Correcting standard errors in two-stage estimation procedures with generated regressands

Feenstra and Hanson [NBER Working Paper No. 6052 (1997)] propose a procedure to correct the standard errors in a two-stage regression with generated dependent variables. Their method has subsequently been used in two-stage mandated wage models [Feenstra and Hanson, Quarterly Journal of Economics (1999) Vol. 114, pp. 907-940; Haskel and Slaughter, The Economic Journal (200 1) Vol. I 11, pp. 163-187; Review of International Economics (2003) Vol. 11, pp. 630-650] and for the estimation of the sector bias of skill-biased technological change [Haskel and Slaughter, European Economic Review (2002) Vol. 46, pp. 1757-1783]. Unfortunately, the proposed correction is negatively biased (sometimes even resulting in negative estimated variances) and therefore leads to overestimation of the inferred significance. We present an unbiased correction procedure and apply it to the models reported by Feenstra and Hanson (1999) and Haskel and Slaughter (2002).