過剰識別制約検定についての続き．
過剰識別制約検定を使うとき，ぼくの理解している範囲では「すべての操作変数が外生だ」が帰無仮説なので，とくに「どれか1つは外生と仮定したうえで」という注釈はつかないものだ，と思っていたのですが，授業の関係で読んでいたAcemoglu et al. (2001, AER, p.1393) に
The overidentification test presumes that one of these instruments, say S, is truly exogenous, and tests for the exogeneity of the others, such as settler mortality. This approach is useful since it is a direct test of our exclusion restriction. However, such tests may not lead to a rejection if all instruments are invalid, but still highly correlated with each other. Therefore, the results have to be interpreted with caution.とあって，dojinくんの言ったとおりです．あー，どういうこっちゃいな．
Acemoglu, Daron, Simon Johnson, James A. Robinson. 2001. The colonial origins of comparative development: An empirical investigation. American Economic Review 91(5), 1369-1401. [Link]