Including local automatic gain control (AGC) circuitry into a silicon cochlea design has been challenging because of transistor mismatch and model complexity. To address this, we present an alternative system-level algorithm that implements channel-specific AGC in a silicon spiking cochlea by measuring the output spike activity of individual channels. The bandpass filter gain of a channel is adapted dynamically to the input amplitude so that the average output spike rate stays within a defined range. Because this AGC mechanism only needs counting and adding operations, it can be implemented at low hardware cost in a future design. We evaluate the impact of the local AGC algorithm on a classification task where the input signal varies over 32 dB input range. Two classifier types receiving cochlea spike features were tested on a speech versus noise classification task. The logistic regression classifier achieves an average of 6% improvement and 40.8% relative improvement in accuracy when the AGC is enabled. The deep neural network classifier shows a similar improvement for the AGC case and achieves a higher mean accuracy of 96% compared to the best accuracy of 91% from the logistic regression classifier.