The Euler equation model for investment with adjustment costs and variable capital utilization is estimated using aggregate US post-war data with econometric methods that are robust to weak instruments and exploit information in possible structural changes. Various alternative identification assumptions are considered, including external instruments, and instruments obtained from Dynamic Stochastic General Equilibrium models. Results show that the elasticity of capital utilization and investment adjustment cost parameters are very weakly identified. This is because investment appears to be unresponsive to changes in capital utilization and the real interest rate.