Reward halving will have no meaningful effect on price or, possibly, might cause a short-term price drop when speculators who have stupidly bought expecting a quick double are disappointed and try to exit en masse.
The dynamic in Bitcoin is exactly the same as in gold mining because Bitcoin, like gold, is a hoarded (i.e. monetary) commodity. Gold/Bitcoin moves up or down almost exclusively due to fluctuations in investment demand, regardless of mine output.
As an example, consider that the insane price volatility of this past Friday occurred with coins being produced at a constant rate (50 every 10 minutes). So clearly the immutability of incremental supply had no impact whatsoever on keeping the Bitcoin price constant as well. The fluctuations in demand (both short and long term) far dwarf the hourly output of 50 (or 25) coins per hour, because even with a 20% inflation rate, the amount of coins already held massively exceeds the amount of new coins being produced at any given time. So coin price is determined by whether existing coin holders decide to sell or keep their coins, and not by anything that the miners are doing. Confidence and demand are the only meaningful price drivers.
Obviously the gold market is much more mature and further along than Bitcoin, but the principles at play are identical. For further stocks-to-flow analysis of monetary commodities, replace "Gold" with "Bitcoin" in James Turk interview below:
Stock to flow ratio is key to understanding "Bitcoin":
http://www.youtube.com/watch?v=M9A7CZgPld8