July 14 (Reuters) - Federal Reserve Chairman Kevin Warsh heads to Capitol Hill on Tuesday to deliver his first congressional testimony since taking over as head of the U.S. central bank.

Warsh's public comments and Senate confirmation hearing have highlighted many of his views, but some important questions remain around his thoughts on the state of the economy, inflation and labor markets - price stability and maximum employment form the Fed's areas of responsibility mandated by Congress.

Here are some open issues lawmakers could explore:

EMPLOYMENT

Warsh has not said much about jobs and the anticipated evolution of the labor force. How does the expected size of the labor force, and the fact that it might shrink steadily over time, matter in his view? Does an economy with low unemployment but low monthly job growth - quite possible given current demographic and immigration trends - satisfy the Fed's mandate to achieve maximum employment?

INFLATION

Warsh has said that when it comes to inflation data and the Fed's 2% target, the focus should be to the "left of the decimal point" - indicating his discomfort with trying to be too precise about things that are imperfectly measured, and also potentially some tolerance for inflation a bit over 2%, an easier standard to hit. But how does that idea relate to inflation that falls below 2%? The Fed has a "symmetric" view of its target, with outcomes that are too low regarded as just as worrisome as outcomes that are too high. Does Warsh agree with that view, or are his thoughts about the inflation target more fluid in terms of what warrants a monetary policy response?

MONEY SUPPLY

The Fed has not actively fretted about the money supply in years, but a reference to it was included last week for the first time in a decade in the first Monetary Policy Report since Warsh became the central bank's chairman. What role does the money supply play in inflation, and how is Warsh planning to rely on it? Would a focus on the money supply mean leaning against current government deficit spending even though the Fed typically regards that issue as off limits for discussion, and the province of elected officials?

EXPECTATIONS

Fed policymakers regard public expectations about inflation as central to how inflation evolves. The Fed's policy framework says the central bank is "prepared to act forcefully to ensure that longer-term inflation expectations remain well anchored." Warsh has not spoken about expectations with the same urgency. Does he agree that expectations are central to inflation outcomes, and does he share with his colleagues the belief that keeping them anchored is perhaps the Fed's top priority?