Call it the great inflation vs. deflation battle.

On the one side, the U.S. TIPS market. In the last few months demand for Treasury Inflation-Protected Securities from investors worried about a resurgence of inflation has reduced supplies of the bonds at Wall Street dealers to a three-year low.

On the other side, Japanese investors. Japan bought a net $105 billion of U.S. government debt in the year to August. That’s even more than China bought during those months. The 17% increase in Japanese holdings in 2009 will only pay off if the U.S. experiences a prolonged period of deflation that drives down the yield and drives up the price of 10-year and longer U.S. Treasury debt.

One of these opinions has to be right, eventually, but it’s dangerous to assume that either has an inside track on the direction of inflation/deflation in the short-term. Investors always tend to see the future through lenses tinted by their experience of the past and that’s exactly what’s going on here.

Japanese investors who are snapping up U.S. Treasuries, for example, are looking backward at deflation in Japan during the country’s lost decade of the 1990s.

During the 1990s, Japan’s economy grew by an average of 1% a year and prices of everything—including financial assets—fell. So far, this decade hasn’t been much better with the economy expanding an average 0.2% annually and consumer prices falling by the same 0.2% a year.

So what happened to Japanese stocks? Not surprisingly, they tanked. The Nikkei 225 stock index fell 67% between January 1990 and October 1998.

And Japanese bonds?  Because long-term interest rates fell as deflation went on and on, bond prices rose. (The price of existing bonds goes up as the interest rate offered on newly issued bonds falls so that the yield on old and new bonds remains the same.) An index compiled by Merrill Lynch shows that Japanese bonds returned 90% during the same period.

And you were wondering why Japanese investors are buying U.S. Treasuries? If the yield on a 10-year U.S. Treasury were to fall from 3.5% (the yield on November 9) to 2.75%, an investor would see a total return of 7.2%, Bloomberg has calculated.

A Japanese investor who was expecting U.S. deflation and lower interest rates would also expect to see some further gains as the U.S. dollar dropped against the Japanese yen.

 U.S. investors, on the other hand, have almost no experience with deflation. Certainly very few investors now alive have lived through a prolonged bout of deflation. Absent personal experience, it feels like an abstract and rather theoretical danger.

Inflation, on the other hand, ravaged the U.S. economy as recently as the late 1970s and 1980s. Older baby boomers might have even had enough money at that stage in their working careers to have invested during that period. One of my first—and still best—personal investments was in zero-coupon U.S. Treasury bonds paying 12% or so as a result of the Federal Reserve ratcheting up interest rates to kill the double digit inflation of that period.

So when U.S. investors look in the rear-view mirror to see what’s gaining on them, they see not deflation but inflation. Comparing the yield on a straight 10-year U.S. Treasury with the yield on a 10-year TIP gives a pretty good gage of the expectations for inflation. (Investors want to pay less for a straight Treasury, which drives the yield up, if they think inflation is going to rise. They are willing to pay more, which drives the yield down, for a TIP if they think inflation is headed up and so the inflation protection from a TIP would be more valuable.) On that scale, the gage has reached its highest level in 15 months showing increased expectations for future inflation.

I think we’re going to travel a very winding road with rallies and slumps in Treasury prices before we get a decision between these two camps. An interview in the Financial Times with James Bullard, head of the Federal Reserve Bank of St. Louis gives a pretty good road map for that trip. Bullard expects that the economy will grow by 3.5% to 4% in 2010. That level of growth, he told the Financial Times, will gradually convince the Federal Reserve that the recovery is sustainable.

Historically, the Federal Reserve has begun raising interest rates about two-and-a-half to three years after a recession has ended. That would put the first interest rate increases in the first half of 2012.

If inflation is showing signs of kicking up, as the TIPS buyers now fear, the Fed will raise interest rates before that in an effort to slow the economy and prevent inflation from taking off.

If deflation seems to be the danger, as Japanese buyers of Treasuries now believe, the Fed will delay raising rates in an effort to pump up growth and to avoid the slightest possibility of a deflationary cycle.

In either case, the key period to watch for some decision in this battle is, right now, about three years away.