Models of time-varying Petschek-like magnetic reconnection assume that plasma conductivity drops abruptly in a local region (diffusion region) of the current sheet. This is accompanied by appearance of a strong pulse of electric field accelerating the electrons which precipitate into the ionosphere and produce the auroral breakup. The speed of poleward arc motion in that case should be proportional to the E_y -field in the diffusion region. Based on model equation describing the relationship between the reconnection rate and plasma conductivity as a function of time , we can evaluate the time variation of the size of the diffusion region and plasma conductivity using as input the observed motion of auroral arcs. By studying 9 events for which auroral TV measurements during auroral breakup have been available, we found that for the typical parameters of the current sheet in the magnetotail, the conductivity has to drop down to the value ∼10⁵ CGS which is 10 orders less than its classical value.