Modeling investment-sector efficiency shocks: When does disaggregation matter?

The most straightforward way to analyze investment-sector productivity developments is to construct a two-sector model with a sector-specific productivity shock. An often used modeling shortcut accounts for such developments using a one-sector model with shocks to the efficiency of investment in a capital accumulation equation. This shortcut is theoretically justified when some stringent conditions are satisfied. Using a two-sector model, we consider the implications of relaxing several of the conditions that are at odds with the U.S. Input-Output Tables, including equal factor shares across sectors. The effects of productivity shocks to an investment-producing sector of our two-sector model differ from those of efficiency shocks to investment in a one-sector model. Notably, expansionary productivity shocks boost consumption in every period, whereas expansionary efficiency shocks cause consumption to fall substantially for many periods.