Subprime Consumer Credit Demand: Evidence from a Lender's Pricing Experiment

We test the interest rate sensitivity of subprime credit card borrowers using a unique panel data set from a UK credit card company. We were given details of a randomized interest rate experiment conducted by the lender between October 2006 and January 2007. Access to such information is rare. We first calibrate an intertemporal consumption model to show that the experimental design has sufficient statistical power to detect economically plausible responses among borrowers. We then find that individuals who tend to utilize their credit limits fully do not reduce their demand for credit when subject to increases in interest rates as high as 3 percentage points. This finding is naturally interpreted as evidence of binding liquidity constraints. We also demonstrate the importance of isolating exogenous variation in interest rates when estimating credit demand elasticities. We show that estimating a standard credit demand equation with the nonexperimental variation in the data leads to severely biased estimates. This is true even when conditioning on a rich set of controls and individual fixed effects.subprime credit; randomized trials; liquidity constraints

Isolating intrinsic noise sources in a stochastic genetic switch

The stochastic mutual repressor model is analysed using perturbation methods. This simple model of a gene circuit consists of two genes and three promotor states. Either of the two protein products can dimerize, forming a repressor molecule that binds to the promotor of the other gene. When the repressor is bound to a promotor, the corresponding gene is not transcribed and no protein is produced. Either one of the promotors can be repressed at any given time or both can be unrepressed, leaving three possible promotor states. This model is analysed in its bistable regime in which the deterministic limit exhibits two stable fixed points and an unstable saddle, and the case of small noise is considered. On small time scales, the stochastic process fluctuates near one of the stable fixed points, and on large time scales, a metastable transition can occur, where fluctuations drive the system past the unstable saddle to the other stable fixed point. To explore how different intrinsic noise sources affect these transitions, fluctuations in protein production and degradation are eliminated, leaving fluctuations in the promotor state as the only source of noise in the system. Perturbation methods are then used to compute the stability landscape and the distribution of transition times, or first exit time density. To understand how protein noise affects the system, small magnitude fluctuations are added back into the process, and the stability landscape is compared to that of the process without protein noise. It is found that significant differences in the random process emerge in the presence of protein noise

Common zeros of inward vector fields on surfaces

A vector field X on a manifold M with possibly nonempty boundary is inward if it generates a unique local semiflow $\Phi^X$. A compact relatively open set K in the zero set of X is a block. The Poincar\'e-Hopf index is generalized to an index for blocks that may meet the boundary. A block with nonzero index is essential. Let X, Y be inward $C^1$ vector fields on surface M such that $[X,Y]\wedge X=0$ and let K be an essential block of zeros for X. Among the main results are that Y has a zero in K if X and $Y$ are analytic, or Y is $C^2$ and $\Phi^Y$ preserves area. Applications are made to actions of Lie algebras and groups

Morse theory on spaces of braids and Lagrangian dynamics

In the first half of the paper we construct a Morse-type theory on certain spaces of braid diagrams. We define a topological invariant of closed positive braids which is correlated with the existence of invariant sets of parabolic flows defined on discretized braid spaces. Parabolic flows, a type of one-dimensional lattice dynamics, evolve singular braid diagrams in such a way as to decrease their topological complexity; algebraic lengths decrease monotonically. This topological invariant is derived from a Morse-Conley homotopy index and provides a gloablization of `lap number' techniques used in scalar parabolic PDEs. In the second half of the paper we apply this technology to second order Lagrangians via a discrete formulation of the variational problem. This culminates in a very general forcing theorem for the existence of infinitely many braid classes of closed orbits.Comment: Revised version: numerous changes in exposition. Slight modification of two proofs and one definition; 55 pages, 20 figure

Indices of the iterates of R3R^3-homeomorphisms at Lyapunov stable fixed points

Given any positive sequence (\{c_n\}_{n \in {\Bbb N}}), we construct orientation preserving homeomorphisms (f:{\Bbb R}^3 \to {\Bbb R}^3) such that (Fix(f)=Per(f)=\{0\}), (0) is Lyapunov stable and (\limsup \frac{|i(f^m, 0)|}{c_m}= \infty). We will use our results to discuss and to point out some strong differences with respect to the computation and behavior of the sequences of the indices of planar homeomorphisms.Comment: 19 pages, 8 figure