With the discovery of FTL that will allow large populations to settle new worlds, world governments repeal contraception laws.

Or, with that same discovery, the increase in morale and enthusiasm has the expected effect.

Or, the "population" represents only the number of people actually registering as tax payers under the world government.  Then, with that same discovery, the government rules that only legal, tax-paying citizens will be considered for off-world emigration.