Can we identify the relative price between consumption and investment?

This paper considers various AK models to investigate inference about the relative price between consumption and investment using NIPA data. We find, that depending on the model used, we can legitimately generate different time series for this price. If we successfully construct a falling price of investment, the model implies an inadmissibly low share of consumption in output. If we use an admissible share of consumption we generate investment prices which increase over time, contrary to the intuition generated by the price of equipment goods.