How Much are SVARs with Long-Run Restrictions Missing without Cyclically Moving Factor Shares?

Under the identification strategy that only innovations to productivity can have a permanent impact on labor productivity, Gali (1999) finds that the contribution of productivity shocks to aggregate fluctuations is negligible. More recently, Fisher (2006) extends Galis's identification to allow for innovations to both productivity and investment to be the only ones that have a long-run impact on labor productivity. He finds that investment shocks---identified through the relative price of investment as investment-specific technical-change---explain almost half of the fluctuations of hours. Here, I explore the quantitative robustness of these empirical results to the explicit introduction of cyclically moving factor shares. To do so, I parsimoniously incorporate into Gali's and Fisher's empirical frameworks the systematic fluctuations of factor shares under the identifying assumption, following Rios-Rull and Santaeulalia-Llopis (2010), that innovations to factor shares are purely redistributive---that is, without effect on long-run productivity. Two striking quantitative findings arise. First, in sharp contrast with previous empirical assessments, productivity shocks identified exactly as in Gali (1999) account for about 30% the variance of hours in the U.S.; and productivity shocks and investment shocks identified exactly as in Fisher (2006) account for, respectively, 43% and 10% of that variance. Second, redistributive shocks to factor shares account for about 20% of the variance of hours. The analysis across European countries reveals even larger contributions of productivity shocks and redistributive shocks, respectively, 63% and 29% of the variance of hours. Further, I find that what generates these results are the dynamic effects that productivity shocks have on labor share that, together with a large response of hours to labor share fluctuations, substantially propagate the effects that productivity shocks have on hours. These results suggests productivity-driven business cycle models that account for the joint dynamics of productivity and factor shares are a fruitful avenue for business cycle research.