State-Dependent Local Projections: Understanding Impulse Response Heterogeneity

An impulse response is the dynamic average effect of an intervention across horizons. We use the well-known Kitagawa-Blinder-Oaxaca decomposition to explore a response’s heterogeneity over time and over states of the economy. This can be implemented with a simple extension to the usual local projection specification that nevertheless keeps the model linear in parameters. Using our new decomposition-based approach, we show how to unpack heterogeneity in the fiscal multiplier, an object that at any point in time may depend on a number of potentially correlated factors, including existing economic conditions and the monetary response. In our application, the fiscal multiplier varies considerably with monetary policy: it can be as small as zero, or as large as 2, depending on the degree of monetary offset.