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


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