  Using direct numerical simulations, we verify that "flow IV" of Roberts
(1972) exhibits dynamo action dominated by horizontally averaged large-scale
magnetic field. With the test-field method we compute the turbulent magnetic
diffusivity and find that it is negative and overcomes the molecular
diffusivity, thus explaining quantitatively the large-scale dynamo for magnetic
Reynolds numbers above $\approx8$. As expected for a dynamo of this type, but
contrary to $\alpha$-effect dynamos, the two horizontal field components grow
independently of each other and have arbitrary amplitude ratios and phase
differences. Small length scales of the mean magnetic field are shown to be
stabilized by the turbulent magnetic diffusivity becoming positive at larger
wavenumbers. Oscillatory decaying or growing solutions have also been found in
certain wavenumber intervals and sufficiently large values of the magnetic
Reynolds number. For magnetic Reynolds numbers below $\approx0.5$ the turbulent
magnetic diffusivity is confirmed to be positive, as expected for all
incompressible flows. Earlier claims of a dynamo driven by a modified
Taylor-Green flow through negative eddy diffusivity could not be confirmed.
