Estimating structural macroeconomic shocks through long-run recursive restrictions on vector autoregressive models: The problem of identification

We demonstrate that a popular method of estimating underlying structural macroeconomic shocks and their impulse-response functions through recursive long-run structural restrictions on a vector autoregressive representation is not uniquely identified. We show, however, that it may be possible to infer additional qualitative restrictions to achieve identification. We illustrate with two applied examples, corresponding to a simple aggregate supply-aggregate demand framework for the USA and to a stochastic Mundell-Fleming-Dornbusch framework for the USA and Japan. The second example also illustrates how over-identifying restrictions of the underlying framework may be examined informally.