Are two weak instruments better than one weak instrument? From my understanding, when using IV regression to eliminate confounding effects, we prefer to have a single strong instrument, over multiple weak instruments which can lead to bias.
My question is, what happens in the case of a single instrument vs multiple (e.g., two) weak instruments.
I ran an arbitrary simulation with 15,000 observations, and noticed that the two instruments actually had a lower bias in their estimate and lower standard error. Is this a surprising result? What is the intuition behind this?

Nothing surprising about this. The standard error of an estimator diminishes with a square root of the sample size. So if you take more measurements and average them, you would always be better than with fewer samples. The same phenomenon was observed outside of statistics, James Surowiecki described in his book the wisdom of the crowd, who quotes many experiments where averaging opinions of many people, even if lacking expertise, often
gave better results than the predictions by experts.
