interactions in the $| e {\overline e} >$ sector. This lower bound on \lam^2 insures that the nonperturbative scale of interest is not removed by the similarity transformation. As an explicit example of the general formalism introduced, we show that the Hamiltonian renormalized to $O(\alpha)$ reproduces the exact spectrum of spin splittings, with degeneracies dictated by rotational symmetry, for the ground state through $O(\alpha^4)$. The entire calculation is performed analytically, and gives the well known singlet-triplet ground state spin splitting of positronium, $7/6 \alpha^2 Ryd$. We discuss remaining corrections other than the spin splittings and how they can be treated in calculating the spectrum with higher precision.Comment: 46 pages, latex, 3 Postscript figures included, section on remaining corrections added, title changed, error in older version corrected, cutoff placed in a windo

Addition theorems for spin spherical harmonics. I Preliminaries

We develop a systematic approach to deriving addition theorems for, and some other bilocal sums of, spin spherical harmonics. In this first part we establish some necessary technical results. We discuss the factorization of orbital and spin degrees of freedom in certain products of Clebsch-Gordan coefficients, and obtain general explicit results for the matrix elements in configuration space of tensor products of arbitrary rank of the position and angular-momentum operators. These results are the basis of the addition theorems for spin spherical harmonics obtained in part II