Functional Equivalence between Intertemporal and Multisectoral Investment Adjustment Costs

Two types of adjustment cost specifications coexist in macroeconomic models with investment: intertemporal adjustment costs which involve a nonlinear substitution between capital and investment in capital accumulation, and multisectoral costs which are captured by a nonlinear transformation between consumption and investment. This paper demonstrates a functional equivalence between these two specifications. One surprising result is that an increase in multisectoral adjustment costs can be equivalent to a decrease in intertemporal adjustment costs, depending upon the size of the intertemporal costs. We then observe that the functional equivalence implies a problem in identifying the two types of adjustment costs and show ways to solve the problem