I just wanted to get some opinions about how do you explain low inflation rate in usa vs. low unemployment rate?

Haha, well of course it's because we're good! On a more thorough note, there are probably several explanations. First of all, thanks to the most recent Nobel winner Ed Phelps, along with Milton Friedman, we know of the concept of the NAIRU - or the non-accelerating inflation rate of unemployment. Essentially it can be thought of as the "natural rate of unemployment." Get below this level and inflation will likely accelerate.
There are numerous structural factors in an economy that determine this natural rate. The US by many estimates has a lower natural rate of unemployment because we have generally had higher productivity growth than Europe over the past couple decades, and we also have lower tax rates. Ed Prescott and Tom Sargent (and I'm sure many other economists) have papers out there that postulate why we have lower unemployment. Personally I trust Sargent a little more (though they are certainly both great economists), but either way it seems that productivity and tax rates play a role.
As for inflation, this one's a little easier. Ever since Paul Volcker in the late 70s/early 80s the Federal Reserve has been less tolerant of higher inflation. Whereas they used to think you could trade-off higher inflation for lower unemployment, they abandoned that view (thanks most likely to our experience of staglation in the 70s as well as the theoretical contributions of Phelps and Friedman. Note that the implication of the NAIRU is that in the long-run the Phillips curve is flat-- aka there is no long-run trade-off between inflation and unemployment, or in other words, you can't "buy" less unemployment with more inflation).
Therefore, we have less inflation largely because the Fed tolerates it less. Furthermore, this may also contribute to explaining why we have had less volatile output and generally lower unemployment. There seems to be a positive correlation between inflation volatility and output volatility (or unemployment volatility, I'm not entirely sure which, though quite frankly it's probably both). Therefore, with lower inflation (and by necessity lower inflation volatility), output will be more stable. More stable economic conditions in turn probably contribute to a healthier economic environment, and hence lower unemployment.
Last point: Look at labor regulations in Europe compared to the US. Europe has generally ridiculously more (and ridiculous in content) labor regulations. Whether you consider yourself laissez-faire or a social democrat, the labor regulations of France and Germany do NOT contribute to a healthy economy (whereas for instance in the Netherlands the social welfare system is much more generous yet they also have low unemployment due to a not-as-rigid labor market). In many continental European countries firms incur heavy costs for firing workers (including having to prove it to court that you are justified in firing employees), which of course serves to reduce hiring.

One interesting theory I have heard is that globalization creates both many jobs (low unemployment) and lots of competition from low cost places like China to keep down costs (low inflation). Seems too simple too me, and far too supply-side, but I find it interesting anyway.
Attending: UC-Davis

U.S. workers tend to have much higher mobility rates than other nations - we're willing to move around to where the jobs are, which might help natural rates of unemployment. If you talk to some (older) Germans, for instance, you'll hear about how they're natives of their city or state first, and the country second. I think I read a paper abstract recently correlating home ownership with higher unemployment...
Attending: Georgetown
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