This paper investigates the long-run convergence of regional house prices in the UK. Existing studies have failed to reach a consensus on whether or not regional house prices exhibit long-run convergence with each other. The application is proposed of a new test involving unit root testing of the first principal component based on regional—national house price differentials. Using mix-adjusted quarterly data for 1973—2006, it is found that the first principal component is stationary. This suggests that all UK regional house prices are driven by a single common stochastic trend. Further analysis suggests that those regions that are more distant from London exhibit the highest degrees of persistence with respect to deviations in house price differentials.

In this paper we examine long-run house price convergence across US states using a novel econometric approach advocated by Pesaran (2007) and Pesaran et al. (2009). Our empirical modelling strategy employs a probabilistic test statistic for convergence based on the percentage of unit root rejections among all state house price differentials. Using a sieve bootstrap procedure, we construct confidence intervals and find evidence in favour of convergence. We also conclude that speed of adjustment towards long-run equilibrium is inversely related to distance.

The paper presents a transient analysis technique for point contact elastohydrodynamic (EHL) lubrication problems using coupled elastic and hydrodynamic equations. Full coupling is made possible by use of a novel differential de¯ection formulation. The way in which the differential de¯ection is incorporated into the overall solution method for a point contact is discussed. A range of spatial and temporal discretization methods are incorporated and compared. The method is validated under transient conditions by a detailed comparison with published work produced using a different, independent method incorporating a moving roughness feature.A comparison of the results with different discretization methods leads to the conclusion that spatial central differencing with a Crank±Nicolson temporal discretization is the most effective ®nite difference scheme, and this is generally equivalent to the ®nite element discretization given in detail in the paper. A comparison of the results produced for moving rough surfaces suggests that the ®nite element formulation is preferred. NOTATIONheight of the surface feature de®ned by equation (12) (m) E 0 effective modulus of elasticity (Pa) f i, j pressure coef®cient in the differential de¯ection equation (m ¡1 ) F factor determining timestepˆU UDt=Dx h ®lm thickness (m) h 0 constant in the ®lm thickness equation (3) (m) L Moes and Bosma non-dimensional parameterˆaE 0 ‰2Z 0 U U=…E 0 R R †Š 1=4 M Moes and Bosma non-dimensional parameterˆ‰w=…E 0 R R 2 †Š‰E 0 R R=…2Z 0 U U †Š 3=4 n c number of neighbouring mesh points in discretization N i shape function p pressure (Pa) p hz maximum pressure in Hertzian contact (Pa) Pˆp=p hz in Figs 4 to 7 R x , R y radii of relative curvature in axis directions (m) R R 2R x R y =…R x ‡ R y † (m) u total de¯ection of the surfaces perpendicular to the xy plane (m) U U, V V mean surface velocities in axis directions (m/s) w load (N) W b width of surface feature de®ned by equation (12) (m) x, y coordinates in the contact plane (m) x b x coordinate of the centre of the ridge feature (m) Z parameter in the viscosity equation (5) a=‰w ln…Z 0 =k †Š a pressure viscosity coef®cient (Pa ¡1 ) g coef®cient in the density equation (6) (Pa ¡1 ) Dt timestep (s) Dx, Dy mesh spacing in coordinate directions (m) Z viscosity (Pa s) The MS was Downloaded from Z 0 viscosity at ambient pressure (Pa s) k coef®cient in the viscosity equation (5) (Pa s) l coef®cient in the density equation (6) (Pa ¡1 ) x slide±roll ratio r density (kg/m 3 ) r 0 density at ambient pressure (kg/m 3 ) s x , s y¯o w coef®cients in axis directions (m s) t 0 non-Newtonian shear stress parameter (Pa) f surface roughness feature (m) w coef®cient in the viscosity equation (5) (Pa ¡1 )

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