They are, unfortunately, directly at odds. Fighting inflation tanks the economy (that's what Paul Volker did in the late 1970s, to tackle "stagflation", and Jimmy Carter's 2nd term hopes), and promoting employment tends to hot up inflation.
Over the past 8 years, the Fed (and other central bankers) have dumped unholy amounts of liquidity into the global economy. That is, they've been "printing money", except that the Fed doesn't actually print money, it simply wills it into existence. It's done this after reducing its own lending rates (the prime rate) to effectively zero wasn't sufficiently stimulating the economy.
It's slightly more complex than that: the Fed distributes that money by buying "assets" from major banks -- it's an auction process, but the goal of the Fed isn't to get valuable assets[1], only to manage how that money's introduced to the economy and keep tabs on its value by way of inflation, as I understand it.
For whatever the reasons, inflation hasn't actually been a problem, though the reasons why are elusive, and several alternatives have been suggested:
1. The money's gone into financial instruments, including stocks and real estate. The rise in major stock market indices and the Fed's balance sheet (its money supply injections) pretty much exactly track one another.
2. It's gone into offshore tax havens. Last numbers I've seen are about $7 trillion from the US, and $25-30 trillion globally, from various sources. The ICIJ and The Guardian have run a multi-year expose on off-shore investment havens, and other financial sources have reported on this.
3. Chasing other investments. Silicon Valley VC money comes from somewhere, and much of it chases start-ups whose ultimate valuation is either advertising potential, or buy-it-to-kill-the-threat-to-us (WhatsApp's purchase by Facebook). Advertising's terrifying because a tremendous amount of it is financial services -- about 40% in "FIRE" industries: finance, insurance, and real estate. Pull the plug on easy money, and all three of those tailspin.
Which gets us to why fighting inflation is seen as such a bad thing. Usually the argument given is "inflation hurts those with fixed incomes", by which most people think of the elderly on social security or pensions. But we've learned how to fix that: you index those systems to inflation, hence SSI's COLA adjustment -- the cost-of-living factor that boosts Social Security payments. Who really get hurt by inflation are those who are holding dollar-denominated assets. Lenders.
That's banks, and holders of bonds (debt), which aren't themselves inflation adjusted. If you've got a home mortgage, inflation is your best friend, because it reduces the amount of your debt (in real terms) while your income increases. Banks, on the other hand, hate that, because their assets (your mortgage) falls in value.
So: the Fed is raising rates to stem inflation fears, even though inflation's been fairly much a non-player. Probably because banks and other lenders / bondholders are getting nervous. And to give itself more maneuvering room.
There's a whole bunch more in this, such as what money "really" is (in a functional / role sense, not the boring old fiat-vs-gold-backed debate), what, whether, why, and how economic growth is, can be extended, is justified, and is based on, and whether or not inflation is an unavoidable element of a collapsing economic system. On that last, the fate of the (specie-based) Roman denarius is quite interesting.
But stay tuned. Things might get interesting.
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Notes:
1. Told to me directly by a regional Fed branch president in a public Q&A.
This is a pretty thoughtful response. I'm not confident enough to really debate the situation today, but it seems like the fed's goal of controlling unemployment has more or less run its course. Unemployment is almost at the lowest since the 2000's. But if it follows some predictions that it will bottom out in 2016, will the fed go back to lowering interest rates?
As many, including the Fed's Janet Yellin, have noted, while unemployment numbers are down, wages haven't risen. That's an indication of net economic vitality, equality, and negotiating power. There's also the continuing debate over just what unemployment measures, and alternate indicators including broader measures of unemployment, or workplace participation rates.
Declaring victory and going home may not match the battlefield status.
The Fed mostly buys government bonds, but also corporate bonds. All their profits are donated to the Treasury, so yes they have no incentive to chase returns. The reason printing hasn't lead to inflation is well known and understood. Inflation is the product of money supply and velocity and velocity was dropping as fast as supply was increasing.
The assets / paper that the Fed were buying in QE2 was pretty much anything banks wanted to throw at them. Though again, the auction element basically meant that less-utterly-grotty-stuff won out over the truly utterly grotty stuff, again, if I'm getting my story straight.
Inflation has to do with money chasing goods. All you've said is that "money wasn't chasing goods". Which gets us to two further questions:
1. Why wasn't that money chasing goods (or real, economically productive, investment opportunitys, by which I specifically exclude financial derivatives or simply "buying" tax sheltering).
2. What is that money chasing?
As I understand, the answers don't do much to make the situation any less bad.
