# functional form for a consumption shock

In a DSGE model, how can I add a disturbance/shock in the consumption of households?

For example given my utility function

$$U(C,H) = \frac{C_t^{1-\theta}}{1-\theta} - \frac{B}{\eta} H_t^\eta,$$ where C is consumption and H is work hours, can I simply add a white noise disturbance term $$\xi_t$$ :

$$U(C,H) = \xi_t \frac{C_t^{1-\theta}}{1-\theta} - \xi_t \frac{B}{\eta} H_t^\eta$$

Or is it better to add a demand shock $$u_t$$ to the IS curve, as in

$$x_t = E_t x_{t+1} - \sigma( i_t + E_t \pi_{t+1} ) + u_t?$$

where $$x$$ is the output gap nad $$\pi$$ the inflation