This quantity was introduced in 1969 by Cheeger [1] to bound from below the spectral gap of the Laplacian on compact Riemannian manifolds, and nowadays (1) is often called an isoperimetric inequality of the Cheeger type. The relationship between more general isoperimetric and certain Sobolev type inequalities was earlier considered by Maz’ya [2] (see for history, for example, [3, 4]). What was ...

This note provides a simple exposition of what IV can and cannot estimate in a model with a binary treatment variable and heterogeneous treatment effects. It shows how linear IV is a misspecification of functional form and the reason why linear IV estimates for this model will always depend on the instrument used is because of this misspecification. It shows that if one can estimate the correct...

This paper estimates a dynamic model of the world oil market and tests whether OPEC countries colluded and whether non-OPEC countries behaved oligopolistically over the period 1970-2004. The model generates estimates of the shadow price of the resource with minimal functional form assumptions. Results support oligopolistic behavior among non-OPEC producers and collusion among OPEC producers exc...

In this issue, Karl Crary and Robert Harper respond to the critique of higher-order abstract syntax appearing in Logic Column 14, “Nominal Logic and Abstract Syntax” (SIGACT News 36(4), December 2005). I am always looking for contributions. If you have any suggestion concerning the content of the Logic Column, or if you would like to contribute by writing a column yourself, feel free to get in ...

An overview of the background of Taylor series methods and the utilization of the differential algebraic structure is given, and various associated techniques are reviewed. The conventional Taylor methods are extended to allow for a rigorous treatment of bounds for the remainder of the expansion in a similarly universal way. Utilizing differential algebraic and functional analytic arguments on ...

This paper proposes a new approach for analyzing the relationship between macroeconomic factors and the income distribution. The conventional method of analysis is regression of summary inequality indices on variables such as the unemployment and inflation rates. Building on the lessons from recent advances in time-series econometrics, we suggest instead that one should first fit a parametric f...

We reexamine Rogers’ (1994) analysis of the biological basis of the rate of time preference. Although his basic insight concerning the derivation of the felicity function holds up, the functional form he uses does not generate the evolutionary equilibrium behavior. Moreover, Rogers relies upon an interior solution for a particular kind of intergenerational transfer. We show such interior soluti...

A discrete symmetry of a preference relation is a mapping from the domain of choice to itself under which preference comparisons are invariant; a continuous symmetry is a one-parameter family of such transformations that includes the identity; and a symmetry field is a vector field whose trajectories generate a continuous symmetry. Any continuous symmetry of a preference relation implies that i...

The language LRTp is a non-deterministic language for exact real number computation. It has been shown that all computable first order relations in the sense of Brattka are definable in the language. If we restrict the language to single-valued total relations (e.g. functions), all polynomials are definable in the language. This paper is an expanded version of [12] in which we show that the non...

This paper proposes pure significance tests for the absence of nonlinearity in cointegrating relationships. No assumption of the functional form of the nonlinearity is made. It is envisaged that the application of such tests could form the first step towards specifying a nonlinear cointegrating relationship for empirical modelling. The asymptotic and small sample properties of our tests are inv...