I recently came across Barro and Redlick QJE (2011) paper, "Macroeconomic Effects from Government Purchases and Taxes", in which the authors instrument for defense spending with an interaction term between defense spending and war year. The outcome of interest is total GDP. They use an instrument to avoid simultaneity bias between GDP and defense spending.
I'm familiar with the main idea of instrumental variable, i.e. the instrument should be correlated with the endogenous variable but uncorrelated with the error term. However, I've never seen someone use an interaction of the endogenous variable as the instrument before.
Why is this valid?