With the Dow Jones Industrial Average up 24% from its March low, both bulls and bears are feeling they will soon be vindicated.

The bulls are finding more evidence that this rally is the start of something lasting. The bears warn that the higher the market goes, the more pain will be suffered on the other side.

Strangely, both are pointing to the same part of the economy to make their opposing cases: the lending system.

“The epicenter of the fear is the idea that banks are full of toxic assets,” says James Paulsen, chief investment strategist at Wells Capital Management, which oversees about $375 billion as Wells Fargo’s money-management arm. He thinks the mortgage-backed securities held by banks are worth much more than people think, and that “we could have a V-shaped recovery” in the economy, and the stock market, as confidence in the lending system returns.

George Feiger thinks that idea is crazy.

“The core of the problem is the credit system and the credit system is severely damaged,” says Mr. Feiger, who oversees $1.3 billion as chief executive of Contango Capital Advisors, a subsidiary of Zions Bancorp. “Unwinding the credit bubble is going to take years, not quarters. We see this stock rally as an opportunity to sell.”

How can smart, experienced investors disagree so strongly, when looking at similar data? Let’s hear from the optimists first.

Mr. Paulsen of Wells Capital expects consumers to begin borrowing more heavily against their homes, and sees economic growth recovering amid a pickup in consumer spending and exports. Even if growth doesn’t return to where it was, he says, the improvement should be enough to pull stocks up from their heavily depressed levels.

He and others point out that even during the troubled 1930s and 1970s, stocks enjoyed strong, albeit temporary, bull markets. The Dow almost doubled from July 9, 1932, through Sept. 7, 1932, and then did it again in the first half of 1933, even as the banking system continued to crumble. Stocks fell again later, but not back to 1932 levels. Historically, the Dow often has rebounded sharply after being down around 50%, as it was this time.

In the optimists’ view, the credit system, juiced by well over $1 trillion in government aid, is slowly repairing itself.

Demand for mortgage refinancing has blossomed as mortgage rates have fallen. Investors are snapping up risky credit instruments such as junk bonds. Last week saw the busiest day for junk-bond sales in more than six months as hospital operator HCA and phone-tower operator Crown Castle International sold debt.

Late last year, yields on corporate bonds were pushed skyward, adding to the difficulty of issuing new bonds. Since late November, however, even junk-bond yields have been falling, a good sign for corporate borrowers. The difference, or spread, between junk-bond yields and Treasury-bond yields has tumbled, according to Merrill Lynch indexes, although it still is almost twice what it was just a year ago.

The optimists point out that banks including J.P. Morgan Chase, Goldman Sachs Group and Citigroup reported better-than-expected first-quarter profits. Banks are able to issue bonds cheaply with government backing, helping increase their lending margins.

It is signs like these that analysts like Michael Darda have been waiting for. Mr. Darda, chief economist at Greenwich, Conn., brokerage firm MKM Partners, was skeptical of the stock outlook as recently as late last year, but not any longer.

“We continue to believe the expansion will build steam into 2010 as an easy Fed policy collides with the spend-out from the fiscal stimulus,” Mr. Darda said in a report. He expects this trend to continue, with the recession ending between June and October. He notes that it is normal for the stock market to recover just ahead of the economy, which makes him bullish now.

The pessimists are turning to similar data to make the opposite case. Bears note that bank profits are due in part to government support, which has reduced the need for write-offs. Some of the new bank lending lately, they add, is because stressed borrowers are being forced to tap their credit lines. And big banks like Citigroup and Bank of America are still relying on government guarantees to sell bonds, a sign that credit markets remain fractured.

“Some people say the economic conditions are starting to bottom here. I would be really surprised if that happens,” says Steve Lehman, who helps oversee a $1.8 billion mutual fund at Federated Investors in Pittsburgh. “The banks are technically insolvent. They have become basically Enron-like hedge funds.”

He worries that the proliferation of home foreclosures, debt write-downs, severely underfunded pension plans and credit-card losses is far from over, which could hobble economic growth and stock recovery.

At some point, Mr. Lehman says, stocks are likely to fall enough that the ratio of stock prices to corporate earnings for broad stock indexes will drop into single digits, from about 13 now, and stay there a while. That happened during major bear markets in the past but hasn’t yet happened this time.

Such a decline could push the Standard & Poor’s 500-stock index below 600 before the selling ends, he says, although stocks could go through plenty of ups and downs before that happens. The S&P 500 finished Friday at 869.60. Its lowest close for the current bear market was its 12-year low on March 9 of 676.53.

“Many of the people I deal with every day want to go back to the good old days,” adds Mr. Feiger of Contango. “I feel I am surrounded by people who are desperate for the party to start again. I don’t see that happening.” He, too, believes the damage is deeper than the optimists realize.

He is particularly concerned about what economists call the “shadow banking system.” That is the system under which banks sold off loans to investors, including other banks. Those sales permitted a vast expansion of credit, but they also tempted banks to be less careful in their lending. And because they then bought back many such loans in the form of asset-backed securities, the banks ironically were among those left holding the bag.

Now investors won’t buy such securities and the shadow banking system has been left for dead. Mr. Feiger estimates that, before the bust, 60% of all loans were held outside the normal banking system. Who, he asks, is going to step up and extend that kind of credit in the future?

Optimistic money managers point out that even if the overall stock pullback isn’t over, the Dow industrials enjoyed five surges of 20% or more from September 1929 until they finally hit bottom in July 1932. The bulls want to get in on such rebounds, and add that it won’t take 2½ years this time for the market finally to hit bottom.

The bears counter that it is still too risky to try to time the market’s violent ups and downs. They feel safer keeping exceptionally large amounts of cash in money-market funds and Treasury bonds.

Whether they wind up changing their minds, and shifting some of that hoard to stocks, could determine how much longer the recent rally continues.

WITH unemployment rising and the financial system in shambles, it’s hard not to feel negative about the economy right now. The answer to our problems, however, could well be more negativity. But I’m not talking about attitude. I’m talking about numbers.

Let’s start with the basics: What is the best way for an economy to escape a recession?

Until recently, most economists relied on monetary policy. Recessions result from an insufficient demand for goods and services — and so, the thinking goes, our central bank can remedy this deficiency by cutting interest rates. Lower interest rates encourage households and businesses to borrow and spend. More spending means more demand for goods and services, which leads to greater employment for workers to meet that demand.

The problem today, it seems, is that the Federal Reserve has done just about as much interest rate cutting as it can. Its target for the federal funds rate is about zero, so it has turned to other tools, such as buying longer-term debt securities, to get the economy going again. But the efficacy of those tools is uncertain, and there are risks associated with them.

In many ways today, the Fed is in uncharted waters.

So why shouldn’t the Fed just keep cutting interest rates? Why not lower the target interest rate to, say, negative 3 percent?

At that interest rate, you could borrow and spend $100 and repay $97 next year. This opportunity would surely generate more borrowing and aggregate demand.

The problem with negative interest rates, however, is quickly apparent: nobody would lend on those terms. Rather than giving your money to a borrower who promises a negative return, it would be better to stick the cash in your mattress. Because holding money promises a return of exactly zero, lenders cannot offer less.

Unless, that is, we figure out a way to make holding money less attractive.

At one of my recent Harvard seminars, a graduate student proposed a clever scheme to do exactly that. (I will let the student remain anonymous. In case he ever wants to pursue a career as a central banker, having his name associated with this idea probably won’t help.)

Imagine that the Fed were to announce that, a year from today, it would pick a digit from zero to 9 out of a hat. All currency with a serial number ending in that digit would no longer be legal tender. Suddenly, the expected return to holding currency would become negative 10 percent.

That move would free the Fed to cut interest rates below zero. People would be delighted to lend money at negative 3 percent, since losing 3 percent is better than losing 10.

Of course, some people might decide that at those rates, they would rather spend the money — for example, by buying a new car. But because expanding aggregate demand is precisely the goal of the interest rate cut, such an incentive isn’t a flaw — it’s a benefit.

The idea of making money earn a negative return is not entirely new. In the late 19th century, the German economist Silvio Gesell argued for a tax on holding money. He was concerned that during times of financial stress, people hoard money rather than lend it. John Maynard Keynes approvingly cited the idea of a carrying tax on money. With banks now holding substantial excess reserves, Gesell’s concern about cash hoarding suddenly seems very modern.

If all of this seems too outlandish, there is a more prosaic way of obtaining negative interest rates: through inflation. Suppose that, looking ahead, the Fed commits itself to producing significant inflation. In this case, while nominal interest rates could remain at zero, real interest rates — interest rates measured in purchasing power — could become negative. If people were confident that they could repay their zero-interest loans in devalued dollars, they would have significant incentive to borrow and spend.

Having the central bank embrace inflation would shock economists and Fed watchers who view price stability as the foremost goal of monetary policy. But there are worse things than inflation. And guess what? We have them today. A little more inflation might be preferable to rising unemployment or a series of fiscal measures that pile on debt bequeathed to future generations.

Ben S. Bernanke, the Fed chairman, is the perfect person to make this commitment to higher inflation. Mr. Bernanke has long been an advocate of inflation targeting. In the past, advocates of inflation targeting have stressed the need to keep inflation from getting out of hand. But in the current environment, the goal could be to produce enough inflation to ensure that the real interest rate is sufficiently negative.

The idea of negative interest rates may strike some people as absurd, the concoction of some impractical theorist. Perhaps it is. But remember this: Early mathematicians thought that the idea of negative numbers was absurd. Today, these numbers are commonplace. Even children can be taught that some problems (such as 2x + 6 = 0) have no solution unless you are ready to invoke negative numbers.

Maybe some economic problems require the same trick.

N. Gregory Mankiw is a professor of economics at Harvard. He was an adviser to President George W. Bush.