This paper introduces the rational inattention hypothesis (RI) -- that agents process information subject to finite channel constraints -- into a stochastic growth model with permanent technology shocks. We find that RI raises consumption volatility relative to output by introducing an endogenous demand shock. Furthermore, it is shown that incorporating RI can provide an additional internal propagation mechanism (measured by the impulse response function and the autocorrelation function of output growth) and generate higher variance of forecastable movements in output. However, we find that RI cannot resolve these puzzles in the RBC literature -- weak internal propagation and low variance of forecastable movements in output, even with what appears to be a very low capacity channel.