There are a number of reasons to think the answer is yes. First, inflation creates distortions in economic decisions concerning saving and investment when the tax system is not fully indexed to inflation. An example of such a distortion is the mortgage interest deduction. It becomes more valuable and induces more (over-) investment in housing at higher rates of inflation, since higher inflation leads to higher nominal mortgage interest rates. Second, there are so-called "shoe-leather costs" of holding money. When inflation is high, currency and non-interest bearing checking accounts are undesirable because they are constantly declining in purchasing power. People will use valuable economic resources (including their time and "shoe leather") to economize on their holdings of such money balances.
In addition, high inflation often is associated with high volatility of inflation and this can make people uncertain about what inflation will be in the future. That uncertainty can hinder economic growth. First, it adds an inflation risk premium to long-term interest rates and it complicates the planning and contracting by business and labor that are so essential to capital formation. Second, people may devote their energies to mitigating the tax and other effects of inflation rather than to developing products and processes that would raise overall living standards. Third, inflation may make it more difficult for households and firms to make correct decisions in response to the signals from market prices: thus when most prices are rising, and especially if they are volatile, it may be more difficult to distinguish between changes in relative prices (the cost of one item relative to another), which may require them to reallocate their spending, and changes in the overall price level, which should not induce such an adjustment.
The empirical evidence is pretty clear that "high" rates of inflation (say, above 10 percent) have deleterious effects on long-term economic growth. For lower inflation rates, like those experienced most of the time in the U.S., the evidence is mixed, with some studies finding significant effects and others finding little or no effect. Nonetheless, many economists believe it is important to aim monetary policy at achieving very low rates of inflation. First, as noted above, there are good theoretical arguments that inflation imposes costs on the economy. Second, for a number of reasons, research may not be likely to detect the benefits of low inflation even if these benefits are significant.
For Further Reading
Cogley, Timothy. 1997. "What is the Optimal Rate of Inflation?" FRBSF Economic Letter Number 97-27, September 19.
Motley, Brian. 1993. "Inflation and Growth." FRBSF Economic Letter Number 93-44, December 31.
__________. 1998. "Growth and Inflation: A Cross-country Study." Federal Reserve Bank of San Francisco Economic Review, Number 1, pp. 15-28.