If the Fed were to pursue a policy of deliberately promoting a higher rate of inflation, it is not necessarily the case that the higher inflation would precede a rise in wages, as suggested in Binyamin Appelbaum's Economix post. The point of a higher inflation policy is to convince businesses that prices will be higher in the future than they would have thought otherwise. For example, if they expected 1.0 percent annual inflation, they would think that prices would be 5 percent higher in 5 years than they are today. If the Fed manages to convince them that inflation will average 2.0 percent, then they will think that prices will be 10 percent higher in 5 years. (I've ignored compounding for simplicity.)
This should not cause businesses to directly raise their prices. If they thought they could raise their prices, they presumably would have already done so. Rather, it would likely change their investment behavior. They know what it costs to invest in new machinery, research and development, new software, etc. If they think they will be able to sell the products that come from this new investment at a higher price in the future, then they will be likely to undertake more investment today.
This would increase investment in the economy and also the demand for labor. Businesses would also be prepared to pay higher wages to workers to carry through this investment. This would allow them to pull workers away from other firms, as well as hiring currently unemployed workers. If this led to upward pressure on wages, all firms would be seeing higher costs, which then lead to the higher prices that the Fed was trying to bring on. By this logic, higher inflation is the result of higher wages. Therefore, there is little basis for concern that wages on average will not keep pace with inflation.
Of course this will not apply to all workers. Some workers will not be in a position to ensure that their wages keep pace with inflation. These workers will be losers from this policy. This is unfortunate, but there are two points to keep in mind.
First, the reason some workers will not be a position to have wages keep pace with inflation is that there is little demand for their labor. In other words, these are workers who are already in a precarious position. A somewhat higher inflation rate (e.g. 3-4 percent rather than 1-2 percent) may cause their real wages to fall more rapidly than they would have otherwise, but they likely were on a downward path already.
The second point is that we don't know how to carry through economic policies that don't result in some people losing. For example, if we have a great new infrastructure project for high speed rail or fast Internet, then people will lose jobs in businesses that were associated with the old modes of transportation or Internet (e.g. restaurants and gas stations along the highway). In some cases, we opt not to think about the losers, but that is a political decision, not a result of having a policy that doesn't produce losers.
We need safety net policies such as unemployment benefits that protect losers, but if a requirement of economic policy is that it have no losers, then we would have to give up on economic policy.
The folks worried about how inflation will leave most workers worse off need to figure out a theory of where the inflation is coming from. I gave a story where the expectation of higher future prices leads firms to increase investment, hiring, and wages, which could then make the expectation of higher inflation self-fulfilling. If we don't see this additional hiring, investment, and wages, then it is difficult to see the process through the Fed can bring about a higher targeted rate of inflation.
Of course if inflation does comes through this channel, then we don't have to worry about wages keeping up with inflation, higher wages will have caused the inflation. Again, not everyone's wages will keep up, but welcome to the world. If increased direct hiring of workers led to a higher rate of inflation, then some workers wages will also not keep up. Should we therefore be fervent supporters of keeping high unemployment forever?