Despite decades of research, parameter estimation for structural equations in macroeconomics remains difficult because of endogeneity issues caused by omitted variables and measurement error. Prominent examples include the estimation of the Phillips curve and the Euler equation for output. In this work, we use sequences of past independently identified structural shocks as instrumental variables to address these endogeneity issues and obtain consistent parameter estimates.

To select the relevant aggregate shocks we develop an instrumental variable estimator where the adaptive lasso is used to form predictions in the first stage. We illustrate our methodology for the Phillips curve, for which we find that after instrumenting inflation expectations and the output gap with monetary shocks, the estimated slope of the Phillips curve is twice as large as with standard methods. Joint with Regis Barnichon, San Fransisco FED).