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Working papers

Working paper # 2001/01

Indeterminate Steady-State Equilibria in a One-Sector Neoclassical Model
Kirill Borissov
19 June, 2001 pdf (borussov.pdf  154Kb)


This paper introduces a dynamic model based on the assumption that the rich are more patient than the poor. All consumers are identical in their exogenous parameters; the division of the population into rich high-patient savers and poor low-patient spenders occurs endogenously. The main result is that at equilibrium the real wage rate, the interest rate (= profit rate), and the shares of savers and spenders in the population are indeterminate.
Keywords: overlapping generations, bequest motive, Sraffian indeterminacy
JEL classification numbers: C62, D91, O41.

Acknowledgements. The author gratefully acknowledges the financial support from the Research Support Scheme of the Open Society Support Foundation, grant No.: 822/1999.

Working paper # 2001/02

On Proportional Excess for NTU games
Sergei Pechersky
30 October, 2001pdf (pchersk.pdf 202Kb)


An axiomatic approach is developed to define the "proportional excess" on the space of positively generated NTU games. This excess generalizes to NTU games the proportional TU excess v(S)/x(S). Five axioms are proposed, and it is shown that the proportional excess, which possess Kalai’s properties except the boundary condition (it equals 1, rather than 0), is the unique excess function satisfying the axioms. The properties of proportional excess and related solutions are studied. In particular, for the proportional (pre)nucleolus a geometric characterization, which modifies the Maschler-Peleg-Shapley geometric characterization of the standard TU nucleolus, is given.

Keywords: cooperative NTU games, excess function, nucleolus, prenucleolus, (Minkowski) gauge function

Working  paper # 2002/01

A simple test for unit root bilinearity
Wojciech Charemza (University of Leicester, UK)
Mikhail Lifshits  (St.Petersburg State University, Russia)
Svetlana Makarova (European University at St.Petersburg , Russia)
29 March, 2002 pdf (makarova.pdf 339Kb)


The paper introduces a t-ratio type test for detecting bilinearity in a stochastic unit root process. It appears that such process is a realistic approximation for many economic and financial time series. It is shown that, under the null of no bilinearity, the tests statistics are asymptotically normally distributed. Proofs of this asymptotic normality requires the Gihman and Skorohod theory for multivariate diffusion processes. Finite sample results describe speed of convergence, power of the tests and
possible distortions to unit root testing which might appear due to the presence of bilinearity. It is concluded that the two-step testing procedure suggested here (the first step for the linear unit root and the second step for its bilinearity) is consistent in the sense that the size of step one test is not affected by the possible detection of bilinearity at step two.

Keywords: Time series econometrics, testing, nonstationary bilinear processes.
JEL classification numbers: C12, C22, G15.

Working paper #2002/02

Indeterminacy of Distribution in a General Equilibrium Model.
Kirill Borissov
May, 2002 pdf (boris.pdf 263Kb)


The dynamic general equilibrium model introduced in this paper is based on the assumption that the rate of time preference depends on the level of utility. It is assumed that the rich are more patient than the poor. It is shown that steady-state equilibria exist and that these equilibria are indeterminate.


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