Tham khảo tài liệu 'handbook of empirical economics and finance _2', tài chính - ngân hàng, tài chính doanh nghiệp phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 12 Handbook of Empirical Economics and Finance estimation of p in the model yig xg p zig 7 s Eis is equivalent to the following two-step procedure. First do OLS estimation in the model yig 8g z ig7 Eig where 8g is treated as a cluster-specific fixed effect. Then do feasible GLS FGLS of ỹg z gf on Xg. Donald and Lang 2007 give various conditions under which the resulting Wald statistic based on pj is TG L distributed. These conditions require that if zig is a regressor then Zg in the limit is constant over g unless Ng rc . Usually L 2 as the only regressors that do not vary within clusters are an intercept and a scalar regressor xg . Wooldridge 2006 presents an expansive exposition of the Donald and Lang approach. Additionally Wooldridge proposes an alternative approach based on minimum distance estimation. He assumes that 8g in yig 8g z ig7 Eig can be adequately explained by xg and at the second step uses minimum chi-square methods to estimate p inu a xgp. This provides estimates of p that are asymptotically normal as Ng rc rather than G . Wooldridge argues that this leads to less conservative statistical inference. The X2 statistic from the minimum distance method can be used as a test of the assumption that the 8g do not depend in part on cluster-specific random effects. If this test fails the researcher can then use the Donald and Lang approach and use a T distribution for inference. Bester Conley and Hansen 2009 give conditions under which the f-test statistic based on formula is VG G 1 times TG 1 distributed. Thus using ug ựG G 1 ug yields a TG 1 distributed statistic. Their result is one that assumes G is fixed while Ng rc the within group correlation satisfies a mixing condition as is the case for time series and spatial correlation and homogeneity assumptions are satisfied including equality of plim jN- XgXg for all g. An alternate approach for correct inference with few clusters is presented by Ibragimov and Muller 2010 . Their method is best .
