Net Worth and Housing Equity in Retirement

This paper documents the trends in the life-cycle profiles of net worth and housing equity between 1983 and 2004. The net worth of older households significantly increased during the housing boom of recent years. However, net worth grew by more than housing equity, in part because other assets also appreciated at the same time. Moreover, the younger elderly offset rising house prices by increasing their housing debt, and used some of the proceeds to invest in other assets. We also consider how much of their housing equity older households can actually tap, using reverse mortgages. This fraction is lower at younger ages, such that young retirees can consume less than half of their housing equity. These results imply that 'consumable' net worth is smaller than standard calculations of net worth.

Owner-Occupied Housing as a Hedge Against Rent Risk

Many people assume that the most significant risk in the housing market is that homeowners are exposed to fluctuations in house values. However, homeownership also provides a hedge against fluctuations in future rent payments. This paper finds that, even though house price risk endogenously increases with rent risk, the latter empirically dominates for most households so housing market risk actually increases homeownership rates and house prices. Further, the net effect of rent risk on the demand for homeownership increases with a household's expected length of stay in its home, as the cumulative rent volatility rises and the discounted house price risk falls. Using CPS data, the difference in the probability of homeownership between households with long and short expected lengths of stay is 2.9 to 5.4 percentage points greater in high rent variance places than low rent variance places. The sensitivity to rent risk is greatest for households that devote a larger share of their budgets to housing, and thus face a bigger gamble. Similarly, the elderly who live in high rent variance places are more likely to own their own homes, and their probability of homeownership falls faster with age (as their horizon shortens). This aversion to rent risk might help explain why older households do not consume much of their housing wealth. Finally, we find that house prices capitalize not only expected future rents, but also the associated rent risk premia. At the MSA level, a one standard deviation increase in rent variance increases the house price-to-rent ratio by 2 to 4 percent.

Owner-occupied housing as a hedge against rent risk

The conventional wisdom that homeownership is very risky ignores the fact that the alternative, renting, is also risky. Owning a house provides a hedge against fluctuations in housing costs, but in turn introduces asset price risk. In a simple model of tenure choice with endogenous house prices, the authors show that the net risk of owning declines with a household’s expected horizon in its house and with the correlation in housing costs in future locations. Empirically, they find that both house prices, relative to rents, and the probability of homeownership increase with net rent riskHousing ; Housing - Prices

Remark on the (Non)convergence of Ensemble Densities in Dynamical Systems

We consider a dynamical system with state space $M$, a smooth, compact subset of some ${\Bbb R}^n$, and evolution given by $T_t$, $x_t = T_t x$, $x \in M$; $T_t$ is invertible and the time $t$ may be discrete, $t \in {\Bbb Z}$, $T_t = T^t$, or continuous, $t \in {\Bbb R}$. Here we show that starting with a continuous positive initial probability density $\rho(x,0) > 0$, with respect to $dx$, the smooth volume measure induced on $M$ by Lebesgue measure on ${\Bbb R}^n$, the expectation value of $\log \rho(x,t)$, with respect to any stationary (i.e. time invariant) measure $\nu(dx)$, is linear in $t$, $\nu(\log \rho(x,t)) = \nu(\log \rho(x,0)) + Kt$. $K$ depends only on $\nu$ and vanishes when $\nu$ is absolutely continuous wrt $dx$.Comment: 7 pages, plain TeX; [email protected], [email protected], [email protected], to appear in Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 8, Issue

Non-ergodicity of the motion in three dimensional steep repelling dispersing potentials

It is demonstrated numerically that smooth three degrees of freedom Hamiltonian systems which are arbitrarily close to three dimensional strictly dispersing billiards (Sinai billiards) have islands of effective stability, and hence are non-ergodic. The mechanism for creating the islands are corners of the billiard domain.Comment: 6 pages, 8 figures, submitted to Chao

The largest eigenvalue of rank one deformation of large Wigner matrices

The purpose of this paper is to establish universality of the fluctuations of the largest eigenvalue of some non necessarily Gaussian complex Deformed Wigner Ensembles. The real model is also considered. Our approach is close to the one used by A. Soshnikov in the investigations of classical real or complex Wigner Ensembles. It is based on the computation of moments of traces of high powers of the random matrices under consideration

Evolution of collision numbers for a chaotic gas dynamics

We put forward a conjecture of recurrence for a gas of hard spheres that collide elastically in a finite volume. The dynamics consists of a sequence of instantaneous binary collisions. We study how the numbers of collisions of different pairs of particles grow as functions of time. We observe that these numbers can be represented as a time-integral of a function on the phase space. Assuming the results of the ergodic theory apply, we describe the evolution of the numbers by an effective Langevin dynamics. We use the facts that hold for these dynamics with probability one, in order to establish properties of a single trajectory of the system. We find that for any triplet of particles there will be an infinite sequence of moments of time, when the numbers of collisions of all three different pairs of the triplet will be equal. Moreover, any value of difference of collision numbers of pairs in the triplet will repeat indefinitely. On the other hand, for larger number of pairs there is but a finite number of repetitions. Thus the ergodic theory produces a limitation on the dynamics.Comment: 4 pages, published versio

Fluctuation theorem for stochastic dynamics

The fluctuation theorem of Gallavotti and Cohen holds for finite systems undergoing Langevin dynamics. In such a context all non-trivial ergodic theory issues are by-passed, and the theorem takes a particularly simple form. As a particular case, we obtain a nonlinear fluctuation-dissipation theorem valid for equilibrium systems perturbed by arbitrarily strong fields.Comment: 15 pages, a section rewritte

Can Owning a Home Hedge the Risk of Moving?

For households that face a possibility of moving across MSAs, the risk of home owning depends on the covariance of the sale prices of their current houses with the purchase prices of their likely future houses. We find empirically that households tend to move between highly correlated MSAs, significantly increasing the distribution of expected correlations in real house price growth across MSAs, and so raising the moving-hedge value of owning. Own/rent decisions are sensitive to this hedging value, with households being more likely to own when their hedging value is greater due to higher expected correlations and likelihoods of moving. JEL (D14, R21, R23, R31