I watched research prices during my test last night. They do not change with inflation. Forgot about facilities though...
As for the high inflation, I just chose a poor, small country (Montenegro) and built as many research centers as possible and pushed the funding up to the max. Lowering taxes as low as you can without breaking the bank will increase the inflation effect, and raising domestic prices (but not too much, or else you'll reduce demand greatly) further fuels this. Even with such a high inflation rate, I was so poor in the beginning I'm still making nearly 100% profit on exports, even though my GDP/c has quintupled.
Overall, it just takes some playing around, and just letting it go. Don't bother trying to control inflation.
I have seen where building research centers is more efficacious at raising inflation. In my game as So CA in the US-CA scenario I start out as a big agrarian region, short on consumer goods, timber and water; and strong on food, petrol and military goods. I was able to halt the drop in inflation at 1.7% by building 2 research centers. I also built a consumer goods factory, about 6 good timber plants and 3 large water plants. I always look for the biggest plants AI can build to get the best effect from building production facilities. I also researched digital social services since that gives a 5% increase in education while dropping it's cost 5%. Seemed to actually do some good for my education and thusly my GDP/c.
I actually was able to halt the drop without going below about 21% domestic markup on food to about 38% markup on consumer goods and timber. I did increase research spending significantly from the beginning, but nowhere near maxed out. I managed this about 3 months into the game where I finally got my GDP/c rising at a good clip of about 15 points a turn.
The cost was a mere $65 billion annual deficit which was burning a hole in my treasury. I knew I had to back it off and actually managed to shed $40 billion of deficit in a month and still leave a reasonable 4.5 point increase in GDP/c per day. I finished the game after a year at 2.8% inflation and 5.7 unemployment, a real improvement over all of my other attempts. I even had a 110 credit rating and my last bond was reissued at 4.3%. I was able to add to my treasury each day, even running a $25 billion annual deficit, with my exports.
The manual says keep efficiency investment at recommended levels, which I take it to mean the middle of the bar. I even try to go over that and get efficiency in the low to mid 90's. It almost seems like that's counterproductive as that really kills profit margin by jacking up production costs. Does jacking up efficiency help add employment? To me it would seem that the more I jack up efficiency investment the more workers I'm adding to the mix but it almost doesn't seem to pan out. If that were the case then adding more production/resource facilities should also help jack up employment but it sure doesn't seem like it to me. It almost seems like it's better to pare down production/resource facilities and jack up efficiency to keep the profits from domestic sales up so that that extra profit creates more jobs who knows where.
So do you also eschew researching units and just splitting between research efficiency and general tech level at the beginning? Does that also help jack up the education rating quickly? I also found that running up my immigration fee to about $23,000 to $28,000 helps keep my GDP/c and literacy rating higher. Then on the 12th I drop back to zero to get my WM manna cheaper and then on the 15th I jack it back up again.