Hi Evelyn,

no, weak instruments are unfortunately a bad thing. The consequences may be:

a) The effect of X is biased (most notably in small samples) and this bias may be even larger than when using a simple OLS regression without the instrument. Hence, the cure may be worse than the disease

b) The SE of the X - Y effect is strongly increased reducing the power to find a significant effect

c) The power of the Hausman test is reduced

Here is some literature about weak instruments. Hope that helps

Best,

Holger

Bound, J., Jaeger, D. a., & Baker, R. M. (1995). Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak. Journal of the American Statistical Association, 90(430), 443-450. doi:10.1080/01621459.1995.10476536

Hall, A., Rudebusch, G. D., Wilcos, D. W., Differentials, M.-f. W., Markets, L., & Oaxaca, R. (1996). Jugding instrument relevance in instrumental variables estimation. International Economic Review, 37(2), 283-298. doi:10.1080/00420986820080431

Murray, M. P. (2006). The bad, the weak, and the ugly: Avoiding the pitfalls of instrumental variables estimation. SSRN Electronic Journal, 1-45. doi:10.2139/ssrn.843185

Murray, M. P. (2006). Avoiding invalid instruments and coping with weak instruments. Journal of Economic Perspectives, 20(4), 111-132. doi:DOI 10.1257/jep.20.4.111

Staiger, D., & Stock, J. H. (1997). Instrumental variables regression with weak instruments. Econometrica, 65(3), 557-586.

Stock, J. H., Wright, J. H., & Yogo, M. (2002). A survey of weak instruments and weak identification in generalized method of moments. Journal of Business & Economic Statistics, 20(4), 518-529.

Thank you. that helps me a great deal.