I understand that increasing the frequency band means increasing the data rate.
You should make a distinction between the frequency band which is sets the frequency range that the cellular signal is supposed to occupy and the bandwith of the signal itself.
The frequency band says nothing about the datarate.
What does influence the datarate is the channel width or occupied bandwidth of the signal. For example a 4 G, see here, the bandwidth for both 3G and 4G systems is 20 MHz.
That means that a channel can be 20 MHz wide.
The frequency band then dictates the actual frequency, for example 2100 MHz, see here for 4G
The higher datarate for 4G systems is achieved within the same 20 MHz channel bandwidth that 3 G uses. Only in 4 G more complex modulation techniques are used to increase the datarate.
Also note that although 4G does allow a wider choice in frequency bands (there's more "frequency space" to choose from) compared to 3G, this does not result in a higher datarate. It allows for more choice and flexibility. The actual frequency bands licensed for use (for 3G or 4G) depend on the country and region and are dictated by the local organization assigned to deal with this. For example in the US that is the FCC.