(Shiller seems to believe that) throughout history the most common cause of changes in interest rates is a shift in the supply of credit. Perhaps in most cases lower interest rates are associated with more investment. If that were true, his mistake would be more forgivable. But the truth is exactly the opposite. Shifts in the demand for credit are usually the dominant factor. In the vast majority of cases, relatively low interest rates are associated with low levels of investment and relatively high interest rates are associated with high levels of investment. So there is no "puzzle" on either theoretical grounds (theory doesn't predict more investment) or empirical grounds (low interest rates are not usually associated with high levels of investment.)
This sort of mistake is frequently made by economists, even economists that are much more distinguished than I am. Why does it matter? Because it's one cause of the Great Recession. If the Great Recession had been associated with interest rates rising from 5% to 8% (instead of falling close to zero) most economists would have blamed the recession on a tight money policy at the Fed. Well the recession was caused by a tight money policy at the Fed, but because most economists reason from price changes they did not see this. Hence the Fed was under no pressure to do the right thing. And when big government institutions are under no pressure to do the right thing, they rarely do the right thing.