Large-N and Large-T Properties of Panel Data Estimators and the Hausman Test

By Assumption 7(i), as N →∞,

By the weak law of large numbers (WLLN) and Assumption 7, as N →∞,we
have

(¹¹32,32  ¹¹32,33 II32,z

II3⁰ 2,33 II33,33 II33,z

^II3⁰ 2,z    ^II3⁰3,z    ^IIz,z

From Assumption 7 and WLLN with the assumption that Eg_32,i (z_i) = Eg_33,i (z_i)
= 0, it follows that

as N →∞. In addition, by WLLN with Assumption 5,

μ ⅛. ) →p μ 0 )^,                  (57)

as N →∞. The results (53)-(57) indicate that

N X I2,i,NI2,i,N →p ^ξ2^{,                      (58)}

i

as N →∞. Finally, by Lemma 12, (52) and (58) imply (49).

Proof of (50): Notice that

N ∑D1T 1∑(xι,it - Exι,it)
it

41

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