  We study the dependence of turbulent transport coefficients, such as the
components of the $\alpha$ tensor ($\alpha_{ij}$) and the turbulent magnetic
diffusivity tensor ($\eta_{ij}$), on shear and magnetic Reynolds number in the
presence of helical forcing. We use three-dimensional direct numerical
simulations with periodic boundary conditions and measure the turbulent
transport coefficients using the kinematic test field method. In all cases the
magnetic Prandtl number is taken as unity. We find that with increasing shear
the diagonal components of $\alpha_{ij}$ quench, whereas those of $\eta_{ij}$
increase. The antisymmetric parts of both tensors increase with increasing
shear. We also propose a simple expression for the turbulent pumping velocity
(or $\gamma$ effect). This pumping velocity is proportional to the kinetic
helicity of the turbulence and the vorticity of the mean flow. For negative
helicity, i.e. for a positive trace of $\alpha_{ij}$, it points in the
direction of the mean vorticity, i.e. perpendicular to the plane of the shear
flow. Our simulations support this expression for low shear and magnetic
Reynolds number. The transport coefficients depend on the wavenumber of the
mean flow in a Lorentzian fashion, just as for non-shearing turbulence.
