where Ynt=y1t⋯ynt′ and 𝜖nt are n × 1 vectors. Assuming that Yns = 0 if s ≤ 0, because our sample starts on January 19, and no laboratory confirmed case was reported before January 19 in cities outside Wuhan. Xnt=x1t′⋯xnt′′ is an n × k matrix of the control variables. Hnt,s(αwithin) is an n × n diagonal matrix corresponding to the s-day time lag, with parameters αwithin={αwithin,τk}k=1,⋯,Kwithin,τ=1,2. For example, for s = 1,⋯ , 7, the i th diagonal element of Hnt,s(αwithin) is 17∑k=1Kwithinαwithin,1kh¯ct,ik1, and for s = 8,⋯ , 14, the i th diagonal element of Hnt,s(αwithin) is 17∑k=1Kwithinαwithin,2kh¯ct,ik2. Mnt,s(αbetween) is constructed similarly. For example, for s = 1,⋯ , 7 and i≠j, the ij th element of Mnt,s(αbetween) is 17∑k=1Kbetweenαbetween,1km¯ijtk1. Zntτ is an n × KWuhan matrix corresponding to the transmission from Wuhan. For example, the ik th element of Znt1 is m¯i,Wuhan,tk1z¯t1.