Cointegrated Sectoral Productivities and Investment-Specific Technology in U.S. Business Cycles

Applying Johansen cointegration test to U.S. annual data constructed from the EU KLEMS database, the paper documents that the productivities of consumption-goods and equipmentgoods sector are cointegrated. It confirms further, using the non-linear cointegration test framework developed by Kapetanios et al. (2006), that the cointegrating relation is non-linear. The cointegration of sectoral productivities is also documented in the empirical findings of SchmittGrohé and Uribe (2011). I successfully derive a theoretical proposition that implies that sectoral productivities of the consumption-goods and equipment-goods sectors are cointegrated if and only if the aggregate neutral productivity and the investment-specific technology are cointegrated. Plus, I consider the non-linear cointegration of sectoral productivities to examine the role of the common stochastic trend of sectoral productivities in explaining the movements of investment-specific technology as well as those of interesting macroeconomic aggregates such as output, consumption, investment and hours worked. For this end, I construct a two-sector dynamic stochastic general equilibrium (DSGE) model where the productivities of the consumption and equipment sectors feature a non-linear error correction (NEC) in the vector error correction model (VECM). The maximum likelihood estimation successfully estimates most of structural parameters, including the sectoral capital shares, and it identifies all structural shocks. The paper finds that the innovations of common stochastic trends of sectoral productivities account for half of consumption, 79 percent of investment, and only 6 percent of hours worked variabilities in long-run.