Two structural cointegrated models of consumption, labor income and wealth are specified and estimated with US data using the approach of Pagan and Pesaran (2008). We find that consumption and labor income are weakly exogenous in the estimated reduced form model and show that this imposes restrictions on the structural model. These restrictions imply that the structural shock with transitory effects can only appear in the structural equation for wealth. One of our structural models yields two permanent shocks that are identical to those obtained by Lettau and Ludvigson (2011) using the method of Gonzalo and Ng (2001). Following Lettau and Ludvigson we interpret the shocks as a productivity shock and a reallocation shock. The reallocation shock has an inverse effect on labor income and wealth, but has little effect on consumption, a result that is consistent with the permanent income hypothesis. Using an alternative restriction - which allows consumption growth to respond to contemporaneous labor income growth - to identify the two permanent shocks produces one important difference in our results. The reallocation shock now has a pronounced effect on consumption, a finding that can be explained if a sizable proportion of consumers are liquidity constrained.