Under the same (Chole)sky: DNK models, timing restrictions and recursive identification of monetary policy shocks

Recent structural VAR studies of the monetary transmission mechanism have voiced concerns about the use of recursive identification schemes based on short-run exclusion restrictions. This paper characterizes the effects on impulse propagation of informational constraints embodying classical Cholesky-type timing restrictions in otherwise standard DSGE models. We formally show that timing restrictions can produce non-trivial moving average components of rational expectations solutions, or even serve as an independent source of model-based nonfundamentalness, thereby hampering impulse response analysis via VAR procedures. We then derive population conditions for existence of VAR representations of DSGE economies exhibiting timing restrictions, and numerically explore their bearing on shock identification in a range of monetary models of the business cycle. Our analysis reveals that dynamic New Keynesian models admit invertible equilibrium representations as well as fast-converging VAR coefficient matrices under empirically tenable parameterizations. This alleviates concerns about identification and lag truncation bias: low-order Cholesky-VARs do well at retrieving the true aggregate effects of monetary policy shocks in a Cholesky world.