Shock Elasticities and Impulse Responses Jaroslav Boroviˇcka Lars Peter Hansen New York University University of Chicago and NBER
[email protected] [email protected] Jos´eA. Scheinkman Columbia University, Princeton University and NBER
[email protected] April 14, 2014 Abstract We construct shock elasticities that are pricing counterparts to impulse response functions. Recall that impulse response functions measure the importance of next- period shocks for future values of a time series. Shock elasticities measure the contri- butions to the price and to the expected future cash flow from changes in the exposure to a shock in the next period. They are elasticities because their measurements com- pute proportionate changes. We show a particularly close link between these objects in environments with Brownian information structures. There are several alternative ways in which one may approach the impulse prob- lem .... One way which I believe is particularly fruitful and promising is to study what would become of the solution of a determinate dynamic system if it were exposed to a stream of erratic shocks that constantly upsets the continuous evolu- tion, and by so doing introduces into the system the energy necessary to maintain the swings. Frisch (1933) 1 Introduction Impulse response function characterize the impact of “a stream of erratic shocks” on dy- namic economic models. They measure the consequences of alternative shocks on the future variables within the dynamical system. These methods are routinely used in linear time series analysis, and they can be generalized to nonlinear environments. See Gallant et al. (1993), Koop et al. (1996), and Gourieroux and Jasiak (2005) for nonlinear extensions.