Banks, like other companies, can finance their activities either with debt or with equity. And one common proposal to make the banking system safer is to force banks to rely more on equity-finance and less on debt-finance by increasing the required capital ratio that they have to hold in order to lend. People who own stock in banks hate this idea, since it would involve sharply devaluing the value of their existing shares. But it would clearly make the financial system less vulnerable to runs, so a key question is whether there's any good reason not to do it. The most simplistic answer is "no", that per the Modigliani-Miller Theorem the capital structure of a firm is irrelevant so we could get a free lunch here.
But that's not right. What Modigliani-Miller says is that capital structure is irrelevant in the absence of taxes, bankruptcy costs, agency costs, and asymmetric information none of which applies.
Douglas Elliot has an informative column in which he tries to take a look at those factors and delivers a back of the envelop calculation that raising the ratio of common equity to total assets for banks from 5% to 30% would increase the cost of loans by almost two percentage points, which obviously would have a big impact on the economy.*
Now that said, assuming you're not talking about implementing this change overnight it seems like the Federal Reserve should be able to offset the contractionary impact of making loans more expensive. Manipulating interest rates, after all, is what the Fed is all about. Here's where it gets interesting. Elliot pointed out to me over email that higher capital ratios offset by expansionary monetary policy would still have the impact of shifting loan activity. On net, people and firms who depend on bank lending would end up paying more to borrow while firms that can obtain loans directly from financial markets by issuing bonds would end up borrowing more cheaply. This does not make for a great political slogan ("you'll pay a higher interest rate on your credit card bill, but it's okay because Cargill will be able to issue bonds at a lower rate") but I think it might be a feature rather than a bug.
Louis Hyman's very interesting book Borrow: The American Way of Debt argues that we don't pay enough attention to the shifting modes of credit and debt over time. Once upon a time credit overwhelmingly meant business credit, which then expanded into the personal sphere primarily in the special case of houses and what you might call household investment goods (cars, large appliances). That then metastasized into the all-in culture of consumer debt and credit that we know from the past 25 years. The shift that would be induced by higher capital ratios would serve as something of a countervailing force, disproportionately encouraging business borrowing to finance investment while discouraging consumer borrowing to enhance consumption. That plus a safer, less run-prone banking system sounds like a big win to me. It's not a costless win by any means—people enjoy their mortgages and consumer credit—but a win nonetheless.
* Correction: An earlier version of this post wrongly said that Elliot favors the kind of very high capital ratios we're talking about here.